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Answer:

The function in the vertex form is y = (x + 2.5)² - 15.25

Step-by-step explanation:

The vertex form of the quadratic function y = ax² + bx + c is:

y = a(x - h)² + k, where

∵ The given function is y = x² + 5x - 9

∴ a = 1, b = 5, c = -9

→ Use a and b to find h

∵ h = [tex]\frac{-b}{2a}[/tex]

∴ h = [tex]\frac{-5}{2(1)}=-2.5[/tex]

∴ h = -2.5

→ Find y at x = -2.5

∵ y = (-2.5)² + 5(-2.5) - 9 = 6.25 - 12.5 - 9

∴ y = -15.25

∴ k = -15.25

→ Substitute a, h, k in the vertex form above

∴ y = 1(x - -2.5)² + -15.25

∴ y = (x + 2.5)² - 15.25

The function in the vertex form is y = (x + 2.5)² - 15.25

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Answer:

c

Step-by-step explanation:

Answer:false

Step-by-step explanation:

Answer:

P(≥ 7 males) = 0.0548

Step-by-step explanation:

This is a binomial probability distribution problem.

We are told that Before 1918;

P(male) = 40% = 0.4

P(female) = 60% = 0.6

n = 10

Thus;probability that 7 or more were male is;

P(≥ 7 males) = P(7) + P(8) + P(9) + P(10)

Now, binomial probability formula is;

P(x) = [n!/((n - x)! × x!)] × p^(x) × q^(n - x)

Now, p = 0.4 and q = 0.6.

Also, n = 10

Thus;

P(7) = [10!/((10 - 7)! × 7!)] × 0.4^(7) × 0.6^(10 - 7)

P(7) = 0.0425

P(8) = [10!/((10 - 8)! × 8!)] × 0.4^(8) × 0.6^(10 - 8)

P(8) = 0.0106

P(9) = [10!/((10 - 9)! × 9!)] × 0.4^(9) × 0.6^(10 - 9)

P(9) = 0.0016

P(10) = [10!/((10 - 10)! × 10!)] × 0.4^(10) × 0.6^(10 - 10)

P(10) = 0.0001

Thus;

P(≥ 7 males) = 0.0425 + 0.0106 + 0.0016 + 0.0001 = 0.0548

Answer:

Step-by-step explanation:

Let the number TJ thinks of be n.

If he finds 1/3 of the number, the expression that models this situation is expressed as:

1/3 of n

= 1/3 * n

= n/3

hence the expression that models the scenario is n/3

Answer:

1/3n-5

Step-by-step explanation:

Answer:

7/8 is the simplified fraction for 56/64 by using the GCD or HCF method. Thus, 7/8 is the simplified fraction for 56/64 by using the prime factorization method.

Step-by-step explanation:

Answer:

.43

Step-by-step explanation:

I just plugged in -6 into all the x's

hope this is right and helps :)

Answer:

x-intercept (-7.5, 0)

y-intercept (0, 5.5)

Hope this helps!

Answer:

1=4 being the co interior angle

2=3 being the opposite angle

Answer:

A. 0.9510

B. 0.0480

C. 0.0490

D. No, I would not feel comfortable accepting the shipment if one item was found defective, because the probability is quite small to obtain 1 or more defective items.

A: How many total hours were worked this week?

Answer- 14 hours were worked this week

B: How many overtime hours were worked?

Answer- 36 overtime hours were worked

I hope this helps you out!!

Answer:

A. 41 hours were worked the whole week

Answer:

Yes.

Step-by-step explanation:

[tex]6^{3}[/tex] × [tex]7^{3}[/tex] = [tex]42^{3}[/tex]

74,088 = 74,088

Answer:

1.3

Step-by-step explanation:

Just put it in the caculator

Answer:

Up 4 and right 3

Step-by-step explanation:

Rise over run. Rise is either up(positive) or down(negative). Run is either left(negative) or right(positive).

Answer:

the width is 39 in

Step-by-step explanation:

length is 52. there are two "length" sides witch = 104

the perimiter is all sides added. 182-104= 78

78= both of the width sides so 78 divide by 2 = 39in

Answer:

x= -5

Step-by-step explanation:

3(5x+10)+10=6x-(x+10)

15x+30+10=6x-x-10

15x+40=5x-10

15x-5x=-10-40

10x=-50

x=-5

Answer:

x= -5

Step-by-step explanation:

trustttt mannn

Answer:

2 mm

Step-by-step explanation:

let the radius of the semi-circle be r

Then,

length of curved portion = 1/2 x circumference = (1/2) (2)(π)r = πr

length of straight portion = diameter of circle = 2r

Hence, we can write an expression for the perimeter

Perimeter = length of curved portion + length of straight portion

Perimeter = πr + 2r

Perimeter = (π + 2)r

since we are given the perimeter = 5.14, assuming that π=3.14, our equation becomes:

5.14 = (3.14 + 2)r

5.14 = 5.14 r

r = 5.14 / 5.14 = 1

Hence, diameter = 2r = 2(1) = 2 mm

Answer:

1.0

Step-by-step explanation:

you have to follow the arrow

Answer:

0.09

Step-by-step explanation:

First off, we can write 0.9 as a fraction. Reading this, we would say "nine tenths"; this means the number in fraction form is 9/10.

The word "of" in mathematics means we multiply. Thus when we take 1/10 "of" 9/10, we multiply the two:

1/10(9/10)

To multiply fractions, multiply the numerators and multiply the denominators:

1/10(9/10) = (1*9)/(10*10) = 9/100

Converting this back to a decimal, we read 9/100 as "nine one-hundredths"; this means decimal form is 0.09.

Answer:

x < -5

Step-by-step explanation:

first you do 12 - 7 which equals to 5

and then put x < becuase -12 is less than -7

Answer:

4.57 hours

Step-by-step explanation:

Answer:

The slope of the line is two.

Step-by-step explanation:

Recall that to find the slope between any two points, we can use the slope formula:

[tex]\displaystyle m = \frac{y_2-y_1}{x_2-x_1}[/tex]

Let (6, 8) be our (x₁, y₁) and let (1, -2) be our (x₂, y₂). Substitution yields:

[tex]\displaystyle m=\frac{(-2)-(8)}{(1)-(6)}[/tex]

Subtract:

[tex]\displaystyle m=\frac{-10}{-5}[/tex]

Divide:

[tex]m=2[/tex]

Therefore, the slope of the line is two.

Answer:

2

Step-by-step explanation:

Answer:

The pattern goes by subtracting -24 from the previous number

1st - 160

2nd - 136

3rd - 112

4th - 88

5th - 64

6th - 40

7th - 16

The 7th term is 16.

Answer:33.2

Step-by-step explanation:

7.1 + 9.5 + 9.5 + 7.1

you have to find the distance for each point and add them all up.

I think it's A :)))

..........

Answer: 496

Step-by-step explanation:

Answer:

f(0) = 12

Step-by-step explanation:

You want to substitute 0 for x

f(0) = 5(0) + 12

f(0) = 12

Answer:

13

Step-by-step explanation:

Substitute 0 for x and simplify. f(0)=(5)0+12=1+12=13.