Use the derivative function, f ' ( x ) , to determine where the function f ( x ) = − 2 x 2 + 13 x − 8 is increasing.

Answer:

60 years

Step-by-step explanation:

Eventually, the multiples of each number will reach 60.

Answer:

Lay the net out with the dimensions then multiply for each shape and add all of the areas to get the total surface area of your prism.

Step-by-step explanation:

this is how you work it out with the net

Answer:

You must lay out the net, find the area of each shape and multiply, and then add each dimension.

Answer:

Both give remainder 0 for the polynomial

Step-by-step explanation:

p(-2) = (-2)² - (-2) - 6

= 6 - 6 = 0

p(3) = (3)² - 3 - 6

= 9 - 9 = 0

Answer:

what's that

Step-by-step explanation:

Answer:

9599

Step-by-step explanation:

use technology.

Answer:

9595

Step-by-step explanation:

x = 331 x 29

= 9595

331

x 29

----------

9595

you can start by dividing the total length of the road by the distance that can be repaired per week:

13 km ÷ 3 1/2 km/week = 3.71 weeks

Rounding up, it will take 4 weeks to repair the entire 13 km stretch of road.

The LCM of A = 3² × 5⁴ × 7 and B = 3⁴ × 5³ × 7 × 11 is 3898125 using Prime factorization.

Given are two numbers which are showed in the prime factorized form.

A = 3² × 5⁴ × 7

B = 3⁴ × 5³ × 7 × 11

Prime factorization is the factorization of a number in terms of prime numbers.

In order to find the LCM of these two numbers, we have to first match the common primes and write down vertically when possible and then bring down the primes in each column.

A = 3² ×         5³ × 5 × 7

B = 3² × 3² × 5³ ×       7 × 11

Bring down the primes in each column.

LCM = 3² × 3² × 5³ × 5 × 7 × 11

        = 3898125

Hence the LCM is 3898125.

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Answer:

\(\textsf{B.} \quad f(x)=\dfrac{1}{(x+2)(x-1)}\)

Step-by-step explanation:

Asymptote: a line which the curve gets infinitely close to, but never touches.

From inspection of the graph, we can see that the asymptotes are:

This means that the function is undefined when x = -2, x = 1 and y = 0.

For a rational function to be undefined, the denominator equals zero.

Therefore,

So the equation of the function is:

\(f(x)=\dfrac{1}{(x+2)(x-1)}\)

Look at the vertical asymptotes

They are

So factor up the denominator

Hence the rational function is 1/(x+2)(x-1)

Option B

0, 5, 5, 1, 2

is evaluate

Only two real numbers satisfy x² = 23, so A is the set {-√23, √23}. B is the set of all non-negative real numbers. Then you can write the intersection in various ways, like

(i) A ∩ B = {√23} = {x ∈ R | x = √23} = {x ∈ R | x² = 23 and x > 0}

√23 is positive and so is already contained in B, so the union with A adds -√23 to the set B. Then

(ii) A U B = {-√23} U B = {x ∈ R | (x² = 23 and x < 0) or x ≥ 0}

A - B is the complement of B in A; that is, all elements of A not belonging to B. This means we remove √23 from A, so that

(iii) A - B = {-√23} = {x ∈ R | x² = 23 and x < 0}

I'm not entirely sure what you mean by "for µ = R" - possibly µ is used to mean "universal set"? If so, then

(iv.a) Aᶜ = {x ∈ R | x² ≠ 23} and Bᶜ = {x ∈ R | x < 0}.

N is a subset of B, so

(iv.b) N - B = N = {1, 2, 3, ...}

Answer:

9

Step-by-step explanation:

Answer:

1 : 2  =  3 : 6  =  4 : 8

Step-by-step explanation:

All three ratios equal 1/2, so all three ratios are equal to each other.

Hopefully this helps!

Brainliest please?

Answer:

Whole numbers less than 5 may be termed as Rational numbers.

Answer:

x = 3

y = -10

Step-by-step explanation:

  5x + y = 5                                                                    y = 3x - 19

  5x + 3x - 19 = 5

  8x - 19 = 5

  8x = 24

   x = 3

Now put x in to solve for y

y = 3(3) - 19

y = 9 - 19

y = -10

Let's check

5(3) - 10 = 5

15 - 10 = 5

5 = 5

So, x = 3 and y = -10 is the correct answer.

Answer:

s(t)=8t

Step-by-step explanation:

The length of the sides of a square are initially 0 cm and increase at a constant rate of 8 cm per second.

Let the length of the Square = s

\(\dfrac{ds}{dt}=8 $cm/seconds, s_0=0 cm\)

We solve the differential equation above subject to the given initial condition.

\(\dfrac{ds}{dt}=8\\ds=8$ dt\\Take the integral of both sides\\\int ds=\int 8$ dt\\s(t)=8t+C, where C is the constant of integration\\When t=0, s=0cm\\s(0)=0=8(0)+C\\C=0\\Therefore, s(t)=8t\)

The formula that expresses the side length of the square, s (in cm), in terms of the number of seconds, t , since the square's side lengths began growing is:

s(t)=8t (in cm)

Answer: y = 1/2 or y = -1/2

Step-by-step explanation:

First move the 1 to the side with the 0

-4y^2 = -1 // -1 because when you move a number to the other side of the equation  you have to multiply -1

Then divide by -4 on each side

y^2 = 1/4

square root each side

|y| = 1/2 // sq rt y^2 becomes an absolute value because when you square root a square it automatically becomes an absolute value

so the answer would be y = 1/2 or -1/2

to check just put it into the equation as y. Both work.

EXPLANATION:

 \(1-4y^2=0\\1^2-(2y)^2=0\\(1-2y)(1+2y)=0\\\)

⇒  \(1-2y=0\)   or   \(1+2y=0\\\)

⇒ \(2y=1\)  or   \(2y=-1\\\)

⇒ \(y= \frac{1}{2}\)  or  \(y=\frac{-1}{2}\)

P/s:   \(A^2-B^2=(A-B)(A+B)\)

Ok done. Thank to me :>

Answer:

25.13 or 8pi

Step-by-step explanation:

Answer:

area of trapezoid =0.5 x (sum of bases) x height

Plodding in the given values we get:

Area of trapezoid= 0.5 x (11+9) x 5.5 = 27.5 sqaure feet

To find the area of the triangle, we can use the formula

Area of a triangle = 0.5 x base x heigh

Plugging in the given values we get:

Area of triangle = 0.5 x 11 x 5.5 = 30.25 square feet

Therefore, the area of the triangle is greater than area of trapezoid.

Step-by-step explanation:

the reason for this is because the triangle has a greater heigh (5.5 ft) than the trapezoid, and the base light of the triangle (11 ft) is equal to one of the bases of the trapezoid, which allows it to cover a greater area fro thr same base length.

Answer:

The area of the kite is greater than the area of the trapezoid.

Step-by-step explanation:

Area of rectangle:

A = LW

A = 11 ft × 5.5 ft

A = 60.5 ft²

Area of trapezoid:

A = (1/2)(B + b)h

A = (1/2)(11 ft + 9 ft)(5.5 ft)

A = 55 ft²

Since the trapezoid lies inside the rectangle, with two triangles missing,  it makes sense that the area of the trapezoid is smaller than the area of the rectangle.

Area of kite:

A = 2 × area of triangle

A = 2 × bh/2

A = 2 × 11 ft × 5.5 ft / 2

A = 60.5 ft²

The area of the kite is greater than the area of the trapezoid.

The area of a kite is half the product of the lengths of its diagonals. One diagonal of the kite has the same length as the rectangle. The other diagonal of the kite has twice the width of the rectangle. Therefore, the area of the kite equals the area of the rectangle. The trapezoid has a smaller area than the rectangle, so the trapezoid has a smaller area than the kite.

The inverse of f(x) = 3x³ + 8 is \(\sqrt[3]{\frac{x-8}{3}}\).

Two functions f(x) and g(x) are inverse functions if (fog)x = x and (gof)x = x.When we combine two functions by means of arithmetic operations we call them composite function.

According to the given question we have to determine the inverse of         f(x) = 3x³ + 8.

This can be written as

y = 3x³ + 8.

Now we'll switch x and y meaning everywhere there is x we'll replace with y and vice versa.

x = 3y³ + 8.

Now we'll solve for y.

3y³ = x - 8.

y³ = (x - 8)/3.

y = \(\sqrt[3]{\frac{x-8}{3}}\).

f(x⁻¹) =\(\sqrt[3]{\frac{x-8}{3}}\).

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Answer:

A. 31 Km

Step-by-step explanation:

\(circumference = 2\pi \:r\)

radius equals the diameter divided by 2

\(r = \frac{d}{2} \)

In this case the diameter is 10, so the radius is 5.

finally,

\(2\pi(5) = 31.415\)

rounded to the nearest whole number gives us

31 Km.

Answer:

g(f(-1)) = 2

Step-by-step explanation:

f(x) = 2 + x

g(x) = 3 - x

if you need to find g(f(-1)); find f(-1) first

f(-1) = 2 + (-1) = 1

f(-1) =1; now plug this into g(1)

g(1) = 3 - 1 = 2

The general form of a quadratic equation is given by:

y = ax² + bx + c

Use the given values on the table to obtain a system of equations.

for the point (-3 , 0.5):

0.5 = a(-3)² + b(-3) + c

0.5 = 9a - 3b + c (1)

for the point (-2 , 1):

1 = a(-2)² + b(-2) + c

1 = 4a - 2b + c (2)

for the point (0 , 5):

5 = a(0)² + b(0) + c

5 = c

replace c= 5 into the equation (1) and (2) and simplify like terms:

0.5 = 9a - 3b + 5

-4.5 = 9a - 3b (3)

1 = 4a - 2b + 5

-4 = 4a - 2b (4)

multiply the equation (3) by -2 and multiply the equation (4) by 3, then, sum the equations:

9 = -18a + 6b

-12 = 12a - 6b

-3 = -6a

from the previous equation, solve for a:

-3 = -6a

a = 1/2

Next, replace a=1/2 into the equation (4) and solve for b:

-4 = 4a - 2b

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

-4 = 2 - 2b

2b = 2 + 4

2b = 6

b = 3

Hence, the values of a, b and c are:

a = 1/2

b = 3

c = 5

The inequality representing the given situation is -

300x + 700y ≤ 7500

Advertising is the practice and techniques employed to bring attention to a product or service. Advertising aims to put a product or service in the spotlight in hopes of drawing it attention from consumers.

Given is that Bobby Flay is deciding how to advertise a new gourmet restaurant that he is opening. An online ad costs $300, and a TV ad costs $700. He has $7,500 to spend on the ads.

We can write the inequality as -

300x + 700y ≤ 7500

where -

{x} - number of online ads posted

{y} - number of TV ads poste

Plot the inequality on the graph. The shaded region represents the possible number of advertisements of each category Bobby can use to advertise.

Therefore, the inequality representing the given situation is -

300x + 700y ≤ 7500

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The weight of large box will be 45 pounds.

The weight of small box will be 30 pounds.

What is an expression?

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

The combined weight of a large box and a small box is 75 pounds.

And, The truck is transporting 55 large boxes and 70 small boxes.

Total weight of boxes = 4575 pounds

Now,

Let weight of large box = x

And, Weight of small box = y

Here, The combined weight of a large box and a small box is 75 pounds.

So, We can formulate;

⇒ x + y = 75   ...(i)

And, Total weight of boxes = 4575 pounds

So, We can formulate;

⇒ 55x + 70y = 4575   ...(ii)

Solve both equation as;

From (i);

x = 75 - y

Substitute in equation (ii), we get;

⇒ 55(75 - y) + 70y = 4575

⇒ 4,125 - 55y + 70y = 4575

⇒ 15y = 4575 - 4,125

⇒ 15y = 450

⇒ y = 30

And, x = 75 - 30 = 45

Thus, The weight of large box will be 45 pounds.

The weight of small box will be 30 pounds.

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Answer:

Step-by-step explanation:

\((x - 3)2 = 49 \\ \frac{(x - 3)2}{2} = \frac{49}{2} \\ x - 3 = 24.5 \\ x - 3 + 3 = 24.5 + 3 \\ x = 27.5 \\ \)

Answer:

\(x = -4\\\\x = 10\)

Step-by-step explanation:

\(~~~~~(x-3)^2 = 49\\\\\implies (x-3)^2 -49 = 0\\\\\implies (x-3)^2 -7^2 = 0\\\\\implies (x-3+7)(x-3-7) = 0\\\\\implies (x+4)(x-10) = 0\\\\\implies x = -4,~ x = 10\)

Answer:

2, -4

Step-by-step explanation:

substitute

\(\begin{bmatrix}2x+3y=-8\\ 3x+y=2\end{bmatrix}\)

simplify

\(\begin{bmatrix}3\cdot \frac{-8-3y}{2}+y=2\end{bmatrix}\)\(\begin{bmatrix}\frac{-24-7y}{2}=2\end{bmatrix}\\\)

isolate

\(x=\frac{-8-3\left(-4\right)}{2}\)

and then u get x = 2

and y = 4

Step-by-step explanation:

A = a + (n - 1) d

A - a = (n - 1)d

(A - a)/d = n - 1

n = 1 + (A - a)/d

Using probability we know that we have full probability or 1 that we will draw a coin that will have ethe value of at least $0.10.

A probability is a numerical representation of the likelihood or chance that a specific occurrence will take place.

Both proportions ranging from 0 to 1 and percentages ranging from 0% to 100% can be used to describe probabilities.

Simply put, probability is the likelihood that something will occur.

When we don't know how an occurrence will turn out, we can discuss the likelihood or likelihood of various outcomes.

So, we have the chart:

Penny = 2/5 = 0.4

Nickel = 1/5 = 0.2

Dime = 1/4 = 0.25

Then, the probability of getting a value of at least $0.10

P(E) = 3/3

P(E) = 1

Therefore, using probability we know that we have full probability or 1 that we will draw a coin that will have ethe value of at least $0.10.

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From the given information, the probability that either event will occur is 0.7.

From the given Venn diagram,

Number of A = 4

Number of B = 24

Number of others  = 12

Total number = A + B + others = 4 + 24 + 12 = 40

Probability of event A occurring = number of A / Total number = 4/40 = 1/10 = 0.1

Probability of event B occuring = number of B / Total number = 24/40 = 3/5 = 0.6

Now, the probability of either event will occur = P(A or B) = P(A) + P(B)

P(A or B)  = 0.1 +0.6 = 0.7

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