Mathematics College

graphing transformations

Answers

Answer 1

Each of the graphs should be matched with the appropriate function as follows;

Graph 1: D. f(x) = (x - 2)² + 3

Graph 2: C. f(x) = -(x - 2)² - 3

Graph 3: B. f(x) = -(x - 3)² - 2

Graph 4: C. f(x) = (x - 3)² + 2

What is the general form of a quadratic function?

In Mathematics and Geometry, the standard or general form of a quadratic function can be modeled and represented by using the following quadratic equation;

y = ax² + bx + c

Where:

a and b represents the coefficients of the first and second term in the quadratic function.c represents the constant term.

Mathematically, the vertex form of a quadratic function is modeled by this equation:

f(x) = a(x - h)² + k

Where:

h and k represents vertex of the graph.a represents leading coefficient.

In conclusion, we can logically deduce that each of the given quadratic function were either vertically translated or horizontally translated.

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Related Questions

determine the value of x (asap)

Answers

The values of the missing terms are 1) 24 and 2) 1.6.

Given are two similar figures, we need to find the value of x,

According to the definition of similar figures, the ratios of the corresponding sides are equal,

So,

1) GE / EF = RS / TR

5/6 = 20/x

5x = 120

x = 24

2) JH / LK = WX / ZY

3.84 / 2.04 = 3.2 / x

3.84x = 2.04 × 3.2

3.84x = 6.528

x = 1.7

Hence, the values of the missing terms are 1) 24 and 2) 1.6.

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HELP PLEASEE!! The aquarium has 6 fewer yellow fish than green fish. 40% of the fish are yellow. How many green fish are in the aquarium? Show your work. Show all steps please.

Answers

Green fish: x
Yellow fish: x - 6

So, the total number of fish = x + (x - 6) = 2x - 6

40% of the fish are yellow, so:
0.4 (2x - 6) = x - 6
0.8x - 2.4 = x - 6
- 0.2x = - 3.6
x = 18

Thus, green fish = 18

Find the surface area of the cube.

You should have atleast 2 steps shown in your work.

(Need help!!!)

Answers

Step-by-step explanation:

Each of the six sides is 7 mm x 7 mm = 49 mm^2

times six sides : 6 * 49 mm^2 = 294 mm^2

Answer:Area = Side2 = a2

Therefore, the total surface area of a cube = 6 × (area of each side)

= 6 × a2 = 6a2 Square Unit

soooooooooo

Mrs hanger is painting the following picture of a h to hang in the entryway of her home she has made the following scale as her model the scale is used on the drawing is 1:6 on the scale drawing h is centered on the page and 5/6 inches from the top bottom and sides of the drawing as you can see the h is to be painted red in the center of a rectangular beige background what is the actual width of the painting what is the actual height of the painting what is the actual height of the h actual width of the h through the center actual distance from the left edge of the painting to the left edge of the h

Answers

To find the actual dimensions of the painting, we need to first find the dimensions of the scale drawing. We know that the height of the h on the scale drawing is 5/6 inches, and the scale is 1:6. Therefore, the actual height of the h is:

Actual height = (5/6) x 6 = 5 inches

To find the actual width of the h through the center, we can use the same scale. The width of the h on the scale drawing is 1/3 inches (since the h is symmetric). Therefore, the actual width of the h through the center is:

Actual width = (1/3) x 6 = 2 inches

The actual width of the painting is equal to the actual width of the h plus twice the distance from the left edge of the painting to the left edge of the h. On the scale drawing, the distance from the left edge of the h to the left edge of the drawing is (1/6) inches. Therefore, the actual width of the painting is:

Actual width = 2 + 2 x (1/6) = 2 1/3 inches

To find the actual height of the painting, we need to add twice the distance from the top of the h to the top of the painting, and twice the distance from the bottom of the h to the bottom of the painting. On the scale drawing, the distance from the top of the h to the top of the drawing is (5/6) inches, and the distance from the bottom of the h to the bottom of the drawing is also (5/6) inches. Therefore, the actual height of the painting is:

Actual height = 5 + 2 x (5/6) = 6 2/3 inches

Great coffee cup fountain

Answers

According to Karissa's method, Brand B is the winner as it is the most effective and less costly and must be promoted in commercials.

How to solve

Given:-

Data collected by the official observations for each brand at 10 minute intervals.

To find which method should be applied to determine the winner? why? which brand should be declared the winner and promoted in the commercial?

In this given data and what to be obtained is described in it.

Step 2/2

Kariss's method should be applied to determine the winner.

As it fills the amount of liquid paper towel can soak, which of liquid paper can soak, which would directly relate the costs of purchasing on other.

Side Bryce's method should not be used are time is not be used are time is not as important factor as papers A, B, and C have marginal differences.

So Karissa's method would directly help us to determine the most cost-effective to efficient towel brand.

Based on the table:-

Brand A= 40 towels per minute

Brand B= 17 towels per minute

Brand C= 30 towels per minute

In this the solution is obtained by dividing the number of towels by the minute and solving the solution is obtained.

So, according to Karissa's method Brand B is the winner as it is the most effective and less costly and must be promoted in commercials.

Answers

Answer:

down your esophagus into your stomach

Step-by-step explanation:

After you swallow, peristalsis pushes the food down your esophagus into your stomach. Stomach. Glands in your stomach lining make stomach acid and enzymes that break down food. Muscles of your stomach mix the food with these digestive juices.

A box falls off a window ledge on a tall building. The height of the box above the ground can be found using the function h(t)=-16t^2+150, where r stands for the number of seconds since the box fell.
a). Find the height of the window ledge.

Answers

Answer:

The height of the window ledge is the height of the box when t = 0. So, we need to find h(0).

```

h(0) = -16(0)^2 + 150

h(0) = 150

```

Therefore, the height of the window ledge is 150 feet.

Step-by-step explanation:

You pick a card at random.
1 2 3
What is P(divisor of 54)?
Write your answer as a percentage.
%

Answers

The probability in percentage form is P(divisor of 54) = 29.6%

How to find the probability?

The divisors of 54 are:

2, 3, 6, 9 (in the range we care)

Now, in a standard deck there are 52 cards, we have 4 sets, and each of these sets has one of each of the values above.

So out of the 52 cards, there are 4*4 = 16 divisors of 54, then the probability is:

P(divisor of 54) = 16/54

P(divisor of 54) = 0.296

To write it as a percentage just multiply it by 100%.

P(divisor of 54) = 0.296*100% = 29.6%

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The heights in inches of players on Tracy basketball team are shown. Find the mean of the data:

Player Height. (In.)
58,60,61,59,63

Answers:
56.8in
58.5in
60in
60.2in

Answers

Answer:

To find the mean of the data, we add up all the heights and then divide by the number of players:

Mean = (58 + 60 + 61 + 59 + 63) / 5

Mean = 301 / 5

Mean = 60.2 inches

Therefore, the mean height of the players on the Tracy basketball team is 60.2 inches.

The answer is 60.2in.

Step-by-step explanation:

Solve for x. Assume that lines which appear to be diameters are actual diameters.

Answers

Answer:

x = 9

Step-by-step explanation:

We Know

A circle is 360°

An angle is 85° & one is 130°

Find x

We Take

85° + 130° + 16x + 1 = 360°

216 + 16x = 360°

16x = 144°

x = 9

Solve the following for θ, in radians, where 0≤θ<2π.
−7cos2(θ)+4cos(θ)+6=0
Select all that apply:

1.07
3.96
0.31
2.32
1.68
2.43

Answers

Answer:correct answers are 3.96

2.32

Step-by-step explanation:We can solve this quadratic equation in cos(θ) by using the substitution u = cos(θ):

-7u^2 + 4u + 6 = 0

Now we can use the quadratic formula to solve for u:

u = (-b ± sqrt(b^2 - 4ac)) / 2a

where a = -7, b = 4, and c = 6. Substituting these values, we get:

u = (-4 ± sqrt(4^2 - 4(-7)(6))) / 2(-7)

u = (-4 ± sqrt(136)) / (-14)

u = (2 ± sqrt(34)) / 7

Therefore, either:

cos(θ) = (2 + sqrt(34)) / 7

or:

cos(θ) = (2 - sqrt(34)) / 7

Since 0 ≤ θ < 2π, we can find the two solutions in the interval [0, 2π) by using the inverse cosine function:

θ = arccos((2 + sqrt(34)) / 7)

θ = arccos((2 - sqrt(34)) / 7)

Using a calculator, we find:

If a company uses standard costs to record its inventory in the general ledger, what would the journal entry be for a purchase of direct materials with a favorable price variance?

Answers

The journal entry for the company is Debit - Raw Materials Inventory - Standard Cost, Credit - Accounts Payable - Actual Cost.

When a company uses standard costs to record its inventory in the general ledger, the journal entry for a purchase of direct materials with a favorable price variance would be as follows

Debit - Raw Materials Inventory - Standard Cost

Credit - Accounts Payable - Actual Cost

The debit entry would record the standard cost of the direct materials purchased, and the credit entry would record the actual cost of the direct materials purchased, which is lower than the standard cost due to the favorable price variance.

It's important to note that this journal entry assumes that the company is using a perpetual inventory system, where the inventory account is updated continuously as purchases and sales occur. If the company is using a periodic inventory system, the journal entry would be different and would involve adjusting the cost of goods sold account at the end of the period.

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full method please

(-9+5)+7×(-3)please

Answers

Evaluating the expression (-9+5)+7×(-3), we get -25

Evaluating the expression

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

(-9+5)+7×(-3)

Evaluate the expressions in the bracket

So, we have

-4 + 7 * -3

Evaluate the products

So, we have

-4 - 21

Lastly, we have

-25

Hence, the solution is -25

Answers

The expression that is equivalent to this polynomial "x²+12" is option A. (x + 2√3i) (x — 2√3i)

How did we get the value?

In mathematics, a polynomial is an expression consisting of variables and coefficients that concern only the operations of addition, subtraction, multiplication, and nonnegative integer exponents.

A. (x + 2√3i) (x — 2√3i)

= (x² + 2√3i)² (i² = -1)

= (x² - 12x (— 1)

= x² + 12

B. (x + 6i) (x - 6i)

= (x² - (6i)²

= x² + 36

C. (x + 2√3)²

= x² + 4√3x + 12

D. (x + 2√3) (x - 2√3)

= x² - (2√3)²

= x² - 12

Therefore, the correct answer is as given above. Option A. (x + 2√3i) (x — 2√3i) is equivalent to the given polynomial.

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The complete question goes thus:

Which expression is equivalent to this polynomial?

x²+12

OA. (x + 2√3i) (x — 2√3i)

B. (x+6)(x-61)

Oc. (x + 2√3)2

OD. (x + 2√3) (x - 2√3)

Kevin is k years old. Ben is 8 years older than Kevin. Hannah is 2 times older than Ben. What is Hannah’s age?

Answers

Answer:

2k+16

Step-by-step explanation:

Kevin: k

Ben: 8 years older than k, k+8

Hannah: 2 times Ben's age, 2(k+8)=2k+16

Solve using the elimination method, and also determine whether a system is consistent or inconsistent, and whether the equations are dependent or independent.

Please helppp <3

Answers

To solve using the elimination method, we need to eliminate one of the variables.

Multiplying the first equation by 3, we get:

9x = 165 - 21y

Now we can write the system as:

9x = 169 - 22y

9x = 165 - 21y

Subtracting the second equation from the first, we get:

0 = 4 - y

Solving for y, we get:

y = 4

Substituting y = 4 in the first equation, we get:

3x = 55 - 7(4)

3x = 27

x = 9

Therefore, the solution to the system is (x, y) = (9, 4).

The system is consistent and independent, since it has a unique solution.

Part E
Isaiah wants to compute his total earnings after picking 10 baskets of each fruit.
Complete the equations and find Isaiah's total earnings. Enter your answers in the boxes.
Apples: 10 x ____ = ____
24+ ___ = a
Peaches: 10 x ____ =
18+____= p
Total: a+p=$ ___

Answers

Isaiah's total earnings after picking 10 baskets of apples and peaches each is: $117

How to solve Algebra Word Problems?

Algebraic word problems are defined as questions that require translating sentences to equations, then solving those equations. The equations we need to write will only involve. basic arithmetic operations. and a single variable. Usually, the variable represents an unknown quantity in a real-life scenario.

We are told that Isaiah as already earned $24 picking apples and $18 picking peaches.

Amount for each basket of apple = $3 each

Amount for each basket of Peach = $4.5 each

Thus, for 10 baskets each:

Apples = 10 * 3 = $30

a = 24 + 30

a = $54

Peaches = 10 * 4.5 = $45

p = 18 + 45

p = $63

Total earnings = a + p

= $54 + $63

= $117

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Complete question is:

Isaiah picks fruit at a local orchard. He has already earned $24 picking apples and $18 picking peaches. He earns $3 for each basket of apples and $4.50 for each basket of peaches picked.

Isaiah wants to compute his total earnings after picking 10 baskets of each fruit.

Complete the equations and find Isaiah's total earnings. Enter your answers in the boxes.

Apples: 10 x ____ = ____

24+ ___ = a

Peaches: 10 x ____ =

18+____= p

Total: a+p=$ ___

I've been struggling a lot with interpreting what this problem wants me to find.

The plane departs an airport at 9:00 AM and flies 200 mph southwest. A second plane ldeparts the same airport at 9:30 AM and flies 320 mph northwest. Find the bearing of the second plane from the first one at 10:00 AM.

The reason: I've heard some people say a bearing has to be in one direction (north). I've also heard that a bearing has to be an acute angle and some insist there is an answer to this greater than 90º.

I drew out a diagram with a right triangle, legs of 200 and 160 (320 ÷ 2 for the half hour), separated my right triangle into two triangles with 45º angles, and went from there.

Where the hypotenuse and the 160 side meet, the angle is 51.34º. The 200 side makes a 38.66º angle (both came from arctan). I know for a fact there is an 83.66º angle that can be found.

Trouble is, I'm not sure if that's the actual bearing or not. Everything SEEMS correct there, but I've just heard so many other answers on this that I'm not sure who or what to believe!

Figured I'd see what everyone else thought. It's the "second from the first" that I'm struggling with semantically too. I can do the math just fine here.

Answers

Answer:

6.34°

Step-by-step explanation:

You want to know the bearing of a second plane from the first at 10 a.m. when the first leaves at 9 a.m. and flies 200 mph SW, while the second leaves at 9:30 a.m. and flies 320 mph NW.

Locations

The first plane flies for an hour at 200 mph, so is 200 miles from the airport on a bearing of 180° + 45° west of south, or 225°.

The second plane flies for half an hour at 320 mph, so is 160 miles from the airport on a bearing of 360° -45° west of north, or 315°.

Direction

The vector in the direction of the second plane from the first is found by subtracting the location of the first plane from the second:

vector of interest = (160∠315°) -(200∠225°)

A suitable calculator can tell you the difference is ...

vector of interest = 256∠6.34°

The second plane is on a bearing of 6.34° from the first.

Additional comment

You are correct that an angle of 83.66° is involved. That would be the measure of the direction vector counterclockwise from the +x axis. You want the bearing angle, measured clockwise from the +y axis (North), so the angle you're looking for is 90° -83.66° = 6.34°.

If you work enough of these problems, you will find that it doesn't matter how you measure the angles, as long as you do it consistently. The second attachment shows the arithmetic using distance∠bearing. The effect is to swap the x, and y coordinates so that they are (N, E) coordinates, rather than the usual (E, N) coordinates. This doesn't have to be confusing. A diagram usually helps.

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11. If the revaluation of the asset is higher than the carrying value, the following entries will be made via the revaluation account; Debit Asset account and Credit Capital account of each partner. True/False?

Answers

Answer:

False. If the revaluation of the asset is higher than the carrying value, the following entries will be made: Debit Asset account and Credit Revaluation reserve account. The revaluation reserve account is a balance sheet account and does not affect the capital accounts of the partners directly. However, the revaluation reserve may indirectly affect the capital accounts of the partners if the revaluation reserve is distributed to the partners or used to offset losses in the future. It is worth noting that the specific accounting treatment may vary depending on the accounting standards being used by the company.

Step-by-step explanation:

26=-9w-2w-18?????????????????

Answers

Answer:

w = -4

Step-by-step explanation:

Hope this helps

26 = 9w - 2w -18
26= 11w -18
+18. +18
44 = 11w
11. 11
4 = W

find the least common denominator

Answers

To find the least common denominator (LCD), you need to find the smallest multiple that two or more denominators have in common.

For example, if you need to add 1/3 and 1/4, you need to find the least common multiple (LCM) of 3 and 4, which is 12. So, the LCD is 12.

Another example, if you need to add 1/2, 1/3, and 1/4, you need to find the LCM of 2, 3, and 4, which is 12. So, the LCD is 12.

Therefore, the least common denominator depends on the denominators of the fractions you are trying to add or subtract.

Claim: The standard deviation of pulse rates of adult males is 12 bpm. For a random sample of 173 adult males, the pulse rates have a standard deviation of 10.6bpm. Find the value of the test statistic.

Answers

Based on the standard deviation given and the sample size, the test statistic can be found to be 134.20.

The test statistic can be found by the formula:

= ((Sample size - 1) x Standard deviation of sample²) / Standard deviation of population

Solving gives:

= ((173 - 1) x 10.6²) / 12²

= 19,325.92 / 144

= 134.20

Hence, the test statistic is 134.20.

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plot the point whose polar cord are (3, -135 degrees) pick graph below

Answers

The plot of the given point must be at.

the third circle and at the 9th ray clockwise from the positive x-axis.

How to plot the point in polar coordinates?

Here we want to plot the point (3, -135°).

Remember that a point whose polar coordiantes are (R, θ) must be ploted along the circumference of a circle of radius R, at the angle θ measured counterclockwise from the positive x-axis.

Then here we need to have a circle of radius of 3 units, and plot the point at -135° from the positive x-axis.

Now, each of the rays has 15° on it, then the point should be graphed on the third circle (radius of 3 units) and at the 9th ray clockwise from the positive x-axis (clockwise because the angle is negative, and 9th ray because 9*15 = 135)

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Find the quotient of x+4/x^2 dividend by 2/x

Answers

The division of the given algebraic expression is: (x + 4)/2x

How to divide algebraic problems?

The division algorithm for polynomials says, if p(x) and g(x) are the two polynomials, where g(x) ≠ 0, we can write the division of polynomials as: p(x) = q(x) × g(x) + r(x).

Where:

p(x) is the dividend.

q(x) is the quotient.

We want to solve:

[(x + 4)/x²] ÷ 2/x

Thus, we can simplify to:

[(x + 4)/x²] * x/2

= (x + 4)/2x

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What meaning of the statement this: subgroups partition groups into subsets of equal size?

Answers

Answer:

This statement means that subgroups divide a larger group into smaller groups, and each of these smaller groups has the same number of things in it. For example, if there are 12 people in a group, and they form subgroups of 3 people each in a group, there will be 4 groups total, and each individual subgroup will have 3 people in it.

Which of the following functions are vertical translations of f(x)=√x?
Select all that apply.
A. K(x)=√√√-5+x
B. n(x) = -7+ √x
C. g(x)=√x -4
D. h(x)=3+√x
E. m(x)=√5x

Answers

Answer:

The function f(x) = √x is the square root function.

A vertical translation of a function is a transformation that shifts the graph of the function up or down without changing its shape.

Option (A) is a vertical translation of f(x) because it shifts the graph of f(x) to the right by 5 and then applies three square root operations. However, it is not a vertical translation that shifts the graph up or down.

Option (B) is a vertical translation of f(x) because it shifts the graph of f(x) down by 7 units.

Option (C) is a vertical translation of f(x) because it shifts the graph of f(x) down by 4 units.

Option (D) is a vertical translation of f(x) because it shifts the graph of f(x) up by 3 units.

Option (E) is not a vertical translation of f(x) because it involves multiplying the input of f(x) by a constant factor of 5.

Therefore, the options that are vertical translations of f(x) are (B), (C), and (D).

Step-by-step explanation:

a principle has given a class 75 dollars to help pay for a field trip to the zoo

Answers

Answer:

5p + 75> 386

Step-by-step explanation:

principal has given $75

Total cost of trip = $386

price of a pie = $5

5p + 75 ≥ 386

Triangle ABC
A
B
C
and triangle DEF
D
E
F
are similar. What is the measure of side DF
D
F
?

Answers

Answer:

DF = 15 cm

Step-by-step explanation:

since the triangles are similar then the ratios of corresponding sides are in proportion, that is

[tex]\frac{DF}{AC}[/tex] = [tex]\frac{EF}{BC}[/tex] ( substitute values )

[tex]\frac{DF}{9}[/tex] = [tex]\frac{25}{15}[/tex] ( cross- multiply )

15 DF = 9 × 25 = 225 ( divide both sides by 15 )

DF = 15

Answer:

Step-by-step explanation:

1. Use the Pythagorean theorem for triangle ABC

a squared (one side of the triangle) + b squared (another side) = c squared (hypotenuse)

c squared - b squared = a squared

225 - 81 = 144 ( Find the square root )

which is 12

since Triangle ABC is the same with Triangle DEF then

DF = 12

Give the equation of the circle centered at the origin and passing through the point (0, 6).

Answers

The equation of circle is x² + y² = 36.

We have,

Center= (0, 0)

Passing point = (0, 6)

We know the equation of circle is

(x-h)² + (y-k)² = r²

where (h, k) be the center and r be the radius.

Now, the radius of circle is

= √(6-0)² + (0-0)²

= √36

= 6 unit

So, the equation of circle

(x-0)² + (y-0)² = 6²

x² + y² = 36

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if a baseball team has lost 50 matches out of the 120 matches played in total find out their winning percentage

Answers

Answer:

58.3%

Step-by-step explanation:

120-50=70 (wins)

120 is 100% wins

70. ??

We multiply 70 by 100% then divide by 120.

To find the winning percentage of a baseball team, we need to divide the number of games won by the total number of games played and multiply by 100%.

The number of games won by the team can be calculated by subtracting the number of games lost from the total number of games played:

Number of games won = Total number of games played - Number of games lost
Number of games won = 120 - 50
Number of games won = 70

Now, we can calculate the winning percentage using the following formula:

Winning percentage = (Number of games won / Total number of games played) x 100%

Plugging in the numbers, we get:

Winning percentage = (70 / 120) x 100%
Winning percentage = 58.33%

Therefore, the winning percentage of the baseball team is 58.33%.

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