to solve the equation 3x-7=x-2, Alex says the first step is to subtract x from both sides. Danny says the first step is to add 7 to both sides.
a.Solve the equation using Alex's method of first subtracting x from both sides.

b.Solve the equation using Danny's method of first adding 7 to both sides.

c.Who is correct, Alex or Danny? Justify your answer.

d. Is there another correct first step for solving this equation? If so, identify it and use it to solve the equation. If not,explain why not.

Answer:

[tex]y=0.25x[/tex]

Step-by-step explanation:

We are given that a graph which shows the relationship between the late fines the library charges and the number of days late.

From given graph we can see that

The graph passes through the points (2,0.5)  and (10,2.5).

We have to find the equation for the relationship.

Slope formula:[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]

By using the formula

Slope of graph=[tex]m=\frac{2.5-0.5}{10-2}[/tex]

Slope of graph=m=[tex]\frac{2}{8}=\frac{1}{4}[/tex]

Point slope- form:[tex]y-y_1=m(x-x_1)[/tex]

We have [tex]y_1=2.5,x_1=10[/tex]

Substitute the values then we get

The equation of for the relationship

[tex]y-2.5=\frac{1}{4}(x-10)[/tex]

[tex]y-2.5=0.25x-2.5[/tex]

[tex]y=0.25x-2.5+2.5=0.25x[/tex]

Hence, the equation for the relationship is given by

[tex]y=0.25x[/tex]

[tex]\bf y = 3x - 5\qquad \qquad \boxed{(\stackrel{x}{1}~~,~~\stackrel{y}{?})}\qquad \qquad y = 3(\stackrel{x}{1})-5\implies y = -2 \\\\[-0.35em] ~\dotfill\\\\ ~\hfill (1,-2)~\hfill[/tex]

Answer:

There is not much that can be done to figure out how to write 0.1875 as a fraction, except to literally use what the decimal portion of your number, the .1875 , means. Since there are 5 digits in 1875 , the very last digit is the "100000th" decimal place. So we can just say that .1875 is the same as 1875/100000.

Step-by-step explanation:

Answer:

fraction decimal

3/16   0.1875

hope this helps :3 & sorry if its wrong

Answer:

227.4 miles

Step-by-step explanation:

If Hong travelled 37.9 each day, then in 6 days :

37.9 × 6 = 227.4 miles

Answer:

227.4 miles  hope this helps :3

Answer:  7) vertex = ∠H       sides = HG and HI

                8) ∠H, ∠IHG, ∠GHI, ∠4

                9) ∠HVI, ∠HVJ, ∠IJV

NOTES:

1) The vertex is the point where the two segments, rays, or lines connect.

2) When naming an angle, the vertex is ALWAYS written in the middle with the sides on the left and right.

The expression 28(15+9) can be simplified and rewritten using the distributive property as Option D. 28 x 15 + 28 x 9. This is the correct equivalent expression.

To determine which expression is equivalent to 28(15+9), we should first simplify the expression inside the parentheses:

Step 1: Simplify inside the parentheses: 15 + 9 = 24.

Step 2: Multiply by 28: 28 x 24.

Now, let's break it down further:

Using distributive property: 28(15+9) can be rewritten as 28 x 15 + 28 x 9, which will result in distributive multiplication.

Therefore, the equivalent expression is Option D.  28 x 15 + 28 x 9.

Complete question:

Which expression is equivalent to 28(15+9) ?

A. 28 + 15 x 28 +9

B. 28 x 15 +9

C. 28 + 15 + 28 +9

D. 28 x 15+28 x 9

Answer:

Cost of one roll of plain wrapping: [tex]\$5[/tex]

Cost of one roll of holiday wrapping paper:  [tex]\$19[/tex]

Step-by-step explanation:

Let be "p" the cost in dollars of one roll of plain wrapping paper and "h" the cost in dollars of one roll of holiday wrapping paper.

Based on the information given, we can set up this system of equations:

[tex]\left \{ {{5p+13h=272} \atop {11p+16h=359}} \right.[/tex]

In order to solve it, we can use the Substitution method. The steps are:

1. Solve for "p" from the first equation:

[tex]5p+13h=272\\\\5p=272-13h\\\\p=\frac{272-13h}{5}[/tex]

2. Substitute the above into the second equation and solve for "h":

[tex]11(\frac{272-13h}{5})+16h=359\\\\598.4-28.6h+16h=359\\\\-12.6h=359-598.4\\\\h=\frac{-239.4}{-12.6}\\\\h=19[/tex]

3. Substitute the value of "h" into [tex]p=\frac{272-13h}{5}[/tex]:

[tex]p=\frac{272-13(19)}{5}\\\\p=5[/tex]

Kim is 16 and her sis is 8 because 8+8 equals 16 and 8+16 equals 24

Answer:

13 and 23

Step-by-step explanation:

create an equation to solve:

(2x-3) + x = 36

3x - 3 = 36 combine like terms

+3 +3 add 3 to both sides

3x = 39

3 3 divide both sides by 3

x = 13

13 is the first number

the 2nd number is 3 let than twice the first so we create and solve a new equation:

2x - 3 = ?

2(13) = ? substitute 13 from the

smaller number to solve

23 = the 2nd number

Answer:

30

Step-by-step explanation:

Substitute the given values for y and z into the expression

zy + 4y = (2 × 5) + (4 × 5) = 10 + 20 = 30

Answer:30

Step-by-step explanation:2x5+4x5=30

Answer:

if x=2 (r) then 2x+1=5

Step-by-step explanation:

Considering an "if and if only" type of function then the answer is A. if x=2 then 2x+1=5

Answer:

√3 is greater than 1/3:

√3 = about 1.7

1/3 = about .3

The square root of 3 is greater than 1/3.

To determine which of the two real numbers is greater, we can compare their values directly. The square root of 3 is a well-known irrational number, and its approximate value is 1.732. On the other hand, 1/3 is a rational number with a value of approximately 0.333.

Let's compare the two:

- The square root of 3: [tex]\sqrt(3)[/tex]  = 1.732

- One third: 1/3 = 0.333

It is clear that 1.732 (the approximate value of √3) is greater than 0.333 (the approximate value of 1/3). Therefore, the square root of 3 is greater than 1/3.

Answer:

Step-by-step explanation:

continuing from the 3rd line....

10x - 1 = 10x + 8     (subtract 10x from both sides)

10x - 10x - 1 = 10x -10x + 8

-1 = + 8   (this last line is not part of the solution but i'm showing it here so you can see what is going on, obviously -1 cannot be 8)

Since   -1  ≠ 8, the equation has no (i.e zero) solutions

Greatest revenue = Company D with 6.8 x 10^7

Least revenue = Company C with 9.0 x 10^4

Difference = 6.8 x 10^ 7 - 9.0 x 10^4

= 68000000 - 90000

= 6.79 x 10^7

Answer is D

The difference in revenue between the company with the greatest revenue and the one with the least revenue is  6.79 x [tex]10^7[/tex]

Option D is the correct answer.

We have,

From the table,

D has the greatest revenue.

C has the lowest revenue.

Now,

D revenue = 6.8 x [tex]10^7[/tex]

C revenue = 9 x [tex]10^4[/tex]

The difference in revenue between the company with the greatest revenue and the one with the least revenue.

= 6.8 x [tex]10^7[/tex] - 9 x [tex]10^4[/tex]

= 67910000

= 6791 x [tex]10^4[/tex]

= 6.79 x [tex]10^7[/tex]

Thus,

The difference in revenue between the company with the greatest revenue and the one with the least revenue is D. 6.79 x [tex]10^7[/tex]

Learn more about expressions here:

https://brainly.com/question/3118662

#SPJ3

Answer:

Step-by-step explanation:

four hundred one thousand, three hundred seventy-eight

Answer:

three hundred and six billion, four thousand, two hundred and ten

10!

There's two halves in a whole. So we could do 5 x 2 to get our answer. Hope this helps!

Answer:

see the explanation

Step-by-step explanation:

Let

x ----> the price of the shirt

y ---> he price of the pants

we have that

The price of three shirts plus the price of two paints must be equal to $300

so

[tex]3x+2y=300[/tex]

This is the equation of the line in standard form

Convert to slope intercept form

[tex]y=mx+b[/tex]

Isolate the variable y

[tex]3x+2y=300[/tex]

subtract 3x both sides

[tex]3x+2y-3x=-3x+300[/tex]

[tex]2y=-3x+300[/tex]

Divide by 2 both sides

[tex]y=-1.5x+150[/tex] ----> equation of the line in slope intercept form

Find out the x-intercept

Remember that the x-intercept is the value of x when the value of y is equal to zero

In this problem, the x-intercept is the price of the shirt when the price of the paints is equal to zero

Using the Standard Form, identify the x-intercept of the graph

The standard form is

[tex]Ax+By=C[/tex]

The x-intercept is C/A

we have

[tex]3x+2y=300[/tex]

so

[tex]300/3=100[/tex]

The x-intercept is the point (100,0)

That means---> The price of the shirt is $100 when the price of the paints is equal to $0

Alternative method to find out the x-intercept (equation in slope intercept form)

[tex]y=-1.5x+150[/tex]

For y=0

[tex]0=-1.5x+150[/tex]

solve for x

[tex]1.5x=150[/tex]

[tex]x=\$100[/tex]

The x-intercept is the point (100,0)

Answer:

you should give the person who first answered this brainliest

Step-by-step explanation:

Good morning ☕️

______

Answer:

She is 20 years old

____________________

Step-by-step explanation:

Let x be the age of the daughter.

Let y be the age of the mother.

then , we have to solve the system:

y=2x (1)

y+20=1.5(x+20) (2)

If we substitute y by 2x in the second equation we get :

(2) 2x+20=1.5(x+20) ⇔ 2x+20=1.5x+30 ⇔ 2x-1.5x=30-20

⇔ 0.5x=10 ⇔ x=20.

By the way the mother’s s age = 40 years.

:)

Answer:

A = 3244

B = 864

C = 3080

Step-by-step explanation:

 700 + a = 3944

 -700          -700

a = 3244

 3944 - b = c - 80 = 3000

c - 80 = 3000

  +80       +80

c = 3080

3944 - b = c ---> 3944 - b = 3080

                          -3944        -3944

                               -b = -864 --->  [tex]\frac{-b}{-1} = \frac{-864}{-1}[/tex]

The solution to the system of equations is:

a= 2380,

b= 864

c= 3080

The given equations are:

1. [tex]\(700 + a = 3944 - b\)[/tex]

2. [tex]\(3944 - b = c - 80\)[/tex]

3. [tex]\(c - 80 = 3000\)[/tex]

From equation 3, we can solve for [tex]\(c\)[/tex]:

[tex]\[c - 80 = 3000\][/tex]

Adding 80 to both sides:

[tex]\[c = 3080\][/tex]

Now, substituting this value of [tex]\(c\)[/tex] into equation 2:

[tex]\[3944 - b = 3080\][/tex]

Solving for [tex]\(b\)[/tex] :

[tex]\[b = 3944 - 3080\]\\b = 864\][/tex]

Finally, substituting the values of [tex]\(b\)[/tex] and [tex]\(c\)[/tex]  into equation 1:

[tex]\[700 + a = 3944 - 864\]\\700 + a = 3080\][/tex]

Solving for [tex]\(a\)[/tex]:

[tex]\[a = 3080 - 700\]\\a = 2380\][/tex]

So the solutions for the variables are [tex]\(a = 2380\), \(b = 864\), and \(c = 3080\)[/tex].

For such more question on equations

https://brainly.com/question/2972832

#SPJ12

Answer:

PW = 11

Step-by-step explanation:

Given that the triangles are similar then the ratio of corresponding sides are equal, that is

[tex]\frac{RQ}{WV}[/tex] = [tex]\frac{RP}{PW}[/tex] ← substitute values

[tex]\frac{12}{6}[/tex] = [tex]\frac{22}{PW}[/tex] ( cross- multiply )

12PW = 132 ( divide both sides by 12 )

PW = 11

Answer:

C. 32 cm³

Step-by-step explanation:

[tex] {a}^{2}\frac{h}{3} = V[/tex]

[tex]({4})^{2}( \frac{6}{3}) = (16)(2) = 32[/tex]

a → length\base edge

I am joyous to assist you anytime.

Answer:

Step-by-step explanation: To find the area of the pyramid shown, we can first start by finding the area of the base. To find the area of the base, we can multiply the length by the width. Notice that both the length and the width of a square are equal so the area of a square will be equal to the length of a side multiplied by the length of a side.

Area = Length x Width = (side) (side)

Area = Side²

(4 cm²) = 16 cm².

Therefore, the area of the bases is 16 cm².

Now, let's finish the problem.

Image provided.

Answer:

34,879 × 10 = 348,790

Step-by-step explanation:

The answer is 348,790 because 34,879 multipled by 10 is 348,790 as shown in the picture above ^^

Answer:

348790

Step-by-step explanation:

According to the Power of 10 rule, whenever you divide by 10 [⅒], you move the decimal mark to the left each time, and of course, whenever you multiply by 10, you move the decimal mark to the right each time. In this case, the decimal mark is just after the 2, so multiplying by 10 will add a zero to the number, making it 348790 [three forty-eight thousand, eight hundred seventy-nine].

I am joyous to assist you anytime.

Answer:

Undefined

Step-by-step explanation:

The slope of a line parallel to the line x = 5 is undefined because the line would be a straight vertical line. Vertical lines don't have a slope because it is impossible to measure rise/run. Hope this helps!

The corresponding composite function for (f∘g)(x) include the following: (f∘g)(x) = 4 - 15x.

In Mathematics and Geometry, a function composition is an operation (∘) that combines two functions f(x) and g(x), in order to produce a composite function h(x) = (g∘f)(x), such that h(x) = g.

In this exercise, we would determine the corresponding output values for the given composite function by using the substitution method as follows;

f(x) = 3x + 1

g(x) = 1 - 5x

(f∘g)(x) = 3(1 - 5x) + 1

(f∘g)(x) = 3 - 15x + 1

(f∘g)(x) = 4 - 15x.

Complete Question:

Let f(x)=3x+1 and g(x)=1-5x. Find (f∘g)(x).

Answer:

Option b) (-26,-5)

Step-by-step explanation:

We are given the following information in the question.

The x-coordinate changes from -21 to-16. Thus its value increases 5 units.

The y -coordinate changes from -9 to -13. Thus, it decreases by a value of 4 units.

So to obtain the coordinates in the box:

x-coordinate

We decrease 5 units from -21 that is -21 - 5 = -26

y- coordinate

We add 4 units to -9 that is -9 + 4 = -5

So, the coordinates in the box is given as:

Option b) (-26,-5)

Answer:

w=4

Step-by-step explanation:

2(48)+2(8w)+2(6w)=208

1) Start by Distributing the value outside of the parenthesis:

96+16w+12w=208

2) Combine alike terms:

96+28w=208

3) Subtract 96 from both sides:

28w=112

4)Divide both sides by 28 to isolate w:

w=4

Let me know if you do not understand :)

Answer:

it's associatively property of addition

(a+b)+c= a+(b+c)

Answer:

21

Step-by-step explanation:

It might be 21/30 , hope it helps though :)

Answer:

21 is the un known value.

Step-by-step explanation:

10 times 3=30

7 times 3 = 21

so 21/30 is your answer.

Answer:

Step-by-step explanation:

41:2

41:43

This is because the question wants the number of burgers with onions to the total amount of burgers. The question already states 41 have onions. It also states the total amount of burgers is 43. Therefore, your answer is 41:43.