A building has an entry the shape of a parabolic arch 22 ft high and 28 ft wide at the base, as shown below.

A parabola opening down with vertex at the origin is graphed on the coordinate plane. The height of the parabola from top to bottom is twenty two feet and its width from left to right is twenty eight feet.

Answer:

FH = 35.64

Step-by-step explanation:

(∠A = 360 so the other angle is 40)

By law of cosines,

FH² = AH² + FA² - 2(AH)(FA) * cos(A)

= 30² + 25² - 2(30)(25) * cos(80)

= 900 + 625 - 1500 * 0.17

= 1525 - 255

FH²  = 1270

FH = √1270

FH = 35.64

The final function is f(x) =  ( \(b^3-4b^2\)+\(63b\)-487b)(b+7)+3021.

What is function?

A mathematical phrase, rule, or law that establishes the link between an independent variable and a dependent variable (the dependent variable). In mathematics, functions exist everywhere, and they are crucial for constructing physical links in the sciences.

Here the given function f(x)=\(b^4 + 3b^3-35b^2-46b+28\) and d(x)=b+7.

Now using long division then,

=>           \(b^3-4b^2\)+\(63b\)-487b

    \(\\b+7)\overline{b^4 + 3b^3-35b^2-46b+28 }\\\\\)

    (-)      \({b^4+7b^3}\)

                  \(\overline{-4b^3+35b^2+46b-28}\)

    (-)           \(-4b^3-28b^2\)

                             \(\overline{63b^2-46b+28}\)

     (-)                     \(63b^2+441b\)

                                     \(\overline{-487b-28}\)

     (-)                             \(\underline {-487b-3049}\)

                                                3021

Quotient q(x) =   \(b^3-4b^2\)+\(63b\)-487b

Remainder r(x) = 3021

Hence the final function is f(x) =  ( \(b^3-4b^2\)+\(63b\)-487b)(b+7)+3021.

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If all of the points on the scatter plot are directly on a straight line with a negative slope, the product-moment correlation coefficient is a negative one.

A scatter chart, also known as a scatter plot, is a graph that shows the relationship between two variables. They are a powerful chart type that allows readers to see a relationship or trend that would be impossible to see in almost any other format.

Accordingly, when all of the points on a scatter plot fall on a straight line, the connection between the two variables is perfect linear. The correlation coefficient (r) will be either +1 or -1 in this scenario.

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The statement that is true about the function is:

A function, in mathematics, an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).

Given:

The minimum value of the curve = (1.9, -5.7),

The maximum value = (0, 2)

The point the function crosses the x-axis (the x-intercept) = (-0.7, 0), (0.76, 0), and (2.5, 0)

The point the function crosses the y-axis (the y-intercept) = (0, 2)

The given points can be plotted using MS Excel, from which we have:

F(x) is less than 0 over the interval from x = -∞, to x = -0.7, and the interval from x = 0.76 to x = 2.5.

Hence, the correct option is A.

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Answer:

i think its b

Step-by-step explanation:

Answer:

multiply both sides by 2

Step-by-step explanation:

you mtiply because you are doing the opposite of division. the f and the 2 are being divided.

Answer:

1: is in fact graph 3 2: however I do not use a ray tool so sorry on that one brother

Answer:

  402 mi²

Step-by-step explanation:

Extending the vertical segments divides the figure into 3 rectangles:

  left: 22 mi by 12 mi

  center: 13 mi by 6 mi

  right: 20 mi by 3 mi

The area of each rectangle is the product of its length and width. The total area is the sum of the areas of the three rectangles:

  total area = (22·12 +13·6 +20·3) mi² = (264 +78 +60) mi² = 402 mi²

There is no alternate exterior angle corresponding to ∠8.

Alternate Exterior Angles – Alternate exterior angles are the pair of angles on the outer side of the two parallel lines but on the opposite side of the transversal.

here, we have,

Given is a geometrical figure as shown in the image.

A pair of alternate exterior angles exist for a pair of parallel lines.

Hence, there is no alternate exterior angle corresponding to ∠8.

Therefore, there is no alternate exterior angle corresponding to ∠8.

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Answer:

60 units squared.

Step-by-step explanation:

Area of a parallelogram = Base * Height

In other words, A = b*h

base is 6 and height is 10

A = 6 * 10

A = 60.

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The value of the underlined digit in the number 27,416,385.( 4 is the underlined number.) is the hundred thousandths place.

The symbols, from 0 to 9 can be described as a digit. For instance, the numbers 2 and 3 are used to represent the number 23.  however amount is represented by a number.

It should be noted that It may be expressed using one, two, three, or even more digits however only single symbol used to represent a number is a digit in the case above we can see that 4 is the hundred thousandths place.

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The 9/32 of whole pizza Troy had for breakfast. The whole bag of coffee weighs 10/7 pounds

A fraction is defined as a part of a whole quantity.

1. Leftover pizza = 3/8

Pizza used as breakfast = 3/4 of left-over pizza

= 3/4 of 3/8

The of is calculated by the use of multiplication

The fractions are multiplied as follows:

Pizza used as breakfast = 3/4 * 3/8

= 3 * 3 / 4 * 8

= 9/32

2. 3/5 of bag of coffee weighs = 6/7 pounds

1 bag of coffee weighs = 6/7 ÷ 3/5

The fractions are divided as follows:

Thus, = 6/7 * 5/3

= 6 * 5 / 7 * 3

= 30/21

= 10/7 pounds

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Answer:

6,000 Video Games

Step-by-step explanation:

To find out how many video games Cloey sold on Sunday, we need to add the number of video games she sold on Friday and Saturday and then subtract that total from the total number of video games she sold over the three days:

Total number of video games sold on Friday and Saturday = 3,878 + 8,999 = 12,877

Total number of video games sold over the three days = (number sold on Friday) + (number sold on Saturday) + (number sold on Sunday)

We know that the total number of video games sold over the three days is the sum of the number sold on Friday and Saturday plus the number sold on Sunday. We can rearrange this equation to solve for the number sold on Sunday:

Number sold on Sunday = Total number sold over three days - Number sold on Friday and Saturday

Substituting in the values we know, we get:

Number sold on Sunday = (number sold on Friday) + (number sold on Saturday) + (number sold on Sunday) - (number sold on Friday) - (number sold on Saturday)

Number sold on Sunday = Total number sold over three days - Number sold on Friday and Saturday

Number sold on Sunday = (3,878 + 8,999 + X) - 12,877

Number sold on Sunday = X - 0

Simplifying this expression, we get:

Number sold on Sunday = 6,000

Therefore, Cloey sold 6,000 video games on Sunday.

We are asked to factor

We want to take out something that is common in both the terms.

One term is "3x"

Another is "6"

We can clearly see that a factor of "3" is common.

Thus, when we take out 3,

3x becomes x

6 becomes 2

So, the factorization is:

The total value of the loan with quarterly compounded interest is approximately $45,288.38, while the total value of the loan with monthly compounded interest is approximately $45,634.84. The difference in total interest accrued is approximately $346.46.

Part A: To determine the total value of the loan with quarterly compounded interest, we can use the formula for compound interest:

A = P(1 + r/n)^(nt),

where:

A is the total value of the loan,

P is the principal amount (initial loan amount),

r is the interest rate (in decimal form),

n is the number of times interest is compounded per year,

and t is the number of years.

Given:

P = $20,000,

r = 9% or 0.09,

n = 4 (quarterly compounding),

t = 10 years.

Substituting the values into the formula, we have:

A = 20000(1 + 0.09/4)^(4*10).

Calculating this value, we find:

A ≈ $45,288.38.

Therefore, the total value of the loan with quarterly compounded interest is approximately $45,288.38.

Part B: To determine the total value of the loan with monthly compounded interest, we follow the same formula but with a different value for n:

n = 12 (monthly compounding).

Substituting the values into the formula, we have:

A = 20000(1 + 0.09/12)^(12*10).

Calculating this value, we find:

A ≈ $45,634.84.

Therefore, the total value of the loan with monthly compounded interest is approximately $45,634.84.

Part C: The difference between the total interest accrued on each loan can be calculated by subtracting the principal amount from the total value of each loan.

For the loan with quarterly compounding:

Total interest = Total value - Principal

Total interest = $45,288.38 - $20,000

Total interest ≈ $25,288.38.

For the loan with monthly compounding:

Total interest = Total value - Principal

Total interest = $45,634.84 - $20,000

Total interest ≈ $25,634.84.

The difference between the total interest accrued on each loan is approximately $346.46.

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The number of workers required to meet the labor demand of 800hr/wk is 20.

Data;

The number of workers need to meet the labor cost can be calculated as

\(\frac{800}{40} = 20\)

The number of workers required to meet the labor demand of 800hr/wk is 20.

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The values that are missing from the transaction will be 155.15 and -223.75.

It should be noted that a transaction simply means the agreement between the buyer and the seller to exchange a good or service.

In this situation, the table shows four transactions and the resulting account balance in a bank account, but some numbers are missing.

In this situation, it should be noted that the transaction amount in transaction 3 will be:

= 337.50 - 182.35

= 155.15

The amount in transaction 4 will be:

= -182.35 - 41.40

= - 223.75

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Answer:

-6

Step-by-step explanation:

(3 x 6) - (3 x 14)

= 18 - 42

= -24

-24/4

= -6

Answer: 4x+2(x+12)=27

Step-by-step explanation: The first equation, y=x+12 shows what y is, so you can just add it into the equation with parentheses. If the y is next to a number, it means that whatever y is (in this case, it’s x+12), y will multiply by the number next to it, (2, in this case). Then you can just solve from there for x.

Answer:

The answer is 32

Step-by-step explanation:

The formula for finding the area of a trapezoid is:

         ((base 1 + base 2)/ 2 )* h

Now all you have to do is substitute the numbers in.

Note: bases will always be the ones like 12 and 4 in this case. We have just named then 1 and 2.

Answer:

32 square units

Step-by-step explanation:

\(\displaystyle A=\frac{1}{2}(b_1+b_2)h=\frac{1}{2}(12+4)(4)=\frac{1}{2}(16)(4)=\frac{1}{2}(64)=32\)

Note that \(b_1\) and \(b_2\) are the lengths of each base of the trapezoid, so it doesn't matter which is which.

The solution of the equation (2w - 1) / 5 + w + 2 = 2w will be 3.

The allocation of weights to the important variables that produce the calculation's optimum is referred to as a direct consequence.

The definition of simplicity is making something simpler to achieve or grasp while also making it a little less difficult.

The equation is given below.

(2w - 1) / 5 + w + 2 = 2w

Simplify the equation, then we have

(2w - 1) / 5 + w + 2 = 2w

(2w - 1) / 5 = w - 2

2w - 1 = 5w - 10

3w = 9

w = 3

The solution of the equation (2w - 1) / 5 + w + 2 = 2w will be 3.

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The complete question is given below.

Answer:0.03125

Step-by-step explanation:

GOO*OOGLE

Step-by-step explanation:

(1/2)^5   = 1/2 * 1/2 * 1/2 * 1/2 * 1/2 =   1/32

Answer:

  (c)  y = 3^x

Step-by-step explanation:

A function is described as exponential if the independent variable is found in the exponent.

  y = x^(1/2) . . . a square root function, not exponential

  y = 2x^3 . . . . a cubic (polynomial) function, not exponential

  y = 3^x . . . . . an exponential function

The scatter plot shows a [positive linear] association.

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

The image of the scatter plot

On the scatter plot, we can see that

The points appear to be on a straight line

Also, we can see that

As the x values increases the y values increases

This represents a positive linear association.

Hence, the association is a positive linear association.

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Answer:

(-3,-1) -> (3,1)

Step-by-step explanation:

Reflection over the y-axis:

When we reflect a point (x,y) over the y-axis, it's y-coordinate is kept, while the x-coordinate changes signal. So

(3,-1) -> (-3,-1)

Clockwise rotation of 180º

Both coordinates of the point change signals. So

(-3,-1) -> (3,1)

Answer:

no solution

Step-by-step explanation:

Multiplying the second equation by 2 gives 2x-14y=38.

Adding this to the first equation, we get 0=9, and thus there is no solution.

Answer:

Well the absolute value of 7 is 7 and 7+8 would be 15.

Step-by-step explanation:

Answer: 15

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The length of an edge is the cubic root of the volume.

Cubic root 1.8 = 1.2 meters