Please Help!!!
Gina wants to take dance classes. She compares two dance studios to determine which has the best deal for her. Dance World charges a rate for each class. Toe Tappers charges a rate for each class plus a one-time registration fee. The system of equations shown models the total costs for taking x classes at each.
Dance World: y = 15x
Toe Tappers: y = 25 + 12.5x

How many classes would Gina need to take for the total cost to be the same at both dance studios?
A: 10
B: 15
C: 100
D: 150

Answer:

Area of the triangle = 469.4 ft²

Step-by-step explanation:

By applying Sine rule in the given triangle WXY,

[tex]\frac{\text{SinW}}{\text{XY}}=\frac{\text{SInY}}{\text{WX}}=\frac{\text{SinX}}{\text{WY}}[/tex]

Since m∠X + m∠Y + m∠W = 180°

m∠X + 40° + 27° = 180°

m∠X = 180° - 67°

m∠X = 113°

Now substitute the measures of sides and angles given in the picture,

[tex]\frac{\text{Sin27}}{\text{XY}}=\frac{\text{SIn40}}{38}=\frac{\text{Sin113}}{\text{WY}}[/tex]

[tex]\frac{\text{Sin27}}{\text{XY}}=\frac{\text{SIn40}}{38}[/tex]

XY = [tex]\frac{38\text{(Sin27)}}{\text{Sin40}}[/tex]

XY = 26.84

Area of the triangle = [tex]\frac{1}{2}(\text{XY})(\text{XW})(\text{SinX})[/tex]

                                = [tex]\frac{1}{2}(26.84)(38)(\text{Sin113})[/tex]

                                = 469.42

                                ≈ 469.4 ft²

Answer:

[tex]\boxed{15}[/tex]

Step-by-step explanation:

Set the output equal to 0.

[tex]-2x^2 +20x+150=0[/tex]

Factor left side of the equation.

[tex]-2(x+5)(x-15)=0[/tex]

Set factors equal to 0.

First possibility:

[tex]-2(x+5)=0\\x+5=0\\x=-5[/tex]

Second possibility:

[tex]x-15=0\\x=15[/tex]

The value or prize cannot be negative.

[tex]x\neq -5\\ x=15[/tex]

Answer:

B

Step-by-step explanation:

Because this equation is just a normal greater than symbol, it has to be a dotted line.

This graph starts at -2 and goes up 1 and right 3(this cancels out C as an option)

Than you shade the region with the larger number vaules, since it is greater than.

Answer:

d. (x + 5)

Step-by-step explanation:

The factorization of 2x^2 - 4x - 70 is (x + 5)(2x - 14)

Answer:

2( x + 5 ) × ( x - 7 )

Step-by-step explanation:

2x² - 4x - 70

2( x² - 2x - 35)

2( x² + 5x - 7x - 35)

2(x × (x + 5) -7 (x + 5))

2(x + 5 ) × (x - 7)

The question above is not well arranged. Please find the well arranged question below for proper understanding.

Complete Question:

A cone fits inside a square pyramid as shown. For every cross section, the ratio of the area of the circle to the area of the square is StartFraction pi r squared Over 4 r squared EndFraction or StartFraction pi Over 4 EndFraction.

A cone is inside of a pyramid with a square base. The cone has a height of h and a radius of r. The pyramid has a base length of 2 r.

Since the area of the circle is StartFraction pi Over 4 EndFraction the area of the square, the volume of the cone equals

A. StartFraction pi Over 4 EndFraction the volume of the pyramid or StartFraction pi Over 4 EndFractionStartFraction pi Over 4 EndFraction (StartFraction (2 r) (h) Over 3 EndFraction) or One-sixthπrh.

B. StartFraction pi Over 4 EndFraction the volume of the pyramid or StartFraction pi Over 4 EndFractionStartFraction pi Over 4 EndFraction (StartFraction (2 r) squared (h) Over 3 EndFraction) or One-thirdπr²h.

C. StartFraction pi Over 2 EndFraction the volume of the pyramid or StartFraction pi Over 2 EndFraction or Two-thirdsπr²h.

D. StartFraction pi Over 2 EndFraction the volume of the pyramid or StartFraction pi Over 4 EndFraction or One-thirdπr²h.

Answer:

B. StartFraction pi Over 4 EndFraction the volume of the pyramid or StartFraction pi Over 4 EndFraction (StartFraction (2 r) squared (h) Over 3 EndFraction) or One-thirdπr²h = 1/3πr²h

Step-by-step explanation:

We have two geometric shapes in the question.

a) A cone and b) a square pyramid

The cone has a height of h and a radius of r. The pyramid has a base length of 2 r.

The volume of a cone =1/3πr²h

Where πr² = Area of the circle at the base of the cone

Hence, Volume of a cone = 1/3 × Area of the circular base of a cone × Height

The volume of a square pyramid = 1/3a²h

Where a² = Area of the square base of the pyramid

Hence, Volume of a square pyramid = 1/3 × Area of the square base of a pyramid × height(h)

Base area of a cone / Base area of a square pyramid = π/4

Base area of a circle = Base area of a pyramid × π/4

Volume of a cone = 1/3πr²h

Volume of a cone = 1/3 × Base area of a square pyramid × π/4 × h

Note that:

Volume of a square pyramid = 1/3a²h

= 1/3 × Base area of a square pyramid × height

Hence,

Volume of a cone = Volume of a square pyramid × π/4

= StartFraction pi Over 4 EndFraction the volume of the pyramid

Or

Where a = base length = 2r

Volume of the square pyramid = 1/3 × 2r² × h = 1/3 × 4r²h

Volume of a cone = Volume of a square pyramid × π/4

Substituting = 1/3 × 4 × r²× h × π/4

Volume of a cone = 1/3 πr²h

Or

Volume of a cone = Volume of a square pyramid × π/4

Volume of a square pyramid when base length is 2r = 1/3 × (2r)² × h = (2r²)h/3

Substituting (2r²)h/3 for volume of a square pyramid in volume of a cone , we have:

Volume of a cone = π/4 × 2r²h/3

=

StartFraction pi Over 4 EndFractionStartFraction pi Over 4 EndFraction (StartFraction (2 r) squared

Therefore, Option B is correct

Answer:

B

Step-by-step explanation:

Answer

24 frames per second

Step-by-step explanation:

Total frames=86,400

Total time=1 hour

Find frame per second

1 hour= 60 minutes*60 seconds

1 hour=3600 seconds

Frame per second=Total frames/Total number of seconds

=86,400/3600

=24 frames per second

Answer:

2[tex]x^{4}[/tex] + x³ - x² + 54x - 56

Step-by-step explanation:

Area (A) is calculated as

A = length × width

   = (x² - 2x + 8)(2x² + 5x - 7)

Each term in the second factor is multiplied by each term in the first factor, that is

x²(2x² + 5x - 7) - 2x(2x² + 5x - 7) + 8(2x² + 5x - 7) ← distribute all parenthesis

= 2[tex]x^{4}[/tex] + 5x³ - 7x² - 4x³ - 10x² + 14x + 16x² + 40x - 56 ← collect like terms, thus

A = 2[tex]x^{4}[/tex] +x³ - x² + 54x - 56

The expression which represents the area of Dylan’s room will be 2x⁴ - 7x³ - 21x² + 82x - 56.

What is the area?

The area is the space occupied by any shape, find out by multiplying its length and breadth.

We have,

Lenght =  (x² – 2x + 8)

and

Breadth = (2x² + 5x – 7)

Now, simplifying the above expressions,

(x² – 2x + 8)

It can be written as , Using middle term split method,

x² – 4x + 2x + 8

= x(x – 4) - 2(x - 4)

= (x – 4) (x - 2)

In the same way,

(2x² + 5x – 7)

= 2x² +7x  - 2x – 7

= x(2x +7)  - 1(2x + 7)

= (x - 1) (2x +7)

So,

So,

Using the area formula,

i.e.

Area = Length × Breadth

Area =  (x² – 2x + 8) ×  (2x² + 5x – 7) = (x – 4) (x - 2) (x - 1) (2x +7)

Now,

Area = 2x⁴ - 7x³ - 21x² + 82x - 56

Hence we can say that the expression which represents the area of Dylan’s room will be  2x⁴ - 7x³ - 21x² + 82x - 56.

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The number of boxes can't be negative or in fractions.

so the domain would be "All whole numbers from 0 to 10"

Answer:

A) All whole numbers from 0 to 10.

Step-by-step explanation:

The domain of a function is given by the available values of the independent variable.

In this case you have that the independent variable is the number of boxes, and the available values of this variable are integers in between 0 and 10, by including 0 and 10.

Then, the domain of the functions composed by all positive integers number from 0 to 10 including 0 and 10.

A) All whole numbers from 0 to 10.

Answer:

The answer is option B

Step-by-step explanation:

Area of a triangle is

[tex] \frac{1}{2} \times b \times h[/tex]

Where b is the base

h is the height

The base of the triangle is 5 times the height is written as

b = 5h

Area of the triangle is 1440cm²

[tex]1440 = \frac{1}{2} \times 5h \times h[/tex]

[tex]1440 = \frac{1}{2} 5 {h}^{2} [/tex]

[tex]2880 = 5 {h}^{2} [/tex]

Divide both sides by 5

[tex] {h}^{2} = 576[/tex]

Find the square root of both sides

[tex]h = \sqrt{576} [/tex]

Hope this helps you

Answer:

0.726 galones

Step-by-step explanation:

De la pregunta anterior, se nos dice que

1 botella = 2.75 litros de agua

Se nos pide encontrar cuántos galones puede contener.

En la pregunta, nos dicen

1 litro = 0.264 galones

2.75 litros =

Multiplicación cruzada

2.75 litros × 0.264 galones

= 0.726 galones.

Por lo tanto, 0.726 galones pueden caber en la botella

Answer:

Distance= y - 4  

Step-by-step explanation:

Step-by-step explanation:

The inequality is [tex]\frac{x}{-3}[/tex] >2

x is less than -6  and -6 is excluded so it will be represented by an empty circle and a line going toward negative values

so it's D

Answer:

The mode is the number that occurred the most often. The range is the difference between the highest and lowest values.

Step-by-step explanation:

Answer:

Mode:The number whose repetaed the most is the set (there can be multiple)

Range: The largest number minus the smallest = The range

Answer:

25 degrees

Step-by-step explanation:

The two given angles are vertical, so we can set their measures equal to each other and then solve for x.

4x + 50 = 150

4x = 100

x = 25

Answer:

x = 25

Step-by-step explanation:

The angles are vertical angles, so their measures are equal.

4x + 50 = 150

4x = 100

x = 25

Answer:

4.7 feet³ of water

Step-by-step explanation:

Diameter of 4 feet

Radius = 2 feet

Height = 0.75 feet

Formula for Volume = 2·[tex]\pi[/tex]·radius·height

But she only wants to fill half, so divide by 2, cancels the 2 in the formula for volume, giving us: [tex]\pi[/tex]·radius·height

[tex]\pi[/tex]·2·0.75 = 4.71 feet³

Answer: 37

Step-by-step explanation:

Given that:

Total number of beads on her necklace = 50

Percentage of blue beads = 26%

Therefore, number of blue beads :

Percentage number of blue beads × total number of beads on necklace

Number of Blue beads = 26% × 50

= 0.26 × 50 = 13

Number of Blue beads = 13

Therefore, number of beads that aren't blue :

Total number of beads - number of blue beads

50 - 13 = 37

Number of beads that aren't blue = 37

Answer:

20 m/s

Step-by-step explanation:

Assuming initial velocity is 0:

[tex]v_{f} = v_{i} + at[/tex]

[tex]v_{f} = at[/tex]

[tex]v_{f} =[/tex] 4m/s^2 * 5s = 20 m/s

Answer:

If you accelerate at 4 m/s/s for 5 seconds you accelerate by 20 m/s. Therefore, you started out at 3 m/s.

Step-by-step explanation:

Answer:

7 is the least.

Step-by-step explanation:

Their are 12 balls, and 6 of them are red. if you are to pick every single ball except the red ones, you cut the number of balls in half, and are left with 6 red balls, and 6 balls picked. Your next pick must be a red ball, making 7 picks.

Answer:

  7.5 times

Step-by-step explanation:

Your calculator can tell you the ratio ...

  [tex]\dfrac{3\times10^8}{4\times10^7}=\dfrac{30\times10^7}{4\times10^7}=\dfrac{30}{4}=\boxed{7.5}[/tex]

The population of the US is 7.5 times as great as the population of California.

Answer:

Ones: 91

Hundredths: 91.20

Step-by-step explanation:

All numbers that comprises the digits, 91.20, have place value.

The 9 in the digit has a place value of tens, i.e. 9*10 = 90.

The 1 has a place value of one's, i.e. 1*1 = 1

The 2, after the decimal point to the right, has a place value of tenth, i.e. 1*10-¹ = ⅒ = 0.1

While the zero has a place value of hundredth.

Therefore, the digits, in the ones place = 91

In the hundredths place = 91.20

Answer: C. 71,224,900

Based on the power, move the decimal point that many spaces to the right. (e.g., If it's 7.9 × 10^3, then move the decimal three spaces to the right, and you'd get 7900.)

3.14159 × 10^7 = 31415900

9.897752 × 10^6 = 9897752

2.468 × 10^7 = 24680000

Out of all the numbers mentioned in the question, 71,224,900 is the only one that's greater than 3.14159 × 10^7 = 31415900.

Answer:

1) From the measure of 40°, you can write:

tan(40°) = 100/x, where x is the base from the building to the tower

⇒x=100/tan(40°) = 119,18 m

2) From the measure of 30°, you can write

tan(30°) = y / 119,18, where y is the height from the roof of Jill's building to the top of the tower.

Then, y = tan(30°) * 119,18 = 68,81 m

3) The height of Jill's building is 100 - 68,81 = 31,19 m

When the height of the tower is 100 meters, the height of Jill's apartment building is 31.19m

Let the base from the building to the Rowe be represented by x. Based on the information given, the value will be:

x = 100/tan 40°

x = 119.18m

The height can be represented as:

= 100 - [tan30° × 119.18]

= 100 - 68.81

= 31.19m

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Answer:

3, 5, 7

Step-by-step explanation:

As per triangle inequality theorem:

Assume the sides are equal to 3 smallest odd numbers: 1,3 and 5

The next triple is: 3, 5 and 7

So 3, 5, 7 is the combination of smallest odd numbers to make sides of a triangle

Answer:

Step-by-step explanation:

Factorize 175 and 50

175 = 5 * 5 * 7

50  = 5 * 5 * 2

[tex]\frac{\sqrt[3]{175}}{\sqrt[3]{}50}=\sqrt[3]{\frac{175}{50}}\\\\\\ =\sqrt[3]{\frac{5*5*7}{5*5*2}}\\\\\\=\sqrt[3]{\frac{7}{2}}[/tex]

Answer:

There is no price difference between the two stores.

Step-by-step explanation:

The dependent t-test (also known as the paired t-test or paired samples t-test) compares the two means associated groups to conclude if there is a statistically significant difference amid these two means.

In this case a paired t-test is used to determine if there is a price difference between the two stores.

The hypothesis for the test can be defined as follows:

H₀: There is no price difference between the two stores, i.e. d = 0.

Hₐ: There is a price difference between the two stores, i.e. d ≠ 0.

From the information provided the sample mean and standard deviation are:

 [tex]\bar d=-0.464\\\\S_{d}=1.019[/tex]

Compute the test statistic value as follows:

 [tex]t=\frac{\bar d}{S_{d}/\sqrt{n}}=\frac{-0.464}{1.019/\sqrt{10}}=-1.4399\approx -1.44[/tex]

The test statistic value is -1.44.

Decision rule:

If the p-value of the test is less than the significance level then the null hypothesis will be rejected and vice-versa.

The degrees of freedom is:

n - 1 = 10 - 1 = 9

Compute the p-value of the test as follows:

[tex]p-value=2\cdot P(t_{\alpha/2, (n-1)}>-1.44)[/tex]

               [tex]=2\cdot P(t_{0.10/2, 9}>-1.44)\\=2\times 0.092\\=0.184[/tex]  

*Use a t-table.

The p-value of the test is 0.184.

p-value= 0.184 > α = 0.10

The null hypothesis was failed to be rejected.

Thus, it can be concluded that there is no price difference between the two stores.

Answer:

∠ GDH = 67.5°

Step-by-step explanation:

The measure of the chord- chord angle GDH is half the sum of the measures of the arcs intercepted by the angle and its vertical angle.

∠ GDH = [tex]\frac{1}{2}[/tex](GH + EF) = [tex]\frac{1}{2}[/tex] (90 + 45)° = 0.5 × 135° = 67.5°

Answer:

30+48 is equivalent to 48+30

Answer:

30+48

Step-by-step explanation:

equivelent just flip them

Answer:

1. a. b = - 8

b. x = 8

c. x = 11

d. x = 5

2. 12 soccer balls and 8 basketballs can be purchased.

Step by step explanation

a. [tex] - 14 + 6b + 7 - 2b = 1 + 5b[/tex]

Calculate the sum

[tex] - 7 + 6b - 2b = 1 + 5b[/tex]

Collect like terms

[tex] 7 + 4b = 1 + 5b[/tex]

Move variable to L.H.S and change it's sign

Similarly, Move constant to R.H.S and change its sign

[tex]4b - 5b = 1 + 7[/tex]

Collect like terms

[tex] - b = 8[/tex]

Change the signs on both sides of the equation

[tex]b = - 8[/tex]

-----------------------------------------------------------------

b. [tex] \frac{5x + 10}{ - 6} = - 5[/tex]

Apply cross product property

[tex]5x + 10 = - 5 \times ( - 6)[/tex]

Multiply the numbers

[tex]5x + 10 = 30[/tex]

Move constant to R.H.S and change its sign

[tex]5x = 30 - 10[/tex]

Calculate the difference

[tex]5x = 20[/tex]

Divide both sides of the equation by 5

[tex] \frac{5x}{5} = \frac{20}{5} [/tex]

Calculate

[tex]x = 4[/tex]

----------------------------------------------------------------

c. [tex] - 15 = \frac{ - 8x - 17}{7} [/tex]

Apply cross product property

[tex] - 15 \times 7 = - 8x - 17[/tex]

Multiply the numbers

[tex] - 105 = - 8x - 17[/tex]

Swap the sides of the equation

[tex] - 8x - 17 = - 105[/tex]

Move constant to R.H.S and change its sign

[tex] - 8x = - 105 + 17[/tex]

Calculate

[tex] - 8x = - 88[/tex]

Change the signs on both sides of the equation

[tex]8x = 88[/tex]

Divide both sides of the equation by 8

[tex] \frac{8x}{8} = \frac{88}{8} [/tex]

Calculate

[tex]x = 11[/tex]

------------------------------------------------------------------

D. [tex]5 = 6x + 5(x - 10)[/tex]

Distribute 5 through the parentheses

[tex]5 = 6x + 5x - 50[/tex]

Collect like terms

[tex]5 = 11x - 50[/tex]

Swap both sides of the equation

[tex]11x - 50 = 5[/tex]

Move constant to R.H.S and change its sign

[tex]11x = 5 + 50[/tex]

Calculate the sum

[tex]11x = 55[/tex]

Divide both sides of the equation by 11

[tex] \frac{11x}{11} = \frac{55}{11} [/tex]

Calculate

[tex]x = 5[/tex]

------------------------------------------------------------------

2.

Solution,

No.of students in soccer = x

No.of students in basketball = y

Total no.of students = 20

i.e x + y = 20 → equation ( i )

Cost of soccer ball = $ 7

Cost of basketball = $ 10

Total budget = $ 164

i.e 7x + 10 y = 165 → equation ( ii )

In equation ( i ),

x + y = 20

Move 'y' to R.H.S and change its sign

x = 20 - y

Put the value of x in equation ( i )

[tex]7(20 - y) + 10y = 164[/tex]

[tex]140 - 7y + 10y = 164[/tex]

[tex]3y = 164 - 140[/tex]

[tex]3y = 24[/tex]

[tex]y = \frac{24}{3} [/tex]

[tex]y = 8[/tex]

Now, put the value of y in equation ( i ) ,

x + y = 20

[tex]x + 8 = 20[/tex]

[tex]x = 20 - 8[/tex]

[tex]x = 12[/tex]

Hence, 12 soccer balls and 8 basketballs can be purchased.

Hope this helps...

Best regards!!

Answer:

1. b = -8

2. x = 8

3. x = 11

4. x = 5

hope that helpwd

Answer:

y = [tex]-\frac{1}{3}x+5[/tex]

Step-by-step explanation:

Let the equation of the given line is,

y = mx + b

where 'm' = slope of the line

b = y-intercept of the line

Since slope of a line passing through two points [tex](x_1, y_1)[/tex] and [tex](x_2, y_2)[/tex] is represented by,

m = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]

If the points are (0, 5) and (-3, 6),

Slope of the line 'm' = [tex]\frac{6-5}{-3-0}[/tex]

                                 = [tex]-\frac{1}{3}[/tex]

y-intercept of the line 'b' = 5

Therefore, equation of the given line will be,

y = [tex]-\frac{1}{3}x+5[/tex]

Answer:

[tex]\displaystyle \sin \theta = \frac{4}{5}[/tex] if [tex]\displaystyle \cos\theta = -\frac{3}{5}[/tex] and [tex]\theta[/tex] is in the second quadrant.

Step-by-step explanation:

By the Pythagorean Trigonometric Identity:

[tex]\left(\sin \theta\right)^2 + \left(\cos\theta)^2 = 1[/tex] for all real [tex]\theta[/tex] values.

In this question:

[tex]\displaystyle \left(\cos\theta\right)^2 = \left(-\frac{3}{5}\right)^2 = \frac{9}{25}[/tex].

Therefore:

[tex]\begin{aligned} \left(\sin\theta\right)^2 &= 1 -\left(\cos\theta\right)^2 \\ &= 1 - \left(\frac{3}{5}\right)^2 = \frac{16}{25}\end{aligned}[/tex].

Note, that depending on [tex]\theta[/tex], the sign [tex]\sin \theta[/tex] can either be positive or negative. The sine of any angles above the [tex]x[/tex] axis should be positive. That region includes the first quadrant, the positive [tex]y[/tex]-axis, and the second quadrant.

According to this question, the [tex]\theta[/tex] here is in the second quadrant of the cartesian plane, which is indeed above the [tex]x[/tex]-axis. As a result, the sine of this

It was already found (using the Pythagorean Trigonometric Identity) that:

[tex]\displaystyle \left(\sin\theta\right)^2 = \frac{16}{25}[/tex].

Take the positive square root of both sides to find the value of [tex]\sin \theta[/tex]:

[tex]\displaystyle \sin\theta =\sqrt{\frac{16}{25}} = \frac{4}{5}[/tex].