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2 years ago

Find the axis of symmetry of 2x^2 + 12x + 16 Show your work

Mathematics

1 answer:

raketka [301]2 years ago

6 0

The vertex form:

$y=a(x-h)^2+k\\\\(h,\ k)-vertex$

The axis of symetry is x = h.

$y=ax^2+bx+c\to h=\dfrac{-b}{2a}$

We have

$y=2x^2+12x+16\to a=2,\ b=12,\ c=16$

Substitute:

$h=\dfrac{-12}{(2)(2)}=\dfrac{-12}{4}=-3$

<h3>Answer: x = -3</h3>

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Find the limit of the function algebraically. limit as x approaches negative nine of quantity x squared minus eighty one divided

scoray [572]

Let me express the equation clearly:

lim x→-9 (x²-81)/(x+9)

Initially, we solve this by substituting x=-9 to the equation.

((-9)²-81)/(-9+9) = 0/0

The term 0/0 is undefined. This means that the solution is not see on the number line because it is imaginary. Other undefined terms are N/0 (where N is any number), 0⁰, 0×∞, ∞-∞, 1^∞ and ∞/∞. One way to solve this is by applying L'Hopitals Rule. This can be done by differentiating the numerator and denominator of the fraction independently. Then, you can already substitute the x=-9.

(2x-0)/(1+0) = 2x = 2(-9) = -18

The other easy way is to substitute x=-8.999 to the original equation. Note that the term x→-9 means that x only approaches to -9. Thus, you substitute a number that is very close to -9. Substituting x=-8.999

((-8.999)²-81)/(-8.999+9) = -18

7 0

2 years ago

At Greenwood Landscaping, rock costs $47.50 per ton. How much would 2.5 tons cost?

Grace [21]

Answer:

Hey!

Your answer is $118.75!

Step-by-step explanation: How did I get this?

STEP 1: So we know that for a ton of rock costs us $47.50...

To get 2 tons all we have to do is to MULTIPLY $47.50 by 2...

(47.50 x 2 = 95)

STEP 2: So for $95, you will get 2 tons of rock!

Now to get the .5 tons of rock in price form, we have to get the price of the whole 2.5 tons and DIVIDE BY 2

(47.50 ÷ 2 = 23.75)

STEP 3: So now we have the costs for 2 tons and the price for HALF a ton.

What we do now is easy...we ADD THE VALUES TOGTHER!

(95 + 23.75 = $118.75)

The result of $118.75 after adding them together is the PRICE OF 2 TONS!

I HOPE THIS HELPED YOU!

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2 years ago

Brianna has 4 pink bracelets one third of all her braces are pink how many places does Rihanna have the brand has 4 pink bracele

tankabanditka [31]

Can you retype this? It's kind of hard to understand what you are saying

3 0

2 years ago

Lucy is using a one-sample t ‑test based on a simple random sample of size n = 22 to test the null hypothesis H 0 : μ = 16.000 c

slega [8]

Answer:

The value of test statistic is 1.338

Step-by-step explanation:

We are given the following in the question:

Population mean, μ = 16.000

Sample mean, $\bar{x}$ = 16.218

Sample size, n = 22

Alpha, α = 0.05

Sample standard deviation, s = 0.764

First, we design the null and the alternate hypothesis

$H_{0}: \mu = 16.000\text{ cm}\\H_A: \mu < 16.000\text{ cm}$

We use one-tailed t test to perform this hypothesis.

Formula:

$t_{stat} = \displaystyle\frac{\bar{x} - \mu}{\frac{\sigma}{\sqrt{n}} }$

Putting all the values, we have

$t_{stat} = \displaystyle\frac{16.218 - 16.000}{\frac{0.764}{\sqrt{22}} } = 1.338$

Thus, the value of test statistic is 1.338

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3 years ago

Help me. Two numbers have a sum of 30. Half of their difference is 7. Find the numbers.

igor_vitrenko [27]

Answer:

the correct answers are 22 and 8

7 0

2 years ago

Read 2 more answers