For which inequality is x= 5 a solutionx < 2x > 9x < 18x > 42

Answer:

45f.

Step-by-step explanation:

home is 60f.cold

we turn heat in order to raise the temprature by15

and 60minus 15 is 50

Answer:

75f

Step-by-step explanation:

since you raise the temperature you need to add those 2numbers together so 60+15=75f degrees

Answer: 19.6 feet

Step-by-step explanation:

Using the Pythagorean theorem,

[tex]x^2 +(x+6)^2 =48^2\\\\x^2 +x^2 +12x+36=2304\\\\2x^2 +12x-2268=0\\\\x^2 +6x-1134=0\\\\x=\frac{-6 \pm \sqrt{6^2 -4(1)(-1134)}}{2(1)}\\\\x \approx 30.8 \text{ } (x > 0)\\\\\implies x+(x+6) \approx 67.6\\\\\therefore (x+(x+6))-48 \approx 19.6[/tex]

Mode

2 x 5 = 10

6 x 5 = 30

5 x 5 = 25

3 x 5 = 15

7 x 5 = 35

8 x 5 = 40

9 x 5 = 45

2 x 5 = 10

4 x 5 = 20

7 x 5 = 35

4 x 5 = 20

7 x 5 = 35

The mode is 35 because it is repeated 3 times.

The value of x and y of system of equations are 3 and -1. A group of equations involving one or more variables is known as a system of equations.

A group of equations comprising one or more variables is known as a system of equations. The variable mappings that satisfy each component equation, or the points where all of these equations cross, are the solutions of systems of equations.

A collection of values for a variable that simultaneously fulfil each equation is the solution to a system of equations. A system of equations must be solved by identifying all possible sets of variable values that make up the system's solutions.

Solution for x-y=4, 2x+y=5

x - y = 4

2x + y = 5

Substitute 4 = x+ y

2(4+y) + y =5

Simplify

8 + 3y = 5

Isolate y for 8 + 3y = 5 ; y = -1

For x = 4 + y

Substitute y= -1

x= 4-1

x=3

The solutions to the system of equation are :

x =3 , y = -1

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The equation which represents total pay P and the number of copies sold N is P = 2300 + 90N and the total pay for 22 copies sells will be $4280.

How to form an equation?

Determine the known quantities and designate the unknown quantity as a variable while trying to set up or construct a linear equation to fit a real-world application.

In other words, an equation is a set of variables that are constrained through a situation or case.

Total pay = base salary + additional

Total pay = base salary + number of copies × per copy price

P = 2300 + N × 90

P = 2300 + 90N

Now for 22 copies

P = 2300 + 90(22) = $4280

Hence, the equation which represents total pay P and the number of copies sold N is P = 2300 + 90N and the total pay for 22 copies sells will be $4280.

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Answer: 9/20 or 0.45 as a decimal :)

a. The images coincide because rotations preserve rays.

b. Transformations preserve distances, so the image of point A and point E are the same distance along the same ray from C and they have to coincide.

c. The rotation would also make the image of B equal with D. So there is a rigid motion that takes CBA onto CDE.

Transformations are classified into rigid and non-rigid, according to the definitions presented as follows:

In this problem, the transformation was a rotation of triangle BAC over vertex C, generating triangle EDC.

A rotation is a rigid transformation, hence the distances are preserved.

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Answer:

The answer will

be 0

Step-by-step explanation:

=9+4×8-8

=13×0

=0

Solution:

Given:

An exponential function is of the form:

To get the exponential function for the relation;

Part A:

Relating this to the parameters given:

The exponential function that models the problem is;

Part B:

On the twenty-third day,

Therefore, he would have saved 4,194,304 pennies on the twenty-third day.

Answer:

134.375

Step-by-step explanation:

43 is 32% of what number

32% = 0.32

43/0.32 = 134.375

The amount invested at 8% is $26,333.33.

The amount invested at 2% is $8,666.66.

What is simple interest?

Simple compound interest is a method of calculating the amount of interest charged for a fixed rate and total over a fixed period of time. With simple interest, the principal is always the same, unlike compound interest, which adds interest to the previous year's principal to calculate the next year's interest.

                        interest = principal * rate * time

Given data:

             Principal  = $35000

             Interest = $2280

             time = one year.

Let 'x' represent the amount invested at 8%, then '35000-x' represents the amount invested at 2%.

                         interest = principal * rate * time

                         2280 = 0.08x + 0.02(35000 - x)

                         2280 = 0.08x + 700 - 0.02x

                         2280 - 700 = 0.06x

                         x = 1580/0.06

                         x = 26333.33

and

          35000 - x = 35000 - 26333.33

                         x = 8666.66

Hence, The amount invested at 8% is $26,333.33.

             The amount invested at 2% is $8,666.66.

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Answer:

[tex]a_n=n^2 + 3[/tex]

Step-by-step explanation:

To find the nth term of a quadratic sequence, we need to determine the quadratic function that generates the sequence.

Given quadratic sequence:

4, 7, 12, 19, 28, ...

Begin by calculating the first differences between consecutive terms:

[tex]4 \underset{+3}{\longrightarrow}7 \underset{+5}{\longrightarrow} 12\underset{+7}{\longrightarrow} 19\underset{+9}{\longrightarrow} 28[/tex]

As the first differences are not the same, we need to calculate the second differences (the differences between the first differences):

[tex]3\underset{+2}{\longrightarrow} 5 \underset{+2}{\longrightarrow} 7\underset{+2}{\longrightarrow}9[/tex]

As the second differences are the same, the sequence is quadratic and will contain an n² term.

The coefficient of the n² term is half of the second difference.

As the second difference is 2, the coefficient of the n² term is 1.

Now we need to compare n² with the given sequence (where n is the position of the term in the sequence).

[tex]\begin{array}{|c|c|c|c|c|c|}\cline{1-6}n&1&2&3&4&5\\\cline{1-6}n^2&1&4&9&16&25\\\cline{1-6}\sf operation&+3&+3&+3&+3&+3\\\cline{1-6}\sf sequence&4&7&12&19&28\\\cline{1-6}\end{array}[/tex]

We can clearly see that the algebraic operation that takes n² to the terms of the sequence is add 3.

Therefore, the expression to find the the nth term of the given quadratic sequence is:

[tex]\boxed{a_n=n^2 +3}[/tex]

Answer:

$104.14

Step-by-step explanation:

5.2% of $98.99

= $5.15

Price of the shoes + tax

= $98.99 + $5.15

= $104.14

The inequality represented by the graph attached is y > -3x + 6

An equation is an expression showing the relationship between two or more numbers and variables.

An inequality is used to show that two numbers or variables are non equal to each other.

The graph attached shows a straight line inequality. It passes through the point (0, 6) and (2, 0). Hence, the straight line has the equation:

y - 6 = [(0 - 6)/(2 - 0)](x - 0)

y - 6 = -3(x)

y = -3x + 6

Based on the dotted line and the shaded region, the inequality is y > -3x + 6

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Answer: ∠WZY=150°

Step-by-step explanation:

Analysis :

ΔWXY is an isosceles triangle

perpendicular to WX intersecting:

XY at A

∠XWA = 21°

∠WXA = 90°-21° = 69°

Now, ΔXYZ is equilateral,

∠XYZ = ∠YXZ = 60°

Then,

∠WXZ = ∠WXA - ∠YXZ

= 69°-60°

= 9°

Since the angles of a triangle = 180°

∠WZY = ∠WZX = 180° - ∠XWA - ∠WXZ

= 180° - 21° - 9°

= 150°

Answer:

4 shots were scored

Answer:

exponents / the little x next to the 5

Answer: You move "x"s to one side, numbers to another and so the first operation is moving +4 to another side and making it -4

The value of equation is  x = [tex]2\sqrt{2} and x = - 2\sqrt{2}[/tex] and method is used "Direct keeping Method".

Given,

In the question:

The equation is :

2[tex]x^{2}[/tex] – 7 = 9

To solve the above equation and explain which method to solve the equation?

Now, According to the question:

2[tex]x^{2}[/tex] – 7 = 9

2[tex]x^{2}[/tex] = 9 + 7

2[tex]x^{2}[/tex] = 16

[tex]x^{2}[/tex] = 8

x = [tex]2\sqrt{2} and x = - 2\sqrt{2}[/tex]

{There is no one- time item}

The method is used for solving equation is the "Direct keeping Method"

Hence, The value of equation is  x = [tex]2\sqrt{2} and x = - 2\sqrt{2}[/tex] and method is used "Direct keeping Method".

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Answer:

Use the square root property of equality.

There is no x term.

Add and divide to isolate x^2.

Step-by-step explanation:

Answer:  360,000

Reason:

Think of 360 as 360.0

We move the decimal point 3 spots to the right to get to 360,000.0 or simply 360,000; this movement of 3 to the right is directly because of the exponent over the 10.

The 10^3 represents "thousand", so "360 x 10^3" is "360 thousand" = 360,000.

A false statement could be that

"the maximum height attained by the diver was 20 feet

The function given is,

The graph of the function will be shown below

a) The zeros of a function, also referred to as roots or x-intercepts, occur at x-values where the value of the function is 0 (f(x) = 0).

Hence, from the graph above the zeros of the function is at

b) The function's domain is

c) The function's long-run behaviour is that:

Hence, the answer is

Let  p be the function that gives the cost , in dollars, of producing 1 watt of solar energy years after 1977. Here is a table showing the values of  from 1977 to 1987.

t         p(t)                       p(10)-p(0)

0 80                          p(10)

1 60                          p(10)- p(0)/10-0

2 45                            p(10-0)

3 33.75

4 25.31

5 18.98

6 14.24

7 10.68

8 8.01

9 6.01

10 4.51

Which phrase best captures the average rate of change in the price of solar energy between 1977 and 1987?

Which phrase best captures the average rate of change in the price of solar energy between 1977 and 1987?

Which equation best captures the yearly average increase rate of solar prices between 1977 and 1987?

This discussion aims to help students remember what average rate of change for a function means and how it is computed. Select students to explain what each expression's value in this context means. For instance, the cost difference for a solar cell between 1977 and 1987 is represented by the formula p(10)- p(0), whereas the percent change between 1977 and 1987 may be calculated as p(10)/p(0). The fact that the real phrase for the average rate of change, p(10)-p(0)/10-0=-7.55, reveals that the price declined by -$7.55 on average per year since the expression considers the whole difference in price between the 1977 and 1987 divided by the total number of years that passed.

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The dimension of the rectangle that has the maximum area is 7.5 by 7.5 feet.

Let the length of the rectangular field be x and the width be y

Now the perimeter is 30

Therefore 2(x + y)=30

or, x + y = 15

or, y = 15 - x

Area of the rectangle = xy

Now we substitute the value of y

area = x ( 15 - x ) = 15x - x²

Now for the maximum area we have to differentiate the area function.

f(x) = 15x - x²

f'(x) = 15-2x

Now the differentiated function is equated to 0 to get the value of x for which the area is  maximum.

15-2x = 0

or, x =7.5

therefore y -= 15 - x = 1 5 - 7.5 = 7.5 feet.

Hence for the area to be maximum the dimension of the field should be 7.5feet by 7.5 feet .

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Answer:

y=1/3x-3

Step-by-step explanation:

The number of gallons of paints that will be made if 28 drops is used is 20 gallons

A rate is a ratio that compares two different quantities which have different units. For example, if we say John types 50 words in a minute, then his rate of typing is 50 words per minute. The word "per" gives a clue that we are dealing with a rate.

The total number of drops used to make 5 gallons is 7drops, i.e 4+3=7

this means to make 1 gallon 5/7 drops of color will be used

Therefore for 28 drops , 5/7×20 gallons will be made

= 20gallons

Therefore the gallons made with 28drops is 20gallons.

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Answer:

Any value other than 3 will work.

functionWe have:

The functions f and g have the same y-intercept, this is (0,4).

And the behavior as x approaches infinity is:

In the function f, value of the function approaches - 1.

In the function g, value of the function approaches - 1, too.

Therefore, they have the same behavior.

Answer: they have the same y-intercept and the same behavior as x approaches infinity.

Solution

where:

F=future value = 45000

P=present value

r=rate (as a decimal) = 7%=0.07

n=number of compounding periods per year = 1

t=number of years = 6

Therefore the present value deposited today = $29,985.40