Factor 40x+15xy using the Greatest Common Factor (Divisor).

Answer:

D. 15x² + 62x + 63

Step-by-step explanation:

                  rectangle area: length * width

Here the length is ( 3x + 7 ) and width is (5x+9)

using the formula:

( 3x + 7 )(5x+9)

15x²+27x+35x+63

15x² + 62x + 63

Answer:

D. 15x^2 + 62x +63

Step-by-step explanation:

Area of rectangle = L x W

L = 3x + 7 ; W = 5x + 9

=> A = (3x + 7) x (5x +9) = 15x^2 + 62x +63

No triangle can be constructed with the given angles of 90 degrees, 60 degrees, and 60 degrees, as the sum of the angles exceeds the total of 180 degrees required for a valid triangle.

To determine the number of triangles that can be constructed with angles measuring 90 degrees, 60 degrees, and 60 degrees, we need to consider the conditions for triangle construction.

In a triangle, the sum of all angles must be equal to 180 degrees. Since we already have two angles of 60 degrees each, the sum of these angles is 60 + 60 = 120 degrees.

To form a valid triangle, the sum of all three angles must be equal to 180 degrees. However, in this case, the sum of the given angles (90 + 60 + 60 = 210 degrees) exceeds 180 degrees. Therefore, it is not possible to construct a triangle with angles measuring 90 degrees, 60 degrees, and 60 degrees.

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Answer:

ccccccc

Step-by-step explanation:

Each payment for the franchise rights to open and operate Pepperoni's specialty pizza restaurant is approximately $3,640.04.

To find the amount of each payment, we can use the formula for the present value of an ordinary annuity:

PV = PMT * [(1 - (1 + r)^(-n)) / r],

where PV is the present value (worth) of the franchise rights, PMT is the amount of each payment, r is the interest rate per period, and n is the number of periods.

In this case, the present value (worth) of the franchise rights is $70,000, the interest rate per period is 7.92% or 0.0792, and the number of periods is 12 (payments for two years).

Substituting these values into the formula, we have:

$70,000 = PMT * [(1 - (1 + 0.0792)^(-12)) / 0.0792].

Now, we can solve this equation for PMT. Using a calculator, the amount of each payment is approximately $3,640.04.

Therefore, each payment for the franchise rights to open and operate Pepperoni's specialty pizza restaurant is approximately $3,640.04.

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Answer:

Step-by-step explanation:

1) 9 x 4 = 36

9 + 4 = 13

2) 9 x -4 = -36

9 + (-4) = 5

3) 4 x3 = 12

4+ 3 = 7

4) -4 x 3 = -12

-4 + 3 = -1

The measure of ∠s is 22 degrees according to corresponding and straight line angle.

We will use the rrelation between angles to find the measure of each. We see that ∠158 degree and angle r are corresponding angles and hence they will be equal. Thus, it can be said that angle r = 158 degree.

Now, angle r and angle s is present on same line. It means the sum of these two angles will be 180 degree. Using the relation to find angle s.

158 + angle s = 180

Angle s = 180 - 158

Subtract the values

Angle s = 22 degrees

Hence, ∠s measures 22 degrees.

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Answer:

7, 7, 60, 60, 60

Step-by-step explanation:

When you draw the circles thhey all hhave radius AB so AB=AC=BC =7

and since all sides are congruent you have a equilateral treangle so all angles are equal to 180/3=60

Answer:

y = -2/3x + 13/3

Step-by-step explanation:

y = mx + c

m = -2/3

y = -2/3x + c

Put in your point (2,3):

3 = -2/3 (2) + c

3 = -4/3 + c

3 + 4/3 = c

13/3 = c

so

y = -2/3x + 13/3

The evidence that supports Alex's conclusion that the NCX-10 was the bottleneck were large inventories and increasing production rates of machines.

Consistently large inventories of units waiting to be processed by the NCX-10, consistently small inventories of units that have been processed by the NCX-10 but are waiting to be processed by the next machine in line, and the total production of the plant increasing when they ensured the NCX-10 was never idle.

Additionally, increasing production rates of other machines in the plant made almost no difference, which further supports the idea that the NCX-10 was the bottleneck.

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The four subsets of (Siamese, domestic shorthair) are (Siamese, domestic shorthair), (Siamese), (domestic shorthair), and the empty set.

A subset is a set that is contained within another set. To list all the subsets of a given set, we can use the power set formula. The power set of a set S is defined as the set of all subsets of S, including the empty set and S itself. For example, for a set S = {a, b, c}, the power set is:

P(S) = {∅, {a}, {b}, {c}, {a, b}, {a, c}, {b, c}, {a, b, c}}

In this case, the given set is (Siamese, domestic shorthair). We can use the power set formula to list all the subsets of this set:

P(S) = {∅, {Siamese}, {domestic shorthair}, {Siamese, domestic shorthair}}

Therefore, the four subsets of (Siamese, domestic shorthair) are (Siamese, domestic shorthair), (Siamese), (domestic shorthair), and the empty set.

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Answer:

$10.50

Step-by-step explanation:

The value of y is 17/5.

A midpoint is defined as in the middle of the line connecting two points a position known as a midpoint. A location in the middle of a line connecting the two points that are equally far from both points is the midpoint.

Let two points A (x₁, y₁) and B (x₂, y₂), the midpoint between A and B is given by,

M(x, y) = (x₁ + x₂)/2, (y₁ + y₂)/2

Given that H is the midpoint of FG

G(4x, 6y + 6), H(4, 15)  and F(2y+2, 2x+4)

⇒ (4x+2y+2)/2 = 4  and (6y+6+2x+4)/2 = 15

⇒ (4x+2y+2) = 8  and (2x+6y+10) = 30

⇒ 4x+2y = 6  and 2x+6y = 20

⇒ 2x+y = 3  and x+3y = 10

⇒ x = 10 - 3y

Substitute the value of x into 2x+y = 3

⇒ 2(10 - 3y) +y = 3

⇒ 20 - 6y +y = 3

⇒ 5y = 17

⇒ y = 17/5

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Answer:

Its C i just took the test and got this right!!!

Step-by-step explanation:

The side 3 cm, 4 cm, and 5 cm will satisfy the Pythagoras equation. Then the correct option is C.

The Pythagoras theorem states that the sum of two squares equals the squared of the longest side.

The Pythagoras theorem formula is given as

H² = P² + B²

The converse of the Pythagorean theorem using side lengths chosen from 2 cm, 3 cm, 4 cm, and 5 cm.

The side 3 cm, 4 cm, and 5 cm will satisfy the Pythagoras equation.

5² = 4² + 3²

25 = 16 + 9

25 = 25

The side 3 cm and 4 cm is normal to each other.

Then the correct option is C.

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The probability that more than 5 engines are defective is approximately 0.1685 using the binomial approximation.

The binomial approximation is used to approximate the probability of a given event occurring a certain number of times in a specified number of trials, given a certain probability of the event occurring on each trial.

We can use this approximation to calculate the probability that more than 5 engines are defective.

Let X be the number of defective engines out of 40.

Then X follows a binomial distribution with n = 40 and p = 0.03, where p is the probability that any given engine is defective.

Using the binomial approximation, we can approximate the distribution of X with a normal distribution with mean

μ = np and standard deviation σ = √(np(1-p)).

We can then use the normal distribution to approximate the probability that more than 5 engines are defective.

P(X > 5) = P(X >= 6)

We can use the normal distribution to approximate this probability as follows:

Z = (X - μ) / σZ

= (6 - (40*0.03)) / √(40*0.03*(1-0.03))Z

= 0.9577

Using a standard normal distribution table or calculator, we can find that the probability of Z being greater than 0.9577 is approximately 0.1685.

Therefore, P(X > 5) = P(X >= 6) ≈ 0.1685.

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Answer:

-3, 3, 9

Step-by-step explanation:

Answer on Edge

\((\stackrel{x_1}{1}~,~\stackrel{y_1}{9})\qquad (\stackrel{x_2}{8}~,~\stackrel{y_2}{8}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{8}-\stackrel{y1}{9}}}{\underset{\textit{\large run}} {\underset{x_2}{8}-\underset{x_1}{1}}} \implies \cfrac{ -1 }{ 7 } \implies - \cfrac{1 }{ 7 }\)

We have a cube that has a side length of a = 1 cm.

We can calculate the volume of the cube as:

Answer: the volume of a cube with side length of 1 cm is 1 cm³.

Answer:

The average cost per vet visit was $19.25.

Step-by-step explanation:

From the information given, you can find the average cost per visit by dividing the total amount paid for a year's worth of vet visits by the number of visits:

269.50/14= $19.25

According to this, the answer is that the average cost per vet visit was $19.25.

Answer:

This may be a function of the absolte value family.

f(x) = IxI.

f(x) = x if x ≥ 0

f(x) = -x  if x ≤ 0

Where this is the parent function, and the graph is shown below in green.

If the coefficient is positive, then the lines open upwards, and we will have a minimum (in this case, when x = 0).

And also in this case, we have symmetry around the value x = 0.

Now, the vertex can also be an absolute maximum if the coefficient is negative, like in the example shown below in color blue (the equation for the blue graph is f(x) = -3*IxI )

Answer:

sure, i'll try my best!

Step-by-step explanation:

❤️✨

Answer:

ftftftftftfjhgrew

Step-by-step explanation:

4weyye45y5e4

Answer:

w = 36 centimeters

y = 24 centimeters

Step-by-step explanation:

The exact question is as follows :

Given - Janelle drew KL in isosceles trapezoid FGHJ to create similar trapezoids FKLJ and KGHL.

To find - Based on the given information, what are the values of y and w in centimeters?

Solution -

We can see that from the diagram,

Trapezoid FKLJ is 3 times bigger than Trapezoid KGHL

So,

The side KL = 3 times side GH

⇒12 = 3×4

⇒12 = 12 centimeters

So,

side FJ = 3 times side KL

⇒w = 3×12

⇒w = 36 centimeters

Now,

The side KF = 3 times side KG

⇒KF = 3×8

⇒KF = 24

Now,

We know,

In  isosceles trapezoid  two opposite sides (the bases) are parallel, and the two other sides (the legs) are of equal length

So,

Side LJ = side KF

⇒y = 24 centimeters

∴ we get

w = 36 centimeters

y = 24 centimeters

When dealing with the simultaneous occurrence of two events A and B, the probability can be determined by using the probability of one event and the conditional probability of the other event given that the first event has occurred. Both P(A) * P(B|A) and P(B) * P(A|B) are valid ways to calculate this probability.

The concept of probability is fundamental in various fields such as mathematics, statistics, and even in everyday life. The probability of the simultaneous occurrence of two events A and B is a critical concept in probability theory. According to the definition, the probability of A and B occurring at the same time is equal to the probability of A multiplied by the conditional probability of B given that A has occurred. This equation is also valid in the reverse case, where the probability of B and A occurring simultaneously is equal to the probability of B multiplied by the conditional probability of A given that B has occurred.

Understanding the relationship between the probability of two events and their conditional probabilities is essential in predicting the likelihood of these events happening together. In real-life situations, this concept can be used to determine the probability of two events such as the success of a product launch and the corresponding increase in sales. The probability of these two events occurring simultaneously can be predicted by analyzing the probability of the product launch's success and the conditional probability of sales increasing given that the product launch is successful.

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To find the average value of f(x) = 2x - 2 over the interval [1, 2], we need to use the following formula:

Average value of f(x) over [a,b] = (1/(b-a)) * integral of f(x) from a to b

So, in our case, a = 1 and b = 2, and f(x) = 2x - 2. Therefore, we have:

Average value of f(x) over [1, 2] = (1/(2-1)) * integral of (2x - 2) dx from 1 to 2

= 1 * [(x^2 - 2x) / 2] from 1 to 2

= [(2^2 - 2(2)) / 2] - [(1^2 - 2(1)) / 2]

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

= 0 - (-1/2)

= 1/2

Therefore, the average value of f(x) = 2x - 2 over the interval [1, 2] is 1/2.
Hi! To find the average value of f(x) = 2x - 2 over the interval [1, 2], you can use the formula:

Average value = (1/(b-a)) * ∫(f(x)dx) from a to b

In this case, f(x) = 2x - 2, a = 1, and b = 2.

Average value = (1/(2-1)) * ∫(2x - 2)dx from 1 to 2 = ∫(2x - 2)dx from 1 to 2

Now, evaluate the integral:

∫(2x - 2)dx = x^2 - 2x + C

Next, find the definite integral:

(x^2 - 2x)|1 to 2 = (4 - 4) - (1 - 2) = 0 - (-1) = 1

Finally, calculate the average value:

Average value = 1 = 1

So, the average value of f(x) = 2x - 2 over the interval [1, 2] is 1.

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The factored form of the quadratic equation 2x² + 25x + 50 is (2x + 5)(x + 10)

Factoring quadratics is a method of expressing the quadratic equation ax² + bx + c = 0 as a product of its linear factors as (x - k)(x - h), where h, k are the roots of the quadratic equation ax² + bx + c = 0.

Therefore, let's factor the equation 2x² + 25x + 50.

2x² + 25x + 50

The two numbers one can multiply and add to get 100 and 25 respectively are 20 and 5.

Therefore,

2x² + 20x + 5x + 50

2x(x + 10)+ 5(x + 10)

Therefore,

(2x + 5)(x + 10)

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Answer:

-1  3/ 4

Step-by-step explanation:

It takes 53 years until we run out of gas.

Given,

Reserves of natural gas = 6500 TCF

Consumption per year = 123 TCF

Therefore,

years left ( x )= Reserves of natural gas / Consumption per year  

                     = 6500/123

                     = 52.8 years

                  x = 53 years approximately

So, it takes 53 years until we run out of gas at this rate of consumption.

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