y = −x2 − 8x − 15 vertex

Answers

Answer 1

Answer: The vertex is (-4,1)

Explanation: I used -b/2a to find the x, then plugged in -4 to find the y, which is 1.


Related Questions

How do you do this question?

Answers

4 Answers: A, B, C, D

=======================================================

Explanation:

f(x) is continuous when x >= 1. The only discontinuity for f(x) is when x = 0, but 0 is not part of this interval.

f(x) is positive for any valid x value in the domain since x^6 is always positive. In general, x^n is positive for all x when n is any even number.

f(x) is decreasing. You can see this through a table of values or through a graph. For anything in the form 1/(x^k), it will be a decreasing function because x^k gets larger, so 1/(x^k) gets smaller, when x goes to infinity.

--------------------

The conditions to use the integral test have been met. So we have to see if [tex]\displaystyle \int_1^{\infty}f(x)dx[/tex] converges or not.

Let's integrate and find out

[tex]\displaystyle \int \frac{1}{x^6} dx = \int x^{-6} dx\\\\\\ \displaystyle \int \frac{1}{x^6} dx = \frac{1}{1+(-6)}x^{-6+1}+C\\\\\\ \displaystyle \int \frac{1}{x^6} dx = \frac{1}{-5}x^{-5}+C\\\\\\ \displaystyle \int \frac{1}{x^6} dx = -\frac{1}{5}*\frac{1}{x^5}+C\\\\\\ \displaystyle \int \frac{1}{x^6} dx = -\frac{1}{5x^5}+C\\\\[/tex]

So we have

[tex]\displaystyle g(x) = \int f(x) dx\\\\\\\displaystyle g(x) = \int \frac{1}{x^6} dx\\\\\\\displaystyle g(x) = -\frac{1}{5x^5}+C\\\\\\[/tex]

Meaning that,

[tex]\displaystyle \int_{a}^{b} f(x) dx = g(b)-g(a)\\\\\\\displaystyle \int_{a}^{b} \frac{1}{x^6} dx = \left(-\frac{1}{5b^5}+C\right)-\left(-\frac{1}{5a^5}+C\right)\\\\\\\displaystyle \int_{a}^{b} \frac{1}{x^6} dx = -\frac{1}{5b^5}+\frac{1}{5a^5}\\\\\\[/tex]

If we plug in a = 1 and apply the limit as b approaches positive infinity, then the expression [tex]-\frac{1}{5b^5}+\frac{1}{5a^5}[/tex] will turn into [tex]\frac{1}{5}[/tex]

Therefore,

[tex]\displaystyle \int_{1}^{\infty} \frac{1}{x^6} dx = \frac{1}{5}\\\\\\[/tex]

Because this integral converges, this means the series [tex]\displaystyle \sum_{n=1}^{\infty}\frac{1}{n^6}[/tex] also converges as well by the integral test.

<1 and <2 are supplementary, so one of the angles is acute,

Find one counterexample to show that each conjecture is false.

Answers

Answer:

make each of the supplementary angles 90, then they are equal.                                                                                                                                                                                                                                                                                                                  

Step-by-step explanation:

A factory makes sheets of metal that are 4 5/8 inches thick. If a worker at the factory makes
a stack of 5 of the sheets, how many inches thick will the stack be?
Write your answer as a fraction or as a whole or mixed number.

Answers

23 1/8

5 (4 + 5/8)
20 +3 1/8
23 1/8

Zeke's birthday party will cost $6 if he invites 3 guests. If there are 8 guests,
how much will Zeke's birthday party cost? Assume the relationship is
directly proportional. *

Answers

If Zeke invites 8 guests, his party will cost $16. Its $2 per guest

Determine whether each relationship below is true or false.

Answers

Answer:

1. True

2. False

3. True

4. False

5. True

Step-by-step explanation:

For 1, you want to see the reduced fraction of 2/6 so you want to divide 2/6 by 2, it is 1/3 and 2/3 is greater than 1/3.

For 2, you want to multiply 5 by 2. and then do the same thing for 6, 6 x 2. Now you want to see if they match.

For 3, you want to make both fractions into decimals so 1/8 is 0.125 and 1/4 is 0.25 and see which is larger.

For 4, you want to see if you can simplify any of them. 2/4 can be simplifed to 1/2. So, it is false because you can see that 2/4 is the same as 1/2

For 5, you want to divide both fractions by 2, so 4/10 would be 2/5 and 4/6 would be 2/3. So it is true.

The answers for the given expressions are given below,

1. True

2. False

3. True

4. False

5. True

What is an expression?

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

For 1, you want to see the reduced fraction of 2/6 so you want to divide 2/6 by 2, it is 1/3, and 2/3 is greater than 1/3.

For 2, you want to multiply 5 by 2. and then do the same thing for 6, 6 x 2. Now you want to see if they match.

For 3, you want to make both fractions into decimals so 1/8 is 0.125 and 1/4 is 0.25, and see which is larger.

For 4, you want to see if you can simplify any of them. 2/4 can be simplified to 1/2. So, it is false because you can see that 2/4 is the same as 1/2

For 5, you want to divide both fractions by 2, so 4/10 would be 2/5, and 4/6 would be 2/3. So it is true.

To know more about an expression follow

https://brainly.com/question/13780981

#SPJ2

• Number of psychology textbooks sold: The number is not correct
A textbook store sold a combined total of 334 biology and psychology textbooks in a week. The number of biology textbooks sold was 84 more than the number
of psychology textbooks sold. How many textbooks of each type were sold?

Answers

Answer:

209 biology books and 125 psychology books were sold.

Step-by-step explanation:

x = biology books y = psychology books

334 = x + y

x = y + 84

x - y = 84

y = x - 84

Using these systems of equations, we can see that (209,125) is the only possible answer. Elimination, substitution, or guess and check are all viable methods to solve this problem. I can explain further if needed! :)

Find the area of the figure. (Sides meet at right angles.)
9 in
in
5 in
B in
4 in

Answers

Answer:

48 in²

Step-by-step explanation:

A1 = 9 x 4 = 36

A1 = 4 x 3 = 12

Total = 36 + 12

        = 48 in²

Find the distance between the points (3, 2) and (15,-3).

Answers

(12,1) would be the new points so count from there!

Consider the reflection of angle abc across the line of reflection pt

Answers

Answer:

bro are you talking about some picture

Step-by-step explanation:

What is X- y= 3 in a graph

Answers

Answer:

You must first put the equation into slope-intercept form (y = mx + b). To do this, subtract x from both sides to isolate y. Then, since y will be negative, divide each side by -1, resulting in y = x - 3. Since a 1 is understood to be in front of the x, the slope is 1

How to graph:

x-0 y- -3 or (0,-3)

x- 3 y-0 or (3,0)

If you graph these points you should get your graph

Can two distinct lines intersect in more than one point?

Answers

No because like if two distinct lines can intersect in no more than one point

How can i use multiplication/division to calculate a percent of a number?

Answers

Answer:

for example you are given a percentage and numbers you cross multiply

Step-by-step explanation:

hope it helps cause I don't know how to explain the answer

2. Mr. Winter is putting away
48 chairs. He can put away
the chairs in stacks of 10 or
as single chairs. What are all
of the ways Mr. Winter can put
away the chairs?
Wh

Answers

he can make 4 stacks, leaving 8 chairs as single chairs

4. The cost of a long-distance telephone call is $.50 for making the call and $.10 per minute. What is the slope? What does it represent?

Answers

$$$$$$$$$$$$$$$$$$$$$$$$$$

This situation can be represented by y=.10x+.50
Therefore the slope is .10
This means that for every minute, the caller is charge .10, and the base rate of .50

what do you mean by '^' next to everything?

Answers

Answer:

power of for example 4 to the power of 2. 2 means square

Find the graph that matches the equation below.
y=-1/3x-1

Answers

Answer:

A

Step-by-step explanation:

3. Select two numbers that have 4 as their greatest
common factor. Mark all that apply.
12
Part
A 2,4
B
4,8
C
8. 12
D 8. 16
E
12. 24
I’m

Answers

Answer:

B and C

Step-by-step explanation:

All others have higher factors than 4

Answer:

B,(4,8) &C,(8,12)

Step-by-step explanation:

A,(2,4)=2=2

4=2^2(GCF of 2&4 is 2)

B,(4,8)=4=2^2

8=2^3(GCF of 4&8 is 4)

C,(8,12)=8=2^3

12=2^2*3(GCF of 8&12 is 4)

D,(8,16)=8=2^3

16=2^4(GCF of 8&16 is 8)

E,(12,24)=12=2^2*3

24=2^3*3(GCF of 12&24 is 12).

i hope it helps you

The sum of three consecutive integers is 42. Determine the value of the smallest
integer.

Answers

Answer:

13.

Step-by-step explanation:

[tex]42 = a + (a+1) + (a+2) = 3a + 3 = 3(a+1)[/tex]

Then, [tex]a+1 = 14[/tex], so [tex]a=13.[/tex]

Bella is in school at math class. Her teacher, Mrs. Williams asks her "What's 9-3 divided by 1/3 + 1 equal to?" help Bella answer the question without using a calculator.

Answers

Que paso que soaso por que yo no le tiendo que paso que paiooo por qhejbocjnsuwojrfnoedorjdowxxexisxecejxiwxbfuwbduwbxuwjuxbwxuwbdiwbxiwnixwnfinfiwndinwdinwidnwixjwixjiwnxiwnfiixwnxiwnxiw
As I believe this is an exponent the answer is 729\ 1/3 +1 sorry if this isn’t far enough

Beck uses 25 robux to buy 3 spins on a game she likes, she spends 8 thousand robux to finally roll a good item.How much spins did she get?

Answers

Answer:

960

Step-by-step explanation:

8000/25 = 320

320 • 3 = 960

The answer is 960 :)

please gyus help me out ..... urgent need......for 20 points please gyus answer it .....​

Answers

Answer:

I wish I could help you but i have not learn yhat yet. so sorrry :( pleaser forgive jme....... please i beg u plase

Step-by-step explanation:

Convert decimal to a mixed number: 10.5 =

Help please

Answers

The answer would be 10 1/2

A dance floor is in the shape of a rectangle.
It is 27 meters long and 16 meters wide.
What is its perimeter?

Answers

Answer:

86 meters

Step-by-step explanation:

27+27+16+16=54+32=86 meters

Which of the following functions is graphed below?

Answers

The second answer, B
It’s the second one It’s b

What are the zeros of x (3 - 18x) = 0 ?

Answers

Answer:

x=3⋅±  2

​  

=±4.2426

x=0

Step-by-step explanation:

While I was walking to schoed this morning I saw 2 ants and 2 butterflies.
My teacher taught me that an insect has 6 legs. Ants one butterflies are
both intects! How many legs were there all together?

Answers

Answer:

it would me 24 legs

Step-by-step explanation:

hope that helps

They are 24 legs in total

If the expression 4x+3 is equal to 1 to the same value of x, what is the expression 4x+8 equal to for the same value of x?

Answers

Answer:

6

Step-by-step explanation:

4x + 3 = 1

4x =-2

x = -1/2 so 4x +8 =4(-1/2) +8=6

The width of a rectangle is 5 times the length. If the perimeter is 72, find the dimensions of the rectangle.

Answers

Answer:

l=6

b=30

Step-by-step explanation:

b=5l

perimeter= 72

2(l+b)= 72

l+b= 36

l+5l= 36

6l= 36

l= 6

b=5l= 6*6= 30

A mixture requires 4 cups of water for every 7 cups of flour used. How many cups of water should be used with 28 cups of flour

Answers

Answer:

16 cups of water

formula for calculating average speed

Answers

The most common formula for average speed is distance traveled divided by time taken. The other formula, if you have the initial and final speed, add the two together, and divide by 2
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