HAPPY BIRTHDAY!
You have decided to give your best friend a bag of red
and green marbles for his birthday. Your friend likes
green marbles better than red ones, so the bag has
twice as many green marbles as red. The label on the
bag says it contains a total of 84 marbles.
How many green marbles are in the bag? Write a
system of equations for this problem. Then solve the
problem using any method you like. Be sure to check
your solution

Answer:

Step-by-step explanation:

Given,

Let's assume, width of rectangle x feet and length of the Rectangle be 12 + 2x respectively. To Calculate the length and width of rectangle we'll use the formula of area of rectangle:

[tex] \\ \star \: { \underline{ \boxed { \pmb{ \sf{ \purple{Area _{(rectangle)}= Length \times width}}}}}} \\ \\ [/tex]

Substituting the required values:

[tex]\dashrightarrow \sf \: \: \: \: (12 +2x) (x) = 320 \\ [/tex]

[tex]\dashrightarrow \sf \: \: \: \: 12x + 2x^2 = 320 \\ [/tex]

[tex]\dashrightarrow \sf \: \: \: \: 12x + 2x^2- 320 = 0 \\ [/tex]

[tex]\dashrightarrow \sf \: \: \: \: 2x^2 + 12 - 320 = 0 \\ [/tex]

[tex]\dashrightarrow \sf \: \: \: \: 2(x^2 + 6x - 160) = 0 \\ [/tex]

[tex] \dashrightarrow \sf \: \: \: \: 2(x^2 + 16x - 10x - 160) = 0 \\ [/tex]

[tex]\dashrightarrow \sf \: \: \: \: 2(x - 10)(x + 16) = 0 \\ [/tex]

[tex]\dashrightarrow \: \: \: \: \underline{ \boxed{ \purple{ \pmb{ \rm{ x = 10 \: or \: -16}}}}} \\ [/tex]

Hence,

[tex]~[/tex]

[tex] \underline{\therefore{ \pmb { \frak{Length \: and \: width \: of \: rectangle \: is \: 32 \: and \: 10 \:ft}}}}[/tex]

Answer:

y - 2 = 6 (x - 1)

Step-by-step explanation:

Slope intercept form equations look like this:

y - y1 = m (x - x1)

***m = [tex]\frac{y2-y1}{x2-x1}[/tex]

Using the point (1,2), we know that x1 = 1 and y1 = 2. Let's sub these values into the slope intercept equation:

y - 2 = m (x - 1)

To complete this equation, we need to find slope. Pick out another point on the graph and plug into the slope equation. We can use point (2,8), where (1,2) = Point 1 and (2,8) = Point 2.

[tex]\frac{y2-y1}{x2-x1}=\frac{8-2}{2-1} =\frac{6}{1} =6[/tex]

Now that we know m = 6, let's plug that back into the original equation to get our final answer:

y - 2 = 6 (x - 1)            

I hope this helps!

Answer:

Step-by-step explanation:

Remark

You are given the diameter but the formula uses the radius. So your first job is find the radius. Then you use this value in the formula to find the volume. Substitute

Givens

pi = 3.14

d = 3.8

r = d/2

r = 3.8/2 = 1.9

Formula

V = (4/3) * pi * r^3

Solution

V = (4/3) * 3.14 * 1.9^3

V = 4/3 * 3.14 * 6.859

V = 28.7163

Answer:

Step-by-step explanation:

16/3 / 20/9 = 16/3 x 9/20= 12/5 which is 2 2/5e

The given dimensions of the, Check Box, bag, suitcase, and watermelons, we have;

First part;

Volume of the Check box is 2,772 in.³

Volume of the black bag is 1728 in.³

Volume of the blue bag is 2700 in.³

Second part;

Third part;

Volume of the Carry-on baggage Check box, V_c can be found as follows;

V_c = 22 × 14 × 9 = 2772

Volume of the black bag, V_b, can be found as follows;

V_b = 18 × 12 × 8 = 1728

Volume of the blue bag, V_bl, can be found as follows;

V_bl = 18 × 15 × 10 = 2700

Given that the height, depth and width of the black bag are smaller than the height, depth and width of the check box

Second part;

Volume of the smaller suitcase is found as follows;

V_s = 25×8×9 = 1800

Volume of the bigger suitcase is found as follows;

V_b = 75 × 20 × 18 = 27,000

The number of times, the bigger suitcase is larger than the smaller suitcase is therefore;

n = 27,000 ÷ 1809 = 15

Third part

The volume of the watermelon = 720 in.³

Which gives;

10 × 9 × H = 720

H = 720 ÷ (10 × 9) = 8

To maximize the number of watermelons, we have;

The length, 10, is a factor of 20

The width, 9, is a factor of 18

Therefore, we have;

Two rows of watermelon, and two layers of watermelon

Number of watermelon in a row is therefore;

R = 75 ÷ 8 ≈ 9

Maximum number of watermelon is therefore;

Max_n = 9 × 2 × 2 = 36

Learn more about finding the volume of a figure here:

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Answer: 0.29

Step-by-step explanation:

OQ is the side opposite angle P, QP is the side opposite angle O, and PO is the side opposite angle Q.

This means that tangent = opposite/adjacent, the tangent of angle O is the opposite side, QP, over the length of the adjacent side, OQ. (It cannot be PO since that's the hypotenuse)

This means that the tangent of O is 7/24, which is about 0.29

Answer:

area = 6

perimeter = 12

Step-by-step explanation:

area:

1.8+3.2 = 5

5*2.4 = 12

12/2 = 6

perimeter:

3+4+1.8+3.2 = 12

Answer:

x=140(corresponding angle)

Corresponding angles that are in the same position on two parallel lines intersected by a transversal line on the parallel lines.

Corresponding angles are equal

The 140° angle on line m and the x° angle on line n are corresponding angles.

The value of x is 140°

The angles that are in the same position on two parallel lines intersected by a transversal line on the parallel lines.

Corresponding angles are equal.

We have,

The figure is given,

Line m and Line n are parallel.

t line is the transversal line on the two parallel lines, line m and line n.

We see that,

140° angle on line m is corresponding to the x° angle on line n.

Corresponding angles are equal.

So,

140° = x°

x° = 140°

Thus,

The 140° angle on line m and the x° angle on line n are corresponding angles.

The value of x is 140°

Learn more about corresponding angles here:

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Answer:  Dilated and then translated

Step-by-step explanation:

Answer:

dilated and then translated

Step-by-step explanation:

Rectangle A has been enlarged (dilated) and then translated up and to the right.

Step-by-step explanation:

X + Y = 90

Y = 24

X = 6x

X + 24 = 90

X = 66

x = X/6 = 66/6 = 11

Answer:

4, 3, 4

Step-by-step explanation:

The unsimplified ratio of squares to triangles is 6:8, which simplifies to 3:4. That means, for every 3 squares, there are 4 triangles

As stated above, the simplified ratio of squares to triangles is 3:4

Answer:

146.7

Step-by-step explanation:

The equation for finding the volume of a pyramid is [tex]V = \frac{l w h}{3}[/tex].
For this pyramid, the height is 8, the width is 5, and the length is 11.
[tex]\frac{11x5x8}{3}[/tex]=146.67
146.67 rounded to the nearest tenth = 146.7.

Answer:

Step-by-step explanation:

There are 6 angles, 3 pairs of vertical angles that sum to 360°.

Set below equation and solve for x:

Opposite angles are equal and linear pairs are supplementary

The glide translation and the reflection over x-axis are illustrations of transformation

The new ordered pairs for P'and S'are (x - 2, -y)

The given parameters are:

Glide translation (x-2, y)

Reflection over x axis

Assume the coordinates of point P and S are (x,y)

When translated, the new points would be:

(x-2, y)

The rule of reflection over the x-axis is:

[tex](x,y) \to (x,-y)[/tex]

So, we have:

[tex](x - 2,y) \to (x - 2,-y)[/tex]

Hence, the new ordered pairs for P'and S'are (x - 2, -y)

Read more about transformation at:

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Answer:

[tex]\boxed{\sf{4(5x+3y-7)}}[/tex]

Step-by-step explanation:

It is necessary to find the factors and solve them using their expressions in order to solve this problem.

7*4=28

3*4=12

5*4=20

Rewrite the problem down.

5*4x+3*4y+7*4

Solve.

Common term of 4.

4(5x+3y-7)

I hope this helps you! Let me know if my answer is wrong or not.

[tex]========================================[/tex]

In order to factor this expression, we should factor out the common term (divide all terms in the polynomial by the common term)

In this case, the common term is

4

Note:- Usually, we factor out the G.C.F. (Greatest Common Factor)

So here, the G.C.F. is 4.

Why 4? Because in this trinomial (a polynomial with 3 terms) all 3 terms are divisible by 4.

So divide all the terms

5x

3y

-7

Put 4 outside the parentheses:

4(5x+3y-7)

Is the trinomial in its simplest form? Sure!

Hence, we are done! :)

[tex]================================[/tex]

Hope everything is clear; if you need any more clarification/explanation, kindly let me know, and I will comment and/or edit my answer. :)

Answer:

For the 1st row:

6.38 - 6 19/50 - 638%

Step-by-step explanation:

I would suggest using MathPapa if you are trying to do it quick. MathPapa will only really help with finding fractions and percentages, though. To get the decimal, need to find percentages then move decimal to the left 2 times.

ex. 125% -> 1.25

I hope this helps! Have a blessed rest of your night!

Answer:

Step-by-step explanation:

25% of classrooms is 3, find 100%

Since 100% is 4 times 25%, the corresponding number will also be 4 times greater:

Answer:

624.396

Step-by-step explanation:

I did the math myself XD

Hey there!

Let's make an equation

=> 9h = 144

{ Make h the subject of formula}

=> 9h = 144

=> 9h/9 = 144/9

=> h = 144/9

=> h = 16

Answer:

Explanation:

False statements:

Answer:

By examining the table of ordered pairs, notice that the function f(x) is the cube of [tex]x[/tex].  Therefore,  [tex]f(x)=x^3[/tex]

By examining the table of ordered pairs, notice that as [tex]x[/tex] increases by a constant value, the value of the function g(x) increases by the common ratio of 3. Therefore, [tex]g(x)=3^x[/tex]

From the table, both functions equal 27 when [tex]x=3[/tex], therefore, the point of intersection of the two functions is (3, 27).

As x increases past [tex]x=3[/tex], g(x) increases quicker than f(x) since g(x) is an exponential function and f(x) is a cubic polynomial.

So the following statements are true:

Please refer to the attached graph of both functions with plotted ordered pairs.

Answer: a prediction of the number of hot cocoas sold when the temperature is 0F

Step-by-step explanation: i did it on delta math

The line's y-intercept represent ''Number of hot cocoas sold''.

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

Chloe has a part-time job at an ice skating rink selling hot cocoa.

She decided to plot the number of hot cocoas she sold relative to the day's high temperature and then draw the line of best fit.

Now,

Since, She decided to plot the number of hot cocoas she sold relative to the day's high temperature and then draw the line of best fit.

Hence, By the graph we have;

The line's x - intercept represent ''Temperature''.

And, The line's y-intercept represent ''Number of hot cocoas sold''.

Thus, The line's y-intercept represent ''Number of hot cocoas sold''.

Learn more about the mathematical expression visit:

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Answer:

m<A = 30 degrees.

Step-by-step explanation:

m < C in triangle ABC = m < C in EDC so

x + 13 + 42 + x + 13 = 180

2x = 180 - 13 - 13 - 42

2x = 112

x = 56.

So m < C = 56+13 = 69.

m < B = m < D = 81

M < A = 180 - 69 - 81

= 180 - 150 = 30.

Answer:

50/529

Step-by-step explanation:

Total: 5 + 10 + 8

= 23

P(A and B) = P(A) x P(B)

P(A and B) = 5/23 x 10/23

P(A and B) = 50/529

The solid above is a triangular prism. Therefore, the surface area of the triangular prism is 157.2 cm².

The figure above is a triangular prism. The surface area of a triangular prism can be calculated as follows:

Surface area = bh + l(p)

where

Therefore,

p = 6 + 6 + 6 = 18 cm

l = 7 cm

b = 6 cm

h = 5.2 cm

Therefore,

Surface area = (6 × 5.2) + 7(18)

Surface area = 31.2 + 126

Surface area = 157.2 cm²

learn more on surface area here: https://brainly.com/question/2835293

1) The x-axis represents the energy ([tex]E[/tex]), in joules. The y-axis represents the amplitude ([tex]x[/tex]), in milimeters.

2) The curve depicts an monotonous decrecent rate of change.

3) The amplitude is directly proportional to the root square of the energy.

In this question we have a relationship between two variables, in which we must apply principles of functional analysis to respond three questions presented in the statement.

Now we proceed to answer the three questions below:

To learn more on functions, we kindly invite to check this verified question: https://brainly.com/question/12431044

Answer: 14085 m^3.

Step-by-step explanation: To find the volume of a right rectangular prism, you need to multiply the length, width, and height.  The equation is below:

l x w x h = V where l is the length, w is the width, h is the height, and V is the volume of the right rectangular prism.

The length of this recycling bin is 9 meters, the width is 5 meters, and the height is 313 meters.  Now that we know the length, width, and height, we can substitute the variables with the information we've gathered.

9 x 5 x 313 = 14085.

Therefore, 14085 m^3 is your answer.

Have a great day! :)