Solve the inequality and graph the solution on the line provided. -2 + 6x > 34 Л ^ < OT Inequality Notation: Number Line: 8 12 6 2 10 -8 -2 0 4 -6 -12 -10 -4 Click and drag to plot line. Submit Answer at

Explanation

We are given the equation:

We are to use the vertical line test to determine if the equation is a function or not

The vertical line test is a graphical method of determining whether a curve in the plane represents the graph of a function by visually examining the number of intersections of the curve with vertical lines.

The typical example below helps give a better explanation

So for the function

We can observe that the equation is not a function because the vertical line cuts the graph in more than one point

This is shown below for values of x = and x =8

The coordinates of the quadrilateral after translation will be : A'( 0 , 6 ) , B'( 6 , 4) , C'( 0 , 1 ) and D'( 4 , -2 )

The given quadrilateral in the graph has the coordinates:

A(1,8) , B(7,7) , C(1,4) , D(5,4)

When this figure is translated 1 unit to the left and 3 units downwards we get :

A ( 1 , 8 ) → A'( 0 , 5 )

B ( 7 , 7 ) → B'( 6 , 4 )

C ( 1 , 4 ) → C'( 0 , 1 )

D ( 5 , 4 ) → D'( 4 , 1 )

Hence the translated figure will have the coordinates:

A'( 0 , 6 ) , B'( 6 , 4) , C'( 0 , 1 ) and D'( 4 , -2 ) .

In Euclidean geometry, a translation or transformation is still a geometric change that entails shifting every point in a figure, shape, or space uniformly in one direction.

Moving the origin of the coordinate system or adding a constant vector to each point are other ways to conceptualize translation.

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Step 1

Given; What is the equation of the line that passes through (5, 2) and is

perpendicular to y =

10x + 7?

Step 2

The slope of the given line is;

Slope of perpendicular lines have the following relationship;

Therefore the required equation will be in the form of;

Find b, the y-intercept

Thus the answer will be; Option B

The ordered pair that represents the location of point P is (6,5)

Explanation:

In order to determine the position of point P, we will need to trace its position to the x axis and also trace its position to the y axis.

Tracing its position to the x axis, we find it corresponds to 6 units

Tracing its position to the y axis, we find it corresponds to 5 units.

This because each line represents 1 units. After the 4 units, the next line is 5 units.

Using the coordinates (x,y):

The ordered pair that represents the location of point P is (6,5)

Due to the circular shape, one complete rotation of the flag is equal to the circumference of a circle with radius 12 ft.

Then, use the following formula for the cirumference:

C = 2π·r

where r is the radius. In this case, r = 12 ft and π = 3.14. Replace the previous values into the formula for C:

C = 2(3.14)(12 ft)

C = 75.36 ft

Hence, the flag has to travel 75.36 ft to complete a full rotation

We can use density as a factor of conversion.

To find the mass in grams of the volume of acetone, multiply the volume by the density (always check the units, that in this case are consistent because 1cm^3=1mL):

To find the volume of the mass of acetone, divide the mass by the density:

Given: ( -100 ) + ( -4 ) + ( -2 + 6) ( 3 )

Required: Evaluation

Explanation:

We shall here use BODMAS rule.

First solve the brackets and the addition and subtraction

Further,

Solving

Final Answer:

Money invested = $1420

Final money = $1621.4

Effective yield = [ 1 + i/n]^n - 1

i = nominal rate let's consider 10%

n = number of payments 12 payments because it is in a year

Effective yield = [1 + 0.1/12]^12 - 1

= [ 1 + 0.00833]^12 - 1

= [1.0083]^12 - 1

= 1.1 - 1

Effective yield = 0.10 %

It is a trapezoid

Solution

- The transformation for reflection over the y-axis is given below:

- We have been given the coordinate of B to be (-5, -2) as shown below:

- Thus, applying the transformation formula given above, we have:

- Thus, the reflected point B' is

- This is shown below:

Explanation:

The question wants us to obtain the circumference of the circle given that the diameter of the circle is 13 meters.

To do so, we will use the formula:

Therefore, the circumference will be

Rounding off to the nearest whole number, we will have 41 meters

In this problem we know that

Applying the exterior angle theorem

10x+30=58+(7x-1)

solve for x

10x-7x=57-30

3x=27

Find m

mm

Find mmm

Solution

We know that :

g(x) = f(x) + k

For this case the answer is:

the value of k is: 4

Okay, here we have this:

Considering the provided information, we are going to calculate the requested probability, so we obtain the following:

Probability of getting tails and rolling a two=Probability of getting tails * Probability of getting a two

And basing ourselves on the fact that when tossing a coin there are two possible events and in this case a favorable one, and when tossing the die there are 6 possible events and one favorable for this case, we have:

Probability of getting tails and rolling a two=1/2*1/6

Probability of getting tails and rolling a two=1/12

Finally we obtain that the probability of getting tails and rolling a two is 1/12.

Write an expression in simplest form that represents the income from w women and m men getting a haircut and shampoo. Women: haircut $45 shampoo $12. Men: haircut $15 shampoo $7

the income is equal to

45w+12w+15m+7m

combine like terms

57w+22m

where

w is the number of women

m is the number of men

Answer : 6

We are given the above fraction to be

The answer is 6

Before you can change a division operator to a multiplication operator, we need to find the reciprocal of the left hand side fraction

The fraction at the left hand side is 1/8

The reciprocal of 1/8 is 8

We have in total 2 1/2 so we need to divide this in 5 equal parts

First we will convert our mixed number into a fraction

Then we divide between 5

ANSWER

1/2 case

Solution:

Step 1: Find the slope of the line:

Given the points (X1, Y1)=(-4,-5) and (X2, Y2)= (1,5), we have that the slope of the line that passes through the points (-4,-5) and (1,5) is:

Step 2: Write the provisional equation of the given line. If the slope of the line is m=2, we get that the provisional equation of this line is:

Step 3: Find the y-intercept b. Take any point (x,y) on the line and replace its coordinates into the above equation and then solve for b. For example, take the point (x,y)=(1,5), then we obtain:

this is equivalent to:

solving for b, we get:

that is:

Step 4: Write the equation of the line. If the given line has slope m=2 and y-intercept b = 3, then its equation would be:

and in terms of x, this is equivalent to:

So that, we can conclude that the correct answer is:

The given equation is

To find the x-intercept, we make y = 0.

To find the y-intercept, we make x = 0.

The sequence is given by .

a. The indicated term

b. The indicated term

c. The indicated term

By finding the differences between dependent values, you can determine the degree of the model for data given as ordered pairs. If the first difference is the same value, the model will be linear. If the second difference is the same value, the model will be quadratic.

Also you can solve it by plotting the dots. If the graph seems a straight line it is linear and quadratic if it is a parabola.

For the data set given it is a linear relation

Line of best fit: y=3.18x+54.92

For x=7;

y=3.18*7+54.92

y=77.18

ANSWER

• m = 2

• b = -5

EXPLANATION

This equation is written in slope-intercept form,

Where m is the slope and b is the y-intercept.

In this case, the slope is m = 2 and the y-intercept is b = -5. This tells us that the line intersects the y-axis at y = -5, so that is our first point. Then, we can find the next point using the slope,

The next point is 1 unit to the right of the y-intercept, and 2 units up,

To draw a line we only need two points, so we have to draw a line passing through these two points.

One tablet contains 150 mg of the active ingredient. Then, 90 tablets contain

1 gram is equivalent to 1,000 mg​, then 13500 mg is equivalent to

There are 13.5 grams of the active ingredient in the entire bottle

Given the following function:

We will find the end behavior of the function.

the given function has a degree = 3 (odd)

And the leading coefficient is positive

the end behavior will be as follows:

So, the answer will be:

The end behavior of the function is down to the left and up to the right.

===============================================================

Part (2), we will find the y-intercepts

The y-intercept is the value of y when x = 0

So, we will substitute x = 0 and then solve y

So, the answer will be:

y-intercept = (0, 0)

================================================================

Part 3: we will find the zeros of k(x)

The zeros of the function are the values of x which make k(x) = 0

So, we will write the equation k(x) = 0 and then solve it for x.

So, the answer will be:

Zeros of k: 0,5

===============================================================

Part 4: we will find the graph of k(x)

From the previous parts, we can conclude that

The graph of the function will be as shown in option D

Mrs. Manny needs 5.2 hours to grade her students' assignments. It would take Lexi 6.4 hours to grade the assignments alone.

In one hour, Mrs. Manny completes 1 / 5.2 = 0.1923 of the work.

In one hour, Lexi completes 1 / 6.4 = 0.15625 of the work

Together, they complete 0.1923 + 0.15625 = 0.34856 of the work.

The full work would take them 1 / 0.34856 = 2.87 hours.

It would take 2.87 hours for them to finish the task together.

Given,

Multiply 1st equation by 5.

Solve equations (2) and (3)

Put x =-5/2 in equation (1)

Further solved as,

Therefore, the value of x and y is -5/2 and 3.

1) In this inequality 3x ≥ 9 we have to find a set of values for x.

3x ≥ 9 Divide both sides by 3

x ≥3

2) We can express this set of solutions in the number line as well. Since is greater than or equal to we'll use a closed dot. To include this 3.

3) Hence the graph above represents that every value greater than and the 3 satisfies the restraint x ≥3.

The following image shows a diagram (not to scale) of the triangle with the indicated measurements:

We will label them as "a" and "b" for reference:

And we need to find the hypotenuse of the triangle, which is the side that is opposite to the 90° angle. We will label the hypotenuse as "c":

To solve the problem we have to us The Pythagorean Theorem:

Substituting the values of the legs a and b:

Since 60^2=3,600 and 80^2=6,400:

Finally, to find the hypotenuse "c", take the square root of both sides of the equation:

The length of the hypotenuse is 100 cm.

Answer: 100cm

So,

Remember that the simple interest of an initial amount after "t" years, can be found using the following formula:

Where A is the final amount, P is the initial amount, r is the rate and t are the years involved.

If we replace our values, Emma will has the following amount after 8 years:

So, Emma will has $2,960 after 8 years.

To find the amount that Paul will has, we should remember what the compound interest is.

Remember that the compound interest is given by the formula:

Where A is the final amount, P is the initial amount, i is the rate and n are the years involved.

If we replace our values, Paul will has the following amount of money after 8 years:

So, Paul will has $3187,70 after 8 years.

Therefore, the correct answer is A.