DO NOT ANSWER W/O EXPLANATION PLEASE! NEED WRITTEN SOLUTION.In triangle ABC, an altitude is drawn from vertex C to the line containing AB. The length of this altitude is h and h=AB. Which of the following is true?
I. Triangle ABC could be a right triangle.
II. Angle C cannot be a right angle.
III. Angle C could be less than 45 degrees.

Answers

Answer 1

Answer:

We have altitude h to side AB and AB=h, i.e. the altitude is congruent to the side it goes to.

That's all kinds of triangles. One way to see them is using two horizontal parallel lines h apart, the bottom one with a base AB=h somewhere on it. Then any C on the top line makes a triangle ABC with altitude h=AB.

Let's go through the choices.

I. ABC could be a right triangle. That's TRUE.

We could have the isoscleles right triangle, C directly above B, so AC is the leg and an altitude, AB=AC and B is the right angle.

II. Angle C cannot be a right angle. That's TRUE.

The biggest angle C can be is when it's over the midpoint of AB, so if AB=2, h=2, and

$AC=√(2^2+1^2)=√(5)$

$C_{\textrm{max}} = 2 \arctan(1/2) \approx 53.13^\circ$

III. Angle C could be less than 45 degrees. That's TRUE.

As long as C stays on our top parallel, we can make it as acute as we like by going farther away from AB.

All true. Hmmm.

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A polling company conducts an annual poll of adults about political opinions. The survey asked a random sample of 419 adults whether they think things in the country are going in the right direction or in the wrong direction, 54% said that things were going in the wrong direction. How many people would need to ve surveyed for a 90% confidence interval to ensure the margin or error would be less than 3%?

Answers

Answer: 747

Step-by-step explanation:

When prior estimate of population proportion (p) is given , then the formula to find the sample size is given by :-

$n=p(1-p)((z^*)/(E))^2$

, where z* = Critical value and E = Margin of error.

As per given , we have

p= 0.54

E= 0.03

Critical value for 90% confidence : z* = 1.645

Then, the required sample size is given by :-

$n=0.54(1-0.54)((1.645)/(0.03))^2$

$n=0.2484(54.8333333333)^2$

$n=746.862899999\approx747$

Hence, the number of people would be needed = 747

A company’s total cost from manufacturing and selling x units of their product is given by: y = 2x2 – 600x + 49,000. How many units should be manufactured in order to minimize cost, and what is the minimum cost?a. (100, $9,000)b. (125, $3,250)c. (150, $4,000)d. (170, $4,800)e. (200, $9,000)

Answers

Answer: Option 'c' is correct.

Step-by-step explanation:

Since we have given that

$y=2x^2-600x+49000$

We need to find the number of units in order to minimize cost.

We first derivative w.r.t. x,

$y'=4x-600$

For critical points:

$y'=0\n\n4x-600=0\n\n4x=600\n\nx=(600)/(4)\n\nx=150$

Now, we will check whether it is minimum or not.

We will find second derivative .

$y''=4>0$

So, it will yield minimum cost.

Minimum cost would be

$y(150)=2(150)^2-600* 150+49000\n\ny(150)=\$4000$

Hence, At 150 units, minimum cost = $4000

Therefore, Option 'c' is correct.

What is the solution of | x + 5 | > 7

Answers

Step-by-step explanation:

inequality form would be x<-12 or >2

I hope this helps

Answer:

Step-by-step explanation:

(x+5)>7

x+5>7

x>7-5

x>2

Which of the following describes the roots of the polynomial function f(x)=(x-3)*(x+6)²?-3 with multiplicity 2 and 6 with multiplicity 4
-3 with multiplicity 4 and 6 with multiplicity 2
O3 with multiplicity 2 and-6 with multiplicity 4
O3 with multiplicity 4 and -6 with multiplicity 2

Answers

Final answer:

The roots of the polynomial function f(x)=(x-3)*(x+6)² are 3 and -6.

Explanation:

The polynomial function f(x)=(x-3)*(x+6)² can be factorized as follows:

f(x) = (x-3)*(x+6)*(x+6)

This means that the expression (x-3) represents one of the linear factors of the polynomial, while (x+6) represents a quadratic factor. To find the roots of the polynomial, we set each factor equal to zero and solve for x:

(x-3) = 0 -> x = 3

(x+6) = 0 -> x = -6

Therefore, the roots of the polynomial function f(x)=(x-3)*(x+6)² are 3 and -6.

Learn more about Polynomial roots here:

brainly.com/question/31214281

What is the value of the expression? 8 + 2 x 3--------------
5 x 2 - 8

Answers

2 x 3 6

-------------- = -------- = 3

5 x 2 - 8 2

Molly runs 3 miles on Monday, Wednesday,amd Friday she runs twice as far on Saturday as she does on Monday.How many total mules did she run each week

Answers

she run a total of 15. If you add 3 miles to everyday she ran and then add 6 on saturday then you would get 15.

Answer: 15 miles

Step-by-step explanation:

So, Molly runs 3 miles and theres 3 days. Monday, Wednesday, and Friday. 3 x 3 is 9 and on Friday she runs twice the amount. So 3x2 is 6 and 9+6 is 15.

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