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otez555 [7]
2 years ago
7

Graph by using the slope and the y intercept.

Mathematics
1 answer:
Mashutka [201]2 years ago
6 0

1. a) equation of the line :

  • y =  \dfrac{2}{5}x   - 7

y - intercept = -7

so, it will pass through point (0, -7)

and if we plug the value of x as 5, we get

  • y =  (\dfrac{2}{5}  \times 5) - 7

  • y = 2 - 7

  • =  - 5

so, it will pass through point (5, -5) too

now, just plot the points (0 , -7) and (5 , -5) and join them.

2. b) equation of line is :

  • y =  - 3x + 5

here, y - intercept = 5

so the line passes through point (0 , 5)

now, Plugging the value of x = 1 we get :

  • y =(  - 3 \times 1) + 5

  • y =  - 3 + 5

  • y = 2

so, the given line passes through point (1 , 2)

plotting the points, we can get our required line.

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Describe the steps in solving the linear equation 3(3x-8)=4x+6
tatiyna
Multiply everything in the parenthesis by 3.

9x - 24 = 4x + 6

Add 24 to both sides.

9x = 4x + 30

Subtract 4x from both sides.

5x = 30

Divide both sides by 5.

x = 6

Hope this helps!
6 0
3 years ago
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The manager of a store that specializes in selling tea decides to experiment with a new blend. She will mix some Earl Grey tea t
marishachu [46]

Let us say that:

x = mass from Earl Grey Tea

y = mass from Orange Pekoe Tea

 

So that:

x + y = 600

and that:

6 x + 4 y = 4.5 * 600

6 (600 – y) + 4 y = 2700

3600 – 6y + 4y = 2700

-2y = -900

y = 450 pounds

x = 600 – 450 = 150 pounds

 

Answer:

<span> Earl Grey Tea = 150 pounds</span>

<span>Orange Pekoe Tea = 450 pounds</span>

4 0
3 years ago
2nd Question.... Will mark brainiest
stiks02 [169]

Answer:

c

Step-by-step explanation:

40x3.14=125.6

8 0
2 years ago
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lara31 [8.8K]

Answer:

a

n

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2

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Step-by-step explanation:

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3 0
2 years ago
1. What are the solutions (coordinate points) to the system of equations?
Leto [7]

Question 1

The given system of equations is:

y =  {x}^{2}  + 5x + 6 \\ y = 3x + 6

Equate the two equations:

{x}^{2}  + 5x + 6 = 3x + 6

Rewrite in standard form:

{x}^{2}  + 5x - 3x + 6 - 6 = 0

{x}^{2}   + 2x = 0

x(x + 2) = 0

x = 0 \: or \: x =  - 2

When we put x=0, in y=3x +6, we get:

y = 3(0) + 6 = 6

One solution is (0,6)

When we put x=-2, into y=3x+6, we get:

y = 3( - 2) + 6 = 0

Another solution is (-2,0)

The solutions are; (0,6) and (-2,0)

Question 2:

The function is

f(x) =  {x}^{6}  -  {x}^{4}

Let us put x=-x,

f( - x) =  {( - x)}^{6}  -  {( - x)}^{4}

This gives:

f( - x) =  {x}^{6}  -  {x}^{4}

We can observe that:

f(x) = f( - x)

This is the property of an even function.

Question 3:

The given function is

f(x) =  {x}^{2}  + 3x - 2

The average rate of change of f(x) from x=a to x=b is given as:

\frac{f(b) - f(a)}{b - a}

This is the slope of the secant line connecting the two points on f(x)

From x=2 to x=6, the average rate of change

=  \frac{f(6) - f(2)}{6 - 2} \\   =  \frac{ {6}^{2}  + 3 \times 6 -  2 -  {2}^{2}   -  3 \times 2  + 2 }{4} \\   =  \frac{36 + 18 - 4  - 6}{4}  \\  =  \frac{44}{4}   \\ = 11

The average rate of change is 11

3 0
3 years ago
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