The function y = f(x) is graphed below. What is the average rate of change of the
function f(x) on the interval -8 ≤ x ≤ 8?

Answer:

The simplified form is -26x^2 + 56x -15

Step-by-step explanation:

We need to solve the expression:

3x(-2x+7)-5(x-1)(4x-3)

Multiplying the terms outside the bracket with the terms inside the bracket.

=-6x^2+21x-5(x(4x-3) -1(4x-3))

= -6x^2+21x-5(4x^2-3x-4x+3)

= -6x^2+21x-5(4x^2-7x+3)

Now multiply -5 with the terms inside the bracket

= -6x^2+21x -20x^2 +35x -15

Now, Combining the like terms:

= -6x^2 -20x^2 +21x+35x -15

Adding the like terms

= -26x^2 + 56x -15

So, the simplified form is -26x^2 + 56x -15

-26^2+56x-15 yea that should be the answer

Answer: 79

Step-by-step explanation:

[tex]\sqrt{k+2}-9=0\\\\\sqrt{k+2}=9\\\\k+2=81\\\\k=\boxed{79}[/tex]

Answer:

D) k = 79

Step-by-step explanation:

Given equation: [tex]\sf\sqrt{k+2}-x=0[/tex]

Steps:

1. Substitute 9 as the value of x in the equation:

[tex]\sf\sqrt{k+2}-9=0[/tex]

2. Add 9 to both sides:

[tex]\sf\sqrt{k+2}-9+9=0+9\\\\\Rightarrow \sqrt{k+2}=9[/tex]

3. Square both sides of the equation:

[tex]\sf\left(\sqrt{k+2}\right)^2=9^2\\\\\Rightarrow k+2=81[/tex]

4. Subtract 2 from both sides:

[tex]\sf k+2-2=81-2\\\\\Rightarrow k = 79[/tex]

5. Check your work:

[tex]\sf\sqrt{k+2}-x=0\ \textsf{[ substitute 79 for k, and 9 for x ]}\\\\\sqrt{79+2}-9=0\ \textsf{[ add ]}\\\\\sqrt{81}-9=0\ \textsf{[ take the square root ]}\\\\9-9=0\ \textsf{[ subtract ]}\\\\0=0\ \checkmark[/tex]

Answer:

{-3, 2, -5, 1, 6}

Step-by-step explanation:

The domain is the set of input values.

Answer:

4 ^3sqrt(2)

Step-by-step explanation:

two 2's can come out of the square root and it leaves one left in it and 2x2 is 4 which is on the outside.

The answers to the following question is

1) KL = 10

2) TE= 15 cm

3) angle PUT= 13

4) angle SQP = 21

Two triangles are similar if they have the same ratio of corresponding sides and equal pair of corresponding angles. If two or more figures have the same shape, but their sizes are different, then such objects are called similar figures.

1) Using similarity property in given triangle

SR/ KI= SJ / JK

AS, JK= 2 SJ

SR/ KI= SJ / 2 SJ

5/ KI =  1/2

KL= 10

2) As, the diagonal of parallelogram bisect equally each other then

VE = TE

AS, VE = 15

So, TE= 15 cm

3) As, PU is the bisector of angle SUT

angle PUT= 1/2 (angle SUT)

PUT = 1/2 (26)

angle PUT= 13

4) As PQ is the bisector SQR

angle PQR= angle SQP = 21

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Answer: -1(x+2)^2+10

Step-by-step explanation:

1. The coefficient of -x^2 is just the number in front, which in this case would be a = -1 So now the function is -1(x^2+4x)+6 since negative one has been factored out of the first two terms.

2. Half of the coefficient of x would be 2 since x has a coefficient of 4, and half pf 4 is 2. Squared, it is 4. That will be added inside the bracket. Subtracted on the outside is the same equation but multiplied by a, which we found out was -1 in the beginning. So, the function becomes -1(x^2+4x+4)+6-(-4).

3. Factor the inside equation to find that it’ll become (x+2)^2, and simplify the outside to get 10. The function will now be;

f(x)=-1(x+2)^2+10

Hope that made sense and make sure to check just in case I did the math wrong :]

The question was incomplete. Below you will find the missing image.

Only the Saki's triangle can be solved using law of cosines.

Law of cosines formula is used to find missing including angle or missing side.
It is used in SAS and SSS triangles.
If a, b & c are three sides and C be the vertices opposite to side c then,
c²=a²+b²-2ab×CosC
Here in the given image we see that,
In Anna's triangle, there is one side and one angle.
So, it is not possible to solve with law of cosines.
In Yuna's triangle, there are two angles and one side.
So, also it is not possible to solve with law of cosines.
In Carley's triangle, there are three angles.
Also in this case, law of cosines it not possible to use.
In Saki's triangle, there are three sides are given. So, it is a SSS triangle.
We can apply the law of cosines here in this triangle.

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Answer:

275x packages of 720 cashews

Step-by-step explanation:

450-175=275

(a+1)b

a=15 and b=45

(15 + 1) x 45 = 720

The translation of the parabola from y = (x – 5)² + 5 to y = (x − 0)² + 0 will be (-5, -5). Then the correct option is B.

It's the locus of a moving point that keeps the same distance between a stationary point and a specified line. The focus is a non-movable point, while the directrix is a non-movable line.

The equation of a quadratic function, of vertex (h, k), is given by:

y = a(x – h)² + k

where a is the leading coefficient.

The translation of the parabola is given below.

y = (x – 5)² + 5 → y = (x − 0)² + 0

Then the translation will be (-5, -5).

Then the correct option is B.

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Answer:

The product xy is constant, so the relationship is an inverse variation.

Step-by-step explanation:

Inverse variation is the mathematical relationship between two variables which can be expressed by an equation in which the product of two variables is equal to a constant.

inverse variation is the relationships between variables that are represented in the form of y = k/x, where x and y are two variables and k is the constant value. It states if the value of one quantity increases, then the value of the other quantity decreases.

Here, the product xy is constant and gives the product as 960.

The relationship is inverse relationship.

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Total Earned Saturday: $45

Total Earned Sunday: $63

Total: $108

Time and a quarter means that you divide his normal rate by 4 and add that to his normal rate.

9/4 = 2.25     2.25 + 9 = 11.25

Jarvis makes $11.25 an hour on Saturdays.

Since he worked 4 hours, you multiply,

11.25 x 4 = 45.

Time and three quarters mean that you multiply his normal rate by 3/4 and add that to his normal rate

9x0.75 = 6.75     6.75 + 9 = 15.75

Jarvis makes $15.75 an hour on Sundays. Since he worked 4 hours, you multiply 15.75 x 4 = 63.

To get the total, you add his earnings on Saturday and earnings on Sunday

45 + 63 = 108.

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Answer:

It is not arithmetic, so therefore there is no common difference

Step-by-step explanation:

An arithmetic sequence is a sequence where each term increases by adding/subtracting some constant k. There is no constant term in the above pattern.

Answer:

  not an arithmetic sequence

Step-by-step explanation:

An arithmetic sequence is a sequence of numbers that have a common difference. That is, the difference between any term and the previous term is constant for the sequence. Other kinds of sequences have other relationships between the differences.

The "first" differences of this sequence are ...

The first differences are not constant. However, we notice the "second" differences are constant. These are the differences of successive first differences.

The first differences are not constant, so this sequence is not an arithmetic sequence.

For polynomial sequences, the level of constant difference tell you the degree of the polynomial describing the sequence. This sequence has constant 2nd-level differences, so can be described by a 2nd degree (quadratic) polynomial:

  f(n) = 1.5n² +1.5n +1 . . . . . a quadratic sequence

__

Additional comment

Sequences that are exponential have differences that have a common ratio. That ratio is the same at every level. It is the base of the exponential function.

Answer:

I hope it helps .in case you don't understand any part ,feel free to ask.

Step-by-step explanation:

to "solve" this I need an equation.

this whole expression must be equal to something.

without that I can only try to simplify the expression.

remember that

a/b / c/d = ad / bc

so, here we have

3a/(((a²/x) - 1)(a/x - 1)) = 3a/(a³/x² - a²/x - a/x + 1) =

= 3a/(a³/x² - a²/x - a/x - a/a) =

= 3a/((a²/x² - a/x - 1/x - 1/a)×a) = 3/(a²/x² - a/x - 1/x - 1/a)

Answer:

Step-by-step explanation:

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

Answer:  [tex]\textsf{y = 5/7x + 51/7}[/tex]

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

Given: [tex]\textsf{Goes through (1, 8) and is parallel to y = 5/7x + 7}[/tex]

Find:  [tex]\textsf{Write an equation that follows that criteria}[/tex]

Solution: We know that our equation is going to parallel to the line that was given therefore the slope would stay the same at 5/7.  We also have a point so we can plug in the values into the point-slope form, distribute, and solve for y.

Plug in the values

Distribute

Add 8 to both sides

Therefore, the final equation that follows the description that was provided in the problem statement is y = 5/7x + 51/7.

Answer:

The right graph

Step-by-step explanation:

Because the equation is in point slope form, we know it passes through (3,1) and has a slope of 2/3.

The z-score of an appliance that stopped working at 64 months is 2.

The mean of observations is equal to the ratio of sum of all the observations and the number of observations.

Given, the set of life spans of an appliance is normally distributed with a mean mu = 48 months and a standard deviation sigma = 8 months

The z-score is then calculated as

z = x - μ /σ

For an appliance that stopped working at 64 months, we have

x = 64

On substituting the values, we get

z = 64-48/8

z = 2

Hence, the z-score of an appliance that stopped working at 64 months is 2

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Answer:

D on edge

Step-by-step explanation:

2

Answer:

Step-by-step explanation:

Givens

Parallelogram EASY with diagonal ES

<AES = 40

<Y = 110

Solution

<AES = 40               GIVEN

<ESY = 40                     Z THEOREM OF A PRALLELOGRAM

<A = <Y                         PROPERTY OF A PARALLELOGRAM

<A = <110                      <A = 110 BECAUSE <Y = 110

<YES = 180 - <Y           -<ESY EVERY TRIANGLE HAS 180o

<YES = 180 - 110 - 40    SIMPLIFY

<YES = 30

<YEA = <YES + <AES    WE KNOW BOTH ANGLES ON THE RIGHT.

<YEA = 30 + 40             COMBINE

<YEA = 70

You could do <YEA by noting that consecutive angles of a Parallelogram equal 180

Answer:

[tex]1 \frac{1}{5} [/tex]

Step-by-step explanation:

[tex]3 \times \frac{2}{5} \\ \frac{3}{1} \times \frac{2}{5} = \frac{6}{5} \\ \frac{6}{5} = 1 \frac{1}{5} [/tex]

Answer:

40°

Step-by-step explanation:

Given l \\ m,

m∠13 = m∠7 (alternate interior angles)

m∠13+m∠15 = 180° (Sum of angles in a straight line)

[tex]6x+4+(14x-4)=180\\6x+4+14x-4=180\\20x=180\\x=\frac{180}{20} \\=9\\\\[/tex]

Substitute x to find m∠13

m∠13= 6x+4 = 6(9)+4 = 36 + 4 = 40°

The multiplicative rate of change is 2/3

The complete question is in the image

The multiplicative rate of change is then calculated as:

r = y2/y1

This gives

r = 4/6

Simplify

r = 2/3

Hence, the multiplicative rate of change is 2/3

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Answer:

b.

Step-by-step explanation:

Step-by-step explanation:

1. first multiply -1 times all elements of matrix A

2. then multiply 1/3 by all elements of matrix B

3. then add each corresponding entries to get the result.

from step 1. matrix A will be

-4 -2. -1. -3

-2. 0. 1. -3

step 2. matrix B will be

3. -1. -2. -4

3. -10. 10. -1

add each corresponding elements to get

-1. -3. -3. -7

1. -10 11. -4

Answer:

4x55x2

Step-by-step explanation:

4 kids 55trys 50 50 odds

It takes 16,064 years for the 500g of radium to decay to 5g.

Here we have the decay equation:

[tex]Q(t) = Q_0*e^{-k*t}[/tex]

Where Q₀ is the initial amount, and k is the decay constant.

We know that:

Q₀ = 500g

k = 0.00043

And we want to find the value of t such that Q(t) = 5g, so we need to solve:

[tex]5 = 500*e^{-0.00043*t}\\\\5/500 = e^{-0.00043*t}\\\\0.001 = e^{-0.00043*t}[/tex]

Now we can apply the natural logarithm in both sides:

[tex]ln(0.001) = ln(e^{-0.00043*t})\\\\ln(0.001) = -0.00043*t\\\\\frac{ln(0.001)}{-0.00043} = t = 16,064.5[/tex]

So it takes 16,064 years for the 500g of radium to decay to 5g.

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The intersecting secant theorem states the relationship between the two intersecting secants of the same circle. The given problems can be solved using the intersecting secant theorem.

When two line secants of a circle intersect each other outside the circle, the circle divides the secants into two segments such that the product of the outside segment and the length of the secant are equal to the product of the outside segment other secant and its length.

a(a+b)=c(c+d)

1.)

6(x+6) = 5(5+x+3)

6x + 36 = 25 + 5x + 15

x = 4

2.)

4(2x+4)=5(5+x)

8x + 16 = 25 + 5x

3x = 9

x = 3

3.)

8x(6x+8x) = 7(9+7)

8x(14x) = 112

112x² = 112

x = 1

4.)

(x+3)² = 16(x-3)

x² + 9 + 6x = 16x - 48

x² - 10x - 57 = 0

x = 14.0554

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True. We can probably expect that yacht sales will go down and the government will not collect lots of new tax revenues.

It is given that the US government has put a 20% luxury tax and the price elasticity for these yachts is elastic at 2.50.

Due to the new tax on luxury goods, it can be estimated that the sales of yachts go down as the maximum retail price of the yachts will become more expensive. This can mean that fewer people than before will be able to afford the yachts. Due to fewer sales, the government will not have enough tax revenues.

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Let [tex]A(x_A,\ y_A),\ B(x_B,\ y_B)[/tex]. Then a slope of the line AB represent the formula:

[tex]m=\dfrac{y_B-y_A}{x_B-x_A}[/tex]

Substitute the coordinate od the points to the formula of a slope.

[tex]A.\\(4,\ 6),\ (2,\ 2)\\\\m=\dfrac{2-6}{2-4}=\dfrac{-4}{-2}\\\\\huge\boxed{m=2}[/tex]

[tex]B.\\(8,\ 8),\ (2,\ 4)\\\\m=\dfrac{4-8}{2-8}=\dfrac{-4}{-6}\\\\\huge\boxed{m=\dfrac{2}{3}}[/tex]

[tex]C.\\(8,\ 2),\ (2,\ 4)\\\\m=\dfrac{4-2}{2-8}=\dfrac{2}{-6}\\\\\huge\boxed{m=-\dfrac{1}{3}}[/tex]

[tex]D.\\(6,\ 2),\ (2,\ 4)\\\\m=\dfrac{4-2}{2-6}=\dfrac{2}{-4}\\\\\huge\boxed{m=-\dfrac{1}{2}}[/tex]

The values of the trigonometry ratios are:

1: sin α = -12/13 and tan α > 0, find cos α and cot α

Because tan α > 0, then it means that cos α and sin α are negative

So, we have:

sin²α + cos²α = 1

Substitute sin α = -12/13

(-12/13)² + cos²α = 1

This gives

cos²α = 1 - (-12/13)²

Evaluate the squares

cos²α = 1 - 144/169

Evaluate the difference

cos²α = 25/169

Take the square root of both sides

cos α = - 5/13

The cotangent ratio is represented as:

cot α = cos α/sin α

This gives

cot α = (-5/13)/(-12/13)

Evaluate

cot α = 5/12

Hence, cos α = - 5/13 and cot α = 5/12

2: tan α = -12/5 for α in quadrant IV, find sec α and cot α

Because α is in quadrant IV, then it means that sec α is positive

cot α = 1/tan α

This gives

cot α = 1/(-12/5)

Evaluate

cot α = -5/12

Also, we have:

sec²α = 1 + tan²α

Substitute tan α = -12/5

sec²α = 1 + (-12/5)²

Evaluate the squares

sec²α = 1 + 144/25

Evaluate the sum

sec²α = 169/25

Take the square root of both sides

sec α = 13/5

Hence, cot α = -5/12 and sec α = 13/5

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