- The ordered pairs (0,0), (2, 4), (4,8), and (6, 12) represent a function. What is the rule for this

F(x)=-(x+2)^2+3 put in standard form

Natasha_Volkova [10]

Answer:

F(x)=-x^2-4x-1

Step-by-step explanation:

According to PEMDAS, do the exponent part for the parentheses, sense it goes first.

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

Then distribute the - sign

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

Then you simplify

F(x)= -x^2-4x-1

8 0

2 years ago

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Which of the following equations represents a line that is perpendicular to y=3x+11 and intercepts the line at the point, (-2, 5

yaroslaw [1]

If the line is perpendicular the slope is the reciprocal so it would be
Y=-1/3x
Then if the line has to go through the point (-2,5) the y-intercept must be 5 making the answer
Y=-1/3x+5

7 0

3 years ago

A manufacturer of running shoes knows that the average lifetime for a particular model of shoes is 15 months. Someone in the res

Alexus [3.1K]

Answer:

Step-by-step explanation:

Hello!

So you have a new type of shoe that lasts presumably longer than the ones that are on the market. So your study variable is:

X: "Lifetime of one shoe pair of the new model"

Applying CLT:

X[bar]≈N(μ;σ²/n)

Known values:

n= 30 shoe pairs

x[bar]: 17 months

S= 5.5 months

Since you have to prove whether the new shoes last more or less than the old ones your statistical hypothesis are:

H₀:μ=15

H₁:μ≠15

The significance level for the test is given: α: 0.05

Your critical region will be two-tailed:

$Z_{\alpha /2} = Z_{0.025}= -1.96$

$Z_{1-\alpha /2} = Z_{0.975}= 1.96$

So you'll reject the null Hypothesis if your calculated value is ≤-1.96 or if it is ≥1.96

Now you calculate your observed Z-value

Z=x[bar]-μ ⇒ Z= 17-15 = 1.99

σ/√n 5.5/√30

Since this value is greater than the right critical value, i.e. Zobs(1.99)>1.96 you reject the null Hypothesis. So the average durability of the new shoe model is different than 15 months.

I hope you have a SUPER day!

5 0

3 years ago

Explain why the graph below does not represent a direct variation

Nitella [24]

Answer:

C. The line does not go through the origin.

Step-by-step explanation:

We have been given a straight line graph that doesn't pass through origin (0,0) and has y-intercept at (0,3).

Now we need to decide why that graph doesn't represent a direct variation.

We know that graph represents variation when it passes through origin. But since given graph doesn't passes through origin so it doesn't represent the direct variation.

Correct choice is :

C. The line does not go through the origin.

4 0

3 years ago

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Verify seca(1-sina)(seca+tana)=1

beks73 [17]

Seca(1-sina)(seca+tana)=1
Left hand side
=(1-sina) (seca +tana) / cosa
=seca +tana - sinaseca - sinatan / cosa
=seca + tana -tana -(sin^2a/cosa) / cosa
=(1/cosa - sin^2a/cosa) / cosa
= (1-sin^2a / cosa) / cosa
= (1-sin^2a)/ (cos^2a)
=1 (verified)

5 0

3 years ago

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