MATHEMATICS HIGH SCHOOL

What is one of the solutions to the following equations? y2+x2=53
Y-x=5

Answers

Answer 1
Answer: (1)  y² + x² = 53
(2)  y - x = 5 ⇒ y = x + 5

subtitute (2) to (1)

(x + 5)² + x² = 53      |use (a + b)² = a² + 2ab + b²

x² + 2x·5 + 5² + x² = 53

2x² + 10x + 25 = 53     |subtract 53 from both sides

2x² + 10x - 28 =0     |divide both sides by 2

x² + 5x - 14 = 0

x² - 2x+ 7x - 14 = 0

x(x - 2) + 7(x - 2) = 0

(x - 2)(x + 7) = 0 ⇔ x - 2 = 0 or x + 7 = 0 ⇔ x = 2 or x = -7

subtitute the values of y to (2)

for x = 2, y = 5 + 2 = 7
for x = -7, y = 5 + (-7) = 5 - 2 = 3

Answer: x = 2 and y = 7 or x = -7 and y = 3

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What is not the sum to 13

Answers

Answer:

Step-by-step explanation:

3 plus 3 is not 13

A caterer knows that 18 heads of lettuce are needed to make dinner salads fro 70 people. How many heads of lettuce are needed for a party of 175 people?

Answers

45 because 70 multiplied by 2 equals 140. There are 35 left over which is half of 70 meaning you have to multiply 18 by 2.5 to get your answer.

If a bicycle cost $70.50 but it's on sale for 47% off how much is the discount what is the sale price

Answers


first multiply the two terms together to find out how much money is being discounted

$70.50 x .47 = 33.135

now subtract that number from $70.50

$70.50 - 33.135 = $37.37

ANSWER: the discount is $33.14 & the sale price is $37.37

In which quadrant is the number -14 – 5i located on the complex plane? a.I b.II C.III D IV​

Answers

I believe It’s c.III (quadrant 3)

If p varies directly with q, and p = 10 when q = 5, what is the value of p when q = 20? A.p = 40

B.p = 1

C.p = 100

D.p = 28

Answers

A. p=40 because if you look at your question carefully q is half of p so if q=20 which is half of 40 then that means p=40

A calculator is allowed on this question.For what value of the coefficient, C, will the equation have no solution?
HELP PLS HOW DO I DO THIS STEP BY STEP!!

Answers

Answer:

  C.  2/3

Step-by-step explanation:

You want the value of C that makes the equation have no solution.

  (3/4)(5 +(C/2)x) +2 = (x +7)/4

Simplify

A calculator is not needed to simplify the equation. We can start by multiplying both sides by 4.

  3(5 +(C/2)x) +8 = x +7

  15 +(3C/2)x +8 = x +7

  (3C/2)x +23 = x +7

No solution

This will have no solution if the coefficient of x is the same on both sides of the equal sign.

  3C/2 = 1

Multiplying by 2/3 gives ...

  C = 2/3

The value 2/3 for C will make the equation have no solution, choice C.

__

Additional comment

When C=2/3, the equation becomes one that reduces to ...

  (x +23)/4 = (x +7)/4 . . . . . no value of x will make this true.

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Answer:

2/3

Step-by-step explanation:

3/4 * (5+ 2/3/2*x)+2 = x+7/4

Simplify

3/4(5+ 1/3x)+2 = x+7/4

15/4 + 1/4x +2 = x+7/4

23/4 + 1/4x = x+7/4

Cancel terms (multiply by 4 to get rid of 4)

23 + x = x + 7

23 = 7

false :)
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