what are some equivalent expressions for :
120.5y + 80.5y + 65.5y

The volume of the lid is approximately 113.8 cubic inches.

The volume of the lid can be found by multiplying the area of the triangular base by the height of the lid. The area of a triangle can be found by using the formula: Area = (base x height) / 2. In this case, the base is 6 1/2 inches and the height is 3 1/2 inches. Plugging these values into the formula, we get: Area = (6.5 x 3.5) / 2 = 11.375 square inches. Now, to find the volume of the lid, we multiply the area by the height: Volume = 11.375 x 10 = 113.75 cubic inches. Rounding to the nearest tenth, the volume of the lid is 113.8 cubic inches.

The volume of the lid is 113.8 cubic inches.

To determine the volume of the lid of the jewelry box, we need to use the formula for the volume of a triangular prism, which is V = (1/2 * base * height of triangular base) * height of the prism.

First, calculate the area of the triangular base:

Next, multiply the area of the triangular base by the height of the prism:

Therefore, the volume of the lid to the nearest tenth is 113.8 cubic inches.

Answer:

55m

Step-by-step explanation:

a²+b²=c²

19 x 19 = 361

52 x 52 = 2704

2704 + 361= 3065

the square root of 3065 is 55.4 so round that to 55.

Answer:

I believe it would be true

The value of x that satisfies the equation 41 - x = 157 is x = -116.

To solve for x in the equation 41 - x = 157, we need to isolate x on one side of the equation.

Let's go step by step:

Step 1: Start with the given equation.

41 - x = 157

Step 2: Get rid of the constant term on the left side (41) by subtracting it from both sides of the equation.

(41 - x) - 41 = 157 - 41

Simplifying the left side:

41 - 41 - x = 157 - 41

0 - x = 116

Step 3: We have -x on the left side, and we want to solve for x, so we need to get rid of the negative sign in front of x.

To do that, we can multiply both sides of the equation by -1.

When we multiply a number by -1, the sign changes.

(-1) * (-x) = (-1) * 116

Simplifying the left side:

x = -116

Step 4: Now we have found the value of x, which is x = -116.

To verify our solution, we can substitute the value of x back into the original equation and see if it holds true:

41 - (-116) = 157

Simplifying:

41 + 116 = 157

157 = 157

Since both sides of the equation are equal after simplification, our solution x = -116 is correct.

Therefore, the value of x that satisfies the equation 41 - x = 157 is x = -116.

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Answer: 5.8 ft

Step-by-step explanation:

We can use the Pithagorean Theorem in this problem, in order to find the length of the rope:

[tex]h^{2}=a^{2}+b^{2}[/tex]

Where:

[tex]h[/tex] is the length of the rope (the hypotenuse of the right triangle formed by the height of the tent, the rope and the ground)

[tex]a=5 ft[/tex] is the height of the tent (one of the legs of the right triangle)

[tex]b=3 ft[/tex] is the other leg of the right triangle

Solving the equation with the given data:

[tex]h^{2}=5^{2}+3^{2}[/tex]

Finding [tex]h[/tex]:

[tex]h=\sqrt{(5 ft)^{2}+(3 ft)^{2}}[/tex]

[tex]h=\sqrt{25 ft+9 ft}[/tex]

[tex]h=5.83 ft \approx 5.8 ft[/tex] This is the total length of nylon rope

Answer:

C Both relation and function.

Step-by-step explanation:

This would pass the vertical line test so it is both a relation and a function

Answer:

Answer:

Step-by-step explanation:

Let x represent the cost of one package of tulip bulbs.

Let y represent the cost of one bag of daffodil bulbs.

Ava bought 6 packages of tulip bulbs and 12 bags of daffodil bulbs for a total of $198. This means that

6x + 12y = 198- - - - - - - - - - - - -1

Grace spent $254 buying 14 packages of tulip bulbs and 12 bags of daffodil bulbs. This means that

14x + 12y = 254- - - - - - - - - - - - 2

Subtracting equation 2 from equation 1, it becomes

- 8x = - 56

x = - 56/-8

x = 7

Substituting x = 7 into equation 1, it becomes

6 × 7 + 12y = 198

42 + 12y = 198

12y = 198 - 42

12y = 156

y = 156/12

y = 13

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Step-by-step explanation:

Answer:

Step-by-step explanation:

Let x represent the cost of one package of tulip bulbs.

Let y represent the cost of one bag of daffodil bulbs.

Ava bought 6 packages of tulip bulbs and 12 bags of daffodil bulbs for a total of $198. This means that

6x + 12y = 198- - - - - - - - - - - - -1

Grace spent $254 buying 14 packages of tulip bulbs and 12 bags of daffodil bulbs. This means that

14x + 12y = 254- - - - - - - - - - - - 2

Subtracting equation 2 from equation 1, it becomes

- 8x = - 56

x = - 56/-8

x = 7

Substituting x = 7 into equation 1, it becomes

6 × 7 + 12y = 198

42 + 12y = 198

12y = 198 - 42

12y = 156

y = 156/12

y = 13

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Answer:

11

Step-by-step explanation:

6 : 1

66 : X

X/66 = 1/6

X = 11

Answer:

The right answer is, -420

Step-by-step explanation:

Because we use common factor:

60 (x - 15)

We multiply for each term:

60 (x) - 60 (15)

60 (8) - 60 (15)

We solve:

480 - 900 = -420

Answer:

24 stations

Step-by-step explanation:

we know that

six stations represent 25% of the stations offered

so

using a proportion

Find out how many stations represent a percentage of 100%

[tex]\frac{6}{25\%}=\frac{x}{100\%}\\\\x=6(100)/25\\\\x=24\ stations[/tex]

Answer:

B) associative

Step-by-step explanation:

The associative property of multiplication says you can choose which pair of numbers to multiply first, so when every operation is multiplication, you can move parentheses without changing the answer.

The given equation 4×7×3 = 7×4×3 demonstrates the Commutative Property. This is the property which states that the order in which numbers are multiplied or added does not affect the result.

The equation 4×7×3 = 7×4×3 demonstrates the Commutative Property. In mathematics, the Commutative Property refers to the fact that the order in which numbers are multiplied does not change the result of the multiplication. This is why we can rearrange the factors 4, 7, and 3 in any order and still get the same product.

For instance, we can express the commutative property of multiplication as a×b = b×a. So, in your example, the equation 4×7×3 = 7×4×3, is an application of this principle as you are simply rearranging the order of numbers being multiplied.

Please remember that this rule applies only to addition and multiplication, not subtraction or division.

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Question 1: Option B: [tex]\frac{10}{14}=\frac{5}{7}[/tex]

Question 2: Option C: [tex]\frac{12}{18}=\frac{4}{6}[/tex]

Solution:

Question 1:

Given ratio is [tex]\frac{10}{14}[/tex].

To find the equivalent ratio of [tex]\frac{10}{14}[/tex].

10 and 14 have the common factor 2.

So divide both numerator and denominator by the common factor 2.

[tex]$\frac{10}{14}=\frac{10\div2}{14\div 2}[/tex]

    [tex]$=\frac{5}{7}[/tex]

[tex]$\frac{10}{14}=\frac{5}{7}[/tex]

Hence option B is the correct answer.

Question 2:

Given ratio is [tex]\frac{10}{14}[/tex].

To find the equivalent ratio of [tex]\frac{12}{18}[/tex].

12 and 18 have the common factor 3.

So divide both numerator and denominator by the common factor 3.

[tex]$\frac{12}{18}=\frac{12\div3}{18\div 3}[/tex]

    [tex]$=\frac{4}{6}[/tex]

[tex]$\frac{12}{18}=\frac{4}{6}[/tex]

Hence option C is the correct answer.

Answer:

V=lwh/3

Step-by-step explanation:

Answer:

7

Step-by-step explanation:

to edge a lawn =10.he edged 4 lawn =10multiplied by 4=40

2nd. total -40=180-40=140

3rd. when he mows 1 lawn he is paid 20 what about when he is paid 140=140 divided by 20 =7

Makoto mowed 7 lawns to earn $180.

Let's denote the number of lawns Makoto mowed as m. Since he edged 4 lawns, that part of the income is 4 times $10, which sums up to $40. The total income from mowing is then $20 times the number of lawns he mowed, which is m. The equation representing Makoto's earnings is:

20m + 40 = 180

Subtracting 40 from both sides gives us:

20m = 140

Dividing both sides by 20 to solve for m gives us:

m = 7

Answer: A/5+30*5

Step-by-step explanation:

The app uses 2^28 bytes.

Step-by-step explanation:

⇒ 4^4 × 2^20 = (2²)^4 × 2^20 = 2^8 × 2^20

                       = 2^8+20

                       = 2^28 bytes (using the law of exponents a^m × a^n = a^m+n)

Answer:

2x ÷ 4 = 8

Step-by-step explanation:

2x ÷ 4 = 8

2x/4 = 8

2x = 32

x = 16

Answer

3

Step-by-step explanation:

the formulas say it

Final answer:

To find the width of a rectangle when the length is 2 units more than the width and the area is known to be 48 units, you can use algebraic equations to determine the width. In this case, the width of the rectangle is 6 units.

Explanation:

To find the width of the rectangle:

Let x be the width of the rectangle.

Since the length is 2 units more than the width, the length is x + 2.

Given that the area is 48 units, use the formula for the area of a rectangle: width x length = area. Therefore, x(x + 2) = 48.

Solve for x by setting up the equation: x^2 + 2x - 48 = 0.

Factor the quadratic equation: (x + 8)(x - 6) = 0.

Since the width cannot be negative, the width of the rectangle is 6 units.

The width of the rectangle is 6 units.

According to the question, the length is 2 units more than the width, so we can express the length as ( w + 2 ) units.

The area of a rectangle is given by the product of its length and width. Therefore, we can set up the following equation to represent the area of the rectangle:

[tex]\[ \text{Area} = \text{length} \times \text{width} \] \[ 48 = (w + 2) \times w \][/tex]

Expanding the right side of the equation, we get:

[tex]\[ 48 = w^2 + 2w \][/tex]

To find the value of w, we need to solve the quadratic equation. Let's rearrange the equation to set it equal to zero:

[tex]\[ w^2 + 2w - 48 = 0 \][/tex]

Now, we can factor this quadratic equation:

[tex]\[ (w + 8)(w - 6) = 0 \][/tex]

Setting each factor equal to zero gives us two possible solutions for w:

[tex]\[ w + 8 = 0 \quad \text{or} \quad w - 6 = 0 \][/tex]

Solving for w, we get:

[tex]\[ w = -8 \quad \text{or} \quad w = 6 \][/tex]

Since the width of a rectangle cannot be negative, we discard the negative solution. Therefore, the width of the rectangle is:

[tex]\[ w = 6 \text{ units} \][/tex]

Given:

The equation of the line passes through the point (6,9) and is perpendicular to the line whose equation is [tex]4 x-6 y=15[/tex]

We need to determine the equation of the line.

Slope:

Let us convert the equation to slope - intercept form.

[tex]-6 y=15-4x[/tex]

   [tex]y=\frac{2}{3}x-\frac{5}{2}[/tex]

From the above equation, the slope is [tex]m_1=\frac{2}{3}[/tex]

Since, the lines  are perpendicular, the slope of the line can be determined using the formula,

[tex]m_1 \cdot m_2=-1[/tex]

  [tex]\frac{2}{3} \cdot m_2=-1[/tex]

      [tex]m_2=-\frac{3}{2}[/tex]

Therefore, the slope of the equation is [tex]m=-\frac{3}{2}[/tex]

Equation of the line:

The equation of the line can be determined using the formula,

[tex]y-y_1=m(x-x_1)[/tex]

Substituting the point (6,9) and the slope [tex]m=-\frac{3}{2}[/tex] in the above formula, we get;

[tex]y-9=-\frac{3}{2}(x-6)[/tex]

Simplifying the terms, we get;

[tex]2(y-9)=-3(x-6)[/tex]

[tex]2y-18=-3x+18[/tex]

[tex]3x+2y=36[/tex]

Thus, the equation of the line is [tex]3x+2y=36[/tex]

The equation of a line that is perpendicular to the line 4x - 6y = 15 and passes through the point (6,9) is 3x + 2y = 36. This is because the slope of the new line is the negative reciprocal of the slope of the given line, and the line passes through the given point (6,9).

The subject of this question is mathematics, specifically in the topic of linear equations. To find the equation of a line that is perpendicular to a given line and passes through a certain point, we first need to find the slope of the given line. The standard form of the equation of a line is Ax + By = C. The given line is 4x - 6y = 15. We can find its slope by taking the negative reciprocal of the coefficient of x (A) over the coefficient of y (B), so the slope of the given line is -4/-6 = 2/3. Since we want a line that is perpendicular to the given line, the slope of the line we are looking for would be the negative reciprocal of the slope of the given line, which would be -3/2, because perpendicular lines have slopes that are negative reciprocals of each other. Using the point-slope form of a line, y - y1 = m(x - x1), where m is the slope and (x1, y1) is the given point, the equation of the line we are looking for is y - 9 = -3/2(x - 6), which simplifies to 2y - 18 = -3x + 18 and further simplifies to 3x + 2y = 36. So the answer is none of the given options.

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Let the two numbers be [tex]x,y[/tex].

We have

[tex]\begin{cases}x+y=-\frac{1}{3}\\x-y=18\end{cases}[/tex]

From the second equation, we derive [tex]x=18+y[/tex]

Plugging this value in the first equation, we have

[tex]18+y+y=-\dfrac{1}{3} \iff 2y=-\dfrac{1}{3}-18\iff 2y=-\dfrac{55}{3} \iff y=-\dfrac{55}{6}[/tex]

And we derive

[tex]x=18+y=18-\dfrac{55}{6}=\dfrac{53}{6}[/tex]

Answer:

The two numbers are: -9.17 and 8.83

Step-by-step explanation:

Let the two numbers represent 'x' and 'y'

Their sum is − 1/3 ==>          x + y = -1/3  .................(eqn 1)

Their difference is 18 ==>    x − y = 18  ....................(eqn 2)

from equation 2,

x = 18 + y

therefore, substitute for 'x' in (eqn 1) to get y

(18+y) + y = -1/3

18 + 2y = -1/3

2y = -1/3 − 18

2y = -[tex]18\frac{1}{3}[/tex]

2y = - 55/3

y = (-55/3) / 2

y = -55/3 x 1/2

y = -55/6 = -9.17

Substitute for 'y' in either equation

picking (eqn 2)

x − (-9.17) = 18

x + 9.17 = 18

x = 18 − 9.17

x = 8.83

Answer:

There was 150 hamburgers sold on Saturday

Step-by-step explanation:

Step 1:  Make an equation

2x + x = 450

Step 2:  Solve for x

2x + x = 450

3x / 3 = 450 / 3

x = 150

Answer:  There was 150 hamburgers sold on Saturday

Final answer:

The local hamburger shop sold 150 hamburgers on Saturday. This was found by setting up a system of equations where H represents hamburgers and C represents cheeseburgers, and solving for H.

Explanation:

To determine how many hamburgers were sold on Saturday, we can set up a system of equations based on the information given:

Let H represent the number of hamburgers sold.

Let C represent the number of cheeseburgers sold.

We are told that the total number of hamburgers and cheeseburgers sold is 450, so:

H + C = 450

We also know that the number of cheeseburgers sold was two times the number of hamburgers sold, so:

C = 2H

Now we substitute the second equation into the first one to solve for H:

H + 2H = 450

3H = 450

H = 450 / 3

H = 150

Therefore, on Saturday, the local hamburger shop sold 150 hamburgers.

Option C:

The value of m is 4.

Solution:

Given data:

AB = 4m – 15

BC = 5m –6

AC = 15

To find the value of m:

Using segment addition postulate,

AB + BC = AC

4m – 15 + 5m –6 = 15

Arrange the like terms together.

4m + 5m – 15 – 6 = 15

9m – 21 = 15

Add 21 on both sides of the equation,

9m = 36

Divide by 9 on both sides of the equation.

m = 4

The value of m is 4.

Option C is the correct answer.

Answer:

is 4

Step-by-step explanation:

i got it right on the test

Answer: $1090.80

Step-by-step explanation:

Answer:

$1,090.80

Step-by-step explanation:

Bodily injury; 25/50=$220

Property; 100=$375

Collision deductibles;$250=$185

Comprehensive deductibles;$100=$129

220+375+185+129 = 909

909*1.2=1,090.8

Took the test

Answer:

8x^3 + 4x^2 + 4x -7

Step-by-step explanation:

Add like terms.

Answer: everything is explained in the picture

Step-by-step explanation:

Answer:

[tex]IG=28.9\ ft[/tex]

Step-by-step explanation:

we know that

In the right triangle GHI

[tex]cos(G)=\frac{IG}{GH}[/tex] ----> by CAH )adjacent side divided by the hypotenuse)

substitute the given values

[tex]cos(21^o)=\frac{IG}{31}[/tex]

solve for IG

[tex]IG=cos(21^o)(31)=28.9\ ft[/tex]

see the attached figure to better understand the problem

Answer:

24.6

Step-by-step explanation:

Answer:

5x=-15

Step-by-step explanation:

8x-6x=4-10

2x=-6

x=-3

5x=-15

Answer:

745.12

Step-by-step explanation:

30 x 30 = 900 which is the sign if it were a square

then you subtract the four corner pieces

900 - 4([tex]\frac{1}{2}[/tex](8.8 x 8.8))

900 - 2(77.44)

900 - 154.88

= 745.12