What is the area of a triangle with vertices at (-3, 1), (-6, 5), and (1, 1)?
Enter your answer in the box.

Take the difference between the starting value and the final value to determine the percent change.Subtract the beginning value from its absolute value.Add 100 to the result.

First, figure out how much the two numbers you are comparing differ (rise).After that, multiply the result by 100 and divide the increase by the original number.% growth is calculated as Growth divided by 100.Your response is a percentage decrease if it is a negative amount.

Initial cost = $73.84

Final cost = $72.14

Then

Amount of change = (73.84- 72.14) dollars

                              = 1.7dollars

Then

Percentage change = (1.7/72.14) * 100

                                = 170/72.14 percent

                                = 2.35 percent

So from the above deduction we can easily conclude that the percentage change is 2.35%. I hope the procedure is simple enough for you to easily understand. You can generally use this method for solving similar kind of problems in future without requiring any kind of help from outside.

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a) y=-2780.85+1.447x

b) There are 142.09 voters estimated in the year 2012

Regression analysis is a group of statistical techniques used in statistical modelling to identify relationships between a dependent variable and one or more independent variables. The dependent variable is frequently referred to as the "outcome" or "response" variable, or a "label" in machine learning jargon (often referred to as "predictors," "covariates," "explanatory variables," or "features"). The line (or more complex linear combination) that most closely matches the data in terms of a specified mathematical criterion is found in linear regression, the most common type of regression analysis. For instance, the line (or hyperplane) that minimises the sum of squared differences between the real data and that line is determined when using the ordinary least squares approach (or hyperplane).

x = 11940 / 6 = 1990y = 593.8/6 = 98.9667

let the regression equation be y = a + bx

b = [tex]\frac{ ∑xy - nxy }{∑x^{2} -nx^{2} }[/tex] = [tex]\frac{1182067 - 6 * 1990 * 98.9667}{23760880 - 6 * 1990^{2} }[/tex] = 1.447

a = y - bx = 98.667  -  1.447 x 1990 = -2780.85

The regression equation is

x = 2020 in regression equation

substituting x=2020 in the regression equation

y = 142.09

There are 142.09 voters estimated in the year 2012

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The solution using elimination, for the given system of equation is x = 6 and y = -3.

What is system of equation?

A set or group of equations that you solve all at once is referred to as a "system" of equations. The simplest linear system is the one which has  two equations and two variables. Linear equations (those that graph as straight lines) are easier to understand than non-linear ones.

Given system of equations,

x - y = 9, equation 1

-4x -y = -21, equation 2

Subtracting equation 1 from equation 2 to eliminate y,

-5x = -30,

x = 6

Putting the value of 6 in equation 1,

6 - y = 9

y = -3

Hence, the solution for the given system of equation is x = 6 and y = -3.

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Answer:

  45

Step-by-step explanation:

You want the number described by, "twice the sum of a number and 9 is equal to three times the difference of the number and 9."

Let x represent the number. Then "twice the sum of the number and 9" is ...

  2(x +9)

and "three times the difference of the number and 9" is ...

  3(x -9)

These are equal, so we have ...

  2(x +9) = 3(x -9)

Eliminating parentheses gives ...

  2x +18 = 3x -27

  45 = x . . . . . . . . . . . add 27-2x

The number is 45.

Answer:

Perfect square less than number 47 : 36

Perfect square greater than number 47 : 49

Perect square number closer to 47 : 49

Step-by-step explanation:

The perfect square which is less than 47 is 36 ; 6 x 6 = 36.

The perfect square which is greater than 47 is 49 ; 7 x 7 = 49.

The perfect square number closer to 47 is 49 ; 47 - 36 = 11, 49 - 47 = 2

2 is less than 11 so we know that 49 is the perfect square number closer to 47.

Answer: 80

Step-by-step explanation:

Answer: 125% of 64 would be 80

Step-by-step explanation: First we convert the percent to a decimal. 125%/100 = 1.25. Then we multiply 1.25 by 64 and we would get 80.

Hoped This Helped! Also The Answer Would Obviously Be Above 64 Because Its 125%.

A cyclist rode at an average speed of 15 mph for 30 miles.

It will take 2 hours to cover 30 miles so option (C) is correct.

What are the ratio and proportion?

The ratio is the division of the two numbers.

For example, a/b, where a will be the numerator and b will be the denominator.

Proportion is the relation of a variable with another. It could be direct or inverse.

Given that,

A cyclist rode at an average speed of 15 mph for 30 miles.

So,

15 miles ⇒ hour

Multiply by 2

2 hours ⇒ 30 miles.

Hence "It will take 2 hours to cover 30 miles".

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Answer: Mean:3.9  Range:14  Median:3

Step-by-step explanation:

Answer:

$4

Step-by-step explanation:

Answer:

$4 per pint

Step-by-step explanation:

12 divided by 3 is 4

4$ per pint

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The amount paid each month is, $503.75

What is monthly payment?

The monthly payment is the sum paid each month to cover the loan's outstanding balance over its term. When a loan is obtained, not only the principal, or the sum that was initially lent, but also the interest accrued, must be repaid.

1) As the discount is 7%.

So he pays, 100 - 7 = 93% of the car value

Now, 93% x 6500 = 6045.

This is the value for one year.

From this we have to find the amount paid for each month.

6045/12 = $503.75

Hence, the amount paid for each month is $503.75.

2) Let, the value of Zlatan's house is $749000 after a increase in the value of house.

So, the total percentage increase price is 107% (100 + 7).

We have to fine the initial value of the house.

So,

Initial value of the house = New value of the house / total percentage increase

                                         = 749000/107%

Initial value of the house = $700000

Hence, the initial value of the house is $700000.

3) Assume that Carol's initial weekly wage be $x.

There is 10% decrease in weekly wage.

So,

10% weekly wage = 10% of x = 0.1x

Here,

New wage after 10% decrease = initial weekly wage - 10% of x.

                                                   = x - 0.1x

                                                   = 0.9x

As given the new weekly wage is $306.

We equate $306 and 0.9x.

So

0.9x = 306

     x =  340

Therefore, the initial weekly wages are $340.

Now to find weekly wage when there is 10% increase.

10% of initial weekly wage = (10/100) x 340 = 34

Hence, Wage after 10 % increase = 340 + 34 = $374

4) Let $2000 is placed into a bank account that pays 3% compound interest per year.

We have to find the amount after two years.

Here, P = $2000,  r = 3% = 0.03, n = 2

Amount = P(1 + r)^n = 2000(1 + 0.03)^2 = 2000(1.03)^2 = 2121.80

Hence, $2121.80 will be in the account after 2 years.

5) Let Mary invests $12000 in a savings account. The account pays 1.5% compound interest per year.

We have to find the value after two years.

Here, P = $12000, r = 1.5%, n = 2

So,

Amount = P(1 + r)^n = 12000(1 + 0.015)^2 = 12000(1.015)^2 = 12362.70

Hence, $12362.70 is the value of her investment after 2 years.

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The value of x found by expressing the information as an equation is 100

An equation is a statement usually made using mathematical symbols, numbers and variables, that consists of joining two expressions with an 'equals' sign.

The volume of water in the aquifer = 146,000 ft³

The rate at which water exits the aquifer daily = 500 ft³ per day

Rate at which the aquifer is replenished = x ft³ per day

The time it takes the water to be used up = 1 year

The number of days in a year = 365 days

The value of x can be found by expressing the information as an equation as follows;

The sum of the volume of water in the aquifer and the volume of water that replenishes the aquifer in a year, less the water that exits the aquifer in a year is zero, therefore;

Water in the aquifer; 146,000 - 500 × 365 + x × 365 = 0

-36500 + 365·x = 0

365·x = 36500

x = 36500 ÷ 365 = 100

x = 100

The value of x is 100

The water is replenished at 100 cubic feet per day

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Answer:

(a^2+3a+1) -(3a^2+5a+(-6)) =4a^2-2a+7

Step-by-step explanation:

So, first of all, we can look at the equation and separate them based on the power of each number, and sense we are subtracting, we need to distribute the negative sign all across the second set of numbers.

So, for a^2 we have

a^2-(x) =4a^2

If we subtract a^2 on each side, we get

-(x) =3a^2 but since we don't want a negative, we divide each side by -1 which gives us that the mystery value must equal -3.

x=3a^2

Next, we got to take the second set of like terms

(x)-5a=-2a

We got to add 5a on each side which gives us

x=3a

Finally, we take the last set of like terms

1+-(x) =7

we subtract one from each side to get

-(x) =6

We don't want x to be negative therefore we divide each side by -1 so it will end out

x=-6

The quadratic function that contains the points (-1,1), (0,-2) and (2,4) is f(x) =

2x²-x-2.

To find the quadratic equation we need to put the points in the equation to satisfy it,

The only equation doing it is f(x) = 2x²-x-2 as,

f(x) = 2x²-x-2

For (-1, 1)

1 = 2×(-1)² + 1 -2

1 = 1

Hence (-1,1) satisfies f(x) = 2x²-x-2

For (0, -2)

-2 = 2×(0)² - 0 -2

-2 = -2

Hence (0, -2) satisfies f(x) = 2x²-x-2

For (2, 4)

4 = 2×(2)² -2 -2

4 = 4

Hence (2,4) satisfies f(x) = 2x²-x-2

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No this is incorrect. when a triangle undergoes translation, reflection and rotation congruence of the triangle is still maintained however dilation makes the triangle not to be congruent.

Transformation is a term used in mathematics to refer to the movements made by objects.

Transformation is basically of two major divisions

Non rigid transformation are the transformation where the dimension or size of the object will be different from the image, example is dilation

In rigid transformation, the dimensions of the object is maintained through out the transformation examples of rigid transformation are

Since the transformation types mentioned are all rigid transformation hence all the angles will remain same

Hence we can say that a triangle's congruence is maintained when it is subjected to translation, reflection, and rotation; nevertheless, dilatation renders the triangle incongruent.

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Answer:

-5 X x > 2(-5 X x) +3

-5x >2(-5x + 3)

-5x > -10x + 6

-5x + 10x > 6

5x > 6

x > 6/5

Answer:

4 outfits

Step-by-step explanation:

560-303.02-3.53-28.12=225.33

225.33 -55.45x4=$3.53 remaining

he can buy 4 outfits for $55.45 each

Answer:

AC = 127,26 f    distance from home plate to second base

Step-by-step explanation:

Let call  A , B , C  Home plate,  first base and second base respectively

These three point form a right triangle with legs ( AB  = BC = 90 feet)

we have an isosceles triangle with a right angle and two angles of 45⁰

So we need to compute distance AC (hypotenuse)

AC²  =  AB² + BC²    ⇒  AC²  = 2AB²   ⇒ AC = AB √2

AC = 90 * 1,414

AC = 127,26 f

The slope of a line parallel to the line whose equation 8x + 10y = 60 is -4/5

What is Equation of line ?

A straight line's general equation is y = mx + b, where m denotes the gradient or slope and y = b denotes the point at which the line crosses the y-axis. On the y-axis, this value b is referred to as the intercept.

Given the equation,

8x + 10y = 60

We know, the equation of line is in form of

y = mx + b

m = slope and b = y-intercept

Now, evaluate the given equation

8x + 10y = 60

10y = 60 - 8x

y = (60 - 8x) / 10

y = 60/10 - 8x/10

y  = 6 - 4/5x

y = -4/5x + 6

Which is in the form of equation of line

y = -4/5x + 6

Now, from this slope is - 4/5 and y-intercept is 6

Hence, the slope of a line parallel to the line whose equation 8x + 10y = 60 is -4/5

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Answer:

38.06 but if rounded up 38

Step-by-step explanation:

34,254 divided by 900 equals 38.06

Answer:3 3/4th teaspoons are needed for 5 dozen(60 cookies)

Step-by-step explanation:

Answer:

[tex]3\frac{3}{4} teaspoons[/tex]

Step-by-step explanation:

2 dozens is 24 oatmeal cookies

We divide 1 1/2 by 24 to find how much for each cookie

1 1/2/24

3/2*1/24=3/48=1/16

Now we multiply 1/16 by60

1/16*60/1

60/16

3 12/16

3 3/4 teaspoons

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The years it will take for the hybrid car to depreciates to half of it original value is 4.26 years.

Depreciation is what happens when assets lose value over time until the value of the asset becomes zero, or negligible.

To calculate the amount of years it will take the car to worth half its original value, we use the formula below.

Formula:

Where:

From the question,

Given:

Substitute these values into equation 1 and solve for n

Taking the logarithm of both side,

Hence, the years it will take is 4.26 years.

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19.8 The process is in control as no point is outside the upper or lower control limit.

What does a math centerline mean?

The data for the next six means is 18, 23, 17, 21, 24, and 16.

   The central  line is   k =  20  

Generally the mean of the next six mean is mathematically represented as

        C = 18 + 23 + 17 + 21 + 24 + 16/6

         C = 19.8

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In a case whereby ride-sharing company charges a pick-up fee of $3.50 plus a charge of $4.00 per mile the equation that represents the situation is y = $4.00 x +  $3.50 .

An equation  can be described as the mathematical statement  which is made up of two expressions connected by an equal sign. The concept that will be used is the concept of equation

From the question, pick-up fee of $3.50  was given

charge of $4.00 per mile  was made

Then the equation that models this can be written as y = $4.00 x +  $3.50 .

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The  solution to the system of linear equations  is (3, -1).

A linear equation is an equation in which the highest power of the variable is always 1. It is also known as a one-degree equation. . The standard form of a linear equation in two variables is of the form Ax + By = C. Here, x and y are variables, A and B are coefficients and C is a constant.

2x + 3y = 3

7x - 3y = 24

By adding both the linear equations,

9x = 27

x = 27/9 = 3

x = 3

Substitute the value of x in either of the equations

2 (3) + 3y = 3

6 + 3y = 3

3y = -3

y=-1

Therefore, the solution to the system of linear equations  is (3, -1).

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