A. Does the table represent a proportional relationship?

B. If the relationship is proportional, what is the constant of proportionality?


Total wight in pounds. 12 18 30 60

Number of books. 10 15 25 50

Answer:

Supplementary

Step-by-step explanation:

Supplementary angles add to 180 degrees.

Answer:

Supplementary

Step-by-step explanation:

VSW and TSW combine and make 180. Complementary is when they make up to 90

Answer:

59 in2

Step-by-step explanation:

we know that

The area of the polygon is equal to the area of rectangle plus the area of two triangles

so

Find the area of rectangle

[tex]A_1=LW[/tex]

we have

[tex]L=7\ in\\W=4\ in[/tex]

substitute

[tex]A_1=(7)(4)=28\ in^2[/tex]

Find the area of triangle with height of 6 in

[tex]A=\frac{1}{2}bh[/tex]

we have

[tex]b=7\ in\\h=6\ in[/tex]

substitute

[tex]A_2=\frac{1}{2}(7)(6)=21\ in^2[/tex]

Find the area of triangle with height of 5 in

[tex]A=\frac{1}{2}bh[/tex]

we have

[tex]b=4\ in\\h=5\ in[/tex]

substitute

[tex]A_3=\frac{1}{2}(4)(5)=10\ in^2[/tex]

The total area is

[tex]A=A_1+A_2+A_3=28+21+10=59\ in^2[/tex]

Answer:

The answer is 59 in2

Step-by-step explanation:

Answer:

8

Step-by-step explanation:

set 7x-6 = 12-2x because midpoint segments are equal to each other than solve

9x-6=12

9x=18

x=2

then substitute in values.

B is the midpoint of AC. Using this information, we can set up an equation to solve for AB. After solving for x, we substitute the value back into the equation to find AB. The length of AB is 8 units.

We are given that B is the midpoint of AC. This means that the lengths AB and BC are equal. We can set up an equation to solve for AB.

AB = BC

7x-6 = 12-2x

Now we can solve for x and then find AB.

Bring like terms together:

7x + 2x = 12 + 6

9x = 18

Divide both sides by 9:

x = 2

Now substitute the value of x back into the equation for AB:

AB = 7(2) - 6

AB = 14 - 6

AB = 8

Therefore, AB is equal to 8 units.

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Answer:

Step-by-step explanation:

A) 15 and 12

Answer:

1.5w² + 10w + 16 sq, inches.

Step-by-step explanation:

The height of the portrait without the frame is 1.5 times its width.

Let the height is 1.5w inches and width is w inches.

Now, the frame around the portrait is 2 inches wide.

So, the dimensions of the portrait with frame are (1.5w + 4) inches by (w + 4) inches.

Therefore, the area of the framed portrait will be  

(1.5w + 4)(w + 4)  

= 1.5w² + 10w + 16 sq, inches. (Answer)

Answer:109

Step-by-step explanation:

The inequality obtained from the given statement; 8 less than 5 times a number is 8< 5x.

If the equation or inequality contains variable terms, then there might be some values of those variables for which that equation or inequality might be true.

Such values are called solution to that equation or inequality.

A Set of such values is called solution set to the considered equation or inequality.

Given statement; 8 less than 5 times a number

We know that the 8 is less than 5 times a number So, we first put 8 <.

From the given, we have the value 5 being multiplied by a number, that number can be any variable unless that specifically state which variable to use.

Thus, the inequality;

8< 5x

Hence, The inequality obtained from the given statement; 8 less than 5 times a number is 8< 5x.

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Answer: 2 and 4/5

Explanation: To subtract mixed numbers, first subtract the fractions. Notice here however that we have 2/5 - 3/5 which will give us a negative fraction. Since this will cause us a lot of trouble, instead, let's rewrite the first mixed number.

We can do this by thinking of 8 and 2/5 as 7 + 1 and 2/5 or 7 + 7/5 by changing 1 and 2/5 to the improper fraction 7/5. So 8 and 2/5 can be written as 7 and 7/5.

So we have 7 and 7/5 - 5 and 3/5.

Now, subtract the fractions. So we have 7/5 - 3/5 which is 4/5. Then subtract the whole numbers so we have 8 - 5 which is 2.

2 and 4/5 is in lowest terms so 8 and 2/5 - 5 and 3/5 is 2 and 4/5.

You will receive 0.75 euros for 1 U.S dollar.

In this currency exchange, you receive 6 euros for every 8 U.S dollars. To find out how many euros you will receive for 1 U.S dollar, you can set up a proportion.

Let x represent the number of euros you will receive for 1 U.S dollar. The proportion can be set up as follows: 8 U.S dollars / 6 euros = 1 U.S dollar / x euros.

Now, cross-multiply and solve for x: 8x = 6 * 1. Divide both sides by 8 to isolate x, and you will find that x = 0.75 euros.

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54+9= 63 m = distance and time=35 sec hence, speed= 63/35=9/5=1.8 m/s

time taken to reach water surface= distance/speed=54/1.8=30 sec

Answer:

$3.90 is the answer.

Step-by-step explanation:

9.75 ÷ 2.5 = 39/10 (3.9).

To check do 3.9 × 2.5 = 9.75.

Final answer:

To determine the price per pound of chocolate covered peanuts, divide the total cost ($9.75) by the total weight (2.5 pounds), resulting in $3.90 per pound.

Explanation:

The question asks to calculate the price per pound of chocolate covered peanuts Roman purchased.

Here is a step-by-step explanation:

First, it is important to take note of the total weight of the chocolate covered peanuts, which is 2 1/2 pounds or 2.5 pounds.

Next, we look at the total price paid for the 2.5 pounds, which is $9.75.

To find the price per pound, divide the total price by the total weight: $9.75 ÷ 2.5 pounds.

The price per pound turns out to be $3.90.

Therefore, the price per pound of the chocolate covered peanuts is $3.90.

75,000

Explanation:

This results in getting the answer 75,000.

Answer:

The answer is 75,000

Step-by-step explanation:

To work this out you need to put a line after the thousand like this 75|218 Then if the numer after is 5 or above you round the number up eg 75|818 Would round to 76000

Answer:

Angles of triangle are 40°,60° and 80°.

Step-by-step explanation:

Given:

if angles of a triangle are 2 is to 3 is to 4.

Let the common factor between the angles be 'x'.

So we can say that;

Angle 1 = [tex]2x[/tex]

Angle 2 = [tex]3x[/tex]

Angle 3 = [tex]4x[/tex]

We need to find the value of each angle.

Solution:

Now we know that;

"Sum of all angles of triangle is 180°."

framing in equation form we get;

[tex]Angle \ 1+Angle\ 2+Angle \ 3 =180[/tex]

Substituting the values we get;

[tex]2x+3x+4x=180\\\\9x=180[/tex]

Dividing both side by 9 we get;

[tex]\frac{9x}{9}=\frac{180}{9}\\\\x=20[/tex]

Angle 1 = [tex]2x=2\times20=40\°[/tex].

Angle 2 = [tex]3x=3\times20=60\°[/tex]

Angle 3 = [tex]4x=4\times20=80\°[/tex]

Hence Angles of triangle are 40°,60° and 80°.

Answer:

y ≤ 3x-4

-1 ≤ y ≤ 2

step by step explanation:

the highlighted area is situated under the line of equation y=3x-4 and respectivelybetween the two lines of equations y=-1 and y=2

Then the system of inequalities is :

y ≤ 3x-4

-1 ≤ y ≤ 2

Answer:

y ≤ 3x-4

-1 ≤ y ≤ 2

Answer:

[tex]g(x)=-4(\frac{1}{2})^x[/tex]

Step-by-step explanation:

Given:

The parent function is given as:

[tex]f(x)=4(\frac{1}{2})^x[/tex]

The function [tex]g(x)[/tex] is a reflection of the parent function about the x-axis.

Now, in order to find the function g(x), we need to use the rules of function transformations.

As per transformation rules, when a function is reflected about the x-axis, the function rule is given as:

[tex]f(x)\to-f(x)[/tex]

So, the new function or the reflected function is the negative of the original function.

Therefore, the reflected function [tex]g(x)[/tex] is given as:

[tex]g(x)=-f(x)\\\\g(x)=-4(\frac{1}{2})^x[/tex]

Hence, the function that represents the reflection of the given function across the x-axis is [tex]g(x)=-4(\frac{1}{2})^x[/tex]

The ratio of width to length in simplest form is 19 : 44

Solution:

Given that, A cell phone is 132 mm long and 57 mm wide

Length of cell phone = 132 mm

Width of cell phone = 57 mm

We have to find the ratio of width and length in simplest form

[tex]\frac{Width}{Length} = \frac{57}{132}\\\\\text{Reduce to lowest terms }\\\\\frac{width}{length} = \frac{57 \div 3}{132 \div 3}\\\\\frac{Width}{Length} = \frac{19}{44}[/tex]

In ratio form, we know that,

[tex]\frac{a}{b} = a : b[/tex]

Writing in ratio form, we get

Width : length = 19 : 44

Thus the ratio of width to length in simplest form is 19 : 44

Answer:

D. 15 cm

Step-by-step explanation:

9² + 12² = x²

81 + 144 = x²

225 = x²

√225 = x

15 = x

Answer:

VERTICAL LINES

Step-by-step explanation:

Answer:

15/2

Step-by-step explanation:

2x+3=18

2x=18-3

2x=15

x=15/2

Answer:

$0.85 per tomato

Step-by-step explanation:

A unit rate is the cost for one item. Like $0.99 for this one bag of skittles.

So $3.40 divided by four is $0.85.

The unit rate would be 0.85. If you divide 3.40 by 4 you 0.85

The value of [tex]\log_5{125}[/tex] is 3.

Solution:

Step 1: Given expression is [tex]log_5{125}[/tex].

125 can be expressed as [tex]5^3.[/tex]

[tex]\log_5{125}=\log_5{5}^3[/tex]

Step 2: Using log rule: [tex]\log_a{x^b}=b\log_a{x}[/tex]

 [tex]\log_5{5}^3=3\log_5{5}[/tex]

Step 3: Using log rule: [tex]\log_a{a}=1[/tex]

[tex]\log_5{5}= 1[/tex]

⇒ [tex]3\log_5{5}= 3(1)[/tex]

⇒ [tex]3\log_5{5}= 3[/tex]

∴ [tex]\log_5{125}=3[/tex]

Hence the value of [tex]\log_5{125}[/tex] is 3.

Answer:

Step-by-step explanation:

5*743=(5*700)+(5*40)+(5*3)

Answer:

6 days

Step-by-step explanation:

Answer:

Step-by-step explanation:

You have to find the Least common Multiple of 1,2,3

LCM (1,2,3) = 6

Answer:

26.25 feets

Step-by-step explanation:

Given:

Each headbands requires 1 7/8 feets fabric

Dedra has to  make 14 headbands .

Question asked:

how much fabric will she need  to make 14 headbands = ?

Solution:

By applying unitary method :

Length of fabric require to make a headband = [tex]1\frac{7}{8}[/tex]

                                                                           = [tex]\frac{15}{8}[/tex]

Length of fabric require to make 14 headbands = [tex]14\times\frac{15}{8}[/tex]

                                                                                = [tex]\frac{210}{8}[/tex]

                                                                                = [tex]26.25 feets[/tex]

Therefore, Dedra needs 26.25 feets fabric to make 14 headbands.

Answer:4 out of 19

Step-by-step explanation:

you add them all and then say 4 because that is  yellows amount of marbles

Answer:

C. y - 7 = -13(x -  5)  

Step-by-step explanation:

The point-slope equation for a straight line is

y - y₁ = m(x - x₁)

where m is the slope and(x₁, y₁) is a point on the line.

If m = -13 and  (5, 7) is the point, the equation is

y - 7 = -13(x -  5)

Answer:

C≈12.57

Step-by-step explanation:

The formula for circumference if 2(3.14) * r

The r represents the radius do you would just take 2 * 3.14 which is 6.28.

Next, you would take 6.28 * r (which is 2 meters) and you get 12.566, but if you're rounding it would be 12.57.

Make sure to label your answers

I hope this helped!

Answer: h = 1.25

Step-by-step explanation:

divide 10 by 8 to get 1.25 or 5/4

In this question, you're solving for h.

Solve for h:

10=8h

"h" can't have a number next to it, it has to be by itself, so divide both sides by 8

1.25 = h  

Answer:

1.25 = h

Answer:

3

Step-by-step explanation:

3 times 3 is 9

1/3 of 3 is 1

add them to get 10

Answer:

3

Step-by-step explanation:

[tex]3x \times \frac{1}{3} x = 10 \\ \frac{10}{3} x = 10 \\ 10x = 30 \\ x = 3[/tex]

x-wanted number

Answer:

3(3x+7)

Step-by-step explanation:

9x+21=3(3x+7)

The number of miles Mr Miller drive was 973 miles.

Step-by-step explanation:

Given,

Miles driven on first week = 568 miles

Miles driven on Tuesday this week = 308 miles

Miles driven on Wednesday this week = 97 miles

Total miles driven = Miles in first week + Miles on Tuesday + Miles on Wednesday

Total miles driven = 568 + 308 + 97 = 973 miles

The number of miles Mr Miller drive was 973 miles.

Keywords: addition

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