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The area of the frame not covered by the painting is 192 square inches

Solution:

Given that, A rectangular painting is 24 inches wide and 20 inches tall without the frame

The area of rectangle is given as:

[tex]Area = length \times width[/tex]

Find the area of painting without frame:

Length = 20 inches

Width = 24 inches

[tex]Area\ Without\ Frame = 20 \times 24 = 480[/tex]

Thus area of painting without frame is 480 square inches

With the frame, it is 28 inches wide and 24 inches tall

Find the area of painting with frame:

Length = 24 inches

Width = 28 inches

[tex]Area\ with\ frame = 24 \times 28 = 672[/tex]

Thus area of painting with frame is 672 square inches

What is the area of the frame not covered by the painting

Area of the frame not covered by the painting = Area with farme - Area without frame

Area of the frame not covered by the painting = 672 - 480 = 192

Thus the area of the frame not covered by the painting is 192 square inches

There are 5 short essay questions on test

Solution:

Let "a" be the number of multiple choice questions

Let "b" be the number of short essay questions

Worth of each multiple choice questions = 3 points

Worth of each short essay questions = 8 points

There are 25 questions in total

number of multiple choice questions + number of short essay questions = 25

a + b = 25

a = 25 - b --------- eqn 1

The test is worth 100 points. Theerefore, we frame a equation as:

number of multiple choice questions x Worth of each multiple choice questions + number of short essay questions x Worth of each short essay questions = 100

[tex]a \times 3 + b \times 8=100[/tex]

3a + 8b = 100 --------- eqn 2

Let us solve eqn 1 and eqn 2

Substitute eqn 1 in eqn 2

3(25 - b) + 8b = 100

75 - 3b + 8b = 100

5b = 100 - 75

5b = 25

b = 5

Thus there are 5 short essay questions on test

The number of short essay questions on the test is 5.

The science test is worth 100 points and has 25 questions. Let's represent the number of multiple-choice questions as 'x' and the number of short essay questions as 'y'. Each multiple-choice question is worth three points, so the total number of points for the multiple-choice questions is 3x. Each short essay question is worth eight points, so the total number of points for the short essay questions is 8y. We can write two equations to represent the given information:

x + y = 25 (since there are 25 questions in total)

3x + 8y = 100 (since the total points for the test is 100)

To find the number of short essay questions on the test, we need to solve these two equations. By substituting x = 25 - y into the second equation, we can solve for y.

3(25 - y) + 8y = 100

75 - 3y + 8y = 100

5y = 25

y = 5

Therefore, there are 5 short essay questions on the test.

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Answer:

5 liters of water.

Step-by-step explanation:

Let [tex]y[/tex] be the liters of water that must be added to 15 liters of 40% sugar syrup.

Initially, we have [tex]0.4(15)=6[/tex] liters of sugar syrup, and since adding water does not add any new syrup, the amount of sugar syrup must be the same after the water has been added. After the water has been added, 30% of the solution is sugar syrup, or

[tex]Sugar\:syrup =0.3(15+y)[/tex]

And since this must equal the amount of syrup we had before:

[tex]0.3(15+y)=0.4(15)[/tex]

[tex]4.5+0.3y=6[/tex]

[tex]0.3y=1.5[/tex]

[tex]\boxed{y=5}[/tex]

Thus, 5 liters of water must be added to obtain 30% sugar syrup.

Answer:

5 liters of water

For this case we have the following equation:

[tex]2m + 4s = 16[/tex]

We solve for each of the variables:

For m:

We subtract 4s from both sides of the equation:

[tex]2m = 16-4s[/tex]

We divide by 2 on both sides of the equation:

[tex]m = \frac {16-4s} {2}\\m = \frac {16} {2} - \frac {4s} {2}\\m = 8-2s[/tex]

For s:

We subtract 2m from both sides of the equation:

[tex]4s = 16-2m[/tex]

We divide between 4 on both sides of the equation:

[tex]s = \frac {16} {4} - \frac {2m} {4}\\s = 4- \frac {m} {2}[/tex]

Answer:

[tex]m = 8-2s\\s = 4- \frac {m} {2}[/tex]

Without additional information or a second equation, the values for 'm' and 's' cannot be specifically determined from the equation 2m+4s=16 due to the infinite number of solutions.

The question 2m+4s=16 asks us to find the values of m and s. However, with a single equation and two variables, there are infinite solutions. This is because without additional information or constraints, each variable can take on many different values as long as the equation balances out to 16. Therefore, we cannot determine specific values for m and s without additional equations or information.

To find the values of M and S in the equation 2M + 4S = 16, we can use algebraic methods to solve for the variables.

Step 1: Start by isolating M in the equation. Subtract 4S from both sides of the equation: 2M = 16 - 4S.

Step 2: Divide both sides by 2 to solve for M: M = (16 - 4S)/2.

Now you have an equation that expresses M in terms of S. You can substitute different values for S to find the corresponding values for M. For example, if S = 2, then M = (16 - 4(2))/2 = 4. So, when S = 2, M = 4. Repeat this process for different values of S to find the corresponding values of M.

Answer:

5667

Step-by-step explanation:

Answer:

3510

Step-by-step explanation:

because you have 390 and you multiply it my 9 so you would get 3510 by 9 times

The missing figure is attached down

The length around the outside of the track is about 431 feet

Step-by-step explanation:

A running track has the shape of a rectangle capped with a semicircle on each end

We need to estimate the length around the outside of the track

The length of the outside the track is the length of two semi-circle and two straight lengths of the rectangle

∵ The track is 80 feet wide

- From the figure the width of the track is the diameter of the

  semi-circles

∴ The diameter of each semi-circle = 80 feet

∵ The radius of a circle is half its diameter

∴ The radius of each semi-circle = [tex]\frac{1}{2}[/tex] × 80 = 40 feet

∵ The length of a circle = 2πr

∴ The length of a semi-circle = πr

∴ The length of two semi-circle = 2 × πr

- Substitute r by 40

∴ The length of two semi-circle = 2 × π(40) = 80π feet

∵ The rectangular portion of the track is 90 feet tall

∴ The length of the rectangle = 90 feet

∴ The two straight parts of the track = 2 × 90 = 180 feet

- Add the length of the two semi-circles and the two straight

   parts to find the length of the track

∵ Length of the track = 80π + 180

- Substitute π by 3.141

∴ Length of the track = 80(3.141) + 180

∴ Length of the track = 431.28 ≅ 431 feet

The length around the outside of the track is about 431 feet

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hello that is a hard question but the answer is your face

Answer:

im so sorry about the kid that said that. that was mean

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

Let's call the middle M. If we take triangle PMQ we see that is has a 90 degrees angle. Also both of the other corners are equal so 180=90-2x. x=45 degrees. In a triangle with two 45 degrees angles and a 90 degrees angle the following applies: Both straigth sides are 1:square root of 2 to the oblique side. That means that if say PM=4 that PQ=4sqrt2. Now we'll that to determine PM. PQ=5x so PM=5xsqrt2. The area of parallelogram PQRS then equals to 5xsqrt2×5xsqrt2=25x^2×2=50x^2. So that is C.

Answer: 50

Step-by-step explanation: 25% of 100 is equal to 25, so if we multiply that by 2, we would get 50. To fact-check your answer, always make sure that when you multiply (only for 25% problems) by 4, and you should get the whole number. 50x4=200. Or, just 200 divided by 4. It helps!

Answer:

The total discounted price is 34.93

Step-by-step explanation:

The items in the cart are:

Total cart = $ 41.10

Discount = 41.10 * 0.15 = $ 6.17

Discounted total price = 41.10 - 6.17

Discounted total price = 34.93

Answer:

34.94.

Step-by-step explanation:

First we must find the total price of all the items: =$6.35+$6.35+$12.50+$13.40+$2.50=$41.10.

Next, we can calculate the discount: =(15/100)×$41.10=$6.165.

Therefore, our discounted price is $41.10−$6.165=$34.935≈$34.94.

Answer:

x^3-x^2-17x+12

Step-by-step explanation:

(x+4)(x^2-5x+3)

x^3-5x^2+3x+4x^2-20x+12

x^3-5x^2+4x^2+3x-20x+12

x^3-x^2-17x+12

Answer:

11 pages

Step-by-step explanation:

55% of 20 is 11. I'm sure! Please give be brainliest.!

Answer:

11

Step-by-step explanation:

It's just 55℅ of 20 pages so 20×55℅ will give u 11

Answer:

wat number

Step-by-step explanation:

?????????????????????????????????????????????

The  expression is equivalent to 8/9 divided by 3/4 is 32/27.

The fractional bar is a horizontal bar that divides the numerator and denominator of every fraction into these two halves.

We have to divide the fraction 8/9 by 3/4.

As, the fraction does not allow division then we will perform the multiplication.

So, 8/9 x 4/3

= 32 / 27

Thus, the required fraction is 32/27.

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Answer:

53 teachers

Step-by-step explanation:

Basically, what we need to do here is to find how many teachers there need to be, first. If there are 6,734 students in the school district and if maximum class size is 25, then the number of teachers needed is:

6,734 / 25 = 269.36

Of course, it's obvious that we can't have a decimal number of teachers, so we need to find integer (269 or 270).

If we take 269 teachers and 25 students per class, we get:

269 • 25 = 6,725 students, which is not enough, since there are 6,734 students.

That means that the number of teachers needed is 270.

It is given that there are already 217 teachers, meaning that 270-217=53 teachers have to be supplemented.

52 more teachers must the district have to supplement their staff of 217 teachers.

Given that,

A school district has a student population of 6,734 students.

If the maximum class size is 25 students.

We have to determine,

How many more teachers must the district have to supplement their staff of 217 teachers?

According to the question,

Total number of students = 6,734

Maximum class size = 25 students

Then,

The number of teachers needed is,

[tex]= \dfrac{6734}{25}\\\\= 269.36[/tex]

Here, 269 teachers are needed for each group of 25 students.

Therefore,

The number of more teacher must the district have to supplement their staff of 217 teachers is,

269 - 217 = 52

Hence, 52 more teachers must the district have to supplement their staff of 217 teachers.

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The correct answer is D. (3x2 + 5)(x + 3). Here’s how you can use the grouping method to factor the polynomial completely:

Group the first two terms and the last two terms: (3x3 + 9x2) + (5x + 15)

Factor out the greatest common factor from each group: 3x2(x + 3) + 5(x + 3)

Factor out the common binomial factor: (3x2 + 5)(x + 3)

So, the polynomial 3x3 + 9x2 + 5x + 15 can be factored completely as (3x2 + 5)(x + 3).

Hope it helps.

Answer:

The solution is the point (-2,1)

Step-by-step explanation:

we have

[tex]-2x+3y=7[/tex] ----> equation A

[tex]5x+8y=-2[/tex] ----> equation B

Solve the system of equations by graphing

Remember that the solution of the system is the intersection point both lines

using a graphing tool

The solution is the point (-2,1)

see the attached figure

Answer:

Should be B

Step-by-step explanation:

5 + 2 ( x-4[3x+7(2-x)]

5+2 (x-4[ 4x + 14])

5+2 (17x - 56)

5 + 34x - 112

34x - 107

The simplified answer is [tex]5\frac{2}{9}[/tex].

Option: C.

Step-by-step explanation:

To simply [tex]-3\frac{1}{9} - (-8\frac{1}{3} )[/tex]:

First convert this improper fraction into normal fraction.

[tex]-3\frac{1}{9}[/tex] = [tex]\frac{-28}{9}[/tex].

[tex]-8\frac{1}{3}[/tex] = [tex]\frac{-25}{3}[/tex].

Now we have to simplify [tex]-\frac{28}{9} - (-\frac{25}{3} )[/tex].

= [tex]-\frac{28}{9} + \frac{25}{3}[/tex].

After applying LCM to the denominators, Multiply the second term with 3 in both numerator and denominator.

= [tex]-\frac{28}{9} + \frac{75}{9}[/tex].

=[tex]\frac{-28+75}{9}[/tex].

=[tex]\frac{47}{9}[/tex].

Convert the answer in improper fraction form.

[tex]\frac{47}{9}[/tex] = [tex]5\frac{2}{9}[/tex].

Thus the simplified answer is [tex]5\frac{2}{9}[/tex].

Answer:

The decimal that represents the unshaded portion of the model is 0.4

Step-by-step explanation:

we know that  

Camille shaded 18/30 of a model

That means

The total parts of the model is equal to 30

The shaded parts of the model is 18

To find out the unshaded parts of the model subtract the shaded parts from the total parts

[tex]30-18=12[/tex]

To find out the decimal that represents the unshaded portion of the model, divide the unshaded parts of the model by the total parts of the model

so

[tex]\frac{12}{30}=0.4[/tex]

Answer:

Step-by-step explanation:

Answer:

Step-by-step explanation:

6= -6, -3.4=3.4, 2.25=-2.25, 8 1/5=-81/5

Answer:

Graphing Linear Inequalities differs from graphing regular linear equations. That is it has certain rules to be followed to draw the graph.

Thus if the equation has y < or y > then we use broken line and y= , y≤ and y≥ then we use solid line.

Answer:

d 10x=-3

Step-by-step explanation:

Answer:

Step-by-step explanation:

the quotient is the result of division

the quotient of 6 and z...

6/z <===

** pay attention to the wording...because if it would have said : the quotient of z and 6, it would have been z/6

Answer:

1. a ≥ –4 and a ≤ 4

Step-by-step explanation:

Rule : | a | ≤ 4 ⇔ -4 ≤ a ≤ 4

:)

Answer:

Step 3 because when dividing 7y=-9, you divide by 7, not 9. Kendra divided the whole thing by 9, which is incorrect. You want to get the Y by itself(as in y, not a fraction of y) to solve the rest of the problem.

Step-by-step explanation:

Step 1.

-3x+7y=-15

-2x-7y=5

-5x=10 and x=2

Step 2.

-5x =-10. x = 2.

Step 3.

-3 (2) + 7 y = - 15. - 6 + 7 y = - 15. 7 y = - 9. y = -9/7  = - 1  2/7

Answer:

x is equal to 2

Step-by-step explanation:

2x+4=8

2x=4

x=2

Answer:

x = 2

Step-by-step explanation:

First you must subtract x to both sides leaving you with 2x + 4=8 and you subtract 4 to both sides giving you 2x=4 and lastly to get the x by itself you divide both sides by 2 leaving you with x=2

Answer:

80 students

Step-by-step explanation:

Let the number of voters in the election for class president is x.

So, given that 40% of the voters voted for Gerardo,35% of the voters voted for Leonardo, and 25% of the voters voted for Juju.

So, the number of voters for Leonardo was [tex]x \times \frac{35}{100} = 0.35x[/tex]

Given that, 0.35x = 70

⇒ x = 200

Now, the number of voters for Gerardo was [tex](x \times \frac{40}{100}) = 0.4x = 0.4(200) = 80[/tex].

(Answer)