How do I graph a line with a equation in slope intercept form?An example is y=-3x+3, how do I graph this?

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

SOLUTION

From the question we have

from difference of two squares, we have

Hence the answer is option D

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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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.

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

It will take 18 months before the company starts making a profit.

STEP-BY-STEP EXPLANATION

Given information

Where x is the number of months.

Step 1: Make P(x) = 0

Step 2: Find x from the above equation

Therefore, it will take 18 months before the company starts making a profit.

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

Here we have a geometric sequence, the recursive formula is:

Aₙ = (1/3)*Aₙ₋₁

And the explicit formula is:

Aₙ = (1/3)*ⁿ⁻¹*540

Here we have the following sequence:

540, 180, 60, 20, ...

This seems to be a geometric sequence, to check this, we need to take the quotients between consecutive terms and see if we get the same thing.

180/540 = 1/3

60/180 = 1/3

20/60 = 1/3

So yes, this is a geometric sequence where the common ratio is 1/3, so each term is (1/3) times the previous one, so the recursive formula is:

Aₙ = (1/3)*Aₙ₋₁

And the explicit formula is:

Aₙ = (1/3)*ⁿ⁻¹*A₁

Where A₁ is the first term, in this case 540, so the formula becomes:

Aₙ = (1/3)*ⁿ⁻¹*540

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Expand the left hand side using distributive property:

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

Step-by-step explanation:

a) modal number is 3

b) mean is x = ∑fx/n

= ((5•1)+ (2•10)+(3•15)+(7•4)+(3•5))/(5+10+15+7+3)

= 113/40

= (Decimal: 2.825)

Using bisection, the measure of angle ABD is of m<ABD = 50º.

The bisection of an angle is when the angle is divided into two angles of equal measure.

In the context of this problem, we have that the angle BE bisects the angle DBC, hence the measures of these angles are given as follows:

mDBE = mEBC = 2x + 15.

As shown in the diagram, the entire line forms a ray, meaning that the sum of the measures of the angles is of 180º, hence we can solve for x as follows:

2x + 2(2x + 15) = 180º

2x + 4x + 30 = 180º

6x = 150º

x = 150º/6

x = 25º.

Then the measure of angle ABD is found as follows:

m<ABD = 2x = 2(25) = 50º.

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

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]

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%

SOLUTION

Given the question in the image, the following are the solution steps to answer the question.

STEP 1: Write the given equation

STEP 2: State the law of logarithm

STEP 3: Substitute the given values in the question to get the correct answer

Hence, Answer is:

OPTION A

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:

Notice that

400,000 = 0.4 million

That's why the equation that models that information has the factor 0.4, since it expresses the result in millions of females.

Now, we need to notice that t, in the expression 0.4t + 6.1, is the number of years passed since 2009. So, in the year 2024, we have:

t = 2024 - 2009 = 15

Therefore, the number of females enrolled in 2024 can be estimated to be:

y = (0.4 * 15 + 6.1) million

y = (6 + 6.1) million

y = 12.1 million

Now, to determine the year when 12.9 million females will be enrolled, we first need to find t corresponding to y = 12.9, and then add it to the year 2009.

y = 0.4t + 6.1​

12.9 = 0.4t + 6.1

12.9 - 6.1 = 0.4t

6.8 = 0.4t

t = 6.8/0.4

t = 68/4

t = 17

Therefore, the year when it happens will be:

2009 + 17 = 2026

The linear equation has the solution x = 1 only if the value of b is 6

Here we have the linear equation:

2x + 14 = 10x + b

If we replace x by 1 in that equation, we will get:

2*1 + 14 = 10*1 + b

2 + 14 = 10 + b

16 = 10 + b

To find the value of b such that x = 1 is a solution, we need to isolate b, to do so we need to subtract 10 in both sides.

16 -  10 = 10 + b - 10

6 = b

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To simplify the fraction we will need to facto

hello

to solve this problem, we need to identify the shape of the soup can first since soup is a liquid and carries the shape of whatever container its in.

volume of a cylinder is given as

from the calculations above, the volume of the soup is equal to 673.9cm^3 which corresponds with option D

Answer:

1/3

Explanation:

We can see that from 0 to 1 the number line is divided into 6 parts and the point is right after the second part. Therefore, the fraction that represents point C is 2/6

This fraction is also equal to 1/3 because we can divide the line from 0 to 1 into 3 parts and take the first. The point will be at the exact same position of C.

Therefore, the answer is:

1/3

Given: A and B are two sets such that-

Required: To determine-

Explanation: Since A and B have no common elements, the events are independent events or disjoints or mutually exclusive.

For independent events, we have-

Substituting the values into the formula-

Recall that-

Substituting the values into the formula and further solving as-

Final Answer: a)

b)

Given the function:

You can rewrite it as follows:

You need to remember that the y-value is zero when the function intersects the x-axis. Then, you need to make it equal to zero, in order to find the x-intercepts:

Solving for "x", you get these two values:

In order to find the vertex, you can follow these steps:

1. Find the x-coordinate of the vertex with this formula:

To find the value of "a" and "b", you need to multiply the binomials of the equation using the FOIL Method. This states that:

Then, in this case, you get:

Add the like terms:

Notice that, in this case:

Then, you can substitute values into the formula and find the x-coordinate of the vertex of the parabola:

2. Substitute that value of "x" into the function and then evaluate, in order to find the y-coordinate of the vertex:

Therefore, the vertex of the parabola is:

Knowing the x-intercepts and the vertex of the parabola, you can graph it.

Hence, the answer is:

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

1) 2x+y=5 ...... It is a linear equation

2) y= x + 6 ....... It is a linear equation

Because they are of first degree and they contain x and y (equations of a line)

Okay, here we have this:

Considering that it says "spent", it represents an outflow of money, therefore we take it as negative, so we obtain:

Actual Situation: Initial money - money spent

Actual Situation: 30 - x

Answer:

Step-by-step explanation:

22.57 cm inches are the net weight of the slope

The rate at which the Brock family drinks milk is 4 gallon per day.

According to the question,

We have the following information:

The Brock family uses 12 gallon jug of milk every 3 days.

Now, in order to find the rate at which they drink milk, we will have to divide the amount of milk by the total number of days.

So, we have the following expression:

Rate at which they drink milk = 12/3 galloon per day

Rate at which they drink milk = 4 galloon per day

Now, this the simplified answer because this is a whole number and we can not solve it further.

Hence, the rate at which they drink milk is 4 galloon per day.

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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