Use Heron's Area Formula to find the area of the triangle. (Round your answer to two decimal places.) a = 57 , b = 43 , c = 58

a. The two pentagons are congruent as the transformations they underwent were only translation and rotation, which are rigid motions.

b. The side lengths of ABCDE are given as follows:

The angle measures of FGHIJ are given as follows:

Congruence is only changed with a dilation, as the side lengths are changed.

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Answer:

a. 1; b. 2; c. 1.

Step-by-step explanation:

1] if the given functions are:

[tex]1: \ h=-3.1d^2+4.8;\\2: \ h=-3.5d^2+1.9;\\3: \ h=-1.1d^2+1.6, \ then[/tex]

2] a. d=0, ⇒ max[h] is no.1 (h=-3.1d²+4.8);

b. h=0, ⇒ min[d] is no.2 (h=-3.5d²+1.9);

c. h=0, ⇒ max[d] is no.1 (h=-3.1d²+4.8).

Answer:

The area of the top of the crate can be found by multiplying the length by the width.

        3/4 yard = 9/12 yards

        2/4 yard = 6/12 yards

    2. Now we can find the area by multiplying the length by the width:

     Area = 9/12 yards * 6/12 yards = (9/12) * (6/12) = 3/4 * 1/2 = 3/8                         yards^2

So, the area of the top of the crate is 3/8 yards^2.

Required value of (1513÷3) is 504R1.

What is division?

Division is the opposite of multiplication. If 3 groups of four are multiplied by 12, 12 divided into three equal groups gives 4 in each group.

The main purpose of distribution is to see how many equal groups are formed or how many are in each group in a fair distribution.

In the above example, to divide the 12 donuts into 3 similar groups, you need to put 4 donuts in each group. So, 12 divided by 3 is 4.

Here given two digits are 1513 and 3.

We want to find value of 1513 ÷ 3.

Now,

[tex]1513 ÷ 3 = \frac{1513}{3} = 504 R1[/tex]

Therefore, the quotient is 504 and the remainder is 1.

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Answer:

The price of the uniforms last year was about $79.20.

Step-by-step explanation:

              In order to calculate the price of the uniforms last year, it is important to understand two important thing that can be inferred by what is told in the problem. This year's uniforms are 9.6% more than last year's. The easiest way to understand this line of information is that if we view the prices of the uniform from the perspective of last year's price, we can set the price of last year's uniform as 100% of the original price, and this year's uniform as 109.6% of the original price. Essentially, this year's uniform price is 109.6% of what it would cost you to buy a uniform last year.

             Since you are given the information that this year, the uniforms cost $86.80, you know that $86.80 is 109.6% of last year's uniform cost. Now you can write an equation to solve for last year's price.

             Set last year's uniform price to be represented by the variable [tex]x[/tex], and you will have the function of  [tex]109.6[/tex]% · [tex]x = 86.8[/tex]. In order to solve for [tex]x[/tex], you simply divide both sides of the equation by 109.6%, which you will then get [tex]x = 86.8[/tex] ÷ 109.6%, which can be rewritten as [tex]x=86.8[/tex] ÷ [tex]\frac{109.6}{100}[/tex]  or [tex]x=86.8[/tex] · [tex]\frac{100}{109.6}[/tex] ≈ $79.20. Hence, last year's uniforms costed $79.20.

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(a) The probability that the vehicle is a crossover is 0.30.

(b) Given that the vehicle is not a passenger car, the probability that it is a pickup truck is 0.50.

(c) The probability that the vehicle is a pickup truck, SUV, or minivan is 0.90.

I determined the probabilities based on the information provided in the problem. The problem states that the probability distribution for the type of vehicle chosen is given and lists the probabilities for each type of vehicle (crossover, pickup truck, SUV, minivan, and passenger car). To find the requested probabilities, I simply used basic probability formulas and the given probabilities for each type of vehicle.

P(pickup truck | not passenger car) = P(not passenger car | pickup truck) * P(pickup truck) / P(not passenger car).

0.40 / (1 - 0.20) = 0.50.

The denominator P(not passenger car) is found by subtracting the probability of a passenger car (0.20) from 1, and the numerator P(not passenger car | pickup truck) is 1, since a vehicle can either be a pickup truck or not a pickup truck but not both. The requested probability is then equal to 0.50.

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Answer:

c) S : {30}

So, it is correct answer.

Step-by-step explanation:

mental math be like :-)

Answer:

c = 4

Step-by-step explanation:

if (x - a) is a factor , that is divisible by, of f(x) then f(a) = 0

then for p(x) to be divisible by (x - 1) , p(1) = 0

then

2[tex](1)^{4}[/tex] - 5(1)² + c(1) - 1 = 0

2 - 5 + c - 1 = 0

- 4 + c = 0 ( add 4 to both sides )

c = 4

The equation can be given as y = 0.4x +22 and the monthly cost is $368.4

What is a linear equation?

A linear equation is an expression whose degree is one. The most general linear equation is y = mx + c. Where m is the slope and c is the y-intercept.

A) To find the equation in the form y = mx + b.

We are given two points (390, 178) and (940, 398).

Now we substitute these points into the standard equation y = mx + c

We get

y = mx + b

178 = m * 390 + b

398 = m * 940 + b

We subtract the two equation we get,

550m = 220

m =0.4

Now we substitute these values in the equation 1 we get

178 = 0.4 * 390 + b

178 = 156 + b

b = 22

So the equation is:

y = 0.4x + 22

B) We are asked to find the cost for 866 minutes we substitute x = 866 in the equation

y = 0.4x + 22

y = 0.4 * 866 + 22

y = 346.4 + 22

y = 368.4

So if 866 minutes are used, the total monthly cost will be $368.4.

The equation can be given as y = 0.4x +22 and the monthly cost is $368.4

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Answer:

There are 15 students in class 6

Step-by-step explanation:

Let's call the number of students in class 6 "n".

We know that:

Anton gets 0.2 * n votes

Eva gets 0.1 * n votes

Petra gets (1 - 0.2 - 0.1) * n votes

Kofi gets 9 votes

The total number of votes is n, so we can write:

n = 0.2 * n + 0.1 * n + (1 - 0.2 - 0.1) * n + 9

Simplifying this equation:

0.6 * n = 9

So:

n = 9 / 0.6

n = 15

Answers:

1.             The graph is in the shape of a parabola, there is a vertex point at (20, 400), and the zeros (x-intercepts) of the graph are at the origin of the coordinate plane (0, 0) and (40, 0).

2.            The greatest area possible for a rectangle with a perimeter of 80 meters is 400 [tex]m^2[/tex], and the dimensions of this rectangle will be 20 meters in length and 20 meters in width.

3.             The area of the rectangle whose length is 10 meters and the area of the rectangle whose length is 30 meters are the same, both being 300 [tex]m^2[/tex]. This is because the perimeter is set as 80 meters total, and as they are both rectangles, the opposite sides must be the same length.

               For the rectangle with a length of 10 meters, 2 of the 4 sides will use 20 meters of material, so there will be 60 meters of material left for the remaining 2 sides, or 30 meters per side. So the dimensions of that rectangle would be 10 meters in length and 30 meters in width.

               For the rectangle with a length of 30 meters, it's the same thing, except the length is 30 meters, and the width is 10 meters. And for both rectangles, their areas are 30 meters multiplied by 10 meters, which equals 300 [tex]m^{2}[/tex], so the way these two rectangles are related is that they have the same area.

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Answer:

1.  See below.

2.  400 m²

    20 m x 20 m

3.  300 m²

Step-by-step explanation:

The graph is a parabola that opens downwards.

Its vertex is (20, 400) and its axis of symmetry is x = 20.

From inspection of the given graph, the greatest possible area (y-value) is 400 m².  This is when the length of the rectangle is 20 m.

The largest possible area of a rectangle is when the length equals the width. Therefore, the dimensions of the rectangle with the greatest area possible are:

From inspection of the graph, when the length of the rectangle is 10 m, its area is 300 m².

Similarly, when the length of the rectangle is 30 m, its area is also 300 m².

A rectangle has two pairs of parallel sides of equal length.

Therefore, as both rectangles have the same area, this means that the one pair of parallel sides is 10 m in length and the other pair of parallel sides is 30 m in length.  The dimensions of both rectangles are the same: 10 m x 30 m, where the width and length are interchangeable.

Answer:

the answer is 0.168

Step-by-step explanation:

have a good day!

Answer: Let's call the length of the box "x". Then, the height of the box is 4x and the width is x + 7. The volume of the box is given by the equation:

x * 4x * (x + 7) = 102

Expanding and simplifying the equation, we get:

4x^3 + 28x^2 - 102 = 0

To find the length of the box, we need to solve for x in this equation. One way to do this is to use the cubic formula. However, this formula can be quite complex, so a simpler method would be to use numerical methods such as the bisection method or Newton's method.

Step-by-step explanation:

Answer:

$40

Step-by-step explanation:

We know

Her father gave her $20 for every $50 she saved

$50 + $20 = $70

$50 + 20 + 50 + 20 = $140

$182 - $140 = $42

It is not $50 yet, so her father only give her 2 times

So, her father gives her $40

Answer:

182÷50 = 3.64, 3.64x20=72.8$

her dad gave her 72.8$

The linear approximation of f(1.07) using the tangent line is T(1.07) is 10.77, which is slightly lower than the actual value f(1.07) = 11.77.

First, we need to find the derivative of the function f(x) = x + 10x.

The derivative is given by:

f'(x) = 1 + 10

Next, we need to find the tangent line at the point (a, 6), which means we need to find the value of "a" that makes the tangent line pass through (a, 6). To do this, we use the equation of the tangent line:

y - 6 = (1 + 10)(x - a)

y = (1 + 10)(x - a) + 6

Now we need to use the value of "a" to find the value of f(a) and then use this to find the value of the linear approximation of f(1.07).

Let's assume that the value of "a" is 1.

So, f(a) = f(1) = 1 + 10(1) = 11

And the equation of the tangent line is:

y = (1 + 10)(x - 1) + 6 = 11x - 4

Now, to find the value of the linear approximation of f(1.07), we use the equation of the tangent line:

T(1.07) = 11 * 1.07 - 4 = 10.77

Finally, we compare this value with the actual value of f(1.07), which is:

f(1.07) = 1.07 + 10 * 1.07 = 11.77

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Answer:To convert the elevation of the City of Santa Clara from feet to centimeters, you can use the conversion factors:

1 ft = 12 in

1 in = 2.54 cm

First, convert feet to inches:

75 ft * 12 in/ft = 900 in

Then, convert inches to centimeters:

900 in * 2.54 cm/in = 2286 cm

So, the elevation of the City of Santa Clara is approximately 2286 cm.

Step-by-step explanation:

The 17-foot-long ladder pulled out 3 feet farther from the wall from a distance of 8 feet, indicates, using Pythagorean Theorem that the top of the ladder moves about 2.039 feet down the wall.

Pythagorean Theorem states that the square of the length of the hypotenuse side of a right triangle is equivalent to the sum of the squares of the length of the legs of the right trianglde.

Length of the ladder = 17 foot ladder

Distance of the bottom of the ladder from the wall = 8 feet

The extra distance to which the bottom of the ladder is pulled = 3 feet

The ladder resting on the wall forms a right triangle, with the length of the ladder being the hypotenuse side.

The initial vertical distance reached by the ladder on the wall, h, can be found using Pythagorean Theorem as follows;

h² = 17² - 8² = 225 = 15²

h² = 15²

The initial vertical distance up the wall the ladder reaches, h, is therefore;

h = √(15²) = 15

The ladder initially reaches 15 feet high on the wall

The ladder is then pulled 3 feet farther, from which we get;

New horizontal distance of the ladder from the wall = 8 feet + 3 feet = 11 feet

The square of the new height the ladder reaches up to on the wall, h'², can therefore be found as follows;

h'² = 17² - 11² = 168

√h'² = h' = √(168) = 2·√(42)

The new height the ladder reaches up to on the wall, h' ≈ 2·√(42) feet

The distance the ladder moves down the wall, Δh = h - h', therefore;

Δh = 15 - 2·√(42) ≈ 2.039

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Answer:

y=1.25x+10

Step-by-step explanation:

you can put this into the formula “y=mx+b”. y is the final amount, x is how many times joana gets food or goes on a ride. You can plug into the equation the two parts we know. We know that no matter what, if she goes into the fair, she is going to spend $10 on the admission, even if she does not go on any rides or gets any food. So we put 10 where the “b” is. Then each time she gets food or goes on a ride, she pays another $1.25. Therefore, you can plug 1.25 into where the m is. That leaves you with “y=1.25x+10”.

A. The solution set of the system is {7, 3}

The elimination method is a method used to solve or find a set of solutions to a system of linear equations of two variables by eliminating one of the variables. If the variables are x and y, to determine the x variable we must first eliminate the y variable, or vice versa, if we want to find the y variable, we must first eliminate the x variable.

To eliminate a variable, it must have the same coefficient. So if the coefficients of the variables are not the same then first equate the coefficients by multiplying or dividing them. Then only can determine other variables that will be determined. So in the elimination method you need to eliminate the variable twice.

To eliminate y in order to find the value of x.

9x-y=60 (i) 9x-y=60

x+y=10 (ii) | times (-1)| -x-y= -10

___________ __________ _

10x=70

x=7

Substitute the value x=7 into equation (ii)

x+y=10

7+y=10

y=3

So the solution set is {7, 3}

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Answer:

23 and 16

Step-by-step explanation:

The pattern is to subtract 7 each time.

51 - 7 = 44

44 - 7 = 37

37 - 7 = 30

30 - 7 = 23

23 - 7 = 16

the value of P(A∪B) is 17/20.

Probability is a number expressing the likelihood or chance that a specific event will occur. Proportions ranging from 0 to 1 and percentages ranging from 0% to 100% can be used to describe probabilities.

Given, A neighborhood restaurant is serving dinner to 20 patrons.

Both cash and credit are accepted as modes of payment at the restaurant. Of the 20 customers, 3 have enough cash and a credit card to pay for their dinner, 16 have a credit card, and 4 have enough cash to cover the cost of their meal.

From the general formula of probability:

Probability = (desired outcomes)/(Total outcomes)

Let "A" represent the situation in which a randomly chosen consumer has enough cash,

"B" represents the situation in which a randomly chosen customer has a credit card.

thus,

P(A) = 4/20

P(A) = 1/5

P(B) = 16/20

Also given,

P(A∩B) = 3/20

Since,

P(A∪B) = P(A) + P(B) -P(A∩B)

P(A∪B) = 4/20 + 16/20 - 3/20

P(A∪B) = 17/20

therefore, the value of P(A∪B) is 17/20.

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If the Bitcoin economy had a yearly growth rate of 7% from 2017 to 2019, then the value in 2019 would be $1.07^3 = $1.225. If the economy had a negative growth rate of 5% in 2020, then the value in 2020 would be $1.225 x 0.95 = $1.1638. If the negative growth rate doubled in the next year, then the value in the next year would be $1.1638 x 0.9 = $1.04742.

To calculate the percentage change from 2018 to the next year, we can compare the values of the Bitcoin economy in those two years. The value in 2018 would be $1.07^2 = $1.1449. The percentage change would be ((value in next year - value in 2018) / value in 2018) x 100%. Substituting the values, we get ((1.04742 - 1.1449) / 1.1449) x 100% = -8.5%.

Therefore, the approximate percentage decrease of the Bitcoin economy in the next year, compared to 2018, is approximately 9%. The closest option is "Approximately 9% decrease".

Answer: C.

Step-by-step explanation:

Answer:

[tex]\$25,006[/tex]

Step-by-step explanation:

The total cost of Target shares is [tex](200)(\$56.30)=\$11,260[/tex].

The total cost of Pepsico shares is [tex](200)(\$68.73)=\$13,746[/tex].

Adding these costs together yields [tex]\$11,260+\$13,746=\$25,006[/tex].

If the data below are represented by a comparative bar chart, the bar representing the following will be the tallest:

Cat Failed

The tallest bar of all of these will be the cat failed bar. A comparative bar chart is often designed to compare a set of observations.

From what we can see in the passage, it is clear that the bar chart representing the cat failed group contains the highest number and will likely have the tallest chart of all the others listed. So, the point is to look out for the observation with the highest number and the cat failed group meets the requirement.

Complete Question:

If the data below are represented by a comparative bar chart, the bar representing which of these will be the tallest?

Passed Failed

Cat. 24. 30

Dog 26. 28

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The required global maximum value is 4 and the global minimum value is 3.

The method of determining the derivative of an implicit function by differentiating each term separately, expressing the derivative of the dependent variable as a symbol, and solving the resulting expression for the symbol.

Here,

The critical points can be found by finding the partial derivatives of the function with respect to x and y and setting them equal to zero.

df/dx = 2x - 2y = 0

df/dy = -2x + 4y = 0

Solving the system of equations, we find that the critical points are (1, 2) and (2, 1).

Since (1, 2) is within the bounds of the rectangle D, we need to check the value of f(1, 2) to see if it is a local minimum or local maximum.

f(1, 2) = 1 - 2 + 4 = 3

(2, 1) is also within the bounds of the rectangle D, we need to check the value of f(2, 1) to see if it is a local minimum or local maximum.

f(2, 1) = 4 - 2 + 2 = 4

Since f(1, 2) < f(2, 1), the global maximum is at point (2, 1) and the global minimum is at point (1, 2).

The global maximum value is 4 and the global minimum value is 3.

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Answer:

4.666667, or you can round it to 4.67, depends on what it's asking!

Step-by-step explanation:

The quotient means to divide, so 2/3 = 0.666667

0.666667 * 7 = 4.666667

Hope that helps.

To fully get the answer on the sample space and relative frequency, let's go directly to the analysis of the experiments as given.

(a) Sample space:

(b) Relative frequency of each outcome:

Relative frequency of an outcome is the number of times the outcome appears divided by the total number of trials. In a large number of repetitions of an experiment, the relative frequency of each outcome approaches the theoretical probability of that outcome.

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Answer:

D because angle U is equal to angle W because it is diverting angle