Find the missing side length.
Assume that all intersecting sides meet at right angles.
Be sure to include the correct unit in your answer.

Answer:

(0.5, 2)

Step-by-step explanation:

\(\left(\frac{-4+5}{2}, \frac{0+4}{2} \right)=(0.5, 2)\)

Answer:

Option (3)

Step-by-step explanation:

There are two parallel lines 'p' and 'q' and a transversal line is intersecting these lines at two distinct points.

Each pair of angles formed on the inner side of the parallel lines but opposite sides of the transversal line are the alternate interior angles.

Pair of angles (∠2 and ∠6) and (∠3 and ∠7) are the alternate interior angles.

Since, alternate interior angles are equal in measure,

∠2 ≅ ∠6

∠3 ≅ ∠7

Option (3) will be the answer.

Answer:

the answer is 69

Step-by-step explanation:

you find the square root of 4761

Answer:

its 69

Step-by-step explanation:

The maximum APR with quarterly compounding that the borrower will accept from a lender is 16.132%.

To convert the maximum effective monthly rate of 1% into an APR with quarterly compounding, we can use the formula:

\(APR = [(1 + \dfrac{r}{n})^n - 1] \times 4\)

Where r is the effective monthly rate and n is the number of compounding periods per year. In this case, we want to find the maximum APR with quarterly compounding that the borrower will accept, so we can substitute r = 1% and n = 3:

\(APR = ((1 + \dfrac{0.01}{3})^3 - 1) \times 4\)

APR = (1.0100333³ - 1) x 4

APR = 0.04033 x 4

APR = 0.16132 or 16.132%

Therefore, the maximum APR with quarterly compounding that the borrower will accept from a lender is 16.132%.

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While one runner demonstrated dedication and improvement through a personal best time, the other runner's lack of training and absence of a personal best time suggest a more casual or unprepared approach to the race.

In a race between two runners, one of them had a personal best time, while the other runner neither trained nor had a personal best time.

The runner who had a personal best time implies that they had trained and put in effort to improve their performance. A personal best time suggests that they have achieved their highest level of performance in a race. This indicates that the runner has dedicated time and effort to their training regimen, focusing on improving their speed and endurance.

On the other hand, the runner who neither trained nor had a personal best time implies that they did not invest effort in training or actively seek to improve their performance. They may have participated in the race casually or without specific training goals in mind. As a result, they did not achieve a personal best time, indicating that they did not put in the necessary effort to reach their full potential.

In summary, while one runner demonstrated dedication and improvement through a personal best time, the other runner's lack of training and absence of a personal best time suggest a more casual or unprepared approach to the race.

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The criteria that you can use to show these two triangles are congruent is A. AAS

If all three corresponding sides and all three corresponding angles are equal in size, two triangles are said to be congruent. It stands for "Angle, Angle, Side." Knowing two angles and one side is known as "AAS" (which is not between the angles). to make an AAS triangle work.

To find the other angle, add the three angles to 180°. then utilize the Law of Sines to determine each of the additional two sides. The triangles are said to be congruent when two angles and a non-included side of one triangle match the corresponding angles and sides of another triangle.

In conclusion, the correct option is A.

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The greatest common divisor of 5! and 7! is 840.

To find the greatest common divisor (GCD) of 5! and 7!, we need to calculate the prime factorization of both numbers.

First, let's calculate the prime factorization of 5!:

5! = 5 * 4 * 3 * 2 * 1 = 120.

The prime factorization of 120 is 2^3 * 3 * 5.

Now, let's calculate the prime factorization of 7!:

7! = 7 * 6 * 5! = 7 * 6 * 120 = 5040.

The prime factorization of 5040 is 2^4 * 3^2 * 5 * 7.

To find the GCD of 5! and 7!, we need to find the common factors in their prime factorizations. We take the smallest exponent for each prime factor that appears in both factorizations.

From the prime factorizations above, we can see that the common factors are 2^3, 3, 5, and 7. Multiplying these factors together gives us:

GCD(5!, 7!) = 2^3 * 3 * 5 * 7 = 8 * 3 * 5 * 7 = 840.

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Answer:

x=6

Step-by-step explanation:

This is a vertical line going through (6,0).  If you take this point and the point given and calculate the slope you find the change in y over the change in x.  

0-(-3)/6-6  The slope is undefined because the denominator of the slope would be zero.

If the population of Placerville grew from 4740 a decade ago to 7040 today. Then, the Absolute change = 2300 and percentage change = 48.5 %, which implies that option C is the right choice for this question.

The rate of change between two quantities is given by -

rate of change = new value - old value

The rate of change can be positive or negative.

The rate of change is also called Absolute change.

% of change = (absolute change / old value) x 100

Here, we are given that the population grew from 4740 a decade ago to 7040 today.

hence, we have the old value = 4740 and the new value = 7040.

now let us find the absolute change using the above formula -

Absolute change = new value - old value

Absolute change = 7040 - 4740

Absolute change = 2300

Now, let us find the percentage change using the above formula as follows -

% of change = (absolute change / old value) x 100

% of change = (2300 / 4740) x 100

% of change = 0.485 x 100

% of change = 48.5 %

Hence, we get Absolute change = 2300 and % of change = 48.5 %, which implies that option C is the correct choice for this question.

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The complete question is -

Measurements are made at two different times. Find the absolute change and then find the percentage change. Round answers to the nearest tenth if necessary.

The population of Placerville grew from 4740 a decade ago to 7040 today. Group of answer choices

a. Absolute change: 2300; Percentage change: 32.7%

b. Absolute change: -2300; Percentage change: 32.7%

c. Absolute change: 2300; Percentage change: 48.5%

d. Absolute change: -2300; Percentage change: 48.5%

Answer:

\(\displaystyle \frac{\pi(5e^4+8e^2-1)}{2e^4}\approx9.526\)

Step-by-step explanation:

This can be solved with either the washer (easier) or the shell method (harder). For the disk/washer method, the slice is perpendicular to the axis of revolution, whereas, for the shell method, the slice is parallel to the axis of revolution.  I'll show how to do it with both:

Shell Method (Horizontal Axis)

\(\displaystyle V=2\pi\int^d_cr(y)h(y)\,dy\)

Radius: \(r(y)=2-y\) (distance from y=2 to x-axis)

Height: \(h(y)=2-(-\ln y)=2+\ln y\) (\(y=e^{-x}\) is the same as \(x=-\ln y\))

Bounds: \([c,d]=[e^{-2},1]\) (plugging x-bounds in gets you this)

Plugging in our integral, we get:

\(\displaystyle V=2\pi\int^1_{e^{-2}}(2-y)(2+\ln y)\,dy=\frac{\pi(5e^4+8e^2-1)}{2e^4}\approx9.526\)

Washer Method (Parallel to x-axis)

\(\displaystyle V=\pi\int^b_a\biggr(R(x)^2-r(x)^2\biggr)\,dx\)

Outer Radius: \(R(x)=2-e^{-x}\) (distance between \(y=2\) and \(y=e^{-x}\))

Inner Radius: \(r(x)=2-1=1\) (distance between \(y=2\) and \(y=1\))

Bounds: \([a,b]=[0,2]\)

Plugging in our integral, we get:

\(\displaystyle V=\pi\int^2_0\biggr((2-e^{-x})^2-1^2\biggr)\,dx\\\\V=\pi\int^2_0\biggr((4-4e^{-x}+e^{-2x})-1\biggr)\,dx\\\\V=\pi\int^2_0(3-4e^{-x}+e^{-2x})\,dx\\\\V=\pi\biggr(3x+4e^{-x}-\frac{1}{2}e^{-2x}\biggr)\biggr|^2_0\\\\V=\pi\biggr[\biggr(3(2)+4e^{-2}-\frac{1}{2}e^{-2(2)}\biggr)-\biggr(3(0)+4e^{-0}-\frac{1}{2}e^{-2(0)}\biggr)\biggr]\\\\V=\pi\biggr[\biggr(6+4e^{-2}-\frac{1}{2}e^{-4}\biggr)-\biggr(4-\frac{1}{2}\biggr)\biggr]\)

\(\displaystyle V=\pi\biggr[\biggr(6+4e^{-2}-\frac{1}{2}e^{-4}\biggr)-\frac{7}{2}\biggr]\\\\V=\pi\biggr(\frac{5}{2}+4e^{-2}-\frac{1}{2}e^{-4}\biggr)\\\\V=\pi\biggr(\frac{5}{2}+\frac{4}{e^2}-\frac{1}{2e^4}\biggr)\\\\V=\pi\biggr(\frac{5e^4}{2e^4}+\frac{8e^2}{2e^4}-\frac{1}{2e^4}\biggr)\\\\V=\pi\biggr(\frac{5e^4+8e^2-1}{2e^4}\biggr)\\\\V=\frac{\pi(5e^4+8e^2-1)}{2e^4}\approx9.526\)

Use your best judgment when deciding on what method you use when visualizing the solid, but I hope this helped!

Answer:

stupid noob

Step-by-step explanation:

Answer:

2a-b+5c)(2a-b+5c)

Step-by-step explanation:

4a²+b²+25c²-4ab-10bc+20ca

(2a)²+(-b)²+(5c²)+2*2a*(-b)+2*(-b)*5c+2*5c*2a

(2a-b+5c)²

(2a-b+5c)(2a-b+5c)

The equation that represents the condition is m° + 66° + m° = 120°. Then the value of m is 27°.

When two lines intersect, then their opposite angles are equal. Then the equation is given as,

m° + 66° + m° = 120°

Simplify the equation for m, then the value of 'm' is calculated as,

m° + 66° + m° = 120°

2m° = 120° - 66°

2m° = 54°

m° = 27°

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Answer:

x=12

Step-by-step explanation:

Distribute:

3x - 3 = 2x + 9

Combine like terms to one side:

x = 12

Answer:

x=12

Step-by-step explanation:

3(x-1)=2x+9       - Original equation

3x-3=2x+9        - Distribute 3 through the parentheses

3x-2x-3=9         - Move variable to the left-hand side and change sign

3x-2x=9+3        - Move constant to the right-hand side and change its sign

x=9+3               - Collect like terms and add

x=12                  - Answer

Hope this helps    

There is approximately a 36.11% probability of rolling an odd sum or doubles when a pair of dice is rolled.

Probability is defined as the possibility of an event being equal to the ratio of the number of favorable outcomes and the total number of outcomes.

There are 3 odd numbers among the possible outcomes of each die (1, 3, 5), so there are 3 x 3 = 9 ways to obtain an odd sum:

(1,2), (1,4), (1,6), .... (6,1), (6,3), (6,5)

There are 6 possible outcomes for rolling the same number on both dice, so there are 6 ways to obtain doubles:

(1,1), (2,2), (3,3), (4,4), (5,5), (6,6)

We counted (1,1), (3,3), and (5,5) twice in the above two categories, so we need to subtract 2 from the total count.

Therefore, there are 9 + 6 - 2 = 13 ways to obtain an odd sum or doubles.

Therefore, the probability of rolling an odd sum or doubles is:

P(odd sum or doubles) = 13/36

Thus, there is about a 36.11% probability of rolling an odd sum or doubles when a pair of dice is rolled.

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Answer:

w = -1

Step-by-step explanation:

Answer:

112.5

67.5

Step-by-step explanation:

We know the ratio is:

5:3

So, we can write it as:

5x+3x=180, with 5x being one angle, and 3x being the other

combine like terms

8x=180

divide both sides by 8

x=22.5

5(22.5)=112.5

3(22.5)=67.5

So, one angle is 112.5 and the other is 67.5.

Hope this helps!

Answer:

C

Step-by-step explanation:

\(\left(\frac{f}{g} \right)(x)=\frac{f(x)}{g(x)} \\ \\ \frac{f(x)}{g(x)}=\frac{\sqrt[3]{2x}}{2x+1}\)

The denominator cannot equal 0, so:

\(2x+1 \neq 0 \implies x \neq -\frac{1}{2}\)

STEP - BY - STEP EXPLANATION

What to find?

dh/dt

Given that;

At a sand and gravel plant, sand is falling off a conveyor and onto a conical pile at a rate of 4 cubic feet per minute. The diameter of the base of the cone is approximately three times the altitude.

Since we have that the rate is 4 cubic per minute, then dv/dt = 4 (since v is the volume of the cone at time t.)

The formula for the volume of a cone is

Where r is the radius and h is the height.

We have that, the diameter of the cone is approximately three times the altitude.

That is;

diameter = 3h

But, d = 2r

⇒2r = 3h

⇒ r = 3h/2

Now, we substitute r=3h/2 into equation (1).

Now, differentiate the above with respect to t.

Simplify .

Make dh/dt subject of formula.

Recall that, dv/dt = 4 and h=22

Substituting the values into equation (2), we have;

Therefore, h' = dh/dt = 4/1089π ft/min.

Answer:

About 95% of individuals have IQ scores in the interval 100 ± 2 ( 15 ) = [ 70 , 130 ] .

Step-by-step explanation:

hope this helps

Answer:

Your answer is 12.8

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The meaning is that "If you share seven apples equally with three people, there are 2 1/3 apples for each person."

In this context, a "whole number to the denominator of three and the numerator one" refers to the fact that when the seven apples are divided equally among the three people, each person receives a whole number of apples, plus a fraction.

The denominator of the fraction is three because there are three people sharing the apples,

Tthe numerator of the fraction is one because each person receives one of the three equal parts.

The fraction 1/3 represents the amount of the seventh apple that each person receives. So, each person receives 2 whole apples and 1/3 of another apple, for a total of 2 1/3 apples.

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Answer:

30

Step-by-step explanation:

Since this is a right triangle, we can use a trig function

cos theta = adjacent/ hypotenuse

cos ? = 52/ 60

Take the inverse cos of each side

cos ^ -1 cos ? = cos ^ -1 ( 52/60)

? =29.92643487

To the nearest degree

? = 30

\(answer \\ 30 \\ please \: see \: the \: attached \: picture \: for \: full \: solution \\ hope \: it \: helps\)

Answer:

19.4

Step-by-step explanation:

that is the answer

The equations that represent the diagram given are 7 + 8h = 167, 8h = 160

To find the equation that represent the situation, we should simply count the number h present in the diagram, add it to 7 and equate the entire length to 167 which is the length of the tube.

This can be represented mathematically as

\(7 + h + h + h + h + h + h + h + h = 167\)

we can simplify this further as

\(7 + h + h + h + h + h + h + h + h = 167\\7 + 8h = 167\\\)

This can also be simplified as

\(7 + 8h = 167\\8h = 167 - 7\\8h = 160\)

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The order for the extra materials that are ordered by the man will be between 17.31 ft² and 23.08 ft².

From the information, the man is ordering new tile for her kitchen floor the area of the floor is 115.4 ft.² and wants to order between 15% and 20% extra of the material.

It should be noted that 15% of the material will be:

= 15% × 115.4

= 17.31 ft²

It should be noted that 20% of the material will be:

= 20% × 115.4

= 23.08 ft²

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Answer:

18 red balls, 3 blue balls, 6 yellow balls.

Step-by-step explanation:

a ratio helps us understand the relationship between two or more values (in this case three values). More specifically it tells us how much of one item is present, for every amount another item is also present.

In this example, the ratio of red:blue:yellow is given to be: 6:1:2, which means, for every 6 red balls, there is one blue ball and two yellow balls.

In some cases, a ratio can be simplified, similar to a fraction, by dividing each number by some common factor, but in this case, the ratio cannot be simplified any further.

Instead of directly trying to find how many red, yellow, or blue balls there are first, we can instead try solving for how many group of sixes are there in the total number of red balls. It helps to think of it this way, since for every group of six red balls there are, there is one blue ball and two yellow balls, which means we can just multiply this number by one and two to find the number of blue and yellow balls in their respective orders. For simplicity, let's assign this to the unknown "G".

Using this logic, we can set up the following equation:

\(6G+1G+2G=27\)

For every group of six red balls... there is 6 red balls, 1 blue ball, and 2 yellow balls, adding all these together should give us the total number of balls, which was given to be 27 balls. Now we can just combine the stuff on the left into one term, by adding the coefficients.

\(9G=27\)

Now divide by 9

\(G=3\)

Now that we know the number of group of six red balls there are, we can multiply six, one, and two to find the red, blue, and yellow balls.

\(\text{red balls} = 3 * 6 = 18\\\\\text{blue balls} = 3 * 1 = 3\\\\\text{yellow balls} = 3 * 2 = 6\)

and you can all this together, to double check, which gives us 27.

Answer:

18,3,6

Step-by-step explanation:

Given ,

To Find : The number of red,blue and yellow balls present in the bag

Let us take the variable as 'x' to represent the number of balls in the bag

When we Put the values in a equation,

6x+x+2x = 27

9x = 27

x = \(\frac{27}{9}\)

x = 3

Hence the number of,

Red Balls = 6x = 6 x 3 = 18

Blue Balls = x = 3

Yellow Balls = 2x = 2 x 3 = 6

Answer:

88

Step-by-step explanation: