Review (Monday)
Date:
2. Mrs. Henry purchased 14 gallons of gas
for $34.72. How much did each gallon cost?

Answer:

30

5 × 6 = 30

3 ×10 = 30

6 × 5 = 30

Answer:

Step-by-step explanation:

[tex]LCD\ of\ \dfrac{2}{3}\ and\ \dfrac{1}{6}\ is\ 6:\\\\\dfrac{2}{3}=\dfrac{2\cdot2}{3\cdot2}=\dfrac{4}{6}\\\\LCD\ of\ \dfrac{1}{6}\ ond\ \dfrac{11}{5}\ is\ 30:\\\\\dfrac{11}{5}=\dfrac{(11)(6)}{(5)(6)}=\dfrac{66}{30}\\\\\dfrac{1}{6}=\dfrac{(1)(5)}{(6)(5)}=\dfrac{5}{30}\\\\\dfrac{2}{3}=\dfrac{4}{6}=\dfrac{(4)(5)}{(6)(5)}=\dfrac{20}{30}\\\\\text{Therefore:}\\\\\dfrac{11}{5}+\dfrac{2}{3}+\dfrac{1}{6}=\dfrac{66}{30}+\dfrac{20}{30}+\dfrac{5}{30}=\dfrac{66+20+5}{30}=\dfrac{91}{30}=3\dfrac{1}{30}[/tex]

Answer:

Elliot will make 4 hats and 16 scarves

Step-by-step explanation:

Let x be the number of hats and y be the number of scarves Elliot will make.

Elliott wants to make a total of 20 items, then

x + y = 20

Each hat uses 0.2 kilograms of yarn, so x hats use 0.2x kilograms of yarn and each scarf uses 0.1 kilogram of yarn, then y scarves use 0.1y kilograms of yarn. Elliott wants to use twice as much yarn for scarves as for hats, then

0.1y = 2(0.2x)

Thus,

0.1y = 0.4x

y = 4x

Substitute it into the first equation:

x + 4x = 20

5x = 20

x = 4

y = 20 - 4

y = 16

Hence, Elliot will make 4 hats and 16 scarves

Answer:

0.1s=2.0.2h

h+s=20

Step-by-step explanation:

Answer:

The number of large boxes is 55 and the number of small boxes is 70

Step-by-step explanation:

The complete question is

A delivery truck is transporting boxes of two sizes: large and small. The large boxes weigh 50 pounds each, and the small boxes weigh 20 pounds each. There are 125 boxes in all. If the truck is carrying a total of 4150 pounds in boxes, how many of each type of box is it carrying?

Let

x ------> the number of large boxes

y -----> the number of small boxes

we know that

[tex]x+y=125[/tex] -----> equation A

[tex]50x+20y=4,150[/tex] ----> equation B

Solve the system by graphing

Remember that the solution of the system of equations is the intersection point both graphs

The intersection point is (55,70)

therefore

The number of large boxes is 55 and the number of small boxes is 70

The following system of equations represents the given statement;

x = y+z

y = 2z

10x+15y+40z = 600

They must sell 18 small pizzas, 12 medium pizzas and 6 small pizzas.

Step-by-step explanation:

Let,

Small pizza = x

Medium Pizza = y

Large Pizza = z

Cost of one small pizza = $10

Cost of one medium pizza = $15

Cost of one large pizza = $40

According to given statement;

They usually sells as many small pizzas as medium and large pizzas combined.

x = y+z  

The number of medium pizzas sold is usually twice as many as large ones.

y = 2z

How many of each pizza must they sell to get $600.

10x+15y+40z = 600

The following system of equations represents the given statement;

x = y+z    Eqn 1

y = 2z      Eqn 2

10x+15y+40z = 600    Eqn 3

Putting value of x and y from Eqn 1 and 2 in Eqn 3;

[tex]10(y+z)+15(2z)+40z=600\\[/tex]

We know that y=2z from Eqn 2,

[tex]10(2z+z)+30z+40z=600\\20z+10z+70z=600\\100z=600[/tex]

Dividing both sides by 100;

[tex]\frac{100z}{100}=\frac{600}{100}\\z=6[/tex]

Putting z=6 in Eqn 2;

[tex]y=2(6)\\y=12[/tex]

Putting value of y and z in Eqn 1;

[tex]x=12+6\\x=18[/tex]

They must sell 18 small pizzas, 12 medium pizzas and 6 small pizzas.

Keywords: linear equations, substitution method

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Answer:

8a-28b+15c

Step-by-step explanation:

4(2a)+7(-4b)+(3*c*5)

8a-28b+15c

Answer:

The solution of x for the slope intercept is 2 .

Step-by-step explanation:

Given expression as :

- 9 = - 2 ( x + 3 ) + 1

Or. - 9 = - 2×( x + 3 ) + 1

or, - 9 = - 2 x - 6 + 1

or, - 9 = - 2 x - 5

or, - 9 + 5 = - 2 x

or , - 4 = - 2 x

∴  x = [tex]\frac{-4}{-2}[/tex]

I.e x = 2

Hence the solution of x for the slope intercept is 2 . Answer

Answer:

If you mean the sum ?

55 + 3 = 58

Answer:

58

Step-by-step explanation:

11 x5=55

3x1=3

55+3=58

Answer:

Yes, it can

Step-by-step explanation:

45.67+76.9+66.72+89.3= 278.59

278.59 is less than 500

The merry-go-round can hold all the children.

To find if the merry go around can hold all children, we need to find the total weight of all the children.

[tex]\text{total weight of all children} = Susie\ +\ Johnny\ +\ Grace\ +\ Max\\\\\text{total weight of all children} = (45.67 +76.9+ 66.72+ 89.3)\ pounds = 278.59\ pounds[/tex]

The total weight of all the children is 278.59 pounds, which is less than the maximum capacity of the merry-go-round which is 500 pounds.

So, the merry-go-round can hold all the children.

Answer:

B) 25°

Step-by-step explanation:

Assuming the quadrilateral is the one shown in the picture attached, then a triangle ADC is form, where m∠ADC = 125° and m∠1 = 30°. The addition of the three angles of a triangle is equal to 180°, so:

m∠ADC + m∠1 + m∠2 = 180°

Replacing with the known values and isolating m∠2 we get:

125° + 30° + m∠2 = 180°

m∠2 = 180° - 125° - 30°

m∠2 = 25°

Answer:

it is 25 degrees

Step-by-step explanation:

thanks for your help

plz mark as brainlest.

Answer:

Step-by-step explanation:

Area of pool:

Area of walkway:

If the areas are equal, then:

Final answer:

To find the value of x when the area of the walkway equals the area of the pool, set up an equation and solve for x. The value of x that will make the area of the walkway equal to the area of the pool is x = 2 meters.

Explanation:

To find the value of x when the area of the walkway equals the area of the pool, we need to set up an equation. The area of the pool is the length multiplied by the width, which is 6 meters multiplied by 4 meters, or 24 square meters. The area of the walkway is the total area of the larger rectangle minus the area of the pool.

The total area of the larger rectangle is the length plus twice the width, all multiplied by the width. So, the area of the walkway is x(6 + 2x - 4). Setting the area of the walkway equal to the area of the pool gives us the equation: x(6 + 2x - 4) = 24.

To solve this equation, we can first simplify it by distributing the x through the parentheses: 6x + 2x^2 - 4x = 24. Combining like terms, we have 2x^2 + 2x - 24 = 0. To solve this quadratic equation, we can factor it or use the quadratic formula. Factoring gives us 2(x + 6)(x - 2) = 0. So either (x + 6) = 0 or (x - 2) = 0. Solving for x, we find that x = -6 or x = 2.

Since we are dealing with width, the negative solution x = -6 is not applicable. Therefore, the value of x that will make the area of the walkway equal to the area of the pool is x = 2 meters.

Answer:

3. The superhero is afraid of heights.

"The superhero is afraid of heights." is independent clause because the sentence contains a subject and verb and it's a complete sentence.  

Step-by-step explanation:

An independent clause is a group of words that contains a subject and verb and expresses a complete thought. An independent clause is a sentence.

          Jim studied in the Sweet Shop for his chemistry quiz.

A dependent clause is a group of words that contains a subject and verb but does not express a complete thought. A dependent clause cannot be a sentence. Often a dependent clause is marked by a dependent marker word.  A dependent marker word is a word added to the beginning of an independent clause that makes it into a dependent clause. Some common dependent markers are: after, although, as, as if, because, before, even if, even though, if, in order to, since, though, unless, until, whatever, when, whenever, whether, and while.

          When Jim studied in the Sweet Shop for his chemistry quiz . . .

         (What happened when he studied? The thought is incomplete.)

Answer: choice 3. The superhero is afraid of heights

The other choices are sentences that are incomplete because they need more structue to them. For example, sentence 1 implies that something else is going on during Marvin's guitar time. The other sentences have cliffhangers as well and they arent fully independent or on their own. Sentence 3 expesses a single complete thought without introducing some other related or tangential thought needed to complete that idea.

Answer:

The volume of the new can is [tex]V_2=160x^3\pi\ cm^3[/tex]

Step-by-step explanation:

we know that

If two figures are similar, then the ratio of its volumes is equal to the scale factor elevated to the cube

Let

z ----> the scale factor

In this problem

[tex]z=x[/tex]

The volume of the original can is

[tex]V_1=\pi r^{2}h[/tex]

The volume of the new can is

[tex]V_2=z^{3}V_1[/tex]

[tex]V_2=x^3(\pi r^{2}h)[/tex]

we have

[tex]r=4\ cm\\h=10\ cm[/tex]

substitute

[tex]V_2=x^3(\pi (4)^{2}10)[/tex]

[tex]V_2=160x^3\pi\ cm^3[/tex]

Each person will get 7/30 fraction of pizza

Step-by-step explanation:

Given

[tex]Total\ pizza = 2\frac{1}{3} = \frac{7}{3}\\Total\ people = 10[/tex]

In order to find the fraction of pizza each person will get, we have to divide the total pizza by total number of people

So,

[tex]Share\ of\ one\ person = \frac{\frac{7}{3}}{10}\\=\frac{7}{3} * \frac{1}{10}\\=\frac{7}{30}[/tex]

Hence,

Each person will get 7/30 fraction of pizza

Keywords: Fractions, Division

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Answer:

5 + 42

Step-by-step explanation:

Given

5 - 6x(- 7)

= 5 - 6 × - 7 ← perform multiplication before subtraction

= 5 + 42

= 47

Answer:

Step-by-step explanation:

Use PEMDAS:

P Parentheses first

E Exponents

MD Multiplication and Division

AS Addition and Subtraction

[tex]5-6\times(-7)[/tex]          first - multiplication

[tex]=5+(-6)(-7)=5+42[/tex]         next - addition

[tex]=47[/tex]

Positive integers are 20,22 and negative integers are -22,-20.

Step-by-step explanation:

Let,

2 positive integers are x, x+2

According to given statement;

[tex]x(x+2)=440\\x^{2}+2x=440\\x^{2}+2x-440=0\\x^{2}+22x-20x-440=0\\x(x+22)-20(x+22)=0\\(x+22)(x-20)=0\\Either,\\x+22=0\\x=-22\\Or,\\x-20=0\\x=20[/tex]

If x=-22

Then,

x+2 = -22+2 = -20

Or,

x=20

x+2 = 20+2 = 22

Positive integers are 20,22 and negative integers are -22,-20.

Keywords: Integers, Multiplication

Learn more about multiplication at:

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The two consecutive even integers whose product is 440 are 20 and 22. When considered as positive and negative, they are +20 and -20, +22 and -22, respectively.

To find the two consecutive even integers whose product is 440, we need to employ some algebraic reasoning. Let's denote the first of the two consecutive even integers as x.

Given that even integers follow a pattern of +2, we can denote the next consecutive even integer as x + 2.

Hence, we're solving for the equation x * (x + 2) = 440. Solving this equation will give us our consecutive even integers, which are 20 and 22. In terms of positive and negative integers, they would be represented as +20 and -20, +22 and -22, respectively.

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Answer:

x=3

Step-by-step explanation:

2

x

+

3

=

9

We want to find the variable  

x

, so we have to make it alone. To do so, first subtract  

3

from both sides of the equation:

2

x

+

3

−

3

=

9

−

3

2

x

=

6

Now divide both sides by  

2

:

2

x

2

=

6

2

So the final answer is:

x

=

3

Hope this helps!

Answer: x = 3

Step-by-step explanation: To solve for x in the equation you see here, our goal is to get x by itself.

Our first step will be to isolate the term containing x which in this case is 2x. To isolate 2x, we have to get rid of the 3 by subtracting 3 from both sides of the equation.

On the left, the 3's cancel each other out and we are left with 2x. On the right, 9 - 3 simplifies to 6 and we are left with 2x = 6 which is a one step equation.

To get x by itself, since it's being multiplied by 2, we just divide both sides of the equation by 2. On the left, the 2's cancel and we are left with x. On the right, 6 over 2 simplifies to 3.

Therefore, our answer is x = 3.

Answer:

12

Step-by-step explanation:

12 is the smallest number that divisible by 6 and 12

Answer:

x=-3, y=-6. (-3, -6).

Step-by-step explanation:

-9x+7y=-15

-8x+y=18

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

y=18-(-8x)=18+8x=8x+18

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

-9x+7(8x+18)=-15

-9x+56x+126=-15

47x+126=-15

47x=-15-126

47x=-141

x=-141/47

x=-3

-8(-3)+y=18

24+y=18

y=18-24=-6

x=-3, y=-6.

Answer:

x = 51/28

y= 24/7

Step-by-step explanation:

Answer:

(1, 4)

Step-by-step explanation:

Lets show first the inequality. Putting in numbers what greater than one half times x plus 2 means is:

y > (1/2)x + 2

The procedure is simple: take the points and replace them in the inequality to see which verifies.

(1, 4):

4 > (1/2)*1 + 2

4> 1/2+ 2

4 > 1/2 + 4/2

4> 5/2

8/2> 5/2 ---> I verifies!!!

(-1, 1)

1 > (1/2)(-1) + 2

1> -1/2 + 2

1 > -1/2 + 4/2

1 > 3/2 ---> Not verify!!

(2, 3):

2 > (1/2)*2 + 2

2 > 1 + 2

2 > 3 ---> Not verify!!!

(0, 2)

2 > (1/2)*0 + 2

2 > 2 ---> Not verify!!!

So, the only pair that verifies is (1, 4)

Answer:

a. Segment BC is congruent to segment DE

Step-by-step explanation:

Answer:

[tex]f(x)=(2x+1)(2x-1)[/tex].

Step-by-step explanation:

We want to convert the function into the form that let's us easily find the x-intercept, and it would be for the form [tex](ax+b)(cx+d)[/tex] because then we can find the x-intercept in the following manner:

[tex](ax+b)(cx+d)=0[/tex]

[tex]x=-b/a[/tex]

[tex]x=-d/c[/tex]

We factor our function [tex]f(x)=4x^2-1[/tex] and get

[tex]\boxed{f(x)=(2x+1)(2x-1)}[/tex]

Now this form let's us easily find the x-intercepts:

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

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

and so we pick the second choice: f(x)=(2x+1)(2x-1).

Answer:

b

Step-by-step explanation:

Answer:

ONP and JKI

Step-by-step explanation:

exterior angles are the angles on the outside and if your looking for the alternate exterior angle you would go and find the equivalent angle on the opposite side of the bisector or the ray cutting the parallel lines in half

Answer:

Prices of Toys: As we move to the right, toy sales decrease and suddenly jump up to a certain point when advertising begins. advertising lasts for a while, but as soon as it stops, the toy sales go down. X axis is time and y axis is sales in thousands

Step-by-step explanation:

Answer:

P = 28cm

Step-by-step explanation:

First, all four sides of a rhombus are congruent, meaning that if we find one side, we can simply multiply by four to find the perimeter. Second, the diagonals of a rhombus are perpendicular bisectors of each other, thus giving us four right triangles and splitting each diagonal in half.

Answer:

The runner's unit rate is 0.09 miles/minute.

Step-by-step explanation:

Given:

Distance cover by runner = 8 miles and the time taken = 92 minutes.

Now, to calculate the runner's unit rate.

We put the formula to get the unit rate:

Velocity = distance/time

[tex]v=\frac{d}{t}[/tex]

[tex]v=\frac{8}{92}[/tex]

[tex]v=0.0869[/tex]

v = 0.09 miles/minute (approximately)

Therefore, the runner's unit rate is 0.09 miles/minute.

Final answer:

To find the runner's unit rate, divide the total miles (8) by the total minutes (92), resulting in a rate of 0.08695652 miles per minute or 5.217 miles per hour when converted.

Explanation:

The question is asking to find the unit rate of a runner who runs 8 miles in 92 minutes. To find the unit rate, we need to calculate how many miles the runner can run in one minute. This involves dividing the total miles run by the total minutes taken.

Calculation:
Unit Rate = Total Miles / Total Minutes = 8 miles / 92 minutes = 0.08695652 miles per minute.

For practical purposes and better understanding, it might be useful to convert this unit rate into miles per hour. Since there are 60 minutes in an hour, we simply multiply the unit rate per minute by 60.

Miles per hour = 0.08695652 miles/minute * 60 minutes/hour = 5.217 miles per hour.

Therefore, the runner's unit rate is 0.08695652 miles per minute, or equivalently, 5.217 miles per hour.

Answer:

In litres the volume of the pot of soup is 18.93litre

Step-by-step explanation:

This problem seeks to examine our understanding of unit conversion

Step one

Convert quarts to liters

Definition of quart (symbol: qt)

Quart is a unit of volume in the United States customary and imperial systems of measurement. Multiple.

Step two

If 1 qt=0.946353 litre

20qt=x litre

By cross multiplication we have

x litre = 20*0.946353 litre

x=18.93litre

In litres the volume of the pot of soup is 18.93litre

To convert 20 quarts to liters, you would use the conversion factor of 1 liter equating to 1.06 quarts. Following this conversion, the volume of the soup pot would be approximately 18.87 liters.

You're asked about the volume of a soup pot that contains 20 quarts and wants it to be converted to liters. Based on our comparison, 1 liter is approximately equivalent to 1.06 quarts. So to convert from quarts to liters, you'd divide the amount in quarts by the conversion factor.

Here is a step-by-step process to convert 20 quarts to liters:

 Identify the conversion factor: 1 liter = 1.06 quarts

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Answer:

139.5/1 or 1395/10

Step-by-step explanation:

After 3 months, plant A will be 14.2 centimetres tall and plant B will be 12.7 centimetres tall.

Expression in maths is defined as the relation of numbers variables and functions by using mathematical signs like addition, subtraction, multiplication and division.

To find when to plant A will exceed the height of plant B, we need to set up an equation:

Let t be the number of months, then the height of plant A after t months is:

Height of plant A = 4.7 + 3.5t

The height of plant B after t months is:

Height of plant B = 5.2 + 2.5t

We want to find when to plant A will exceed the height of plant B, so we need to solve the equation:

4.7 + 3.5t = 5.2 + 2.5t

Simplifying, we get:

t = 1.0

Therefore, plant A will exceed the height of plant B after 1 month.

To find the heights of the plants after 3 months, we substitute t = 3 into the equations:

Height of plant A = 4.7 + 3.5(3) = 14.2 centimeters

Height of plant B = 5.2 + 2.5(3) = 12.7 centimeters

Therefore, after 3 months, plant A will be 14.2 centimetres tall and plant B will be 12.7 centimetres tall.

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Final answer:

After solving linear equations for growth over time, Plant A will exceed the height of Plant B after 1 month. After 3 months, Plant A will be 15.2 cm tall and Plant B will be 13.7 cm tall.

Explanation:

The question involves two plants with different initial heights and growth rates. To find out when Plant A will exceed the height of Plant B and their heights after 3 months, we can use linear equations.

Calculation for Exceeding Height:

Let x represent the number of months it will take for Plant A to exceed the height of Plant B. The equation for Plant A's height over time is:

Height of Plant A = 4.7 + 3.5x (in centimeters)

The equation for Plant B's height over time is:

Height of Plant B = 5.2 + 2.5x (in centimeters)

To find out when Plant A exceeds Plant B, we set the equations equal and solve for x:

4.7 + 3.5x = 5.2 + 2.5x

Solving for x, we find that x = 1. Therefore, after 1 month, Plant A will exceed the height of Plant B.

Heights After 3 Months:

Height of Plant A = 4.7 + 3.5(3) = 15.2 cm

Height of Plant B = 5.2 + 2.5(3) = 13.7 cm

1/8*3/4

multiply the numerators together

1*3=3

multiply the denominators together

8*4=32

answer:

3/32

Answer:

The answer is 3/32.

Step-by-step explanation:

You multiply 1/8 x 3/4. 1x3 equals 3 so that is the numerator and 8x4 equals 32 so that is the denominator.