What is the justification for each step in solving the inequality? 3x+1/2<−x+4 Select from the drop-down menus to correctly justify each step.

Answer: CPCTC

Step-by-step explanation:

because in the step before that it was proved that the triangles were congruent and CPCTC is used after they are proved congruent.

By CPCT [Corresponding Part of congruent Triangle]

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hope i helped

-lvr

Answer:

Step-by-step explanation:

0.026803

Answer:

x=0

Step-by-step explanation:

(x^2 + 4x) - 2x = x^2 +x

Combine like terms

x^2 +2x = x^2 +x

Subtract x^2 from each side

2x =x

Subtract x from each

2x-x = x-x

x = 0

Answer:

[tex]x=0[/tex]

Step-by-step explanation:

[tex]x^2+4x-2x=x^2+x[/tex]

Combine like terms.

[tex]x^2+2x=x^2+x[/tex]

Add [tex]-x^2[/tex] and [tex]-2x[/tex] on both sides.

[tex]x^2+2x-x^2-2x=x^2+x-x^2-2x[/tex]

[tex]0=x-2x[/tex]

[tex]0=-1x[/tex]

Divide both sides by [tex]-1[/tex].

[tex]\frac{0}{-1} =\frac{-1x}{-1}[/tex]

[tex]0=x[/tex]

Answer:

Step-by-step explanation:

5x - 2= 6

Question = 5x - 2= 6

1. Isolate the variable

5x - 2= 6

   + 2 + 2

2. Simplify the like terms

6 + 2

= 8

3. Simplify the answer

Simplify by dividing both sides by 5

5x = 8

/5     /5

x = 8/5 or 1.6

The answers are:

x = 1.6

x = 8/5

x = 1  3/5

Hope this helped,

Kavitha

Answer:

144 cm^2

Step-by-step explanation:

8x6+4x10+4x8+4x6

48+40+32+24

80+40+24

120+24

144

Answer and Explanation:

Brielle will run the marathon faster.

Work:

Brielle: 13.1/1.25=10.48*10=104.8 minutes

Joshua: 13.1/1.5=8.73...*18=157.2 minutes

Brielle finished in 104.8 minutes.

Joshua finished in 157.2 minutes.

Brielle finished the half marathon race by 52.5 minutes faster than Joshua.

Hope this helps!!! PLZ MARK BRAINLIEST!!!

Brielle will run the marathon faster. Brielle will take 104.8 minutes to finish the race and  Joshua will take 157.2 minutes to finish the race.

The division is simply dividing a number by another number.

Given in the question the marathon race is of 13.1 miles long.

Brielle takes 10 minutes to cover 1.25 miles.

So to cover 1 mile he will take = 10/1.25=  8 minutes

So to finish the marathon race i.e. to cover 13.1 miles he will take the time= 8*13.1= 104.8 minutes.

Joshua takes 18 minutes to cover 1.5 miles.

So to cover 1 mile he will take = 18/1.5=  12 minutes

So to finish the marathon race i.e. to cover 13.1 miles he will take the time= 12*13.1= 157.2 minutes.

So from above, it is clear that Joshua is taking more time than Brielle to finish the race.

Brielle will run the marathon faster as he takes less time to finish.

Therefore Brielle will run the marathon faster. Brielle will take 104.8 minutes to finish the race and  Joshua will take 157.2 minutes to finish the race.

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Answer:

x ∈ ℝ

Step-by-step explanation:

Since this is a constant function, this domain is the set of all real numbers.

Hope this helped! :)

Answer:

x = -2

Step-by-step explanation:

For this question, the time given confuses me.  I know the rate of return is just total return divided by divided by investment, Assuming that Matt received the $400 in dividends as cash payouts, and they weren't reinvested into buying shares of the stock, then his total return over two years was $500, Now, if Matt's dividends were reinvested into the stock - and if you have a 401(k) or IRA, that's what usually happens - then his ROI would have been only 6% because he only made a profit of $100 on an investment of $1500. Note:  In the real world, in current market conditions, Matt probably would have got about a 5% return on a good stock, and Bella would have received about 0.05% on a savings account.

hope this helped you ;)

Matt probably would have got about a 5% return on a good stock.

The rate of return is just the total return divided by investment.

Consider that Matt received the $400 in dividends as cash payouts, and they weren't reinvested into buying shares of the stock, then his total return over two years was $500.

Now, if Matt's dividends were reinvested into the stock then his ROI would have been only 6% because he only made a profit of $100 on an investment of $1500.

In the real, current market conditions, Matt probably would have got about a 5% return on a good stock, and Bella would have received about 0.05% on a savings account.

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Answer:

Maximum =  756

Minimum =  600

Step-by-step explanation:

A square is a shape that has the large areas of a defined perimeter out of available rectangles. It implies they want the two parentheses to be as similar in value. as a result, to establish the maximum value of P.

And to establish the minimum value, to have the greatest difference for them. 1 + 2 + 3 ... +10=55, which wasn't even but which can be split as similarly as possible into 27 and 28 which have a product of 756. In this question it can be done in a variety of ways, one of which is:

(1 + 3 + 5 + 8 + 10) ×  (2 + 4 + 6 + 7 + 9) = 756

At the very least, the biggest difference can be created if one term is made of the smallest numbers, while the other full of the highest, or:

(1 + 2 + 3 + 4 + 5) × (6 + 7 + 8 + 9 + 10)=600

Answer:

2 cm

10 cm

Step-by-step explanation:

14/7 = 2

This helps to find because area of rectangle = bh or base times height.

A = 1/2 bh

30 = 1/2 b 6

30 = 3b

b = 10

Answer:

b = 2 cm

b = 10 cm

Step-by-step explanation:

Area of a Rectangle: A = lw

Area of a Triangle: A = 1/2bh

We are given area and length, so simply plug it in:

14 = 7w

w = 2 cm

We are given area and height, so simply plug it in:

30 = 1/2(6)(b)

30 = 3b

b = 10 cm

Answer:

B

Step-by-step explanation:

The postulate that can be used to link both triangles is AAS which means Angle Angle side

From the diagram, we can see that we have 2 equal angles and one side in between the two triangles

This means whatever proof we are bringing out is dependent on the two equal angles and the common side between the two triangles

Answer: Debit Supplies Expense $877 and credit Supplies $877

Step-by-step explanation:

From the question, we are informed that a physical count of supplies on hand at the end of may for Masters, inc. showed $1,253 of supplies on hand while the general leger balance before any adjusting is $2,130.

The adjusting entry for office supplies that should be recorded on may 31 will be the difference in the physical count and general ledger balance which is ($2130 - $1253) = $877. We then have to debit Supplies expense $877 and then credit supplies $877

Answer: 8 nickels

Step-by-step explanation:

To find the amount of nickels, we can use system of equations. Let's use n for nickel and d for dimes.

Equation 1

n+d=30

This equation comes from the total amount of coins.

Equation 2

0.05n+0.1d=2.6

This equation comes from the worth of the nickels and dimes added together.

To the amount of nickels, we can use elimination method.

0.1n+0.1d=3

0.05n+0.1d=2.6

Now that the dimes are equal, we can subtrace the equations.

0.05n=0.4

n=8

There are a total number of 8 nickels.

Answer:

The exterior angle is angle 4. The remote interior angles are 1 and 2.

Step-by-step explanation:

An exterior angle is an angle that is between a side of the shape and a line extended from the side next to it.

Remote interior angles in a triangle are the two angles that are not a linear pair with the exterior angle. (A linear pair is a pair of angles that add up to 180 degrees and form a line.) Essentially, the they are the two angles not next to the exterior angle. As a side note, if you add up the measures of the remote interior angles, the sum will be equal to the measure of the exterior angle.

If any of this is confusing, feel free to ask for clarification. I hope this helps! ☺

[tex]\displaystyle\bf\\f(x)=-x^2+2x+4\\\\x_{max}=\frac{-b}{2a}=\frac{-2}{2\times(-1)}=\frac{-2}{-2}=\boxed{\bf1}\\\\y_{max}=\frac{-\Delta}{4a}=\frac{-(b^2-4ac)}{4a}=\frac{-(2^2-4\times(-1)\times4)}{4\times(-1)}=\\\\\\=\frac{-(4-(-16))}{-4}=\frac{-(4+16)}{-4}=\frac{-20}{-4}=\frac{20}{4}=\boxed{\bf5}\\\\\\\textbf{The maximum has the coordinates: }~~\boxed{\boxed{\bf~M(1,~5)~}}[/tex]

Sososos

Step-by-step explanation:

Answer:

16.59

Step-by-step explanation:

Given:

[tex](ax+b)(bx+a)=26x^2+\Box\cdot x+26[/tex]

Expanding the left hand side, we have:

[tex](ax+b)(bx+a)=abx^2+a^2x+b^2x+ab\\=abx^2+(a^2+b^2)x+ab\\=26x^2+\Box\cdot x+26\\ab=26 \implies b=\frac{26}{a}[/tex]

Therefore:

[tex]a^2+b^2=a^2+\dfrac{26}{a} =\dfrac{a^3+26}{a}[/tex]

To find the minimum value, we take the derivative and solve for its critical point.

[tex]\frac{d}{da} (\frac{a^3+26}{a})=\frac{2a^3-26}{a^2}\\$Setting the derivative equal to zero, we have:\\2a^3-26=0\\2a^3=26\\a^3=13\\a=\sqrt[3]{13}[/tex]

Recall that:

[tex]\Box=a^2+b^2=\dfrac{(\sqrt[3]{13}) ^3+26}{\sqrt[3]{13}}\\=\dfrac{13+26}{\sqrt[3]{13}}\\\\\Box=16.59[/tex]

The minimum possible value of the coefficient of x is 16.59.

Answer:

173

Step-by-step explanation:

For sympliciy let the box equal y.

Expanding the left side we get (a*x+b)(b*x+a) = (a*b*(x)^2 + (a^2 + b^2)x + a*b). Hence we have that  (a*b*(x)^2 + (a^2 + b^2)x + a*b) = 26*(x)^2 + x*y + 26. Scince the coefficients of like terms in our equation must be equal, ab=26. Hence (a,b) = (1,26),(26,1),(-1,-26),(-26,-1),(2,13),(13,2),(-2,-13),(-13,-2). Since a^2 + b^2 = y we can see that the only 2 values of y are 677 and 173 (by simply plug in the values of (a,b)), taking the smaller of the two our answer is [173].

Answer:

Please check the answer whether it is correct or not

Answer:

45:40

Step-by-step explanation:

You take the first time and divide 60 by that number (60/4=15) Then you multiply it by the numbers of shoes being created (3*15=45) Repeat this for the other part and you have your answer

Answer:

f^-1(x) = _x__

               5

Step-by-step explanation:

Answer:

[tex] {f}^{ - 1} (x) = \frac{x}{5} [/tex]

Step-by-step explanation:

f(x) = 5x

To find f^-1(x) equate f(x) to y

That's f(x) = y

y = 5x

Interchange the variables

x = 5y

Make y the subject by dividing both sides by 5

y = x/5

The final answer is

f^-1(x) = x/5

Hope this helps you.

Answer:

11 feet by 39 feet.

Step-by-step explanation:

In this case, the perimeter, P, is 100 ft.

If the length of the shed is 6 feet longer than three times the width, that means that the length, L, is equivalent to 6 plus 3 times the width, W.

So, we have an equation: P = 2 * L + 2 * W.

100 = 2 * (6 + 3W) + 2 * W

100 = 12 + 6W + 2W

100 = 12 + 8W

8W + 12 = 100

8W = 88

W = 11

And so, we know that the width is 11 feet.

To solve for the length...

L = 6 + 3W

L = 6 + 3 * 11

L = 6 + 33

L = 39

So, the length is 39 feet.

Now, you have the dimensions of the shed: 11 feet by 39 feet.

Hope this helps!

Answer:

75%

Step-by-step explanation:

27 ÷ 36 = 0.75

0.75 → 75%

75% of the crew are men

Hope this helped! :)

Answer:

               75%  

Step-by-step explanation:

[tex]\dfrac{27}{36}=\dfrac{27:9}{36:9}=\dfrac34=\dfrac{3\cdot25}{4\cdot25}=\dfrac{75}{100}=75\%[/tex]

Answer:

8

Step-by-step explanation:

Each movie costs $4 since the bill increased by $4 when the customer watched a movie.

$29 - $25 = $4

Create an equality using this information.  Solve for x.

25 + 4x > 60

(25 + 4x) - 25 > (60) - 25

4x > 35

(4x)/4 > (35)/4

x > 8.75

Since the bill must stay under $60, round the answer down.  The customer can watch 8 movies with the given price range.

Answer: B. rectangular pyramid

Answer:

1/25

Step-by-step explanation:

The probability of drawing a blue marble, replacing it, then drawing a yellow marble is 1/25.

Given,

A bag contains four red marbles, six green marbles, eight yellow marbles, and two blue marbles.

We need to find the probability of drawing a blue marble, replacing it, then drawing a yellow marble.

A combination is used to select required items from a set where the order of selection does not matter.

It is given by:

n^Cr = n! / r! (n-r)!

Where n = the number of elements present in a set.

Find the number of each marble.

Red marbles - 4

Green marbles - 6

Yellow marbles - 8

Blue marbles - 2

Find the probability of drawing a blue marble

P ( B ) = ^2C_1 / ^20C_1

          = (2! / 1!) / (20! / 19! 1!)

          = 2 / 20

          = 1/10

Find the probability of drawing a yellow marble

P ( Y ) = ^8C_1 / ^20C_1

          = (8! / 1! 7!) / (20! / 191 1!)

          = 8 / 20

          = 2 / 5

Find the probability of drawing a blue marble, replacing it, then drawing a yellow marble

Both the probability is independent so,

P = P ( B ) X P ( Y )

  = 1/ 10 X 2 / 5

  = 1 / 25

Thus the probability of drawing a blue marble, replacing it, then drawing a yellow marble is 1/25.

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Answer:

-7 and -4

Step-by-step explanation:

The graph of the function f(x) = (x + 4)⁶ (x + 7)⁵ cross the X axis at x = -4 and x = -7.

A function is a relation from a set A to a set B where the elements in set A only maps to one and only one image in set B. No elements in set A has more than one image in set B.

Given is a function,

f(x) = (x + 4)⁶ (x + 7)⁵

When the function cross the X axis, the value of the function will be 0.

Let f(x) = 0

(x + 4)⁶ (x + 7)⁵ = 0

This implies that, either x + 4 = 0 or x + 7 = 0

x + 4 = 0 ⇒ x = -4

x + 7 = 0 ⇒ x = -7

Hence the roots are -4 and -7 where the function crosses the X axis.

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Answer:

-1

Step-by-step explanation:

each time it moves by the next even number. (Difference between 5 and 7 is 2, difference between 7 and 3 is 4, difference between 3 and 9 is 6, etc.)

Answer:

r = 3x.

Step-by-step explanation:

The volume of the cylinder = πr^2 h

= π (2x)^2 9x

= 36x^3 π

This is also the volume of the sphere so

36 x^3 π  = 4/3  π r^3

36x^3 = 4/3 r^3

r^3 = 36 x^3 * 3/4

r^3 = 27 x^3

r = cube root of  27 x^3

r = 3x.

Answer:

0.0236 m per minute,

Step-by-step explanation:

Volume of the cone V = 1/3 π r^2 h.

Diameter = 2r = 2h so r = h

and V = 1/3 π h^3

So  the rate of change of volume with height =

dV / dh =  π h^2.

We are given that dV/dt = 6.

So the rate of change of height: dh/dt = dV/dt * dh/dV

= 6 * 1/ π h^2

When  h = 9

dh/dt = 6 / 81π m per minute

= 0.0236 m per minute,