The lowest recorded temperature in a town was 4ºF, without the windchill. With the wind, the temperature felt like 10ºF below zero. On a number line, what is the distance between the two temperatures?

Answer:

Steps 1 and 2

Step-by-step explanation:

Henry applied the distributive property between steps 1 and 2.

The distributive property states that a(b + c) = ab + ac. In step 1, Henry used the distributive property to expand -3(x + 2) and 5(x - 7). This is evident when we rewrite step 1 using the distributive property:

Step 1 (using distributive property):

-3(x + 2) = -3 * x + (-3 * 2) = -3x - 6

5(x - 7) = 5 * x + (5 * -7) = 5x - 35

After applying the distributive property, Henry was able to simplify the equation and move on to step 2. The distributive property is a fundamental property in algebra that helps us expand expressions and make solving equations more manageable. In this case, it allowed Henry to eliminate the parentheses and combine like terms, bringing him closer to solving for the variable x.

Overall, the distributive property played a crucial role in transforming the original equation in step 1 into a simpler form in step 2, enabling Henry to continue solving the equation until he found the value of x in step 5.

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Complete Question

Choose the correct answer form the given options :

Select the correct answer

Henry used these steps to solve an equation:

Step 1: -3(x + 2) = 5( x - 7)

Step 2: -3x - 6 = 5x - 35

Step 3: -8x - 6 = -35

Step 4: -8x = -29

Step 5: x = 29/8

Between which two steps did Henry apply the distributive property?

steps 1 and 2

steps 2 and 3

steps 3 and 4

steps 4 and 5

Answer:

B, between 2.8 and 2.9

Step-by-step explanation:

it is exactly 2.828427125

Answer:

no slope

Step-by-step explanation:

Answer:

80

Step-by-step explanation:

This is a combination question that contains multiple clothing items and to solve such question we multiply the given numbers :

5 × 4 × 4 = 80

Answer:

1290

Step-by-step explanation:

15 x 86 = 1290

Answer:

10,120

Step-by-step explanation:

Answer:

x = 2

Step-by-step explanation:

AC = BC

5x = 10

x = 2

Answer:

Number of nickels = 6

Number of dimes = 14

Number of quarters = 23

Step-by-step explanation:

Total number of coins = 43

Let number of nickels = n

Let number of dimes = d

Let number of quarters = q

[tex]n+d+q=43 ...... (1)[/tex]

Money in n nickels = [tex]n \times 0.05[/tex]

Money in d dimes = [tex]d \times 0.10[/tex]

Money in q quarters = [tex]q \times 0.25[/tex]

Total money = $7.45

[tex]0.05n +0.10d+0.25q = 7.45\\\Rightarrow 5n +10d+25q = 745 .... (2)[/tex]

The sum of the numbers of nickels and dimes is 3 less than the number of quarters.

i.e.

[tex]n+d=q-3[/tex]

Let us put the value  in (1):

[tex]q-3+q=43\\\Rightarrow 2q= 43+3\\\Rightarrow q =23[/tex]

Putting the value of q in (1) and (2):

n+d = 20 .... (3)

[tex]5n+10d+575 =745\\\Rightarrow 5n+10d =170\\\Rightarrow n+2d =34 .... (4)[/tex]

(4) - (3):

d = 14

Now, from (3):

n = 6

Number of nickels = 6

Number of dimes = 14

Number of quarters = 23

Answer:

o45

Step-by-step explanation:

Because 45 is the largest number.

Answer:

[tex] \boxed{ \bold{ \huge{ \boxed{ \sf{65.51\% \: }}}}}[/tex]

Step-by-step explanation:

Given,

Cost price of a car ( CP ) = $ 29,000

Selling price of a car ( SP ) = $ 10,000

Since , SP < CP, there is a loss.

Loss % = ?

First, Finding the loss amount

⇒[tex] \boxed{ \sf{loss = cost \: price \: - selling \: price}}[/tex]

⇒[tex] \sf{loss = 29000 - 10000}[/tex]

⇒[tex] \sf{loss = 19000}[/tex]

Loss amount = Rs 19000

Finding the loss %

[tex] \boxed{ \sf{loss \: percent = \frac{loss}{cost \: price} \times 100\%}}[/tex]

⇒[tex] \sf{loss \: \% \: = \frac{19000}{29000} \times 100\%}[/tex]

⇒[tex] \sf{loss \: \% \: = \: 65.51 \: \%}[/tex]

Loss percent = 65.51 %

Hope I helped!

Best regards!!

Answer:

- 56

Step-by-step explanation:

JT = CJ + CT

4x + 2 = 8x + 5 + 55

4x + 2 = 8x + 60

4x - 8x = 60 - 2

- 4x = 58

x = 58/-4

x = -29/2

x = - 14.5

JT = 4x + 2 = 4(-14.5) + 2 = - 58 + 2 = - 56

Part A

The equation would be y = 12x+200 where x is the number of hours and y is the amount saved. The 200 is what you already have, and then you add on 12x additional dollars.

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Part B

equation would be y = -0.10x+12. You start off with 12 gallons and each time you use up 0.10 gallons of gas for each mile you drive, so in total you use up 0.10x gallons

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Part C

Equation is y = 2x+60. You add on 2x additional points to the 60 you already have

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Part D

x is the number of messages and y is the total monthly bill, so the equation would be y = 0.25x + 35

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Part E

eating x cookies, at 120 calories a piece, means y = 120x is the total number of calories you consume per day. This is just considering the cookies of course and not other meals.

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In each case, the independent variable is the variable that is allowed to change and you know this value (or are given it). For instance, you know how many miles you drive and it varies. The dependent variable relies on the value chosen for the independent variable. So as x changes, then so does y.

Answers & Step-by-step explanation:

Let's define the two terms that we need to identify:

Independent variable: A variable that you have control over.

Dependent variable: A variable you cannot control and depends on other factors.

Let's solve your problems!

___________________________________________________________

Amount saved: dependent variable

Amount earned: independent variable

Explanation:

The amount you can save depends on how much you earn.

___________________________________________________________

Amount of gas: dependent variable

Amount you drive: independent variable

Explanation:

The amount of gas you have affects how much you can drive.

___________________________________________________________

Test grade: dependent variable

Extra credit you gain: independent variable

Explanation:

Your test grade is dependent on the amount of extra credit you earn.

___________________________________________________________

Monthly bill: dependent variable

Number of texts sent: independent variable

Explanation:

The monthly bill is dependent on the number of texts sent.

___________________________________________________________

Amount of calories per day: dependent variable

Amount of cookies eaten: independent variable

Explanation:

The number of calories eaten each day is dependent on how many cookies you eat.

___________________________________________________________

Answer:

D: an endpoint at one end and an arrow on the other or answer hope this helped,

Step-by-step explanation:

Answer:

D

Step-by-step explanation:

A line segment has an endpoint at both ends. A has arrows at both ends.A ray has a endpoint at one end and an arrow at the other.

Answer: Juanita

Step-by-step explanation: The question is referring to ratios of the lemon flavor. Juanita's lemonade is 4:2 and Lydia's is 5:3. 4:2 is a larger ratio than 5:3, so that means that Juanita's recipe has a higher concentration of lemon flavor.

Answer:

i believe it should be E

Step-by-step explanation:

domain is x

range is y

since x is the number of days (0-30) the domain would be [0,30]

for y since she is decreasing 40 every two days that would be 15 days x 40 calories which is 600 (on 30th day)

subtract 600 from 2500 = 1900

so the range would be [1900,2500]

Answer:

Step-by-step explanation:

We can simplify (cross multiply) to get [tex]xy^2=wz[/tex]

Then we easily simplify to get [tex]y=\sqrt{\frac{wz}{x}},\:y=-\sqrt{\frac{wz}{x}};\quad \:w\ne \:0,\:x\ne \:0[/tex]

Answer:

4(5+3)

Step-by-step explanation:

I just did this question and I got it correct trust me ;)

Answer:

4(5 + 3)     (C or 3)

Step-by-step explanation:

Edge 2020

Answer:

x = 18

Step-by-step explanation:

Given:

Finding x for which 3b = 5a:

Answer:

x = 18

Step-by-step explanation:

Plug in 4x-7 for b and 2x+3 for a in 3b = 5a

3(4x-7) = 5(2x +3)

Solve for x:

12x-21 = 10x+15

2x = 36

x=18

Answer:

the answer is 12z-2

Step-by-step explanation:

hope it help

Answer:

12z-2

Step-by-step explanation:

We are given the expression:

10z+2z-2

and asked to combine like terms.

First, let’s analyze each term.

10z : has the variable “z”

2z : has the variable “z”

-2 : does not have a variable

The like terms in this expression are the 2 terms with the variable “z”. Add the 2 terms, 10z and 2z.

10z + 2z -2

(10z+2z)-2

(10+2)z-2

(12)z -2

(12z)-2

12z-2

The expression 10z+2z-2 when simplified is 12z-2.

Answer:

27m3- is the answer equals to 8n 3

Answer:

d=126 degrees

z=28 units

Answer:

It's 11

Step-by-step explanation:

Answer:

11

Step-by-step explanation:

divide 121 by 11 then boom, there u go

Answer:

[See Below]

Step-by-step explanation:

3/4 = 0.75

1/3 = 0.333..

5/8 = 0.625

Largest to Smallest: 3/4, 5/8, 1/3

Answer:

62

Step-by-step explanation:

JL = JK + KL

5x + 2 = 3x - 1 + 27 add like terms

5x + 2 = 3x + 26

2x = 24

x = 12

JL = 12 × 5 + 2

JL = 62

Answer:

(3,11)

Step-by-step explanation:

we find the vertex of

[tex]g(x)=|x-3|[/tex] which is going to be (x,0)

and we add 11 (movement upward) so the vertex is (x,11)

vertex of g(x)

it is going to be when g(x)=0

and that only happens when x=3

so vertex (3,0)

so vertex of f(x)

(3,11)

if you don't believe i leave you the graph

Answer:

Y= - [tex]\frac{38}{9}[/tex] or -4.222...

Step-by-step explanation:

-5=y-[tex]\frac{7}{9}[/tex]

y=[tex]\frac{7}{9}[/tex]-5

y= [tex]\frac{7}{9} - \frac{45}{9}[/tex]

y = - [tex]\frac{38}{9}[/tex]

y= about -4.222...

Answer:

A. (5,2)

Step-by-step explanation:

If you go to solve the equation you would first try to get y by itself in the first equation and you would do that by subtracting x on both sides. Then you would have y=7-x and then you would plug the second equation in for the x and get the equation y=7-y-3 because you distribute the negative sign of the x to both the y and 3. Then you combine like terms and get y=4-y and then add the y to both sides and get 2y=4 and then divide both sides by 2 and get y=2. Then you plug in y in the first equation and get x+2=7. Then you subtract 2 from both sides and get x=5.

Answer:

z < 2

Step-by-step explanation:

4z - 5 < 3

4z < 8

z < 2

Answer:

Step-by-step explanation:

We are given that the factory produces  42,000  computer monitors per day

And the claim is of this amount produces fewer than 660 are defective.

a random sample shows that of 240 monitors 2 are defective

to verify the factory managers claim we need to know how many 240s are there in 42000

=42000/240= 175

Since each 240 will give 2 defective monitors

175 will give= 175*2= 350

350 is less than 660 hence the managers claim is correct