Find the equation of the line with slope – 3 and that contains the point (-2,-6). Write the equation in the form y = mx +b and
identify m and b.

The measure of the indicated arc angle is 134 degrees.

The angle subtended by the arc at the centre of the circle is the angle of the arc.

Therefore, the central angle of an arc is the angle at the centre of the circle between the two radii subtended by the arc.

Hence, the central angle is also known as the arc's angular distance.

Therefore, the measure of an arc is the measure of its central angle.

Hence, the measure of the indicated arc is 134 degrees.

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Answer:

2,152

Step-by-step explanation:

So to find this all you have to do is subract 7,419 and 5,267 to get the answer of 2,152

Hope This Helps <3 <3

Answer:

b = 5

Step-by-step explanation:

All quadratic equations are formed in the format of \(a^{2}\) + bx + c = 0

Using this formula, we can re-arrange the equation to fit the given format.

\(3x^{2}\) - 2 = -5x
\(3x^{2}\) + 5x - 2 = 0

5 is plugged in for "b" in this equation, therefore b = 5.

The height of the building is approximately 227 feet.

In the given question, a man wants to measure the height of a nearby building. He places a 7 ft pole in the shadow of the building so that the shadow of the pole is exactly covered by the shadow of the building.

The total length of the building's shadow is 162 ft, and the pole casts a shadow that is 5.5 ft long. We have to determine the height of the building.The given situation can be explained with the help of a diagram.

As shown in the figure above, let AB be the building and CD be the 7 ft pole. The height of the building is represented by the line segment AE, which is to be determined. Let the length of the shadow of the pole be CD and that of the building be BD.

Therefore, the length of the total shadow will be BC or CD + BD.According to the question, the shadow of the pole is exactly covered by the shadow of the building. This implies that the two triangles AEF and CDF are similar. Hence, the corresponding sides are proportional. Therefore, we have:AE/EF = CD/DF

On substituting the values from the given data, we get:

AE/(EF + 5.5) = 7/5.5.... (1)

Similarly, we can write from the given data:

BD/DF = 162/5.5.... (2)

From equations (1) and (2), we can write:

AE/(EF + 5.5) = BD/DF => AE/(EF + 5.5) = 162/5.5.... (3)

On solving the above equation for AE, we get:

AE = (7/5.5) × (162/5.5 - 5.5)≈ 226.6 ft

Therefore, the height of the building is approximately 227 feet.

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Answer:

19.5959179423 or when simplified, 19.6

Step-by-step explanation:

Answer:

blah blah blah blah blah blah blah blah blah

The value of y is 4√3

Similar triangles have the same corresponding angle measures and proportional side lengths. The corresponding angles of similar triangles are congruent or equal.

Also , the ratio of corresponding sides of similar triangles are equal.

There are two triangles that are similar

Therefore;

y /16 = 4/y

y² = 48

y = √48

y = √16 × √ 3

y = 4√3

Therefore, the value of y is 4√3

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Answer:

(0,1)

Step-by-step explanation:

Answer:

3,0,-6,0

Step-by-step explanation:

x1=3 because 3+0+0=3

since x2 and s2=0.

Answer:

The answer is (a²+1)(2a+1)

Answer:B

Step-by-step explanation:

Answer:

Step-by-step explanation

D

because V = 1/3Hxr

                              ^

                             pie

so 1/3(5)pie(1.75)

1.75 is from the diameter 1/2 which makes 1.75 the radius

Step-by-step explanation:

\( \frac{135}{100} \times \frac{280}{1} = 378\)

The correct statement about the quadratic function is given as follows:

C. The second difference would be constant.

A quadratic function is modeled as follows:

y = ax² + bx + c.

Then the first difference, which is the first derivative of the quadratic function, is obtained as follows:

y = 2ax + b.

(applying the x^n derivative rule from the table of derivatives).

The second difference, which is the second derivative of the quadratic function, is obtained as follows:

y = 2a.

(again applying the x^n derivative rule from the table of derivatives).

The coefficient a is a constant, hence the second difference would be constant and the correct option is given by option C.

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Answer: 4

This problem requires basic division. If the restaurant divided 4/5 kg of butter with 1/5 kg on each dish, you would need to compute 4/5 divided by 1/5.

4/5 ÷ 1/5

Using the "KFC" method, or Keep, Change, Flip, you would keep the first number (in this case, 4/5), change the division sign, and flip the fraction to 5/1, or 5. We now have this:

4/5 x 5

To compute this equation, you must multiply the numerators of both of the numbers together. In this case, you would compute (4x5)/5, resulting with 20/5, or 4.

You can check this answer by re-multiplying the numbers together. 1/5 kg of butter per dish, multiplied by the total amount of dishes, 4, you would result in the original 4/5 kg of butter.

Hope this helps!

Step-by-step explanation:

\(\qquad\quad {:}\leadsto\sf \dfrac {2x (x+7)}{\cancel{(x-3)}}\times {\dfrac {(x-9)\cancel{(x-3)}}{8x^2 (x+7)}}\)

\(\qquad\quad {:}\leadsto\sf \dfrac {2x\cancel{(x+7)}}{x-3}\times {\dfrac {x-9}{8x^2 \cancel{(x+7)}}}\)

\(\qquad\quad {:}\leadsto\sf \dfrac{2x (x-9)}{8x^2}\)

\(\qquad\quad {:}\leadsto\sf \dfrac {\cancel{2x}^2-18x}{\cancel{8x}^2}\)

\(\qquad\quad {:}\leadsto\sf \dfrac {18x}{4}\)

\(\qquad\quad {:}\leadsto\sf \dfrac {9x}{2}\)

\(\qquad\quad {:}\leadsto\sf 4.5x \)

Answer:

Your answer for both is 31 degrees

Step-by-step explanation:

Because they are similar we know their angles are the same. If you know the rule about triangles' interior angles always add up to 180, then you can just easily find this out.

First you do

82+67 = 149

Take that answer and minus it by 180

180-149 = 31

Answer:

*Using < for angle symbol*

m<E= 61 degrees

m<G= 119 degrees

Step-by-step explanation:

Because the two triangles are similar (meaning they have either length of sides or angle measurements in common, we can assume that they have the same angles because they are not the same size. We know that m<A= 82 degrees, which means so will m<D. You add the 82 and the 37 (from m<F) together to find 119. You subtract this from 180 (the total angle measurement of a triangle) to find m<E= 61. To find m<G, you subtract the 61 from 180, the angle measurement of a straight line, to find 119.

Hope this helps! Have a nice day :)

The scale factor is 4.

Important information:

From the given figure it is clear that:

DG = 2

D'G' = 8

The scale factor is:

\(k=\dfrac{D'G'}{DG}\)

\(k=\dfrac{8}{2}\)

\(k=4\)

Therefore, the scale factor is 4.

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The statement that is true about the function is:

A function, in mathematics, an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).

Given:

The minimum value of the curve = (1.9, -5.7),

The maximum value = (0, 2)

The point the function crosses the x-axis (the x-intercept) = (-0.7, 0), (0.76, 0), and (2.5, 0)

The point the function crosses the y-axis (the y-intercept) = (0, 2)

The given points can be plotted using MS Excel, from which we have:

F(x) is less than 0 over the interval from x = -∞, to x = -0.7, and the interval from x = 0.76 to x = 2.5.

Hence, the correct option is A.

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\(10:\dfrac{1}{5}=10\cdot5=\boxed{50}\)

Answer:

50!

Step-by-step explanation:

hope it helps thanks to the first person who helped

Answer:

The answer is 16

Step-by-step explanation:

Hi there!

The angles shown are supplementary

Supplementary angles have a measure of 90 degrees

This means that 3x + 5 + 37 = 90

3x + 5 + 37 = 90

Combine like terms

3x + 42 = 90

Take away 42 from each side

3x = 48

Divide by 3

x = 16

Hope this helps! :)

Answer:

O B) 16

Step-by-step explanation:

90° (total) - 37° = 53°

(3x+5) = 53°

(3x-5)  = -5°         Subtract 5 from both sides!

3x = 48               Solve

x = 16

The probabilities are

i. P(male) ≈ 0.503

ii. P(hybrid) ≈ 0.324

iii. P(hybrid|male) ≈ 0.208

iv. P(hybrid|female) ≈ 0.441

v. P(female|hybrid) ≈ 0.677

P(hybrid|male) and P(male|hybrid) are not equal because the sample may not be representative of the entire population.

What is probability?

Probability is a measure of the likelihood of an event occurring, expressed as a number between 0 and 1, with 0 indicating an impossible event and 1 indicating a certain event.

a.

i. P(male) = number of males in the sample / total number in the sample = 154 / 306 ≈ 0.503

ii. P(hybrid) = number of hybrid cars purchased / total number in the sample = 99 / 306 ≈ 0.324

iii. P(hybrid|male) = number of males who purchased a hybrid / total number of males in the sample = 32 / 154 ≈ 0.208

iv. P(hybrid|female) = number of females who purchased a hybrid / total number of females in the sample = 67 / 152 ≈ 0.441

v. P(female|hybrid) = number of females who purchased a hybrid / total number of people who purchased a hybrid = 67 / 99 ≈ 0.677

b.

i. P(male) represents the probability of randomly selecting a male from the sample of 306 people who purchased a Honda Civic.

ii. P(hybrid) represents the probability of randomly selecting a car from the sample that has a hybrid engine.

iii. P(hybrid|male) represents the probability of selecting a hybrid car given that the person selected is male.

iv. P(hybrid|female) represents the probability of selecting a hybrid car given that the person selected is female.

v. P(female|hybrid) represents the probability of selecting a female given that the car selected has a hybrid engine.

c. No, P(hybrid|male) and P(male|hybrid) are not equal. P(hybrid|male) represents the probability of selecting a hybrid car given that the person selected is male, while P(male|hybrid) represents the probability of selecting a male given that the car selected has a hybrid engine. These probabilities are different because the sample is not necessarily representative of the entire population.

Hence, the probabilities are

i. P(male) ≈ 0.503

ii. P(hybrid) ≈ 0.324

iii. P(hybrid|male) ≈ 0.208

iv. P(hybrid|female) ≈ 0.441

v. P(female|hybrid) ≈ 0.677

P(hybrid|male) and P(male|hybrid) are not equal because the sample may not be representative of the entire population.

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The fish tank has a total volume of 288 inch³. As a result, Jessica's new fish tank has a capacity of 288 inch³ for water.

The volume of a rectangular prism can be calculated using the formula:

V = l x b x h..........(i)

where,

V ⇒ Volume

l  ⇒ length

b ⇒ width

h ⇒ height

From the question, we are given the values,

l = 8 inches

b = 4 inches

h = 9 inches

Putting these values in equation (i), we get,

V = 8 x 4 x 9

⇒ V = 288 in³

Therefore, the fish tank has a total volume of 288 inch³. As a result, Jessica's new fish tank has a capacity of 288 inch³ for water.

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The additive inverse of the polynomial is +7y²-x²y+3xy+7x².

The additive inverse can be defined as when we add a number to some number and get result as zero.

Given polynomial:

-7y²+x²y-3xy-7x²

As, the value of additive inverse is same as of the number but the sign of the additive inverse is opposite.

So,

=  +7y²-x²y+3xy+7x²

Check:

-7y²+x²y-3xy-7x² + 7y²-x²y+3xy+7x²

= -7y²+  7y² +x²y -x²y -3xy +3xy -7x² +7x²

=0

Hence, the additive inverse of the polynomial is +7y²-x²y+3xy+7x².

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the statement is true for all positive integers n. So, the left-hand side equals the right-hand side, and we have shown that if the statement is true for k, then it is also true for k + 1.

An integer is a whole number that can be either positive, negative or zero. Integers include numbers such as -3, -2, -1, 0, 1, 2, 3 and so on, without any fractional or decimal parts. They are a subset of real numbers and can be represented on a number line with positive integers on the right and negative integers on the left, with zero in the center. Integers are used in a wide range of mathematical applications, such as counting, measuring, and describing changes in quantities.

by the question.

To prove this statement by induction, we need to show that:

The statement is true for n = 1 (base case)

If the statement is true for some positive integer k, then it is also true for k + 1 (inductive step)

Here are the steps to prove this statement by induction:

Base case (n = 1):

When n = 1, the left-hand side of the equation is:

2(1)Σr² r=1 = 2(1)1² = 2

And the right-hand side of the equation is:

1/3(2(1) + 1) (4(1) + 1) = 1/15(3)(5) = 1

So, the statement is not true for n = 1. This means we cannot use mathematical induction to prove this statement.

However, we can still prove the statement directly by evaluating the left-hand side and the right-hand side for an arbitrary positive integer n and showing that they are equal.

Inductive step:

Assume the statement is true for some positive integer k, i.e.

2kΣr² r=1 = k/3(2k + 1) (4k + 1)

We need to show that the statement is also true for k + 1, i.e.

2(k + 1)Σr² r=1 = (k + 1)/3(2(k + 1) + 1) (4(k + 1) + 1)

We start with the left-hand side:

2(k + 1)Σr² r=1

= 2kΣr² r=1 + 2(k + 1) ² (by adding the next term in the summation)

= k/3(2k + 1) (4k + 1) + 2(k + 1) ² (by the inductive hypothesis)

= k (8k² + 14k + 6)/3(2k + 1) (4k + 1) + 2(k + 1)² (by simplifying the expression)

= (8k³ + 26k² + 22k + 6)/3(2k + 1) (4k + 1) + 2(k + 1) ²

= (8k³ + 26k² + 22k + 6 + 6(2k + 1) (4k + 1))/3(2k + 1) (4k + 1)

= (8k³ + 26k² + 22k + 6 + 48k² + 26k + 6)/3(2k + 1) (4k + 1)

= (8k³ + 74k² + 48k + 12)/3(2k + 1) (4k + 1)

= (k + 1)/3(2(k + 1) + 1) (4(k + 1) + 1)

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Answer:

2(x + 6)

Step-by-step explanation:

If we let the number be "x", then the sum of the number and six is x + 6. To find twice the sum, we multiply this expression by 2:

2(x + 6)

Therefore, the expression that represents twice the sum of a number and six is 2(x + 6)

Answer:

hope this explanation helps you

Answer:

\(\textsf{b)} \quad -\dfrac{3\sqrt{13}}{13}\)

Step-by-step explanation:

Trigonometric ratios

\(\sf \sin(\theta)=\dfrac{O}{H}\quad\cos(\theta)=\dfrac{A}{H}\quad\tan(\theta)=\dfrac{O}{A}\)

where:

\(\textsf{If}\; \tan(\theta)=-\dfrac{2}{3} \implies \sf O=2 \; \textsf{and} \; A=3.\)

Use Pythagoras Theorem to calculate the length of the hypotenuse:

\(\sf \implies O^2+A^2=H^2\)

\(\implies \sf H=\sqrt{O^2+A^2}\)

\(\implies \textsf{H}=\sqrt{2^2+3^2}\)

\(\implies \textsf{H}=\sqrt{13}\)

Therefore, substituting the values of A and H into the cosine ratio:

\(\implies \cos \theta=\dfrac{3}{\sqrt{13}}\)

\(\implies \cos \theta=\dfrac{3}{\sqrt{13}}\cdot \dfrac{\sqrt{13}}{\sqrt{13}}\)

\(\implies \cos \theta=\dfrac{3\sqrt{13}}{13}\)

As the terminal side of the angle is in Quadrant II, and cosine is negative in Quadrants II and III, the exact value of cos(θ) is:

\(\implies \cos \theta=-\dfrac{3\sqrt{13}}{13}\)