The area of a rectangular wall of a barn is 32 square feet. It’s length is 4 feet longer than the width. Find the length and width of the wall of the barn

Answer:

Total bikes and cars are 260

Step-by-step explanation:

Cars: [tex]n_{cars}185[/tex]

Bikes: [tex]n_{bikes}=n_{cars}-113=72[/tex]

Total: [tex]n_{total}=n_{bikes}+n_{cars}=257[/tex]

Rounding to the nearest ten: 260

Answer:

Only option D is correct as a dilation by a scale factor of 1/2 with the origin as the center of dilation would transform the object which would still be similar to the original figure, but it would no longer be congruent to the original figure due to reduction in size due to a dilation by a scale factor of 1/2.

Step-by-step explanation:

When we transform a certain shape, we normally associate the original shape as 'object', while the transformed shape is associated as "image',

If any shape like triangle, parallelogram or any other certain quadrilateral is rotated, reflected or translated, it wold preserve the same size. Hence, the resulting transformed image would be similar and also called 'congruent' to the original object.

But, if any shape like triangle, parallelogram or any other certain quadrilateral is enlarged or resized, it would certainly change in size. Therefore, the resulting transformed image would still be considered as similar, but it would no longer congruent to the original object.

Hence, when two transformation are performed on a figure in the coordinates plane. The first transformation is a translation 8 units to the left. A dilation by a scale factor of 1/2 with the origin as the center of dilation would transform the object which would still be similar to the original figure, but it would no longer be congruent to the original figure due to reduction in size due to a dilation by a scale factor of 1/2.

In all other cases, like a clockwise rotation of 90 degrees about the center, A clockwise rotation of 180 degrees about the center and a dilation by a scale factor of 1 with the origin as the center of a dilation would not not alter the size of the shape, and the resulting transformed image would be similar as well as called 'congruent' to the original object.

Hence, only option D is correct as a dilation by a scale factor of 1/2 with the origin as the center of dilation would transform the object which would still be similar to the original figure, but it would no longer be congruent to the original figure due to reduction in size due to a dilation by a scale factor of 1/2.

Therefore, only option D is correct.

Keywords: dilation, transformation

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The Sedona transformation that will result in an image that is similar to, but not congruent to the original figure is D. A dilation by a scale factor of 1/2 with the origin as the center of dilation.

To get an image that is similar but not congruent to the original figure, we shall perform a transformation that changes the size of the figure while keeping the same shape.

This is because when a figure is translated 8 units to the left, its position changes, but its size and shape remain the same.

A dilation by a scale factor of 1/2 with the origin as the center of dilation means the image would be reduced to half of its original size while maintaining the same shape.

This transformation results in a figure that is similar but not congruent to the original figure, as it has the same shape but a different size.

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Answer: about 1

Step-by-step explanation:

Bc 1 mil minutes are 1.902 of a year

Hey there!

First, set up an exponential equation that represents the rate at which your original amount, 1000, gains interest:

y = 1000(1.24)^x

Y represents the value after X years. 1.24 represents the rate at which the money gains interest, 1 + 0.24 (your 24% interest rate in decimal form). 1000 is your original amount.

Now, set this equation equal to 64000, graph y = 64000 and y = 1000(1.24)^x on a graphing calculator, and see where the two equations intersect in order to solve for x.

They intersect when x is about 19.334, as seen in the graph below (it is very zoomed in so that you can see where the two functions intersect). Therefore, it will be about 19 years after the year in which you deposited the 1000 dollars before the money is worth 64000 dollars.

Final answer:

The midpoint of the line segment with endpoints C(6,-8) and D(-4,10) is calculated to be at (1, 1) by averaging the x and y coordinates of the endpoints.

Explanation:

The midpoint of a line segment with endpoints C(6,-8) and D(-4,10) can be found by averaging the x-coordinates and the y-coordinates of the two endpoints. To do this, add together the x-coordinates, 6 and -4, and divide by 2 to find the x-coordinate of the midpoint. Add together the y-coordinates, -8 and 10, and divide by 2 to find the y-coordinate of the midpoint.

The calculations are as follows:
x-coordinate: (6 + (-4)) / 2 = 1
y-coordinate: (-8 + 10) / 2 = 1

Therefore, the midpoint of CD is (1, 1).

Answer:

0.800 is the answer. If you want an explanation let me know.

Step-by-step explanation:

Answer:

x = -2

y = 3

Step-by-step explanation:

Write the system the following way:

4x + 5y = 7

-3x +y  = 9

we need to eliminate one unknown by multiplying one equation for a suitable number in such a way that when we add the equations one unknown is eliminated.

If we multiply the second eq. by -5 the y is eliminated

4x + 5y = 7

15x -5y = -45

add the equations

19x = -38 ===> x = -38/19 ===> x = -2

Now replace this value in any equation to get y. For example, in 1st one.

4(-2) + 5y = 7 ===> -8 +5y = 7 ===> 5y = 7+8 ===> 5y = 15 ===> y = 15/5 ===>

y=3

Answer:

The salesperson will earn total commission of $ 445 .

Step-by-step explanation:

The salesperson gets 5% commission for first $2500, and 8% for above that.

So, for sale of $ 6500, the salesperson will earn commission,

$ [tex](2500 \times \frac {5}{100} + (6500 - 2500) \times \frac {8}{100})[/tex]

= $ [tex](125 + (4000) \times \frac {8}{100})[/tex]

= $ (125 + 320)

= $ 445

Answer:

Step-by-step explanation:

tan 0 = 1/ cot 0

so, tan 0=11/60,

cot 0= 1/ (11/60)

cot 0= 60/ 11

Answer:

It is clear that the annual premium = $1080

Explanation:

Given:

As the total term amount for life insurance is given in the question which is $200,000

rate per $1000 unit = $5.40

Simple Calculation Procedure to get the annual premium:

First step:  

Let’s assume $1000 is one unit and the mentioned rate per $1000 unit is $5.40. Now, all you need is to find total number of $1000 units in total term insurance amount ($200,000).  

So,  

divide $200,000 by $1000 to establish the total number of  

1000 units in $200,000 = $200,000/$1000 = 200  

Second step:

As 200 is found to be the total number of $1000 units in $200,000.

So, just multiply 200 with $5.40 to ultimately find the annual premium

            i.e. $5.40 × 200 = $1080

Hence, it is clear that the annual premium = $1080

Keywords: life insurance, annual premium, premium term rate

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There are 168 sweets altogether

Richard, Henry and Gavin share some sweets in the ratio 5 : 4 : 3

Let "5a" be the share of Richard

Let "4a" be the share of Henry

Let "3a" be the share of Gavin

Richard gets 70 sweets

share of Richard = 70

5a = 70

To find: number of sweets altogether

number of sweets altogether = share of richard + share of henry + share of gavin

number of sweets altogether = 5a + 4a + 3a

number of sweets altogether = 12a = 12(14) = 168

Thus there are 168 sweets altogether

Answer:

P'(7, - 8 )

Step-by-step explanation:

Given the translation rule

(x, y ) → (x + 4, y - 3 )

This means add 4 to the original x- coordinate and subtract 3 from the original y- coordinate, thus

P(3, - 5 ) → P'(3 + 4, - 5 - 3 ) → P'(7, - 8 )

Answer:

15t^2-ts

Step-by-step explanation:

-3t^2-2t(4s-9t)+7ts

-3t^2-8ts+18t^2+7ts

-3t^2+18t^2-8ts+7ts

15t^2-ts

The expression −3t^2−2t(4s−9t)+7st can be simplified to 15t^2-st.

This expression is a quadratic equation in the form of −3t^2−2t(4s−9t)+7st. To simplify, we can start by distributing the -2t across the terms inside the parentheses:

−3t^2−8st+18t^2+7st

Combining like terms, we get:

15t^2-st

So, the expression −3t^2−2t(4s−9t)+7st in simplest form is 15t^2-st.

Answer:

The domain is the interval [5,∞)

Step-by-step explanation:

we have

[tex]y = \sqrt{x-5}-1[/tex]

we know that

The radicand (number under a radical) must be greater than or equal to zero

so

[tex]x-5\geq 0[/tex]

solve for x

Adds 5 both sides

[tex]x-5+5\geq 0+5[/tex]

[tex]x\geq 5[/tex]

therefore

The domain is the interval [5,∞)

All real numbers greater than or equal to 5

Answer:

x >= 5

Step-by-step explanation:

Edge 2021

Answer:

It's (-8,7) I believe, I hope this helps!

Step-by-step explanation:

Answer:

xy = 1

Step-by-step explanation:

Given

[tex]x+y=\dfrac{1}{x}+\dfrac{1}{y}\\ \\x+y\neq 0[/tex]

Simplify the first expression:

[tex]x+y=\dfrac{1}{x}+\dfrac{1}{y}\\ \\x+y=\dfrac{y+x}{xy}\ [\text{Add fractions in the left side}]\\ \\1=\dfrac{1}{xy}\ [\text{Divide by }x+y \ (\text{it can be done since})\ x+y\neq 0]\\ \\xy=1\ [\text{Cross multiply}][/tex]

Answer:

12

Step-by-step explanation:

simplify: 15 + -3

combine: 15 + -3 = 12

The numerical expression 15-3 is equal to 12.

A numerical expression is a mathematical phrase containing only numbers and operational symbols (such as +, -, *, /) without any variables. It represents a specific value when the numbers are replaced with actual values. For example, "3 + 5 * 2" is a numerical expression that evaluates to 13.

The numerical expression 15-3 can be solved by subtracting 3 from 15. You can start with the number 15 and subtract 3 to get the result.

15 - 3 = 12

So, the numerical expression 15-3 is equal to 12.

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Answer: 576 inches

Step-by-step explanation:

Carlos’ height :587+12=599

Joel’s height: 599-23=576

:)

Answer:

Step-by-step explanation:

Height of Dan = 587 inches

Height of Carlos = 587 + 12 = 599 inches

Height of Joel = 599 - 23 = 576 inches

Answer:

225.5

Step-by-step explanation:

220 + (2.5% × 220) =

220 + 2.5% × 220 =

(1 + 2.5%) × 220 =

(100% + 2.5%) × 220 =

102.5% × 220 =

102.5 ÷ 100 × 220 =

102.5 × 220 ÷ 100 =

22,550 ÷ 100 =

225.5

Answer:

225.5

Step-by-step explanation:

So, you would start by doing

220 times 2.5% that would equal 5.5

Then you would add

220 + 5.5 = 225.5

Therefore your answer will be 225.5

Answer:

Cost of each Computer is $225 and Cost of each Printer is $150.

Step-by-step explanation:

Let the cost of the Computers be 'x'.

Let the cost of Printer be 'y'.

Given:

If he buys three computers and one printer, the cost is $825.

framing in equation form we get;

[tex]3x+y =825 \ \ \ \ \ equation\ 1[/tex]

Also Given:

if he buys 4 computers and 2 printers, the cost is $1200.

framing in equation form we get;

[tex]4x+2y =1200 \ \ \ \ \ equation\ 2[/tex]

Now Multiplying equation 1 by 2 we get;

[tex]2(3x+y)=825\times 2\\\\6x+2y=1650 \ \ \ \ \ equation\ 3[/tex]

Now Subtracting equation 2 from equation 3 we get;

[tex](6x+2y)- (4x+2y) = 1650-1200\\\\6x+2y-4x-2y = 450\\\\2x=450\\\\x=\frac{450}{2} =\$225[/tex]

Now Substituting the value of x in equation 1 we get;

[tex]3x+y=825\\\\3\times 225+y=825\\\\675+y =825\\\\y = 825 -675\\\\y = \$150[/tex]

Hence Cost of each Computer is $225 and Cost of each Printer is $150.

Answer:

Cost of each Computer is $225 and Cost of each Printer is $150.

Answer:

Position from point A= 383.33 meters

Step-by-step explanation:

A concept to know is that the integral of velocity will give you the distance traveled.

[tex]d=\int\limits^{t_1}_{t_0}{v(t)} \, dt[/tex]

where the interval of integration are the starting time and ending time.

I let the starting time be t₀ = 0, and the ending time t₁=10 for the 10 seconds that it traveled.

I did the integration and got 383.33m traveled in 10 seconds.

So the answer is 383.33 meters.

Ignore the final answer in the image. I misread the question.

Answer:

B.  9, 9x, 18x

Step-by-step explanation:

The value in each box is the product of the row heading and column heading. You can find the missing column heading by dividing the box value (162) by the row heading (18).

The correct terms are 9, 9x, and 18x. Hence, option B is correct.

To factorize the quadratic expression x² + 27x + 162, we need to find two numbers that multiply to 162 (the constant term) and add up to 27 (the coefficient of x). These numbers are 9 and 18.

Identify the constant term (162) and the coefficient of the linear term (27).

Find two numbers that multiply to 162 and add to 27. These numbers are 9 and 18.

Rewrite the middle term using these numbers: x² + 9x + 18x + 162.

Factor by grouping: (x² + 9x) + (18x + 162).

Factor out the greatest common factor from each group: x(x + 9) + 18(x + 9).

Factor out the common binomial factor: (x + 9)(x + 18).

Therefore, the factorization of x² + 27x + 162 is (x + 9)(x + 18).

Based on this factorization, the correct terms from the choices provided are (B) 9, 9x, and 18x.

Answer:

32

Step-by-step explanation:

The sum of the first $15$ digits is 32.

Arithmetic operations can also be specified by the subtract, divide, and multiply built-in functions.

Let $x = 0.666666.....  

$x =  = 6/9  = 2/3

And  .606060.....  = 60/99

⇒(2/3) (60/99)

⇒ (2/99)(60/3)

⇒(2/99)(20)

⇒  40/99

⇒ .040404.........

So, the sum of the first 15 digits  = 8(4) + 7(0) + 0 = 32

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Answer: [tex]4\ feet[/tex]

Step-by-step explanation:

The exercise provides you the following Quadratic function:

[tex]h(t)=4+60t-16t^2[/tex]

Then, based on the information given in the exercise, you can conclude that, when the ball strikes the bat, the time in seconds is the following:

[tex]t=0[/tex]

Therefore, in order to calculate the height in feet of the ball when it strikes the bat, you need to subsititute [tex]t=0[/tex] into the function and    then evaluate.

Then, you get this result:

 [tex]h(0)=4+60(0)-16(0)^2\\\\h(0)=4+0-0\\\\h(0)=4[/tex]

12.9794 meters or 13 meters (rounded)

You can find out this answer by looking at the 2 formulas given. Then set up a ratio and cross multiply to get your answer.

Hope this helped! (Please mark me brainliest!)

Answer:

12.9794 meters or 13 meters (rounded)

Step-by-step explanation:

You can find out this answer by looking at the 2 formulas given. Then set up a ratio and cross multiply to get your answer.

Answer:

28

Step-by-step explanation:

The function that we have in this is f(x) = 4x.  We can see this in 4 * 4 = 16,  5 * 4 = 20 and 6 * 4 = 24.   Therefore,  following the pattern,  7 * 4 = 28.

The function p(x) is obtained by subtracting g(x) from f(x)

The rule of p(x) is p(x) = 5.5 x - 50

Step-by-step explanation:

A drill team is raising money by holding a car wash

We need to describe how can you use f(x) and g(x) to obtain a function p(x) that gives the team's profit for washing x cars, and then write a rule for p(x)

∵ The team earns $6.00 for each car washed

∵ f(x) represent the team's total earning for washing x cars

- Equate f(x) by the product of x and 6

∴ f(x) = 6 x

∵ The team's expenses include $50.00 for advertising plus $0.50

    in materials for each car washed

∵ g(x) represent the team's total expenses for washing x cars

- Equate g(x) by the sum of 50 and the product of 0.5 and x

∴ g(x) = 50 + 0.5 x

The profit = total earning - total expenses

∵ f(x) is the total earning for washing x cars

∵ g(x) is the total expenses for washing x cars

∵ p(x) represents the team's profit for washing x cars

- Subtract g(x) from f(x) and equate the difference by p(x)

∴ p(x) = f(x) - g(x)

The function p(x) is obtained by subtracting g(x) from f(x)

∵ f(x) = 6 x

∵ g(x) = 50 + 0.5 x

∴ p(x) = 6 x - (50 + 0.5 x)

- Simplify the right hand side

∴ p(x) = 6 x - 50 - 0.5 x

- Add the like term

∴ p(x) = 5.5 x - 50

The rule of p(x) is p(x) = 5.5 x - 50

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Answer:

  B, C

Step-by-step explanation:

The solution space is the area to the right of the X where the lines cross. Only points B and C are in that space. Point E is on the line, but the line is not included in the solution space.

_____

The lines are drawn as though the inequality were an equation. The solution space is above the first line (which has negative slope) because y > ... indicates the solution is values of y above (>) the line.

The solution space is below the second line, which has positive slope, because y < ... indicates the solution is values of y below (<) the line.

Answer:

Step-by-step explanation:

Given that the percentage of physicians who are women is 27.9%. In a survey of physicians employed by a large  university health system,

45 of 120 randomly selected physicians were women.

Sample size n = 120

Sample proportion p = [tex]\frac{45}{120} \\=0.375[/tex]

H0: p = 0.279

Ha: p >0.279

(Two tailed test at 5% significance level)

p difference = 0.096

STd error of p assuming H0 true

= [tex]\sqrt{\frac{pq}{n} } \\=\sqrt{\frac{0.279(0.721}{120} } \\=0.041[/tex]

Test statistic Z = [tex]\frac{0.096}{0.041} \\=2.345[/tex]

Z critical value one tailed is 1.645

Since Z statistic > 1.645 we reject H0

There is evidence to conclude that the proportion of women physicians at the university health system exceeds

27.9%

Answer:

(5,1)

Step-by-step explanation:

A vertex is where two or more curves, lines, or edges meet