0, 7, 26, 63, _ , 215.
What is the missing number in the given sequence?
What is the pattern?

Answer:

A ⊆ B

Step-by-step explanation:

180° rotation about the origin change the coordinates from (x,y) to (-x,-y). In this exercise:

A = (-4, 5) -> (4, -5)  

B = (-3, 1) -> (3, -1)

C = (-5, 2) -> (5, -2)

Translation 7 units up change the coordinates from (x, y) to (x, y+7). Continuing with the exercise:

(4, -5) -> (4, 2)

(3, -1) -> (3, 6)

(5, -2) -> (5, 5)

Which are not the coordinates of triangle DEF.

Reflection across the x-axis change the coordinates from (x, y) to (x, -y). In this exercise:

A = (-4, 5) -> (-4, -5)  

B = (-3, 1) -> (-3, -1)

C = (-5, 2) -> (-5, -2)

In 180 rotation (x,y) becomes (-x,-y) , In translation 7 units (x, y) becomes (x, y+7) and in reflection across  x-axis (x, y) becomes (x, -y).

180° rotation about the origin change the coordinates from (x,y) to (-x,-y). It means if an object having coordinates (3,4) then it will be (-3,-4).

Translation 7 units up change the coordinates from (x, y) to (x, y+7). It means if an object having coordinates (3,4) then it will be (3,4+7).

Reflection across the x-axis change the coordinates from (x, y) to (x, -y). It means if an object having coordinates (3,4) then it will be (3,-4).

Hence we can summarize the above phenomenon as in 180 rotation (x,y) becomes (-x,-y) , In translation 7 units (x, y) becomes (x, y+7) and in reflection across  x-axis (x, y) becomes (x, -y).

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area = S^2

 side = 12 miles

12^2 = 144

 area = 144 miles

$4100*(1+0.04/12)^(12*10)

4100*1.490832682=

$6112.41

Answer:

x = 2.75

Step-by-step explanation:

5x - 2 = x + 9

5x = x + 11

4x = 11

Answer:

$371.3944

Step-by-step explanation:

Principal = 150

Time = 8 years

Rate of interest = 12% = 0.12

No. of compounds per year = n = 1

Formula: [tex]A=P(1+\frac{r}{n})^{nt}[/tex]

Where A is the amount

P is the principal

r is the rate of interest in decimals

t = time in years

n = no. of compounds per year

Substitute the values in the formula :

[tex]A=150(1+\frac{0.12}{1})^{8}[/tex]

[tex]A=371.3944[/tex]

Hence the value of 150 after eight years if you earn 12 percent interest per year is $371.3944

To find the range of sales that will earn you between $40 and $50, you can set up two inequalities and solve them to find the minimum and maximum sales required.

To find the range of sales that will earn you between $40 and $50, we can set up two inequalities.

First, let's find the minimum sales required to earn $40. We can use the inequality 5x >= 40, where x represents the sales. This inequality represents the condition that earning $5 for every $50 in sales should be greater than or equal to $40.

Next, let's find the maximum sales required to earn $50. We can use the inequality 5x <= 50, where x represents the sales. This inequality represents the condition that earning $5 for every $50 in sales should be less than or equal to $50.

To solve these inequalities:

For the first inequality, divide both sides by 5, giving us x >= 8. This means the minimum sales required to earn $40 is $8.

For the second inequality, divide both sides by 5, giving us x <= 10. This means the maximum sales required to earn $50 is $10.

Therefore, the range of sales that will earn you between $40 and $50 is $8 to $10.

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The volume of the cylinder is  1177.5 cubic inches.

Given that the diameter of the cylinder is 10 inches, the radius r is half of that, so [tex]\( r = \frac{10}{2} = 5 \)[/tex] inches.

The height h is three times the radius, so [tex]\( h = 3r = 3 \times 5 = 15 \)[/tex] inches.

Now, we can substitute these values into the formula for the volume of a cylinder:

[tex]\( V = \pi r^2 h \)\\ \( V = 3.14 \times (5)^2 \times 15 \)\\ \( V = 3.14 \times 25 \times 15 \)\\ \( V = 3.14 \times 375 \)\\ \( V = 1177.5 \) cubic inches.[/tex]

Rounded to the nearest tenth.

Answer:

Identify: Step 6 and step 7

Correction:

I think step 6 is just not necessary and should be removed.  

And step 7 should be the transitive property of equality not the Substitution Property of Equality

A loss of 6 yards is represented by -6, and a loss of 5 yards by -5. After losses of 6 and 5 yards, and a gain of 12 yards, the team will be 1 yard past their original starting position, not exactly back to the original position.

A loss of 6 yards can be represented by the number -6, and a loss of 5 yards can be represented by the number -5.

When the football team on the next play gains 12 yards, we add this value to their previous position, which results from adding -6 and -5. To determine if the team returns to their original starting position, we calculate -6 + -5 + 12. The sum of -6 and -5 is -11, then adding 12 gives 1, which means the team advances 1 yard past the original starting position, not just back to it.

Therefore, the team will not be at their original starting position after gaining 12 yards, they will be 1 yard ahead.

To find Ron's age, we set up equations based on their age relations and the total sum of their ages. After solving the system of equations, we determine that Ron is 15 years old.

The question deals with a basic age-related algebra problem. To solve for how old Ron is, we can set up a system of equations based on the information provided:

Let R represent Ron's age.

Let S represent Sam's age.

Let T represent Ted's age.

From the information:

Ron is half as old as Sam, so R = 1/2 * S

Sam is three times as old as Ted, so S = 3 * T

The sum of their ages is 55, so R + S + T = 55

Substituting the expressions for R and S in terms of T into the third equation gives:

1/2 * (3 * T) + 3 * T + T = 55

Simplifying and solving for T, we find that:

1.5T + 3T + T = 55

5.5T = 55

T = 10

Now we can find Sam's age:

S = 3 * 10 = 30

And Ron's age:

R = 1/2 * 30 = 15

Therefore, Ron is 15 years old.

Answer: The answer is B if you don't know what B is here:

|–322.25| > |–241.75| is the correct answer.

Hope this helps!

Step-by-step explanation:

Answer:  The values are

[tex]\cos\theta=-\dfrac{1}{2},~~\textup{and}~~\tan\theta=\sqrt3.[/tex]

Step-by-step explanation:  For an angle [tex]\theta[/tex],

[tex]\sin \theta=-\dfrac{\sqrt3}{2},~\pi<\theta<\dfrac{3\pi}{2}.[/tex]

We are given to find the values of [tex]\cos\theta[/tex] and [tex]\tan \theta[/tex].

Given that

[tex]\pi<\theta<\dfrac{3\pi}{2}\\\\\\\Rightarrow \theta~\textup{lies in Quadrant III}.[/tex]

We will be using the following trigonometric properties:

[tex](i)~\cos \theta=\pm\sqrt{1-\sin^2\theta},\\\\(ii)~\tan\theta=\dfrac{\sin\theta}{\cos\theta}.[/tex]

The calculations are as follows:

We have

[tex]\cos\theta=\pm\sqrt{1-\sin^2\theta}\\\\\\\Rightarrow \cos \theta=\pm\sqrt{1-\left(-\dfrac{\sqrt3}{2}\right)^2}\\\\\\\Rightarrow \cos\theta=\pm\sqrt{1-\left(\dfrac{3}{4}\right)}\\\\\\\Rightarrow \cos\theta=\pm\sqrt{\left(\dfrac{1}{4}\right)}\\\\\\\Rightarrow \cos\theta=\pm\dfrac{1}{2}.[/tex]

Since [tex]\theta[/tex] is in Quadrant III, and the value of cosine is negative in that quadrant, so

[tex]\cos\theta=-\dfrac{1}{2}.[/tex]

Now, we have

[tex]\tan\theta=\dfrac{\sin\theta}{\cos\theta}=\dfrac{-\frac{\sqrt3}{2}}{-\frac{1}{2}}=\sqrt3.[/tex]

Thus, the values are

[tex]\cos\theta=-\dfrac{1}{2},~~\textup{and}~~\tan\theta=\sqrt3.[/tex]

Since the given theta lies in third quadrant, then you can use the fact that only tangent and cotangent are positive in third quadrant, rest are negative.

The value of cos and tan for given theta is:

[tex]cos(\theta) = -\dfrac{1}{2}\\\\ tan( \theta) = \sqrt{3}[/tex]

If angle lies between 0 to half of pi, then it is int first quadrant.

If angle lies between half of pi to a pi, then it is in second quadrant.

When the angle lies between [tex]\pi[/tex] and [tex]\dfrac{3\pi}{2}[/tex], then that angle lies in 3rd quadrant.

And when it lies from [tex]\dfrac{3\pi}{2}[/tex] and 0 degrees, then the angle is in fourth quadrant.

Only tangent function and cotangent functions.

In first quadrant, all six trigonometric functions are positive.

In second quadrant, only sin and cosec are positive.
In fourth, only cos and sec are positive.

We can continue as follows:

[tex]sin(\theta) = -\dfrac{\sqrt{3}}{2}\\ sin(\theta) = sin(\pi + 60^\circ)\\ \theta = \pi + 60^\circ[/tex]

Thus, evaluating cos and tan at obtained theta:

[tex]cos(\pi + 60^\circ) = -cos(60) = -\dfrac{1}{2}\\ tan( \pi + 60^\circ) = tan(60) = \sqrt{3}[/tex]

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The number of students in the seventh grade would prefer chocolate ice cream over vanilla ice cream is 80

The proportion formula is used to depict if two ratios or fractions are equal. The proportion formula can be given as a: b::c : d = a/b = c/d where a and d are the extreme terms and b and c are the mean terms.

The proportional equation is given as y ∝ x

And , y = kx where k is the proportionality constant

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Given data ,

Let the proportion be represented as A

Now , the value of A is

If 40% of the sample of 50 students prefer chocolate ice cream, we can use that percentage to estimate the number of students who prefer chocolate ice cream out of the entire seventh-grade class of 200 students.

40% of 50 = (40/100) x 50 = 20 students in the sample prefer chocolate ice cream.

On simplifying the proportion , we get

To estimate the number of students in the entire seventh-grade class who prefer chocolate ice cream, we use the same percentage:

40% of 200 = (40/100) x 200 = 80 students in the seventh grade are expected to prefer chocolate ice cream over vanilla ice cream.

Hence , based on the sample proportion, we can estimate that 80 students in the seventh grade would prefer chocolate ice cream over vanilla ice cream.

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