help with my homework
rewrite as a single power using laws of exponents

(3²) x 3⁷ ÷ 3⁸​

The equation of the parabola is:y = -13/36(x + 2)² + 5.

Equation is a mathematical statement that two expressions are equal. It is written as an expression that shows the equality of two values using mathematical symbols. Equations are used to solve problems by finding the unknown value. They are used in almost all branches of mathematics, and help to explain the behavior of physical and chemical systems.

The equation of a parabola with vertex (x_0,y_0) and that passes through (x_1,y_1) can be expressed as
y = a(x - x_0)² + y_0
where a is a constant.

In this case, the vertex of the parabola is (-2, 5) and it passes through (4, -8). We can substitute these values for x_0, y_0 and x_1, y_1 into the equation to get:

y = a(x - (-2))² + 5

We can solve for a by substituting the coordinates of the given point (4, -8) into the equation:

-8 = a(4 - (-2))² + 5

-8 = a(6)^2 + 5

-8 = 36a + 5

-13 = 36a

a = -13/36

Therefore, the equation of the parabola is:

y = -13/36(x + 2)²+ 5

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The required equation of the parabola is y = -13/36(x + 2)² + 5.

A parabola is a type of curve that is defined by a quadratic equation of the form y = ax² + bx + c.

In geometric terms, a parabola is the set of all points in a plane that are equidistant from a fixed point (called the focus) and a fixed line (called the directrix).

The equation of a parabola with vertex (x₁, y₁) that passes through
(x₂, y₂) can be expressed as

                        => y = a(x - x₁)² + y₁

Where a is a constant.

Here we have

The vertex of the parabola is (-2, 5) and it passes through (4, -8).

Substitute (-2, 5) in the formula y = a(x - x₁)² + y₁

=>  y = a(x - (-2))² + 5

Solve for a by substituting the coordinates of the given point (4, -8) into the equation:

=> -8 = a(4 - (-2))² + 5

=> -8 = a(6)² + 5

=> -8 = 36a + 5

=> -13 = 36a

=> a = -13/36

Therefore,

The required equation of the parabola is y = -13/36(x + 2)² + 5.

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The value of the car decreases from year to year by 15%.

A kind of function that would explain this type of pattern is an exponential decay function [tex]f(x) = 10000(0.15)^x[/tex].

You need the decay rate to find the function the actuary is using.

In Mathematics and Statistics, a population or physical asset (car) that decreases at a specific period of time represent an exponential decay. This ultimately implies that, a mathematical model for any population or physical asset that decreases by r percent per unit of time is an exponential equation of this form:

P(t) = I(1 - r)^t

Where:

Next, we would determine the constant ratio in each representation as follows;

Constant ratio, r = a₂/a₁ = a₃/a₂ = a₄/a₃ = a₅/₄

Constant ratio, r = 8520/10,000 = 7213/8250 = 6,100/7213 = 768/192

Constant ratio, r = 85.

By substituting the given parameters, we have the following:

P(t) = I(1 - r)^t

f(x) = 10,000(1 - 85/100)^x

f(x) = 9,600(1 - 0.85)^x

f(x) = 9,600(0.15)^x

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Answer:24,000 pounds

Step-by-step explanation: a ton is 2,000 pounds so 12 times 2,000 is 24,000

Step-by-step explanation:

Slope intercept form is   y = mx + b  

Re-arrange given equation  to

2y = 4x-6        divide by 2

y = 2x -3          done.

Answer:

MO/KO = NO/LO

5/10 = 3/LO

5/10 = 3/x

Step-by-step explanation:

Since KLO and MNO are similar, that means the corresponding sides share a common proportion:

Note how corresponding sides MO and KO are given measurements, that means we can find the common proportion by dividing MO/KO (which is 5/10). Knowing the proportion between the corresponding sides between MO and KO, we can find LO by finding its corresponding side and setting up a proportion. LO's corresponding side is NO (with a measurement of 3):

5/10 = 3/LO

Other options also work:

MO/KO = NO/LO               since MO = 5 units, KO = 10 units, & NO = 3 units

5/10 = 3/x                           since any value can be set to a variable, LO = x

Answer & Step-by-step explanation:

Part A: The explicit equation for f(n) that represents the number of lionfish in the bay after n years can be written as:

f(n) = 9000 * (1 + 0.69)^n

where 9000 is the initial number of lionfish, 0.69 is the growth rate, and n is the number of years.

Part B: To find the number of lionfish in the bay after 6 years, we substitute n = 6 into the explicit formula from Part A and simplify:

f(6) = 9000 * (1 + 0.69)^6 = 9000 * (1.69)^6 = 9000 * 11.34 = 102,060.5

Rounding to the nearest whole number, there will be approximately 102,061 lionfish in the bay after 6 years.

Part C: The recursive equation for f(n) can be found by subtracting 1,400 from the previous year's population and then applying the annual growth rate. Thus, we have:

f(1) = 9000 f(n) = f(n-1) - 1400 + 0.69f(n-1) = 0.69f(n-1) - 1400

where f(1) is the initial number of lionfish and n represents the number of years after the first year.

The equation of a circle having endpoints of diameter as (4,9) and (4,-3) is (x - 4)² + (y - 3)² = 36.

The "center" of circle is called as midpoint of diameter.

The "x-coordinate" of "mid-point" is = (4+4)/2 = 4, and

The "y-coordinate" of "mid-point" is = (9+(-3))/2 = 3.

So, center of circle is (4,3),

The radius of circle is half the length of the diameter, which is distance between two endpoints of diameter. We find distance using distance formula:

⇒ distance = √((x₂ - x₁)² + (y₂ - y₁)²), where (x₁,y₁) and (x₂,y₂) are "end-points" of diameter.

⇒ distance = √((4 - 4)² + (9 - (-3))²)

⇒ √(144) = 12.

So, radius is 6.

The equation of circle with center (h,k) and radius "r" is : ⇒ (x - h)² + (y - k)² = r²,

Substituting the values

We get,

⇒ (x - 4)² + (y - 3)² = 6²,

⇒ (x - 4)² + (y - 3)² = 36,

Therefore, the equation of the circle is (x - 4)² + (y - 3)² = 36.

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122° 43’ 12” is written in decimal degree form, to the nearest thousandth, as approximately: 122.720.

In order to convert 122° 43’ 12” to decimal degree form, we can use the formula which is expressed as:

decimal degrees = degrees + (minutes / 60) + (seconds / 3600)

Substituting the given values into the stated formula above, we have the following:

decimal degrees = 122 + (43 / 60) + (12 / 3600)

decimal degrees = 122.720

Rounding to the nearest thousandth, we get:

122.720 ≈ 122.720

Therefore, 122° 43’ 12” is approximately equal to 122.720 degrees to the nearest thousandth.

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The apothem is the vocabulary for a. The regular polygon's area is 319.8 cm².

We may use the following formula to calculate the area of the polygon:

Area = (1/2) × Perimeter × Apothem

The perimeter of a polygon is calculated by multiplying the number of sides by the length of each side, as shown below:

Perimeter = the number of sides multiplied by the length of each side

Perimeter = 6 × 14 cm (because to the regular hexagon shape)

Perimeter = 84 cm

Use the fact that it forms a right triangle with half of one side length and the apothem as the legs and the apothem as the hypotenuse to find the apothem. Thus,

a² = s² - (s/2)²

a² = 196 - 49

a² = 147

a = √(147) = 7.65 cm

Now we can enter our values into the area formula:

Area = (1/2) × Perimeter × Apothem

Area = (1/2) × 84 cm × 7.65 cm

Area = 319.8 cm²

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The distance AB is 10 units and other coordinates are calculated below

Given that

C = (3, 3) and D = (3, y)

The length is 7 units

So, we have

y - 3 = 7

Evaluate

y = 4

So, one possible value of y is 4

Given that

B = (r, 2) and C = (5, 2)

The length is 10 units

So, we have

r - 5 = 10

Evaluate

r = 15

So, one possible value of r is 15

Finding the coordinates of A

We have

AB = 4 units and B = (15, 2)

So, we have

A = (15, 2 + 4)

Evaluate

A = (15, 6)

Here, we have

A = (a - 7, b) and D = (a + 3, b)

The distance because they have the same y-coordinates is

Distance = |a - 7 - a - 3|

Evaluate

Distance = 10

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Answer:

Step-by-step explanation:

If 9 units = 36 inches,

then 9 ÷ 9 = 36 ÷ 9 inches

∴ 1 unit = 36/9 inches

Answer:

The answer is 4/1(in)

Step-by-step explanation:

1/9 yard to in

1yd=36in

1/9yards=4in

and

9unit=36in

1 unit=36/9

1unit=4in

therefore 1unit=1/9yards

A slope of 15 simply means that the rate of change of the value on the y-axis with respect to the x-axis is equal to 15.

In Mathematics and Geometry, the slope of any straight line can be determined by using the following mathematical equation;

Slope (m) = (Change in y-axis, Δy)/(Change in x-axis, Δx)

Slope (m) = rise/run

Slope (m) = (y₂ - y₁)/(x₂ - x₁)

By substituting an assumed data points into the slope formula, we have the following;

Slope (m) = (80 - 20)/(6 - 2)

Slope (m) = 60/4

Slope (m) = 15.

In this context, we can reasonably infer and logically deduce that a slope of 15 denotes the rate of change of a straight line on a graph.

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The expression that gives Angela the total amount of money she will make per hour is y = 10x + 25.

In equation y = 10x + 25, x represents the number of hours she babysits, and y represents the total amount of money she will make, which is equal to the flat rate of $25 plus $10 per hour.

So, for example, if she babysits for 3 hours, the total amount of money she will make is:

y = 10(3) + 25 = 30 + 25 = $55

Therefore, the correct answer is A, y = 10x + 25.

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a) Number of elements in sample size is 11.

b) Probability P(E) is 0.45.

a) The sample space is the set of all possible outcomes when drawing a single card from the deck. Since there are 11 cards in total, the sample space has 11 elements.

b) We want to find the probability of drawing an even-numbered card, which includes the red cards numbered 2, 4, and 6, and the black cards numbered 2 and 4. There are five such cards in total, so the probability of drawing an even-numbered card is:

P(E) = number of even-numbered cards / total number of cards

P(E) = 5 / 11

P(E) = 0.4545 or approximately 0.45

Therefore, the probability of drawing an even-numbered card from the deck is about 0.45.

Correct Question:

A special deck of cards has 6 red cards, and 5 black cards. The red cards are numbered 1, 2, 3, 4, 5, and 6. The black cards are numbered 1, 2, 3, 4 and 5. The cards are well shuffled and you randomly draw one card.

R = card drawn is Red

E = card drawn is even-numbered

a) How many elements are there in the sample space.

b) What is the probability P(E).

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Answer:

49 text messages

Step-by-step explanation:

3.49/68 = 0.05 oer text

we can use this unit rate for text sent $2.45

$2.45/.05 per text message = 49 text messages

Given that the triangles are congruent, we can conclude that

From the question, we are to determine what can be concluded from the fact that triangle QGL and triangle BRN are congruent

If ΔQGL and ΔBRN are congruent, we can infer that

QG = BR

LG = NR

QL = BN

Also, in terms of angles

∠LGQ = ∠NRB

∠QLG = ∠BNR

∠LQG = ∠NBR

In addition,

If two triangles are congruent, the areas of the triangles will be equal to each other

Thus,

We can conclude that

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The total number of students on the honor roll increased by approximately 19.3%.

What is percenatge?

Percentage is a way of expressing a fraction or a portion of a whole number as a portion of 100. It is often denoted by the symbol %. For example, 50% represents 50 parts out of 100, or 50/100, which simplifies to 1/2.

Let's first find the total number of students on the honor roll last year:

Total number of students on the honor roll last year = 100 (boys) + 50 (girls) = 150

This year, the number of boys on the honor roll increased by 19%, which means the new number of boys on the honor roll is:

New number of boys on the honor roll = 100 + 0.19(100) = 119

Similarly, the new number of girls on the honor roll is:

New number of girls on the honor roll = 50 + 0.20(50) = 60

Therefore, the total number of students on the honor roll this year is:

Total number of students on the honor roll this year = 119 (boys) + 60 (girls) = 179

The percentage increase in the total number of students on the honor roll is:

Percentage increase = [(Total number of students on the honor roll this year - Total number of students on the honor roll last year) / Total number of students on the honor roll last year] x 100%

Percentage increase = [(179 - 150) / 150] x 100% = 19.3%

Therefore, the total number of students on the honor roll increased by approximately 19.3%.

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The measure of the angle enclosed by the 19 inch and 23 inch sides is  81 degrees in the triangle.

In a triangle, the sum of the measures of the three angles is always 180 degrees.

Let the angle enclosed by the 19 inch and 23 inch sides x.

The Law of Cosines states that for a triangle with sides a, b, and c, and angle C opposite side c:

c² = a² + b² - 2ab cos(C)

Let's choose the 27 inch side as side c.

Then we have:

27² = 19² + 23²- 2(19)(23)cos(x)

729 = 850 - 874cos(x)

-121 = -874cos(x)

cos(x) = 0.1386

x=81 degrees

Hence, the measure of the angle enclosed by the 19 inch and 23 inch sides is  81 degrees.

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Answer:

18 - x

Step-by-step explanation:

f(x) = 6 - x

g(x) = x/3 + 8

f(2x) = 6 - (2x) => 6 - 2x

g(3x + 9) = (3x+9)/3 + 9 = x + 3 + 9 => x + 12

(6 - 2x) + (x + 12)

Simplified:

18 - x

Answer:

A ratio of 3:1 means that there are 4 parts altogether. The fractions from the ratio can therefore be deduced as. 43 and 41. These represent the percentages: 75%:25%

Answer:

Step-by-step explanation:

The ratio can be converted into a fraction

therefore we can divide by the denominator in order to convert 30 Euros to a 3:1 ratio.

The fraction =3/4 and 1/4

so we have to divide 30 by 4

= 7.5 Euros

so;

3:1

(22.5):(7.5)

(45/2):(15/2)

45:15

divide by 15

3:1

The slope and y-intercepts of each line, respectively, are:

5. m = -2; b = 6       6. m = 5/3; b = 10/3       7. m = -1/4; b = 4

Slope of a line is calculated as, m = change in y / change in x.

5. Given (2, 2) and (3, 0):

Slope of the line (m) = change in y / change in x = 2 - 0 / 2 - 3

m = 2/-1

m = -2

To find the y-intercept (b), substitute m = -2 and (x, y) = (2, 2) into y = mx + b:

2 = -2(2) + b

2 = -4 + b

2 + 4 = b

b = 6

6. Given (1,5) and (4, 10):

Slope of the line (m) = change in y / change in x = 10 - 5 / 4 - 1

m = 5/3

To find the y-intercept (b), substitute m = 5/3 and (x, y) = (1, 5) into y = mx + b:

5 = 5/3(1) + b

5 - 5/3 = b

b = (15 - 5)/3

b = 10/3

7. Given (8, 2) and (-8, 6):

Slope of the line (m) = change in y / change in x = 6 - 2 / -8 - 8

m = 4/-16

m = -1/4

To find the y-intercept (b), substitute m = -1/4 and (x, y) = (8, 2) into y = mx + b:

2 = -1/4(8) + b

2 = -2 + b

2 + 2 = b

b = 4

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The quarts of paint used by Mieko to paint his living room is equal to 3 quarts.

Total paint bought by Mieko = 2 gallons

Amount of paint used  to paint bedroom = 1/4 of the paint.

Amount of paint used on the hallway = 3 quarts

Since 1 gallon is equal to 4 quarts.

Convert gallons to quarts.

Mieko bought 2 gallons of paint, which is equivalent to 8 quarts

She used 1/4 of the paint on her bedroom,

which is 1/4 x 8 quarts = 2 quarts.

She also used 3 quarts of paint on the hallway.

This implies,

The total amount of paint used on the bedroom and hallway is equal to,

2 quarts + 3 quarts = 5 quarts

The amount of paint used in the living room is the remaining amount of paint is equal to,

8 quarts - 5 quarts = 3 quarts

Therefore, Mieko used 3 quarts of paint in the living room.

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The above question is incomplete, the complete question is:

Mieko bought 2 gallons of paint. She used 1/4 of the paint on her bedroom, 3 quarts on the hallway, and the rest of the paint in the living room. How many quarts of paint did Mieko use in the living room?

The expected number of trips a customer needs to make to get a complete set of letters is 6 trips.

This problem can be modeled using the concept of a geometric distribution, where the number of trials required to achieve the first success (getting a complete set of letters) follows a geometric distribution.

The probability of getting a specific letter on any given purchase is 1/6, since there are six letters and they are equally likely to be given away. Therefore, the probability of not getting a specific letter on any given purchase is 5/6.

Let X be the random variable representing the number of purchases needed to obtain a complete set of letters. Since each purchase is independent of the others, X follows a geometric distribution with a probability of success p = 1/6.

The expected value of a geometric distribution with probability of success p is given by E(X) = 1/p. Therefore, the expected number of trips to the store that a customer needs to make to get a complete set is:

E(X) = 1/p = 1/(1/6) = 6

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Answer:

First, we need to move the constant term to the other side of the equation:

y + x^2 - 16x = -100

Next, we need to "complete the square" by adding and subtracting a constant term that will allow us to write the left-hand side of the equation as a perfect square. To do this, we need to take half of the coefficient of the x-term (-16), square it, and add that to both sides of the equation:

y + x^2 - 16x + 64 = -36 + 64

Now, we can simplify the left-hand side by factoring it as a perfect square:

(y + (x - 8)^2) = 28

So the equation, in completed square form, is:

y + (x - 8)^2 = 28

Step-by-step explanation:

gg

Answer:

To solve the equation, we can begin by isolating the expression in the parentheses:

2(x^2 + x - 11)^3/2 = 54

Divide both sides by 2:

(x^2 + x - 11)^3/2 = 27

Take the cube root of both sides:

x^2 + x - 11 = 3∛27

Simplify the cube root:

x^2 + x - 11 = 3∛(27) = 3*3 = 9

Rearrange the equation:

x^2 + x - 20 = 0

Factor the quadratic:

(x + 5)(x - 4) = 0

Therefore, the solutions are x = -5 and x = 4.

To check for extraneous solutions, we need to make sure that these values do not make the original equation undefined. Since there are no square roots or denominators, there are no restrictions on x, and both solutions are valid.

So, the solutions to the equation are -5 and 4, in increasing order.

Answer: figure ii

Step-by-step explanation:

Every 30th person on a list of county residents, is the most representative sample of the population of interest.  Option A

A representative sample is a small group of individuals who, as closely as possible, reflect a larger group.

The best representative sample will be obtained by taking every 30th person on a list of county residents.

This is due to the fact that it requires choosing people from the entire county's resident population as opposed to only those who frequent a certain region (options B and C) or a particular group (option D, high school students).

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The selling price of the item after a percentage of markup by 15 % is given by S = $ 23

Given data ,

Let the initial price of the item be A = $20

Now , let the selling price of the item after percentage mark up be S

where percentage markup = 15 %

So , the amount of markup is M = ( 15 )% x 20

M = 20 x 0.15

M = $ 3

And , the selling price S = A + M

S = $ 20 + $ 3

S = $ 23

Hence , the selling price is S = $ 23

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