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Ede4ka [16]
3 years ago
14

Write the slope intercept form through: (5,1) and(2, -2)

Mathematics
1 answer:
victus00 [196]3 years ago
3 0

We see that the slope of this line is \frac{-2-1}{2-5}=1, so we plug this and the point (5,1) into the point-slope form y-y_1=m(x-x_1) (note that there's nothing special about the point I picked; you can choose any point on the line):

y-1=x-5. This rearranges to the slope-intercept form \boxed{y=x-4}.

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Jermaine, Keira, and Leon are buying supplies for an art class. Jermaine bought 2 canvases, 4 tubes of paint, and 2 paint brushe
maria [59]

Answer:

canvas $3

tube of paint $5

paint brush $4

Step-by-step explanation:

We need to choose variables for the prices of the different items, translate the sentences into equations, and solve a system of equations.

1. Define variables

Let c = price of 1 canvas, t = price of 1 tube of paint, and b = price of 1 brush.

2. Translate sentences into equations

"Jermaine bought 2 canvases, 4 tubes of paint, and 2 paint brushes for $34."

2c + 4t + 2b = 34

"Keira spent $22 on 1 canvas, 3 tubes of paint, and 1 paint brush."

c + 3t + b = 22

"Leon already has plenty of paint, so he bought 3 canvases and 2 paint brushes for $17."

3c + 2b = 17

The system of equations is

2c + 4t + 2b = 34       Eq. 1

c + 3t + b = 22           Eq. 2

3c + 2b = 17               Eq. 3

Since the third equation has only the variables c and b, we use the first equations to eliminate variable t and give us an equation in only c and b.

3 * Eq. 1 - 4 * Eq. 2

2c + 2b = 14

c + b = 7            Eq. 4

Eq. 3 and Eq. 4 form a system of equations in two variables.

3c + 2b = 17      Eq. 3

c + b = 7          Eq. 4

Solve Eq. 4 for b.

b = 7 - c        Eq. 5

Substitute into Eq. 3.

3c + 2(7 - c) = 17

3c + 14 - 2c = 17

c = 3

Plug in c = 3 into Eq. 5.

b = 7 - 3

b = 4

Plug in c = 3 and b = 3 into Eq. 2.

c + 3t + b = 22           Eq. 2

3 + 3t + 4 = 22

3t + 7 = 22

3t = 15

t = 5

Answer:

canvas $3

tube of paint $5

paint brush $4

7 0
3 years ago
3.5y−12=1.5(y−2)<br> A) One solution<br> B) No solution<br> C) Infinite solutions
Montano1993 [528]

Answer:

Step-by-step explanation:

3.5y - 12 = 1.5y - 3

2y -12 = -3

2y = 9

y = 4.5

the answer is a. one solution

5 0
3 years ago
suppose that x and y vary inversely and x=1 when y=12. write a function that models the inverse variation. graph the function an
larisa [96]

Answer:

y=12/x

Step-by-step explanation:

if y=12, and x=1 so

general formula y=12/x

for x=5 , y=12/5=2.4

you can graph by ploting points such as (1,12), (5, 2.4),...

6 0
3 years ago
Can someone please please please help.?
Luden [163]

Answer:

<h2>43°</h2>

Step-by-step explanation:

In a cyclic quadrilateral, the sum of two opposite angles are equal.

m<R + m<P = 180°

plugging the values:

3y + 8 + y = 180°

Combine the like terms:

4y + 8 = 180°

Subtract 8 on both sides

4y + 8 - 8 = 180 - 8

Calculate the difference

4y = 172

divide both sides of the equation by 4

4y/4 = 172/4

calculate

y = 43°

Hope this helps...

5 0
3 years ago
Read 2 more answers
In ΔQRS, the measure of ∠S=90°, SR = 7, QS = 24, and RQ = 25. What is the value of the tangent of ∠Q to the nearest hundredth?
TEA [102]

Answer:tanQ=

adjacent

opposite

​

=

24

7

​

≈0.2917≈0.29

Step-by-step explanation:

trust me bro

8 0
3 years ago
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