Determine when the function is positive, negative, increasing, or decreasing.

Answer:

10% of $520

=$52

Money made this week :

$520+$52=$572

Saving:

10% of $572

=$57.2

Money left:

$572-$57.2=$514.8

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Answer: We have been given that,

     Oliver's weekly earnings = $520

      His earnings this week = 10% of $520 +$520

                                               = $520+$52= $572

As he saves 10% of his weekly earnings so he would have been left with

= 10% of $572

= $57.2

So, he only has $52.7 left for spending money this week

Step-by-step explanation:

Answer:

The population is expected to grow at a rate of 1.36% each year. What is the population of the town in 2006? Round your answer to the nearest whole number.

Step-by-step explanation:

For the given points (6, y) and (-8, 4) having slope = 1/7 the value of y = 10.

What is the slope of a line?

A line's slope, also known as its gradient, is defined as the value of a line's steepness or direction in a coordinate plane. Slope can be calculated using various methods given a line equation or the coordinates of points on a straight line.

If P(a, b) and Q(c, d) are two given points on a coordinate plane, then the slope of line PQ can be computed using the formula

                      [tex]Slope(m)=\frac{d - b}{ c - a}[/tex]

The given points are (6, y) and (-8, 4).

and the slope of the line is given as m = 7.

By using the slope of a line formula, we get

                       [tex]m = \frac{8-y}{-8-7}\\\\ \frac{1}{7}= \frac{8-y}{-8-7}\\\\\frac{1}{7}= \frac{8-y}{-14}\\\\\\8-y=-2\\y=8+2\\y=10[/tex]

Hence,  the value of y is 10.

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The values of x and y are 2 and -7 respectively, this forms an ordered pair of (6,-7) and (2,1).

Given the equation and ordered pair the question;

To determine, the y-value, plug the x-value into the equation and solve for y.

y = -2x + 5

Plug in x = 6

y = -2( 6 ) + 5

y = -12 + 5

y = -7

Determine the x-value by plunging in the y-value into the equation and solve for x.

y = -2x + 5

Plug in y = 1

1 = -2x + 5

1 + 2x = 5

2x = 5 - 1

2x = 4

x = 4/2

x = 2.

Therefore, the ordered pair are (6,-7) and (2,1).

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According to the scatterplot (graph) provided, the weight for someone who is 1.4 meters tall is predicted to be 34.8 kilograms.

A scatterplot is also referred to as scatter diagram, scattergram, or scatter chart and it can be defined as a type of graph which is used for the graphical representation of the values of two (2) variables, with the resulting points showing any association between the data set.

For this exercise, the height (M) was plotted on the x-axis of the scatterplot (graph) while the weight (in kg) would be plotted on the y-axis of the scatterplot (graph).

From the scatterplot which models the relationship between the height (M) and weight (in kg) of a person, an equation for the line of best fit is given by:

Weight, kg = -114.3 + 106.5M

When M = 1.4 meters, we have the following weight:

Weight, kg = -114.3 + 106.5(1.4)

Weight, kg = -114.3 + 149.1

Weight, kg = 34.8 kg.

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Complete Question:

According to the graph provided, the weight for someone who is 1.5 meters tall is predicted to be close to ____ kilograms.

One bag of cat food costs $6 and one bag of dog food costs $9.

What is system of equations?

A finite set of equations for which common solutions are sought is referred to in mathematics as a set of simultaneous equations, often known as a system of equations or an equation system.

The problem states that c equals the cost of bag of cat food and d equals the cost of bag of dog food.

Last week she paid $117 for 6 bags of cat food and 9 bags of dog food.

Therefore, the equation becomes,

6c + 9d = 117         ..(1)

This week she paid $87 for 4 bags of cat food and 7 bags of dog food.

Therefore, the equation becomes,

4c + 7d = 87         ..(2)

Now to solve the system of equations

To solve the first equation for c.

6c + 9d = 117

6c = 117 - 9d

[tex]c = \frac{117}{6}-\frac{9d}{6}[/tex]

Plug value of c in equation (2).

[tex]4(\frac{117}{6}-\frac{9d}{6}) +7d = 87\\78 - 6d + 7d = 87\\d = 87-78\\d = 9[/tex]

Plug d = 9 in equation (1)

6c + 9(d) = 117

6c + 9(9) = 117

6c + 81 = 117

6c = 117 - 81

6c = 36

c = 6

Hence, one bag of cat food costs $6 and one bag of dog food costs $9.

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The value of x so the the the function has the given value is as follows:

A function relates an input to an output.

In other words, a function is a special relationship among the inputs and their outputs codomain) where each input has exactly one output value.

Therefore, let's find the value of x so that the function has the given values.

m(x) = -3/5x - 4;  m(x) = 2

let's find the value of x when  m(x) = 2

2 = - 3/5x - 4

2 + 4 = - 3/5x

6 = - 3/5 x

cross multiply

-3x = 30

x = 30 / - 3

Hence,

x = - 10

w(x) = 5/6x - 3; w(x) = -18

let's find the value of x when  w(x) = -18

- 18 = 5/6x - 3

- 18 + 3 = 5 / 6 x

- 15 = 5 / 6 x

5x = - 90

x = -90 / 5

Hence,

x = - 18

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Answer:add 5 to both sides

Step-by-step explanation:

The first step to find the quotient of a long division problem is to Divide the terms with highest degreee

A quotient is a quantity produced by the division of two numbers. For example 16/4 ,the number that is being divided (in this case, 16) is called the dividend, and the number that it is being divided by (in this case, 4) is called the divisor. The result of the division(5) is the quotient.

The step that is needed to find a quotient of a division are

1.Divide the terms with the highest degree

2.Multiply terms by the divisor

3.Place the result in the quotient

4. Subtract the product from the dividend

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I hope this helps. Have a great rest of your day!

Answer:

20 mph

Step-by-step explanation:

If it took the car originally 12 minutes to travel the road with an average speed of 60 mph. Than you would just divide the average speed by three because it is taking 3 times the amount of time than it would originally.

36/12=3

60/3=20

20 mph

The equivalent quotient to -5/8 are; -5/8 and .5/-8.

The correct answer options are options A and C

A quotient is the number resulting from the division of one number by another. For instance, the quotient of 12 divided by 4 is 3.

A divisor number or expression that another is to be divided by. For instance, in "42 ÷ 3" the divisor is the 3.

Dividend is a number or expression that is to be divided by another. For instance, In "42 ÷ 3" the dividend is the 42.

Complete question:

Given options:

A. -5/8

True

B. 5/8

False

C.5/-8

True

D. -(5/-8)

False

E. -5/-8

False

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The equation of the parabola exists y = 3/80(x - 20)² - 15

In the coordinate plane, a parabola exists algebraically represented using the standard equation. A parabola's general equation exists written as,

y = a(x - h)² + k

where (h, k) signifies the vertex.

y² = 4ax is the typical equation for a normal parabola.

substitute the values in the above equation, we get

y = a(x - 20)² - 15

simplifying the above equation, we get

0 = a(0 - 20)² - 15

0 = 400a - 15

a = 15/400

a = 3 / 80

Therefore, the equation of the parabola exists y = 3/80(x - 20)² - 15.

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Equation of the perpendicular line in slope intercept form is [tex]y = \frac{5}{2}x + 2[/tex]

Option A is correct

What is equation of line in slope intercept form?

The most general form of equation of line in slope intercept form is given by y = mx + c

Where m is the slope of the line and c is the y intercept of the line.

Slope of a line is the tangent of the angle that the line makes with the positive direction of x axis.

If  [tex]\theta[/tex] is the angle that the line makes with the positive direction of x axis, then slope (m) is given by

m = [tex]tan\theta[/tex]

The distance from the origin to the point where the line cuts the x axis is the x intercept of the line.

The distance from the origin to the point where the line cuts the y axis is the y intercept of the line.

Here, the given line is

2x + 5y = 10

5y = -2x + 10

[tex]y = -\frac{2}{5}x + \frac{10}{5}\\y = -\frac{2}{5}x + 2[/tex]

Slope of the given line is [tex]-\frac{2}{5}[/tex]

Slope of the line perpendicular to this given line is [tex]\frac{5}{2}[/tex]

The line passes through (-2, -3)

Equation of the required line

[tex]y - (-3) = \frac{5}{2}(x - (-2))\\y + 3 = \frac{5}{2}(x + 2)\\2y + 6 = 5x + 10\\2y = 5x + 10 - 6\\2y = 5x + 4\\y = \frac{5}{2}x + \frac{4}{2}\\y = \frac{5}{2}x + 2[/tex]

Equation of the perpendicular line in slope intercept form is [tex]y = \frac{5}{2}x + 2[/tex]

Option A is correct

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Answer: (4,-3)

Step-by-step explanation:

4x+5y=1       (1)

3x-2y=18     (2)

Multiply both parts of equation (1) by 2 and both parts of equation (2) by 5:

8x+10y=2

15x-10y=90

Sum these equations:

23x=92

Divide both parts of the equation by 23:

x=4

Substitute the value of x=4 into equation (1):

4(4)+5y=1

16+5y=1

16+5y-16=1-16

5y=-15

Divide both parts of the equation by 5:

y=-3

Thus, (4,-3)

Answer:

18.0833333333

Step-by-step explanation:

online calculator

Answer:

I believe the first one is log8(5/3), the second is log5(3), and the third is -2log2(5)

Step-by-step explanation:

I got this by applying the properties of logarithms which are:

logₐ mn = logₐ m + logₐ n (product property)

logₐ m/n = logₐ m - logₐ n (quotient property)

logₐ mn = n logₐ m (power property)

logb = (log꜀ a) / (log꜀ b) (change of base property)

The circumference of the circle is 21.98cm and the area of the circle is 38.465 square cm.

Circumference of the circle:

The Circumference (also known as) perimeter of circle = 2πR

where,

R is the radius of the circle

π is the mathematical constant with an approximate value is 3.14.

Area of circle:

The formula to find the area of the circle is;

A = πr²

Where r represents the radius of the circle.

Given,

The diameter of the circle is 7 cm.

Here we need to find the circumference and the area of a circle.

Here we have the value of diameter, in order to find the circumference we have to find the value of radius that can be derived by dividing the diameter by 2.

So, the radius is

=> 7/2 = 3.5

Now the circumference of the circle is calculated as,

C = 2 x π x 3.5

When the value of π = 3.14

Therefore, the circumference of the given circle is,

=> C = 2 x 3.14 x 3.5

=> C = 21.98

Now, the area of the circle is,

=> A = π x (3.5)²

=> A = 3.14 x 12.25

=> 38.465

Therefore, the area of the circle is 38.465 square cm.

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Answer:

Step-by-step explanation:

You subtract 583 from 400 (400-583)

Then you get 183

The number of pavers required is 961.

The area is the region defined by an object's shape. The area of a shape is the space covered by a figure or any two-dimensional geometric shape in a plane.

Given data

A driveway is being surfaced with concrete pavers in the shape of regular hexagons. If the driveway is a 24-by-26-foot rectangle with pavers 6 inches wide across the flats.

We have to determine how many pavers are needed

We know that area of a regular hexagon

A = (3√3)/2 a^2

= (3√3)/2 〖(6)〗^2

= (3 x 1.732)/2  x 36

= 93.528 sq.inches

Now area of rectangle

= l x w

= 24 x 26 x (12)2        (1feet = 12 inches)

= 89856 sq.inches

Now pavers required

= 89856/93.528

= 960.73

= 961

Therefore the number of pavers required is 961.

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Answer:

5 bath towels

2 washcloths

Step-by-step explanation:

160 = 2⁵ × 5

64 = 2⁶

HCF= 2⁵ = 32

160 ÷ 32 = 5

64 ÷ 32 = 2

Answer:

Step-by-step explanation:

The mean of the data is 3.85 using the stem-and-leaf plot.

It means the average feet that the heavy ball was thrown is 3.85 feet, which is the typical number.

To find the mean of a data set that is represented by a stem-and-leaf plot, first, list out all the data values that are represented on the stem-and-leaf plot, add all the values, and divide by the number of values that were represented on the stem-and-leaf plot.

Given the stem-and-leaf plot, using the key, the data points represented are:

2.0, 2.1, 2.4, 3.1, 3.2, 3.6, 4.1, 4.3, 4.7, 5.1, 5.1, 6.5

Mean = [2.0 + 2.1 + 2.4 + 3.1 + 3.2 + 3.6 + 4.1 + 4.3 + 4.7 + 5.1 + 5.1 + 6.5]/12

Mean = 46.2/12

Mean = 3.85 feet

The mean of 3.85 feet means that the average distance that the heavy ball was thrown in feet is 3.85.

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Answer:

The graph of a function f is the set of points which satisfy the equation y = f(x). ... However, of these two answers, only x = −2 fits in the domain.

Step-by-step explanation:

120 ounces of 35% salt and 90 ounces of water is needed to obtain 210 ounces of a mixture that is 20% salt.

An equation shows the relationship between two or more numbers and variables.

Let x represent the amount of water and y represent the amount of 35% solution.

She wants to obtain 210 ounces of a mixture that is 20% salt. Hence:

x + y = 210   (1)

Also:

0% of x + 35% of y = 20% of 210

0.35y = 42

y = 120

x + y = 210

x + 120 = 210

x = 90

120 ounces of 35% salt and 90 ounces of water

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Answer in multiple forms depending on what needed

Answer:

c = 3

Step-by-step explanation:

48- (3c+4)=4(c+5)+3

48-3c-4=4(c+5)+3 Distributed the - sign

48 -3c -4= 4c+20 +3 Distributed the 4

44-3c =4c+23 Combined like terms

21-3c=4c Subtract 23 from both sides

21=7c Add 3c to both sides

3=c

By using unitary method it is obtained that -

Scale used my Colton = 1 : 500

What is unitary method?

Unitary method is the process in which the value of single unit can be calculated from the value of multiple unit and the value of multiple unit can be calculated from the value of single unit. Sometimes Value of single unit can be less than the value of multiple unit. For example - The relation between the cost of a commodity and the quantity of the commodity

Sometimes Value of single unit can be more than the value of multiple unit. For example - The relation between the number of men and the number of days taken by those men to do a certain job.

Here unitary method is used

18 mm long field in the drawing is equivalent to 9000 mm long field in real

1 mm long field in the drawing is equivalent to [tex]\frac{9000}{18}[/tex] mm long field in real

1 mm long field in the drawing is equivalent to 500 mm long field in real

Scale used by Colton 1 : 500

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