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pochemuha
2 years ago
7

Solve the following System Of Equations Using Substitution or Elimination Methods. Show Work.

Mathematics
1 answer:
Ostrovityanka [42]2 years ago
8 0

Answer:

There are two pairs of solutions: (2,7) and (-1,4)

Step-by-step explanation:

We will use substitution.

y = x^2 + 3

y = x +5

Since the second equation is equal to y, replace y in the first equation with the second equation.

y = x^2 + 3

x + 5 = x^2 + 3

Rearrange so that one side is equal to 0.

5 - 3 = x^2 - x

2 = x^2 - x

0 = x^2 - x - 2

You may use quadratic formula or any form of factoring to find the zeros (x values that make the equation equal to 0).

a = 1, b = -1, c = -2

Zeros = \frac{-b + \sqrt{b^{2}-4ac }  }{2a} and \frac{-b - \sqrt{b^{2}-4ac }  }{2a}

Zeros = 2 and -1

Now that you have your x values, plug them into the equations to find their corresponding y values.

y = x^2 + 3

y = (2)^2 + 3

y = 7

Pair #1: (2,7)

y = x^2 + 3

y = (-1)^2 + 3

y = 4

Pair #2: (-1,4)

Therefore, there are two pairs of solutions: (2,7) and (-1,4).

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fredd [130]

Answer:

3.6

Step-by-step explanation:

5 0
3 years ago
In a sample with m = 40 and s = 8, what is the z-score corresponding to x = 38?
Alika [10]
Z = (x - m)/s
z = (38-40)/8
z = -2/8
z = -1/4
z = -0.25

The z score is -0.25
7 0
3 years ago
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Simplify The Expression<br> (2n−9)−5(−2.4n+4)
Jlenok [28]

Answer:

14n-29

Step-by-step explanation:

Remove the unnecessary parenthesis around the (2n-9)

(2n-9)-5(-2.4n+4)

Distribute the -5 into the -2.4n+4

2n-9-5(2.4n+4)

2n-9+12n-20

Combine like terms

2n-9+12n-20

14n-9-20

14n-29

3 0
3 years ago
A line includes the points (-39,49) and (0,0). What is its equation in slope-intercept form?
malfutka [58]

Answer:

The equation in the slope-intercept form will be:

y=-\frac{49}{39}x+0

Step-by-step explanation:

Given the points

  • (-39,49)
  • (0,0)

Finding the slope between the points using the formula

\mathrm{Slope}=\frac{y_2-y_1}{x_2-x_1}

\left(x_1,\:y_1\right)=\left(-39,\:49\right),\:\left(x_2,\:y_2\right)=\left(0,\:0\right)

m=\frac{0-49}{0-\left(-39\right)}

m=-\frac{49}{39}

We know that the point-slope of the line equation is

y-y_1=m\left(x-x_1\right)

substituting m=-\frac{49}{39} and (-39,49)  in the equation

y-y_1=m\left(x-x_1\right)

y-49=\frac{-49}{39}\left(x-\left(-39\right)\right)

Now writing the equation in slope-intercept form

y=mx+b

where m is the slope and b is the y-intercept

y-49=\frac{-49}{39}\left(x-\left(-39\right)\right)

y-49=\frac{-49}{39}\left(x+39\right)

\mathrm{Apply\:the\:fraction\:rule}:\quad \frac{-a}{b}=-\frac{a}{b}

y-49=-\frac{49}{39}\left(x+39\right)

\mathrm{Add\:}49\mathrm{\:to\:both\:sides}

y-49+49=-\frac{49}{39}\left(x+39\right)+49

y=-\frac{49}{39}x+0              ∵ y=mx+b

Where

m=-\frac{49}{39} and the y-intercept i.e. b=0

Therefore, the equation in the slope-intercept form will be:

y=-\frac{49}{39}x+0

5 0
3 years ago
You need a 35% alcohol solution. On hand, you have a 715 mL of a 20% alcohol mixture. You also have 90% alcohol mixture. How muc
asambeis [7]

Answer:

90% Solution

Step-by-step explanation:

5% of 90 + 90% of x = 75% of (90 + x)

5×90/100 + 90x/100 = 75×90/100 + 75x/100

Or 90x/100 - 75x/100 = 75×90/100 - 5×90/100

Or 15x/100 = 90×70/100

Or X = 420ml

You Will Need ML Of The 90% Solution To Obtain ML Of The Desired 75% Solution.

6 0
2 years ago
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