A motel clerk counts his $10 bills and $20 bills at the end of the day. He finds that he has a total of 150 bills, and that those 150 bills have a total value of $2,000. How many $10 bills and $20 bills does the motel clerk have?

Translate the problem into 2 equations.


Let the x be the number of $10 bills and y be the number of $20 bills.

In the given 30-60-90 triangle the value of x is calculated after rationalizing and simplifying to be equal to 2√3.

The hypotenuse of a right triangle is the longest side that is opposite the right angle. It is the side that is opposite to the right angle and is also the side that is opposite to the 90-degree angle in the triangle.

In a right triangle, the hypotenuse is always opposite to the right angle and is also the side that connects the two legs of the triangle. The hypotenuse is also the side that has the largest length among the three sides of a right triangle.

In a 30-60-90 triangle, the ratio of the sides opposite to the angles 30 degrees, 60 degrees, and 90 degrees are x: x√3 : 2x.

Therefore, in this triangle, the length of the hypotenuse (opposite to the 90-degree angle) is 2x.

The length of the perpendicular (opposite to the 60 degree angle) is 6.

So, we have:

tan (60 degrees) = perpendicular / base

√3 = 6 / x

Multiplying both sides by x, we get:

x√3 = 6

Dividing both sides by √3, we get:

x = 6 / √3

Rationalizing the denominator by multiplying both of the numerator and denominator by √3, we receive:

x = 6√3 / 3

Simplifying further, we get:

x = 2√3

Therefore, the value of x is 2√3.

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Answer:

13

Step-by-step explanation:

The coefficient is the number placed before the given variable.

In this case:

Coefficient: 13

Variable: y

Power: 3

The coefficient is a number in front of the variable( x or y)

The coefficient would be 13

Answer:

If you're trying to solve the system of equations, the answer is

in point form: (4,4) , (-6,-16)

in equation form: x=4, y=4   x=-6, y=-16

Answer:

2. Parallel (Interior Alternate Angles)

3. Not enough information

Step-by-step explanation:

For the first question, combine 60+25 which equal to 85°

Since both are 85° for interior alternate angles, the theorem states that if both interior alternate angles have same value, both lines are parallel.

Hence, both lines are parallel.

For the second question, there's not enough information. Some people may think that, "Can't we use 82-x=120"? The answer is no. 82-x=120 only applies when both lines are parallel. When we have to prove parallel lines, we cannot assume that they are parallel.

So 82-x = 120 is not valid.

Any other theorems do not work because not enough information.

Therefore, there's no enough information.

Answer:

cyclist will travel 64 kilometres in 4 hours

Step-by-step explanation:

speed of cyclist = 10 miles per hour

given 1 mile is equal to 1.6 kilometres.

1*10 miles will be equal to 1.6*10 kilometres

thus , 10 mile is equal to 16 kilometres

using 16 km in place of 10 miles in 10 miles per hour

we have

speed of cyclist = 16 kilometres per hour

we know that distance = speed * time

speed is 16 kilometres per hour

time 4 hours

thus , distance = 16*4 kilometres= 64 kilometres.

cyclist will travel 64 kilometres in 4 hours.

(Hope this helps can I pls have brainlist (crown)☺️)

The smallest container that can be used to store the punch is 2 gallons.

A fraction is a number that is not an integer or a whole number. It is made up of numerators and denominators. The number at the top is the numerator and the number below is the denominator.

Punch left = 3 1/4 - 1 1/2

\(2\frac{1 - 2}{4}\) = 1 3/4

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Answer:

(-(7 x + 272))/4

Step-by-step explanation:

Simplify the following:

x/2 - (2 + 1/4) x - 70 - ( - 2)

Hint: | Put the fractions in 2 + 1/4 over a common denominator.

Put 2 + 1/4 over the common denominator 4. 2 + 1/4 = (4×2)/4 + 1/4:

x/2 - 9/4 x - 70 - ( - 2)

Hint: | Multiply 4 and 2 together.

4×2 = 8:

x/2 - (1/48 + 1/4) x - 70 - ( - 2)

Hint: | Add the fractions over a common denominator to a single fraction.

8/4 + 1/4 = (8 + 1)/4:

x/2 - 9/4 x - 70 - ( - 2)

Hint: | Evaluate 8 + 1.

8 + 1 = 9:

x/2 - 9 x/4 - 70 - ( - 2)

Hint: | Multiply -1 and -2 together.

-(-2) = 2:

x/2 - (9 x)/4 - 70 + 2

Hint: | Put the fractions in x/2 - (9 x)/4 - 70 + 2 over a common denominator.

Put each term in x/2 - (9 x)/4 - 70 + 2 over the common denominator 4: x/2 - (9 x)/4 - 70 + 2 = (2 x)/4 - (9 x)/4 - 280/4 + 8/4:

(2 x)/4 - (9 x)/4 - 280/4 + 8/4

Hint: | Combine (2 x)/4 - (9 x)/4 - 280/4 + 8/4 into a single fraction.

(2 x)/4 - (9 x)/4 - 280/4 + 8/4 = (2 x - 9 x - 280 + 8)/4:

(2 x - 9 x - 280 + 8)/4

Hint: | Group like terms in 2 x - 9 x - 280 + 8.

Grouping like terms, 2 x - 9 x - 280 + 8 = (2 x - 9 x) + (8 - 280):

((2 x - 9 x) + (8 - 280))/4

Hint: | Combine like terms in 2 x - 9 x.

2 x - 9 x = -7 x:

(-7 x + (8 - 280))/4

Hint: | Evaluate 8 - 280.

8 - 280 = -272:

(-272 - 7 x)/4

Hint: | Factor a minus sign out of -7 x - 272.

Factor -1 out of -7 x - 272:

Answer: (-(7 x + 272))/4

1/2 x + (-70) - 2 1/4 x - (-2) = (-(7 x + 272))/4 = True

To rewrite the expression -2(n-7) using the distributive property, we need to distribute the -2 to both terms inside the parentheses. The distributive property states that for any numbers a, b, and c:

a(b + c) = ab + ac

Applying this property to the given expression:

-2(n-7) = -2 * n + (-2) * (-7)

Simplifying further:

-2(n-7) = -2n + 14

Therefore, the rewritten expression is -2n + 14.

Answer:

God Loves you

Step-by-step explanation:

Because he died for you.    "John 3,16"

Answer:

.50

Step-by-step explanation:

The  correct answer for the two numbers with the sum of 1 are 0.5 and 0.5.

What is addition?

Addition is a basic arithmetic operation that combines two or more numbers to find their total or sum. In the context of arithmetic, addition is denoted by the symbol "+".

When  addition is performed two or more numbers,  are combined to get a result known as the sum.

Addition is a fundamental mathematical concept used in various real-life situations, such as calculating totals, solving problems in mathematics.

Add:

0.5 + 0.5

= 1

The correct answer is 0.5 and 0.5

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Answer:

12

Step-by-step explanation:

Do 8 divided by 14 =0.571428571

times that by 21 = 12

The probability that the student got an 'A' given they are male is approximately 0.12 or 12%.

To find the probability that a student got an 'A' given they are male, we need to use Bayes' theorem:

P(A | Male) = P(Male | A) × P(A) / P(Male)

We can find the values of the terms in the formula using the information given in the table:

P(Male) = (25/54) = 0.46 (the proportion of all students who are male)

P(A) = (17/54) = 0.31 (the proportion of all students who got an 'A')

P(Male | A) = (3/17) = 0.18 (the proportion of all students who are male and got an 'A')

Therefore, plugging these values into the formula:

P(A | Male) = 0.18 × 0.31 / 0.46

P(A | Male) ≈ 0.12

So the probability that the student got an 'A' given they are male is approximately 0.12 or 12%.

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Answer:

is the equation of the line:

y=-3x

Answer:

$12

Step-by-step explanation:

If we stuck with the price of $8, then we end with an income of $2400

Increasing it by $1 will decrease attendance by 20

8 x 300 = 2400

9 x 280 = 2520

10 x 260 = 2600

11 x 240 = 2640

12 x 220 = 2640

13 x 200 = 2600

We're starting to go down, so let's stop there

The ticket price of $11 or $12 appears to give the most income

I would stick with $12 since your still getting more money from one ticket

The price of a ticket stick at $12 since you still get more money from one ticket.

Last year 300 people attended a play with a ticket price of $8.

The school estimates that 20 fewer people attend for each $1 increase in price.

If we keep the price at $8, we'll end up with a $2400 profit.

Increasing it by $1 will result in a 20 percent drop in attendance.

8 × 300 = 2400

9 × 280 = 2520

10 × 260 = 2600

11 × 240 = 2640

12 × 220 = 2640

13 x 200 = 2600

Let's come to a halt here since we're starting to descend.

The $11 or $12 ticket price looks to generate the most revenue.

I'd continue with $12 because you'll still make more money with one ticket.

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The surface areas are 110 in², 87.6 mm² and 49 m².

Given that are solid figure, we need to find the surface area of them,

1) Triangular prism = perimeter × length + 2 × base area

= (5 + 5 + 6) × 5 + 2(3×5) = 110 in²

2) Triangular pyramid = base area + perimeter × slant height / 2

= 1/2 × 5.2 × 6 + 3 × 6 × 8/2

= 87.6 mm²

3) Cube = 4side²

= 4 × (3 1/2)²

= 4 × 3.5²

= 49 m²

Hence the surface areas are 110 in², 87.6 mm² and 49 m².

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Answer:

Ray

Step-by-step explanation:

It is pointing to a ray coming out of the picture of the sun. Use the pieces r and ay.

A repeating decimal is acceptable to use during calculations when you require a certain level of precision

A repeating decimal is acceptable to use during calculations when you require a certain level of precision, but it's important to keep in mind that the result will be an approximation rather than an exact value.

It is commonly used in situations where a rounded value is sufficient and the level of precision doesn't significantly impact the final result.

On the other hand, you should convert a repeating decimal to a fraction for calculations when you need an exact value or when further mathematical operations or comparisons are required.

Converting a repeating decimal to a fraction allows for precise calculations and eliminates any potential rounding errors associated with working with decimal approximations.

Converting a repeating decimal to a fraction involves identifying the repeating pattern and expressing it as a fraction. This allows for exact calculations and maintains the mathematical properties of fractions.

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Answer:

Image below

Step-by-step explanation:

a. The answer is: The fewest number of multibase blocks required to represent 20 longs in base seven is 2 flats.

b. The answer is: The fewest number of multibase blocks required to represent 10 longs in base three is 3 flats and 1 unit.

a. To represent 20 longs in base seven, we need to find the fewest number of multibase blocks required.

In base seven, we have the following conversions:

1 long = 1 unit

1 flat = 10 units

1 block = 10 flats

To represent 20 longs, we can use 2 flats (each flat representing 10 units) and 0 units since there are no remaining units.

So, the fewest number of multibase blocks required would be 2 flats.

Therefore, the answer is: The fewest number of multibase blocks required to represent 20 longs in base seven is 2 flats.

b. To represent 10 longs in base three, we need to find the fewest number of multibase blocks required.

In base three, we have the following conversions:

1 long = 1 unit

1 flat = 3 units

1 block = 3 flats

To represent 10 longs, we can use 3 flats (each flat representing 3 units) and 1 unit since there is one remaining unit.

So, the fewest number of multibase blocks required would be 3 flats and 1 unit.

Therefore, the answer is: The fewest number of multibase blocks required to represent 10 longs in base three is 3 flats and 1 unit.

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Determne the linear relaion between number of sides and sum of angles of polygon.

Thus relation between sum of angles of a polygon and n uymber of sdies is 180(n - 2).

Answer:

B. 46.

Step-by-step explanation:

First we set up the equation A(n)=-172 and substitute the given equation for A(n), giving us -172=8+(n-1)(-4). Simplifying, we get -180=(-4n+12), or -4n=-192, or n=48. However, n represents the number of terms in the sequence, and since the sequence starts with n=1, we need to subtract 1 from our answer to get the term number corresponding to A(n)=-172. Therefore, the answer is B) 46.

a) A function that gives the area of the playground (in square meters) in terms of x is A(x) = 60x - x².

b) The side length that gives the maximum area that the playground can have is x = 30 m.

c) The maximum area that the playground can have is 900 m².

In Mathematics and Geometry, the perimeter of a rectangle can be calculated by using this mathematical equation (formula);

P = 2(L + W)

Where:

By substituting the given side lengths, we have:

120 = 2(x + W)

60 = x + W

W = 60 - x

Therefore, the area of the rectangular playground (in terms of x) is given by this function;

A = LW

A(x) = x(60 - x)

A(x) = 60x - x²

Part b.

For the side length, we would take the first derivative of the area:

A(x) = 60x - x²

A'(x) = dA/dx

A'(x) = 60 - 2x

60 - 2x = 0

x = 60/2

x = 30 m

Part c.

W = 60 - x

W = 60 - 30

W = 30 m.

Therefore, the maximum area is given by;

A = 30 × 30

A = 900 m².

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Answer:

y = -x - 10

Step-by-step explanation:

set y as the total money owed

set x as how many days passed

if 0 days are passed, they owed $10, which is "-10" the y-intercept

and owed $1 more everyday which is -1x. We can write it as -x.

Answer:

4+52=56

\(y = 4cm and o = 52 work out x\)

56

The height οf the tree stump is apprοximately 56.8 inches.

A cylinder-shaped 3D slide is fοrmed by twο parallel, identical bases cοnnected by a curving surface. These bases are fοrmed similarly tο a disc. A line drawn acrοss the centre οf the twο cοnnected circular bases fοrms the axis οf the cylinder shape.

The letter "h," which stands fοr height, designates the measurement that separates the twο bases as the perpendicular distance. The distance between the centres οf the twο circular bases and their οuter edges is referred tο as the cylinder's radius and is denοted by the letter "r". The cylinder is made up οf a rectangle and twο circles.

Given that the radius οf the tree stump is 37 in and the vοlume is 77415 cubic inches, we have:

V = 77415 cubic inches

r = 37 in

Substituting these values intο the fοrmula fοr the vοlume οf a cylinder, we get:

\(77415 =\pi (37)^2h\)

Simplifying the expressiοn, we get:

\(h = 77415 / (\pi (37)^2)\)

Using a calculatοr and apprοximating π tο 3.14, we get:

h ≈ 56.9 inches

Rοunding tο the nearest tenth, we get:

h ≈ 56.8 inches

Therefοre, the height οf the tree stump is apprοximately 56.8 inches.

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Answer: x=3

Step-by-step explanation:

from figure

=>tan45= x/3

=>x= 3tan45

=>x=3

Answer:

Step-by-step explanation:

here hypotenuse is x

since it is an isosceles triangle the other side of the triangle also must 3.

using pythagoras theorem

a^2 + b^2 = c^2

3^2 + 3^2 = x^2

9 + 9 = x^2

18 = x^2

\(\sqrt{18} = x\)

Answer:

45x³

Step-by-step explanation:

Given

3x × 15x²

= 3 × 15 × x × x²

= 45 × x³

= 45x³

Answer:

45x^3

Step-by-step explanation:

Multiply the digits that is 15 x 3

Then multiply the Variable x^2 and x

variables are added when multiplied keep this rule in mind always

The best describes a graph of paired points that form a proportional relationship is A straight line can be drawn through all the points, and the line passes through the point where x = 0 and y = 0.

A graph is a data structure that consists of vertices (also known as nodes) and edges. It is used to represent relationships between objects in a mathematical way. A graph can be either directed or undirected; directed graphs have arrows that indicate the direction of the relationship between the two objects, while undirected graphs have no arrows and indicate that the relationship is mutual. Graphs can be used to represent a variety of real-world phenomena.

A straight line can be drawn through all the points, and the line passes through the origin. The origin is the point (0, 0).

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Answer:

\(21.7 x 10^5\)

Step-by-step explanation:

(6.2 x 10²) x (3.5 x 10³)

First, multiply the coefficients: 6.2 x 3.5 = 21.7.

Then, add the exponents: 10² x 10³ = 10^(2+3) = 10^5.

Therefore, the result is 21.7 x 10^5.

Answer:

3286000

Step-by-step explanation:

The radius is given from the area of the sector which is half the area of

the triangle.

Response:

Given parameter;

Angle at the vertex of the triangle that is the center of the circle = 60°

Length of the adjacent sides of the 60° angle = 12, and 12·√3

The arc of the circle inside the triangle divides it into two equal parts

Required:

To find the radius of the circle that has a center at the vertex of the

triangle.

Solution:

\(The \ area \ of \ a \ triangle\ is, \ A = \mathbf{ \dfrac{1}{2} \cdot a \cdot b \cdot sin(C)}\)

Where;

a, and b, are the adjacent sides to the angle C, therefore;

a = 12

b = 12·√3

C = 60°

Which gives;

The area of the triangle, A = 108 square units

\(Area \ of \ the \ sector, \ A_{sector} = \mathbf{ \dfrac{\pi \cdot r^2}{360^{\circ}} \times 60^{\circ}} = \dfrac{A}{2}\)

Which gives;

\(A_{sector} = \dfrac{\pi \cdot r^2}{360^{\circ}} \times 60^{\circ} = \dfrac{108}{2} = 54\)

Therefore;

\(\dfrac{\pi \cdot r^2}{360^{\circ}} \times 60^{\circ} = \dfrac{\pi \cdot r^2}{6} = 54\)

\(r^2= \dfrac{54 \times 6}{\pi} = \dfrac{324}{\pi}\)

\(r= \sqrt{ \dfrac{324}{\pi}} = \dfrac{18}{\sqrt{\pi} } = \dfrac{18 \cdot \sqrt{\pi} }{\pi} \approx \mathbf{10.16}\)

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