What is the image point of (-12, —8) after the transformation R270 oD ?

The general form of the equation of a line is:

y=mx+b

Where m is the slope of the line and b is the intercept with the y axis.

Since the intercept is the point where the line intersects the y-axis, if a line goes through the origin, then is intercept equals 0, b = 0, which is the case for the first and last line, then, their equation looks like this:

y=mx

When the slope (m) is a positive number, the line goes up as x increases, when the slope (m) is negative, the line goes down as x increases, then the equation of the first line must be: y=x and y= -x for the last line.

For the second line, we can see that it crosses he axis at y= -3, then its intercept equals -3, that's why the equation of this line is y = x - 3

Given that the triangles are similar, then their corresponding sides are in proportion, that is,

Substituting with data and solving for BX:

We have the next information

4 cups of water

1 cup lemon concentrate

in total, we have 5 cups of lemonade

5 ----- 100%

1 ------ x

x is the percentage of lemon concentrate

the percentage of lemon concentrate in the lemonade is 20%

Answer:

[tex]y-10=\dfrac{1}{3}(x-9)[/tex]

Step-by-step explanation:

[tex]\boxed{\begin{minipage}{4.4cm}\underline{Slope Formula}\\\\Slope $(m)=\dfrac{y_2-y_1}{x_2-x_1}$\\\\where $(x_1,y_1)$ and $(x_2,y_2)$ \\are two points on the line.\\\end{minipage}}[/tex]

To find the equation of a line that passes through two given points, first find its slope by substituting the given points into the slope formula.

Define the points:

Substitute the points into the slope formula:

[tex]\implies m=\dfrac{9-10}{6-9}=\dfrac{-1}{-3}=\dfrac{1}{3}[/tex]

Therefore, the slope of the line is ¹/₃.

[tex]\boxed{\begin{minipage}{5.8 cm}\underline{Point-slope form of a linear equation}\\\\$y-y_1=m(x-x_1)$\\\\where:\\ \phantom{ww}$\bullet$ $m$ is the slope. \\ \phantom{ww}$\bullet$ $(x_1,y_1)$ is a point on the line.\\\end{minipage}}[/tex]

To find the equation in point-slope form, simply substitute the found slope and one of the given points into the point-slope formula:

[tex]\implies y-10=\dfrac{1}{3}(x-9)[/tex]

The ratio between MD and DC IS

The ratio of ON to LN

The ratio CM to CD

The ratio of OL to LN

To make the

Answer:

The answer will be D because you have to look very close and make sure the 1 is on the x-intercept and not the y-intercept.

Answer is the first option, a reflection over the y-axis

Answer:

6 +2v

Step-by-step explanation:

This is distributive property. That means you will multiply each term inside the parentheses by the term on the outside of the parentheses.

2(3 + v)

2(3) + 2(v)

6 +2v

In this case, we'll have to carry out several steps to find the solution.

Step 01:

Data

Expression:

5(6 + 4x)

Step 02:

5(6 + 4x)

A.

5 = factor 1

(6 + 4x) = factor 2

B.

5 = factor 1 ( 1 term)

(6 + 4x) = factor 2 (2 terms)

C.

variable term: 4x

coefficient = 4

That is the full solution.

The function representing the volume of the rectangular prism is given to be:

Since we are expected to find the volume using the graph, we can prepare a table of values for the function using values of h as integers from 1 - 5, such that:

The completed table is shown below:

Hence, we can plot these points on a graph using a graphing calculator for ease of work. This is shown below:

The maximum volume of the prism is represented by the highest point on the graph. The graph's highest point is at:

The corresponding value for the volume as can be seen on the graph is:

This is the maximum volume of the prism.

To the nearest cubic foot, the maximum volume of the rectangular prism is 24 cubic feet.

The equation of the population function is is P = 224(1.17)ⁿ

From the question, the given parameters are:

The above parameters imply that the rate of change of the population every year is

Rate = Population after one year/Initial population

Substitute the known values in the above equation

So, we have

Rate = 263/224

Evaluate the quotient

Rate = 1.17

The exponential function can be represented as

P = Initial population * (Rate)ⁿ

So, we have

P = 224(1.17)ⁿ

Hence, the complete equation is P = 224(1.17)ⁿ

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The required rate of the increase in the population is 17% and the equation is fulfilled as P = 224 (1.17)ⁿ.

As per the question, the population of the 2 years are given as 224 and the preceding year's population is 263 and equation is illustrated the exponential growth is given as P = 224(__)ⁿ. The blank space in the equation is to be filled.

The function which is in format f(x) =aˣ where a is constant and x is variable,  the domain of this exponential function lies   (-∞, ∞).

Here,
The given function of the population is incomplete as rate of growth is missing, So,
The rate is given as,
Rate = 263 - 224 / 224
Rate = 0.17 or 17%
Growth  = 1 + 0.17 = 1.17
now, put this growth rate in the blank space.
So,
P =  224 (1.17)ⁿ

Thus, the required rate of the increase in the population is 17% and the equation is fulfilled as P = 224 (1.17)ⁿ.

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Statement Problem: Does the relation in the table represent direct variation, inverse variation, or neither? If it is direct or inverse variation, write an equation to represent the relation. Explain your answer.

Solution;

We observe that as the value of x is increasing, the value of y is decreasing. Hence, it has a feature of an inverse variation.

When two variables are inversely related;

But;

Thus, we have;

Thus, the equation to represent the information is;

The equation to represent the information is;

given the expression

we are loking 2 numbers whose multiplication is equal to 12

and other 2 number whose multiplication is equal to 21

the sum of the cross multiplication is equal of 19, as follows

factor is

correct answer option B

Answer: The Curved Line on Top

Step-by-step explanation: A positive-valued function of a real variable. So the top one

Just learned about this in Algebra 1 about 4 days ago.

Hello!

Let's call these sides a, b, and c:

• a = 35mm

• b = 53mm

• c = 70mm

To be a triangle, it must satisfy the existence condition of triangles, that is:

Let's check each of them:

Answer:

Yes! There are infinitely many triangles that can be created.

Give the radius of a circle, r, we can find its area by using:

In the picture, the 30 ft segment passes from on side of the circle to the other passing thourhg tht center, so it is the diameter. The radius is half the diameter, so:

Now, we can use the formula for the area to find it:

So, the area is approximately 706.9 ft².

Since the events are independent, we have the following property:

That is, the probability of A is the same as the probability of A given B (since the events are independent, event B does not affect event A).

So, if P(A) = 0.3, therefore P(A|B) is also equal to 0.3.

Answer:

The slope is 5.

Step-by-step explanation:

To solve this, you could have plotted the two points, drew a line between them, and then calculated the slope by counting on the graph the line's rise/run.

To slove this by finding the slope with the points:

(5 - 0) / (0 - - 1) = 5 / 1 = 5

The slope is 5

B ( 1, 4)

K (4, -3)

We plot the points and after that, calculate their angles, then we measure 270 clockwise to calculate the new points.

The endpoints of the new segment are

B' = (-4.5, 1)

K' = (3, 4)

These are the points of the new segment

The probability of the girl being born to a couple is 0.949. Yes, it is effective in increasing the likelihood that the baby will be a girl as the number of girls is more than the number of boys.

What is probability?

Probability means possibility. The value of probability can only be from 0 to 1. Its basic meaning is something is likely to happen. It is the ratio of the favorable event to the total number of events.

Given

In a test of sex-selection technique, results consisted of 284 female babies and 15 baby boys.

Total children = 284 + 15 = 299

The probability of the girl being born to a couple will be

[tex]P = \frac{284}{299}[/tex]

P = 0.9498

Thus, the probability of the girl being born to a couple is 0.9498.

Yes, it is effective in increasing the likelihood that the baby will be a girl as the number of girls is more than the number of boys.

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Answer:

Step-by-step explanation:

22.57 cm inches are the net weight of the slope

Monthly salary = $1120

Comission percentage = 14%

Janet's sales = $94,100

1. Amount of commission

Multiply the sales amount (94,100) by the Commission percentage in decimal form (divided by 100).

94,100 x (14/100) =

94,100 x 0.14 = $13,174

2. Gross pay

Add the amount of commission and the monthly salary:

13,174+1120 = $14,294

Supplementary angles sum up to 180 degrees.

Since mZA and mZB are given to be (8x - 27) and (4x + 3) respectively, we need to know the value of x to be able to find

Supplementary angles sum up to 180 degrees.

Since mZA and mZB are given to be (8x - 27) and (4x + 3) respectively, we need to know the value of x to be able to find

Answer:

=1.875

Step-by-step explanation:

Add: 1/

2

+ 1/

4

= 1 · 2/

2 · 2

+ 1/

4

= 2/

4

+ 1/

4

= 2 + 1/

4

= 3/

4

It is suitable to adjust both fractions to a common (equal, identical) denominator for adding, subtracting, and comparing fractions. The common denominator you can calculate as the least common multiple of both denominators - LCM(2, 4) = 4. In practice, it is enough to find the common denominator (not necessarily the lowest) by multiplying the denominators: 2 × 4 = 8. In the following intermediate step, it cannot further simplify the fraction result by canceling.

In other words - one half plus one quarter is three quarters.

Exponentiation:  No. 1 ^ 2 = 3/

4

^ 2 = 32/

42

= 9/

16

In other words - three quarters raised to the power of squared is nine sixteenths.

Multiple: No. 2 * 2 = 9/

16

* 2 = 9 · 2/

16 · 1

= 18/

16

= 9 · 2/

8 · 2

= 9/

8

Multiply both numerators and denominators. Result fraction keep to lowest possible denominator GCD(18, 16) = 2. In the following intermediate step, cancel by a common factor of 2 gives 9/

8

.

In other words - nine sixteenths multiplied by two is nine eighths.

Add: 3/

4

+ the result of step No. 3 = 3/

4

+ 9/

8

= 3 · 2/

4 · 2

+ 9/

8

= 6/

8

+ 9/

8

= 6 + 9/

8

= 15/

8

It is suitable to adjust both fractions to a common (equal, identical) denominator for adding, subtracting, and comparing fractions. The common denominator you can calculate as the least common multiple of both denominators

The triangles KMP and AYC, are congruent angles, because we are told that:

Thus, to find our answers we compare both triangles.

a) KM is approximately equal to AC.

That is because, as we can see in the following image, they are corresponding sides:

b) CY is approximately equal to MP.

That is because they are corresponding sides, they are the short side of each triangle. And since the triangles are equal, CY and MP are also equal:

c) for the same reasons as the previous two, PK anf AY, are corresponding sides:

d) and e)

The corresponding angles of Y and K are represented in the following image:

rrespon

Given the modulus function expressed as:

Since the function is a modulus function, the dependent variables "y" will all be a positive value

Using the values of x to be -5, 8, and 13 to determine the ordered pairs

When x = -5

y = |-5 - 8|

y = |-13|

y = 13

The first ordered pair will be (-5, 13)

If x = 8

y = |8 - 8|

y = |0|

y = 0

The second ordered pair will be (8, 0)

If x = 13

y = |13 - 8|

y = |5|

y = 5

The third ordered pair will be at (13, 5)

The graph of the function is as shown below:

When two figures are similar, the relation or proportion between same measures is the same. So answer is option d.

To solve for j'

4j + 2 = h

subtract 2 from both-side of the equation

4j + 2-2 = h -2

4j = h-2

divide both-side of the equation by 4

4j/4 = h-2/4

Let W be the time of the wong family and N the time of the Nguyen family. We are told that the output rate of the Wong family is 35 L/h and the output for the Nguyen family is 20 L/h, if the total water output is 2100 L, then we can write this mathematically as:

Where "35W" is the total water output of the wong family and "20N" is the total water output of the Nguyen family. The two outputs combined must be 2100. We are also told that the total time is 75 hours, therefore we have:

We get a system of two equations and two variables. We can solve for "W" in equation (2), by subtracting "N" from both sides:

Now we can replace this value in equation (1):

Now we apply the distributive property:

Now we add like terms;

Now we subtract 2625 from both sides:

Now we divide both sides by 15:

Now we replace this value in equation (2) where we already solved for W:

Therefore, the time for the Wong family is 40 hours and the Nguyen family is 35 hours.