Paul designed a patio for his backyard. The patio will cost
$3 per square foot to construct. His design and the scale
he will use to build the patio are both shown below.
How much will Paul spend constructing the patio?
Scale
1 cm = 3 ft.
5 cm
4 cm
8 cm
dollars
6.4 cm

The perimeter of the triangle  STU is 20.6 units

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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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)

Brian is correct, because the graph shows the circle with a center (-3, 2) and a radius of 2.

Since, The circle is a closed two dimensional figure , in which the set of all points is equidistance from the center.

We have to given that;

Brian says the graph shows the circle with a center (-3, 2) and a radius of 2.

And, Mia says the graph shows all possible centers for a circle that passes through (-3, -2) with a radius of 2.

Now, By given graph we can see that,

Center of circle = (- 3, 2)

And, Radius of circle = - 1 + 3 = 2

Hence, Brian is correct, because the graph shows the circle with a center (-3, 2) and a radius of 2.

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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.

1. In terms of x and y, the height of the tree is  and

2. The height of the tree is 6.71 meters

Since, From the question, we are to determine the height of the tree in terms of x and y

Hence, By Using SOH CAH TOA, we can write that

tan t° = h / y

h = y × tan t°

Also, We get;

tan s° = h / x

h = x × tan s°

2. If m ∠t = 38° and y = 3 meters,

Then, the height of the tree;

h = 3 × tan 38°

h = 3 × 0.78 meters

h = 2.34 meters

Hence, the height of the tree is 2.34 meters.

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Axiom of Infinity states that there is at least one set that contains an infinite number of elements.

A basic tenet of set theory, the Axiom of Infinity affirms the existence of an endless set. In plainer language, it proves that at least one set has elements with an infinite number.

This axiom is crucial because it enables rigorous and consistent mathematical reasoning about and interaction with infinite collections. It offers a fundamental premise for many infinity-related mathematical notions and structures, including infinite sequences, series, and cardinality.

The Axiom of Infinity ensures that mathematics is not restricted to only finite quantities and allows for the exploration of the rich and intriguing realm of infinite structures by declaring the existence of an endless set.

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Graph is attach below for this question and the equation of this graph is

A(x) = 400(1.25)ˣ +0

We have,

In mathematics, "graph" can refer to (at least) two different things. In elementary mathematics, the term "graph" indicates a plot or a function graph. A graph is, in the language of mathematicians, a set of points and the connections between some subset of those points (which may be empty).

Given that the boat's value increasing at a rate of 25% per year.

So after each year the value becomes = 1 + 25% = 1 + 0.25 = 1.25 of the previous year.

So the equation becomes: A(x) = 400(1.25)ˣ +0

Since, b = 1.25 > 1, so A(x) is a increasing function. And for every value of x, A(x) < 0.

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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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Answer:x=9

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

The equation of the graph is (b) y = (x + 4)(x + 2)(x - 1)

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

The graph

The graph is a polynomial graph with the following zeros and multiplicities

The equation is then represented as

y = (x - zero) to the exponent of the multiplicities

So, we have

y = (x + 4)(x + 2)(x - 1)

Hence, the equation of the graph is (b) y = (x + 4)(x + 2)(x - 1)

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The real dimensions of the object are 144 inches by 216 inches.

Given that, 6:1 scale with dimensions of 24 inches by 36 inches.

The basic formula to find the scale factor of a figure is expressed as,

Scale factor = Dimensions of the new shape ÷ Dimensions of the original shape.

In a 6:1 scale, the real dimensions of an object would be 6 times the scaled dimensions. Therefore, the real dimensions of the object given in the question would be 24 inches x 6 = 144 inches by 36 inches x 6 = 216 inches. So, the real dimensions of the object are 144 inches by 216 inches.

Therefore, the real dimensions of the object are 144 inches by 216 inches.

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If the hypotenuse of an isosceles right-angled triangle is 3√2 cm, then each of the side of the triangle is 3 cm.

Given that,

Hypotenuse of the right angled triangle = 3√2 cm

Since the triangle is isosceles, the other two sides or the legs of the triangle will have equal length.

Let x be the length of each leg.

Using Pythagoras theorem,

x² + x² = (3√2)²

2x² = 18

x² = 9

x = 3

Hence the length of each side is 3 cm.

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By the Side-Angle-Side (SAS) congruence criterion, triangle ABC is congruent to triangle BAD.

To prove that triangle ABC is congruent to triangle BAD based on the given information, we can apply the Side-Angle-Side (SAS) congruence criterion.

AC is congruent to BD (Side)

angle CAB is congruent to angle DBA (Angle)

To prove triangle ABC congruent to triangle BAD using the SAS congruence criterion, we need to show that they share two congruent sides and a congruent angle between them.  

Side AB is common to both triangles.

Side AC is congruent to BD (given).

angle CAB is congruent to angle DBA (given).

By satisfying the SAS congruence criterion, we can conclude that triangle ABC is congruent to triangle BAD.

The SAS congruence criterion states that if two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then the two triangles are congruent.

In this case, we have side AB in common, and side AC is congruent to BD, along with angle CAB being congruent to angle DBA.

Therefore, all the conditions of the SAS criterion are satisfied.

Hence, we can conclude that triangle ABC is congruent to triangle BAD based on the given information.

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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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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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Answer:

c = 45 and e = 30

Step-by-step explanation:

Since we know that A = 45, B = 90, we can calculate C knowing that the total angle of a triangle is 180, so you do 180-45-90 = 45

Finding the angle C helps us find F by subtracting 45 from 180, since a straight line is 180 degrees, which is 135.

We know that E = 15, and what was said earlier about how the toal angle is 180 in a triangle, we can subtract 15 and 135 from 180, which is 30.

Hope that answers your question

Answer:

Step-by-step explanation:

Answer:

b ≈ 54.94

Step-by-step explanation:

using the Sine rule in Δ ABC

[tex]\frac{a}{sinA}[/tex] = [tex]\frac{b}{sinB}[/tex] = [tex]\frac{c}{sinC}[/tex]

where a is the side opposite ∠ A, b is opposite ∠ B , c is opposite ∠ C

we require to calculate ∠ B

∠ B = 180° - (42 + 41.5)° = 180° - 83.5° = 96.5°

to find b using the pair of ratios

[tex]\frac{b}{sinB}[/tex] = [tex]\frac{a}{sinA}[/tex] ( substitute values )

[tex]\frac{b}{sin96.5}[/tex] = [tex]\frac{37}{sin42}[/tex] ( cross- multiply )

b × sin42° = 37 × sin96.5° ( divide both sides by sin42° )

b = [tex]\frac{37sin96.5}{sin42}[/tex] ≈ 54.94 ( to 2 decimal places )

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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Answer:

y = (1/2)log₂ (x - 7) - 5

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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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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Answer: 60 in.

Chain of Thought Reasoning:

Step 1: P = 2L + 2W

Step 2: 18 = 2L + 2(4)

Step 3: 18 = 8 + 2L

Step 4: 10 = 2L

Step 5: 5 = L

Step 6: Convert feet to inches: 1 foot = 12 inches

Step 7: 5 feet = 5 * 12 inches

Step 8: 5 feet = 60 inches

Therefore, the length of the rectangular yard is 60 inches.

1/4 or 0.25 is the probability that the coin shows heads and the die shows an odd number.

To find the probability that the coin shows heads and the die shows an odd number, we need to consider the possible outcomes for each event and calculate the probability of their intersection.

For the coin toss, there are two possible outcomes: heads (H) or tails (T). Each outcome has an equal chance of occurring, so the probability of the coin showing heads is 1/2.

For the die roll, there are six possible outcomes: 1, 2, 3, 4, 5, or 6. Out of these outcomes, three numbers (1, 3, and 5) are odd. Again, each outcome has an equal chance of occurring, so the probability of rolling an odd number is 3/6 or 1/2.

To find the probability of both events occurring, we multiply the individual probabilities:

Probability of coin showing heads = 1/2

Probability of die showing an odd number = 1/2

Probability of both events occurring = (1/2) * (1/2) = 1/4

Therefore, the probability that the coin shows heads and the die shows an odd number is 1/4 or 0.25.

This means that out of all possible outcomes from tossing a coin and rolling a die, there is a 1 in 4 chance that the coin shows heads and the die shows an odd number. It's important to note that this calculation assumes fair and unbiased coin and die, where the probabilities of each outcome are equally likely.

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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

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.

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

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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Answer:

26.74 degrees!

Step-by-step explanation:

The formula you can plug the numbers into is:

angle = L / r

Angle = the central angle

L = the length of the arc

r = radius of the circle

The output of the exponential function when x = 5 is given as follows:

f(5) = 96.

An exponential function has the definition presented as follows:

[tex]y = ab^x[/tex]

In which the parameters are given as follows:

The parameter values for this problem are given as follows:

Hence the function is given as follows:

[tex]f(x) = 3(2)^x[/tex]

The numeric value at x = 5 is given as follows:

[tex]f(5) = 3(5)^x = 96[/tex]

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