The sum of the first and second of three consecutive even integers is 158. find the three even integers.

Enter the giveaway for points

Nookie1986 [14]

Answer:

Thxx for points how do I enter

Step-by-step explanation:

8 0

3 years ago

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What are the coordinates of A’, the image of A(-7, 9), after a rotation of -180° about the origin?

Dmitry_Shevchenko [17]

Answer:

7,-9

Step-by-step explanation:

4 0

3 years ago

A spotlight on the ground shines on a wall 12 m away. If a man 2 m tall walks along the x-axis from the spotlight toward the bui

Sedbober [7]

Answer:

0.675 m/s

Step-by-step explanation:

Let height of shadow= y,CD=x

Height of man=2 m

Speed of man= $\frac{dx}{dt}=1. 8 m/s$

$\triangle ABD\sim\triangle ECD$

Therefore, $\frac{AB}{EC}=\frac{BD}{CD}$

$\frac{y}{2}=\frac{12}{x}$

$xy=24$

Differentiate w.r.t t

$x\frac{dy}{dt}+y\frac{dx}{dt}=0$

$x\frac{dy}{dt}=-y\frac{dx}{dt}$

$\frac{dy}{dt}=-\frac{y}{x}\frac{dx}{dt}$

When the man is 4 m from the building

Then, we have x=12-4=8 m

$\frac{dx}{dt}=1.8 m/s$

Substitute the values in above equation then, we get

$8y=24$

$y=\frac{24}{8}=3$

Substitute the values then we get

$\frac{dy}{dt}=-\frac{3}{8}\times 1.8=-0.675 m/s$

Hence, the length of his shadow on the building decreasing at the rate 0.675 m/s.

8 0

3 years ago

An educational psychologist wishes to know the mean number of words a third grader can read per minute. She wants to make an est

MrRa [10]

Answer:

85% level of the confidence interval is

(26.337, 26.662)

Step-by-step explanation:

Explanation:-

Given the size of the sample 'n' = 295

Mean of the sample x⁻ = 26.5

The Standard deviation of the Population = 2.7

85% level of the confidence interval is determined by

$(x^{-} - Z_{0.15} \frac{S.D}{\sqrt{n} } , x^{-} + Z_{0.15} \frac{S.D}{\sqrt{n} })$

Critical value Z₀.₁₅ = 1.036

85% level of the confidence interval is determined by

$(x^{-} - Z_{0.15} \frac{S.D}{\sqrt{n} } , x^{-} + Z_{0.15} \frac{S.D}{\sqrt{n} })$

$(26.9 -1.036 \frac{2.7}{\sqrt{295} } , 26.5 + 1.036 \frac{2.7}{\sqrt{295} })$

( 26.5 - 0.1628 , 26.5+0.1628)

(26.3372,26.6628)

7 0

3 years ago

Venita is factoring the expression 32ab-8b. She determines the GCF and writes the factored expression as 8b(4a-0). Which best de

Nimfa-mama [501]

Let's go through the steps of factoring that Venita should take.

1.) Find the greatest common factor (GCF). We only have two terms, so that makes it pretty easy.
32 = 1, 2, 4, 8, 16, 32
8 = 1, 2, 4, 8
The greatest common factor of 32 and 8 is 8. We can also factor out a b since that term appears in each part of the original expression. The GCF and variable should go on the outside of the parentheses.
8b( )

2.) Now let's figure out what should go in the middle of the parentheses. To do this, use the original expression and divide each term. This is written in the parentheses.

32ab ÷ 8b = 4a
8b ÷ 8b = 1

This would then result in the factored expression 8b(4a - 1). You can always check this by using the distributive property. Distribute 8b out to both expressions:
8b x 4a = 32ab
8b x 1 = 8b
32ab - 8b is the expression she started with, so your factored expression works!

Now that we went through the steps to solve the factored expression, let's check her answer. The only difference between Venita's and ours is that she has 0 as the second term while we have a 1. It seems that she had subtracted the GCF from the second term instead of dividing.

6 0

3 years ago

Read 2 more answers