Which calculation correctly uses prime factorization to write in simplest form?

The linear function which can be used to represent the situation is y = 6.4x + 1900 and airplane weight if it is carrying 60 gallons of fuel is 2,284 pounds

y = mx + b

where,

Now, we can use the two sets of data points given to us to first solve for the slope m as:

m = (2188 - 2060) / (45 - 25)

= 128 / 20

= 6.4

y - yo = m(x - xo)

y - 2060 = 6.4(x - 25)

y - 2060 = 6.4x - 160

y = 6.4x - 160 + 2060

y = 6.4x + 1900

x = 60

So,

y = 6.4x + 1900

y = 6.4(60) + 1900

y = 384 + 1900

y = 2,284 pounds

Therefore, the weight of the airplane if it is carrying 60 gallons of fuel is 2,284 pounds

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The greatest number of bouquets they can be divided into if there will be the same number of roses in each bouquet and the same number of tulips in each bouquet is 5.

Given that:-

Number of roses Mary has = 65

Number of tulips Mary has = 104

We have to find the greatest number of bouquets they can be divided into if there will be the same number of roses in each bouquet and the same number of tulips in each bouquet.

HCF (65, 104) = 13

Hence, the groups of 13 roses and 13 tulips will together make a bouquet.

From 65 roses, 65/13 = 5 bouquets can be made.

From 104 tulips, 104/13 = 8 bouquets can be made.

Min (5,8) = 5.

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The expression y=[tex]x^{p} +2x^{q}[/tex]. [tex]\frac{dy}{dx}=11x^{10}+10x^{4}[/tex], where dy/dx is derived function. The p and q values are 11 and 5.

Given that,

The expression y=[tex]x^{p} +2x^{q}[/tex]

[tex]\frac{dy}{dx}=11x^{10}+10x^{4}[/tex], where dy/dx is derived function.

Derived function means for any value of the independent variable, the value of another function is the instantaneous rate of change of the specified function at that value of the independent variable.

We have to find the p and q values.

Take expression

y=[tex]x^{p} +2x^{q}[/tex]

[tex]\frac{dy}{dx}=px^{p-1}+2qx^{q-1}[/tex]

[tex]11x^{10}+10x^{4}=px^{p-1}+2qx^{q-1}[/tex]

Here,

we can see p=11 and

2q=10

q=5

Therefore, the p and q values are 11 and 5.

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Answer: 53.1

Step-by-step explanation: Divide 35.40 by 2 to get 17.7. now add 35.40 with 17.7 and you get 53.1

The slope of the line is 2 / 3.

The slope of a line can be found as follows:

The slope of a line is change in y with respect to change in x.

In other words, the slope of a line is rise over run.

Therefore,

slope = y₂ - y₁ / x₂ - x₁

Using (0, 3)(-3, 1)

Hence,

x₁ = 0

x₂ = -3

y₁ = 3

y₂ = 1

Therefore,

slope = 1 - 3 / -3 - 0

slope = -2 / -3

slope = 2 / 3

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ANSWER:

STEP-BY-STEP EXPLANATION:

We must convert the following statement "A number multiplied by -8 subtracted from the sum of 8 and two times the number" into a mathematical expression.

We know that "a number" would be x.

Therefore:

1. The total amount that was paid for the car will be $23960.

2. The interest that Mai pay on the loan will be $1160.

1. From the information, in order to pay for a $22,800 car, Mai made a down payment of $3,800 and took out a loan for the rest and on the loan, she paid monthly payments of $420for 4 years.

The total amount that was paid for the car will be:

= $3800 + ($420 × 4 years)

= $3800 + ($420 × 48)

= $3800 + $20160

= $23960

2. The interest that Mai pay on the loan will be:

= $23960 - $22800

= $1160

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Answer:

1.4 Relations and Functions

A relation is a correspondence between two sets. If x and y are two

elements in these sets and if a relation exists between x and y, then x

corresponds to y, or y depends on x.

DEFINITION OF A FUNCTION:

Let X and Y two nonempty sets. A function from X into Y is a relation that

associates with each element of X, exactly one element of Y.

However, an element of Y may have more than one elements of X

associated with it.

That is for each ordered pair (x,y), there is exactly one y value for each x,

but there may be multiple x values for each y. The variable x is called the

independent variable (also sometimes called the argument of the

function), and the variable y is called dependent variable (also

sometimes called the image of the function.) x = y2 is not a function from X into Y, because there

is not exactly one y value for each x.

Solving for y, you get y =

which means there are two possible values for y

Step-by-step explanation:

In geometry, you can use deductive rules to prove conjectures.

Geometry is defined as a subfield of mathematics that examines the measurement and relationships of surfaces, solids, solid surfaces, angles, and points. The calculation of a triangle's angles is a geometry example.

Geometry will categorize, quantify, and lack a counterexample. Once a concept has been defined, it can be utilized in subsequent definitions; for instance, parallel lines can be used in the definition of a parallelogram once they have been defined. classification, counterexample, quantification, and parallelogram.

Given Data

In geometry, you can use deductive rules to

In geometry, you can use deductive rules to prove conjectures.

In geometry, deductive rules can be used to demonstrate whether a particular assertion or conjecture is true or untrue. We narrow down a result proving a statement must be true or untrue by using deductive principles, such as definitions, postulates, and other theorems, in a logical order.

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The The set of all numbers greater than or equal to -10 and less than 9 will be -10, -9, -8, -7, -6, -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5, 6, 7, and 8.

It should be noted that from the information, we are to find the set of all numbers greater than or equal to -10 and less than 9.

This simply means the numbers from -10 to 8.

Therefore, the numbers will be -10, -9, -8, -7, -6, -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5, 6, 7, and 8.

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Applying the rules for the polar equations, the correct pairs are given in the image at the end of the answer.

The most well known polar equation rules are given as follows:

For the first pair, when x = 2, we have that:

rcos(θ) = 2.

r = 2/cos(θ)

r = 2 sec(θ), as one divided by the cosine is the secant.

For the second pair, we have that:

x² + y² = 36.

x² + y² = r², hence:

r² = 36

r = 6.

For the third pair, we have that:

x² + y² = 2y

r² = 2rsin(θ).

r²/r = 2sin(θ).

r = 2sin(θ).

For the fourth pair, we have that:

[tex]x = \sqrt{3}y[/tex]

[tex]\frac{y}{x} = \frac{1}{\sqrt{3}}[/tex]

[tex]\frac{y}{x} = \frac{\sqrt{3}}{3}[/tex]

Then the angle theta is given as follows:

θ = arctan(sqrt(3)/3) = pi/6.

For the fifth pair, we have an angle in which the sine and the cosine are equal, hence this angle is of 45º = pi/4.

The image at the end of the answer shows all the matched pairs.

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Given:

The radius of the circle = 2.4 kilometers

The measure of the arc = 150°

The length of the arc is given by the formula:

Note: we will convert the angle from degrees to radian

So, the length of the arc =

So, the answer will be option D. 2π km

Line AB is parallel to CD, for instance, as indicated by the formula AB ll CD.

How do parallel lines work?

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Answer:

2.4m

Step-by-step explanation:

The question has already done most of the work for you. To find the initial height, simply set t = 0 and substitute it into the function.

[tex]d(0) = {0}^{2} + 2.4 + 3.2(0) \\ = 2.4m[/tex]

Answer:

B

Step-by-step explanation:

By the triangle inequality theorem, the sum of the lengths of the two shorter sides needs to be greater than the length of the longest side.

recall the formula for velocity, which involves distance and time:

velocity = distance / time

since the woman's velocity is: 4.5 Km/h, then in order to cover 10 km, we need to find the time in the equation:

4.5 km/h = 10 km / t

multiply both sides by the time (t)

4.5 * t = 10

divide both sides by 4.5 in order to isolate t completely

t = 10 / 4.5

then

t = 2 hours and 0.2222 hours which can be translated into minutes by multiplying this by 60: 40/3 = 13 minutes and 0.33333 minutes. which can be converted into seconds by multiplying it by 60: 20 seconds

Then she will cover that distance in 2 hours, 13 minutes and 20 seconds.

The representation of the expression is x/2 - 10 = -18

The mathematical statement is given as

"10 less than the quotient of a number and 2 is -18"

In expressions, quotient mean divide i.e. /

So, we have the following representation

"10 less than the quotient of a number and 2 is -18" ⇒  10 less than a number/2 is -18"

Let the number be x

So, we have

"10 less than the quotient of a number and 2 is -18" ⇒  10 less than x/2 is -18"

Less than as used here means minus

So, we have

"10 less than the quotient of a number and 2 is -18" ⇒  x/2 - 10 is -18

Rewrite as

"10 less than the quotient of a number and 2 is -18" ⇒  x/2 - 10 = -18

Hence, the expression represented by "10 less than the quotient of a number and 2 is -18" is  x/2 - 10 = -18

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Recall that [tex]\phi = 1 + \frac1\phi[/tex].

In the integral, substitute [tex]y=1+x^\phi[/tex], so that [tex]x=(y-1)^{1/\phi} = (y-1)^{\phi-1}[/tex] and [tex]dx = (\phi-1) (y-1)^{\phi-2} \, dy[/tex]. We have

[tex]\displaystyle I = \int_0^\infty \frac{dx}{(1+x^\phi)^\phi} \\\\ ~~~~ = \frac1\phi \int_1^\infty \frac{(y-1)^{\phi-2}}{y^\phi} \, dy[/tex]

Substitute [tex]y=\frac1z[/tex] and [tex]dy=-\frac{dz}{z^2}[/tex] to transform [tex]I[/tex] to

[tex]\displaystyle I = \frac1\phi \int_0^1 \left(\frac1z-1\right)^{\phi-2} z^{\phi-2} \, dz \\\\ ~~~~ = \frac1\phi \int_0^1 (1-z)^{\phi-2} \, dz[/tex]

Finally, substitute [tex]u=1-z[/tex].

[tex]\displaystyle I = \frac1\phi \int_0^1 u^{\phi-2} \, du \\\\ ~~~~ = \frac1\phi \cdot \frac1{\phi-1} = \frac{\phi-1}{\phi-1} = \boxed{1}[/tex]

To find the arc length we need to know the angle subtended by the arc.

From the diagram we notice that angle MNK is of 180°.

We also notice that:

Then the angle subtended by the arc MKL is 218°.

Now that we know this we need to remember that the arc length is given by:

in this case the radius is 3 ft (The radius is half the diameter) then we have that:

Therefore the arc length is 11.4 ft.

Using it's concept, the probabilities are given as follows:

a) Both go off on schedule: 0.30 = 30%.

b) Both go off on schedule: 0.2 = 20%.

A probability is calculated as the number of desired outcomes in the experiment divided by the number of total outcomes in the experiment.

From the text of the problem, the probability of A and not B is of 0.2, that is:

A x (1 - B) = 0.2.

We can multiply the probabilities as the events are independent.

In item a, the probability of neither is of 0.2, hence:

(1 - A) x (1 - B) = 0.2.

From the first equation, we have that:

A = 0.2/(1 - B).

From the second equation, we have that:

(1 - A) = 0.2/(1 - B).

Hence:

A = 1 - A

2A = 1

A = 0.5.

Then we can find B as follows:

(1 - A) x (1 - B) = 0.2.

1 - B = 0.2/0.5

1 - B = 0.4

B = 0.6.

The probability of both is:

A x B = 0.5 x 0.6 = 0.30 = 30%.

For item b, we consider that:

(1 - A) x B = 0.3.

We also have that:

A x (1 - B) = 0.2.

From the first equation:

B = 0.3/(1 - A).

Then, replacing on the second:

A x (1 - 0.3/(1 - A)) = 0.2

Which has a solution of:

A = 0.5, B = 0.4.

Hence the probability of both is:

0.4 x 0.5 = 0.2 = 20%.

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Answer:

9 mileds

Step-by-step explanation:

Using the slope formula, the value of k in the coordinates of the point given is: k = 6.

If we are given two points that lie on a line, (x1, y1) and (x2, y2), the formula that is used to find the slope (m) of the line is given as:

Slope (m) = [tex]\frac{y_2 - y_1}{x_2 - x_1}[/tex] = change in y / change in x..

Given the following:

(k, -9) = (x1, y1)

(1, -6) = (x2, y2)

Slope (m) = -3/5

Plug in the values into the formula used for calculating the slope of a line:

(-6 -(-9))/(1 - k) = -3/5

3/(1 - k) = -3/5

Cross multiply and solve for the value of k

-3(1 - k) = 3(5)

-3 + 3k = 15

Add 3 to both sides

-3 + 3k + 3 = 15 + 3 [subtraction property of equality]

3k = 18

Divide both sides by 3

3k/3 = 18/3 [division property of equality]

k = 6

The value of k is: 6. Therefore, the points on the line that have a slope of -3/5 are (6, -9) and (1, -6).

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The slope of the line has increased, meaning it has become a positive number. This shift means that this year the data points were placed higher than the previous year.

We have the following function:

a) The initial height occurs at t=0. By substituting this value into the function, we get

which gives

since sin(-Pi/2) is equal to -1, we have

Then, H(0)= 5, so the height is 5 feets.

b) The car will make a full rotation when the argument is shifted 2Pi:

at this point H(t) must be equal to 5 feets. Then, we have

and we must find t. If we move +15 to the left hand side, we obtain

By moving the coefficient 10 the the right hand side, we get

we can note that when

this implies that the argument of our last result is

By moving 2Pi to the right hand side, we have

Now, by moving 2Pi to the right hand side, we have

which gives

so, t is given by

That is, n 1 minute, the car will take one full rotation.

c) The maximum height of the car ocurrs at t=0.5 min because in one minute it take one full rotation. Then, at t=1/2 we get

which gives

that is, the maximum height is 25 feets

Answer: 12 cups

Explanation

Anna needs 6 pint of milk to produce yoghurt

1 pint = 2 cups

let cups of milk be x

1 pint of milk will give 2 cups

6 pints of milk will give x cups of milk

1 pint = 2cups

6 pints = x cups

Cross multiply

1 * x = 2 * 6

x = 12 cups

Therefore, Anna will need 12 cups of milk to produce a yoghurt.

Answer:Explanation:

No

The sum of the interior angles of a triangle is always 180°. in this case, the sum is:

Then,

46 + 82 + 50 = 178

Since 178 and 180 are distinct, 46°, 82°and 50°​ can't be the angle measures of a triangle.

Answer:

Mai 19

Bill 29

Dante 57

Step-by-step explanation:

assume

mai = X

Bill = Y

Dante = Z

X + Y + Z = 105

Z = 3X

Y = 10 + X

then

X + Y + Z = X + 3X + 10 + X

5X + 10 = 105

5X = 95

X = 19

Y = 29

Z = 57

Th length of the garden when the teacher bought 50 feet of fence is 17 feet.

From the information, the width needs to be the same size as the shed which is 8ft and she bought 50 feet of fence and wants the largest garden she can make,

It should be noted that perimeter is calculated as:

= 2(Length + Width)

In this case, the perimeter is 50 feet.

2(Length + Width) = 50

2(Length + 8) = 50

2L + 16 = 50

2L = 50 - 16

2L =34

Divide

L = 34/3

L = 17 feet.

The length is 17 feet.

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Answer:

what

Step-by-step explanation:

i think maybe like… actually