For which values of x is the inequality 2(1 + x) > x + 8 true?
A) 3 & 2
B) 4 & 3
C) 6 & 5
D) 7 & 8

integer 1: x

integer 2: x + 2

integer 3: x + 4

integer 4: x + 6

integer 1 + integer 2 + integer 3 + integer 4 = sum

     x       +     x + 2     +      x + 4   +     x + 6     = 300

4x + 12 = 300

      4x = 288

        x = 72

Answer: 72, 74, 76, 78

Hey there!!

Co-ordinates for midpoint when two endpoints are given :

... [tex]\frac{x2+x1}{2} , \frac{y2+y1}{2}[/tex]

Given endpoints :-

... ( -1, 7 ) ( 3, -3 )

... [tex]\frac{3-1}{2},\frac{-3+7}{2}[/tex]

... [tex]\frac{2}{2},\frac{4}{2}[/tex]

... [tex]1,2[/tex]

Hence, the midpoint is ( 1,2 )

Hope my answer helps!

The midpoint of the line segment with endpoints (-1,7) and (3,-3) would be (1, 2).

Suppose we've two endpoints of a line segment:

A(p,q), and B(m,n)

Then let the midpoint be M(x,y) on that line segment. Then, its coordinates are:

[tex]x = \dfrac{p+m}{2}\\and \\y = \dfrac{q+n}{2}[/tex]

Given endpoints ; ( -1, 7 ) ( 3, -3 )

[tex]x = \dfrac{-1+3}{2}\\\\\\x = 1\\y = \dfrac{7-3}{2}\\\\ y = 2[/tex]

Hence, the midpoint is ( 1,2 ).

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Solve for w by simplifying both sides of the equation, then isolating the variable.

The answer is A.

f(x) = 2x² - 4x - 3

g(x) = (x - 4)(x + 4)  = x² - 16

f(x) - g(x) = 2x² - 4x - 3 - (x² - 16)

              = 2x² - 4x - 3 - x² + 16

              = x² - 4x + 13

Answer: B

1 + 4x = -5 + 7x

1st step: you need to move 4x to the right and -5 to the left so that all the x's are in one place. 4x will be negative and -5 will be positive when you move them. So it will be:

1+5=7x-4x

2nd step:

3x=6

3rd step: you need to divide both sides into 3, because it is the common divisor.

x=2

1 + 4x = -5+7x

7x - 4x = 1 + 5

3x = 6

You can try to memorize the summary. However, it is better to understand the solution as a whole.

The fraction 7/9 converts to the decimal 0.77777778, which is a repeating decimal as the digit '7' repeats infinitely.

To convert the fraction 7/9 to a decimal, divide 7 by 9. So, when you divide 7 by 9, the answer you get is 0.77777778. This decimal does not terminate (come to an end after a specific number of decimal spaces), instead it repeats. Specifically, the digit '7' repeats indefinitely, so we can say its a repeating decimal.

As an example, if you consider 1/2, when you divide 1 by 2 it gives 0.5, which is a decimal that terminates. However, in our case - when we divided 7 by 9 it gave us 0.77777778 which repeats, hence it is a repeating decimal, not a terminating decimal. This is the key difference between repeating and terminating decimals.

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To find the total change in the number of bushels the farmer has for sale after 5 days, multiply the average number of bushels sold per day by the number of days.

To find the total change in the number of bushels the farmer has for sale after 5 days, we need to multiply the average number of bushels sold per day by the number of days.

The average number of bushels sold per day is 16 and three fourths, which can be written as 16.75.

Multiplying 16.75 by 5 gives us the total change in bushels after 5 days, which is 83.75 bushels.

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If you are just dividing percent's, then each grade would have 12.5 percent.

The number of students that practice the piano more than 3 hours a week is 6

From the dot plot (see attachment), we have the following highlights

Next, we add the total number of students

[tex]Total = 3 + 2 +1[/tex]

[tex]Total = 6[/tex]

Hence, the number of students that practice the piano more than 3 hours a week is 6

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Step 1. Move all terms to one side

[tex]x^2-4x-9-29=0[/tex]

Step 2. Simplify [tex]x^2-4x-9-29[/tex] to [tex]x^2-4x-38[/tex]

[tex]x^2-4x-38=0[/tex]

Step 3. Use the Quadratic Formula

[tex]x=\frac{4+2\sqrt{42} }{2} ,\frac{4-2\sqrt{42} }{2 }[/tex]

Step 4. Simplify solutions

[tex]x = 2 \sqrt{42,} 2-\sqrt{42}[/tex]

Let's solve your equation step-by-step.

[tex]x^{2}[/tex]−4x−9=29

Step 1: Subtract 29 from both sides.

[tex]x^{2}[/tex]−4x−9−29=29−29

[tex]x^{2}[/tex]−4x−38=0

Step 2: Use quadratic formula with a=1, b=-4, c=-38.

[tex]x=\frac{-b+-\sqrt{b^{2} -4ac} }{2a}[/tex]

[tex]x=\frac{-(-4)+-\sqrt({-4})^{2} -4(1)(-38)}{2(1)}[/tex]

[tex]x=\frac{4-+\sqrt{168}}{2}[/tex]

Answer:

[tex]x=2+\sqrt{42}[/tex] or x = -2 [tex]\sqrt{42}[/tex]

The quickest way to do this is to plug the first b-value from each table into the equation to find p-value. Then compare your answer with the p-value from the table to find the one that is greater than your answer.

p = 3.25b  

                  Equation                    Table                   Table compared to Equation

Table A:  p = 3.25(1) = 3.25           p = 2.75                               <

Table B:  p = 3.25(1.5) = 4.875       p = 3.75                              <

Table C:  p = 3.25(2) = 6.50           p = 7.00                                 >

Table D:  p = 3.25(2.5) = 8.125       p = 10.00                               >

Table E:  p = 3.25(3) = 9.75             p = 11.25                               >

Table F:  p = 3.25(3.5) = 11.375       p = 10.50                          <

Answer: C, D, and E

Factor a^2−2ab−6by+3ay

a^2−2ab+3ay−6by

=(a−2b)(a+3y)

Answer:

(a−2b)(a+3y)

the factored expression is:

a(a + y) - 2b(a + 3y)

We can factor the expression [tex]a^2-2ab-6by+ay[/tex] using a combination of grouping and factoring by difference of squares:

We can group the terms based on common factors:

[tex](a^2 + ay) - (2ab + 6by)[/tex]

In the first group, a is the common factor: a(a + y)

In the second group, 2b is the common factor: 2b(a + 3y)

Then we combine the terms

a(a + y) - 2b(a + 3y)

Therefore, the factored expression is:

a(a + y) - 2b(a + 3y)

Answer:

2.81 and 0.3 are two decimals that give a product of 8.43 which is close to 8.4

Step-by-step explanation:

let consider a decimal number 0.3

now consider another decimal number 2.81

now if we multiply these two numbers then we get 8.43 which is also a decimal number and it is close to 8.4.

Answer:

Hence the approximate values are 2.91 and 2.89

Step-by-step explanation:

The area of a quadrilateral is expressed as

A=L*B

Where L=length

B=breadth or width

I. e assuming it has two of its sides equal

Say given area is

A=L*B=8.4 square feet

Let's take the square root of the area A=2.898

=2.89

Approximately

L= 2.9 feet

Let's us divide the area by L to get B

8.4/2.9= 2.91

The required integer is -100$.

It is required to find the integer.

An integer is a whole number (not a fractional number) that can be positive, negative, or zero. Zero is not a fraction or decimal of any number. It is neither positive nor negative.

Given:

The given integer describes withdrawing $100 from your bank account.

According to given question we have,

-100$

negative one hundred

or

minus one hundred

Therefore, the required integer is -100$.

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"·" - product

"+" - sum

x² - square of x

Answer: x · (6 + 8 · x²) = x(6 + 8x²)

The expression "the product of x and the sum of 6 and 8 times the square of x" can be written as [tex]\( x \cdot (6 + 8x^2) \)[/tex].

The mathematical expression "the product of x and the sum of 6 and 8 times the square of x" is represented as [tex]\( x \cdot (6 + 8x^2) \)[/tex]. To simplify, distribute x into the parentheses, yielding 6x + 8x^3. This expression captures the specified operation, where x is multiplied by the sum of 6 and 8 times the square of x.

It is essential to follow the order of operations, ensuring that the square of x is calculated first, then multiplied by 8, and finally added to 6 before multiplying the result by x. This expression forms the algebraic representation of the described mathematical operation.

ANSWER

The correct answer is A

EXPLANATION

To find the ink cost of each card coming from printer  B, we need to find the total cost from printer B and the total number of cards printed by Printer B.

The total hours of all the three printers over the three weeks

[tex]=40+45+55+50+50+30+45+40+60=415[/tex]

The total hours of printer B only

[tex]=50+50+30=130[/tex]

Total number of cards produced over the three weeks

[tex]=7950+7800+9600=25350[/tex]

We can use ratio and proportion to determine the total cards produce by printer B only.

[tex]415:25350[/tex]

[tex]130:x[/tex]

If less, more divides

[tex]x=\frac{130\times 25350}{415} \approx7941[/tex]

Total cost of Printer B in 130 hours

$[tex]=130 \times 15=1950[/tex]

The ink cost

[tex]=\frac{1950}{7941}[/tex]

[tex]=0.2456[/tex]

$[tex]\approx 0.30[/tex]

to 2 decimal places

We can write this line in y-intercept form, and then solve to convert it to standard form.

Y = mx + b

m = slope

b = y-intercept

Y = -1/4x - 2 is the slope-intercept form of the equation.

Now, we can convert this to standard form.

Add 2 to both sides.

y + 2 = -1/4x

Subtract y from both sides.

-1/4x - y = 2

Multiply all terms by -4.

x + 4y = -8 (This is your answer.)

chicken: ($2.99) c

steak: ($5.79) s

chicken + steak = total

2.99c + 5.79s = 50

Answer: D

To tell isf a table is proportional, divide y by x,

if all sets are the same it is proportional.

First table:

3 / -3 = -1

2 / -4 = -2

-1 and -2 are not the same

Table 2:

1/-1 = -1

3/-3 = -1

5/-5 = -1

These are all the same.

Table 2 is correct.

To find porportionality, you must note that: the x and y must have the same value throughout the table when multiplied.

For example:

x     |    y

------------

1     |   2

2    |   4

etc.

In this case, it is multiplied by 2. Now let us look at the problem

---------------------------------------------------------------------------------------------------------------------------

Table 2 is your answer because, you are multiplying -1 each time

x(-1) = y   is your equation

To check, plug in the x, and see if the y is the same value

(-1)(-1) = 1 (True)

(-3)(-1) = 3 (True)

(-5)(-1) = 5 (True)

---------------------------------------------------------------------------------------------------------------------------

hope this helps

Answer:

Because if you add the amount of Ys together it equals 3y

Step-by-step explanation:

we know that

[tex]I=Prt[/tex]

where

I is the amount in interest

P is the investment

r is the interest rate

t is the time in years

Solve for t

[tex]t=I/(Pr)[/tex]

we have

[tex]I=\$1,400\\ P=\$27,000\\ r=4.2\%=0.042[/tex]

substitute

[tex]t=1,400/(27,000*0.042)=1.23\ years[/tex]

therefore

the answer is

[tex]1.23\ years[/tex]

to test the points, substitute the x-coordinate into the equation and if the value of y equals the y-coordinate then the point lies on the graph

(0, [tex]\frac{1}{2}[/tex]) → y = 0 + [tex]\frac{3}{4}[/tex] = [tex]\frac{3}{4}[/tex] ≠ [tex]\frac{1}{2}[/tex]

(0 , [tex]\frac{3}{4}[/tex]) → y = [tex]\frac{3}{4}[/tex] ← on graph

([tex]\frac{3}{4}[/tex], 0) → y = [tex]\frac{3}{8}[/tex] + [tex]\frac{3}{4}[/tex] ≠ 0

([tex]\frac{3}{4}[/tex],[tex]\frac{1}{2}[/tex] → y = [tex]\frac{3}{8}[/tex] + [tex]\frac{3}{4}[/tex] ≠ [tex]\frac{1}{2}[/tex]

([tex]\frac{1}{2}[/tex], 1) → y = [tex]\frac{1}{4}[/tex] + [tex]\frac{3}{4}[/tex] = 1 ← on graph

the points (0, [tex]\frac{3}{4}[/tex]) and ([tex]\frac{1}{2}[/tex], 1) are on the graph

The points that are contained in the graph of the straight line y = (1/2)x + 3/4 are (0,3/4) and (1/2,1).

An equation describes that both sides of the variables and constants are in different forms but they are equal.

To determine if each given point is contained in the graph of the equation Y = (1/2)x + 3/4 we will put the values of x in the equation and determine the corresponding value of y.

When x = 0, y = (3/4).

When x = (3/4), y = 9/8.

When x = 1/2, y = 1.

So, the points that are contained in the graph Y = (1/2)x + 3/4 are (0,3/4), (1/2,1).

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Answer:

Step-by-step explanation:

The line in the graph has a rise of 1 for each run of 1, so its slope is 1/1 = 1. The slope (x-coefficient) of the function f(x) = -7x+1 is -7, so that is not the function shown in the graph.

The wording "the range ... is increasing as the domain increases" is a bit unusual. Usually "domain" and "range" refer to intervals or sets of values over which the function is defined. While it is true that extending the interval of definition (domain) of the function will extend the range of values it produces, we suspect this is supposed to suggest that the slope of the line is positive. (As you pick increasing elements from the domain, the function will map those values to increasing elements of the range.)

box number one: given

box number two: angle addition postulate

box number three: 51 degrees + 39 degrees = m DEF

box number four: 90 degrees = m DEF

box number five: DEF is a right angle

box number six: definition of a right triangle

just took the test and these are the correct answers, hope i helped :)

Solution:

Given : ∠ D E G= 51°, ∠GEF=39°

To prove: Δ D E F is a right triangle.

Proof:

A right angle triangle D E F.

∠ D E F =90°.

Point G is on segment D F, and segment E G is drawn.

Now, taking ∠DEG and ∠GEF into consideration,

∠DEG=51° and ∠GEF=39°→→(Given)

∠DEG + ∠GEF =

∠DEF=51° + 39°

∠DEF=90°,showing Triangle D E F is a right triangle.