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Temka [501]
3 years ago
15

A pair of equations is shown below: y = 8x − 9 y = 4x − 1 Part A: Explain how you will solve the pair of equations by substituti

on or elimination. Show all the steps and write the solution. (5 points) Part B: If the two equations are graphed, at what point will the lines representing the two equations intersect? Explain your answer. (5 points)​ Part A, so to start off this problem i used substitution... after, this is some of the math used to solve this promblem y = 8x - 9 y = 4x - 1 8x - 9 = 4x - 1 ... so after that u can see i was just using substitution so now lets move on to the next step..
Mathematics
1 answer:
babunello [35]3 years ago
7 0

Answer:

see below

Step-by-step explanation:

y = 8x − 9

y = 4x − 1

Since the two equations are both equal to y set them equal to each other

8x -9 = 4x-1

Subtract 4x from each side

8x - 9 -4x = 4x-1-4x

4x -9 = -1

Add 9 to each side

4x-9+9 = -1+9

4x = 8

Divide by 4

4x/4 = 8/4

x=2

Now find y

y =4x-1

y = 4(2) -1

y = 8-1

y = 7

(2,7)

The solution to the system of equations is where the two lines intersect.  When  the two lines are graphed, they will intersect at (2,7)

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Which is the equation of a parabola with a directrix at y = −3 and a focus at (5, 3)? y = one twelfth(x − 5^)2
ankoles [38]

The equation of a parabola with a directrix at y = -3 and a focus at (5 , 3) is y = one twelfth (x - 5)² ⇒ 1st answer

Step-by-step explanation:

The form of the equation of the parabola is  (x - h)² = 4p(y - k), where

  • The vertex of the parabola is (h , k)
  • The focus is (h , k + p)
  • The directrix is at y = k - p  

∵ The focus of the parabola is at (5 , 3)

- Compare it with the 2nd rule above

∴ h = 5

∴ k + p = 3 ⇒ (1)

∵ The directrix is at y = -3

- By using the 3rd rule above

∴ k - p = -3 ⇒ (2)

Solve the system of equations to find k and p

Add equations (1) and (2) to eliminate p

∴ 2k = 0

- Divide both sides by 2

∴ k = 0

- Substitute the value of k in equation (1) to find p

∵ 0 + p = 3

∴ p = 3

Substitute the values of h , k , and p in the form of the equation above

∵ (x - 5)² = 4(3)(y - 0)

∴ (x - 5)² = 12 y

- Divide both sides by 12

∴ \frac{1}{12} (x - 5)² = y

- Switch the two sides

∴ y =  \frac{1}{12} (x - 5)²

The equation of a parabola with a directrix at y = -3 and a focus at (5 , 3) is y =  \frac{1}{12} (x - 5)²

Learn more:

you can learn more about the quadratic equations in brainly.com/question/8054589

#LearnwithBrainly

8 0
3 years ago
Which choice is equivalent to the expression shown below? -3(3y-2x) +2(5x-4y)
kap26 [50]

Answer:

-17y + 16x

Step-by-step explanation:

-3(3y - 2x) + 2(5x - 4y) = -9y + 6x + 10x - 8y = -17Y + 16X.

If it is helpful, plz give me Brainliest.

7 0
3 years ago
I need help plzzzz I don't know how to​
Assoli18 [71]

it would be 48 because you would multiply 8 and 12 but then divide by 2

4 0
2 years ago
Read 2 more answers
What is 22 in centermeters
Gennadij [26K]

Answer:

22 feet in centimeters is 670.56

22 inch in centimeters is 55.88

Step-by-step explanation:

7 0
2 years ago
Ken has $950 in a savings account at the beginning of the summer. He wants to have at least $600 in the account by the end of th
Neko [114]
Every week he withdraws $35 from the $950 in his savings, and he wants at least $600 by the end of the summer. So we could write:

\sf 950-35x\ge 600

Where 'x' is the number of weeks. Now let's solve it for 'x'.

Subtract 950 to both sides:

\sf -35x\ge -350

Divide -35 to both sides, don't forget to switch the sign when dividing/multiplying by a negative number:

\sf x\le 10

So he can only withdraw at money for at most 10 weeks if he wants at least $600 left in his account.
6 0
2 years ago
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