Please help me I do not understand what to do

Answer:

x =- 6, x = 7

Step-by-step explanation:

Given

g(x) = (x - 7)x + 6)

To find the zeros let g(x) = 0, that is

(x - 7)(x + 6) = 0

Equate each factor to zero and solve for x

x + 6 = 0 ⇒ x = - 6

x - 7 = 0 ⇒ x = 7

Answer:

-12

Step-by-step explanation:

First, substitute the variables with the numbers.

(18-(-2*-5))+4(-5)

Using the order of operations, solve in the parentheses before anything else.

(18-(-2*-5))+4(-5)

(18-(10))+4(-5)

We can now multiply 4 by -5.

(18-(10))+4(-5)

(18-10)-20

It's probably easier if we subtract 10 from 18 before subtracting 20.

(18-10)-20

8-20

-12

Hope this helps you out!! Have a wonderful day c:

The town will have a population of 20683 after 5 years

Let the initial population be P₀

P₀ = 17000

Growth rate, R = 4% = 4/100 = 0.04

Time, T = 5

The population after 5 years will be given by the formula:

The town will have a population of 20683 after 5 years

Answer:

5th degree polynomial

Step-by-step explanation:

The degree of a polynomial is the highest sum of the exponents in one term.

So we have the polynomial:

\(6xy^4-3x^3-4\)

Calculate the degree of each term:

1st Term:

\(6xy^4\)

This is the same as:

\(6x^1y^4\)

So, our degree is 1+4=5.

2nd Term:

\(-3x^3\)

There is only one variable. So, the degree is 3.

3rd Term:

\(-4\)

This is the same as:

\(-4x^0\)

So, this is a zeroth degree.

The largest degree is 5.

So, this is a fifth degree polynomial.

Notes:

To be more specific, this is a fifth degree trinomial.

Answer:

third degree

Step-by-step explanation:

it is a third degree polynomial because the equation is considered cubic. cubic means to the 3rd power. its cubic because there's three parts to the equation

The derivative of h(x) is zero, indicating that the function h(x) is a constant function

To find the derivative of the function h(x) = ∫[1 to 8] e× ln(t) dt using the first part of the Fundamental Theorem of Calculus, we can directly differentiate the integral with respect to x.

Let F(x) be the antiderivative of the integrand e× ln(t). By the first part of the Fundamental Theorem of Calculus, we have:

h(x) = F(8) - F(1)

To find the derivative of h(x), we differentiate both sides of the equation with respect to x:

d/dx [h(x)] = d/dx [F(8) - F(1)]

Since F(8) and F(1) are constants, their derivatives with respect to x are zero. Therefore, we have:

h'(x) = 0 - 0

Thus, the derivative of h(x) is zero, indicating that the function h(x) is a constant function.

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Answer:

The side length of a square is the square root of its area. We know that:

x2 + 4x + 4 = (x + 2)2

Therefore, the side length of the square is x + 2

Answer:

y, because it crosses the y-axis.

b, because in y=mx+b b is the y-intercept.

Step-by-step explanation:

This is basically just memorization.

If the two events described in the questions are independent events, the probability of both happening next year is 28.67%.

Independent events refer to events whose occurrence is not interdependent. In other words, if the probability of occurrence of event A is not influenced by the probability of occurrence of event B, then A and B are independent events. Mathematically, independent events are represented as P(A│B) and is calculated by multiplying the individual probabilities of the two events. The formula of probability of two independent events is:

P(A│B) = P(A)*P(B)

Hence,

P(A│B) = 0.47*0.61

P(A│B) = 0.47*0.61

P(A│B) = 0.2867

The probability of two events happening next year is 28.67%.

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On solving the provided question, we can say that here in this rhombus,

angle 1 is 106 and  angle 2 and 3 are 37 each

A rhombus is an equal-sided quadrilateral in Euclidean plane geometry. The term "equilateral triangle" also refers to a quadrilateral whose sides are of the same length. A parallelogram has a unique variation known as a rhombus. In a rhombus, the opposite sides and angles are parallel and equal. A rhombus's diagonal is split in half by a right angle, and each of its sides is the same length. Rhombic diamonds and diamonds are other names for rhombuses. The length of every side is the same. Diagonals are equal in a rhombus. At a 90° angle, parallel lines split in half. 180 degrees is the sum of adjacent angles.

here in this rhombus,

angle 1 is 106

other two side are 360-106-106 = 148

148/2 = 74

so angle 2 and 3 are 37 each

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Answer:

The solution is 24

Step-by-step explanation:

3/4 = n/32

3(32) = 4n

96 = 4n

4n = 96

n = 96/4

n = 24

Answer:

Step-by-step explanation:

Sum of internal angles of a regular polygon is:

We have here 5-sided polygon:

Now sum the given angles measures and solve for x:

Find the measure of angle R:

The area of the region enclosed by one loop of the curve r = sin(10θ) is π/40.

We have to find the area of the region enclosed by one loop of the curve.

The given curve is:

r = sin(10θ)

Consider the region r = sin(10θ)

The area of region bounded by the curve r = f(θ) in the sector a ≤ θ ≤ b is

A = \(\int^{b}_{a}\frac{1}{2}r^2d\theta\)

Now to find the area of the region enclosed by one loop of the curve, we have to find the limit by setting r=0.

sin(10θ) = 0

sin(10θ) = sin0   or    sin(10θ) = sinπ

So θ = 0             or      θ = π/10

Hence, the limit of θ is 0 ≤ θ ≤ π/10.

Now the area of the required region is

A = \(\int^{\pi/10}_{0}\frac{1}{2}(\sin10\theta)^2d\theta\)

A = \(\frac{1}{2}\int^{\pi/10}_{0}\sin^{2}10\theta d\theta\)

A = \(\frac{1}{2}\int^{\pi/10}_{0}\frac{(1-\cos20\theta)}{2}d\theta\)

A = \(\frac{1}{4}\int^{\pi/10}_{0}(1-\cos20\theta)d\theta\)

A = \(\frac{1}{4}\left[(\theta-\frac{1}{20}\sin20\theta)\right]^{\pi/10}_{0}\)

A = \(\frac{1}{4}\left[(\frac{\pi}{10}-\frac{1}{20}\sin20\frac{\pi}{10})-(0-\frac{1}{20}\sin20\cdot0)\right]\)

A = \(\frac{1}{4}\left[(\frac{\pi}{10}-\frac{1}{20}\sin2\pi)-(0-\sin0)\right]\)

A = 1/4[(π/10-0)-(0-0)]

A = 1/4(π/10)

A = π/40

Hence, the area of the region enclosed by one loop of the curve r = sin(10θ) is π/40.

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Answer:

45 bumblebee, 30 star.

Step-by-step explanation:

2:3 = 5

75/5 = 15

15 X 2= 30

15 X 3= 45

Answer:

\(y = \sqrt{x+25} + 5\)

Step-by-step explanation:

Swap x and y

x = y² – 10y

Add 25 to each side to complete the square

x + 25 = y² – 10y + 25

Factor

x + 25 = (y – 5)²

Take the square root of each side

\(\sqrt{x+25}\) = y – 5

Add 5 to both sides

\(\sqrt{x+25}\) + 5 = y

Answer:

r(180°,0) is a rotation of 180° degrees over the origin.

Notice that this rotation moves our figure to the opposite quadrant (so a translation of two quadrants).

Then this is equivalent to:

A reflection over the x-axis followed by a reflection over the y-axis.

Or.

A reflection over the y-axis followed by a reflection over the x-axis.

There is another possible reflection, but it depends on where is our figure.

If the figure is in the first or third quadrant, a reflection over the line y = -x is equivalent to the rotation.

If the figure is in the second or third quadrant, then the reflection over the line y = x is equivalent to the rotation.

We can combine those two and write:

A reflection over the line y = (-1)^n*x.

Where n is the number associated with the quadrant where the figure is in.

C. Using the output of the first function as the input of the second function

Why it is?

When we compose two functions f and g, the output of the first function f(x) becomes the input of the second function g, so we have g(f(x)). This means that we first apply the function f to x, and then we use the result of that operation as the input to the function g.

For example, if we have f(x) = 2x + 1 and g(x) = x², then the composition of the two functions g(f(x)) is:

g(f(x)) = g(2x + 1)

= (2x + 1)²

= 4x² + 4x + 1

In this example, we first apply the function f(x) = 2x + 1 to x, which gives us 2x + 1 as the output. Then we use this result as the input to the function g(x) = x², which gives us the final output of 4x² + 4x + 1.

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The remainder of the f(x) = 3x³ + 6x² - 3x + 2 and divisor x + 3 applying synthetic division is equal to -16.

Use synthetic division and the remainder theorem to find the remainder of f(x) when divided by x- c,

Set up the synthetic division table with c on the left side, and the coefficients of f(x) on the top row.

Bring down the first coefficient of f(x) into the first box below the horizontal line.

Multiply c by the number in the first box and write the result in the second box.

Add the number in the second box to the coefficient in the second column, and write the result in the third box.

Repeat steps 3 and 4 until you reach the last box. The number in the last box is the remainder.

Check if the remainder is zero. If it is zero, then x -c is a factor of f(x),

and g(x) = (x- c) is a factor of f(x).

Dividend is equal to,

f(x) = 3x³ + 6x² - 3x + 2

Divisor is equal to,

g(x) = x + 3

Synthetic division is attached in the figure.

Expressed in remainder theorem

3x² -3x + 6 + ( -16 / x + 3 )

Therefore, the remainder of the synthetic division for the given dividend and divisor is equal to -16.

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Answer:

8

Step-by-step explanation:

4+4

8

You can rewrite it as

2+2+2+2

8

Answer:

She is correct.

Step-by-step explanation:

She is correct.

Triangles QPS and QRS are congruent by SSS since all sides of one triangle are congruent to corresponding sides of the other triangle. Two pairs of sides are marked as congruent, and the third side, QS, is congruent to itself.

Then by CPCTC, angles P and R are congruent.

a)  it costs more money to make 100 photocopies

b) you can buy more than 500 photocopies for $40

What are coordinates?

A pair of numbers that use the separations between the two reference axes to define the location of a point on a coordinate plane. usually represented by the x- and y-values, respectively, (x, y).

a) In the  graph , 100 photocopies cost $10,

For 101  photocopies, the point on the line comes below of 10 on y axis

So, it costs more money to make 100 photocopies

b)  graph arrow shows line moves on...

so, you can buy more than 500 photocopies for $40

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E, "As I was saying, . . .". The salesperson should use this statement if they wished to ignore the objection.

Option E is the best choice to ignore the objection because it allows the salesperson to redirect the conversation back to their main point without directly addressing the objection. The statement implies that the objection is not important enough to interrupt the flow of the conversation.

Ignoring objections is not always the best approach in sales, but if the salesperson chooses to do so, they should use a statement like option E to redirect the conversation back to their main point.


When a salesperson wants to ignore an objection, they should choose a response that does not address the concern raised and instead redirects the conversation back to the topic they were discussing. Option e does this effectively by not acknowledging the objection and continuing with the original discussion.

To ignore an objection, a salesperson should use a statement like option e, which allows them to refocus the conversation without addressing the concern raised.

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Hence, it has been proven that the function f achieves either an absolute minimum or an absolute maximum on the interval (0,1).

Let f : (0,1) → r be a continuous function such that lim x→0 f(x) = lim x→1 f(x) = 0. show that f achieves either an absolute minimum or an absolute maximum on the interval (0,1).Solution:The interval given is a closed interval that is bounded (it is bounded by 0 and 1) and therefore compact. By the extreme value theorem, a continuous function on a compact interval attains its maximum and minimum at some points in the interval. Hence, there exists a and b in the interval (0, 1) such that f(a) is the maximum of f on the interval and f(b) is the minimum of f on the interval.Since lim x→0 f(x) = lim x→1 f(x) = 0, then we may have a, b ≠ 0 or 1. But a and b must be within the interval (0,1).Hence, it has been proven that the function f achieves either an absolute minimum or an absolute maximum on the interval (0,1).The total words used in the answer is 152.

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Answer: $23.92

Step-by-step explanation:

First, we know that 6 bagels is $2.99.

48/6=8

This means that 6 is a multiple of 48, which makes it easier to solve.

$2.99 x 8 = 23.92

= $23.92

Answer:

5 1/5

step-by-step explanation

If you received a gift of $10,000 3 years ago and you want to spend it in 3 years with interest rate is 4%, it will be worth $12,653.19. Option b is correct.

To calculate the future value of a present sum after a specified period, we can use the formula for compound interest:

Future Value = Present Value * (1 + Interest Rate)ᴺ

In this case, the present value is $10,000, the interest rate is 4% or 0.04, and the number of periods is 6 years because you received the gift 3 years ago and want to spend it in 3 years.

Using the formula:

Future Value = \(\$10,000 * (1 + 0.04)^6\)

Future Value = \(\$10,000 * (1.04)^6\)

Future Value = $10,000 * 1.1265319

Future Value ≈ $12,653.19

Therefore, the amount will be approximately $12,653.19. Option b is correct.

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Answer:

The length and width of rectangle are 90 feet and 22.5 feet.

Step-by-step explanation:

Let the,

Now, according to the question substituting all the given values in the formula to find the value of x :

\( \longrightarrow{\pmb{\sf{P = 2(L + W)}}}\)

\( \longrightarrow{\sf{P = 2(L + W)}}\)

\( \longrightarrow{\sf{225= 2 \bigg(x + \dfrac{x}{4} \bigg)}}\)

\( \longrightarrow{\sf{225= 2 \bigg(\dfrac{4x + x}{4} \bigg)}}\)

\( \longrightarrow{\sf{225= 2 \bigg(\dfrac{5x}{4} \bigg)}}\)

\( \longrightarrow{\sf{225= 2 \times \dfrac{5x}{4}}}\)

\( \longrightarrow{\sf{225= \dfrac{2 \times 5x}{4}}}\)

\( \longrightarrow{\sf{225= \dfrac{10x}{4}}}\)

\( \longrightarrow{\sf{10x = 225 \times 4}}\)

\( \longrightarrow{\sf{10x = 900}}\)

\( \longrightarrow{\sf{x = \dfrac{900}{10}}}\)

\(\longrightarrow{\sf{\underline{\underline{x = 90}}}}\)

Hence, the value of x is 90.

Now, we know the value of x. So, calculating the length and width of rectangle :

\(\rule{300}{2.5}\)

The approximate radius of a dodgeball with a volume of 1,436.6 cubic inches is 8 inches.

The volume of a sphere can be calculated using the formula V = (4/3)πr^3, where V is the volume and r is the radius. Rearranging the formula, we get r = (3V/4π)^(1/3). Plugging in the given volume of 1,436.6 cubic inches, we find that the approximate radius of the dodgeball is 8 inches.

The volume of a cylinder can be calculated using the formula V = πr^2h, where V is the volume, r is the radius, and h is the height. Rearranging the formula, we get r = √(V/(πh)). Plugging in the given volume of 226.2 cubic inches and the height of 8 inches, we can calculate the approximate radius. Since the diameter is twice the radius, the diameter of the can is approximately 2 times the calculated radius.

The volume of a cone can be calculated using the formula V = (1/3)πr^2h, where V is the volume, r is the radius (which is half the diameter), and h is the height. Plugging in the given diameter of 10 cm (which gives a radius of 5 cm) and the height of 12 cm, we can calculate the approximate volume of each cone-shaped cup. Note that the volume is given in cubic centimeters (or milliliters) because we used centimeter measurements.

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The composite functions are listed below:

In this problem we find five cases of composite functions, each of which has to be evaluated. A composition between the two functions f and g is defined below:

f ° g(x) = f ( g(x) )

Now we proceed to evaluate each of the five cases by using algebra properties and the definition of the composition of functions:

Case 1

g ° f(3) = g( f(3) )

g ° f(3) = 4 · (2 · 3 + 2) - 3

g ° f(3) = 4 · 8 - 3

g ° f(3) = 29

Case 2

g ° f(x + 1) = g( f(x + 1) )

g ° f(x + 1) = 2 · [(x + 1)² - 2 · (x + 1)] + 1

g ° f(x + 1) = 2 · (x² + 2 · x + 1 - 2 · x - 2) + 1

g ° f(x + 1) = 2 · (x² - 1) + 1

g ° f(x + 1) = 2 · x² - 1

Case 3

h ° g (- 3 · x) = h( g (- 3 · x) )

h ° g (- 3 · x) = 3 · [4 · (- 3 · x) - 3]

h ° g (- 3 · x) = 3 · (- 12 · x - 12)

h ° g (- 3 · x) = - 36 · x - 36

Case 4

f ° g (- 2 - t) = f( g (- 2 - t))

f ° g (- 2 - t) = [4 · (- 2 - t) - 2]² + 1 + 2 · [4 · (- 2 - t) - 2]

f ° g (- 2 - t) = (- 8 - 4 · t - 2)² + 1 + 2 · (- 8 - 4 · t - 2)

f ° g (- 2 - t) = (- 10 - 4 · t)² + 1 + 2 · (- 10 - 4 · t)

f ° g (- 2 - t) = 100 + 80 · t + 16 · t² + 1 - 20 - 8 · t

f ° g (- 2 - t) = 73 + 72 · t + 16 · t²

Case 5

f ° g (x²) = f( g(x) )

f ° g (x²) = 3 · (x² + 4) + 5

f ° g (x²) = 3 · x² + 12 + 5

f ° g (x²) = 3 · x² + 17

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