7) Keith had 100 dollars to spend on 7 books. After
buying them he had 16 dollars. How much did each book cost?
8) Sally spent half of her allowance going to the movies. She washed the family
car and earned nine dollars. What is her weekly allowance if she ended with
sixteen dollars ?
9) Oceanside Bike Rental Shop charges 15 dollars plus 6 dollars an
hour for renting a bike. Joan paid 57 dollars to rent a bike. How many
hours did she pay to have the bike checked out ?
10) On Monday, one hundred sixty-nine students went on a trip to the zoo. All four
buses were filled and nine students had to travel in cars. How many students were
in each bus?

Answer: x=18 inches.

Step-by-step explanation:

You can use the Pythagorean Theorem for help.

To find the length of the third side of a right triangle, you have to do

10 square + 15 square=x square.

100+225=x square

325=x square

x=  [tex]\sqrt{325}[/tex].

The nearest inch would be x= 18 inches.

Answer:  The correct answer is 18 inches

Step-by-step explanation:

Using the Pythagorean Theorem:

c= [tex]\sqrt{a^2+b^2}[/tex]

c=[tex]\sqrt{10^2+15^2}[/tex]

c=18.02776

c= 18 inches

Answer:

y=-1/2x + 5

Step-by-step explanation:

First, since it is perpendicular, you will change the 2x to a fraction form, -1/2x.
Now, input -2(x) and 6(y) into the respective variables.
So, you will get 6=-1/2(-2)+b
6=1
-1 -1
5=b
So, the equation will be y=-1/2x + 5

Steve walked a total of 1.5 miles from the library to school.

A numerical expression is a mathematical statement written in the form of numbers and unknown variables. We can form numerical expressions from statements.

From the given diagram we can conclude that Steve walked a total of

(1.5 + 2) km = 2.5 km from the library to the school.

Now we know 1 km is equal to 0.6 miles.

∴ 2.5 km = (2.5×0.6) miles = 1.5 miles.

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Answer:

3

Step-by-step explanation:

1) Substitute x with 2

b^8

b^2

2) subtract the index

b^8-2

=b^6

3)b^6 ≠ b^8

therefore, 3 is a lie

The conversion of 30 miles per second into miles per minute is 1800 miles per minute and Mercury will travel 5400 miles in 3 minutes at this rate.

According to the question,

We have the following information:

Mercury travels at a rate of approximately 30 miles per second.

We know that there are 1/60 minutes in 1 second.

So, we have the following expression for conversion:

30/(1/60) miles per minute

30*60

1800 miles per minute

Now, we know that following formula is used to find distance:

Distance = speed*time

Distance = 1800*3

Distance = 5400 miles

Hence, the conversion of 30 miles per second into miles per minute is 1800 miles per minute and Mercury will travel 5400 miles in 3 minutes at this rate.

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The equivalent expression of 4(5+y)  by distributing is 20 + 4y.

In maths, an expression is a combination of numbers, variables, functions (such as addition, subtraction, multiplication or division etc.).

Two expressions are said to be equivalent if they have the same value irrespective of the value of the variable(s) in them.

In other words, two mathematical expressions are said to be equivalent if they yield the same result upon solving them.

Therefore, let's find the equivalent expression of 4(5 + y) by distributing it.

Hence,

4(5 + y)  = 20 + 4y

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Based on the information given; there are outliers in the data and this can be attributed to the relatively large standard deviation relative to the mean.

Outliers as the name implies are data values which significantly deviate from the measures of central tendency such as mean and median.

On this note, the major outliers in the scenario are; the minimum and maximum whose values are $18,000 and $350,000 respectively.

It is noteworthy to also know that the relatively large standard deviation with respect to the mean is an indicator of the presence of outliers in the data.

Ultimately, there are outliers in the data given and this follows from the fact that the mean, Q1, Q3 all range between 50,000 - 58,000 while the outliers can register for them LAS

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Answer:9-0

Step-by-step explanation:sdwew

Answer:

x = 35 degrees

Step-by-step explanation:

3x-11+2x+16 = 180

5x +5 = 180

5x = 180 -5

5x = 175

5/5 x = 175/5

x = 35 degrees

Answer:

B.

Step-by-step explanation:

Answer:

x is equal to 10 times 5 is the ans

The measure of arc AB is 30 degrees , so option B is correct .

What is an arc?

An "arc" in mathematics is a straight line that connects two endpoints. An arc is typically one of a circle's parts. In essence, it is a portion of a circle's circumference.

A curve contains an arc. A circle is the most common example of an arc, yet it can also be a section of other curved shapes like an ellipse.

Main Body:

We know that:

The measure of arc AB is equal to the measure of angle 1 by central angle so,

arc AB = m∠1 = 30° -----> by central angle

we have

m∠1= 30°

therefore,

arc AB = 30°, option B is correct.

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Answer:x=2

Step-by-step explanation:

4(x-2) goes to 4x -8 which then goes to 4x=8 which then divided by 4 equals x=2

Answer:

I think it's =

Step-by-step explanation:

they both equal 32.

Answer:

=

Step-by-step explanation:

6^2 - 2^2

36 - 4

32

4 (6 + 2)

24 + 8

32

Answer

3x−2y=12y=1−2x

re

Answer:

x=12 degrees so c

Step-by-step explanation:

Since they are supplementary angles on transversal, 11x+4x=180.

15x=180 so x=12 degrees.

By solving a quotient, we will see that there are 13.33 servings of pasta on Lois' dish.

We know that one serving of pasta is 0.4 cups, and we know that Lois made a dish with (5 + 1/3) cups of pasta.

To see how many servings are in that dish, we need to take the quotient between the total number of cups used and the cups of a single serving.

So we need to solve:

N = (5 + 1/3)/0.4

We can write the numerator as:

5 + 1/3 = 15/3 + 1/3 = 16/3

The denominator as:

0.4 = 4/10 = 2/5

Then the quotient becomes:

N = (16/3)/(2/5)

N = (16/3)*(5/2) = (16*5)/(3*2) = 80/6 = 13.33

There are 13.33 servings on Lois' dish.

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Answer:

D: y = -4/7x + 7

Step-by-step explanation:

Answer:

[tex]y=-\frac{4}{7}x+7[/tex] or option D

Step-by-step explanation:

y=mx+b is the form where m is the slope and b is the y intercept so just fill those in

y=-4/7x+7

Hopes this helps please mark brainliest

With respect to the proportional relationship table, Harry can run 2.6 miles in 28.6 minutes

What is the proportional relationship?

If all of the ratios of the variables are equal, then there is a proportional link between the two variables. In a proportional relationship, one variable is, in other words, always a constant value multiplied by the other variable. In other words, a relationship is proportional if it can be explained by multiplying each pair of data values by a certain amount.

Solution Explained:

A/Q, the table shows the proportional relationship between distance and time.

Given,

Distance                   Time
0.7                             7.7
1.4                              15.4
x                                 28.6

We know, the ratios are equivalent in a proportional relationship
If we divide, 0.7 and 7.7, we get 11
so taking 11 as the constant of proportionality, we get

x X 11 = 28.6
x = 28.6 / 11
x = 2.6

Therefore, Harry can run 2.6 miles in 28.6 minutes.

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Answer:

Harry can run 2.6 miles in 28.6 minutes

Step-by-step explanation:

A/Q, the table shows the proportional relationship between distance and time.

Given,

Distance                   Time

0.7                             7.7

1.4                              15.4

x                                 28.6

We know, the ratios are equivalent in a proportional relationship

If we divide, 0.7 and 7.7, we get 11

so taking 11 as the constant of proportionality, we get

x X 11 = 28.6

x = 28.6 / 11

x = 2.6

Therefore, Harry can run 2.6 miles in 28.6 minutes.

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The number of these patients on average per day that do not have insurance and thus pay cash price for their visits would be = 504 people.

An insurance coverage is defined as the official coverage an individual has over unforseen and inexperienced financial demands.

The average number of patients seen in a day = 22.4.

The number of months patients where seen = 3 months = 90 days

Total number of patients seen would be= 22.4 × 90 = 2,016

The fraction of patients that has insurance= 3/4

Therefore the fraction that doesn't have insurance= 1/4 of 2,016

= 2,016/4

= 504 people.

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Answer:

x = 5.59

Step-by-step explanation:

tan 90⁰ = 16/x

x = atan 90⁰/16

= 5.5852 (to 5 significant figures)

= 5.59 (to 3 significant figures)

The length of the second side of the triangle is 18 m

What is the perimeter of a Triangle?

The perimeter of a triangle is given by the formula

Perimeter of a triangle = Sum of all three sides

Let the sides of the triangle be a , b , c

Perimeter of a triangle = a + b + c

Given data ,

Perimeter of the triangle = 51 m

Let the first side , second side and third side of the triangle be a , b and c respectively

So , a + b + c = 51 m

And , The second side is twice as long as the first

So , b = 2a

And , The third side is 3 meters less than three times the first

So , c = 3a - 3

Substituting the values of a , b and c in the perimeter equation , we get

a + 2a + 3a - 3 = 51

6a - 3 = 51

Adding 3 on both sides , we get

6a = 54

Divide by 6 on both sides , we get

a = 9 m

Substituting the value of a , we get

b = 2a

b = 2 x 9

b = 18 m

c = 3a - 3

c = 3 x 9 - 3

c = 27 - 3

c = 24 m

So the length of the first side , second side and third side is 9m , 18 m and 24 m respectively

Hence , the length of the second side is 18 m

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The amount of flour that is needed if the recipe in question is tripled, is 6 ³ / ₄ cups of flour

The recipe in question needs 2 ¹ / ₄ cups of flour in order to be completed. However, there is a need to triple the recipe to cater for the people being cooked for.

Going by proportionality, the number of cups of flour will also need to be tripled to ensure that it is the right quantity.

The amount of flour needed will therefore be:

= Flour needed in original recipe x 3

= 2 ¹ / ₄ x 3

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

= 9 /4 x 3

= 6.75 cups

= 6 ³ / ₄ cups of flour

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The given system of equations has no solution.

The general equation of a straight line is -

[y] = [m]x + [c]

where -

[m] → is slope of line which tells the unit rate of change of [y] with respect to [x].

[c] → is the y - intercept i.e. the point where the graph cuts the [y] axis.

The general equation of a quadratic equation is -

y = ax² + bx + c

We have the following equations -

y = x² + 6x + 3

y = 3x - 7​

Plot the graph of both equations and the points of intersection would be the solution set. Refer to the graph below. There are no points of intersection, hence these set of equations have no solution.

Therefore, the set of equations of line -

y = x² + 6x + 3

y = 3x - 7​

have no solution

Therefore, the given system of equations has no solution.

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Answer: 0 and 2

Step-by-step explanation:

m^3-4=0

m(m^2-4)=0

m^2-4=0

m^2=4

m=[tex]\sqrt{4}[/tex]

m= +/- 2

Answer:

Step-by-step explanation:

This diagram represents a negative correlation as the first point has a y value of 5.5 and the last point has a y-value of 2, meaning that there is a rise of -3.5, suggesting a negative correlation"

The solution of the system of functions can be found graphically by locating the point of intersection of the graphs of the different functions.

A function is a rule that maps the elements of one set A to the elements of another set B such that each element of A maps directly to only one element of B.

The solution of an equation, which is the expression of equality of two or more functions is found by locating the point of intersection of the graphs of both functions, which corresponds to the point at which the same input value to both functions produces the same output

The graph of the exponential function y = 2ˣ + 1, (which increases exponentially through the points (-1, 1.5), (0, 2), (2, 5)) and the function y = (1/2)ˣ which decreases exponentially from (-3, 8), (-1, 2), (3, 0.125), intersect at the point given by the solution of the equation;

[tex]2^x + 1= \left(\dfrac{1}{2} \right)^x[/tex]

2ˣ×2ˣ + 2ˣ = 1

[tex]2^{2\cdot x} + 2^x = 1[/tex]

[tex]2^{2\cdot x} + 2^x - 1 = 0[/tex]

Let a = 2ˣ

a² + a - 1 = 0

Therefore;

[tex]a = \dfrac{-1\pm \sqrt{1-4\times 1\times (-1)} }{2} = \dfrac{-1\pm \sqrt{5} }{2}[/tex]

[tex]2^x= \dfrac{-1\pm \sqrt{5} }{2}[/tex]

[tex]x=\dfrac{ ln\left( \dfrac{-1\pm \sqrt{5} }{2}\right)}{ln(2)}\approx -0.694[/tex]

y = 2ˣ + 1

[tex]y = 2^{-0.694} + 1 \approx 1.618[/tex]

Which gives;

The solution of the equation, [tex]2^x + 1= \left(\dfrac{1}{2} \right)^x[/tex]is (x, y) = (-0.694, 1.618)

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By using the given chart, the value of h'(4) would be -16.

What is a chain rule in calculus?

According to the chain rule, the derivative of f(g(x)) is f'(g(x)).g' (x). In other words, it aids in the differentiation of 'composite functions'.

Sin(x²), for example, is a composite function because it can be written as f(g(x)) where f(x)=sin(x) and g(x)=x².

The given function is

                                h(x) = f(g(x))

            Now differentiating the above function with respect to x, we get

                               h'(x) = f'(g(x)) * g'(x)

                     Now find h'(4), so put x = 4, we get

                               h'(4) = f'(g(4)) * g'(4)

                     By using the given table, we can write

                                h'(4) = f'(-1) * 8

                                h'(4) = (-2) * 8

                                h'(4) = -16

Hence, by using the given chart, the value of h'(4) would be -16.

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the coordinates of A after translation is (-2, 0)

What is a co-ordinate?

In geometry, a coordinate system may be a system that uses one or a lot of numbers, or coordinates, to unambiguously confirm the position of the points or alternative geometric components on a manifold like Euclidean space.

Main body:

point A = (-5,3)

According to question:

translated by the rules (x,y)- (x+3,y-3)

we need to add 3 to x coordinate and subtract 3 from y coordinate.

New coordinate of A are (-5+3 , 3-3)

Hence New coordinate of A are (-2,0)

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The equation 56 ÷ 8 + 3² = 2⋅2³  is true which is the correct answer would be option (C).

The equation is defined as mathematical statements that have a minimum of two terms containing variables or numbers that are equal.

As per option (A),

39 − 3⋅6 = 6⋅10/4 + 4

39 - 18 = 6 × 5/2 + 4

11 = 30/2 + 4

11 = 15 + 4

11 = 19

This equation is not true.

As per option (B),

8²−5²=4²−7

64 - 25 = 16 - 7

39 = 9

This equation is not true.

As per option (C),

56 ÷ 8 + 3² = 2⋅2³

56 / 8 + 9 = 2 × 8

7 + 9 = 16

16 = 16

This equation is true.

Therefore, the equation 56 ÷ 8 + 3² = 2⋅2³  is true.

Hence, the correct answer would be option (C).

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