A high school chorus has $1000 in its school account at the beginning of the year. They are putting on a fall concert to raise money for a trip later in the year. At the concert last year they sold tickets for $10 each. If they sell tickets at the same price the total amount in the chorus account can be represented by the linear function T = 10x + 1000. If they increase the ticket price to $15, how many tickets will they have to sell to have a total of $4000 in the account?

A) 100 tickets

B) 150 tickets

C) 200 tickets

D) 250 tickets

Factor of [tex]3x^{3} + 12x^{2} + 18x[/tex] is [tex]3x ( x^{2} +4x + 6 )[/tex].

Here,

We have to find factor of [tex]3x^{3} + 12x^{2} + 18x[/tex].

What is Factor?

A number or algebraic expression that divides another number or expression evenly with no remainder.

Now,

Factor of [tex]3x^{3} + 12x^{2} + 18x[/tex] is,

⇒[tex]3x^{3} + 12x^{2} + 18x = 3x (x^{2} + 4x + 6x)[/tex]

Hence,

Factor of [tex]3x^{3} + 12x^{2} + 18x[/tex] is [tex]3x ( x^{2} +4x + 6 )[/tex].

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Answer

Formula

[tex]Circumference\ of\ circle = 2\pi r[/tex]

where r is the radius of a circle.

As shown in the image

Diameter of the circle = 16 .3 cm

[tex]Radius\ of\ the\ circle = \frac{16.3}{2}[/tex]

                                   = 8.15 cm

Put in the formula

[tex]Circumference\ of\ circle = 2\pi\times 8.15[/tex]

As

[tex]\pi = 3.14[/tex]

[tex]Circumference\ of\ circle = 2\times 3.14\times 8.15[/tex]

                                                 = 51.2 cm (approx)

Therefore the circumference of a circle is 51.2cm (approx) .

Option (D) is correct .

The circumference of the circle [tex]\boxed{51.2{\text{ cm}}}.[/tex] Option (D) is correct.

Further explanation:

The formula for the circumference of the circle can be expressed as follows,

[tex]\boxed{{\text{Circumference of circle}} = 2\pi r}[/tex]

The formula for the area of the circle can be expressed as follows,

[tex]\boxed{{\text{Area of circle}} = \pi {r^2}}[/tex]

Here, “r” represents the radius of the circle.

The relationship between the radius and the diameter can be given by,

[tex]\boxed{r =\dfrac{d}{2}}[/tex]

Here, “d” represents the diameter of the circle.

Given:

The options are as follows.

A.[tex]102.4{\text{ cm}}[/tex]

B.[tex]63.4{\text{ cm}}[/tex]

C.[tex]25.6{\text{ cm}}[/tex]

D.[tex]51.2{\text{ cm}}[/tex]

Explanation:

The diameter of the circle is [tex]16.3{\text{ cm}}.[/tex]

The radius of the circle can be obtained as follows,

[tex]\begin{aligned}{\text{Radius}}&= \frac{{16.3}}{2}\\&= 8.15\\\end{aligned}[/tex]

The radius of the circle is [tex]8.15{\text{ cm}}.[/tex]

The circumference of the circle can be obtained as follows,

[tex]\begin{aligned}{\text{Circumference of circle}}&= 2\times\frac{{22}}{7}\times 8.15\\&=\frac{{44}}{7}\times 8.15\\&= 51.2\\\end{aligned}[/tex]

The circumference of the circle [tex]\boxed{51.2{\text{ cm}}}[/tex].Option (D) is correct.

Option (A) is not correct as the circumference of the circleis  .

Option (B) is not correct as the circumference of the circle is  .

Option (C) is not correct as the circumference of the circle is  .

Option (D) is correct as the circumference of the circle is  .

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Answer details:

Grade: High School

Subject: Mathematics

Chapter: Circle

Keywords: Circle, circumference, radius, diameter, area of the circle, angle, sector, arc, approximate.

Answer: 2x = 54

I got this question correct on my lesson.

To find Charles' rate, we can set up an equation using the formula Distance = Rate x Time. The correct equation to solve for Charles' rate x is 2x = 36.

To solve this problem, we can use the equation Distance = Rate x Time. Let's assume that Charles' rate is represented by x. When Charles overtakes Bill, they have traveled the same distance. Bill has been riding for 4 hours at a rate of 9 mph, so his distance is 9 x 4 = 36 miles. Charles overtakes Bill in 2 hours, so his distance is x x 2. Setting the two distances equal to each other, we have 36 = 2x, which simplifies to 2x = 36. Therefore, the correct equation to solve for Charles' rate x is option A, 2x = 36.

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Answer:

{y|−5≤y≤1}

Step-by-step explanation:

The range of the function is y ∈ [-5, 1] or  -5 ≤ y ≤ 1 if the function is  y = 3cos4x - 2 option second is correct.

It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.

We have a function:

y = 3cos4x - 2

As we know, cosx ∈ [-1, 1]

-1 ≤ cosx ≤ 1

-1 ≤ cos4x ≤ 1

-3 ≤ 3cos4x ≤ 3

-5 ≤ 3cos4x - 2 ≤ 1

-5 ≤ y ≤ 1

Thus, the range of the function is y ∈ [-5, 1] or  -5 ≤ y ≤ 1 if the function is  y = 3cos4x - 2 option second is correct.

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Answer:

B. 4

Step-by-step explanation:

This table that shows the input and output values for an exponential function f(x) is,

x                -3          -2       -1      0      1      2       3

f(x)          1/256      1/64    1/16   1/4    1     4       16

Taking [tex]x=2[/tex] and [tex]x=3[/tex] as input (because they are 1 apart), the ratio of output is,

[tex]=\dfrac{f(3)}{f(2)}[/tex]

[tex]=\dfrac{16}{4}[/tex]

[tex]=4[/tex]

Answer:

The correct answer is B. 4

Step-by-step explanation:

Final answer:

The student is performing a probability calculation involving rolling two dice and must enumerate all possible outcomes. The probability of a specific sum is determined by dividing the number of ways to achieve that sum by the total number of possible outcomes, 36 in the case of rolling two dice.

Explanation:

The student's experiment consists of rolling two fair dice and adding the numbers that appear on the faces that land upwards. Each die in this scenario has the numbers 1, 2, and 3 on two opposite faces. When calculating the probability of specific sums resulting from this experiment, we need to consider all the possible outcomes (the sample space) and the number of ways to achieve the sum in question.

To find the probability of any particular sum, one must enumerate each distinct way that sum can occur. There are a total of 36 possible outcomes when rolling two dice (6 outcomes per die × 2 dice). For example, to calculate the probability of getting a sum of 4, we need to consider the possible dice combinations (1+3, 2+2, 3+1) that would result in that sum.

As for the probability of an event, it is the number of favorable outcomes over the total number of possible outcomes. If the event is 'rolling a sum of 4', and there are three combinations out of 36 total that yield that sum, the probability would be 3/36 or 1/12. Remember that we must count each die distinctly; although the numbers are the same (1, 2, 3), a roll of 1 on the first die and 3 on the second die is a different outcome from a roll of 3 on the first die and 1 on the second die.

Answer:

d and a

Step-by-step explanation:

The [tex]x[/tex] coordinates of the point A is [tex]\boxed{\bf 0}[/tex].

The [tex]x[/tex] coordinates of the point B is [tex]\boxed{\bf 0}[/tex].

The [tex]x[/tex] coordinates of the point C is [tex]\boxed{\bf 10}[/tex].

Further explanation:

Given:

The coin labeled as A lies on the [tex]y[/tex]-axis.

The coin labeled as B lies on the origin.

The coin labeled as C lies on the [tex]x[/tex]-axis.

The distance of the point B and C is [tex]10\text{ cm}[/tex].

Concept used:

The point which lies on the [tex]x[/tex]-axis, the value of its [tex]y[/tex]-coordinate is [tex]0[/tex].

The point which lies on the [tex]y[/tex]-axis, their [tex]x[/tex]-coordinate is [tex]0[/tex].

The coordinate of the origin is [tex](0,0)[/tex].

Calculation:

The coin labeled as A lies on the [tex]y[/tex]-axis therefore the [tex]x[/tex]-coordinate of the point is [tex]0[/tex].

The coin labeled as B lies on the origin therefore the [tex]x[/tex]-coordinate of the point is [tex]0[/tex].

The distance from point B to the point C is [tex]10\text{ cm}[/tex] and the coin labeled as C lies on the x axis it means that the [tex]x[/tex]-coordinate of the point is [tex]10[/tex].  

Therefore, the [tex]x[/tex] coordinate of the point A is [tex]0[/tex].

The [tex]x[/tex] coordinate of the point B is [tex]0[/tex].

The [tex]x[/tex] coordinate of the point C is [tex]10[/tex].

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Answer details:

Grade: High school

Subject: Mathematics

Chapter: Coordinate geometry

Keywords: Coordinate geometry, x-axis, y-axis, x-coordinate, y-coordinate, coin, square, three corners, three identical coins.

The movie theater sold 117 adult tickets and 46 child tickets.

To solve this problem, we can set up a system of equations. Let's say the number of adult tickets sold is x and the number of child tickets sold is y. We can then write two equations based on the given information:

We can solve this system of equations by either substitution or elimination. Let's use elimination:

6x + 6y = 978

(6x + 6y) - (11x + 6y) = 978 - 163

-5x = -585

Divide by -5:

x = 117

117 + y = 163

y = 163 - 117

y = 46

Therefore, 117 adult tickets and 46 child tickets were sold.

Answer:

Using formula:

[tex]\text{Time} = \frac{\text{Distance}}{\text{Speed}}[/tex]

As per the statement:

Ravi is driving 440 miles to visit his grandma. if he drives at an average rate of 55 miles per hour.

⇒Speed = 55 miles/hour and Distance = 440 miles.

We have to find how many hours will it take him to get 3/4 of the way there.

Distance to get 3/4 of the way there= [tex]\frac{3}{4} \cdot 440 = 3 \cdot 110 = 330[/tex] miles.

Substitute the given values we have;

[tex]\text{Time} = \frac{330}{55}[/tex]

Simplify:

Time = 6 hours.

Therefore, 6 hours will it take him to get 3/4 of the way there

circumference of a circle= pi multiplied by the diameter

= 20ft x pi

=20 pi feet so the answer is b

Answer:

The value of a+b is 1.

Step-by-step explanation:

The given equation is

[tex]x^2-1x-90=0[/tex]

It is given that this equation has two solutions {a,b}.

First of all find the factors of given equation. The middle term can be written as -10x+9x.

[tex]x^2-10x+9x-90=0[/tex]

[tex](x^2-10x)+(9x-90)=0[/tex]

Taking out common from each parenthesis.

[tex]x(x-10)+9(x-10)=0[/tex]

[tex](x-10)(x+9)=0[/tex]

Using zero product property, we get

[tex]x-10=0\Rightarrow x=10[/tex]

[tex]x+9=0\Rightarrow x=-9[/tex]

The value of a is 10 and b is -9. The sum of both the solutions is

[tex]a+b=10-9=1[/tex]

Therefore the value of a+b is 1.

Answer:

The value of x is 24. The measures of angles 1,2,3,4,5,6,7,8 are 101, 79, 101, 101, 79, 79, 89, 89 respectively.

Step-by-step explanation:

If two line intersect each other, then vertical opposite angles are same.

[tex]3x+19=5x-29[/tex]                    (Vertical opposite angles)

[tex]19+29=5x-3x[/tex]

[tex]48=2x[/tex]

Divide both sides by 2.

[tex]24=x[/tex]

The value of x is 24.

Measure of angle 2 is

[tex]\angle 2 =3x+7=3(24)+7=79[/tex]                (Vertical opposite angles)

The measure of angle 2 is 79°.

Measure of angle 1 is

[tex]\angle 1 =180-\angle 2=180-79=101[/tex]           (Angle 1 and 2 are supplementary angles)

The measure of angle 1 is 101°.

Measure of angle 3 is

[tex]\angle 3 =180-\angle 2=180-79=101[/tex]           (Angle 3 and 2 are supplementary angles)

The measure of angle 3 is 101°.

Measure of angle 4 is

[tex]\angle 4 =4x+5=4(24)+5=101[/tex]                (Vertical opposite angles)

The measure of angle 4 is 101°.

Measure of angle 5 is

[tex]\angle 5 =\angle 2=79[/tex]                (Alternate Interior Angles)

The measure of angle 5 is 79°.

Measure of angle 6 is

[tex]\angle 5 =\angle 6=79[/tex]                 (Vertical opposite angles)

The measure of angle 6 is 79°.

Measure of angle 7 is

[tex]\angle 7 =180-(5x-29)=180-(5(24)-29)=89[/tex]                 (Supplementary angles)

The measure of angle 7 is 89°.

Measure of angle 8 is

[tex]\angle 8 =\angle 7=89[/tex]                 (Vertical opposite angles)

The measure of angle 8 is 89°.