Solve the systems by substitution.
y=4x+6
y = 7x

Answers

Answer 1

Answer:

x = 2

y = 14

Step-by-step explanation:

{y = 4x + 6;

{y = 7x;

.

Let's replace y in the second equation with the value given in the 1st equation:

4x + 6 = 7x

4x - 7x = -6

-3x = -6 / : (-3)

x = 2

x = 2y = 4 × 2 + 6 = 8 + 6 = 14


Related Questions

NEED IMMEDIATELY: The circumference of a circular garden is 65.94 feet what is the diameter of the garden is 3.14 for pie and do not round your answer 

Answers

pi x 2r = circ

2r = circ/pi

r = circ /(2 x pi) =  65.94/(2 x 3.14) = 10.5 feet

Write the point-slope form of the line satisfying the given conditions. Then use the point-slope form of the equation to write the slope-intercept form of the equation.
Slope = 4, passing through (-7,6)

Type the point-slope form of the equation of the line.

(Simplify your answer. Use integers or fractions for any numbers in the equation.)

Type the slope-intercept form of the equation of the line.

(Use integers or simplified fractions for any numbers in the equation.)

Answers

Answer:

 y = 7x + 10

Step-by-step explanation:

Use your point-slope form: y- y1 = m (x - x1) to substitute the given information.

    y - 6 = 7(x - (-4))

Then simplify.

     y - 6 = 7(x + 4)

Next, distribute the 7 into the parenthesis which will give you the point-slope form.

     y - 6 = 7x + 28

In order to write it in slope-intercept form, add 6 to both sides.

    y - 6 + 6 = 7x + 4 + 6

Then simplify to write the equation in slope-intercept form.

    y = 7x + 10

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To write the point-slope form of the equation of a line, we use the formula:

y - y1 = m(x - x1)

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

Given that the slope of the line is 4 and it passes through the point (-7, 6), we can substitute these values into the formula to get:

y - 6 = 4(x - (-7))

Simplifying this equation, we get:

y - 6 = 4x + 28

To write the slope-intercept form of the equation, we need to solve for y:

y = 4x + 34

Therefore, the point-slope form of the equation of the line is y - 6 = 4(x + 7), and the slope-intercept form of the equation of the line is y = 4x + 34.

Candice makes bracelets that contain 2 oval-shaped beads and 8 circular-shaped beads.

She has 32 oval-shaped beads and 38 circular-shaped beads.

How many bracelets can she make?

Answers

To make a bracelet, Candice needs 2 oval-shaped beads and 8 circular-shaped beads.

She has 32 oval-shaped beads, which means she can make 32/2 = 16 bracelets using only the oval-shaped beads.

She also has 38 circular-shaped beads, which means she can make 38/8 = 4.75 bracelets using only the circular-shaped beads.

Since Candice cannot make a fractional number of bracelets, the maximum number of bracelets she can make is limited by the number of circular-shaped beads she has. Therefore, she can only make 4 bracelets using the circular-shaped beads.

So, Candice can make a total of 20 bracelets.

The Bells obtain a 30 year $110,000 conventional mortgage at 10% on a house selling for $130,000 their monthly mortgage payment including principal and interest is $957 determine the total amount they will pay for their house 

Answers

Answer:

what is 5+17894874298748

Answer:

Therefore, the total amount the Bells will pay for their house is $344,520.

Step-by-step explanation:

We can start by using the information about the monthly mortgage payment to calculate the total number of payments they will make over the 30-year term:

30 years × 12 months/year = 360 months

So the Bells will make 360 monthly payments of $957. To find the total amount they will pay for the house, we need to multiply the monthly payment by the number of payments:

$957/month × 360 months = $344,520

Therefore, the total amount the Bells will pay for their house is $344,520.

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A shopkeeper had 4 handbags which were of the same cost price. He sold 3 of them at 40% more than the cost price. He sold the fourth handbag at cost price. He received $260 altogether. Find the cost price of each handbag.

Answers

The original cost of each handbag was $50!

You are fencing in a rectangular area of a garden you have only 150 feet of fence do you want the length of the garden to be at least 40 feet you want the width of the garden to be at least 5 feet what is a graph showing the possible dimensions your garden could have? What vegetables will you use? What will they represent? How many inequalities do you need to write?

Answers

Answer:

Length ≥ 40

Width ≥ 5

Perimeter = 2 × (Length + Width)

2 × (Length + Width) ≤ 150

Step-by-step explanation:

To create a graph showing the possible dimensions of the garden, we need to plot the length and width of the rectangular area on the x and y axes, respectively. Since we want the length to be at least 40 feet and the width to be at least 5 feet, we can represent these constraints by the following inequalities:

Length ≥ 40

Width ≥ 5

We also know that the total length of fencing available is 150 feet, which means that the perimeter of the rectangular area must be less than or equal to 150 feet. The perimeter of a rectangle is given by:

Perimeter = 2 × (Length + Width)

So, we can write the inequality representing the perimeter as:

2 × (Length + Width) ≤ 150

To graph the possible dimensions of the garden, we can plot the points that satisfy all three inequalities on the x-y plane.

Regarding the vegetables, it is not clear what vegetables the user would like to plant in the garden. As such, we cannot provide a specific answer to this question.

In summary, we need to write three inequalities to represent the constraints in the problem, and we can graph the solution space using these inequalities.

. Translate parallelogram ABCD 2 units down and plot it. 2. Translate rhombus EFGH 2 units to the left, 4 units down, and plot it. 3. If the coordinates of the vertices of a square LMNO are L(-5,-5), M(-5,-2), N(-2,-2). What are the coordinates for O? 4. If the coordinates of the vertices of a triangle XYZ are X (2,1), Y(4,4) and Z(5,2). Translate the triangle XYZ 4 units down. What are the new coordinates? 5. Write the coordinates down for the following points:

Answers

Answer:

To translate a shape, we need to move all its vertices by the same amount in the same direction. Here are the answers to the three parts of the question:

1. To translate parallelogram ABCD 2 units down, we need to subtract 2 from the y-coordinates of all its vertices. Let's say the original coordinates of the vertices are A(a,b), B(c,d), C(e,f), and D(g,h). Then the new coordinates of the vertices will be A'(a,b-2), B'(c,d-2), C'(e,f-2), and D'(g,h-2). Plot these new vertices to get the translated parallelogram.

2. To translate rhombus EFGH 2 units to the left and 4 units down, we need to subtract 2 from the x-coordinates and 4 from the y-coordinates of all its vertices. Let's say the original coordinates of the vertices are E(a,b), F(c,d), G(e,f), and H(g,h). Then the new coordinates of the vertices will be E'(a-2,b-4), F'(c-2,d-4), G'(e-2,f-4), and H'(g-2,h-4). Plot these new vertices to get the translated rhombus.

3. If the coordinates of the vertices of a square LMNO are L(-5,-5), M(-5,5), N(5,5), and O(5,-5), and we want to translate it 3 units to the right and 2 units up, we need to add 3 to the x-coordinates and subtract 2 from the y-coordinates of all its vertices. The new coordinates of the vertices will be L'(-2,-7), M'(-2,3), N'(8,3), and O'(8,-7). Plot these new vertices to get the translated square.

A line segment is shown on the coordinate grid.

Select all of the numbers that are included within the range of the line segment.

Answers

Without the specific details or an image of the line segment on the coordinate grid, I'm unable to provide you with the specific numbers included in the range.

To help you generally, a line segment is a part of a line with two endpoints, and it is located on a coordinate grid, which is a two-dimensional plane formed by the intersection of horizontal and vertical lines (x and y axes).

To determine the range of the line segment, you need to identify the y-coordinates of the two endpoints.

The range includes all the y-coordinates between those two points, inclusive of the endpoints. To find the range, observe the line segment and note the y-coordinates of both endpoints. Then, list all the numbers (whole or fractional) between those values, including the endpoints themselves.

Once you have the necessary details or an image of the line segment, feel free to ask again, and I'll be happy to help you identify the numbers within the range.

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I just want to know the answer of that question

Answers

Answer:

I think a

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The value of an industrial embroidery machine is decreasing according to the function defined by:

V(t) = 11,700(3)^-0.15

Where t is the number of years since the machine was purchased. What does the y-intercept represent?

A. The value of the machine after 3 years

B. The amount of time it takes for the value of the machine to reach zero

C. The rate at which the value of the machine depreciates

D. The original value of the machine


I think it is A. The value of the machine after 3 years
What do you think?

Answers

To find the y-intercept of a function, we set the independent variable to zero. In this case, we have:

V(0) = 11,700(3)^-0.15

Simplifying this expression, we get:

V(0) = 11,700(1)

V(0) = 11,700

Therefore, the y-intercept of the function is 11,700. This means that when the machine was purchased (i.e., at t = 0), its value was $11,700.

So, the answer is D. The y-intercept represents the original value of the machine.

x>12 on a number graph

Answers

On a number line graph, the inequality X > 12 would be represented as follows:

What is number line?

A number line is a mathematical tool used to represent and visualize numbers, particularly real numbers, in a linear manner.

On a number line graph, the inequality X > 12 would be represented as follows(check attachment)

The line represents all real numbers, with the arrow pointing towards the right indicating that any number greater than 12 is a solution to the inequality. The circle at the end of the line is an open circle, indicating that 12 is not included in the solution set because the inequality is strict, i.e., X is strictly greater than 12.

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Lulu observes that when she dilates a quadrilateral from a center of dilation outside the
quadrilateral, the corresponding sides of the original figure and its dilated image are
parallel. Which statement best explains why this occurs?

Answers

As a result, the original figure's corresponding sides and those of its enlarged image are parallel.

what is quadrilateral ?

A quadrilateral is a closed, two-dimensional form in geometry that has four straight sides. Four sides, four edges, and four angles make up the polygonal shape. The total of a quadrilateral's internal angles is 360 degrees. Kites, squares, rectangles, parallelograms, and trapezoids are examples of quadrilaterals.

given

Each side of the original figure is expanded to meet the dilation scale factor when a quadrilateral is dilated from an outer centre of dilation, and the sides of the dilated image are parallel.

Parallel lines continue to be parallel after scaling because dilatation scales each side of the quadrilateral by a constant factor.

As a result, the original figure's corresponding sides and those of its enlarged image are parallel.

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Jennifer pours 1/3 quart of milk equally into 4 glasses. How much milk, in quarts, does Jennifer pour into each glass?

Answers

Answer:

1 ⅓

Step-by-step explanation:

there 4 glasses and you put ⅓ in each one therefore 4 x ⅓ = 1 ⅓

On Monday, Tuesday, and Wednesday, Cheryl ran 1 miles each day. On Thursday, she ran 2 miles. On Friday,
she ran 3 miles.
How many miles, in total, did Cheryl run for those five days?
Write your answer as a decimal.

Answers

Cheryl ran a total of 8 miles in five days.

1 + 1 + 1 + 2 + 3 = 8

Written as a decimal, this is 8.0 miles.

Simplify |x/3| if x>0

Answers

Answer: -31x

Step-by-step explanation:

|x|31 becomes -x31 which is -31x

which functions are symmetric with respect to the origin? y=arcsinx and y=arccosx

Answers

Function[tex]y = arcsin(x)[/tex]is symmetric with respect to the origin, while function [tex]y = arccos(x)[/tex] is not. This is as inverse sine function is an odd function, while inverse cosine function is an even function.

If [tex]f(-x) = -f(x)[/tex] for all values of x in the function's domain, then the function is symmetric with regard to the origin. In other words, a function is said to be symmetric with regard to the origin if it passes through the origin and has the same shape on each side of the y-axis.

We must substitute -x for x in each function and simplify to find out if the functions [tex]y = arcsin(x)[/tex] and [tex]y = arccos(x)[/tex] are symmetric with respect to the origin.

According to the equation [tex]y = arcsin(x)[/tex], we get:

[tex]-arcsin = arcsin(-x) (x)[/tex]

Because it is odd, the function[tex]y = arcsin(x)[/tex] is symmetric with respect to the origin.

According to the equation [tex]y = arccos(x)[/tex]:

[tex]x(-arccos) = -arccos (x)[/tex]

Because it is not odd, the function[tex]y = arccos(x)[/tex] is not symmetric with respect to the origin.

In conclusion, [tex]y = arccos(x)[/tex]is not symmetric with regard to the origin, but [tex]y = arcsin(x[/tex] is. Due to the fact that the inverse cosine function is an even function, whereas the inverse sine function is an odd function, this is the case.

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The line of its elements from the upper left corner to the lower right of the second order determinant is called?​

Answers

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The line of its elements from the upper left corner to the lower right of the second order determinant is called the main diagonal.

A rain drop hitting a lake makes a circular ripple. If the radius, in inches, grows as a function of time in minutes according to r(t)=15t+2−−−−√
, find the area of the ripple as a function of time. Find the area of the ripple at t=2
.

Answers

The area of the ripple at t=2 is 32π square inches.

What is area ?

Area is the measure of the size of a two-dimensional surface enclosed by a closed boundary, such as a polygon or a circle. It is typically measured in square units such as square meters, square feet, or square inches.

The equation for the radius of the circular ripple is given by r(t) = √(15t+2). The equation for the area of a circle with radius r is A(r) = πr².

Therefore, the area of the ripple as a function of time is given by:

A(t) = π[r(t)]²

Substituting the expression for r(t), we get:

A(t) = π[(√(15t+2))²]

A(t) = π(15t+2)

A(t) = 15πt + 2π

To find the area of the ripple at t=2, we substitute t=2 into the expression for A(t):

A(2) = 15π(2) + 2π

A(2) = 30π + 2π

A(2) = 32π

Therefore, the area of the ripple at t=2 is 32π square inches.

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For f(x)=3x2 +x2,find: {x: f(x)=0}

Answers

By answering the presented question, we may conclude that Therefore, the solution set to the equation f(x) = 0 is {0}.

what is function?

In mathematics, a function seems to be a link between two sets of numbers in which each member of the first set (known as the domain) corresponds to a specific member of the second set (called the range). In other words, a function takes input from one collection and creates output from another. The variable x has frequently been used to represent inputs, whereas the variable y has been used to represent outputs. A formula or a graph can be used to represent a function. For example, the formula y = 2x + 1 depicts a functional form in which each value of x generates a unique value of y.

the equation:

[tex]3x^2 + x^2 = 0\\4x^2 = 0\\x^2 = 0\\x = 0[/tex]

Therefore, the solution set to the equation f(x) = 0 is {0}.

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Help with math problems

Answers

The value of the equation are 1. (-2√3 + 2)(√3 - 5) = -16 + 8√3 2. (5 - 4√5)(-2 + √5) = -30 + 21√. 3. (-2 - 3√5)(5 - √5) = -5 - 17√5. 4. (√5 - √3)(√5 + √3) = 2.

What are expressions and equations?

An expression is a mathematical sentence without the equal sign that can include variables, operators, and integers. Although it can be appraised or simplified, there isn't a single perfect answer. An expression is, for instance, 3x + 2y.

A mathematical statement that has an equal sign and expresses the equivalence of two expressions is called an equation, on the other hand. To determine the values of variables that meet an equality, equations can be solved. One equation is 3x + 2y = 7, for instance.

1. Multiplying (-2√3 + 2)(√3 - 5), we get:

= -2√3 × √3 + (-2√3 × -5) + (2 × √3) + (2 × -5)

= -2√(3 × 3) + 10√3 - 2√3 - 10

= -2(3) + 8√3 - 10

= -16 + 8√3

Therefore, (-2√3 + 2)(√3 - 5) = -16 + 8√3.

2. Multiplying (5 - 4√5)(-2 + √5), we get:

= 5(-2) + 5√5 + (-4√5)(-2) + (-4√5)(√5)

= -10 + 13√5 + 8√5 - 4(5)

= -30 + 21√5

Therefore, (5 - 4√5)(-2 + √5) = -30 + 21√5.

3. Multiplying (-2 - 3√5)(5 - √5), we get:

= (-2 × 5) + (-2 × √5) + (-3√5 × 5) + (-3√5 × -√5)

= -10 - 2√5 - 15√5 + 3(5)

= -5 - 17√5

Therefore, (-2 - 3√5)(5 - √5) = -5 - 17√5.

4. Multiplying (√5 - √3)(√5 + √3), we get:

= (√5 × √5) - (√3 × √3)

= 5 - 3

= 2

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Find all integer solutions of
x+y=3
3xy-z*z=9

Answers

In conclusion, the integer solutions of the given system of equations are [tex]$(x, y, z) = (1, 2, 0)$ and $(x, y, z) = (-1, 4, 0)$.[/tex]

What is the integer?

An integer is a positive, negative, or zero-valued whole number. It is a number without a fractional or decimal component.

To find all integer solutions of the given system of equations:

[tex]x + y &= 3 \[/tex]

[tex]3xy - z^2 &= 9[/tex]

We can start by solving the first equation for one of the variables. Let's solve for y in terms of x:

[tex]x + y &= 3 \[/tex]

[tex]y &= 3 - x[/tex]

Now we substitute this expression for y into the second equation:

[tex]3xy - z^2 &= 9 \[/tex]

[tex]3x(3-x) - z^2 &= 9 \quad \text{Substituting } y = 3-x \[/tex]

[tex]9x - 3x^2 - z^2 &= 9 \[/tex]

[tex]3x^2 + z^2 &= 9x - 9 \[/tex]

[tex]3x^2 - 9x + z^2 &= -9 \quad \text{(1)}[/tex]

Now we will examine equation (1) for integer solutions.

Case 1: [tex]z= 0[/tex]

If  then equation (1) becomes:

[tex]3x^2 - 9x &= -9 \quad \text{(1a)} \[/tex]

[tex]3x(x-3) &= -9[/tex]

Since we are looking for integer solutions, 3x and x-3 must have opposite signs. The possible pairs of factors of -9 with opposite signs are (3,-3) and (-3,3). So we have two possible sets of equations to solve:

The discriminant is negative, there are no integer solutions. Therefore, there are no integer solutions for the original system of equations when [tex]z \neq 0.[/tex]

In conclusion, the integer solutions of the given system of equations are [tex]$(x, y, z) = (1, 2, 0)$ and $(x, y, z) = (-1, 4, 0)$.[/tex]

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The product of eight and two, minus the product of three and four

Answers

Answer:

4

Step-by-step explanation:

The product of eight and two is 8 x 2 = 16.

The product of three and four is 3 x 4 = 12.

So, the expression "the product of eight and two, minus the product of three and four" can be written as:

16 - 12 = 4

Therefore, the answer is 4.

Solve the systems by elimination.
2x + 4y = -16
-2x + 2y = -2

Answers

Answer: (-2,-3)

Step-by-step explanation:

At a real estate​ agency, an agent sold a house for 343000​$. The commission rate is ​7.5% for the real estate agency and the commission rate for the agent is 30​% of the amount the real estate agency gets. How much did the agency make on the​ house? How much did the agent earn in​ commission?

Answers

Answer: The commission rate for the real estate agency is 7.5% of the sale price, which is:

0.075 x 343000 = $25,725

The agent's commission is 30% of the amount the agency gets, which is:

0.3 x 25725 = $7,717.50

Therefore, the real estate agency made $25,725 on the house and the agent earned a commission of $7,717.50.

Step-by-step explanation:

Victoria is 5 years older than her brother Elliot. Let k represent Elliot's age. Identify the expression that can be used to find Victoria's age.

Answers

Answer:

k+5

Step-by-step explanation:

k= Elliot

Victoria is 5 years older than Elliot

=k+5

Let S be the set R^2. Define addition and multiplication operations on S as follows: for all real numbers a,b,c,d,
(a,b)+(c,d) := (a+c,b+d), (a,b)·(c,d):=(bd−ad−bc,ac−ad−bc).
(a) Prove the right distributive law for S.
(b) What is the multiplicative identity element for S? Explain how you found it. (c)Using (b), prove the multiplicative identity law for S.

Answers

(a) The right distributive law is proven for S.For S, this is expressed as (a,b)·(c,d)=(a,b)·(c,d)=(a·c,a·d+b·c).

(a,b)·(c,d)=(bd−ad−bc,ac−ad−bc)=(a·c,a·d+b·c).

(b) we can deduce that x=1 and y=0. Hence, the multiplicative identity element for S is (1,0).

(c) For S, this is expressed as (a,b)·(1,0)=(a,b). Let (a,b) be an arbitrary element in S. The multiplicative identity law is proven for S.

What is distributive law?

The right distributive law states that the product of a scalar and a vector is equal to the sum of the products of the scalar with each component of the vector.

(a) For S, this is expressed as (a,b)·(c,d)=(a,b)·(c,d)=(a·c,a·d+b·c).

To prove this, we need to show that (a,b)·(c,d)=(a·c,a·d+b·c).

Let (a,b) and (c,d) be two arbitrary elements in S. Then,

(a,b)·(c,d)=(bd−ad−bc,ac−ad−bc)

=(a·c,a·d+b·c).

Therefore, the right distributive law is proven for S.

(b) The multiplicative identity element for S is (1,0). To find this, we need to find a pair of elements (x,y) such that (a,b)·(x,y)=(a,b).

Let (x,y) be an arbitrary pair of elements in S. Then,

(a,b)·(x,y)=(ax−by,ay+bx)

=(a,b).

From this, we can deduce that x=1 and y=0. Hence, the multiplicative identity element for S is (1,0).

(c) The multiplicative identity law states that the product of a scalar and the multiplicative identity element is equal to the scalar itself. For S, this is expressed as (a,b)·(1,0)=(a,b).

To prove this, we need to show that (a,b)·(1,0)=(a,b).

Let (a,b) be an arbitrary element in S. Then,

(a,b)·(1,0)=(a·1−b·0,a·0+b·1)

=(a,b).

Therefore, the multiplicative identity law is proven for S.

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Luther Williams’ charge account statement shows an unpaid balance of $3,987.11. The monthly finance charge is 1.75 percent of the unpaid balance. What is the new account balance? Show your work.

Answers

By adding  the monthly finance charge to the unpaid balance, the new account balance is $4,056.91.

What is addition?

Addition is a mathematical operation that involves combining two or more numbers to produce a sum or total. It is commonly denoted by the plus sign (+) and is one of the four basic arithmetic operations.

To find the new account balance, we need to add the monthly finance charge to the unpaid balance.

First, we need to calculate the monthly finance charge:

Monthly finance charge = 1.75% of unpaid balance

= 0.0175 * $3,987.11

= $69.80

Next, we add the monthly finance charge to the unpaid balance:

New account balance = Unpaid balance + Monthly finance charge

= $3,987.11 + $69.80

= $4,056.91

Therefore, the new account balance is $4,056.91.

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Which number line shows ï > 7? A B 0 1 2 3 4 5 6 7 8 9 10 * 0 1 2 3 4 5 6 7 8 9 10 OF A → B Submit​

Answers

Answer:

The number line that shows ï > 7 would be from 8 to 10, as the symbol > means greater than. So the correct answer is B. Submit B.

Need help
40 points!! I’m

Answers

Answer:

1 shorter than 2 longer than 3 short

Someone help me with this pls!!!

Answers

Answer:
8. A) 3.75

9. B) 5.00

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