Write a system of linear equations.Write two-variable equations in slope-intercept form.
Answers
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
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.
Write the partial fraction decomposition of the rational expression:
(3x-5)/(x^2 - 6X - 16)
Answers
Answer:
Step-by-step explanation:
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:
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°
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?
trigonometry
y=? x=?
Answers
Answer:
y=9cm
x=90°
Step-by-step explanation:
y=9cm(being perpendicular)
x=90°=being perpendicular)
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
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7x + 9 = 58? solve for x
Answers
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:
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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]
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
Help!
Find the measures of the indicated angle in the parallelogram
Answers
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
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
pls help me ill mark brainliest
Answers
Answer:
Step-by-step explanation:
I got 480 in^3
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
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%
HELPME PLEASEEEEEEEEEEEEEEEEEEEEEEEEEEE
Answers
Answer:
Step-by-step explanation:
0.25
B
Aquestion that can be answered by
collecting data that has variability,
Answers
You need to give more info
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:
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:
True or false
A sample space can be written as an organized list, a table or a tree diagram.
Answers
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:
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plz answer ASAP tysm !
Answers
Answer:
I already did
Step-by-step explanation:
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
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)
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:
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
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
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