PLEASE HELP ASAP
△DEF is similar to △RST .



Drag the answer into the box to match each part of △DEF with the corresponding part of △RST.

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:

15

Step-by-step explanation:

n is the number of people and k the number of chairs

here n = 6 and k = 4

note n! = n(n - 1)(n - 2).... × 3 × 2 × 1, thus

[tex]\frac{6!}{4!(6  -4)!}[/tex]

= [tex]\frac{6(5)(4)(3)(2)(1)}{4!(2!)}[/tex]

= [tex]\frac{720}{4(3)(2)(1)2(1)}[/tex]

= [tex]\frac{720}{24(2)}[/tex]

= [tex]\frac{720}{48}[/tex]

= 15

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:

Step-by-step explanation:

the answer is 78.6%

11/14*100=78.6

The total percentage of fat in mayonnaise 78.6 %

What is an Equation?

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the total amount of mayonnaise be A = 14 grams

Let the total amount of fat be B = 11 garms

Now , the equation will be

The total percentage of fat in mayonnaise is =
( total amount of fat / total amount of mayonnaise ) x 100

The total percentage of fat in mayonnaise is = ( 11 / 14 ) x 100

                                                                          = 0.7857 x 100

                                                                          = 78.57 %

Now , on simplifying the equation we get

The total percentage of fat in mayonnaise 78.6 %

Hence , The total percentage of fat in mayonnaise 78.6 %

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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:

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:

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:

16y² - x² shows a correct difference of squares.

Step-by-step explanation:

Following are the given options from which we have to chose which represents the difference of squares.

A) 10y² - 4x²

B) 16y² - x²

C) 8x² - 40x+25

D) 64x² - 48x+9

Difference of square is given by:

a² - b² = (a + b) (a - b)

If we analyze the expressions from the choices given in the question. We should figure out that option B) should be the right answer that shows a difference of squares. i.e. 16y² - x² shows a correct difference of squares. All other options do not represent the difference of perfect squares.

As in option A) 10y² - 4x²

10y²  is not a complete square of any number. Hence, option A) is incorrect.

As in option C) 8x² - 40x+25

Neither of the terms in the expression as shown in option C can be a perfect square. Hence, option C) is incorrect.

As in option D) 64x² - 48x+9

The term 48x+9 in the expression as shown in option D can not be a perfect square. Hence, option D) is incorrect.

Lets take the expression 16y² - x²  of option B) and solve it.

First simplify the terms separately to associate them as perfect squares as shown below:

       ⇒  16y² = (4y)²        Equation (1)

       ⇒   x² = (1x)²           Equation (2)

Now, take the difference of Equation (1) and Equation (2).

        ⇒  16y² - x²

          ⇒ (4y)² - (1x)²       Equation (3)

So,

Equation (3 )shows a difference of squares. It can also be represented as factorizing the difference of two perfect squares such as (4y - x) (4y + x).

Which is  

               (4y - x) (4y + x) = 16y² - x²

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

So, option B) i.e. 16y² - x² shows a correct difference of squares.

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Answer:

the correct answer would be

16y² - x²

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:

a) x=-10,0,11

b) x<-10, 0<x<11

c) x>11, -10<x<0

Step-by-step explanation:

a) Find all the intersecting points of the two graphs.

b) Find all the x values when g(x) (the curving one) is higher than f(x). g(x) or f(x) is kind of like the y coordinate in these graphs. There for to find when f(x)<g(x), you have to find when g(x) is above f(x). Any part of g(x) above the intersecting points is your answer. So we can see that at -10, the curving line is above the straight one, f(x). There for that would be when x<-10, g(x)>f(x). Use these intersection points to figure out the rest.

c) Find all the x values of when the curving line, g(x) is below f(x), the straight line. Use the points where the two lines intersect t start off your answer. For example, we can see the curved line is below the straight one between -10 and 0. Therefore, f(x)>(g) when -10<x<0. x>11 is the only other moment when g(x), the curving line is also below f(x).

I also struggled with this question and I tried my best to explain.

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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Answer:

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

Step-by-step explanation:

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:

20% of the time

Step-by-step explanation:

Marissa spends 20% of the time playing basketball. I figured this out my subtracting all of the other sports from 100% , (the whole), to get 20%.

Hope this helps :)

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:

360,000.

Step-by-step explanation:

9! - 4! (5!)

= 9*8*7*6*5*4*3*2*1 - 4*3*2*1 * 5*4*3*2*1

= 5*4*3*2*1 ( 9*8*7*6 - 4*3*2*1)

=  120( 3024 - 24)

= 120 * 3000

= 360,000

Answer:

the anwer of youre question is B.5 .

Final answer:

20% does not directly convert into a whole number; it represents a fractional part of a whole. If you look at the percent as a part of some quantity, you calculate 20% of that quantity to find the represented part. However, 20% by itself is 0.20 in decimal form, not a whole number.

Explanation:

What is 20% as a whole number?

When talking about percentages, it's important to understand that a percent is a way of expressing a fractional amount as part of a whole divided into 100 parts. For example, 5% means 5 out of 100.

In the case of 20%, you are looking at 20 out of 100. As a whole number, however, percentages less than 100% do not directly convert since they represent a part of a whole, not the whole itself. 20% can be represented as 0.20 in decimal form, which still does not constitute a whole number. The closest concept related to whole numbers would be if you had some quantity that you wish to find 20% of; you would then calculate 20% of that number to find the part it represents. But the 20% by itself remains a fraction, not a whole number.

Answer:

123,000

Step-by-step explanation: 40×15=600

For 1 worker

600×250=123,000

For all 250 workers

The solutions for x are -2, 0, 2

Solution:

Given that,

[tex]\text { Let } a = x^2 + 4[/tex]

Given equation is:

[tex](x^2 + 4)^2 + 32 = 12x^2 + 48[/tex]

[tex](x^2 + 4)^2 + 32 = 12(x^2 + 4)[/tex]

[tex]\text { Subtsitute } a = x^2 + 4 \text{ in above equation }[/tex]

[tex]a^2 + 32 = 12a\\\\a^2 -12a + 32 = 0[/tex]

[tex]\text{ Let us factorize the above equation }\\\\\text{ Splitting the middle term -12a as -4a - 8a we get, }[/tex]

[tex]a^2 -4a - 8a + 32 = 0[/tex]

Taking "a" as common term from first two terms and taking "-8" as common from last two terms

[tex]a(a-4)-8(a - 4) = 0[/tex]

[tex]\text{Taking (a - 4) as common term, }\\\\(a - 4)(a - 8) = 0[/tex]

[tex]\text{Equating to zero we get, }\\\\(a - 4) = 0 \text{ or } (a - 8) = 0\\\\a = 4 \text{ or } a = 8[/tex]

[tex]\text{Now substitute the value of a = 8 and a = 4 in: }\\\\a = x^2 + 4[/tex]

[tex]\text{ For a = 8: }\\\\a = x^2 + 4\\\\8 = x^2 + 4\\\\x^2 = 4\\\\x = \pm2\\\\x = +2 \text{ or } -2[/tex]

[tex]\text{For a = 4: }\\\\a = x^2 + 4\\\\4 = x^2 + 4\\\\x = 0[/tex]

[tex]\text{Thus solutions of } x \text{ are: }\\\\x = 0 \text{ or } x = 2 \text{ or } x = -2[/tex]

Answer:

.2 or 1/5

Step-by-step explanation:

sorry for bad picture

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]

Answer:

x=1, y=2. (1, 2).

Step-by-step explanation:

3x+y=5

5x-4y=-3

---------------

4(3x+y)=4(5)

5x-4y=-3

----------------------

12x+4y=20

5x-4y=-3

---------------

17x=17

x=17/17

x=1

3(1)+y=5

y=5-3

y=2

Answer:

10 000

Step-by-step explanation:

For each choice of the first two digits you have 10 choices for the third digit. Thus you have 10x10x10 = 1000 choices for the first three digits. Finally you have 10 choices for the fourth digit and thus there are 10x10x10x10 = 10 000 possible 4 digit combinations from 0-9.

The correct answer is:

The equation simplifies to [tex]\(x = 0\)[/tex] after combining like terms and isolating [tex](x\), resulting in \(x\)[/tex] being zero.

the equation [tex]\(18x - 2x = 4x\)[/tex] step by step:

1. Original equation:

[tex]\[ 18x - 2x = 4x \][/tex]

2. Combine like terms on the left side:

[tex]\[ 16x = 4x \][/tex]

  Explanation: We add or subtract coefficients of like terms. Here,[tex]\(18x - 2x\) simplifies to \(16x\).[/tex]

3. Subtract [tex]\(4x\)[/tex] from both sides:

 [tex]\[ 16x - 4x = 0 \][/tex]

  Explanation: We want to isolate [tex]\(x\)[/tex] on one side. Subtracting [tex]\(4x\)[/tex] from both sides ensures the equation remains balanced.

4. Simplify:

[tex]\[ 12x = 0 \][/tex]

  Explanation: After subtracting, we simplify the expression [tex]\(16x - 4x\) to \(12x\).[/tex]

5. Divide both sides by [tex]\(12\)[/tex]:

[tex]\[ \frac{12x}{12} = \frac{0}{12} \] \[ x = 0 \][/tex]

  Explanation: To solve for [tex]\(x\), we divide both sides by the coefficient of \(x\), which is \(12\).[/tex]

Therefore, the solution to the equation [tex]\(18x - 2x = 4x\) is \(x = 0\)[/tex]. This means [tex]\(x\)[/tex] is zero, satisfying the equation.

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 )

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:

(A) [tex]r[/tex]  is < than equal to 17

Step-by-step explanation:

Total amount Jim had for the carnival =$25.00

Amount spent on food = $3.75

Amount left with him = [tex]\$25.00-\$3.75=\$21.25[/tex]

Jim plans to sped rest on tickets for rides.

Cost of each ride ticket = $1.25

Given: [tex]r[/tex] represents the number of ride tickets bought.

Using unitary method

If 1 ride ticket cost = $1.25

Cost of [tex]r[/tex] ride tickets in dollars will be = [tex]1.25r[/tex]

Amount spent on rides must be less than or equal to the total amount left with Jim which is =$21.25.

So, we have:

⇒ [tex]1.25r\leq 21.25[/tex]

Dividing both sides by 1.25.

⇒ [tex]\frac{1.25r}{1.25}\leq \frac{21.25}{1.25}[/tex]

∴ [tex]r\leq 17[/tex]

Thus, the inequality representing te number of tickets Jim can purchase is given by:

[tex]r\leq 17[/tex]

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.

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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