MATHEMATICS HIGH SCHOOL

Put the equation y=x²−14x+40 into the form y=(x-h)²+k y= ____

Answers

Answer 1
Answer:

Answer:

y = (x - 7)² - 9

Step-by-step explanation:

the equation of a parabola in vertex form is

y = a(x - h)² + k

(h, k ) are the coordinates of the vertex and a is a multiplier

given

y = x² - 14x + 40

to obtain vertex form use the method of completing the square

add/subtract ( half the coefficient of the x- term )² to x² - 14x

y = x² + 2(- 7)x + 49 - 49 + 40

 = (x - 7)² - 49 + 40

 = (x - 7)² - 9 ← in vertex form

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How do I solve this problem 7x<14 and 1-x<4

Answers

x<2 and x>-3 => x∈(-oo, 2) and x ∈(-3,+oo )=> x∈(-3, 2).

7x < 14

x < 14/7

x < 2

x ∈ (-oo ; 2)

1 - x < 4

1 - 4 < x

- 3 < x

x > - 3

x ∈ (- 3 ; + oo)

_____(.__.__.__.__.__.)____

-oo   - 3             0         2

x ∈ (- 3 ; 2 )

Which irrational number can be multiplied by - 41 to get a product that equals 1?200
SSG

Answers

Answer:

- (1/41)

Step-by-step explanation:

1/41 * 41 = 1, so you just need to multiply this equation by -1 to find the answer.

Which of the following is a binomial experiment?A survey asking 75 people to name their favorite color

A survey asking 75 people to give their age

A survey asking 75 people whom they voted for in the election

A survey asking 75 people if they like the new school building

Answers

A survey asking 75 people if they like the new school building. This is a binomial experiment.

A binomial experiment is called as such when it satisfies these 4 conditions.
1) There is a fixed number of trials. = 75 people
2) Each trial is independent of each other = own opinion
3) There are only two outcome = YES or NO
4) The probability of each outcome remains constant from trial to trial = 50 - 50

Answer:

the answer is D on edge

Step-by-step explanation:

A boy can swim 75 feet in 12 seconds. What is his rate to the nearest mile per hour?

Answers

S=d/t so in this case it's 75/12 which is 6.25. Round it and you got 6 miles per hour.

Answer:

6.25

Step-by-step explanation:

75/12 = 6.25

Let f(x) = -2x^2 and g(x) = 2x - 4. On the set of axes, draw the graphs of y = f(x) andy = g(x).
Using this graph, determine and state all values of x for which f(x) = g(x).

Answers

f(x) = -2x²
g(x) = 2x - 4

                              f(x) = g(x)
                             -2x² = 2x - 4
                       -2x² - 2x = 2x - 2x - 4
                 -2x² - 2x + 4 = -4 + 4
                 -2x² - 2x + 4 = 0
       -2(x²) - 2(x) - 2(-2) = 0
                 -2(x² - x - 2) = 0
                          -2         -2
                      x² - x - 2 = 0
              x² + 2x - x - 2 = 0
x(x) + x(2) - 1(x) - 1(2) = 0
        x(x + 2) - 1(x + 2) = 0
                (x - 1)(x + 2) = 0
   x - 1 = 0    or    x + 2 = 0
     + 1 + 1              -  2 -  2
         x = 1      or       x = -2          
                             f(x) = g(x)
                            -2x² = 2x - 4
                        -2(-2)² = 2(-2) - 4
                           -2(4) = -4 - 4
                                -8 = -8
                                   or
                              f(x) = g(x)
                             -2x² = 2x - 4
                          -2(1)² = 2(1) - 4 
                                -2 = 2 - 4
                                -2 = -2

Solution Sets: {(-2, -8), (1, -2)}

Regular Hexagon ABCDEF rotates 240' counterclockwise about its center to produce hexagon A'B'C'D'E'F'. Which points will A' and B' coincide within the pre image

Answers

Answer:

A' will coincide with C of the pre image, and B' will coincide with D of the pre image.

Step-by-step explanation:

A Regular Hexagon could be imagined as a circle divided into six points on the circle, that are separated by angles of 60° (notice that 6 times 60° is 360°).

Now we name each point as ABCDEF clockwise, and then we rotate the hexagon about its center (counterclockwise)... the original points ABCDEF are renamed as A'B'C'D'E'F' in the rotated hexagon.

As the rotation was of 240°, the points will coincide with some of the original points: point A will "jump" for points, the same as point B.

This means that point A rotated, (wich is A') will coincide with point C pre rotated, and that point B rotated, (wich is B') will coincide with point D pre rotated.
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