Nolan is going to a carnival that has games and rides. Each game costs $2.50
and each ride costs $3.50. Nolan spent $52.50 altogether on 17 games and
rides. Write a system of equations that could be used to determine the
number of games Nolan played and the number of rides Nolan went on.
Define the variables that you use to write the system.

The equation of line through the origin and (-5, 6 ) is y = [tex]-\frac{6}{5}x[/tex]

The slope of a line is the ratio of the amount that y increases as x increases some amount. Slope tells you how steep a line is, or how much y increases as x increases. The slope is constant (the same) anywhere on the line.

the coordinates of the origin is (0, 0) and h other coordinates are (-5, 6)

at x = 0 and y = 0

using the equation of straight line y = mx + c

0 = 0(m) + c

so c = 0

at x = -5, y = 6

6 = -5m +c

but c = 0

6 = -5m

m = -6/5

Equation of line becomes y = -6/5x

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Answer:

x = 90 , y = 43

Step-by-step explanation:

Since AB and AC are congruent , then Δ ABC is isosceles with base angles congruent , that is

∠ ABD = ∠ ACD = 47°

AD is the perpendicular bisector of BC , so

∠ ADB = x = 90

the sum of the 3 angles in Δ ABD = 180° , then

y = 180° - (90 + 47) = 180 - 137 = 43

$18.24

You can find the answer to this by simply dividing the two numbers:

$383 ÷ 21 = $18.24

I hope my answer helped you! If you need more information or help, comment down below and I will be sure to respond if I am online. Have a wonderful rest of your day!

[tex]\sqrt[4]{256x^{6}y^{10} }[/tex]will be 4[tex]x^{3/2} y^{5/2}[/tex]

The number that, when multiplied four times by itself, yields the original number is the fourth root of a number. In other words, the square root of the square root of an integer equals the number's fourth root.

eg:

eg: [tex]\sqrt[4]{81}[/tex] = 3

We are asked

x> 0 and y> 0then

[tex]\sqrt[4]{256x^{6}y^{10} }[/tex]    =  4 [tex]x^{3/2} y^{5/2}[/tex]

As 4 multiplied by 4 , 4 times given 256 and x to the power 6 and root 4 so that will be x to the power 3/2 and y to the 10 and root 4 will give 5/2

thus

[tex]\sqrt[4]{256x^{6}y^{10} }[/tex] will be equivalent to  4 [tex]x^{3/2} y^{5/2}[/tex]

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A class is planning a trip to the local City Museum of Art. The class needs 3 trucks and 1 car to transport all 22 people on the trip.

Generally, To solve this problem, we can set up a system of equations using the information given. Let C be the number of cars needed and T be the number of trucks needed.

The first equation will represent the number of people that can be transported in the cars: 4C + 6T = 22

The second equation will represent the number of drivers: C + T = 4

Now we can solve this system of equations using elimination or substitution.

Using elimination, we can multiply the first equation by 2 and the second equation by 4 to get: 8C + 12T = 44 4C + 4T = 16

Then we can subtract the second equation from the first equation to get: 4C + 8T = 28

Then we can divide both sides by 4 to get: C + 2T = 7

Then we can substitute this value for C in the second equation to get: 7 - 2T = 4 T = 1.5

Since T represents the number of trucks, which must be a whole number, this solution is not possible.

Using substitution, we can solve for C in the second equation and substitute it into the first equation: C = 4 - T 4(4 - T) + 6T = 22 16 - 4T + 6T = 22 2T = 6 T = 3

Substituting this value for T into the second equation, we get: C = 4 - 3 C = 1

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Answer: z > 14

Step-by-step explanation:

Move 3 to the right

Answer: $17.16 dollars

Step-by-step explanation:

first, you divide 9.87 by three which equals $3.29

then you add 1 which is $4.29

Finally, multiply it by 4 which is $17.16

Answer:$17.16

Step-by-step explanation:

The number of animals will the farmer have after 7 months including the 10 cattle are 1280.

For the stated question-

Thus, number of animals after years;

= 10 x  2⁷

= 1280

Thus, number of animals will the farmer have after 7 months including the 10 cattle are 1280.

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The correct values for A, B and C are given as follows:

The table shows the ratios of black to white keys on pianos of various sizes, and these ratios are constant, meaning that the following proportional relationship is established:

A/13 = 18/B = 45/65 = 72/C

Then the value of A can be obtained as follows:

A/13 = 45/65

Applying cross multiplication, we have that:

65A = 13 x 45

A = 13 x 45/65

A = 9.

The value of B can be obtained as follows:

18/B = 45/65

Applying cross multiplication, we have that:

45B = 18 x 65

B = 18 x 65/45

B = 26.

Finally, the value of C can be obtained as follows:

72/C = 45/65

Applying cross multiplication, we have that:

45C = 72 x 65

C = 72 x 65/45

C = 104.

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Answer:

m∠QRS = 30°

m∠SRT = 75°

Step-by-step explanation:

Now,

The sum of m∠QRS and m∠SRT is equal to m∠QRT which is 105°

So,

m∠QRS + m∠SRT = m∠QRT

(6x)° + (14x + 5)° = (105)°

6x + 14x + 5 = 105

20x + 105 - 5

20x = 100

x = 100/20

x = 5

Thus, The value of x is 5°

Now,

m∠QRS = (6x)° = 6 × 5 = 30°

m∠SRT = (14x + 5)° = 14(5) + 5 = 70 + 5 = 75°

Answer:

parallel

Step-by-step explanation:

same slope

Answer:

No solution

Step-by-step explanation:

-2-y=-y

clt

-2=-y+y

-2=0

:ans is -2=0 making it with no solution

Answer:

Hope this helps good luck :)

see explanation

Step-by-step explanation:

Find relationship of length(L) and width(w)

Perimeter = L + W + L + W

[tex]20. = (w+2) + w + (w+2) +w 20. = 4w + 4 -4. -4 16 = 4w 16. = 4w 4. 4 4. = w w = 4 L. = w+2 = 4 +2 L = 6[/tex]

Answer width is 4 meters and length is 6 meters.

The minimum score Sam needs to get on his final exam to get a "C" in the course is 82.

What is a probability?

A random event's occurrence is the subject of this area of mathematics. The range of the value is 0 to 1. Mathematics has incorporated probability to forecast the likelihood of various events.

Given that, Sam's test scores are 62, 71, and 65.

The total score in three test is (62 + 71 + 65) = 198

Assume that, he scored x in the final test.

Total score of Sam is 198 + x.

He needs to score 70% means he needs to score 70 out of 100.

According to question,

(198 + x)/ 400 ≥ 70/100

Multiply both sides by 100:

(198 + x)/ 4 ≥ 70

Multiply both sides by 4

198 + x ≥ 280

x ≥ 280 - 198

x ≥ 82

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Answer:

P= RS. 9000

R=7.6%

T= 9 months

Simple Interest (SI}=?

By using formula,

SI= PTR/100

= 9000* 7.6* 9/ 100* 12

= 615600/1200

= 513

Answer:

To calculate the interest rate for your account, you will need to use the formula for simple interest:

Interest = Principal x Rate x Time

In this case, the principal is the amount of money you deposited, or $600. The time is the number of months the money was in the account, or 18 months. And the interest is the amount of money you earned, or $31.50.

Plugging these values into the formula, we get:

$31.50 = $600 x Rate x 18

To solve for the rate, we can divide both sides of the equation by $600 and 18:

Rate = $31.50 / ($600 x 18)

Simplifying this expression gives us:

Rate = 0.01625

So, the interest rate for your account is approximately 1.625%.

By solving an inequality, we will see that option a is cheaper for more than 60 miles.

We know that option A charges $25 per day plus $0.15 per mile, so the cost for x miles is given by the linear equation:

A(x) = $25 + $0.15*x

While for option B the fixed cost is $10 and the cost per mile is $0.40, so the cost equation is:

B(x) = $10 + $0.40*x

The cost of option a will be smaller when:

$25 + $0.15*x < $10 + $0.40*x

$25 - $10 < $0.40*x - $0.15*x

$15 < $0.25*x

$15/$0.25 < x

60 < x

So for 60 miles the cost is the same, for x > 60 miles the cost of option a will be smaller (because the slope is smaller).

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Option 1 : x < = - 8 represents the given graph of inequality.

In mathematics, an inequality displays the connection between two values in an unbalanced algebraic expression. One of the two variables on the two sides of the inequality may be greater than, greater than or equal to, less than, or less than or equal to another value, according to inequality signs.

Depending on which way the inequality sign is pointing, a sign can be greater or less than. When the open portion of the sign is facing left, >, the value on the left side of the sign is greater than the value on the right. When it is turned to the right, the left value is less than the right value.

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Answer:

39 inches

Step-by-step explanation:

All of the sides are the same length because all of the angles are equal

21 - x = 2x - 3  Set two sides equal to each other and solve for x.  Add x to both sides

21 = 3x - 3  Add 3 to both sides

24 = 3x  Divide both sides by 3

x = 8

Substitute in 8 for x to find the value of a side

2x - 3

2(8) - 3

16 - 3

13

Each side length is 13

3 x 13 = 39

Answer:

360 in commission.

Step-by-step explanation:

If you received a 4% commission on the TVs you sold, and you sold $9,000 worth of TVs, then you would have received 4/100 * $9,000 = $<<4/100*9000=360>>360 in commission.

The ratio of Oats to Maple syrup for 36 cookies is 192 grams: 816 grams. So the answer is Option C. 192 grams: 816 grams.

Comparing two amounts of the same units and determining the ratio tells how much of one quantity is in the other.

when evaluating the relationship between two quantities or numbers. In general, x: y, which can be interpreted as "x is to y," is used to denote a ratio between two quantities.

Here we have

15 Cookies need 80g Oats

=> Amount of Oats for 1 cookie = 80g/15 gms

So the amount Oats for 36 Cookies = 80g/5 × 36 = 192 grams

15 Cookies need 340 grams of Maple syrup

=> Amount of Maple syrup for 1 cookie = 340/15 gram

So the amount of Maple syrup for 36 cookies = (340/15)×36 = 816 grams

By the above calculations,

For 36 Cookies we need 192 grams of Oats and 816 grams of Maple syrup

The Ratio of Oats to Maple syrup = 192 gram: 816 gram

Therefore,

The ratio of Oats to Maple syrup for 36 cookies is 192 grams: 816 grams. So the answer is Option C. 192 grams: 816 grams.  

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The value of the tangent of angle 37° is 3/4. Then the height of the cell tower will be 24.5 meters.

Trigonometric functions examine the interaction between the dimensions and angles of a triangular form.

A specialist gazes toward the highest point of a cell tower. The specialist stands 30 meters from the focal point of the pinnacle with a view of 37° from the level. The designer's eyes are 2 meters over the ground.

Let 'h' be the height of the tower. Then we have

tan 37° = (h - 2) / 30

Simplify the equation, then we have

tan 37° = (h - 2) / 30

3/4 = (h - 2) / 30

4h - 8 = 90

4h = 98

h = 24.5 meters

The level of the cell pinnacle will be 24.5 meters.

The diagram is given below.

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The length of side BC is approximately 10.928.

What is the right triangle?

In a right triangle, the side opposite the right angle is called the hypotenuse. In triangle ABC, side AC is the hypotenuse, and sides AB and BC are the other two sides.

To find the length of side BC, we can use the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the other two sides.

We can use the given information to write the Pythagorean theorem in the form:

AC^2 = AB^2 + BC^2

Substituting the given lengths, we get:

13² = 5² + BC²

Solving for BC, we get:

BC = √(13² - 5²)

= √(144 - 25)

= √(119)

= approximately 10.928

Therefore, the length of side BC is approximately 10.928.

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Answer:

5.75

Step-by-step explanation:

So first you would multiply 2.5*4.6 which is 11.5

Next you would divide 11.5/2 because a triangle is half of a square.11.5/2 is 5.75

Equation used to represent the relation between the number of pages written to the number of hours used with constant of proportionality is

x = 4y.

As given in the question,

Let us consider number of pages write by Bill be 'x'

And number of hours represented by 'y'

Number of hours used by Bill to write 4 pages = 1 hour

Number of pages written by Bill in 1 hour = 4

Given :

Number of pages is proportional to the number of hours

⇒ x ∝ y

⇒ x = ky

Where 'k' is the constant of proportionality.

When x = 4 , y = 1

substitute the value in the equation,

4 = k(1)

⇒ k = 4

Now the required equation with the constant of proportionality k = 4 is:

x = 4y

Therefore, the required equation to represent the relation between number of pages written to the number of hours used with constant of proportionality is equal to x =4y.

The complete question is:

Bill enjoys writing in his spare time. He writes 4 pages per hour. The proportional relationship between the number of pages written to the number of hours is represented by the equation ______. Write the equation in standard form with a constant of proportionality.

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Answer

6

Step-by-step explanation:

There are 3 teams and 18 soccer balls. For each team to have the same number of soccer balls you need to do 18 divided by 3 to get 6. Each time will have 6 soccer balls.