A line has a slope of 3 and passes through the point (1, 1). What is its equation in
slope-intercept form?

Therefore ,the answer that states, "Infinitely many solutions, both sides are equivalent expressions" is the one that should be selected in this case.

Equations are mathematical expressions that have two algebraic expressions on either side of an equals (=) sign.  For an unknown quantity represented by an unknown variable, equations can be solved to determine its value.

Here,

The number of solutions is unlimited if there are more variables than linear independent equations.

A single solution or no solution is possible if there are the same number of linearly independent equations and variables.

In the following scenarios, we are at a loss for solutions:

y = x + 3

y = x - 3

this causes:

x + 3 = x - 3

+3 = -3

Consequently, this system lacks a solution.

The first set of equations is

y = x + 5

y = 2x + 5

You can see that there is only one solution for this system because there are only two variables and two linear independent equations.

Thus, "One solution, the graph of these lines should connect at one point" is what we have here. The key idea is (0, 5)

Another system is:

y =x+x+5 = 2x + 5

y = 2x+ 5

Since both equations are identical and there are just two variables in this situation, there are an endless number of solutions to the system.

The answer that states, "Infinitely many solutions, both sides are equivalent expressions" is the one that should be selected in this case.

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The constant of proportionality (p) for the data points on this graph would then be determined as follows: [tex]p = y/xp = 420/6 = 560/8p = 70.[/tex]

following equation: y = px

Where:

p is the constant of proportionality.

y represents the gems collected.

x represents the game levels.

The constant of proportionality (p) for the data points on this graph would then be determined as follows: [tex]p = y/xp = 420/6 = 560/8p = 70.[/tex]

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Isolate one of the two variables in one of the equations.

(- 2, - 4 )

- 4x + 4y = - 8 → (1)

4x - 6y = 16 → (2)

adding (1) and (2) term by term will eliminate x

0 - 2y = 8

- 2y = 8 ( divide both sides by - 2 )

y = - 4

substitute y = - 4 into either of the 2 equations and solve for x

substituting into (2)

4x - 6(- 4) = 16

4x + 24 = 16 ( subtract 24 from both sides )

4x = - 8 ( divide both sides by 4 )

x = - 2

solution is (- 2, - 4 )

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For the given similar triangle the value of x will be 9 inches.

It is required by law to demonstrate that two triangles are identical in shape, although size is not a requirement. The comparable angles are congruent and the ratio of the respective sides is in the same proportions.

It is given that, the unknown side is x, from the observation it is obtained that the two triangles are similar

The derived formula is, because the sides of the similar triangles are all equal in ratio.

8/6=12/x

x=12×6 / 8

x=9 inches

Thus, for the given similar triangle the value of x will be 9 inches.

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(a) This is the factored form of the equation.

(b) The x - intercepts are  (√2, 0) and (-√2, 0).

(c) The value of f(-1) is -8.

What is x - intercept?

We set y = 0 and solve the equation for x to determine the x-intercept. This is due to the fact that the line crosses the x-axis at y=0. If an equation is not in the form y = mx + b, we can still solve for the intercepts by substituting 0 where necessary and then solving for the final variable. Set x = 0 and then solve for y to find the y-intercept.

(a)  Consider, the given equation

f(x) = 8x^2 - 16

First to factor the equation.

Take 8 common from both the terms,

f(x) = 8(x^2 - 2)

This is the factored form of the equation.

(b) Now to find the x- intercept.

Let y = 8x^2 - 16

Set y = 0

So,

0 = 8x^2 - 16

8x^2 - 16 =0

x^2 - 2 = 0

x^2 = 2

x = ±√2

Hence, the x - intercepts are  (√2, 0) and (-√2, 0).

(c) Now to find the value of f(-1)

plug x = -1 in the given equation.

f(-1) = 8(-1)^2 - 16

f(-1) = 8(1) - 16

f(-1) = 8 - 16

f(-1) = -8

Hence, the value of f(-1) is -8.

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After solving the provided question, The value for a in the system of equations below would yield no solutions for the system is [tex]= > a = 18 - 20\frac{y}{x}[/tex]

several equations at once, multiple equations In algebra, you must work together to solve two or more equations (i.e., the solution must satisfy all the equations in the system). For a system to have a unique solution, there must be an equal number of equations and unknowns.

When there are two variables and you are given two pieces of information about how those variables are related, a system of equations is used. To address a number of typical problems, a system of equations can be employed.

[tex]3x-5y=15\\multiply with 6\\18x -30y = 90\\compare the equation with \\ax-10y=90\\then \\18x -30y = ax-10y\\ax = 18x + 10y -30y\\ax = 18x-20y\\a= (18x -20 y) / x\\[/tex]

[tex]= > a = 18 - 20\frac{y}{x}[/tex]

x≠o

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Brace's boat is 225 feet from the bottom of the lighthouse.

What do you mean by trignoemtry?

Trigonometry (“triangles” and “measures”) is the branch of mathematics that studies the relationship between the side lengths and angles of triangles.

Trigonometry is one of the important branches in the history of mathematics that studies the relationship between the sides and angles of right triangles.

Trigonometric ratios of triangles are also called trigonometric functions. Sine, cosine, and tangent are three important trigonometric functions, abbreviated sin, cos, and tan.

It is given that Dontaya is at the top of a lighthouse which is 250 feet above sea level. From the top, the measure of the angle of depression to Brace's boat on the water is 48 degrees

Let Brace's boat is x feet from the bottom of the lighthouse.

Using trignometric ratios,

tan 48 = [tex]\frac{P}{B}=\frac{250}{x}[/tex]

1.11 = [tex]\frac{250}{x}[/tex]

x = [tex]\frac{250}{1.11} = 225.23[/tex] ≈ 225 feet

Therefore, Brace's boat is 225 feet from the bottom of the lighthouse.

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Answer:

400

Step-by-step explanation:

403.1 rounded is 400

The total bill if the student takes nine credit hours at the community college is T = $1415.

One or more variables can be present in a linear equation, but their maximal possible power is only one. The graph of a linear equation will thus always be a straight line. Y = mx + b, where m denotes the line's slope and b its y-intercept, or point of intersection with the y-axis, is how linear equations are expressed. Many real-world situations, such as the connection between two variables or the distance travelled at a constant pace, may be modelled using linear equations. In order to obtain the value of the variable(s) necessary to make the equation true, one must use algebraic methods.

How to solve?

The total bill, t, for a student carrying fewer than twelve credit hours is given by,

T = 155 n + 20, where n represents the hours taken for semester.

The total bill if the student takes nine credit hours is T = 155(9) + 20 = $1415.

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After checking Judi Imhoff's account statement her new balance is $1003.83

What is an account statement?

A statement of accounts is a document that lists all the transactions you have with a certain client during a specific time period. In order to inform their clients of the amount they owe for purchases made during that time period on credit, company owners typically issue statements of accounts to their clients. The manual explains the statement of accounts' contents and demonstrates how to file it for clients.

Your bank may send you a monthly or annual statement if you have a savings account.

account statement for the quarter. All deposits are reflected on the account statement,

withdrawals, as well as interest that is added to your account.

The new balance = Previous Balance + Interest + Deposits - Withdrawals

The new balance =  $717.52  + $4.36 + ($125.00 + $276.95) - $90.00

So, the new balance of Judi Imhoff is  $1003.83

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Answer:

353340 + x + 33

Step-by-step explanation:

real life sum situation

a) The value of 8^1/3 is 2

b) The value of 8^2/3 is 4

c) The value of 16^3/4 is 8

Information given in the problem

a)   the value of 8^1/3

b)  the value of 8^2/3

c) the value of 16^3/4

This equation represents exponents in fraction form and the basics for the calculation is from

a^(b/c) =

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

Rewriting the expression is done as below

8^1/3

=∛8

= 2

8^2/3

= ∛8²

= 2²

= 4

16^3/4

[tex]\sqrt[4]{16}^{3}[/tex]

= 2³

= 8

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Answer: A.-20

Step-by-step explanation:

f(4)=-2(4)^2+12

f(4)=-2(16)+12

f(4)=-32+12

f(4)=-20

Answer: 35%

Step-by-step explanation:

The total amount of candy is 20, and there is 7 green candy, so we got 7/20. Then we multiplied 20 and 7 by 5, so we got 100 and 35, so we got 35/100, which is 35%

Answer:

x = -2/3; -20/9 so A

Step-by-step explanation:

im 100% percent sure:)

Answer:

3

12

12

48

48

192

192

768

768

I hope I helped you

Answer: [tex]y+3=-\frac{3}{5}(x+5)[/tex]

Step-by-step explanation:

The equation of the given line can be rearranged as follows:

[tex]3x+5y=15\\\\5y=-3x+15\\\\y=-\frac{3}{5}x+3[/tex]

Parallel lines have the same slope, so the slope of the line we need to find is -3/5.

Substituting into point-slope form, the equation of the line is [tex]y+3=-\frac{3}{5}(x+5)[/tex].

Answer: 8.6

same side s C and B

Answer: 7.2

Step-by-step explanation:

Since this is a right triangle we can use the Pythagorean theorem to solve for side b.

Pythagorean theorem: a²+b²=c²

Since the side length opposite the right angle is the hypotenuse we plug 11.2 in for C

(8.6)² + b²=(11.2)²

73.96 + b² = 125.44

b²=51.48

b = 7.17495644586

b=7.2

Answer:

Step-by-step explanation:

for the first car  374/17 = 22 m per second

for bus  414/23 = 18  m per second

so the car is moving faster

car is moving faster than (22-18)=4 m per second from the bus

Answer: Car: 22 meters per second, Bus: 18 meters per second. The bus travels faster at 4 meters per second.

Step-by-step explanation: First, you should write a proportional relationship for meters per second so the car would be 374/17 and the bus would be written as 414/23. This is so you can know that you divide 374 by 17 to get 18, and 374 by 17 to get 22. So, you had it backward, the bus is faster by 4 meters per second, I hope this helped, for me (a 7th grader) this was review math, so I hoped this helped you.

Step-by-step explanation:

let the number be x

So,

(x - 6) × 2 = 22

2x - 12 = 22

2x = 34

x = 17

Thus, the answer is 17

Answer:

  400

Step-by-step explanation:

You want to know the number of foxes predicted after 42 years by y = 50·2^x, where x is measured in 14-year periods.

42 years is 42/14 = 3 14-year periods. Using x=3 in the equation, we predict ...

  y = 50·2^3 = 50·8 = 400

foxes.

After 42 years, there will be 400 foxes.

__

Additional comment

It is often convenient to use time measured in 1-year periods. In that case, the equation could be written ...

  y = 50·2^(t/14)

Then t/14 is the number of 14-year periods when t is in years.

Answer:

5590-149,60

Step-by-step explanation:

sum completed

The answer to this Question based on Thales Theorem is x = 8

What is Thales Theorem?

It says that when we join the mid points of two sides of a triangle the line is parallel to third side of triangle then the length of this joined line is half of length of third side

Here in Question given figure is like trapezium but we can extend it to make a triangle then by thales theorem we need to apply on other two sides hence joined line is parallel to third lines hence will be half of it

Solution:

1/2(x) = 2x - 12

x = 2(2x-12)

x = 4x - 24

24 = 3x

x = 8

Hence required value of x is 8

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Answer: [tex]\displaystyle \frac{-1}{3}[/tex]

Step-by-step explanation:

       The slope of a perpendicular line will always be the reciprocal of the original line's slope. Here, the reciprocal of -3 is [tex]\frac{-1}{3}[/tex].

Answer: A trend line is a line on a scatter plot, drawn near points, that approximates the association between the data sets.

Step-by-step explanation:

2. The linear trend in precipitation is the dominant trend type. The nonlinear trends occur much less frequently and more widely scattered over the globe. However, the nonlinear trends are credible patterns of change in precipitation.

3. The trend is the component of a time series that represents variations of low frequency in a time series, the high and medium frequency fluctuations having been filtered out. This component can be viewed as those variations with a period longer than a chosen threshold

4. The trend component represents changes in time-series data that are unpredictable and cannot be associated with a seasonal, cyclical, or random component. OB. The trend component is the long-term increase or decrease in a variable being measured over time.

5. The trend is the component of a time series that represents variations of low frequency in a time series, the high and medium frequency fluctuations having been filtered out.

6. The trend component is the long-term increase or decrease in a variable being measured over time.

Answer:

-7x(to the power of 2)-2x-16

Explanation:

Answer:

$3.45

Step-by-step explanation:

To find the unit price, there must be one gallon of gas

24.82 : 7.2

?  : 1

Cross multiply: 24.85 = 7.2(?)

divide: 3.45138889 = ?

Round: 3.45

Option (C) is the proper choice, both set A and B  

Describe a function.

It is described as a particular kind of relationship, and each value in the domain is associated to exactly one value in the range according to the function.

These are the ordered pairs:

Set A: (-1, 0), (-2, 1), (4, 3), (3, 4) (3, 4)

Set B: (1, 4), (2, 3), (3, 2), (4, 1) (4, 1)

Set C: (2, 1), (3, 2), (2, 3), (1, 4) (1, 4)

Sets A and B are both functions since they both have sets of x values that are all distinct. Set C is not a function because it repeats the x value of 2, while also providing two distinct y values.

As a result, the function option (C) is the proper choice and the set C: (2, 1), (3, 2), (2, 3), and (1, 4) does not represent the function.

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Answer:

a = 16

Step-by-step explanation:

6 = [tex]\frac{a}{4}[/tex] + 2 ( subtract 2 from both sides )

4 = [tex]\frac{a}{4}[/tex] ( multiply both sides by 4 to clear the fraction )

4 × 4 = a , that is

a = 16