Fred, a frequent business traveler, is considering signing up for a hotel rewards program.
Hotel Elegance is currently offering 881 points for signing up, plus 22 points for every night
Fred books at the hotel. Alternatively, Hotel Paradiso is offering a sign-up bonus of 851
points, plus 23 points per night. If Fred books a certain number of nights, the points he earns
with either hotel will be the same. How many points will he have? How many nights will that
be?

Answer:

5

Step-by-step explanation:

5 x 3 = 15

n x 4 = 4n

3 + 4 = 7

(5 x 3) + (n x 4) = 5(3 + 4)

15 + 4n = 5*7

15 + 4n = 35

4n = 35 - 15

4n = 20

n = 20/4

n = 5

Hence, the value of missing number (n) is 5.

Answer:

36 and -12

Step-by-step explanation:

One of the numbers is x then the second number will be 24-x

\(\frac{x}{24-x} = 3\)

x = 72 - 3x

x = 36

therefore the second number -12

Answer:

x=3

Step-by-step explanation:

x=3, there is no formula or anything...

Answer:

Concept: Caclulating Standard Variables

The inputs 4 and 8 have more than one out, the relation is not a function.

A relation is said to be a function if one input is mapped to one output.

that is, each x-value can only have one y-value.

From the table;

Input, output

4 ----- 1

8 ----- 3

4 ------5

8 ----- 4

4  is an input, it has an output of 1.

4 appeared again as input but this time has an output of 5.

This means one input has more than one output.

Also, 8 is an input, it has an output of 3.

8 appeared again as input but this time has an output of 4.

Which also means one input has more than one output.

Therefore, the relation is not a function.

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Answer:

b

Step-by-step explanation:

Step-by-step explanation:

\(a = \pi {r}^{2} \\ a = \pi {5}^{2} = 78.5 \: {in}^{2} \)

Answer:

The area of this circle is 78.5

Step-by-step explanation:

The area of a circle can be calculated with the equation πr². r stands for "radius", the distance between the center of the circle to any point of its edge which also equals to half of a circles diameter. Since the diameter of this circle is 10 in., its radius is

\(r = d/2 = 10/2 = 5\\\)

Then, we use this to find the area

Area =\(\pi r^2=\pi (5)^2=25\pi=78.5\) (rounded to the first decimal place)

Answer:

Figure STOP is congruent to figure S′T′O′P′.

Step-by-step explanation:

I just took the test

Answer:

Figure STOP is congruent to figure S′T′O′P′.

Step-by-step explanation:

Just finished test and got 100%

Answer:

5^3·g^12·h^9  or 125g^12·h^9

Step-by-step explanation:

The maximum price you can offer for a home is approximately $82,352.94 for a 17% down payment.

To determine the maximum price you can offer for a home, you need to calculate 17% of the total price, which will be your down payment of $14,000.

Let's assume the maximum price you can offer for the home is P dollars.

According to the given information, the down payment requirement is 17% of the total price. So, we can set up the following equation:

\(0.17P = $14,000\)

To solve for P, divide both sides of the equation by 0.17:

P = $14,000 / 0.17

Calculating this expression, we find:

P ≈ $82,352.94

Therefore, the maximum price you can offer for a home in order to have enough money for the 17% down payment is approximately $82,352.94.

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Answer:

B. B x 1/10

Step-by-step explanation:

Lex had b pounds of apples. She gave away 1/10 of the apples. Which of the following expressions represents the weight of apples she gave away?

A. B + 1/10 this would be giving away more than the apples she has

B. B x 1/10, correct

C. B - 1/10 this would be giving 9/10 lb apples away. This represents the apples she kept.

D. B divided by 1/10 Lex does not have this many to give away

Answer:

Look at the picture below

Step-by-step explanation:

Howdy! My name is Christian and I’ll try and help you with this question!

Date: 9/29/20 Time:  8:51 am CST

Answer:

314 cm^2

Explanation:

The formula for the area of a circle is A=3.14r^2

So we have our diameter so to get our radius we just divide that by 2.

Equation:

3.14(10^2)

314

Hope this helps you with your question!

Sincerely,

Christian

cos(tan^(-1)(-2/3)) simplifies to 3√13 / 13.

To evaluate the expression cos(tan^(-1)(-2/3)), we can use the trigonometric identity:

cos(tan^(-1)(x)) = 1 / √(1 + x^2)

In this case, x is -2/3. Substituting the value into the identity:

cos(tan^(-1)(-2/3)) = 1 / √(1 + (-2/3)^2)

Now, let's calculate the value:

cos(tan^(-1)(-2/3)) = 1 / √(1 + 4/9)

                   = 1 / √(13/9)

                   = 1 / (√13/3)

                   = 3 / √13

                   = 3√13 / 13

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The domain and range of the given function is a set of al real numbers and as such;

Domain : (-∞,∞)

Range : (-∞,∞)

We are given the function as f(x)= -3x+7.

In order for us to sketch the graph of this given function, we need to make a function table

Lets assume some random number for x  and find out f(x)

x                f(x) = -3x + 7

-2                 -3(-2) + 7 = 13    

-1                 -3(-1) + 7 = 10

0                 -3(0) + 7 = 7

1                  -3(1) + 7 = 4

We now plot the points as shown in the graph attached

Domain is defined as the set of all x values for which the function is defined while Range is defined as the set of all y values for which the function is defined

In this case, there is no restriction for x  and y and as such the domain and range is a set of all real numbers

Domain : (-∞,∞)

Range : (-∞,∞)

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Complete question is;

Given the following linear function sketch the graph of the function and find the domain and range. ƒ(x) = -3x + 7

Answer:

Step-by-step explanation:

1a. -3 * -4 = 4 * 3

b.7(4+11) = 7(4) + 7(11)

c.6(7-4) = 6(3) - (0) *4

d. -2(6*(-5)) = -2*6*(-5)

2a.-60+4 = -56 = 50

b.-20 / 3 = 6.6 = 6.0 = 6

c. 2.4 = 2.0 = 2

d. 47.19 =40.00 = 40

e. 35.624+ (-4.17) = 31.454 =30.000 = 30

Answer:

5/12

Step-by-step explanation:

3/4 - 1/3

We need to use the common denominator of 12

3/4 * 3/3 = 9/12

1/3 * 4/4 = 4/12

9/12 - 4/12 = 5/12

By subtracting and adding mixed numbers, we can see that at the end she has (5 + 7/8) tubes of paint.

We know that initially Allie had (4 + 3/4) tubes of purple paint, and she sed (2+ 1/4) tubes.

So at this point we need to take the difference between the two mixed numbers, we will get:

(4 + 3/4) - (2 + 1/4) = (4 - 2) + (3/4 - 1/4)

(4 - 2) + (3/4 - 1/4) = 2 + 2/4

2 + 2/4  = 2 + 1/2

Then she founds (3 + 3/8) more. Now we need to add that:

2 + 1/2 + (3 + 3/8) = (2 + 3) + (1/2 + 3/8)

(2 + 3) + (1/2 + 3/8) = 5 + (4/8 + 3/8)

5 + (4/8 + 3/8) = 5 + 7/8

She has 5 + 7/8 tubes of purple paint.

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The slope of this line is -1, which is option (4).The slope of a line can be calculated by dividing the change in y (vertical change) by the change in x (horizontal change). In this case, the change in x is 3.4, and the change in y is -3.4.

The slope of the line of best fit can be obtained by calculating the ratio of the change in the dependent variable, y, to the change in the independent variable, x.

Here, the change in x is equal to 3.4 and the change in y is equal to -3.4.

Slope = change in y / change in x

Substituting the given values:

Slope = -3.4 / 3.4

The numerator and denominator have the same value but opposite signs, resulting in a quotient of -1.

It's important to note that the negative sign indicates a negative slope, meaning the line is sloping downward from left to right.

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Answer:

120

Step-by-step explanation:

Answer:

Formula for area:

\(area = \frac{1}{2} \times( base) \times (height) \\ \\ { \boxed{A = \frac{1}{2}(b)(h) }}\)

according to triangle given;

base, b » 30 ft

height, h » 40 ft

substitute the variables for the equation:

\(A = \frac{1}{2} \times (30) \times (40) \\ \\ A = 30 \times 20 \\ \\ { \boxed{ \boxed{area \: \: A = 600 \: {ft}^{2} }}}\)

If angle BAD=4x° and angle DAC=(3x+8)° then the equation showing angle BAC is equal to (7x+8)°.

Given that angle BAD=4x° and angle DAC=(3x+8)°.

We are required to find the equation showing the angle BAC.

Angle is basically the figure formed by two rays which is called the sides of the angle and sharing a common endpoint called the vertex of the angle.

∠BAD=4x° and ∠DAC=(3x+8)°

To find the equation showing angle BAC we have to just add the two expressions given in the equation.

∠BAC=∠BAD+∠DAC

∠BAC=4x+3x+8

∠BAC=(7x+8)°

Hence if angle BAD=4x° and angle DAC=(3x+8)° then the equation showing angle BAC is equal to (7x+8)°.

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Answer:

The answer is below

Step-by-step explanation:

A function show the relationship between an independent variable and a dependent variable. An independent variable (input) is a variable that does not depend on other variable while a dependent variable (output) is a variable that depends on other variables.

The number of pages read is the dependent variable. Let it be represented as y while the time is the independent variable, let it be represented as x.

Since the  student reads 3 pages of a book every  5 minutes, therefore the function is:

\(y=\frac{3x}{5}\)

Domain is the set of all input (independent variable) while range is the set of all output (dependent variable)

The domain is from 5 minutes to 1 hour, that is 5 minutes to 60 minutes.

Domain = [5, 60]

When x = 60, y = 3(60)/5 = 36

The range = [3, 36]

The simplified expression involving complex numbers is given as follows:

5 + 5i.

Complex numbers are number that have a real and an imaginary part, and are defined as follows:

z = a + bi.

In which:

The basic relation of complex numbers is given as follows:

i² = -1.

The fraction for this problem is given as follows:

(2 + i)(4 - 2i)/(1 + i).

The numerator is simplified as follows:

(2 + i)(4 - 2i) = 8 - 4i + 4i - 2i² = 8 + 2 = 10.

Hence the fraction is of:

10/(1 + i).

To remove the complex number from the denominator, the entire fraction is multiplied by the conjugate of the denominator, hence:

10/(1 + i) x (1 - i)/(1 - i) = 10(1 + i)/(1 - i²) = 10(i + 1)/2 = 5 + 5i.

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Let's write this question as a systems of equations to solve.

x-y=7 (the difference)

x+y=23 (the sum)

Through the process of elimination we get

2x=30

x=15.

With that value of x, we can plug it back into any of the previous equations to get the value of y.

(15)-y=7 (Solve for y)

y=8.

The two numbers are 15 and 8.

Answer:

$37.05

Step-by-step explanation:

If you take 15% and 20% you get (15%+20%) which is 35%, then you take 100%-35% you get 65%, 65% of 57 is 37.05.

Thus Your Answer: $37.05

Answer:

True

True

False

False

True

The graph describes Andres movement in the park relative to the position

of his bike with time.

The correct responses are;

Reasons:

An horizontal line of the graph represents a stationary point on the graph, the x-intercept represent the points when Andre is next to his bike, therefore;

The point with coordinates (17, 1) represent a local minimum of the graph, therefore;

The maximum points are points having higher vertical coordinate values compared to the surrounding points.

The point that gives the highest value of the maximum points, which is at (21, 8.3) is the point at which he was farthest away from the bike.

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Answer: 0.02

Step-by-step explanation: hundreds is 0.0 and its 2 so it would be 0.02

Using place value chart value of \(2\) in the \(304.72\) is quals to \(0.02\) (decimal form).

" Place value is defined as the value represented by each digit of a number on the basis of its position on a number."

According to the question,

Given number ,

\(304.72\)

Place value of all digits in \(304.72\)

Place value of \(4 = ones\)

Place value of \(0 = tens\)

Place value of \(3= hundreds\)

Place value of \(7= tenth\)

Place value of \(2 = hundredth\)

                           \(= \frac{2}{100}\)

                           \(=0.02\) (decimal form)

Hence, value of \(2\) in the \(304.72\) is quals to \(0.02\) (decimal form).

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Answer:

10³

Step-by-step explanation:

10 multiple by 10 and multiple again