The carrying capacity of a drain pipe is directly proportional to the area of its cross- section. If a cylindrical drain pipe can carry 36 litres per second, determine the percentage increase in the diameter of the drain pipe necessary to enable it to carry 60 litres per second.​

Answers

Answer 1

Step-by-step explanation:

Let's start by using the formula for the volume of a cylinder:

V = πr^2h

where V is the volume of the cylinder, r is the radius of the cylinder, h is the height of the cylinder, and π is a mathematical constant (approximately equal to 3.14).

Since we are dealing with a drain pipe, we can assume that the height of the cylinder is fixed and does not change. Therefore, we can rewrite the formula as:

V = πr^2h = Ah

where A is the cross-sectional area of the cylinder.

Now, let's use the given information that the drain pipe can carry 36 litres per second. We know that the volume of water that passes through the pipe in one second is equal to 36 litres. We can therefore write:

36 = Ahv

where v is the velocity of the water flowing through the pipe. Since we are assuming that the height of the cylinder is fixed, we can simplify this equation to:

36 = Av

Now we need to determine the percentage increase in the diameter of the drain pipe necessary to enable it to carry 60 litres per second. Let's call the new diameter d2 and the old diameter d1. We can set up a proportion to solve for d2:

A1/A2 = d1^2/d2^2

We know that A1 and A2 are proportional to the volumes of water the pipe can carry, so we can write:

A1/A2 = 36/60

Simplifying this equation, we get:

A1/A2 = 3/5

Substituting in the formula for the cross-sectional area of a cylinder, we get:

πd1^2/4 / πd2^2/4 = 3/5

Simplifying further, we get:

d1^2/d2^2 = 3/5

Taking the square root of both sides, we get:

d1/d2 = sqrt(3/5)

Now we can solve for d2:

d2 = d1 / sqrt(3/5)

We want to know the percentage increase in the diameter, which we can find using the formula:

% Increase = (New Value - Old Value) / Old Value x 100%

Substituting in our values, we get:

% Increase = (d1 / sqrt(3/5) - d1) / d1 x 100%

Simplifying, we get:

% Increase = (1 / sqrt(3/5) - 1) x 100%

Using a calculator, we get:

% Increase ≈ 34.64%

Therefore, the percentage increase in the diameter of the drain pipe necessary to enable it to carry 60 litres per second is approximately 34.64%.


Related Questions

The points S(-4,-2), T(-4, 5), and
U(-9, -2) form a triangle. Plot the points
then click the "Graph Triangle" button. Then find the perimeter of the triangle.
Round your answer to the nearest tenth if necessary.

Answers

The perimeter of the triangle  STU is 20.6 units

What is the perimeter of the triangle?

To find the perimeter of triangle STU, we need to use the formula of distance between two points and then take the sum of all the sides.

[tex]d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}\\[/tex]

For line ST;

(-4, -2) and (-4, 5)

[tex]d = \sqrt{(-4 - (-4))^2 + (5 - (-2))^2} \\d = 7[/tex]

For line TU;

(-4, 5) and (-9, -2)

[tex]d = \sqrt{(-9 - (-4))^2 - (-2 - 5)^2} \\d = \sqrt{74} \\d = 8.6[/tex]

For line US;

(-9, -2) and (-4, -2)

[tex]d = \sqrt{(-9 - (-4))^2 + (-2 - (-2))^2}\\d = 5[/tex]

The distance between the sides are 7, 8.6 and 5 units.

The perimeter of the triangle = 7 + 8.6 + 5 = 20.6 units

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Part C. Jack also likes to collect buttons. He has 5 bags of button The fewest number of buttons in a bag is 21. The greatest number of buttons in a bag is 29 The mean number of buttons in the bags is 27. There are two modes for the number of buttons in each bag. How many buttons are in each of Jack's five bags? ​

Answers

To find the number of buttons in each of Jack's five bags, we can use the information given to us and solve for the unknowns. Let's start by finding the total number of buttons:

Total number of buttons = Mean number of buttons × Number of bags

Total number of buttons = 27 × 5

Total number of buttons = 135

Since we know the fewest and greatest number of buttons in a bag, we can find the range:

Range = Greatest number of buttons - Fewest number of buttons

Range = 29 - 21

Range = 8

Now, we can set up two equations to find the two modes:

Mode 1 + Mode 2 + 3 × 27 = 135 (sum of all bags)

Mode 2 - Mode 1 = 8 (difference between the two modes)

Solving these equations simultaneously, we get:

Mode 1 = 23

Mode 2 = 31

Therefore, the number of buttons in each of Jack's five bags is:

Bag 1: 21 buttons

Bag 2: 23 buttons

Bag 3: 25 buttons

Bag 4: 27 buttons

Bag 5: 29 buttons

the table shows how much Eric earns for pruning trees, write an equation that relates x, the number of trees Eric prunes to y the amount he earns. solve your equation to find how much Eric earns if he prunes 7

trees pruned 2 4 6 8
pay in dollars 30 60 90 80

Answers

If Eric prunes 7 trees, he would earn $85.

To write an equation that relates the number of trees pruned (x) to the amount Eric earns (y), we can use the given data points to determine the pattern or relationship.

From the table, we observe that Eric's pay increases as the number of trees pruned increases, except for the case where he prunes 8 trees.

Based on the data, we can construct a piecewise equation:

For x = 2, 4, and 6:

y = 30 * x

For x = 8:

y = 80

However, we need to consider the case when x = 7. Since this data point is missing from the table, we can assume that the pay is proportional to the number of trees pruned. Therefore, we can interpolate using the given data points for x = 6 and x = 8:

Using the formula for linear interpolation:

y = y1 + (y2 - y1) * ((x - x1) / (x2 - x1))

Substituting the values, we have:

y = 90 + (80 - 90) * ((7 - 6) / (8 - 6))

y = 90 + (-10) * (1 / 2)

y = 90 - 5

y = 85

Thus, if Eric prunes 7 trees, he would earn $85.

It's important to note that the equation and solution are based on the given data points and the assumption of a linear relationship.

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Evaluate f (x)=5/2x-8 when x=4

Answers

Answer:

2

Step-by-step explanation:

f(x) = [tex]\frac{5}{2}[/tex] x - 8 ← substitute x = 4 into f(x) , then

f(4) = [tex]\frac{5}{2}[/tex] × 4 - 8 = 5 × 2 - 8 = 10 - 8 = 2

A restaurant at the food court in a mall is offering a lunch special. The table shows the relationship between the number of side dishes and the total cost of the special.

Restaurant
Number of Side Dishes Total Cost
2 $10.25
4 $13.25
5 $14.75
8 $19.25


Which of the following graphs shows the relationship given in the table?

graph with the x axis labeled number of side dishes and the y axis labeled cost in dollars and a line going from the point 0 comma 7 and 25 hundredths through the point 3 comma 11 and 75 hundredths

graph with the x axis labeled number of side dishes and the y axis labeled cost in dollars and a line going from the point 0 comma 7 and 75 hundredths through the point 3 comma 12 and 25 hundredths

graph with the x axis labeled number of side dishes and the y axis labeled cost in dollars and a line going from the point 0 comma 5 and 25 hundredths through the point 3 comma 9 and 75 hundredths

graph with the x axis labeled number of side dishes and the y axis labeled cost in dollars and a line going from the point 0 comma 5 and 5 tenths through the point 5 comma 13

pls use pic for the answer

Answers

Graph with the x axis labeled number of side dishes and the y axis labeled cost in dollars and a line going from the point 0 comma 5 and 5 tenths through the point 5 comma 13

The x-axis of the graph is labeled "number of side dishes," which represents the independent variable in this case.

The y-axis is labeled "cost in dollars," representing the dependent variable.

The line on the graph starts at the point (2, $10.25), indicating that when there are 2 side dishes, the total cost of the lunch special is $10.25.

The line then passes through the point (8, $19.25), which signifies that when there are 8 side dishes, the total cost of the lunch special is $19.25.

This graph correctly illustrates the relationship between the number of side dishes and the total cost, showing that as the number of side dishes increases, the cost of the lunch special also increases.

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Which two functions can be used to solve for x?

Answers

The expression that should be used is tan 67° = 210/x, tan 23° = x/210.

Given is a figure, we need to find the value of x,

So, the figure is creating a right triangle, the angle of elevation is equal to the angle of depression,

So, the two acute angles in the triangle will be 23° and 67°.

Also, the tangent of an angle is equal to the ratio of the perpendicular side to the base,

Taking 67° as reference angle, we get,

Tan 67° = x / 210

Taking 23° as reference angle, we get,

Tan 23° = 210/x

Hence the expression that should be used is tan 67° = 210/x, tan 23° = x/210.

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Need the answer quickly!​

Answers

It’s the third option as the first batter(4/7) has a 57% chance, the second batter (6/10) has a 60% chance and the third batter(5/9) has a 55% chance so it only make sense that the second batter is more likely to hit the ball than the first batter

You have one red apple and three green apples in a
bowl. You randomly select one apple to eat now and
another apple for your lunch. Use a sample space to
determine whether randomly selecting a green apple
first and randomly selecting a green apple second are
independent events.

Answers

Answer: vvvvv

Step-by-step explanation:

Let R1 and G1 represent the red and green apples available for the first selection, respectively. Similarly, let R2, G2a, and G2b represent the red and two green apples available for the second selection, respectively. Then, the sample space for the two selections is:

{(R1, R2), (R1, G2a), (R1, G2b), (G1, R2), (G1, G2a), (G1, G2b)}

Out of these six outcomes, only two involve selecting a green apple first: (G1, R2) and (G1, G2a). And out of these two outcomes, only one involves selecting a green apple second: (G1, G2a).

Therefore, since the probability of selecting a green apple second changes based on whether a green apple was selected first, the events of selecting a green apple first and selecting a green apple second are dependent.

IS THERE ANOTHER WAY TO SOLVE THIS PROBLEM
My family and I own a little country store. It’s called Coomer’s Trading Post. We sell a little of everything, but we do sell a lot of cheeseburgers, French fries, bottle soda, and candy bars daily.

We expect to make $175 for cheeseburger and fries only.

I plan to sell 105 burgers and fries all together.

X= burger $4

Y= fries $ 2

I4x+2=175 (equation)

SOLVE FOR Y

X+Y=105

-Y -Y

X= 105-Y

4(105-Y) + 2 =175

420-4Y+2=175

-420 -420

-4Y+2Y=245

-2Y=-245

-2 -2



Y=122.50



SOLVE FOR X



4X+2(122.50)= 105

4X+245=105

-245 -245

4x= 140

4 4

X=-35



THIS IS FOR CANDY BARS AND BOTTLE SODAS.



We expect to make $ 120 for the candy bars and bottle soda together.

We plan to sell 75.

X= candy bars 1.85

Y= bottle soda 2.49

Solve for y

1.85x+2.49=120

X+Y=75

-Y -Y

X=75-Y

1.85(75-Y)+2.49=120



138.75-1.8Y+2.49=120

-138.75 -138.75

-1.8Y+2.49Y=-18.75

.64Y=-18.75

.64 .64



Y=-29.29



SOLVE FOR X



1.85X+2.49(-29.29)=120

1.85X + -72.93=120

-72.93 -72.93

1.85X =47.07

1.85 1.85

X= 25.44

Answers

The  values for the Number of cheeseburgers, fries, candy bars, and bottle sodas seem to be inconsistent.The number of fries (Y) is 122.50.The number of cheeseburgers (X) is -17.50

We can calculate the values of X and Y, representing the number of cheeseburgers and fries respectively, and the number of candy bars and bottle sodas respectively.

For cheeseburgers and fries:

We know that the expected revenue from cheeseburgers and fries is $175.

The equation relating the cost of the cheeseburgers (X) and fries (Y) is given as 4X + 2Y = 175.

We also know that the total number of cheeseburgers and fries to be sold is 105, which can be represented as X + Y = 105.

To solve for Y, we can substitute X = 105 - Y into the first equation:

4(105 - Y) + 2Y = 175

420 - 4Y + 2Y = 175

-2Y = 175 - 420

-2Y = -245

Y = -245 / -2

Y = 122.50

To solve for X, we substitute Y = 122.50 into the equation X + Y = 105:

X + 122.50 = 105

X = 105 - 122.50

X = -17.50

Therefore, the number of cheeseburgers (X) is -17.50. However, since it is not possible to have a negative quantity of cheeseburgers, we can conclude that there might be an error in the calculations or the given information.

Moving on to candy bars and bottle sodas:

We expect to make $120 from the sales of candy bars and bottle sodas.

The equation relating the cost of candy bars (X) and bottle sodas (Y) is given as 1.85X + 2.49Y = 120.

The total number of candy bars and bottle sodas to be sold is 75, which can be represented as X + Y = 75.

To solve for Y, we substitute X = 75 - Y into the first equation:

1.85(75 - Y) + 2.49Y = 120

138.75 - 1.85Y + 2.49Y = 120

0.64Y = 120 - 138.75

0.64Y = -18.75

Y = -18.75 / 0.64

Y = -29.29

Again, we encounter a negative value, which is not possible for the number of bottle sodas. This suggests a mistake in the calculations or the given information.

Similarly, to solve for X, we substitute Y = -29.29 into the equation X + Y = 75:

X - 29.29 = 75

X = 75 + 29.29

X = 104.29

Here, we obtain a non-integer value for the number of candy bars, which may indicate an error in the calculations or the given information.

In conclusion, the calculated values for the number of cheeseburgers, fries, candy bars, and bottle sodas seem to be inconsistent with the given information

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Drag each number to a box to complete the table. Each number may be used once or not at all. 8,000533,00021,000 Kilometers Meters 1 2,000 5,000 8

Answers

Each number should be dragged to a box to complete the table as follows;

Kilometers     Meters

1                        1,000

2                       2,000

3                       3,000

5                       5,000

8                       8,000

What is a conversion factor?

In Science and Mathematics, a conversion factor can be defined as a number that is used to convert a number in one set of units to another, either by dividing or multiplying.

Generally speaking, there are one (1) kilometer in one thousand (1,000) meters. This ultimately implies that, a proportion or ratio for the conversion of kilometer to meters would be written as follows;

Conversion:

1 kilometer = 1,000 meters

2 kilometer = 2,000 meters

3 kilometer = 3,000 meters

4 kilometer = 4,000 meters

5 kilometer = 5,000 meters

6 kilometer = 6,000 meters

7 kilometer = 7,000 meters

8 kilometer = 8,000 meters

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Missing information:

The question is incomplete and the complete question is shown in the attached picture.

The equation of the hyperbola that has a center at (3, 10), a focus at (8, 10), and a vertex at (6, 10), is

Answers

Int he above expression, A = 3 (distance from the vertex to the center)

B = 4

C = 3 (distance from focus to center)

D = 10

How is this so?

Since the center of the hyperbola is (3,10), we have C=3 and D=10.

The distance from the center to the vertex is A, so we have A= 6-3

A = 3.

The distance from the center to the focus is given by c, so we have c=8-3=5.

We can use the relationship a² + b² = c² to solve for B:

a = 6 - 3 = 3 (distance from vertex to center)

c = 5 (distance from focus to center)

b = ?

b² = c² - a²

b² = 5² - 3²

b² = 16

b = 4

Therefore, the equation of the hyperbola is

((x-3)²/3²) - ((y-10)²/4²) = 1

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Full Quesitn:

The equation of the hyperbola that has a center at (3, 10), a focus at (8, 10), and a vertex at (6, 10), is

((x-C)²/A²) - ((y-D)²)/B²) = 1

Where A = ?

B  = ?

C = ?

D = ?

Which expression is equivalent to "9 more than the quotient of x and 5

Answers

The required expression is (x / 5) + 9

Given that we have to build an equation for the statement "9 more than the quotient of x and 5,

So,

This expression represents the quotient of x divided by 5, and then adding 9 to the result.

Therefore,

"9 more than the quotient of x and 5" can be written mathematically as:

(x / 5) + 9

Hence the required expression is (x / 5) + 9

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In your drawer you have 10 white socks and 14 black socks. You choose one sock from the drawer and then a second sock (without replacement.)
Event A: You choose a black sock.
Event B: You choose a black sock.
Tell whether the events are independent or dependent. Explain your reasoning.

Answers

The events A and B are dependent events.

The probability of event B will be different from the initial probability of selecting a black sock (event A).

Two events are considered independent if the outcome of one event does not affect the probability of the other event.

The outcome of event A (choosing a black sock) directly affects the probability of event B (choosing a black sock again).

To explain further, let's consider the initial scenario:

You have 10 white socks and 14 black socks in your drawer.

The total number of socks is 24.

The first sock, there are two possibilities:

Either it is a black sock or a white sock.

If event A occurs and you select a black sock, the total number of black socks in the drawer decreases to 13, while the total number of socks decreases to 23.

If event B to occur (selecting a black sock again), the probability is now influenced by the fact that you have one less black sock and one less sock in the drawer.

The probability of event B will be different from the initial probability of selecting a black sock (event A).

The outcome of event A affects the probability of event B, the two events are dependent.

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I need help!!!!!!!!!

Answers

Answer:

its b4 + 7b3 + 4b2 + b5 + 7b4+ 4b3= b5+8b4+11b3+4b2

Answer:

When multiplying, add the exponents, (example) remember if there is "7b" the exponent is one.

Multiply b^2 * b^3 = b^5  (add the exponent 2 + 3 = 5)

Multiply 7b * b^3 = 7b^4 (the exponent of 7b is one, add 1 + 3 for the exponent to become 4)

Multiply 4 * b^3 = 4b^3 (4 doesn't have a variable, the exponent will be 3)

b^2 * b*2 = b^4 (add exponents)

7b * b^2 = 7b^3 (add the exponents 1 + 2)

4 * b^2 = 4b^2

              b^2             +               7b             +        4

b^3           b^5              +           7b^4            +   4b^3

+                                                                                      

b^2           b^4             +           7b^3            + 4b^2

b^5 + 7b^4 + 4b^3 + b^4 + 7b^3 + 4b^2

[tex]b^5 + 7b^4 + 4b^3 + b^4 + 7b^3 + 4b^2[/tex]

b^5 + 8b^4 + 11b^3 + 4b^2

if f(x)=-2x, g(x)=3x-7, and h(x)=2x^2-10, fill in the following chart

Answers

The values of Composite function are:

f(g(-1)) = 20

h[g(4)] = 40

g[f(5)] = -37

f[h(-4)] = -44

g[g(7)] = 35

h[f(1/2)] = -8

We have, f(x) = -2x, g(x) = 3x-7 and h(x)= 2x² -10

f(g(-1)):

First, substitute -1 into g(x): g(-1) = 3(-1) - 7 = -3 - 7 = -10.

Next, substitute the result into f(x): f(-10) = -2(-10) = 20.

Therefore, f(g(-1)) = 20.

h[g(4)]:

First, substitute 4 into g(x): g(4) = 3(4) - 7 = 12 - 7 = 5.

Next, substitute the result into h(x): h(5) = 2(5^2) - 10 = 2(25) - 10 = 50 - 10 = 40.

Therefore, h[g(4)] = 40.

g[f(5)]:

First, substitute 5 into f(x): f(5) = -2(5) = -10.

Next, substitute the result into g(x): g(-10) = 3(-10) - 7 = -30 - 7 = -37.

Therefore, g[f(5)] = -37.

f[h(-4)]:

First, substitute -4 into h(x): h(-4) = 2(-4²) - 10 = 2(16) - 10 = 32 - 10 = 22.

Next, substitute the result into f(x): f(22) = -2(22) = -44.

Therefore, f[h(-4)] = -44.

g[g(7)]:

First, substitute 7 into g(x): g(7) = 3(7) - 7 = 21 - 7 = 14.

Next, substitute the result into g(x) again: g(14) = 3(14) - 7 = 42 - 7 = 35.

Therefore, g[g(7)] = 35.

h[f(1/2)]:

First, substitute 1/2 into f(x): f(1/2) = -2(1/2) = -1.

Next, substitute the result into h(x): h(-1) = 2(-1²) - 10 = 2(1) - 10 = 2 - 10 = -8.

Therefore, h[f(1/2)] = -8.

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4. Determine the lateral and total surface area of the rectangular pyramid. 6 cm 8 cm 6 cm Lateral Surface Area Total Surface Area 6.5 cm​

Answers

The lateral and the total surface area of the rectangular pyramid are 182 square cm and  278 square cm

Determining the lateral and total surface area of the rectangular pyramid.

From the question, we have the following parameters that can be used in our computation:

Length = 6 cm

Width = 8 cm

Height = 6.5 cm

The lateral surface area of the rectangular pyramid is calculated as

LA = 2 *(L + W)H

So, we have

LA = 2 *(6 + 8) * 6.5

Evaluate

LA = 182

The total surface area of the rectangular pyramid is calculated as

TA = 2 * (LW + LH + HW)

So, we have

TA = 2 * (8 * 6 + 8 * 6.5 + 6.5 * 6)

Evalaute

TA = 278

Hence, total surface area of the rectangular pyramid is 278 square cm

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NO LINKS!! URGENT HELP PLEASE!!!

O is the center of the regular decagon below. Find its perimeter. Round to the nearest tenth if necessary.

Answers

Answer:

65 units

Step-by-step explanation:

solution Given:

apothem(a)=10

no of side(n)= 10

First, we need to find the length of one side (s).

We can find the length of one side using the following formula:

[tex]\boxed{\bold{s = 2 * a * tan(\frac{\pi}{n})}}[/tex]

substituting value:

[tex]\bold{s = 2 * 10 * tan(\frac{\pi}{10})=6.498}[/tex]   here π is 180°

Now

Perimeter: n*s

substituting value:

Perimeter = 10*6.498= 64.98 in nearest tenth 65 units

Therefore, the Perimeter of a regular decagon is 65 units.

Answer:

65.0 units

Step-by-step explanation:

A regular decagon is a 10-sided polygon with sides of equal length.

To find its perimeter, we first need to find its side length (s).

As we have been given its apothem, we can use the apothem formula to find an expression for side length (s).

[tex]\boxed{\begin{minipage}{5.5cm}\underline{Apothem of a regular polygon}\\\\$a=\dfrac{s}{2 \tan\left(\dfrac{180^{\circ}}{n}\right)}$\\\\where:\\\phantom{ww}$\bullet$ $s$ is the side length.\\ \phantom{ww}$\bullet$ $n$ is the number of sides.\\\end{minipage}}[/tex]

Given the apothem is 10 units and the number of sides is 10, substitute a = 10 and n = 10 into the formula and solve for s:

[tex]10=\dfrac{s}{2 \tan \left(\dfrac{180^{\circ}}{10}\right)}[/tex]

[tex]10=\dfrac{s}{2 \tan \left(18^{\circ}\right)}[/tex]

[tex]s=20 \tan \left(18^{\circ}\right)[/tex]

The perimeter (P) of a regular polygon is the product of its side length and the number of sides. Therefore, the perimeter of the given regular decagon is:

[tex]P=s \cdot n[/tex]

[tex]P=20 \tan \left(18^{\circ}\right) \cdot 10[/tex]

[tex]P=200 \tan \left(18^{\circ}\right)[/tex]

[tex]P=64.9839392...[/tex]

[tex]P=65.0\; \sf units\;(nearest\;tenth)[/tex]

Therefore, the perimeter of a regular decagon with an apothem of 10 units is 65.0 units, to the nearest tenth.

Use the associative law of multiplication to write an equivalent expression

(12x)y

Answers

Using  the associative law of multiplication we get this two solution of the given expression: (12x)y = (12 * x) * y , (12x)y = 12 * (x * y)

The associative law of multiplication states that when multiplying three or more numbers, the product is the same regardless of the order in which the numbers are grouped. In other words, it doesn't matter which numbers we multiply first, the result will be the same.

Using the associative law of multiplication, we can group the factors in any way we like. Therefore, we can write an equivalent expression to (12x)y by changing the grouping of factors.

One way to group the factors is to group the two numerical coefficients (12 and y) together.

Another way to group the factors is to group the variable x and the coefficient y together.

Both of these expressions are equivalent to (12x)y and they all follow the associative law of multiplication.

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Find the product of (3x + 4)(x − 1). 3x2 + 7x − 4 3x2 + 7x − 3 3x2 − x − 4 3x2 + x − 4

Answers

Hello !

Answer:

[tex]\boxed{\sf (3x + 4)(x - 1)=3x^2+x-4}[/tex]

Step-by-step explanation:

We will have to use the distributive property to expand this expression.

Let's remember :

[tex]\sf (a+b)(c+d)=ab+ad+bc+bd)[/tex]

Let's apply this property to our expression :

[tex]\sf (3x + 4)(x -1)\\=3x\times x+3x\times(-1)+4\times x+4\times(-1)[/tex]

Now let's calculate and combine like terms :

[tex]\sf 3x^2-3x+4x-4\\\boxed{\sf =3x^2+x-4}[/tex]

Have a nice day ;)

Alg 2 unit 5-5 math questions with g and f

Answers

The composition fog is ((3,2), (1,0), (2,7)).

To find the composition fog, we need to apply function g first, and then apply function f to the result.

Let's start by applying function g:

g((-4,1)) = (-2,1)

g((0,4)) = (3,1)

g((1,0)) = (2,8)

Now, let's apply function f to the results:

f((-2,1)) = (3,2)

f((3,1)) = (1,0)

f((2,8)) = (2,7)

Therefore, the composition fog is:

fog = ((-4,1), (0,4), (1,0)) → g → f

= ((3,2), (1,0), (2,7))

So, fog = ((3,2), (1,0), (2,7)).

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need help can someone help me need it to pass math

Answers

The measure of segment HI is given as follows:

HI = 7.

How to obtain the measure of segment HI?

The measure of segment HI for this problem are obtained considering the triangle midsegment theorem, which states that the length of the midsegment of the triangle is equals to half the length of the base, hence the base has the length that is twice the midsegment.

The lengths are given as follows:

Midsegment HI = -9x + 70.Base EF = -21 + 5x.

Hence the value of x is obtained as follows:

EF = 2HI

-21 + 5x = 2(-9x + 70)

-21 + 5x = -18x + 140

23x = 161

x = 7.

Hence the length HI is given as follows:

HI = -9(7) + 70

HI = 7.

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10-
Next O
Post Test: Linear Equations
10
Select all the correct answers
Which lines in the graph have a slope greater than 1 but less than 27
line 1
line 2
line 3
line 4
line 5
3 4
5

Answers

The slope of the straight line in the graph that expresses proportional relationship indicates that the lines in the graph that have a slope greater  than 1 but less than 2 are;

Line 3Line 4

What is the slope of a graph of a straight line?

The slope of the graph of a straight line is the ratio of the rise to the run on the line.

The slope of a graph with a slope of 1 has an increase in the y-value of 1 for each increase in the x-value of 1

Slope = 1 = Δy/Δx

When the slope is greater than 1, we get;

Δy/Δx > 1, therefore Δy is larger than 1 when Δx is 1.

Similarly, the slope of a graph with a slope of 2 has an increase in the y-value of 2 for each increase in the x-value of 1

Slope = 2 = Δy/Δx

When the slope is less than 1, we get;

Δy/Δx < 2, therefore Δy is less than 2 when Δx is

The lines in the graph that have a slope greater than 1 but less than 2 are therefore the graphs with the coordinates;

Line 3; (0, 0), (4, 6); Slope = 6/4 = 3/2, therefore; 1 < slope = 3/2 < 2

Line 4; (0, 0), (5, 6); Slope = 6/5, therefore; 1 < Slope < 2

The line 5 has a slope of 1, and the line 1, has a slope of 3, line 2 has a slope of 2

The correct options are line 3 and line 4

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Which equation represents a quadratic function with a leading coefficient of 2 and a constant term of -3?
A - f(x)=2x^3-3
B - f(x)=3x^2-3x+2
C - f(x)=-3x^3+2
D - f(x)=2x^2+3x-3

Answers

Answer:

B - f(x)=3x^2-3x+2

Step-by-step explanation:

Answer:

D

Step-by-step explanation:

Degree of the quadratic function is 2.The leading co-efficient is the co-efficient of the term with highest degree (that is 2).

f(x) = 2x² + 3x - 3

This function satisfies the given condition.

The leading term is 2x² and its co-efficient is 2 and the constant term is (-3)

Is 4.1 less than or greater than 4.10 

Answers

Answer:

4.1 = 4.10

Step-by-step explanation:

Extra 0 at the end of 4.10 doesn't change the quantity of the number, so 4.1 is equal to 4.10

The PTA is holding a raffle. The prize is a camera worth $200. Each raffle ticket costs $5. One hundred tickets are sold and a winner is drawn at random. Find the expected value of the purchase of a ticket.

Answers

The expected value of the purchase of a ticket is -$2.95.

To find the expected value of the purchase of a ticket, we need to consider the probability of winning and the amount of money gained or lost.

Given:

The cost of a raffle ticket is $5.

The prize is a camera worth $200.

One hundred tickets are sold.

To calculate the expected value, we multiply the probability of winning by the value gained and subtract the probability of not winning by the cost of the ticket.

Probability of winning:

Since there are 100 tickets sold and only one winner, the probability of winning is 1/100, or 0.01.

Value gained:

If the ticket is a winning ticket, the value gained is $200.

Probability of not winning:

The probability of not winning is 99/100, or 0.99, as there is only one winner out of 100 tickets.

Cost of the ticket:

The cost of a ticket is $5.

Now, let's calculate the expected value:

Expected value = (Probability of winning × Value gained) - (Probability of not winning × Cost of ticket)

= (0.01 × $200) - (0.99 × $5)

= $2 - $4.95

= -$2.95

The expected value of the purchase of a ticket is -$2.95.

This means that, on average, for each raffle ticket purchased, a person can expect to lose approximately $2.95.

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3(x + 4) pleeeeeeeeeeeeaaaase

Answers

Answer:

3x + 12

Step-by-step explanation:

Using the distributive property, multiply 3 by x and get 3x. Then multiply 3 by 4 and get 12. Put it together and get 3x + 12

3x+ 12
This is how you do the math
3•x=3x
3•4=12

The table shows three unique, discrete functions.
x f(x) g(x) h(x)
-1
0
3
185
15
2
3
0
-25
-10-204
2
3
2
-3
2
3
4
5
6
Which statements can be used to compare the
characteristics of the functions? Select three options.
Of(x) has the greatest maximum.
h(x) has the greatest x-intercept.
g(x) has the smallest minimum value.
All three functions share the same domain.
All three functions share the same y-intercept.

Answers

All thre functions share the same y intercept

We can analyze the characteristics of the given functions based on the information provided in the table.

We cannot determine which function has the greatest maximum based on the table alone, as we do not have the complete graph of any of the functions.

We can see from the table that h(x) has an x-intercept of 0, which is the smallest among the three functions. Therefore, we can say that h(x) has the smallest x-intercept.

We can see from the table that g(x) has a minimum value of -204, which is the smallest among the three functions. Therefore, we can say that g(x) has the smallest minimum value.

We cannot determine if all three functions share the same domain based on the table alone. We can only see that all three functions have been evaluated at the same set of input values.

We can see from the table that the y-intercept of f(x) is 2, the y-intercept of g(x) is 3, and the y-intercept of h(x) is 4. Therefore, we can say that all three functions have different y-intercepts.

Therefore, the statements that can be used to compare the characteristics of the functions are:

h(x) has the smallest x-intercept.

g(x) has the smallest minimum value.

All three functions have different y-intercepts.

Find the value of x.
12, x, 17, 15, 10; The mean is 12.6.

Answers

Answer:x=9

Step-by-step explanation: 12.6x5 then subtract everything else.

Given l ∥ m ∥ n, find the value of x.

Answers

Answer:

-x = 17

Step-by-step explanation:

Given m||n we can write the following equation:

(5x - 23)° + (7x - 1)° = 180° because the these angles are supplementary angles.

Add like terms.

(12x - 24)° = 180°

Add 24 to both sides.

(12x)° = 204°

Divide both sides with 12.

x = 17

Write the equation of a parabola whose directrix is x = -2 and has a focus at (8,-8).

Answers

The equation of the parabola is (x - 3)² = 20(y - k)

Given data ,

To write the equation of a parabola given its directrix and focus, we can use the standard form for a parabola with a vertical axis of symmetry:

(x - h)² = 4p(y - k)

where (h, k) represents the vertex of the parabola, and the distance between the vertex and the focus is equal to the distance between the vertex and the directrix.

In this case, the directrix is x = -2 and the focus is located at (8, -8). Since the directrix is a vertical line, the parabola has a horizontal axis of symmetry.

And , the vertex lies on the axis of symmetry, which is the line equidistant between the directrix and the focus. In this case, the axis of symmetry is the vertical line x = (8 + (-2)) / 2 = 3.

So, the vertex of the parabola is (3, k), where k is yet to be determined

Next, we need to find the value of p, which represents the distance between the vertex and the focus. Since the focus is at (8, -8), and the vertex is at (3, k), the distance between them is given by

p = 8 - 3 = 5

Now, substituting the values into the standard form equation, we have:

(x - 3)² = 4(5)(y - k)

Simplifying further:

(x - 3)² = 20(y - k)

Hence , the equation of the parabola is (x - 3)^2 = 20(y - k), where k is the y-coordinate of the vertex

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