Order the steps to show how to solve the system of equations using substitution.

y=6x+1

7x – 2y= –1

Answers

Answer 1

Answer: The correct answer is x=−1/5  and y=−1/5

Step-by-step explanation:

Solve the System by substitution:

y=6x+1 and 7x−2y=−1

Solve y=6x+1 for y:

y=6x+1

Substitute 6x+1 for y in 7x−2y=−1:

7x−2y=−1

7x−2(6x+1)=−1

−5x−2=−1 (Simplify both sides)

−5x−2+2=−1+2 (Add 2 to both sides)

−5x=1

−5x/−5 = 1/−5  (Divide both sides by -5)

x=−1/5

Substitute −1/5 for x in y=6x+1:

y=6x+1

y=6(−1/5)+1

y=−1/5   (Simplify both sides)

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Related Questions

Encuentra el área de la región coloreada.

Answers

12 x 8 = 96
3 x 6 = 18
96 - 18 = 78m

Answer = 78m

Saludos!

1. The cost of bell peppers varies directly with the weight of bell peppers, as shown in the table. Write a direct variation equation to represent this relationship. Then identify the constant of variation and interpret its meaning.

Answers

The constant of variation is 1.75 for every unit increase in x (weight), and the cost(y) value increases by $ 1.75.

What is the equation?

The equation is defined as mathematical statements that have a minimum of two terms containing variables or numbers that are equal.

The difference between two consecutive entries is constant, as we can see = 1.75

⇒ 7 - 5.25 = 1.75

⇒ 8.75-7 = 1.75

⇒ Slope(m) = 1.75

The slope represents the variable's rate of change.

y - 3 = m(x - 5.25)

y - 5.25 = 1.75(x-3)

y = 1.76x

Thus, the constant of variation is 1.75

This indicates that for every unit increase in x (weight), the cost(y) value increases by $ 1.75.

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The question seems to be incomplete the correct question has been attached

The table represents a quadratic function. Write an equation of the function in standard form.

Answers

The equation of the quadratic function in standard form as required in the task content is; f(x) = -x² + 12x - 43.

Standard form equation of a quadratic function.

It follows from the task content that the standard form equation of the quadratic function is to.be determined.

Since the standard form equation can be derived from the vertex form equation as follows;

f(x) = a (x - h)² + k

f(x) = a (x - 6)² - 7

Hence, to find the value of a, Substitute x = 8 and f(x) = -11 so that we have;

-11 = a (8 - 6)² - 7

-11 = 4a - 7

4a = -4

a = -1.

Hence, the equation in vertex form is; f(x) = -1 (x -6)² - 7 and when expressed in standard form we have;

f(x) = -1(x² - 12x + 36) - 7

f(x) = -x² + 12x - 43

Therefore, the required equation in standard form is; f(x) = -x² + 12x - 43.

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Please help ASAP
See Attached!!

Answers

When you add polynomials of different degrees, it is not adding up the degrees, in special cases this may end up with smaller degree polynomials.

When you multiply polynomials of different degrees, it adds up the degrees, and the final polynomial is off the higher degree.

The answers:

a) False, degrees not added,b) False, degrees added but not multiplied.

12) m/GOP = 80°, m/ROP
and m/ROG= 32x + 4. Find x.
R
Q
= 3 +59x,
G

Answers

By using linear pair, we have found that the value of x is 3.

What is linear pair?

Linear pairs of angles are produced when two lines intersect each other at a point. The sum of angles of the linear pair is always 180 degrees.

Given that  Angle QGP = 80°, Angle ROP = 3 + 59x and Angle ROG= 32x + 4. Find x.

Therefore, we can see that Angle ROG and Angle QGP lie in a straight line.

Thus, by linear pair

Angle ROG + Angle QGP = 180

80° + 32x + 4 = 180

32x = 100 - 4

x = 96/32

x = 3

Hence, the value of x is 3.

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Great by is reducing by 250% the regular price of a tally set selling it for $225 the regular price of the tally set is

Answers

The regular price of the tally set is $300.

How to calculate the price?

From the information Illustrated, Great by is reducing by 250% the regular price of a tally set selling it for $225.

Let the regular price be represented by x.

Therefore, x - (25% × x) = 225

x - 0.25x = 225

0.75x = 225

Divide

x = 225 / 0.75

x = 300

The price is $300.

Note that the above percentage in the question is 25% and not 250%.

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A Norman window is a window with a semicircle on top of a regular rectangular window as shown in the diagram. What should the dimensions of the rectangular part of a Norman window be to allow in as much light as possible if there is only 12 ft of the framing material available?

Answers

The dimensions of the rectangular window that gives a maximum area are as follows;

Width = [tex]\dfrac{12}{2+\pi }[/tex] feet and length = 3 feet

What is the maximum value of a function?

The maximum value of a function is given by the point at which the graph of the function has the highest value.

The parameters of the window are;

Length of the framing material available = 12 ft.

The shape of the window = A semicircle on top of a regular rectangular window

Required; The dimension of the rectangular part of the Norman window that allows the most light

Solution;

Diameter of the semicircular part of the window = The width of the rectangular part

Let x represent the width of the window, we have;

Perimeter of the semicircle = π·x/2

Side length of the rectangular window = (12 - π·x/2 - x)/2

Area of the rectangular part of the window, A = x × (12 - π·x/2 - x)/2

Area of the semicircle = π·x²÷4

Area of the window, is therefore;

[tex]A =\dfrac{ x \times (12 - \dfrac{\pi \cdot x}{2} - x)}{2} +\dfrac{ \pi \cdot x^2}{4}[/tex]

At the maximum area, of the rectangular part, we have;

[tex]A_r' =\dfrac{d}{dx}\left( A =\dfrac{ x \times (12 - \dfrac{\pi \cdot x}{2} - x)}{2} \right) = -\dfrac{x\cdot \pi +2\cdot x-12}{2} = 0[/tex]

x·π + 2·x - 12 = 0

The width, x = [tex]\dfrac{12}{2+\pi }[/tex] feet

The length of the rectangle is therefore;

[tex](12 - \pi \cdot \dfrac{6}{2+\pi } - \dfrac{12}{2+\pi })/2 = 6 - \pi \cdot \dfrac{3}{2+\pi } - \dfrac{6}{2+\pi } = 3[/tex]

The length of the rectangular window = 3 feet

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Hector also kept track of the remaining gasoline. The equation shown below can be used to find the gallons of gasoline remaining (g) after distance driven (d)

Answers

The missing values for gallons of gasoline remaining is 11,6,1.

Given that equation shown below can be used to find the gallons of gasoline remaining (g) after distance driven (d).

We want to find the missing values for gallons of gasoline remaining.

The given equation is g=16-(1/20)d

When the distance is 100 then we will find the gallons of gasoline remaining by substituting d=100 in given equation, we get

g=16-(1/20)100

g=16-5

g=11

When the distance is 200 then we will find the gallons of gasoline remaining by substituting d=200 in given equation, we get

g=16-(1/20)200

g=16-10

g=6

When the distance is 300 then we will find the gallons of gasoline remaining by substituting d=300 in given equation, we get

g=16-(1/20)300

g=16-15

g=1

Hence, the missing values for gallons of gasoline remaining when distance 100 is 11, when distance 200 is 6 and when distance 300 is 1.

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Jon can do 64 push-ups in 4 minutes. Paul can do 45 push-ups in 3 minutes. Whose rate is faster?

Answers

Answer:

John's rate is faster than Paul's Step-by-step explanation: John, 64 push-ups/4min = 16 push-ups per minute Paul,

:

A hotel has a budget of $63,750 to repaint the lobby and some hotel rooms. The hotel spent $26,700 on painting the lobby. Each room costs $4,250 to paint. The inequality 26,700 + 4,250n ≤ $63,750 can be used to determine the number of rooms (n) the hotel can repaint.

Which statement about the number of rooms that can be painted is true?

A.
The hotel can repaint 9 rooms.
B.
The minimum number of rooms that can be repainted is 2.
C.
The maximum number of rooms that can be repainted is 2.
D.
The hotel can repaint 2 rooms, but this number is neither the maximum nor the minimum.

Answers

The statement that is true about the number of rooms that can be painted using inequality is; D.

The hotel can repaint 2 rooms, but this number is neither the maximum nor the minimum.

How to solve Inequality Word problems?

We are given;

Budget of hotel to repaint the lobby and some hotel rooms; $63750

Amount spent on painting the lobby = $26700

Cost to paint each room = $4250

Thus, the inequality to represent the given situation is;

26,700 + 4,250n ≤ $63,750

where;

n is number of rooms the hotel can repaint

Subtract 26700 from both sides of the inequality to get;

4250n ≤ 37050

n ≤ 37050/4250

n ≤ 8.717

Since we can't paint only a portion, we leave it as a maximum of 8 rooms

Looking at the given options, the only correct one is option D.

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Bimpe rues 5km per hour faster thean she walk- If she runs for 45 minute and walks for 3 hour.

! BE A GOOD NAJM/ NAJMAH, AL​

Answers

Answer:

See below

Step-by-step explanation:

I think you may have left some info out of your question post, but here is something that may help you:

x = walk speed    km/hr

x + 5 = run speed     km/hr

45 min = 3/4 hr  = .75 hr

(.75)(x+5)      +      3 * x   = total distance   in  km

3.75x + 3.75 = total distance

Find the distance between the two points rounding to the nearest tenth (if necessary).
(-3, 5) and (1,−1)

Answers

[tex]~~~~~~~~~~~~\textit{distance between 2 points} \\\\ (\stackrel{x_1}{-3}~,~\stackrel{y_1}{5})\qquad (\stackrel{x_2}{1}~,~\stackrel{y_2}{-1})\qquad \qquad d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2} \\\\\\ d=\sqrt{(~~1 - (-3)~~)^2 + (~~-1 - 5~~)^2} \implies d=\sqrt{(1 +3)^2 + (-1 -5)^2} \\\\\\ d=\sqrt{( 4 )^2 + ( -6 )^2} \implies d=\sqrt{ 16 + 36 } \implies d=\sqrt{ 52 }\implies d\approx 7.2[/tex]

2.) lee has seven 5-dollar bills and le quarters
in his pocket. How much money would he have
left in his pocket if he buyes a leather jacket
worth $35.20.

Answers

Amount of money left in Lee pocket after he buys a $35.20 leather jacket from the given amount is equal to $1.3.

As given in the question,

Conversion of quarter into dollars is :

1 quarter = 0.25 dollars

Amount of money with Lee in his pocket is equal to :

= ( 7 × 5) dollars + ( 6 × 0.25) dollars

= (35 +1.5) dollars

=$ 36.5

Cost of leather jacket buy by Lee = $35.20

Amount of money left in lee's pockets after purchasing jacket

= $( 36.5 - 35.20)

= $ 1.3

Therefore, amount of money left in Lee pocket after he buys a $35.20 leather jacket from the given amount is equal to $1.3.

The complete question is :

Lee has seven 5-dollar bills and 6 quarters in his pocket. How much money would he have left in his pocket if he buys a leather jacket

worth $35.20?

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pls help ill give brainliest

Answers

Answer:

b= -2

Step-by-step explanation:

This is written in the y=mx+B form. This means that x is our slope, and -2 is our y-intercept (b). This meakes b= -2

-Hope this helped

Answer: x=6.

Step-by-step explanation: First go to the Algebra Calculator.

factorise fully 15x³ + 3x²y​

Answers

Answer: 3x²(5x+y)

Step-by-step explanation:

15x³ + 3x²y​

Apply exponent rule: 15x²x+3x²y

Rewrite 15 as 5*3: 5*3x²x+3x²y

Factor out common terms 3x²: 3x²(5x+y)

Hope this helps!!! :)

a - domain and range
b - intercepts
c - horizontal asymptotes
d - vertical asymptotes
e - oblique asymptotes

Answers

From given graph,

a - domain and range:  (-∞, 3) ∪ (3, ∞)

b - intercepts: x = 0 and y = 0

c - horizontal asymptotes: y = 3

d - vertical asymptotes: x = 3

e - oblique asymptotes: No

In this question, we have been given a graph of a function.

From given graph we need to answer the following questions.

1) domain of function: (-∞, 3) ∪ (3, ∞)

the range of function : (-∞, 3) ∪ (3, ∞)

2) the intercepts:

x = 0, y = 0

3) horizontal asymptotes

A red dotted line y = 3 is a horizontal asymptotes

4) vertical asymptotes

A red dotted line x = 3 is a vertical asymptotes

5) Oblique asymptotes

The graph of function does not have any Oblique asymptotes

Therefore, from given graph,

a - domain and range:  (-∞, 3) ∪ (3, ∞)

b - intercepts: x = 0 and y = 0

c - horizontal asymptotes: y = 3

d - vertical asymptotes: x = 3

e - oblique asymptotes: No

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How many solutions does the equation have?
12x + 6 = 14(2x – 24) because when simplified we get?

a) 6=-6
a) infinitely many solutions
b) x=-6
b) one solution
c) 6=6
c) no solution

Answers

Answer:

One solution: x =21.6

Step-by-step explanation:

Equation

12x + 6 = 14(2x – 24)                    Remove the brackets

Solution

12x + 6 = 28x - 336                      Add 336 to both sides.

12x + 6+336 = 28x - 336             Combine

12x + 342 = 28x -336+336        

12x + 342 = 28x                            Subtract 12x from both sides.

12x-12x + 342 = 28x - 12x             Combine

342 = 16x                                      Divide by 16

342/16 = 16x/16

21.6=x  

a jet left paris and flew toward moscow at an average speed of 410 mph. an air force plane left three hours later and flew in the opposite direction with an average speed of 160 mph. how long does the Air Force plane need to fly before the planes are 3510 miles apart?

Answers

The time the airforce plane needs to before the planes are 3510 miles apart is 8.32 hours.

What is time?

Time is the duration of an event

How to find how long before the planes are 3510 m apart?

Since a jet left paris and flew toward moscow at an average speed of 410 mph. an air force plane left three hours later and flew in the opposite direction with an average speed of 160 mph.

The distance flown by the jet is d = vt where

v = speed of jet = 410 mph and t = time of flight of jet plane

So, d = 410t

Also, the distance flown by the airplane is D = vt' where

v = speed of airplane = 160 mph and t' = time of flight of airforce plane = t + 3 (since it flies 3 hours later)

So, D = 160t'

= 160(t + 3)

Since the total distance apart of the both jet and airplane is D' = d + D, we have

D' = 410t + 160(t + 3)

Given that D = 3510 miles, we have that

410t + 160(t + 3) = 3510

Soving for t, we have

410t + 160t + 480 = 3510

570t = 3510 - 480

570t = 3030

t = 3030/570

t = 5.32 hours

Since t' = t + 3, we have

t' = 5.32 + 3

= 8.32 hours

So, the airforce plane needs to fly for 8.32 hours.

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7/2a+4/2a^2 as a fraction

Answers

Answer:

1/2a (4a+7)

Step-by-step explanation:

First You Divide:7/2a+ 2a^2

Rearrange Terms: 2a^2+ 7/2a

Find the Common Factor: 1/2(4a^2+7a)

Rewrite in the Fraction Form: 1/2a (4a+7)

I know this is the right answer because I learned this in 5th grade.

Please mark me Brainliest!!!

The quotient is a multiple of 4 the dividend is a multiple of 9 the divisior is a factor of 12 possible solution

Answers

67 is not the answers I know this by

Using the quadratic formula to solve 11x2-4x=1, what’s re the values of x

Answers

X 1,2 = 2/11 +- sqrt(15)/11

If a circle has an Area of 84.9056, find the radius and the circumference of the circle.

(Use π=3.14 and do not round.)

Radius =

Circumference =

Answers

The radius = 5.2 and the circumference = 32.656

Answer: Radius is estimated to = 5.2

               Circumference is estimated to = 32.66

Which question can be answered by finding the quotient of 5/6 divided by 1/20?

Answers

The question that can be answered by finding the quotient of 5/6 divided by 1/20 is C. Jared has 5/6 of an hour left to finish making bags. It takes him 1/20 of an hour's to make each bag. How many bags can he make?

How to illustrate the information?

It should be noted that the quotient is the value that is gotten when we divide the numbers given.

In this case, Jared has 5/6 of an hour left to finish making bags. It takes him 1/20 of an hour's to make each bag.

The number of bags will be:

= 5/6 ÷ 1/20

= 5/6 × 20

= 100 / 6

= 17 bags

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Answer:

17 bags

Step-by-step explanation:

List all possible rational roots for the given equation. x^4 - 2 x^2 + 16 x - 15 = 0

Answers

The possible roots for the given equation are, -1,3, -1-2i, -1+2i.

What do you mean by the roots of an equation?

The values of the variable that fulfill the equation are known as the roots of a quadratic equation. In addition, they are referred to as the "solutions" or "zeroes" of the quadratic equation. For instance, x = 2 and x = 5 satisfy the quadratic equation x2 - 7x + 10 = 0 and are hence the roots of the equation.

F(x) = x4-2x2-16x-15 has a root (zero) that you should find.

Finding x values for which F(x)=0 is the goal of the Polynomial Roots Calculator method set.

A tool from the list above is the rational roots test. Only numbers x that can be represented as the quotient of two integers, or rational roots, would be found.

According to the Rational Root Theorem, P and Q are factors of the Leading Coefficient and the Trailing Constant, respectively, if a polynomial zeroes for a rational number P/Q.

The Leading Coefficient is 1 and the Trailing Constant is -15 in this instance.

The component(s) are:

1 is the Leading Coefficient, while 1 is the Trailing Constant.

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y = 3x + 6
What is the gradient?
What is the y-intercept?​

Answers

Answer: Gradient: 3. y-intercept: 6

Step-by-step explanation:

Select the equation of the graph line above. (A) y = x + 5 (B) y = 3x + 5 (C) y = x - 5 (D) y = 3x - 5

Answers

Answer: (D) [tex]y=3x-5[/tex]

Step-by-step explanation:

Using the points (0, -5) and (2, 1), the slope of the line is [tex]\frac{-5-1}{0-2}=3[/tex].

Since the y-intercept is -5, the equation is [tex]y=3x-5[/tex].

Inga is solving 2x2 + 12x – 3 = 0. Which steps could she use to solve the quadratic equation? Select three options. 2(x2 + 6x + 9) = 3 + 18 2(x2 + 6x) = –3 2(x2 + 6x) = 3 x + 3 = Plus or minus StartRoot StartFraction 21 Over 2 EndFraction EndRoot 2(x2 + 6x + 9) = –3 + 9

Answers

Answer:

The answers are:

1. 2(x2 + 6x + 9) = 3 + 18

2. 2(x2 + 6x) = 3

Let's take a look at the first choice:

2(x² + 6x + 9) = 3 + 18

Now, we will multiply 2 with every member of the other multiplier on the left side:

2·x² + 2·6x + 2·9 = 3 + 18

2x² + 12x + 18 = 3 + 18

2x² + 12x - 3 = 18 - 18

2x² + 12x - 3 = 0

Let's take a look at the second choice:

2(x² + 6x) = 3

Now, we will multiply 2 with every member of the other multiplier on the left side:

2·x² + 2·6x = 3

2x² + 12x = 3

2x² + 12x - 3 = 0 Man that was so hard MARK ME Brainilest Thanks Peace

Step-by-step explanation:

A store owner buys sweatshirts for $16 and marks them up 20% to make a profit. The sales tax where his store is located is 7.5%. A customer considers buying one or two sweatshirts from the store. Select all the statements that apply.


One sweatshirt before tax costs $19.20.


One sweatshirt before tax costs $12.80.


The sales tax for two sweatshirts is $1.92.


The sales tax for two sweatshirts is $2.88.


Total cost for two sweatshirts is $41.28.


Total cost for two sweatshirts is $27.52.

Answers

Answer: The correct statements are:

1 SS before tax costs $19.20

Sales tax for 2 SS is $2.88

Total cost for 2 SS is $41.28

Step-by-step explanation:

$16 x 1.20 = $19.20 cost before tax

$19.20 x 0.075 = $1.44 sales tax, one shirt

Sales tax for 2 shirts = $1.44 x 2 = $2.88

Total cost of a shirt = $19.20 + $1.44 = $20.64

Total cost for 2 shirts = $20.64 x 2 = $41.28

Do I need to apply the chain rule when I derive [ln(g(x))]^2?

Answers

To solve the given derivative we need to apply the chain rule.

Given that, [ln(g(x))]².

What is the differentiation?

The process of finding derivatives of a function is called differentiation in calculus. A derivative is the rate of change of a function with respect to another quantity.

The chain rule is a formula that expresses the derivative of the composition of two differentiable functions [tex]f[/tex] and [tex]g[/tex] in terms of the derivatives of [tex]f[/tex] and [tex]g[/tex].

Find the derivative using the chain and power rules.

ln(g²x²)/x

Therefore, to solve the given derivative we need to apply the chain rule.

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30 points for this one man like that is a lot of points

Answers

Answer:

it is a subset where you are going to make sets from that one set

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