The community center has a pottery class each month. Each student pays​ $15 for the class and​ $27 for materials. This month the pottery class brought in a total of​ $714. How many students are in the class this​ month?

Answer:

$1,100 at 3.2% for 3 years -> $105.60

$990 at 3.15% for 4 years  -> $124.74

$1,025 at 2.8% for 5 years​ -> $143.5

Step-by-step explanation:

Simple interest formula is:

A = P*(1 + r*t)

where A if final account, P is principal, r is annual interest rate (as decimal) and t is time in years

Interest earned is A - P, then:

I = P*(1 + r*t) - P = P(1 + r*t - 1) = P*r*t

If P = $1100, r = 0.032 and t = 3, then:

I = 1100*0.032*3 = $105.6

If P = $990, r = 0.0315 and t = 4, then:

I = 990*0.0315*4 = $124.74

If P = $1025, r = 0.028 and t = 5, then:

I = 1025*0.028*5 = $143.5

Answer:

Picture below

Step-by-step explanation:

Answer:

B) Subtract the bottom equation from the top equation.

C) Add the equations.

Step-by-step explanation:

Let us analyze each of the options to see which one of them work.

A) Multiply the top equation by 7, then subtract the bottom equation from the top equation.

Multiplying the top equation by 7 gives:

7 * (16x + 5y) = (1 * 7)

112x + 35y = 7

Then, subtracting the bottom equation from this:

 112x + 35y = 7

-  (16x - 5y = 7)

=> 112x + 35y - 16x + 5y = 7 - 7

112x - 16x + 35y + 5y = 0

96x + 40y = 0

This method didn't eliminate any variable, so it didn't work for us.

B) Subtract the bottom equation from the top equation

This will yield:

  16x + 5y = 1

- (16x - 5y = 7)

=> 16x + 5y - 16x + 5y = 1 - 7

16x - 16x + 5y + 5y = -6

0x + 10y = -6

10y = -6

y = -6 / 10

Hence, one variable has been eliminated. It works.

C) Add the equations

This yields:

  16x + 5y = 1

+ 16x - 5y = 7

  32x + 0y = 8

  32x = 8

=>x = 8 / 32 = 1 / 4

This method works since one variable has been eliminated.

Answer:

A - (4, –1.5)

Step-by-step explanation: Hope it helps :D

Answer:

Its A

Step-by-step explanation:

Took the quiz on Edgenunity

The Step 2 shows the mistake done by Ettiene.

A quadratic equation is a second-order polynomial equation in a single variable x, ax²+bx+c=0. with a ≠ 0 .

It has at least one solution because it is a second-order polynomial equation, which is guaranteed by the algebraic fundamental theorem.

Given:

The given equation is x(x+4)=117.

Step1:  x²+4x=117

Now, b/2 =4/2 =2

Then, add 2² to both the sides of an equation, we get

x²+4x+2²=117+2²

x²+4x+4=117+4

(x+2)²=121

x+2=±√121

x+2=±11

x=±11-2

x=11-2=9 and x=-11-2=-13

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Answer:

7 feet

Step-by-step explanation:

The area of a circle can be found using:

a=3.14*r^2

We know that the area is 153.86 square feet, so we can substitute 153.86 in for a.

153.86=3.14*r^2

Now, we have to solve for r. To do this, we need to get r by itself. First, divide both sides by 3.14

153.86/3.14=3.14*r^2/3.14

153.86/3.14=r^2

49=r^2

Now, r is being squared. The opposite of squared is the square root. So, take the square root of both sides .

√49=√r^2

√49=r

7=r

The radius is 7 feet

The radius of the circle with an area of 153.86 square feet is approximately 7 feet.

To find the radius of a circle given its area, you can use the formula:

Area = π * r^2

In this case, we are given the area as 153.86 square feet.

153.86 = π * r^2

To solve for the radius (r), we need to isolate it. Divide both sides of the equation by π:

153.86 / π = r^2

Now, take the square root of both sides to find r:

r = √(153.86 / π)

Using a calculator or approximating the value of π as 3.14, we can calculate:

r ≈ √(153.86 / 3.14) ≈ √49.0401 ≈ 7

Therefore, the radius of the circle with an area of 153.86 square feet is approximately 7 feet.

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Answer: A

Step-by-step explanation:

Edg

Answer:

d

Step-by-step explanation:

Answer:

d.  Checking account, savings account, money market account, CD

Answer:56.52

Step-by-step explanation:2x3.14=6.28

6.28x3=18.84

18.84x3=56.52

The area of the given polygon is 11.7 cm².

Given is an equilateral triangle with radius of 3 cm, we need to find the area of the polygon,

The radius of a circumcircle of an equilateral triangle is equal to a/√3, where a is the side length of the equilateral triangle.

So,
a/√3 = 3

a = 3√3

Now the side length is 3√3 cm.

Now, the area of an equilateral triangle is:

A = √3 / 4 × side²

= √3 / 4 × (3√3)²

= √3 / 4 × 27

= 11.7 cm²

Hence the area of the given polygon is 11.7 cm².

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Final answer:

(Option C: (3 + i)/2 and (3 - i)/2

The solutions to the quadratic equation 2x^2 - 6x + 5 = 0 are 1.5 + 0.5i and 1.5 - 0.5i, as the discriminant is negative and indicates there are no real solutions, only complex ones.

Explanation:

The solutions of the quadratic equation 2x2 - 6x + 5 = 0 can be calculated using the quadratic formula, which is:

x = (-b ± √(b2 - 4ac)) / (2a)

For the given equation, a = 2, b = -6, and c = 5. Plugging these values into the quadratic formula, we get:

x = (6 ± √((-6)2 - 4(2)(5))) / (2(2))
x = (6 ± √(36 - 40)) / 4
x = (6 ± √(-4)) / 4

Since the discriminant (b2 - 4ac) is negative, this equation has no real solutions and two complex solutions. The final solutions are:

x = (6 ± 2i) / 4

x = (3 ± i)/ 2
x = 1.5 ± 0.5i

The solutions are 1.5 + 0.5i and 1.5 - 0.5i.

Answer:

Quadratic Equation:

[tex]3x^2=2x +5[/tex]

[tex]\text{Standard Form: } 3x^2-2x-5=0[/tex]

From the standard form of a Quadratic Function, we get:

[tex]a=3,\:b=-2,\:c=-5[/tex]

Discriminant:

[tex]\Delta=\left(-2\right)^2-4\cdot \:3\left(-5\right)[/tex]

[tex]\Delta=\left(-2\right)^2+4\cdot \:3\cdot \:5[/tex]

[tex]\Delta=64[/tex]

From the discriminant, we conclude that the equation will have two real solutions.

State that:

[tex]b^2-4ac <0:\text{The equation has no real solutions, the solutions are complex}[/tex]

[tex]b^2-4ac =0:\text{The equation has 1 real solution}[/tex]

[tex]b^2-4ac >0:\text{The equation has 2 real solutions}[/tex]

By the way, solving the equation given:

[tex]$x=\frac{2\pm\sqrt{64}}{2\cdot \:3}$[/tex]

[tex]$x=\frac{2\pm\sqrt{64}}{6}$[/tex]

[tex]$x=\frac{2\pm8}{6}$[/tex]

[tex]$x_{1} =\frac{10}{6}=\frac{5}{3} $[/tex]

[tex]$x_{2}=\frac{-6}{6} =-1$[/tex]

The equation is 4x + 9 = 45 which is the correct answer would be option (C).

An equation is a mathematical statement that shows that two expressions are equal. It consists of two sides, separated by an equal sign (=). The left side and the right side of the equation can contain variables, constants, and mathematical operations.

Option A: 9x - 7 is not an equation because it does not have an equal sign.

Option B: (b + 7) x 3 is not an equation because it does not have an equal sign.

Option C: 4x + 9 = 45 is an equation because it has an equal sign and shows that the left side and the right side are equal.

Option D: (⅔)x - 3 > c is not an equation because it does not have an equal sign. Instead, it is an inequality, which shows that one expression is greater than or less than another expression.

Hence, the correct answer would be an option (C).

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Answer:

5/6 of an hour is 50 minutes.

2/3 of an hour is 40 minutes.

0.25 of an hour is 15 minutes.

Answer:

0.33....(1/3

Step-by-step explanation:

-3/-3*-3

-3/9

-0.33..

Answer:

[tex]\sqrt{41}[/tex]

Step-by-step explanation:

[tex]\sqrt{(3-(-1))^2+(3-(-2))^2}=\sqrt{16+25}=\sqrt{41}[/tex]

Hope this helps!

Answer:

5.8<x<6.0 I think

Step-by-step explanation:

why?

Answer:

1/119

Step-by-step explanation:

(3×4×5)+[(3×4×5)-1)

60+(60-1)

60+59

119

1/119

Answer:

You need to find the cycle. It will be easier to show if a graph with it was shown

Step-by-step explanation:

Answer:

You need to find a cycle of the graph. But there is no graph. Download the graph to this page. Have a great day

Step-by-step explanation:

Answer:

x= 103°

Step-by-step explanation:

The angle next to angle x is 77° because it is a corresponding angle to the original 77° angle (corresponding angles is basically a pair that lies in the same position as each other, as is the case with the 77° angle and the angle to the right of x°).

Now that we know that the adjacent angle to x is 77°, you can find x. Note that the line x and 77° are lying on is parallel. This means that they are supplementary angles, which means that the sum of both angles is equal to 180°. Insert this into an equation:

[tex]180=x+77[/tex]

Solve for x. Use inverse operations to subtract 77 from both sides:

[tex]180-77=x+77-77\\\\180-77=x[/tex]

Simplify subtraction:

[tex]103=x[/tex]

x is 103°.

The events that are mutually exclusive are Landing on a shaded sector and landing on the number three and Landing on an unshaded sector and landing on a number less than 2.

Mutually exclusive means that a combination of occurrences can never occur.

a) landing on a number greater than three while in a shaded area:

This is possible; for example, you could land in the 4.

b) landing in an even number on a dark sector.

Again, sector 4 is an even number and a shaded sector, thus these events do not conflict.

c) uncolored and odd number

This event is not mutually exclusive because you can land in the 3, which is unshaded and an odd number.

d) Landing on a shaded sector and landing on the number three

Because 3 is an unshaded sector, you can never land in 3 and a shaded sector at the same time; the two are mutually exclusive.

e) Landing on an unshaded sector with a number less than two.

Because 1 is the only integer smaller than 2, and sector 1 is darkened, these events are mutually exclusive.

Answer:

a is the correct answer

Answer:

B 6/13 times 5/12 equals 5/26

Step-by-step explanation:

if the total marbles are 13, then 13 has to be the denominator

they said that 2 orange marbles are selected

then it is 6/13 times 5/13

Hopes this helps

Answer:

I think it is C

Step-by-step explanation:

I am right

Answer:

2 x 5 x 7= 70. Answer is B. o 70ft3. Have a great day

Step-by-step explanation:

Answer:

70 ft3

Step-by-step explanation:

Answer:

The answer is C.

Step-by-step explanation:

In order to find the value of expression, you first have to solve x by substracting 6 to both sides then divide it by 5 :

[tex]5x + 6 = 10[/tex]

[tex]5x + 6 - 6 = 10 - 6[/tex]

[tex]5x = 4[/tex]

[tex]5x \div 5 = 4 \div 5[/tex]

[tex]x = \frac{4}{5} [/tex]

Next, you have to substitute the value of x into the expression :

[tex]let \: x = \frac{4}{5} [/tex]

[tex]10x + 3[/tex]

[tex] = 10( \frac{4}{5} ) + 3[/tex]

[tex] = 8 + 3[/tex]

[tex] = 11[/tex]

The expression '6x - 6 degrees' is a linear algebraic function possibly related to geometry, where degrees might denote the measure of an angle.

The expression 6x - 6 degrees represents a linear function where x is typically a variable that stands for an unknown value to be determined, or it can represent an input into the function. The term degrees suggests that it may be related to angles in a geometric context. This expression simplifies to 6 times x minus 6 degrees, where the degrees could represent the measurement of an angle in geometry, or possibly a temperature dependent on the context, which is not provided here. When dealing with geometric problems, one often converts these expressions to a standard measurement, such as converting to radians or using decimal degrees for precision.

Answer:

In order for synthetic division to be pretty straightforward, the divisor must be of the first degree (that is, the power of x must be exactly one.) and must have the binomial form x - a.

Unlike Long Division which makes use of the polynomials given directly, Synthetic Division makes use of the coefficients of this polynomials.

Answer: 19

Step-by-step explanation:

Answer:

E (10)

Step-by-step explanation:

In a right triangle with the legs that have a factor of √2, and the factor is the same, then the hypotenuse of the same triangle is the side length * √2:

so 5√2 * √2 = 10

ANSWER: 10 or E

Answer:

41.9 units³

Step-by-step explanation:

(please see attached for reference)

The volume of a cone is given by:

V = (1/3) πr²h    where,

V = volume (we are asked to find this)

π = 3.142

r = radius = given as 2

h = height = given as 10

Substituting the known values into the above equation,

V = (1/3) πr²h

= (1/3) (3.142) (2²)(10)

= 41.893

= 41.9 units³  (nearest tenth)

Answer:

4 Doughnuts

Step-by-step explanation:

.80+.80+.80+.80+1.20=4.40. You can't buy half a doughnut.

Answer:

A. 113.1 yd^2

Step-by-step explanation:

2 × 22/7 × radius = 37.7 yd

radius = 37.7 × 7/44

= 5.9977 yd

Area = 22/7 × radius × radius

= 22/7 × 5.9977^2

= 113.056 yd^2