Which table represents a proportional relationship?

A geometric sequence goes from one term to the next by always multiplying or dividing by the constant value except 0. The constant number multiplied (or divided) at each stage of a geometric sequence is called the common ratio (r).

A geometric series is the sum of an infinite number of terms of a geometric sequence.

A geometric series is convergers if |r| < 1.

A geometric series is diveres if |r| > 1.

Calculate the common ratio:

[tex]r=\dfrac{18}{27}=\dfrac{18:9}{27:9}=\dfrac{2}{3}\\\\r=\dfrac{12}{18}=\dfrac{12:6}{18:6}=\dfrac{2}{3}\\\\r=\dfrac{8}{12}=\dfrac{8:24}{12:4}=\dfrac{2}{3}[/tex]

[tex]\left|\dfrac{2}{3}\right| < 1[/tex]

Therefore exist the sum.

Formula of a sum of a geometric series:

[tex]S=\dfrac{a_1}{1-r},\qquad|r| < 1[/tex]

Substitute:

[tex]a_1=27,\ r=\dfrac{2}{3}[/tex]

[tex]S=\dfrac{27}{1-\frac{2}{3}}=\dfrac{27}{\frac{1}{3}}=27\cdot\dfrac{3}{1}=81[/tex]

[tex]\huge\boxed{S=81}[/tex]

[tex]\bf{-5x^{2} +10x-25 }[/tex]

[tex]\bf{Rewrite \ 10 \ as:5\cdot2.}[/tex]

[tex]\bf{Rewrite \ 25 \ as:5\cdot5.}[/tex]

[tex]\bf{=-5x^2+5\cdot \:2x-5\cdot \:5}[/tex]

[tex]\bf{Factor \ the \ common \ term \ 5.}[/tex]

[tex]\bf{=5(-x^{2} +2x-5) \ \ \to \ \ \ Answer }[/tex]

Answer:

Infinitely Many Solutions

Step-by-step explanation:

[tex]10x-6y=-8\\-10x+6y=8\\\0 = 0\\[/tex]

Answer:The answers are 0.084 or -1.184

Step-by-step explanation:

The solution is in the attached file

Answer:

6 units

Step-by-step explanation:

5--1=6

The product of all the values of a, such that f(a)=f(2a) is -1/2

Given the function below;

f(x)=1/x + x

f(a) = 1/a + a

f(2a) = 1/2a  + 2a

If f(a) = f(2a), hence;

1/a + a = 1/2a + 2a

Collect the like terms

1/a - 1/2a = 2a - a

2-1/2a = a

1/2a = a

Cross multiply

2a² = 1

a² = 1/2

a = ±√1/2

The values of a are √1/2 and -√1/2

Product = -√1/2 * √1/2

Product = -1/2

Hence the product of all the values of a, such that f(a)=f(2a) is -1/2

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Answer:

y^-1 = 3x - 6

Step-by-step explanation:

f(x) = 1/3x + 2

The inverse function is where we swap out y for x and x for y. f(x) represents y, so we will be replacing it with x. Then, we solve and get a new equation for the inverse of y.

x = 1/3y + 2 (subtract 2 from both sides)

x - 2 = 1/3y (multiply by 3 on both sides)

y^-1 = 3x - 6

Brainliest, please :)

Answer:

f(x) = 3x- 2

Step-by-step explanation:

The easiest way to find the inverse of a function is to replace y with x and rearrange the equation.

x = 1/3y + 2

-2            -2

______________

x-2 * 3  = 1/3y * 3

y = 3x-2

Answer:528 apple trees

Step-by-step explanation:Listen 198/6=33 so then just multiply 33x16 that equals 528 hope this helps

The total area of the given right trapezoidal prism is gotten as; A = 2592 sq.units

The formula to find the Surface Area of a Trapezoidal Prism is;

A = h(b + d) +l(a + b + c + d) unit square.

Where;

h = height

b and d are the lengths of the base

a + b + c + d is the perimeter

l is length

Thus;

A = 12(25 + 15) + 32(13 + 25 + 13 + 15)

A = 480 + 2112

A = 2592 units square

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Hello,

check for x = 2, we can see h(x) = 0

h(x) = √(x - 2) ⇒ h(2) = √(2 - 2) = √0 = 0 ⇒ ok

h(x) = √x - 2 ⇒ h(2) = √2 - 2 ≠ 0 ⇒ not this answer

h(x) = √x + 2 ⇒ h(2) = √2 + 2 ≠ 0 ⇒ not this answer

h(x) = √(x + 2) ⇒ h(2) = √(2 + 2) = √4  ≠ 0 ⇒ not this answer

So the answer is  h(x) = √(x - 2)

The value of x in the triangle is (d) 7

The complete question is in the attached image.

From the attached image of the triangle, we can see that the triangle is a right triangle, and x can be solved using the following sine function

[tex]\sin(45) = \frac{x}{7\sqrt 2}[/tex]

Evaluate sin(45)

[tex]\frac 1{\sqrt 2} = \frac{x}{7\sqrt 2}[/tex]

Solve for x

[tex]x = \frac{7\sqrt 2}{\sqrt 2}[/tex]

Divide

x = 7

Hence, the value of x in the triangle is (d) 7

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Answer:

Hi  sorry if the reply is late! The answer is

OPTION (B)m∠AVC+m∠CVB=m∠AVB

Step-by-step explanation:

Given: It is given that a point C is inside ∠AVB and ∠AVC=39° and ∠CVB=23°.

From the figure, we can see that C is inside ∠AVB, therefore ∠AVB is divided into two parts that is ∠AVC and ∠CVB, thus

m∠AVC+m∠CVB=c

⇒39°+23°=62°

Step-by-step explanation:

[tex]f(x) = 4x[/tex]

[tex] \: [/tex]

[tex]y = 4x[/tex]

[tex]4y = x[/tex]

[tex]y = \frac{x}{4} [/tex]

[tex] {f}^{ - 1} (x) = \frac{ x}{4} [/tex]

[tex]h(x) = \frac{x}{4} [/tex]

The answer is D.

Hello !

Answer :

100% of x ⇒ 100/100 × x = 1 × x = x

200% of y ⇒ 200/100 × y = 2 × y = 2y

Answer:

3

[tex]3 {y}^{0} [/tex]

[tex] = 3 \times 1[/tex]

[tex] = 3[/tex]

If any numbers or constant power is zero then it will be 1

Answer:

3

Step-by-step explanation:

So anything to the power of zero is equal to 1. So you have the equation: [tex]3y^0=3(1)=3[/tex]

If this doesn't make much sense, I sometimes like to use identities to show why this is. So since you're most likely learning exponents, you likely know the identity: [tex]\frac{x^a}{x^b}=x^{a-b}[/tex] well you can use this identity to express the equation: [tex]\frac{x^a}{x^a}=x^{a-a}=x^0[/tex]. and since x^a should equal x^a, and it's being divided by it self, this is equal to 1.

Btw if you didn't understand the identity: [tex]\frac{x^a}{x^b}=x^{a-b}[/tex] I'll try to briefly explain it. The reason this is true, is because you can cancel stuff out if it's being multiplied in the denominator and numerator. For example: [tex]\frac{3a}{3}[/tex]. I can cancel out the 3, because if I multiply 3 by a, and then divide by 3, I'm going to be left with a, because they're inverse to each other. This should hold true for exponents. So you can think of the identity more like: [tex]\frac{x*x*x...\text{a amount of times}}{x*x*x\text{b amount of times}}[/tex] seeing it like this might help understand why you subtract, since you're just cancelling out the x's.

I'll give you a more definitive example to help you grasp it in an example so: [tex]\frac{2^4}{2^2}=\frac{2*2*2*2}{2*2}=\frac{2*2}{1}=2^2[/tex]. See how I canceled out 2 of the 2's, well all I was really doing was subtracting 2 from the degree of the numerator, or in other words I was subtracting the degree of the denominator from the numerator since the bases were the same which is exactly what the identity is doing.

a) Solve the first equation for [tex]x[/tex].

[tex]x + 3y = 7 \impiles x = 7 - 3y[/tex]

Substitute this into the second equation and solve for [tex]y[/tex].

[tex]2x + 4y = 12 \implies 2(7 - 3y) + 4y = 12 \\\\ \implies 14 - 6y + 4y = 12 \\\\ \implies -2y = -2 \\\\ \implies \boxed{y=1}[/tex]

Solve for [tex]x[/tex].

[tex]x = 7 - 3y \implies x = 7-3\times1 \\\\ \implies \boxed{x = 4}[/tex]

b) Eliminate [tex]y[/tex] by combining the two equations in appropriate parts, namely

[tex]2 (2x - y) + (3x + 2y) = 2\times3 + (-3)[/tex]

and solve for [tex]x[/tex].

[tex]2 (2x - y) + (3x + 2y) = 2\times3 + (-3) \implies 4x - 2y + 3x + 2y = 6 - 3 \\\\ \implies 7x = 3 \\\\ \implies \boxed{x = \dfrac37}[/tex]

Solve for [tex]y[/tex].

[tex]2x - y = 3 \implies 2\times\dfrac37 - y = 3 \\\\ \implies \dfrac67 - y = 3 \\\\ \implies -y = \dfrac{15}7 \\\\ \implies \boxed{y = -\dfrac{15}7}[/tex]

To have solution for f(x)=log3(x-2)-2. x must be x >2 or x ( 2, ∞) .

f(x)=log3(x-2)-2

Functions is the relationship between sets of values. e g y=f(x), for every value of x there is its exists in set of y. x is independent variable while Y is dependent variable.

Since,
f(x)=log3(x-2)-2
The above function will goes to infinity when we put x = 2.
So the given function has solution for x > 2.

Thus, the To have solution for f(x)=log3(x-2)-2. x must be x >2 or x ( 2, ∞) .

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Answer:

The simplified form of [tex]12 q-(-6 q) \text { is } 18 q[/tex].

Step-by-step explanation:

[tex]- Given: $12 q-(-6 q)$\\ - Simplify.\\ - The simplified form of $12 q-(-6 q)=(12+6) q$ i.e., $18 q$.[/tex]

Answer:Liam started a weight-loss program when Luke did. The first week, he lost 1 pound less than 3/2 times the pounds Luke lost the first week. The second week, he lost 4 pounds less than 5/2 times the pounds Luke lost the first week. The third week, he lost 1/2 pound more than 5/4 times the pounds Luke lost the first week.Assuming they both lost the same number of pounds over the three weeks, complete the following sentences.Step-by-step explanation:

The expression that is a prime polynomial is:

B. [tex]x^3 - 27y^2[/tex].

A prime polynomial is a polynomial that cannot be factored.

In this problem, item b gives a prime polynomial, as:

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The rate of change of the linear function represented by the table is 3

The rate of change of a function is also known as the slope of a function. The equation for calculating the slope is expressed as:

Slope = y2-y1/x2-x1

using the coordinates from the table (-2, -13) and (-1, -10)

Substitute

Slope = -10-(-13)/-1-(-2)

Slope = -10+13/-1+2

Slope =3

Hence the rate of change of the linear function represented by the table is 3

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Answer:

p=4

Step-by-step explanation:

plug x=-1 into the polynomial with the unknown

(-1)³+p(-1)+(-1)+6=0

-1-p-1+6=0

-p+4=0

p=4

The probability that the mean clock life would differ from the population mean by greater than 12.5 years is 98.30%.

Given mean of 14 years, variance of 25 and sample size is 50.

We have to calculate the probability that the mean clock life would differ from the population mean by greater than 1.5 years.

μ=14,

σ=[tex]\sqrt{25}[/tex]=5

n=50

s orσ =5/[tex]\sqrt{50}[/tex]=0.7071.

This is 1 subtracted by the  p value of z when X=12.5.

So,

z=X-μ/σ

=12.5-14/0.7071

=-2.12

P value=0.0170

1-0.0170=0.9830

=98.30%

Hence the probability that the mean clock life would differ from the population mean by greater than 1.5 years is 98.30%.

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There is a mistake in question and correct question is as under:

What is the probability that the mean clock life would differ from the population mean by greater than 12.5 years?

Answer:

C. Decreasing

Step-by-step explanation:

The graph is decreasing because the graphed line read from left to right is slanting down.

Hope this helps!

If not, I am sorry.

Answer:

Step-by-step explanation:

Hello

If a graph is constant, it doesn't have any change at all.

If a graph is increasing, it looks like this-:

[tex]\Huge\nearrow[/tex]

If a graph is decreasing, it looks like this-:

[tex]\searrow[/tex]

Since the given graph is most similar to [tex]\searrow[/tex], it's decreasing.

[tex]\pmb{\tt{done~!!}}[/tex]

[tex]\orange\hspace{300pt}\above2[/tex]

The value of x based on the information given in the triangle is D. x = 1.

From the information given, it stated that the triangles are similar.

In this case, both triangles have side 4 and 5. Therefore, we are to find the last side. This will be:

4x - 1 = x + 2

Collect like terms

4x - x = 2 + 1

3x = 3

x = 3/3

x = 1

Therefore, the correct option is D.

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Answer:

x=1

Step-by-step explanation:

Answer:

your answer please mark me as brainlist

[tex]\huge\boxed{11\ \text{units}}[/tex]

To solve this, we need to find the distance between points C and D.

The distance formula is:

[tex]\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

Substitute the values from points [tex]C(x_1, y_1)[/tex] and [tex]D(x_2, y_2)[/tex].

[tex]\sqrt{(-4-(-4))^2+(-5-6)^2}[/tex]

Subtract.

[tex]\sqrt{0^2+(-11)^2}[/tex]

Evaluate the powers.

[tex]\sqrt{0+121}[/tex]

Solve for the final answer.

[tex]\sqrt{121}\\\boxed{11}[/tex]

Answer:

=============

Let the pizza was shared between x people.

Set up equation and solve for x:

If we exclude Lemo, the number of friends is 4.