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Answer:

Please check the explanation.

Step-by-step explanation:

Given the function

[tex]f\left(x\right)=\:x^2\:+8x+4[/tex]

Let's rewrite the function by completing the square.

[tex]0=x^2+8x+4[/tex]

Subtract 4 from both sides

[tex]x^2+8x+4-4=0-4[/tex]

Simplify

[tex]x^2+8x=-4[/tex]

Rewrite in the form (x+a)²=b

[tex]x^2+8x=-4[/tex]

Rewrite in the form x²+2ax+a²

solve for a, 2ax = 8x

[tex]2ax=8x[/tex]

Divide both sides by 2x

[tex]\frac{2ax}{2x}=\frac{8x}{2x}[/tex]

simplify

[tex]a = 4[/tex]

Add a²=4² to both sides

[tex]x^2+8x+4^2=-4+4^2[/tex]

[tex]x^2+8x+4^2=12[/tex]

Apply perfect square formula

(a+b)²= a²+2ab+b²

[tex]\left(x+4\right)^2=12[/tex]               ∵ [tex]x^2+8x+4^2=\left(x+4\right)^2[/tex]

Thus,

[tex]\left(x+4\right)^2=12[/tex]

Answer:

0.5

Step-by-step explanation:

Answer: 1/2

Step-by-step explanation:

y=1/2x-3

Answer:

A

Step-by-step explanation:

Just took the exam

Using confidence interval concepts, it is found that the margin of error is 5.

A confidence interval (CI) is a range of estimates for an unknown parameter in frequentist statistics. A confidence interval has the format (a,b).

The margin of error is half the difference between the two bounds, that is:

M  =  (  b  -  a  )  /  2

In this problem, the interval is (32, 42), hence, and the margin of error is:

M  =  (  42  -  32 )  /  2  =  10  /  2  =  5

Therefore the margin of error is 5.

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Answer:

i think D

Step-by-step explanation:

Answer:

WARNING! .39 AND .76 IS WRONG.

THE PEOPLE ABOVE ARE INCORRECT.

THE ANSWER IS EITHER .37 OR .62

I believe the correct answer is .62 --> .25 + .37 = .62 . This also makes sense.

(C)

ED2021

The probability that a randomly chosen college student exercises in the morning or afternoon are 0.37.

Probability refers to a possibility that deals with the occurrence of random events. The probability of all the events occurring need to be 1.

From the given Venn diagram, we see that

Probability that the student exercises in the afternoon

P(A) = 0.14 + 0.37 = 0.51

Probability that the student exercises in the morning

P(M) = 0.25 + 0.37 = 0.61

Now, the probability that a randomly chosen college student exercises in the morning or afternoon

P(A ∩ M) = 0.37

Learn more about probability here;

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Answer:

im not sure but i think its 55.2

Step-by-step explanation:

48+15%=55.2

Answer:

I'm pretty sure it's neither? You need a graph or something for that

Answer:

I think its perpendicular

Step-by-step explanation:

When writing these points on a graph they make a square so when you connect the lines from the coordinates they cross making them perpendicular!

Answer:

A.) The inequality 25m + 70 < 350 represents the fact that the student must save more than $11.20 each week to meet the goal. I hope this helped u :)

Step-by-step explanation:

25 x 11.20 = 280

280+70=$350

but since the student wants to save more than $350 that's why it says the student must save MORE than $11.20 each week :)

Answer:

1) D

2) C

3) B

4) A

Step-by-step explanation:

type them into desmos online calculator to see the lines

Hi there! :)

[tex]\large\boxed{\text{B. 11 cm.}}[/tex]

Begin by using Pythagorean theorem to solve for the length of the diagonal of the base:

a² + b² = c²

Use the length and width in the equation:

8² + 3² = c²

64 + 9 = c²

73 = c²

c ≈ 8.54 cm

Now, we can find the length of the diagonal of the prism using our calculated diagonal of the base and the height. Use the same equation:

(8.54)² + 7² = c²

73 + 49 = c²

122 = c²

√122 = c

c = 11.05 ≈ 11 cm. The correct answer is B.

Answer:

i think it might be 15m

Step-by-step explanation:

Answer:

c)

Step-by-step explanation:

Answer:

1:2

Step-by-step explanation:

Answer:jkcv

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Step-by-step explanation:

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Answer:

y = 8x

Step-by-step explanation:

The slope is 8, the y-intercept is 0. The slope-intercept form is written:

y = mx + b

So this situation would be written y =  8x + 0 or just y = 8x.

Hope it helps!

Answer: A, B, C, and E

Step-by-step explanation:

If both sides are real numbers, then the product will be a real number.

If in at least one of the sides we have a complex number, then the product will be real if:

The other number is zero.

The other number is the conjugate of the first.

This is when:

Suppose we have a number:

z = a + b*i

The conjugate will be:

w = a - b*i

And the product between them is:

(a + b*i)*(a - b*i) = a^2 + a*b*i - a*b*i + b^2 = a^2 + b^2

Then the options that will have a real answer are:

A. (4+5i)(4-5i) = 4^2 + 5^2 = 16 + 25 = 41

B. (4 + 91)*(41 - 9) = 3040

C. (3 + 2*i)*(3 -2*i) = 3^2 + 2^2 = 9 + 4 = 13

E. (312 + 7i)*(312 - 7i) = 312^2 + 7^2 = 97,393

Answer:

the answer above is correct

Answer:

boxes

7

8

58.1

119.7

Step-by-step explanation:

look when u solve this it equals

8.3(7)+7.7(8)=119.7 but it tells u to add 61.6 so u go backwards subtract

119.7-61.6

58.1

just plug in

8.3(7)+7.7(8)=____+61.6

plug in

58.1+61.6

119.7

Answer:

1.7 everyday

Step-by-step explanation:

Answer: Many people assume that because DNA is so small, we can't see it without powerful microscopes. But in fact, DNA can be easily seen with the naked eye when collected from thousands of cells.

Answer: 31 degrees

Step-by-step explanation:

The student must incline her camera at 31 degrees to take the picture of bird.

The angle of inclination of a line is the angle formed by the intersection of the line and x-axis.

According to the given question

height of pole = 12m

distance of student from the pole = 20m

Let the angle of inclination be x degrees.

therefore

for the angle of inclination

In ΔABC we have

[tex]tanx=\frac{12}{20}[/tex]

[tex]tanx=\frac{3}{5}[/tex]

[tex]x=tan^{-1} \frac{3}{5}[/tex]

[tex]x = tan^{-1}( 0.6)[/tex]

x = 31 degrees

Hence, the student must incline her camera at 31 degrees to take the picture of bird.

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Answer:

Following are the solution to the question:

Step-by-step explanation:

The objective is to find the orthogonal trajectory of the family curves:

[tex]x^2+2y^2=17k^2[/tex]

The family curves are: [tex]x^2 + 2y^2=17k^2[/tex]  

Differentiate the equation with the respect of x.

[tex]\to x^2+2y^2=17k^2 \\\\\to 2x+4y \frac{dy}{dx} =0\\\\\to \frac{dy}{dx} =- \frac{2x}{4y}\\\\\to \frac{dy}{dx} =- \frac{x}{2y}[/tex]

The negative reciprocal is:

[tex]\to \frac{dy}{dx} =-\frac{1}{-\frac{x}{2y}}\\\\\to \frac{dy}{dx} = \frac{2y}{x}[/tex]

Integration of the above equation:

[tex]\to \frac{dy}{dx} = \frac{2y}{x} \\\\\to \int \frac{dy}{2y} = \int \frac{dx}{x}\\\\\to \frac{1}{2} \log y = \log x + \log C\\\\\to \log y = 2 \log x + 2\log C \\\\\to \log y = \log x^2 +\log C^2 \\\\\to y = Ax^2 \ \ \ \ \ \ \ \ \ (A=C^2)[/tex]

Hence, the orthogonal trajectory of the family of the curves [tex]x^2 + 2y^2 =17k^2 \ \ is \ \ y=Ax^2[/tex]

9514 1404 393

Answer:

  see below

Step-by-step explanation:

When the intercepts are given, plot those and draw a line through them.

_____

Additional comment

The equation shown with the graph is the equation of a line in "intercept form." It is especially useful in a case like this where the intercepts are given.