Which statements are true? Check all that apply.
Please answer :)

Answer:

Harry can first substitute 30 for t. He can then multiply [tex]\frac{1}{3}[/tex] by 30 to get a product of 10. Since, 15 is not equal to 15, Harry's solution is not correct.

Step-by-step explanation:

Harry solves the equation [tex]\frac{1}{3}t = 15[/tex]. He says the solution is 30.

Now, to check whether Harry correct or not, Harry can first substitute 30 for t. He can then multiply [tex]\frac{1}{3}[/tex] by 30 to get a product of 10. Since, 15 is not equal to 15, Harry's solution is not correct.

This is an alternate way to check the answer obtained is correct or not. (Answer)

The number of five- and ten-dollar bills that Salim has are; 6 and 3

We are given two equations;

x + y = 9 - - - - (eq 1)

5x + 10y = 60 - - - (eq 2)

Where;

x represents the number of five-dollar bills.

y represents the number of ten-dollar bills.

Making x the subject in eq 1 gives;

x = 9 - y

Put 9 - y for x in eq 2 to get;

5(9 - y) + 10y = 60

45 - 5y + 10y = 60

5y + 45 = 60

5y = 60 - 45

5y = 15

y = 15/5

y = 3

Thus;

x = 9 - 3

x = 6

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Answer:

Step-by-step explanation:

=

The answer is 14+2/3x

I hoped this helped :)

1. [tex]\frac{x^3}{x^8}=x^{-5}[/tex]

2. [tex]\frac{6x}{2x^8} = 3x^{-7}[/tex]

3. [tex]\frac{28x^6}{21x^2} = \frac{4}{3}x^4[/tex]

Step-by-step explanation:

1. x^3/x^8

Given fraction is:

[tex]\frac{x^3}{x^8}[/tex]

When the bases are same in both numerator and denominator then the exponents can be added

i.e.

[tex]\frac{x^a}{x^b} = x^{a-b}[/tex]

So,

[tex]\frac{x^3}{x^8} = x^{3-8} = x^{-5}[/tex]

Part b:

[tex]\frac{6x}{2x^8}\\= \frac{3.2.x}{2.x^8}\\=\frac{3x}{x^8}\\=3x{1-8}\\=3x^{-7}[/tex]

Part c:

Given

[tex]\frac{28x^6}{21x^2}\\= \frac{7.4.x^6}{7.3.x^2}\\=\frac{4}{3} x^{6-2}\\=\frac{4}{3}x^4[/tex]

Keywords: Fractions, exponents

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Answer:

She lands on 92.

Step-by-step explanation:

92=58+2+30+2

where she lands = 58+34

92 = 58 + 2x + y   where x=2 and y=32

Final answer:

Sally started on square 58 and used three cards with values of +2, +30, and +2, respectively. The equation for her moves is 58 + 2 + 30 + 2, which equals 92. Hence, she landed on square 92.

Explanation:

Sally's game piece was initially on square 58. To find out where she landed after using her cards, we can write an equation that adds the values on the cards to her starting position. Sally played three cards with the following values: +2, +30, and +2.

The equation to show Sally's moves is:

Starting position + first card + second card + third card = new position

58 + 2 + 30 + 2 = new position

Now, let's calculate the total:

58 + 2 = 60
60 + 30 = 90
90 + 2 = 92

Therefore, Sally's new position after using all her cards is on square 92.

Answer:

85,200

Step-by-step explanation:

21,300*2=42,600

42,600*2 = 85,200

Answer:3.2%

Step-by-step explanation:

Answer:

Owen's songs were played on 3 movies and on 7 commercials.

Step-by-step explanation:

System of Equations

Let's call C the number of commercials on which Owen's songs were played and M the number of movies on which Owen's songs were played. We know Owen's songs were played on 4 more commercials than movies, it can be expressed as

[tex]C=M+4[/tex]

Owen will earn $50 every time one of his songs is played in a commercial and he will earn $140 every time one of his songs is played in a movie, so his total earnings are

[tex]140M+50C=770[/tex]

We have a system of linear equations that can be easily solved by using the formula for C in the above equation

[tex]140M+50(M+4)=770[/tex]

Operating

[tex]140M+50M+200=770[/tex]

Reducing

[tex]190M=770-200=570[/tex]

Solving

[tex]M=570/190=3[/tex]

The number of commercials is

[tex]C=M+4=7[/tex]

Owen's songs were played on 3 movies and on 7 commercials.

Answer:

1) X stands for individual acts and y,  group acts. 2) Each scenario describes a different period in minutes, but each one respecting their different amounts (individual and group acts). 3) [tex]S=\left \{ 5,10 \right \}[/tex]

Step-by-step explanation:

Completing with what was found:

1) Here is a summary of the scenario your classmate presented for the talent show:Main show The main show will last two hours and will include twelve individual acts and six group acts.Final show The final show will last 30 minutes and will include the top four individual acts and the top group act.The equations he came up with are: 12x+ 6y= 120, 4x+ y= 30

1. What do x and y represent in this situation?

X stands for individual acts and y,  group acts.

Besides that, In the system of equation, they represent the time for x, and the time for y.

2. Do you agree that your classmate set up the equations correctly? Explain why or why not.

Yes, that's right. Each scenario describes a different period in minutes, but each one respecting their different amounts (individual and group acts). Either for 120 minutes or 30 minutes length. And their sum totalizing the whole period.

3. Solving the system by Elimination

[tex]\left\{\begin{matrix}12x+ 6y= 120\\ 4x+ y= 30\end{matrix}\right.\\\left\{\begin{matrix}12x+ 6y= 120\\ 4x+ y= 30\:*(-3)\end{matrix}\right.\\\left\{\begin{matrix}12x+ 6y= 120\\ -12x+ -3y= -90\end{matrix}\right.\\3y=30\Rightarrow y=10\\4x+(10)=30\Rightarrow 4x=20\Rightarrow x=5\\S=\left \{ 5,10 \right \}[/tex]

Answer:

Step-by-step explanation:

Answer: i'm pretty sure it is called repeating

Answer:

Since there is a 50-50 chance of a person at the party choosing a gift card, and since there can only be 1 of 2 outcomes, we can assume that there will either be more people choosing a gift card than not, or there will be more people not choosing a gift card than are. So, that means that there would be 23 people (more or less) choosing a gift card and 22 people (more or less) not choosing a gift card or vice-versa.

Answer:

sin(71°)

Step-by-step explanation:

Sine lags behind cosine by 90°

In other word, cos(∅) = sin(90° - ∅)

cos(19°) = sin(90° - 19°)

= sin(71°)

Answer:

Alex is wrong in calculating his dive distance.

Actual distance of his Dive is 30 feet.

Step-by-step explanation:

Given:

Distance from where he dive from = 15 feet

Distance he reached after dive = 15 feet

Also Given:

Alex says that the two distances are opposites,

Also Total distance of dive according to Alex = 15 +-15 =0 feet

Solution:

Now we know that;

The diving board is 15 feet above the water level, and then he reached 15 deep in the water, but here it is important to know that even he is above the surface of the water he is diving in the water and then he reached 15 deep in the water.

So the two distances are in the same direction.

From above scenario we can say that

Total Distance of dive will be = 15 +15 =30 feet.

Hence We can say that Alex is wrong in calculating his dive distance. Actual Dive distance is 30 feet.

Answer:

N = 55

Step-by-step explanation:

which is :

where c is the hypotenuse

a is the adjacent

b is the opposite

c = 73

a = 48

b = N

now plug these in the formula

73^2 = 48^2 + N^2

now make N the subject of formula

73^2 - 48^2 = N^2

3025 = N^2

[tex]\sqrt{3025} \\[/tex] = N

N = 55 --- the murder was not done with a fallen object

The total cost of a meal with an 18% tip is calculated by converting the tip to a decimal (0.18), multiplying it by the meal cost, and adding it to the original cost. For a $72 meal, the total with tip would be $84.96.

To calculate the total cost of a meal including an 18% tip, you first convert the tip percentage to a decimal by dividing by 100. For an 18% tip, this gives you 0.18. Then, multiply the cost of the meal by this decimal to find the amount of the tip. Finally, add the tip to the original cost of the meal to find the total cost including the tip.

Example Calculation

If the cost of the meal is $72, the tip would be calculated as follows:

Therefore, the total cost of the meal with an 18% tip would be $84.96.

the weight of train A is 334 tons, and the weight of train B is 20 tons.

Let's denote:

- The weight of train A as x tons,

- The weight of train B as y tons.

We're given two pieces of information:

1. The total weight of both trains is 354 tons: [tex]\( x + y = 354 \)[/tex].

2. Train A is heavier than train B by 314 tons: [tex]\( x = y + 314 \).[/tex]

Now, we can set up a system of equations using these two pieces of information and solve for x and y.

From equation (2), we have:

[tex]\[ x = y + 314 \][/tex]

We can substitute this expression for x into equation (1):

[tex]\[ (y + 314) + y = 354 \][/tex]

Now, let's solve for y:

[tex]\[ 2y + 314 = 354 \][/tex]

[tex]\[ 2y = 354 - 314 \][/tex]

[tex]\[ 2y = 40 \][/tex]

[tex]\[ y = \frac{40}{2} \][/tex]

[tex]\[ y = 20 \][/tex]

Now that we have found the weight of train B, we can substitute this value into equation (2) to find the weight of train A:

[tex]\[ x = 20 + 314 \][/tex]

[tex]\[ x = 334 \][/tex]

So, the weight of train A is 334 tons, and the weight of train B is 20 tons.

Answer:

Option C

Step-by-step explanation:

We want to select the expression that can be used to find the slope of the line going through the points (–7, 3) and (1, –9)

Recall that the slope is given by:

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

We substitute the points into the formula to get:

[tex] \frac{ - 9 - 3}{1 - - 7} [/tex]

Therefore the third choice is correct.

Answer:

C

Step-by-step explanation:

Answer:

option D. 126 cm

Step-by-step explanation:

step 1

Find the scale factor

we know that

If two figures are similar, then the ratio of its corresponding sides is proportional and this ratio is called the scale factor

In this problem

Triangles PQR and XYZ are similar by AA Similarity Theorem

so

[tex]\frac{XY}{PQ}=\frac{YZ}{QR}=\frac{XZ}{PR}[/tex]

Let

z ---> the scale factor

[tex]z=\frac{XY}{PQ}[/tex]

substitute the given values

[tex]z=\frac{30}{5}=6[/tex]

step 2

Find the perimeter of triangle XYZ

we know that

If two figures are similar, then the ratio of its perimeters is equal to the scale factor

Let

z ----> the scale factor

p_1 ----> the perimeter of triangle XYZ

p_2 ---> the perimeter of triangle PQR

so

[tex]z=\frac{p_1}{p_2}[/tex]

The perimeter of triangle PQR is

[tex]p_2=5+10+6=21\ cm[/tex]

we have

[tex]z=6\\p_2=21\ cm[/tex]

substitute

[tex]6=\frac{p_1}{21}[/tex]

[tex]p_1=6(21)=126\ cm[/tex]

therefore

The perimeter of triangle XYZ is 126 cm

The Perimeter of ΔXYZ that is similar to ΔPQR is: 126 cm.

The corresponding side lengths of similar figures are proportional, that is, their ratios are equal.

Given that ΔPQR and ΔXYZ are similar, we would have the following ratios:

PQ/XY = PR/XZ = QR/YZ

Find XZ and YZ using their ratios:

PQ/XY = PR/XZ

Substitute

5/30 = 6/XZ

XZ = (6 × 30)/5

XZ = 36 cm

5/30 = 10/YZ

YZ = (10 × 30)/5

YZ = 60 cm

Perimeter of ΔXYZ = XY + XZ + YZ

Perimeter of ΔXYZ = 30 + 36 + 60

Perimeter of ΔXYZ = 126 cm.

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Answer:

198 cm²

Step-by-step explanation:

We are given the dimensions of a rectangular prism;

3cm 9cm and 6cm

We are required to determine its surface area;

We need to know that;

Surface area of a rectangular prism is given by;

A = 2(WL+HL+WH)

Where L, W and H are length , width and height respectively;

Assuming;

Width is 3 cm

Length is 9 cm, and

Height is 6 cm

Then;

Area = 2 ( (3×9) + (6×9) + (3×6))

        = 2(99)

       = 198 cm²

Therefore, the area of the rectangular prism is 198 cm²

Final answer:

The surface area of a rectangular prism with dimensions 3 cm by 9 cm by 6 cm is 198 square centimeters.

Explanation:

To find the surface area of a rectangular prism with dimensions of 3 cm, 9 cm, and 6 cm, we need to calculate the area of all six faces of the prism and then sum those areas. The formula to find the surface area (SA) of a rectangular prism is:

SA = 2lw + 2lh + 2wh

where l is the length, w is the width, and h is the height.

Substituting our given dimensions into the formula gives us:

SA = 2(3 cm)(9 cm) + 2(3 cm)(6 cm) + 2(9 cm)(6 cm)

SA = 2(27 cm²) + 2(18 cm²) + 2(54 cm²)

SA = 54 cm² + 36 cm² + 108 cm²

SA = 198 cm²

So, the total surface area of the rectangular prism is 198 square centimeters.

Answer:

2.73

Step-by-step explanation:

2 4/5 + 17/15

8/5 + 17/15

By Elysium

(24 + 17)/15

41/15

2.73

Answer: 18

Step-by-step explanation:

9+9

Answer:

18 choice C

Step-by-step explanation:

Answer:

A=41

B=20

C=8

D=3

Step-by-step explanation:

You need to first of all fill the intersection (yellow region). This is the number of people who use both.

This means B=20

Region A is those who use F only. So you must subtract the number who use both.

This means that A=61-20=41

Region C is those who use G+ only.

This means C=28-20=8

Now A+B+C+D=72

This implies that:

41+20+8+D=72

69+D=72

D=72-69

D=3

Answer:

The page numbers are 46 and 47.

Step-by-step explanation:

Given:

Qasim hussain opened his account book. He observed that the sum of page numbers of the two pages in front of him is 93.

Now, to find the page numbers.

Let the first page number be [tex]x.[/tex]

And the other page number be [tex]x+1.[/tex]

As, given he observed that the sum of page numbers of the two pages in front of him is 93.

According to question:

[tex]x+(x+1)=93[/tex]

[tex]x+x+1=93\\2x+1=93[/tex]

Subtracting both sides by 1 we get:

[tex]2x=92[/tex]

Dividing both sides by 2 we get:

[tex]x=46.[/tex]

So, the first page number = 46.

And the other page number = [tex]x+1=46+1=47.[/tex]

Therefore, the page numbers are 46 and 47.

Answer:

[tex]m^2(10m+49)[/tex]

Step-by-step explanation:

[tex]Given \ \ 8m^3+2m^3+49m^2\\\\=m^3(8+2)+49m^2 \ \ \ \ \ \ \ (adding\ like\ terms)\\\\=10m^3+49m^2\\\\=10m\times m^2+49m^2\\\\=m^2(10m+49)[/tex]

Answer:

x = -1

y = -1

Step-by-step explanation:

3x - y = -2

2x + y = -3

Multiply equation 1 by 2 and equation 2 by 3

We have

2x3x - 2xy = 2x-2

3x2x + 3xy = -3x3

Equation 1 6x - 2y =-4

Equation 2 6x + 3y = -9

Subtract equation 2 from 1

We have -5y = 5

Divide both sides by -5

y = 5/-5 = -1

Now Substitute y = -1 into any of the equations to get x

Using equation 1 , we have

3x - (-1) = -2

3x +1 = -2

Collect like terms

3x = -2 -1

3x = -3

Divide both sides by 3

x = -3/3 = -1

Answer

First of all, we need to identify the type of equation this is...

Since we are solving two at a go, it means it's a simultaneous equation.

Now, we need to solve them differently.

Taking the first one which says...

3x -y = -2

Then we say

When x is 0, y =?

So in the equation above , we replace x with 0

Meaning- 3x-y = -2

3(0) -y= -2

0 -y= 2

-y =-2

Y =2

Also, when y =0.

3x- 0 =-2

3x=-2

X=-2/3.

Also for the other equation

2x+ y =-3

When x= 0 in the above equation

2(0) + y= -3

0 +y=-3

Y=-3

When y = 0

2x+ 0= -3

2x = -3

X=-3/2

The above is what well plot on the graph.

t

Step-by-step explanation:

Option B is correct, the surface area of the ramp will be 210 square cm.

a three dimensional shape can be defined as a solid figure or an object or shape that has three dimensions—length, width, and height.

Let h be the height and b be the base of the triangle. Let L₁, L₂, and L₃ be the length and W be the width of the rectangle.

Then the surface area of the triangular prism will be given as,

Surface area = 2 Area of triangle + 3 Area of rectangle

Surface area = (h x b) + (L₁ + L₂ + L₃) x W

Sean must determine how much paint he will use to cover all of the edges of his ramp.

The surface area of the ramp is calculated as,

SA = (8 x 6) + (5 + 6 + 7) x 9

SA = 48 + 18 x 9

SA = 48 + 162

SA = 210 square cm

Hence, the surface area of the ramp will be 210 square cm. Then the correct option is B.

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The first investment can be shown as T=500*1.05^2 which is $551.25

The second investment can be shown as T=500*e^(0.03*12*2) which is $1027.22

So the second investment is better

Hope that helped!