Write an absolute value inequality that represents all real numbers more than 4 units away from x

Notice that the arc GH has the same measure as the angle GFH, which also has the same measure as the angle EFI since they are vertical angles.

On the other hand, EFI and IFS are adjacent angles, then:

Observe that the measure of the angle EFS is 90°. Since the measure of IFS is 20°, substitute those values into the equation to find the measure of EFI:

Thereore, the measure of GH is 70°.

Answer:

Step-by-step explanation:its a  69420 dum as

Let's assume X is the original price of the flat-screen TV

The store is advertising a 17% off sale in that price, so the real sale price should be less than the original price

To calculate a % discount, we proceed as follows:

Compute the discount:

discount = 17% of X

Recall a percentage can be expressed as the number divided by 100, that is:

discount = 17 / 100 * X = 0.17X

Now we have the discount, we calculate the actual or sale price, which is the original price minus the discount:

sale price = original price - discount

sale price = X - 0.17X

We apply simple algebra to simplify the expression, just subtracting 1-0.17=0.83

sale price = 0.83X

We know the sale price is $664, thus:

0.83X = 664

Finally, we solve for X

This means that the original price of the TV was $800. Let's verify our result

By solving the equations, we can conclude that the two numbers are 4 and 6.

So, the two numbers are:

The equation will be:

Now, solve this equation for 'x' as follows:

Now, 4x - 20:

Therefore, by solving the equations, we can conclude that the two numbers are 4 and 6.

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To find the Z a/2 for the 96% confidence. We write the confidence level in decimal form, in this case 0.96.

Now:

and then:

Now we subtract this value to 0.5 to know the value we need to find in the Z table:

Now we look at the Z table for this value, by finding we notice that this happens when Z=2.05.

Therefore the Z a/2 value is 2.05

Answer:

sorry if this is wrong

I just answered it according to the question you gave not the pic

Step-by-step explanation:

x = 65

11x + x = 180

12x = 180

x = 180 ÷ 12

= 15

Answer:

9f

Step-by-step explanation:

f(9) = f * (9)

a) Multiply.

f * (9) = 9f

Jade share 4 1/3 cups of chocolate by 1/3 among his friends

The mixed fraction = 4 1/3

Fraction = 1/3

Therefore, the answer is 13

Answer:

A

Step-by-step explanation:

the opposite sides of a parallelogram are parallel

then QT is parallel to RS

Q → T has the translation

(x, y ) → (x + 2, y- 7 ) , so

R → S has the same translation from R (0, 3 )

S = (0 + 2, 3 - 7 ) → S (2, - 4 )

Using the law of sines:

Solve for A using the data provided:

Step 1

Given; The client is to receive cimetidine 300mg by mouth every 6 hours. The medication is available as cimetidine 300mg/5ml.

Required; How many teaspoons should the nurse instruct the client to take?

Step 2

Thus, the client takes 300mg every six hours. This means that the nurse will instruct the client to take 1 teaspoon every 6 hours.

Answer;

The height of the building is given as  1026.43 feet

This is the term that is used to refer to the angle that is usually formed from the horizontal line to the angle of sight of a person.

We have to make use of the trig function that tells us that

tan(∅) = opposite length /adjacent length.

where ∅ = 11 degrees

adjacent length = 1

opposite length = x

When we put these values in the formula we would have

tan 11 = x / 1

0.1944 = x /1

we have to cross multiply to get x

x = 0.1944 x 1

= 0.1944

Then the height of the building would be 0.1944 x  5280 feet

= 1026.43 feet

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Let d and s be the cost of a double and single- occupancy room, respectively. Since a double-occupancy room cost $20 more than a single room, we can write

On the other hand, we know that 15 double-rooms and 26 single-rooms give $3088, then, we can write

Solving by substitution method.

In order to solve the above system, we can substitute equation (A) into equation (B) and get

By distributing the number 15 into the parentheses, we have

By collecting similar terms, it yields,

Now, by substracting 300 to both sides, we obtain

then, s is given by

In order to find d, we can substitute the above result into equation (A) and get

Therefore, the answer is:

Given a quadratic equation of the form:

The discriminant is:

And we can know the number of solutions with the value of the discriminant:

• If D < 0, the equation has 2 imaginary solutions.

• If D = 0, the equation has 1 real solution

• If D > 0, the equation has 2 real solutions.

Equation One:

Then, we calculate the discriminant:

D = 0

There are 1 real solution.

Equation Two:

Calculate the discriminant:

D = -116

There are 2 imaginary solutions.

Equation Three:

Calculate the discriminant:

D = 100

There are 2 real solutions.

Answers:

Equation 1: D = 0, One real solution.

Equation 2: D = -116, Two imaginary solutions.

Equation 3: D = 100, Two real solutions.

Solution:

Given:

Given that the annual income of a company over a 6-year period is described by the equation:

The annual income at the end of each year since 2001 is as shown in the table below:

Required: To evaluate the company's approximate annual income in 2009.

Solution:

Given the annual income described as

The number of years between 2001 and 2009 is evaluated as

thus, it's been 8 years since 2001.

The annual income in 2009 is thus evaluated by substituting 8 for the value of x in the annual income function.

This gives

Hence, the company's approximate annual income in the year 2009 will be $ 258000.

The third option is the correct answer.

The expected value of the game is $1.83.

To begin we need to find the value of a

We apply the Pythagorean theorem

Now we find theta

Here we use the tangent that is the oppositive side over the adjacent side

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

Step 01:

Data

point 1 (2 , 60) x1 = 2 y1 = 60

point 2 (4 , 120) x2 = 4 y2 = 120

Step 02:

slope formula

The answer is:

30

Answer:

Explanation:

We were given the following information:

This is a normal distribution curve

Mean = 53

Standard deviation = 9

We are to find the area right of x = 71

This is calculated as shown below:

We will proceed to plot this on a graph as sown below:

The area to the right of x = 71 (highlighted in red above) is given by using a Standard z-score table:

Therefore, the area that lies to the right of x = 71 is 0.0228 or 2.28%

Answer:

The line of symmetry is x = -3

Explanation:

Given a quadratic function, we know that the graph is a parabola. The general form of a parabola is:

The line of symmetry coincides with the x-axis of the vertex. To find the x-coordinate of the vertex, we can use the formula:

In this problem, we have:

Then:

a = -1

b = -6

We write now:

For this part, we need to find the x-intercepts. This is, when y = 0:

To solve this, we can use the quadratic formula:

And solve:

Since there is no solution to the square root of a negative number, the function does not have any x-intercept. The correct option is ZERO x-intercepts.

To find the y intercept, we need to find the value of y when x = 0:

The y-intercept is at (0, -13)

Now we need to find two points in the parabola. Let-s evaluate the function when x = 1 and x = -1:

The two points are:

(1, -20)

(-1, -8)

Now, we can use 3 points to find the graph of the parabola.

We can locate (1, -20) and (-1, -8)

The third could be the vertex. We need to find the y-coordinate of the vertex. We know that the x-coordinate of the vertex is x = -3

Then, y-coordinate of the vertex is:

The third point we can use is (-3, -4)

Now we can locate them in the cartesian plane:

And that's enough to get the full graph:

In this question, we are given two lines.

1) y = 0.5*2^x

2) y = 2x + 25

The standard equation of a line is y = mx + b, where m is the slope and b is the y-intercept.

The positive slope moves the line upwards and the negative slope moves the line downwards.

If we compare both the equations, we see the 2nd equation maps with the standard line form. Hence, the second equation is a line with the slope equals to 2 and y-intercept equals 25. As the slope is positive, the line is moving upwards.

The standard equation of an exponential function is y = a*b^x, where b is the base, x is the exponent and a is the y-intercept.

The positive value of the base moves the function upwards and the negative value moves it downwards.

If we compare both the equations, we see the 1st equation maps with the standard exponential form. Hence, the 1st equation is an exponent form with the base to 2 and y-intercept equals 0.5. As the base is positive, the line is moving upwards.

Answer:

12

Explanation:

In the bag, the guaranteed ratio of peanut to raisin = 5:2

Number of peanuts = 30

Let the number of raisins =x

We therefore have that:

The number of raisins in the bag is 12.

The given geometric series is

In a geometric series, there is a common ratio between consecutive terms defined as

The sum of the first n terms of a geometric series is given by

Where a is the first term.

From the given series

a = 120

Hence, the sum of the first 8 terms is

Simplify the brackets

Simplify further

Therefore, the sum of the first 8 terms is

Line p is perpendicular bisector of line MN. This means that it divides line MN equally. Thus, point B is the midpoint of line MN. Thus, we would find the midpoint of line MN by applying the midpoint formula which is expressed as

(x1 + x2)/2, (y1 + y2)/2

Looking at the given points of line MN,

x1 = - 5, y1 = 2

x2 = 7, y2 = - 1

Midpoint = (- 5 + 7)/2, (2 + - 1)/2

Midpoint = 2/2, 1/2

Midpoint = 1, 1/2

We would find the slope of line MN. The formula for finding slope is expressed as

m = (y2 - y1)/(x2 - x1)

Looking at the given points of line MN,

x1 = - 5, y1 = 2

x2 = 7, y2 = - 1

m = (- 1 - 2)/(7 - - 5) = - 3/(7 + 5) = - 3/12 = - 1/4

If two lines are perpendicular, it means that the slope of one line is the negative reciprocal of the slope of the other line. This means that the slope of line p is 4/1 = 4

Thus, line p is passing through point (1, 1/2) and has a slope of 4

The equation of a line in the slope intercept form is expressed as

y = mx + c

where

m represents slope

c represents y intercept

To determine the equation of line p, we would substitute m = 4, x = 1 and y = 1/2 into the slope intercept equation. It becomes

1/2 = 4 * 1 + c

1/2 = 4 + c

c = 1/2 - 4

c = - 7/2

Substituting m = 4 and c = - 7/2 into the slope intercept equation, the equation of line p would be

y = 4x - 7/2

SOLUTION

We will be using the annual compound interest formula to solve this question.

After a down payment of 0.15 x $225,000 = $33750

The principal value will be $225,000 - $33750 = $191250

Put all these values into the compound interest formula above,

we will have:

The mortgage total if they finance the closing costs will be:

$923,297.63

The volume will be given by:

The volume of the half cylinder on top, plus the volume of the rectangular prims, plus the volume of the half cylinder on the right:

so:

The volume of the half cylinder on top is:

The volume of the half cylinder on the right is:

The volume of the rectangular prism is:

Therefore, the total volume is:

Given the equation:

Let's identify the type of polar graph for the equation.

To identify the type of polar graph, use the formula below to get the Cartesian form:

Thus, we have:

We have the graph of the equation below:

We can see the graph forms a Limacon with an inner loop.

Therefore, the type of polar graph for the given equation is a limacon with inner loop.

ANSWER:

Let that unknown number be x

⇒Mathematically this is written as

[tex]5(x)-6=9\\5x-6=9\\5x=9+6\\5x=15\\\frac{5x}{5} =\frac{15}{5} \\x=3[/tex]

This just means that the unknown number is 3

GOODLUCK!!

Answer:

nine plus six

= 15 ÷ five

answer Three