MATHEMATICS HIGH SCHOOL

Which zero pair could be added to the function so that the function can be written in vertex form?A.3, –3
B.6, –6
C.9, –9
D.36, –36

Answers

Answer 1
Answer: The function in this problem should be: f(x) =x² + 12x + 6 

y = x² + 12x + 6
y - 6 = x² + 12x 

x² ⇒ x * x
12x ⇒ 2*6*x
missing number is 6² = 36 

y - 6 + 36 = x² + 12x + 36

(x+6)(x+6) ⇒ x(x+6)+6(x+6) ⇒ x² + 6x + 6x + 36 = x² + 12x + 36

y + 30 = x² + 12x + 36
y = (x+6)² - 30

Choice is D. 36,-36

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Solve the system of equations 3x+2y=14 2x-4y=4

Answers

3x + 2y = 14....multiply by 2
2x - 4y = 4
----------------
6x + 4y = 28 (result of multiplying by 2)
2x - 4y = 4
----------------add
8x = 32
x = 32/8
x = 4

2x - 4y = 4
2(4) - 4y = 4
8 - 4y = 4
-4y = 4 - 8
-4y = -4
y = -4/-4
y = 1

solution is (4,1)

Each day, 895 people visit the museum. How many people visit the museum in 5 days

Answers

Answer:

the correct answer is 895*5=4505

Step-by-step explanation:

hope it helps

In Chemistry class, Andrew has earned scores of 64, 69, and 73 on three tests. He must maintain an average of 70 to pass the course. What score must Andrew earn on the final exam to pass the course?

Answers

64 + 69 + 73 = 206 ÷ 3 = 68 ish
if he get at least 74 :
64 + 69 + 73 + 74 = 280 ÷ 4 = 70
he will pass course with straight 70

Help please and thank you!

Answers

Answer:

  25.  (x, y) = (5, 11)

  26.  (x, y) = (-1, 1)

Step-by-step explanation:

Both equations are of the form y=( ), so you can set the expressions for y equal to each other. Or, you can subtract the equation with the smaller y-coefficient from the other one.

25.

  x +6 = y = 2x +1 . . . . . equate expressions for y

  5 = x . . . . . . . . . . . subtract x+1

  y = 5+6 = 11 . . . . . using the first equation to find y

  (x, y) = (5, 11)

__

26.

  (y) -(y) = (3x +4) -(x+2) . . . . subtract the first equation from the second

  0 = 2x +2 . . . . . . . . . . . . . . simplify

  0 = x + 1 . . . . . . . . . . . . . . . . divide by the x-coefficient

  x = -1 . . . . . . . . . . . . . . subtract the constant

  y = -1 +2 = 1 . . . . . . . . . use the first equation to find y

  (x, y) = (-1, 1)

_____

Of course, when we say "subtract ..." or "divide ..." we mean that you should do the same operation to both sides of the equation. That way the equal sign remains valid. You can always use an expression or variable in place of its equal (this is the substitution property of equality).

The expression (x+1) that we subtract in problem 25 is the smaller x-term plus the constant on the opposite side of the equal sign. That way, we eliminate both the unwanted x-term and the unwanted constant. You can do these operations one at a time (and you were probably taught to do it that way). That is, subtract x; subtract 1.

For 26, the method of solution that puts both the variable and the constant on the same side of the equation and 0 on the other side has certain advantages. Subtracting one side of the equation from both sides (to make an expression equal to zero) will always work, regardless of the expressions involved. After simplification, you can divide by the coefficient of the variable to get the form x+constant=0, and the answer is always x = -constant. These simple instructions require no judgment. You may find it easier to choose to subtract the side with the smaller coefficient, so the result has a positive coefficient. That's not necessary, but it can reduce anxiety and errors.

Is (x +1) a factor of f(x) = x^3 + x^2 −4x − 4? Select the appropriate response:
Yes
or
No

Answers

Answer:

Yes

Step-by-step explanation:

f(x) = x^3 + x^2 −4x − 4

Factor by grouping  taking x^2 out of the first group and -4 out of the second

0 = x^3 + x^2      −4x − 4

     x^2(x+1)     -4(x+1)

Factor out (x+1)

0=(x+1)(x^2-4)

Now we have the difference of squares

0=(x+1) (x-2)(x+2)

x+1 is a factor

Answer:

Yes

Step-by-step explanation:

( x^3 + x^2) (-4x - 4)

x^2 ( x+1) -4 (x+1)

(x^2 - 4) (x+1)

(x-2) (x+2) (x+1)

X= 2 x=-2 x=-1

What is the slope of the line that passes through the pair of points?
(1, 7), (10, 1)

Answers

(x_1;\ y_1);\ (x_2;\ y_2)\n\nthe\ slope:m=(y_2-y_1)/(x_2-x_1)\n----------------------\n(1;\ 7);\ (10;\ 1)\n\nm=(1-7)/(10-1)=(-7)/(9)=-(7)/(9)
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