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2 years ago

Write each parabola in the form y-k=a(x-h)^2 aand determine its vertex.

Mathematics

2 answers:

mezya [45]2 years ago

6 0

Answer:

Step-by-step explanation:

$y=-x^2-4x-1\\=-(x^2+4x+4)+4-1\\=-(x+2)^2+3\\\\Vertex=(-2;3)\\\\$

$y+x^2+2=0\\y=-x^2-2\\\\y=-(x-0)^2-2\\Vertex=(0;-2)\\$

Viefleur [7K]2 years ago

5 0

Answer:

Step-by-step explanation:

You might be interested in

In a survey of 1,000 women aged 22 to 35 who work full time, 545 indicated that they would be willing to give up some personal t

sp2606 [1]

Answer:

Yes, there is convincing evidence that the majority of women age 22 to 35 who work full-time would be willing to give up some personal time for more money.

No ;

Step-by-step explanation:

n = 1000

x = 545

Phat = x / n = 545/1000 = 0.545

H0: p ≤ 0.5

H1: μ > 0.5

The test statistic :

(phat - p0) ÷ √(p(1 - P0) / n)

Test statistic :

(0.545 - 0.5) ÷ √(0.5(0.5) / 1000)

0.045 / 0.0158113

Test statistic = 2.846

α = 0.01

Decison :

Reject H0 ; if Pvalue < α

Using the Pvalue from Test statistic (Z) calculator :

Pvalue = 0.002214

With Pvalue < α ; We reject H0 and conclude that there is convincing evidence that the majority of women age 22 to 35 who work full-time would be willing to give up some personal time for more money.

No, making generalization about all women would not be reasonable as the data employed for the research mainly focuses on a particular

7 0

3 years ago

The function f(x) = x + 3 represents the length of a rectangle. The function g(x) = 12x − 5 represents the width of the rectangl

Furkat [3]

Answer:

186

Step-by-step explanation:

The area is given by ...

(f • g)(3) = f(3) • g(3) = (3+3) • (12•3 -5) = (6)(31)

(f • g)(3) = 186

6 0

3 years ago

Please help me simplify 4^8/4^5

Oksi-84 [34.3K]

Answer:

Step-by-step explanation:

Hope it helped!

4 0

3 years ago

Read 2 more answers

Find four consecutive integers with a sum of 106.

grandymaker [24]

4 consecutive integers...
x, x + 1, x + 2, x + 3

x + x + 1 + x + 2 + x + 3 = 106
4x + 6 = 106
4x = 106 - 6
4x = 100
x = 100/4
x = 25

x + 1 = 25 + 1 = 26
x + 2 = 25 + 2 = 27
x + 3 = 25 + 3 = 28

ur 4 integers are : 25,26,27,28

6 0

3 years ago

Two boys and three girls are auditioning to play the piano for a school production. Two students will be chosen, one as the pian

finlep [7]

Answer:

30% is the correct answer.

Step-by-step explanation:

Total number of boys = 2

Total number of girls = 3

Total number of students = 5

To find:

Probability that the pianist will be a boy and the alternate will be a girl?

Solution:

Here we have to make 2 choices.

1st choice has to be boy (pianist) and 2nd choice has to be girl (alternate).

$\bold{\text{Required probability }= P(\text{boy as pianist first}) \times P(\text{girl as alternate})}$

Formula for probability of an event E is given as:

$P(E) = \dfrac{\text{Number of favorable cases}}{\text {Total number of cases}}$

For $P(\text{boy as pianist})$ , number of favorable cases are 2 (total number of boys).

Total number of cases = Total number of students i.e. 5

So, $P(\text{boy as pianist})$ is:

$P(\text{boy as pianist}) = \dfrac{2}{5}$

For $P(\text{girl as alternate})$ , number of favorable cases are 3 (total number of girls).

Now, one boy is already chosen as pianist so Total number of cases = Total number of students left i.e. (5 - 1) = 4

$P(\text{girl as alternate}) = \dfrac{3}{4}$

So, the required probability is:

$\text{Required probability } = \dfrac{2}{5}\times \dfrac{3}{4} = \dfrac{3}{10} = \bold{30\%}$

6 0

3 years ago