Write a system of linear equations.Write two-variable equations in slope-intercept form.

Write A System Of Linear Equations.Write Two-variable Equations In Slope-intercept Form.

Answers

Answer 1

Answer:

A linear relation can be written in the slope-intercept form as:

y = a*x + b

Where a is the slope, and b is the y-intercept.

And if a line passes through the points (x₁, y₁) and (x₂, y₂), the slope can be written as:

a = (y₂ - y₁)/(x₂ - x₁)

Now let's look at our lines.

The left one passes through the points (0, -3) and (-2, 0)

Then the slope of this line is:

a = (0 - (-3))/(-2 - 0) = 3/-2 = -(3/2)

Then the line will be something like:

y = -(3/2)*x + b

Knowing that this line passes through the point (0, -3), we know that when x = 0, we must have y = -3

Then:

-3 = (-3/2)*0 + b

-3 = b

So the first linear equation is:

y = -(3/2)*x - 3

Now let's look at the second line, this one passes through the points (0, 2) and (1, 0)

Then the slope of this line is:

a = (0 - 2)/(1 - 0) = -2

And we can write the line as:

y = -2*x + b

Knowing that this line passes through the point (0, 2), we know that when x = 0 we must have y = 0, replacing that we get:

2 = -2*0 + b

2 = b

Then the equation of this line is:

y = -2*x + 2

Now that we know both equations we can write our system as:

y = (-3/2)*x - 3

y = -2*x + 2

To solve it, we need to remember that y = y

then:

(-3/2)*x - 3 = y = -2*x + 2

(-3/2)*x - 3  = -2*x + 2

We can solve this for x.

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

(1/2)*x = 5

x = 5((1/2) = 5*2 = 10

And to find the y-value, we need to input this x-value in one of the equations:

y = -2*10 + 2 = -20 + 2 = -18

Then the solution of the system is the point (10, -18)


Related Questions

Find the area of the shape below

Answers

Answer:

3sqft

Step-by-step explanation:

Note that you can draw the segment AH and notice that you have 2 triangles with base 2ft and height 1.5ft each.

The area will be 2 * (2ft * 1.5ft / 2) = 3sqft

Answer:

6 ft^2

Step-by-step explanation:

Area: A = (ab)/2 where a is the H-A and b is M-T

Plugin the numbers: A = (2 x 6)/2 = 6 ft^2

The function f(x) = (x − 4)(x − 2) is shown.

On a coordinate plane, a parabola opens up. It goes through (2, 0), has a vertex at (3, negative 1), and goes through (4, 0).
What is the range of the function?

all real numbers less than or equal to 3
all real numbers less than or equal to −1
all real numbers greater than or equal to 3
all real numbers greater than or equal to −1

Answers

Answer:

Last Option : all real numbers greater than or equal to −1

Step-by-step explanation:

Answer:

D.all real numbers greater than or equal to −1

Step-by-step explanation:

7x + 9 = 58? solve for x

Answers

Answer: x=7

Answer Explanation: 7x=58-9...
58-9 is 49...
7x=49...
Divide 49 by 7 and you get 7.

The solution to the equation 7x + 9 = 58 is x = 7.

To solve the equation 7x + 9 = 58 for x, we can follow these steps:

Subtract 9 from both sides of the equation to isolate the term with x:

7x + 9 - 9 = 58 - 9

7x = 49

Divide both sides of the equation by 7 to solve for x:

7x / 7 = 49 / 7

x = 7

Therefore, the solution to the equation 7x + 9 = 58 is x = 7.

To know more about equation:

https://brainly.com/question/29657983


#SPJ6

HELP I REALLY NEED HELP WITH THIS
Write an equation with a variable AND solve it. A truck contained 77 gallons of gas. It leaked 11 gallons per minute, m, until here were 22 gallons left. How many minutes passed?
Equation:
Answer:

Answers

Answer:

answer = 5

Step-by-step explanation:

77-22=55

55÷11=5

There are 9 apples in each
Box. How many Apples are in
in 6 boxes

Answers

Answer:

I believe h do 9 times 6. and u should get 54

write an equation in point-slope form of the line that passes through the point (3, 5) and has a slope or -1

Answers

Answer:

y = -x + 8

Step-by-step explanation:

m = -1  ; x1 = 3 ; y1 = 5

Slope point form: y - y1 = m(x -x1)

y - 5 = -1(x - 3)

y -  5 = -1x - 3 *(-1)

y - 5 =-x + 3

    y =  -x + 3 + 5

     y = -x + 8

plz answer ASAP tysm !

Answers

Answer:

I already did

Step-by-step explanation:

HELPPP. 6th GRADE MATH!!! ITS EASY IF YOU ARE GOOD AT IT!!!
:( No links and non-useful answers will be reported. Please help!

Answers

Answer:

1. Howard

2. Peter

Step-by-step explanation:

Answer:

1 is A, 2 is B

Wesley sailed his boat due north for 18 miles, then due east for another 18 miles. Approximately how
far is Wesley from where he began?

Answers

Answer:

8\sqrt(2)

Step-by-step explanation:

HELPME PLEASEEEEEEEEEEEEEEEEEEEEEEEEEEE

Answers

The answer is b because it is in between

Answer:

Step-by-step explanation:

0.25

B

SEND HELP

Write the standard form of the equation of the circle.

Answers

9514 1404 393

Answer:

  (x +4)^2 +(y +6)^2 = 18

Step-by-step explanation:

The standard form equation for a circle centered at (h, k) with radius r is ...

  (x -h)^2 +(y -k)^2 = r^2

The center of the given circle is (-4, -6). The radius (or squared radius) can be found by putting the point (-7, -3) into the left-side expression.

  (-7 -(-4))^2 +(-3 -(-6))^2 = r^2 = 9 +9 = 18

Then the equation of the circle is ...

  (x +4)^2 +(y +6)^2 = 18

number of side number of triangle sum of the measure of the angles ​

Answers

Answer:

Quadrilateral

#sides = 4

#∆ = 4-2 =2

sum= n(4-2)180° = 360°

pentagon

#sides =5

#∆ = 5-2 = 3

sum = n = (5-2)180° = 540°

Octagon

#sides = 8

#∆= 8-2 = 6

sum = n = (8 - 2)180° = 1080°

Nonagon

#sides =9

#∆ =9-2 = 7

sum = n=(9-2)180° = 1260°

Heptagon

#sides= 7

#∆= 7-2 = 5

sum = n= (7-2)180° = 900°

ok soo ima need help !! {re-posting this one}


question-
Select all of the ratios that are equivalent to 6:16.
2:8
3:8
12/18
30/80
18 to 48

Answers

Answer:

3:8

30/80

18 to 48

Step-by-step explanation:

3:8 (6 and 16 divided by 2)

30/80 (6 and 16 times 5)

18 to 48 (6 and 16 times 3)

Write the partial fraction decomposition of the rational expression:
(3x-5)/(x^2 - 6X - 16)​

Answers

Answer:

Step-by-step explanation:

Help Please‼️ Thank you

A company has a total of 209 employees in the marketing and sales offices. For every 5 people employed in sales, there are 14 employed in marketing.

How many people in the office work in marketing?

How many people in the office work in sales?

Answers

Answer:

154 people work in marketing.

55 people work in sales.

Step-by-step explanation:

For every 5 people employed in sales, there are 14 employed in marketing.

This means that:

5/(5+14) = 5/19 of people work in sales.

14/(5+14) = 14/19 of people work in marketing.

Total of 209 people:

14*209/19 = 154

154 people work in marketing.

5*209/19 = 55

55 people work in sales.

evaluate the expression for the given value 3a^2 + 6b^3. a=3 b=2​

Answers

Answer:

5. is the answer

Step-by-step explanation:

Each day you do homework for m minutes and watch tv for 30 minutes. which expression can you use to find out how many minutes you do both activities in 5 days. explain you reasoning.

a. 5m+30
b. 5(m+6)
c. 5(m+30)
d. m(5+30)

Answers

Answer is c for sure 100%

What is the precent of increase from 75 to 93?

Answers

Answer:

24%

Step-by-step explanation:

Percentage increase formula

(New value - Original value) ÷ Original value

Then multiple by 100

(93-75)/75 = 0.24

0.24 × 100% = 24%

The courtyard outside East Middle School is in the shape of a rectangle and half-circle.
What is the approximate area of the courtyard?

Answers

Answer:

The correct option is the third one counting from the top. (5892 m^2)

Step-by-step explanation:

First, we need to remember that:

For a rectangle of length L and width W, the area is:

A = L*W

For a circle of diameter D, the area is:

A = pi*(D/2)^2

Where pi = 3.14

In the image, we can see a rectangle and half a circle, the total area of the image will be equal to the area of the rectangle plus the area of the half circle.

In the image, we can see a rectangle of length L = 100m and width W = 50m

Then the area of the rectangle is:

A = 100m*50m = 5000m^2

And we can see that for the half-circle the diameter is D = 50m

Note that the area of a half-circle is half of the area of a complete circle, then the area of that half-circle is:

A = (1/2)*(3.14*(50m/2)^2) = 981.25 m^2

If we add these two areas we get:

Total area =  5000m^2 + 981.25 m^2 = 5981.25 m^2

If we round it up, we get:

Total area = 5982 m^2

The correct option is the third one counting from the top.

The table describes some of the solutions of the inequality 6x < 18 which graph best describes the solutions of 6x < 18? ​

Answers

Answer:b

Step-by-step explanation:

Answer:

Step-by-step explanation:

whats the ansewr to 4/7--3/7

Answers

Answer:

1

Step-by-step explanation:

4-3=1 denominator never changes may i be marked brainliest?

Find the missing value for the exponential function represented by the table below.
Then select the graph that best fits the equation.
a.
8.232, Graph A
c.
9.213, Graph A
b.
8.756, Graph B
d.
-8.232, Graph B

Answers

Answer:

To find the missing value for the exponential function, we need to identify the common ratio (r) of the exponential function, as the function can be represented as y = a(r^x), where a is the initial value.

Starting with the first two points, we can set up an equation:

24 = a(r^-2)

16.8 = a(r^-1)

Dividing the second equation by the first equation, we get:

16.8/24 = (r^-1)/(r^-2)

0.7 = r

Now we can use the third point to solve for a:

11.76 = a(0.7^0)

11.76 = a

Finally, we can use the last point to solve for y:

y = 11.76(0.7^x)

Plugging in x = 1, we get:

y = 11.76(0.7)

y = 8.232

Therefore, the missing value is 8.232, and the graph that best fits the equation is Graph A.

The missing value for the exponential function is 8.232.

The graph that best fits the equation is Graph A.

What is exponential Function?

An exponential function is a Mathematical function in the form f (x) = [tex]a^x[/tex], where “x” is a variable and “a” is a constant which is called the base of the function and it should be greater than 0.

We know the standard form of exponential function is

y = a[tex](r^x)[/tex], where a is the initial value.

Now, taking the first two points we get

24 = a([tex]r^{-2[/tex])

and, 16.8 = a([tex]r^{-1[/tex])

Dividing the above equation we get

16.8/24 = ([tex]r^{-1[/tex])/ ([tex]r^{-2[/tex])

r = 0.7

Now, find the value of a

11.76 = a([tex]0.7^0[/tex])

11.76 = a

So, y = 11.76([tex]0.7^x[/tex])

For x=1 the above equation gives

y = 11.76(0.7)

y = 8.232

and the graph that best fits the equation is Graph A.

Learn more about Exponential Equation here:

https://brainly.com/question/17246770

#SPJ7

True or false
A sample space can be written as an organized list, a table or a tree diagram.

Answers

Answer: true I think

pls help me ill mark brainliest

Answers

Answer:

Step-by-step explanation:

I got 480 in^3

Two sides of an isosceles triangle are 4 and 8. Which of the following choices could be the measure of the third side?
A. 10
B. 8
C. 6
D. 4

Answers

Answer:

8 is answer. isoceles triangles must have two equal sides, where the smaller makes the base and the two larger are the legs.

Step-by-step explanation:

The measure of the third side of an isosceles triangle is 8 units.

What is an isosceles triangle?

An isosceles triangle is a triangle with (at least) two equal sides. A polygon that consists of two equal sides, two equal angles, three edges, three vertices and the sum of internal angles of a triangle equal to 180°.

For the given situation,

The sides of an isosceles triangle are 4 and 8.

In isosceles triangle, two sides have equal length and the base should be less.

From the measurements given, the base could be 4 units and the third side is same as 8 units.

Hence we can conclude that the measure of the third side of an isosceles triangle is 8 units.

Learn more about an isosceles triangle here

https://brainly.com/question/12951731

#SPJ2

Can someone solve for x? And maybe explain it in a simple way?

Answers

Answer:

x=10

Step-by-step explanation:

Because of the two parallel lines, the ratio between the sides must be the same.  Since the bottom is 12 to 18 (a ration of two to three) we know that x and x+5 would have the same ratio.  Logically, x would have to equal 10 so that x+5 would equal 15 and a ratio of two to three would exist there too.  If you go to solve a problem and the answer isn’t obvious, jut set up a ratio.

12/18=x/(x+5)

then cross multiply and solve

12(x+5)=18x

12x+60=18x

60=18x-12x

60=6x

10=x

Answer:

x=10

Step-by-step explanation:

You can set it up as a proportion, since the lines are parallel, the sections are proportionate to each other.

[tex]\frac{x}{12} = \frac{x+5}{18} \\18x=12(x+5)\\18x=12x+60\\6x=60\\x=10[/tex]


Aquestion that can be answered by
collecting data that has variability,

Answers

You need to give more info

trigonometry
y=? x=?

Answers

Answer:

y=9cm

x=90°

Step-by-step explanation:

y=9cm(being perpendicular)

x=90°=being perpendicular)

Help!
Find the measures of the indicated angle in the parallelogram

Answers

The internal angles of a parallelogram add to 360 degrees. A parallelogram must have equivalent opposite interior angles. Therefore angles a and c are the same and angles b and d are the same. We now know that angles a and c add to 102 degrees so we do (360-102)/2. Which is 129 degrees for both angles. The answer is 129 degrees for angle b

Latoya bought 8 pounds of potatoes at a local wholesaler for $18. Her friend Herman bought 6 pounds of potatoes at the supermarket for $15. Herman thinks he got the better deal because $15 is less than $18. Use this information for Parts A, B, and C below.

Answers

Answer:

Latoya got a better deal because she paid less than Herman by 25 cents

Step-by-step explanation:

Latoya 18 divided by 8= $2.25

Herman 15 divided by 6= $2.50

So Latoya saves $0.25 cents

Other Questions
An airplane has an airspeed of 500 kilometers per hour (k/hr) in anortherly direction (N 0 E). The wind velocity is 60 k/hr in a southeasterly (S45E)direction. Let Va be the velocity of the plane relative to the air and Vw be the velocityof the wind (both in terms of i and j). 1. Find vg = va + vw, the path of the plane relative to the ground. Round coefficients to the nearest tenth.2. Find the actual speed and direction of the airplane relative to the ground. Round to the nearest tenth. which of the following is a person who authorized an agent to act on his or her behalf i need 17 thanksssssssss (-12-13) (-14-15-16) math question plzz help ill give you brainliest Which of the following is the equation of a line in slope-intercept form for aline with slope = 1 and y-intercept at (0,-1)?please help Using the verb COSTAR discuss prices of food items in Spanish speaking markets. Give the price of something singular and something plural. Are having bad dreams considered trauma? The arms race between the United States and the Soviet Union began when the United States first launched a nuclear missile. the Soviet Union developed its own atomic bomb. the Soviet Union launched its first satellite. NASA created the Mercury program. What is the 109th term of the arithmetic sequence {963, 936, 909, 882, }?a.3,879b.2,674c.-1,980d.-1953 HELP PLZ THIS IS DUE IN 30 MIN :,) Which economic mindset does best to help maximize profits in a global market: fair trade or free trade? Which is punctuated incorrectly Please help me asap i need help quickly The Cotton Gin Andrea Brecheen The cotton gin was one of the most amazing and tragic inventions of early America. The cotton gin is credited to the brilliant and creative American inventor Eli Whitney. Because Whitney's invention made cotton harvesting easier, it allowed farmers in the South to increase production. The cotton gin simplified the process of removing the cotton from the seeds, a process formerly done by hand. As a result, Southern plantations increased their production of cotton from 750,000 bales in 1830 to 2.85 million bales just 20 years later. Because of the increase in production, the farmers in South became even more dependent on cotton for revenue. This new reliance on cotton increased the need for slavery. More slaves were needed to farm the ever expanding cotton plantations. If Whitney had known the effects his invention would have on slavery, he never would have created it. Read the passage. Which sentence from the text is an opinion that needs more support to be considered valid? As a result, Southern plantations increased their production of cotton from 750,000 bales in 1830 to 2.85 million bales. . ." If Whitney had known the effects his invention would have on slavery, he never would have created it. "Because Whitney's invention made cotton harvesting easier, it allowed farmers in the South to increase production." "Because of the increase in production, the farmers in South became even more dependent on cotton for revenue." WORTH BRAINLIEST! AND 31 POINTS! PLS HELP! does anyone have the answers to the modern carpentry book review questions for chapter 21,22, and 23 Two students prepared aqueous solutions of LiCl and measured the properties, as shown in the table above. Both students observed that the solid LiCl readily dissolved in H2O. The students drew particle diagrams to explain the changes in the enthalpy and entropy of dissolution for LiCl based on their results and observations. Based on this information, the better particle diagram was drawn by which student, and why is that diagram more accurate?A) The better particle diagram was drawn by Student 1 because when LiCl dissolves in water, it dissociates into Li+ and Cl ions causing an increase in entropy.B) The better particle diagram was drawn by Student 1 because when LiCl dissolves in water, it dissociates into Li+ and Cl ions indicating that the dissolution of LiCl is exothermic.C) The better particle diagram was drawn by Student 2 because it shows that LiCl does not dissociate, resulting in a decrease in entropy for the dissolution of LiCl.D) The better particle diagram was drawn by Student 2 because it shows that LiCl does not dissociate, resulting in an endothermic process for the dissolution of LiCl. Answer the following questions,(a) Which community is Dhan Nach related to?(b) Who is the founder of Jainism?(c) Who is the Greek god of love?(d) Name the oldest religion in the world.(e) Who is known as 'Itihans Shiromani' in Nepali literature?(f) Which country does Mr. Bean belong to? PLEASE ANSWER ASAP! NO FILE LINK!! How does Annabeth help them get past Cerberus? What does this show about Annabeth's character? (ANSWER BOTH PARTS OF THE QUESTION. USE COMPLETE SENTENCES, CORRECT GRAMMAR, AND NEEDED CONVENTIONS)THIS IS FROM PERCY JACKSON PLEASE. Help with question 12 The spinner below is spun twice what is the probability of the arrow landing on a three and then on an odd number