Which statements about the graph of the function f(x) = -x² - 4x + 2 are true? Select three options.
The domain is {x|x ≤-2}.
The range is {yly ≤ 6}
The function is increasing over the interval (-∞, -2).
The function is decreasing over the interval (-4,00).
The function has a positive y-intercept

Answer:

AABC and AXYZ are similar triangles. The lengths of two sides of each triangle are shown. Find the lengths of the third side of each triangle

The simplified expression of [tex]\frac{1}{a + 1} + \frac{1}{a - 1} - \frac{2a}{a^2 + 1} - \frac{4a}{a^4 + 1}[/tex] is [tex]\frac{8a}{a^8 - 1}[/tex]

The expression is given as:

[tex]\frac{1}{a + 1} + \frac{1}{a - 1} - \frac{2a}{a^2 + 1} - \frac{4a}{a^4 + 1}[/tex]

Add the first two terms

[tex]\frac{a - 1 + a + 1}{(a + 1)(a - 1)} - \frac{2a}{a^2 + 1} - \frac{4a}{a^4 + 1}[/tex]

Evaluate

[tex]\frac{2a}{a^2 - 1} - \frac{2a}{a^2 + 1} - \frac{4a}{a^4 + 1}[/tex]

Evaluate the first two terms

[tex]\frac{2a^3 + 2a - 2a^3 + 2a}{(a^2 - 1)(a^2 + 1)} - \frac{4a}{a^4 + 1}[/tex]

Evaluate

[tex]\frac{4a }{a^4 - 1} - \frac{4a}{a^4 + 1}[/tex]

Take the LCM

[tex]\frac{4a^5 + 4a - 4a^5 + 4a }{(a^4 - 1)(a^4 + 1)}[/tex]

Evaluate the like terms

[tex]\frac{8a}{a^8 - 1}[/tex]

Hence, the simplified expression is [tex]\frac{8a}{a^8 - 1}[/tex]

Read more about expressions at:

https://brainly.com/question/723406

#SPJ1

The cost of 45 packets of instant noodles given the direct variation is $52.335

let

n = k × p

k = constant of proportionality

34.88 = k × 30

34.88 = 30k

k = 34.88/30

k = 1.16266666666666

Approximately,

k = 1.163

Find n when p = 45

n = k × p

= 1.163 × 45

n = $52.335

Learn more about variation:

https://brainly.com/question/6499629

#SPJ1

Answer:

Step-by-step explanation:

eq of line perpendicular to 3x+5y=10 is

5x-3y=a

where a is constant.

it passes through (3,2)

5(3)-3(2)=a

a=15-6=9

reqd. eq. is 5x-3y=9

or

3y=5x-9

y=5/3 x-3

gradient=5/3

y-intercept=-3

or

5y=-3x-10

y=-3/5 x-2

slope=-3/5

slope of reqd. line=-1/(-3/5)=5/3

eq. of line through (3,2) is

y-2=5/3(x-3)

3y-6=5x-15

3y=5x-15+6

3y=5x-9

y=5/3 x-3

Answer:

If the x-6 is all under the sqrt, the last answer is right:

6<= x <= infinity

If only x is under the sqrt and - 6 is NOT under the sqrt, then:

0 <= x <= infinity is the correct answer.

Step-by-step explanation:

You can look at the equation and or graph to determine the domain of a function. The domain is all the x's that may go into the equation or all the x's on the graph of the function. Inside of a squareroot symbol the number inside there must be positive. While considering the equation, only x's that keep that inside positive can be used.

For sqrt(x-6), x has to be 6 or bigger.

For sqrt(x) - 6, x has to be 0 or bigger.

The graph of the inequality can be seen in the image at the end.

Here we have the inequality:

y ≥ 4x - 3

To graph this we need to graph the line:

y = 4x - 3

With a solid line (because the points on the line are solutions) and then shade the region above that line.

The graph of the inequality can be seen below.

If you want to learn more about inequalities:

https://brainly.com/question/18881247

#SPJ1

Step-by-step explanation:

to be a tangent, it would have to have a 90° angle with the radius (12).

and that would make the triangle ABCenter of the circle a right-angled triangle.

and then Pythagoras must apply :

c² = a² + b²

with c being the Hypotenuse (the baseline opposite of the 90° angle). in our case the 20-line.

so,

20² = 12² + 16²

400 = 144 + 256 = 400

yes, it is confirmed, because the Pythagoras principle applies, it is a right-angled triangle, and therefore AB is indeed a tangent.

Answer:

the line AB is tangent to the circle

Step-by-step explanation:

we have :

16² + 12² = 256 +144 = 400

On the other hand:

20² = 400

Then

16² + 12² = 20²

Then

According to the Pythagorean theorem:

The line AB is perpendicular to the radius of the circle

Which means the line AB is tangent to the circle.

Hello,

    9k - 2  88

⇔ 9k - 2 + 2 ≥ 88 + 2

⇔ 9k ≥ 90

⇔ 9k/9 ≥ 90/9

⇔ k ≥ 10

S = [10 ; + ∞ [

Answer:

k ≥ 10

Step-by-step explanation:

9k - 2 ≥ 88

Step 1 : Add 2 on both sides.

9k - 2 + 2 ≥ 88 + 2

9k + 0 ≥ 90

9k ≥ 90

Step 2 : Divide 9 on both sides.

9k/9 ≥ 90/9

k ≥ 10

Using it's concept, the desired probability is:

P(Female|Junior) = 75%.

A probability is given by the number of desired outcomes divided by the number of total outcomes.

In this problem, there are 8 Junior Students, out of which 6 are Female, hence the probability is:

P(Female|Junior) = 6/8 = 0.75 = 75%.

More can be learned about probabilities at  https://brainly.com/question/24372153

#SPJ1

Step-by-step explanation:

Answer

a - 8

------------+

2

Answer:

50%

Step-by-step explanation:

In rhe beginning, there were 24 + 20 = 44 students trying out in total. After a week, there are 44 - 6 - 2 = 36 students remaining. Of those 36 students, 18 of them are trying out for the basketball team. The percentage of students trying out for the basketball team would be 18/36 = 0.5 = 50%

Answer: B

Step-by-step explanation:

The area of entire rectangle is (9)(4)=36.

The area of the square inside is [tex]x(x)=x^2[/tex]

Subtracting the areas, we get [tex]36-x^2[/tex]

Answer:

C. 29

Step-by-step explanation:

[tex]f(x) = -3x^3 + 2x^2 +24[/tex]

• To calculate [tex]f(-1)[/tex] , we have to replace x with -1 in the definition of [tex]f(x)[/tex] , and calculate the value:

[tex]f(-1) = -3(-1)^3 + 2(-1)^2 + 24[/tex]

         ⇒ [tex]-3(-1) +2(1) + 24[/tex]

         ⇒ [tex]3 + 2 + 24[/tex]

         ⇒ [tex]29[/tex]

[tex]\huge\boxed{\textsf{C.}\ 29}[/tex]

We have this equation:

[tex]f(x)=-3x^3+2x^2+24[/tex]

Substitute [tex]x=-1[/tex]:

[tex]f(-1)=-3(-1)^3+2(-1)^2+24[/tex]

Simplify to find the final answer:

[tex]\begin{aligned}f(-1)&=-3(-1)+2(1)+24\\&=3+2+24\\&=5+24\\&=\boxed{29}\end{aligned}[/tex]

Answer:

1/100

Step-by-step explanation:

The answer is 1/100 because we don't know how many people are in the group but do know that only 1 person has been taken from the group and the probability will be 1 out of how many people are in the group so we just put 100 there as we don't know how many people are in the group.

Ps: Sorry if this is wrong, this is just a guess.

the price that they should charge on the 2 year extended warranty is in order to break even is $10.

the price at which the company would breakeven is:

= percentage of product that will fail x replacement cost

solving gives:

= 4% x 250

= $10

find out more on warranty cost at https://brainly.com/question/25750069.

#SPJ1

Answer: None

Step-by-step explanation:

There is no triangle with an angle measure of 0 degrees.

Answer:

9 and 11  

Step-by-step explanation:

First number = x -2

Second number = x

  and   2x = 3(x-2)  - 5

            2x = 3x - 6 - 5

             x = 11

              first number = 11-2 = 9

The value of x in the given expression is; x = wz/y

We are given the expression;

w/x = y/z

Now, we want to find the value of x which means we want to make x the subject of the formula. Thus;

Multiply both sides of the given expression by x to get;

(w/x)*x = (y/z)*x

⇒ w = xy/z

Now, multiply both sides by z/y to get;

w(z/y) = (xy/z) * (z/y)

wz/y = x

Thus, the value of x in the given expression is;

x = wz/y

The correct question is;

If w/x = y/z, then what is the value of x

Read more about Subject of Formula at; https://brainly.com/question/10643782

#SPJ1

The composite function of the paintings Jenny completes in a year is

[tex]P(J(y))=\frac{1}{2}J(y)+1[/tex]

A composite function is a function made of other functions, where the output of one function is the input to the other function.

An example of the composite functions 2x+3 and [tex]x^{2}[/tex] together make the composite function [tex](2x+3)^{2}[/tex]

We have [tex]P(w)=\frac{1}{2}w+1[/tex]

Here, P(w) represents the number of paintings Jenny completes in some w weeks. and

J(y)  represents the number of weeks per year.

As J(y) is the number of weeks spent per year in painting, we can calculate the paintings completed in a year by substituting

w as J(y) in the equation we have

Then the equation becomes:[tex]P(J(y))=\frac{1}{2}J(y)+1[/tex]

Hence this is the composite function that would represent the number of paintings Jenny completes in a year.

Learn more about composite functions here:

https://brainly.com/question/10687170

#SPJ4

Answer:   [tex]\boldsymbol{(x + 4)^2 + (y + 6)^2 = 49}\\\\[/tex]

Work Shown:

[tex](h,k) = (-4,-6) = \text{center}\\\\r = 7 = \text{radius}\\\\(x - h)^2 + (y - k)^2 = r^2\\\\(x - (-4))^2 + (y - (-6))^2 = 7^2\\\\\boldsymbol{(x + 4)^2 + (y + 6)^2 = 49}\\\\[/tex]

To check the answer, you can use a graphing calculator like GeoGebra or Desmos or similar.

Answer:

0.026

Step-by-step explanation:

Twenty-Six = 26 ( But for simplicity in the Next Step write it as 26.)

Then Twenty-Six Thousandths = 0.026

James must mix 60 millilitres of 10% solution and 40 millilitres of 50% solution.

Given that, James needs to mix a 10% acid solution with a 50% acid solution to create 100 millilitres of a 26% solution.

Let the acid solution needs to mix with 10% be x ml and the acid solution needs to mix with 50% will be 100 - x ml.

Now,

10% x + 50% ( 100 - x ) = 26% ×100

⇒[tex]\frac{10x}{100} +\frac{50(100-x)}{100}=\frac{2600}{100}[/tex]

⇒10x + 50( 100 - x ) = 2600

⇒10 x + 5000 - 50x = 2600

⇒10 x - 50 x = 2600-5000

⇒-40 x = -2400

⇒x=60

Therefore, James must mix 60 millilitres of 10% solution and 40 millilitres of 50% solution.

To learn more about the percentage visit:

https://brainly.com/question/13450942.

#SPJ1

Answer:

5

Step-by-step explanation:

2 × 2 = 4

3× 3 = 9

4 × 4 =16

5 × 5 =25

16 is the only number and closest number to 21 to subtract from

The expression is equivalent to 2 , option C is the right answer.

An expression in maths is a statement that contains , constants , variables and mathematical operators.

The expression given in the question is

[tex]\rm \dfrac { 4^{\frac{5}{4}} * 4^{\frac{1}{4}}} {4^{\frac{1}{2}}}[/tex]

Applying exponent rule

[tex]\rm a^m * a^n = a^{m+n}[/tex]

[tex]\rm \dfrac { 4^{\frac{5}{4} +\frac{1}{4}}} {4^{\frac{1}{2}}}[/tex]

Applying exponent rule

[tex]\rm \dfrac{a^m}{a^n} = a^{m-n}[/tex]

[tex]\rm { 4^{\frac{5}{4} +\frac{1}{4} -{\frac{1}{2}}}[/tex]

On solving the exponents

=(6/4) -(1/2)

=4/4

=1

=[tex]\rm 4^{\frac{1}{2}}[/tex]

= 2

Therefore the expression is equivalent to 2 , option C is the right answer.

To know more about Expression

https://brainly.com/question/14083225

#SPJ1

The equation for total pay is y = 10/8x.

Division is the mathematical operation that is used to determine the quotient of a number. In order to determine the total pay for hours from 0 to 8, the pay per hour has to be determined. To determine this value, divide $10 by 8.

Pay per hour = $10 / 8

y = 10/8x.

To learn more about division, please check: https://brainly.com/question/194007

#SPJ1

Answer:

Step-by-step explanation:

The best way to answer a question like this one is to use a graphing program on the internet. This graph was done with desmos

It looks to me that the equation is g(x)  = 10(x - 5)^2 - 37

I checked to see that this is correct, and thank goodness it is.

The graph is shown below.

Answer:

any # where -2<=x<7

Step-by-step explanation:

(x-7) would be negative and (x+3) positive, resulting in f(x) being negative.

Answer: $36.68 or $35.97. Read below.

Step-by-step explanation: You need to multiply the 12 foot by 12 foot and you would get 144 sq feet. Then divide 47 into 144. You will be left with 3.06, and if you need to round, you can round that to 3. Then you need to multiply 3 by $11.99 and you will be left with the cost for the paint, which is $35.97 if you do round to a three, and $36.68 if you do not round the three. So your answer is either $36.68 or $35.97 depending on whether you round or not.