4.The value of x isis order these expressions from least to greatest:χ1- xx-1-1 = x

Given the phrase:

-3 times r is at least 33

Let's translate the given phrase into an inequality.

• Part A.

Let's figure out the inequality in steps.

-3 times r is written as:

-3r

-3 times s is at least 33 means that -3r is greater than or equal to 33.

Hence, we have the inequality:

• Part B.

Let's solve the inequality for r.

To solve for r, divide both sides of the inequality by -3:

• Part C.

Let's express the solution in interval notation.

Here, the solution is:

It means s must be less than or equal to 11.

Therefore, the solution in interval notation is:

ANSWER:

• A) -3r ≥ 33

• B) r ≤ -11

• C) (-∞, -11]

Since each year cost $8,800 for two years tuition he will need $17,600 then if he want to save at least this much in five years according to the table he needs to save $200 monthly

Given :

The number of votes to win is at least 225 votes

three-fourths of the seventh-grade students voted for him and he won.

Let the number of students = x

So, the inequality will be:

Solve the inequality :

Multiply both sides by 4/3

Answer:

His guaranteed wage is 35$, and he makes 7$per each table, so 7$*table.

1) if he waits on t (tables)= 20 --> 35$+7*20

so he makes 35$+140$= 175$

2) t tables: 35$+7*t

Solution

For this case we know the total surface area given by:

384 cm^2

And we have the following: 108+48 +108+48 = 312 cm^2

the ramianing area is:

384 -312= 72 cm^2

And we can do the following:

2*9*? = 72

Solving for ? we got:

? = 72/18 = 4 cm

the final answer is:

The area of each missing face is: 36 cm^2

The lenght of each missing edge is: 4 cm

Answer:

x = 83

Step-by-step explanation:

Add 27 to both sides

x - 27 +27 = 56 + 27

x = 83

We have a right triangle with sides 12 cm, 15 cm and 19 cm.

The area of the triangle is half the product of the legs, as they represent the base and height of the triangle:

NOTE: The legs are the shortest sides that form the right angle of the triangle.

Answer: the area of the triangle is 90 cm^2

We have the following information

and the function

In order to find the average rate, we need to find y1 and y2. Then, by substituting x1 into the function, we have

Similarly, by substituting x2, we get

Therefore, the average rate is given by

which gives

Therefore, the average rate is

The greatest number that divides 30 and 60 without leaving a remainder is its GCF.

Find the GCF of 30 and 60 by listing their factors. We get the following:

The factors of 30 are: 1, 2, 3, 5, 6, 10, 15, 30

The factors of 60 are: 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60

Since the greatest common factor of the two numbers is 30, then the greatest number that divides 30 and 60 without remainder is 30.

Answer:

See the steps of solution:

Answer:

2/7 (or) 0.285

Step-by-step explanation:

Given problem,

→ 5/7 - (3/14 + 3/14)

Let's solve the given problem,

→ 5/7 - (3/14 + 3/14)

→ (5/7) - (6/14)

→ ((5 × 2)/(7 × 2)) - (6/14)

→ (10/14) - (6/14)

→ (10 - 6)/14

→ 4/14 = 2/7

Hence, required answer is 2/7.

To answer this question we will use the following diagram as reference:

Let d be the distance from the base of the cliff to Emily's boat, then, from the above diagram we can set the following equation:

Then:

Simplifying the above result we get:

Answer:

1 gal = 4 qt

Multiply by 4

12 1/2 (4) = 50 qt

In order to determine the associated algebraic equation of the given statement, you consider part by part.

Two times x: 2x

minus the quantity 7 times y: - 7y

equals 20: = 20

Which is equivalent to:

2x - 7y = 20

Answers:

Vertex: (4, -9)

axis of symmetry: x = 4

Domain: (-∞, ∞)

Range: [-9, ∞)

Explanation:

If we have a quadratic function with the form y = ax² + bx + c, the x-coordinate of the vertex will be at x = -b/2a

So, for f(x) = x² - 8x + 7, we get a = 1, b = -8 and c = 7, then the x-coordinate of the vertex will be:

Then, the y-coordinate will be the value of f(x) when x = 4

Therefore, the vertex of the equation is the point (x, y) = (4, -9).

The axis of symmetry is located in the vertex, since the parabola opens up, the axis of symmetry is the vertical line x = 4.

To graph the function, we need to find some points before and after the vertex. So, we will give values to x as 2, 3, 5, and 6. Then, we can calculate f(x) as:

So, to graph the function, we will use the points (2, -5), (3, -8), (5, -8), (6, -5) and the vertex (4, -9). Therefore, the graph is:

Finally, the domain is the set of values that the variable x can take. In this case, x can be any number, so the domain is the set of all real numbers or written as an interval

(-∞, ∞)

And the range is the set of all values that f(x) can take. In this case, f(x) is always greater than -9, so the range is the set [-9, ∞)

Given:

900 digits are used for the page numbers. How many pages are in the textbook, starting with page 1

We will find the number of the pages of the book as follows

The number of digits from 1 to 9 = 9

The number of digits from 10 to 99:

There are 90 numbers, each number has 2 digits

So, the number of digits from 10 to 99 = 90 x 2 = 180

The number of digits from 100 to 999:

There are 900 numbers, and each number has 3 digits

so, the number of digits from 100 to 999 = 900 x 3 = 2700

The overall digits are given = 900

So, number of digits from 1 to 99 = 9 + 180 = 189

Subtract 189 from 900 = 900 - 189 = 711

Divide 711 by 3 = 237

So, the number of pages that have 3 digits = 237

So, the number of pages of the book = 237 + 99 = 336

So, the answer will be 336 pages

STEP - BY - STEP EXPLANATION

What to do?

Write the compound inequality of the given graph.

Given:

Step 1

Determine the two inequality separately.

Step 2

Combine the two inequalities

ANSWER

The compound inequality is

4≤x < 6

To break even, the equations must satisfy that

Substituting the explicit form of the equations, we get:

Subtracting 50x, we get:

Dividing by 16, we get:

Answer:

Multiply

Here, we want to select the arithmetic operation that could be used to evaluate the given indices expression

The key to solving this is to use an important indices relationship

That is;

Hence, we have to multiply the powers

So the correct option here is multiply

The general equation of a line is

where m is the slope and b the y-intercept

we can find m by the formula

where (x2,y2) is a right point of (x1,y1) then if we replace the point of the exercise we can find the slope of the line

value of the slope is -1

now to find y-intercept or b we replace the slope and a point of the line on the general equation

for example i will use (3,1)

no we can replace the slope -1 and b 4 on the general equation to have the equation of the line to the exercise

Given the following question:

Which graph represents 2 > y

Both equations are graphed as follows

Since the sign is not less than or equal to it won't be a red line, but a dotted red line.

Your answer is option C.

Given the system:

Let's clear x from equation 1:

And substitute (A) in equation 2:

Solving for y:

Now, let's use (A) to calculate x:

This way,

Solution

- The mean formula is given as:

- Thus, we can find the mean as follows:

Final Answer

The mean distance is 10.4 miles

We know that:

where theta is the angle we are trying to find; to get the angle we take the inverse tangent at both sides of the equation. Then:

Therefore, the angle we are looking for is 50°

4)

In the case of a square, its diagonals are equal and bisect each other, meeting at 90°.

In our case, using a diagram,

Therefore,

Solving the system of equations for a and b,

Finding a,

In the given figure :

Step 1 has 3 square, step 2 has 6 number of square

step 3 has 11 number of squares

step 4 has 18 number of squares

So, the sequence is 3, 6, 11, 18

As we can see that the figure makes a complete square and two more squares

So the expression will be :

Answer : C)

to find Q we need to make 2 distance measure

that they fulfill these conditions

PS=RQ and RS=QP

the formula of distances between 2 points is

Distance PS

Distance RQ

where x and y are de coordinates of Q

Distance RS

Distance QP

now solve the equals

PS=RQ

RS=QP

if I subtract the two equations I will get

and i will solve to find x

the value of x is 2, then I can replace x on any equation to find y

so replacing

use factor to solve y

then y will have two values

the real coordinate is y=3 because if is y=-5 the point dont form a rectangle

if x=2 and y=3 the point Q is (2,3)

Solution:

Given:

The equation of a circle is gotten by;

Substituting these values into the equation to get the value of r;

Thus, the equation of the circle is;

When people take medicine, the drug gets metabolized by the body and eliminated at a constant rate.

Suppose the initial amount of a drug in the body is 549 mg and it is eliminated at a rate of 12% per hour.

Let f(x) refer to the amount of drug left in the body after I hours.

(a) Write down an exponential function to model this situation. Write your answer using function

notation

(b) How much of the drug is left in the body after 12 hours? Round to the nearest whole number.

(c) How much of the drug is left in the body after 180 minutes? Round to the nearest whole number

Part a)

Let

t -----> number of hours

f(x)=a(1+r)^t

where

a=549 mg

r=12%=0.12

substitute

f(x)=549(1+0.12)^t

Part b)

For t=12 hours

substitute in the function

f(12)=549(1.12)^12

Part c)

For t=180 minutes

Remember that

1 h=60 minutes

so

180 minutes=180/60=3 hours

For t=3 hours

substitute

f(3)=549(1.12)^3

You need to rotate the figure to see the new orientation