Consider the functions below. f(x)=8x^2+x+3, g(x)=4x-1, h(x)=3x+6. Which of the following statements is true?
A.
As x approaches infinity, the value of g(x) eventually exceeds the values of both f(x) and h(x).
B.
Over the interval [3, 5], the average rate of change of g and h is more than the average rate of change of f.
C.
Over the interval [0, 2], the average rate of change of f and h is less than the average rate of change of g.
D.
As x approaches infinity, the values of g(x) and h(x) eventually exceed the value of f(x).

Answer: 7 1/16  and 1 9/16

Step-by-step explanation:  1 3/8 x 1.5 is 1 3/8 x 1 5/10  11/8 x 15/10 which is 165/80. We divide it by 5/5 to get 33/16. This as a mixed number is 2 1/16.  We add 5 to get 7 1/16.

5/8 divided by 0.4 is 5/8 divided by 2/5. We divide this by first finding the reciprocal of 2/5 which is 5/2. 5/8 x 5/2 = 25/16. This as a mixed number is 1 9/16.

Answer:

If line EF is parallel to line CD, it will not intersect plane L.

Answer:

10b/y^2

Step-by-step explanation:

Hope this helps! :)

Based on the percentage of the first, second, and third acids, the milliliters of each acid that should be used to make 100 ml of 18% are:

Assuming the concentration of the 40% acid is denoted as x, the other acid concentrations would be:

10% acid = 4x

20% = 100 - 5x

The target solution is 100ml of 18%.

Solving gives:

(10% × 4x) + (20% × (100 - 5x)) + (40% × x) = 18% x 100

(80% × x) + 20 - x = 18

(80x - 100x) / 100 = 18 - 20

-20x / 100 = -2

20x = 200

x = 200 / 20

x = 10 ml

The 10% solution:

= 10 x 4

= 40 ml

20% acid:

= 100 - (5 x 10)

= 50 ml

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I'm not sure if the last two apostrophes are part of the quote - "Solve ... " - or if you mean the second derivative [tex]x''[/tex]. I think you mean the first interpretation, but I'll include both cases since they are both solvable.

If the former is correct, separate variables to solve.

[tex]x' = -9tx \implies \dfrac{dx}{dt} = -9tx \implies \dfrac{dx}x = -9t\,dt[/tex]

Integrate both sides to get

[tex]\ln|x| = -\dfrac92 t^2 + C[/tex]

Solve for [tex]x[/tex].

[tex]e^{\ln|x|} = e^{-9/2\,t^2 + C} \implies \boxed{x = Ce^{-9/2\,t^2}}[/tex]

If you meant the latter, then the ODE can be rewritten as

[tex]9t x'' + x' = 0[/tex]

Reduce the order of the equation by substituting [tex]y(t) = x'(t)[/tex] and [tex]y'(t) = x''(t)[/tex].

[tex]9t y' + y = 0[/tex]

Solve for [tex]y'[/tex] and separate variables.

[tex]y' = -\dfrac y{9t} \implies \dfrac{dy}{dt} = -\dfrac y{9t} \implies \dfrac{dy}y = -\dfrac{dt}{9t}[/tex]

Integrate.

[tex]\ln|y| = -\dfrac19 \ln|t| + C[/tex]

Solve for [tex]y[/tex].

[tex]e^{\ln|y|} = e^{-1/9 \,\ln|t| + C} \implies y = Ct^{-1/9}[/tex]

Solve for [tex]x[/tex] by integrating.

[tex]x' = Ct^{-1/9} \implies x = C_1 t^{8/9} + C_2[/tex]

Answer: no real solution

Thus, the function has no x- intercept

Step-by-step explanation:

a) The probability is P = 1/9

b) The probability is P = 1/3.

First, we need to count the total number of outcomes (different cars that can be made with the given options):

Then there are 2*3*3 = 18 different cars.

a) Picking a blue hybrid car with an interior that is not leather.

There are 2 cars that meet that condition:

2 out of the 18 cars meet the condition, then the probability is:

P = 2/18 = 1/9

b) picking an electric car in a color other than blue is

The cars that meet the condition are:

So 6 out of the 18 cars meet the condition, then the probability is:

P = 6/18 = 1/3

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[tex] {\qquad\qquad\huge\underline{{\sf Answer}}} [/tex]

The given figure shows a vertical hyperbola with its centre at origin, and as we observe the figure, we can conclude that :

Length of transverse axis is :

[tex]\qquad \sf  \dashrightarrow \: 2b = 12[/tex]

[tex]\qquad \sf  \dashrightarrow \: b = 6[/tex]

length of conjugate axis is :

[tex]\qquad \sf  \dashrightarrow \: 2a = 8[/tex]

[tex]\qquad \sf  \dashrightarrow \: a = 4[/tex]

Equation of hyperbola ~

[tex]\qquad \sf  \dashrightarrow \: \cfrac{ {y}^{2} }{ {b}^{2} } - \cfrac{ {x}^{2} }{ {a}^{2} } = 1[/tex]

plug in the values ~

[tex]\qquad \sf  \dashrightarrow \: \cfrac{ {y}^{2} }{ {6}^{2} } - \cfrac{ {x}^{2} }{ {4}^{2} } = 1[/tex]

[tex]\qquad \sf  \dashrightarrow \: \cfrac{ {y}^{2} }{ {36}^{} } - \cfrac{ {x}^{2} }{ {16}^{} } = 1[/tex]

Answer:

[tex]\dfrac{y^2}{36}-\dfrac{x^2}{16}=1[/tex]

Step-by-step explanation:

Standard form equation of a vertical hyperbola

[tex]\dfrac{(y-k)^2}{a^2}-\dfrac{(x-h)^2}{b^2}=1[/tex]

where:

From inspection of the graph:

Substitute the found values into the formula:

[tex]\implies \dfrac{(y-0)^2}{6^2}-\dfrac{(x-0)^2}{4^2}=1[/tex]

[tex]\implies \dfrac{y^2}{36}-\dfrac{x^2}{16}=1[/tex]

The function that could be represented by Rebecca’s graph is f(x) =-2(5/4)^x+3

The properties are given as:

For an exponential function to keep decreasing, one or more the following must be true:

For the left end of an exponential function to approach a constant, the following must be true:

The equation that has the above properties is f(x) =-2(5/4)^x+3

Hence, the function that could be represented by Rebecca’s graph is f(x) =-2(5/4)^x+3

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An angle is produced at the point where two or more lines meet. Thus the value of LP required in the question is approximately 14.

Two lines are said to be perpendicular when a measure of the angle between them is a right angle. While parallel lines are lines that do not meet even when extended to infinity.

From the question, let the length of LP be represented by x.

Thus, from the given question, it can be deduced that;

LM ≅ PN = 20

KP = KN - PN

    = 30 - 20

KP = 10

LP = x

Also,

<MLP is a right angle, so that;

< KLP = < KLM - <PLM

         = 126 - 90

<KLP = [tex]36^{o}[/tex]

So that applying the Pythagoras theorem to triangle KLP, we have;

Tan θ = [tex]\frac{opposite}{adjacent}[/tex]

Tan 36 = [tex]\frac{10}{x}[/tex]

x = [tex]\frac{10}{Tan 36}[/tex]

  = [tex]\frac{10}{0.7265}[/tex]

x = 13.765

Therefore the side LP ≅ 14.

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Answer:

C looks most correct

Step-by-step explanation:

Answer:

-5^x + 3x - 2.

Step-by-step explanation:

(f - g) (x) = f(x) - g(x)

=  -5^x - 4 - (-3x - 2)

= -5^x - 4 + 3x + 2

= -5^x + 3x - 2.

Answer:

y=1/4x-1/2

Step-by-step explanation:

Step-by-step explanation:

"congruent" for lines simply means they are equally long.

15. yes. AB = EF = 3

16. yes. BD = DF = 8

17. no. AC = 5, CD = 6

18. yes. AC = DE = 5

19. no. BE = 13, CF = 14

20. no. CD = 6, DF = 8

[tex]x^3[/tex] is strictly increasing on [0, 5], so

[tex]\max\{x^3 \mid 0\le x\le5\} = 5^3 = 125[/tex]

and

[tex]\min\{x^3 \mid 0 \le x\le5\} = 0^3 = 0[/tex]

so the integral is bounded between

[tex]\displaystyle \boxed{0} \le \int_0^5x^3\,dx \le \boxed{125}[/tex]

The examples of insurable interest is an employer under certain arrangements.

Insurable interest is a investment that protects anything subject to a financial loss. A person or entity has an insurable interest in an item, event, or action when the damage or loss of the object would cause a financial loss or other hardshapes. In order to have an insurable interest a person or entity would take out an insurance policy protecting the person,item, or event in question. The insurance policy is able to  mitigate the risk of loss if something happens to the asset-like becoming damaged or lost.

Examples of insurable interest are:

Hence the examples of insurable interest is an employer under certain arrangements.

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Answer: Insurable interest means you must have a financial stake in the risk being insured. You can’t claim insurance for a risk that you don’t face directly.

If Rob’s dad’s car is stolen, his father will receive the insurance money, not Rob.

Step-by-step explanation: Edmentum

Using a system of equations, it is found that the total amount of money the two ladies spent was of $782.

A system of equations is when two or more variables are related, and equations are built to find the values of each variable.

In this problem, the variables are:

Mrs smith had $46 more than Mr.s Wilson at first, hence:

x = y + 46.

Mrs Wilson spent 4/7 of her money on some clothes and, and Mrs. Smith spent 3/5 of her on household items, then they remained with an equal amount, so:

[tex]\frac{2}{5}x = \frac{3}{7}y[/tex]

Since x = y + 46, we have that:

[tex]\frac{2}{5}(y + 46) = \frac{3}{7}y[/tex]

14(y + 46) = 15y

y = 14 x 46

y = $644

x = 644 + 46 = $690

Hence the amount they spent is given as follows:

[tex]\frac{3}{5}x + \frac{4}{7}y = \frac{3}{5} \times 690 + \frac{4}{7} \times 644 = 782[/tex]

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Answer:

simplification of the original equation is below/

Step-by-step explanation:

9+4t=-3(1-2t) can be simplified into

9+4t=-3+6t because of distributing the -3 to both the 1 and -2t.

however, this can simplified to

4t-6t=-3-9

and this can simplify to

-2t=-12

which can simplify to

t = 6

give brainliest please!

hope this helps :)

Answer:

Step-by-step explanation:

23

The radius of the circle of the circle equation (x + 3/8)^2 + y^2 = 1 is 1 unit

The circle equation of the graph is given as:

(x + 3/8)^2 + y^2 = 1

The general equation of a circle is represented using the following formula

(x - a)^2 + (y - b)^2 = r^2

Where the center of the circle is represented by the vertex (a, b) and the radius of the circle is represented by r

By comparing the equations (x - a)^2 + (y - b)^2 = r^2 and (x + 3/8)^2 + y^2 = 1, we have the following comparison

(x - a)^2 = (x + 3/8)^2

(y - b)^2 = y^2

1 = r^2

Rewrite the last equation as follows:

r^2= 1

Take the square root of both sides of the equation

√r^2 = √1

Evaluate the square root of 1

√r^2 = 1

Evaluate the square root of r^2

r = 1

Hence, the radius of the circle of the circle equation (x + 3/8)^2 + y^2 = 1 is 1 unit

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Answer:

1.

2. Additive Identity

3. Associative Property

4. Multiplication Inverse Property

5. Multiplication Property of 0

6. Commutative Property

7.

8.

Step-by-step explanation:

The revenue function in terms of q will be 200q - 3q².

The following can be deduced based on the information given:

P(q) = 200 - 3q

C(q) = 75 + 80q - q²

The revenue function in terms of q will be:

= Price × Quantity

= (200 - 3q) × q

= 200q - 3q²

The profit will be:

= Total revenue - Total cost

= (200q - 3q²) - (75 + 80q - q²)

= 200q - 3q² - 75 + 80q + q²

= -2q² + 280q - 75

= 2q² - 280q + 75

The average cost function will be:

= Total cost / Quantity

= (75 + 80q - q²) / q

= 75/q + 80 - q

The marginal cost will be 80 - 2q.

The marginal revenue will be 200 - 6q.

The marginal cost when q = 20 will be:

= 80 - 2q

= 80 - 2(20)

= 80 - 40

= 40

The marginal revenue when q = 20 will be:

= 200 - 6q

= 200 - 6(20)

= 200 - 120

= 80

The company should decrease production from 20 units in order to gain more profit.

The production level that gives the largest profit for the company will be gotten by finding the second derivative for the profit function as illustrated in the question. The profit function is 2q² - 280q. Then the production level will be 4.

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The probabilities of the given events are:

A. P(even) = P(A) = 7/15

B. P(multiple) = P(B) = 3/15

C. P(prime) = 6/15

D. P(B|A) = 3/7

Probability is defined as the ratio of the number of favorable outcomes of an event to the total number of possible outcomes.

P(E) = n(E)/n(S)

The given sample space is S = {1,2,3,4,5,6,7,8,9,10,11,12,13,14,15}

So, n(S) = 15

A. The selected number is even:

Consider the event as A.

The set of even numbers in the given sample is {2,4,6,8,10,12,14}

So, n(A) = 7

Then, the required probability is

P(A) = n(A)/n(S)

       = 7/15

B. The selected number is a multiple of 4:

Consider the event as B.

The set of multiples of 4 in the given sample is {4,8,12}

So, n(B) = 3

Then, the required probability is

P(B) = n(B)/n(S)

       = 3/15

C. The selected number is prime:

Consider the event as C.

The set of prime numbers in the given sample is {2,3,5,7,11,13}

So, n(C) = 6

Then, the required probability is

P(C) = n(C)/n(S)

       = 6/15

D. calculate P(B|A):

Since events B and A are dependent events of the same sample,

n(A∩B) = 3 and the set is {4,8,12}. Then, P(B|A) is

P(B|A) = n(A∩B)/n(A)

⇒ P(B|A) = 3/7

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Answer:

13

Step-by-step explanation:

3x + 7

x = 2

3 × 2 + 7 = 6 + 7 = 13

Hi there.

3x+7

x=2 :

3(2)+7

6+7

13

That's it.

Answer:

  (a)  π + (-π) = 0

Step-by-step explanation:

You want a counterexample for the statement that irrationals are closed under addition.

A set is closed under addition if adding members of the set always results in a member of the set.

This shows that adding members of the set can result in a rational number. This is the counterexample you're looking for.

Irrelevant. 1/2 is rational, so is not a member of the set of irrationals.

An example of a sum that is an element of the set. This is not a counterexample.

Irrelevant. 1/2 is rational, so is not a member of the set of irrationals.

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Answer: [tex]\Large\boxed{A.~y=3x+4}[/tex]

Step-by-step explanation:

Given information

Slope = 3

Point = (-3, -5)

Given the format of the equation

Slope-intercept form: y = mx + b

Substitute values into the equation

y = (3)x + b

y = 3x + b

Substitute the given point into the equation to get the value of [ b ]

(-5) = 3(-3) + b

-5 = -9 + b

b = -5 + 9

b = 4

Therefore, the equation of the line is [tex]\Large\boxed{y=3x+4}[/tex]

Hope this helps!! :)

Please let me know if you have any questions

Answer: -6

Step-by-step explanation:

[tex]-3x+\frac{1}{2}y=-3\\\\\frac{1}{2}y=3x-3\\\\y=6x-6[/tex]

For there to be infinite solutions, b = -6.

Answer:

The function is odd because f(-x) = -f(x)

Step-by-step explanation:

[tex]f(x)=8x^3[/tex]
[tex]f(-x)=8(-x)^3[/tex]
[tex]f(-x)=-8x^3[/tex]
[tex]-f(x)=-(8x^3)[/tex]
[tex]-f(x)=-8x^3=f(-x)[/tex]
[tex]f(-x)=-f(x)[/tex], therefore the function is odd

The function is odd because f(-x)=-f(x).

A relation is a function if it has only One y-value for each x-value.

The given function is f(x)=8x³.

We need to find which statement would be true in the given options.

Let us find this by taking x as -x.

f(-x)=8(-x)³

We know that when a negative sign is multiplied three times we get negative sign.

f(-x)=-8x³

-f(x)=-(8x³)

-f(x)=-8x³=f(-x)

f(-x)=-f(x)

By the definition of odd function f(-x)=-f(x).

Hence, the function is odd because f(-x)=-f(x).

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Answer:

56kg

Step-by-step explanation:

If 6m of a rod is 21 kg, then 21/6 will give us the weight of 1m of the rod. 21/6 = 3.5 kg

16*3.5 = 56 kg

Answer:

Step-by-step explanation:

t(-7)= 3(-7)= -21

s(-21)= 2-(-21)= 2 + 21= 23