The sum of two numbers is 30 and their difference is 12 find the 2 numbers

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:

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:

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:

Median = 78

Step-by-step explanation:

Arrange the data in ascending order

54  68   70  72  75   76   76   76   76  80  88   88   88   88  88   92   92   93

Total number = 18

Median = average of middle terms = average of 9th and 10th term

= ( 76 + 80)/2 = 156/2 = 78

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:

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°)

The answer is 14+2/3x

I hoped this helped :)

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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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

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.

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!

Answer: B, the second one

Step-by-step explanation:

In the first one your distance stays the same while your time increases. The second one the distance decreases as the time increases, the third one is a double increase and than the last one the distance stays the same as the time increases and than changes to Decrease increases

Answer:

B is the corrcet one! :)

Step-by-step explanation:

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.

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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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.

The experimental probability of the next sandwich sold being tuna on wheat bread is 23 out of 137 sandwiches sold, or approximately 0.168.

The problem describes an experimental probability scenario where stopping after having recorded multiple outcomes does not affect the probability of the next outcome. Experimental probability is calculated by taking the number of times an event occurs and dividing it by the total number of trials.

In this case, a total of 137 sandwiches were sold (22 ham on white bread + 24 ham on wheat bread + 21 turkey on white bread + 22 turkey on wheat bread + 25 tuna on white bread + 23 tuna on wheat bread). Out of these, 23 were tuna on wheat bread.

The experimental probability of the next sandwich being a tuna on wheat bread is therefore 23/137, or approximately 0.168, if this same pattern continues.

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Final answer:

The terms in the expression are 7, 4p, -5, p, and 2q. The like terms in the expression are 4p and p. To simplify the expression, the like terms can be combined by adding their coefficients.

Explanation:

The terms in the expression are:

Like terms in the expression are terms that have the same variable(s) raised to the same power. In this expression, the like terms are:

To simplify the expression, we can eliminate the like terms by combining their coefficients. Adding 4p and p, we get 5p. Therefore, the simplified expression is:

7 + 5p - 5 + 2q

It is not possible to find the values of p and q without additional information.

To find the solutions to the equation y = 2x - 3, substitute different x-values and solve for y.

The given equation is y = 2x - 3.

To find the ordered pairs that are solutions to this equation, substitute different x-values and solve for y.

Let's take the first ordered pair (294.5, 61) as an example:

Therefore, the ordered pair (294.5, 61) is not a solution to the equation y = 2x - 3.

Repeat the same process for the other two ordered pairs to determine if they are solutions to the equation.

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: 12.5m(2+m)

Step-by-step explanation:

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:

Step-by-step explanation:

=

The numbers that replaces each blank to make the inequality a true statement are 48 and 32. The new inequality is 48/24 > 1/4 > 4/32.

In Mathematics and Euclidean Geometry, an inequality is a relation that compares two or more numbers and variables in an algebraic equation based on any of the following inequality symbols:

Based on the information provided, we can logically deduce the following incomplete inequality;

_/24 > 1/4 > 4/_

In order to make the left-hand side of the inequality true, we must have a number that is greater 1/4 or 0.25;

48/24 = 2

48/24 > 1/4

2 > 0.25 (True)

In order to make the right-hand side of the inequality true, we must have a number that is less than 1/4 or 0.25;

4/32 = 0.125

1/4 > 4/32

0.25 > 0.125 (True).

In conclusion, any number that is greater than 1/4 would make the left-hand side of the inequality true while any number that is less than 1/4 would make the right-hand side of the inequality true.

Complete Question:

Use symbols. Replace each __ with a number to make _/24 >1/4 > 4/_ a true statement.

Answer:

Step-by-step explanation:

Answer: i'm pretty sure it is called repeating

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)