Mathematics College

Solve for a 6(a+3)=18+6a

Answers

Answer 1
Expand

(6a + 18 = 18 + 6a)

Cancel 6a on both sides

(18 = 18)

Since both sides are equal, there are infinitely many solutions.
Answer 2

The equation 6(a+3) = 18+6a is an identity after canceling out like terms on both sides, which implies that the solution for 'a' is all real numbers.

To solve for a in the equation 6(a+3) = 18+6a, we begin by expanding the left side of the equation:

6a + 18 = 18 + 6a

We notice that there are terms on both sides of the equation that can be cancelled out. The 6a on the left side can be subtracted from both sides, as well as the constant 18.

After cancelling out these terms, we are left with:

0 = 0

This equation suggests that the original equation is an identity, meaning that the value of a can be any real number, as the original equation holds true for all values of a.

Related Questions

Pre cal/cal master needed

F(x)= 2x^2 + 3x-2 and g(x)= x-2

find equation for f(g(x))

My answer : 2x^2 -8 +3x-8

True answer: 2x^2 -5x

How do we get true answer? I plugged in g(x) into the x's of F(x) but got a waaaaaay different answer.

Answers

Take x-2 and insert it into 2x^2 + 3x-2 where the x is located 
2x^2 + 3x-2
2(x-2)^2 + 3(x-2)-2

Now work out 2(x-2)^2 + 3(x-2)-2 also follow PEMDAS
2(x-2)^2 + 3(x-2)-2 
Since (x-2)^2 is an Exponent, lets work with that first and expand (x-2)^2.
(x-2)^2
(x -2)(x-2)
x^2 -4x + 4
Now Multiply that by 2 because we have that in 2(x-2)^2
(x-2)^2  =  x^2 -4x + 4
2(x-2)^2  =  2(x^2 -4x + 4)
2(x^2 -4x + 4) = 2x^2 - 8x + 8
2x^2 - 8x + 8

Now that 2(x-2)^2 is done lets move on to 3(x-2).

Use the distributive property and distribute the 3
3(x-2) = 3x - 6

All that is left is the -2 

Now lets put it all together 
2(x-2)^2 + 3(x-2)-2

2x^2 - 8x + 8 + 3x - 6 - 2

Now combine all our like terms 
2x^2 - 8x + 8 + 3x - 6 - 2
Combine:  2x^2      =  2x^2 
Combine: -8x + 3x  =  -5x
Combine:  8 - 6 - 2 =   0

So all we have left is
2x^2 - 5x





Find the true balance:
Check register balance:$463.80
Bank statement balance: $592.53
Outstanding checks: $49.80 and $86.93
Service charge: $8.00

A. $592.53

B. $584.53

C. $327.07

D. $455.80

Answers

Answer:

D. $455.80

Step-by-step explanation:

True Balance = Bank Statement - Outstanding Checks

= $592.53 - ($49.80 + $86.93)

= $455.80

Problem Page A science fair poster is a rectangle 48 inches long and 24 inches wide. What is the area of the poster in square feet?

Answers

48/12 = 4 feet

24/2 = 2 feet

 4 *2 = 8 square feet

Answer:

                     8 feet squared

Find the numerator of the equivalent fraction with denominator 12 :

1/2

Answers

The answer is 6/12 is 1/2. To figure half of 12 you could've divided it by 2 or .5 because they are the same
Final answer:

The numerator of the equivalent fraction with denominator 12 for 1/2 is 6. This comes from multiplying both the numerator and denominator of 1/2 by the same number (6).

Explanation:

To find the numerator of the equivalent fraction with denominator 12 for 1/2, we simply multiply both parts of the fraction by the same number such that the denominator becomes 12. We know that 2 * 6 equals 12, so we multiply the numerator 1 by 6 as well, which gives us the numerator 6.

Therefore, the fraction 1/2 is equivalent to 6/12.

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Find the area of the rectangle?! Please :)

Answers

Multiply the length and width: 
L*W = 36*(x-3) = 36*x - 36*3 = 36x - 108

The answer is 36x - 108
(the units are "square kilometers" or "sq km" or "km^2")

Find the probability of randomly selecting 4 good quarts of milk in succession from a cooler containing 20 quarts of which 5 have spoiled

Answers

Need 4 good quarts out of 20, of which 5 have spoiled.

=>

Need 4 good quarts out of 15 good quarts out of 20.

Getting

P(G)=15/20
P(GG)=(15/20)(14/19)
P(GGG)=(15/20)(14/19)(13/18)
P(GGGG)=(15/20)(14/19)(13/18)(12/17)
=91/323

(fractions provide exact answers in probability problems.  Decimals are approximate most of the time).
Final answer:

The question asked is related to probability, which is a topic in Mathematics. After calculating the probability of selecting a good quart of milk four times in a row (considering that the quantity decreases each time a good quart is selected), the probability equates approximately to 0.3 or 30%.

Explanation:

The given question is a statistical problem related to probability and involves the concept of independent events. In this case, each quart of milk being good or spoiled is an independent event, meaning the outcome of one event doesn't affect the other.

In the cooler, there are 20 quarts of milk in total, 15 of which are good (20 - 5 spoilt quarts equals 15 good ones). Hence, the probability of selecting a good quart of milk at first is 15/20, or 0.75.

After removing one good quart, there are now 14 good quarts out of 19. Hence, the probability of drawing a second good quart is 14/19. We can calculate the probabilities for the third and fourth quarts in the same way, resulting in 13/18 and 12/17 respectively.

Since these are independent events, the probability of all these events happening is the product of their individual probabilities. Therefore, the answer is 0.75* (14/19)* (13/18)* (12/17), which is approximately 0.3 or 30%.

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what is the value of the underlined digit? 587

Answers

There is no underlined dogit
If the line is under the 5 it's five hundreds, in the 8 eight hundreds, and the 7 seven ones.

Convert 1.2x10^(-2) into standard form

Answers

Its scientific Notation here's your answer:

1.2×10^-2

Sense its negative you will have to go left.

.0012

So your answer is
.0012

n standard form, we express it without using scientific notation, so [tex]1.2\times10^{-2}[/tex] becomes 0.012.

We have,

In scientific notation, a number is expressed as the product of a coefficient between 1 and 10 and a power of 10.

Given [tex]1.2\times10^{-2}[/tex],

We can rewrite it by moving the decimal point two places to the left to obtain 0.012.

The coefficient 0.012 is between 0.01 and 0.1, which is equivalent to 1/100 or 1 divided by 10 raised to the power of 2.

Thus, we can write it as 1.2 multiplied by 10 raised to the power of -2.

Thus,

In standard form, we express it without using scientific notation, so [tex]1.2\times10^{-2}[/tex] becomes 0.012.

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The denominator of a fraction is 1 more than the numerator. If both the numerator and denominator are decreased by 3, the resulting fraction is equal to 4/5. Find the fraction

Answers

Sent a picture of the solution to the problem (s).

which is 625 written as a power of 5 (exponets) A. 4*5 B.3*5 C.5*3 D.5*4

Answers

625 written as a power of 5 = 5^4
because
5^4 = (5) * (5) *(5) * (5)  =625

answer is
D.5^4
If 625 is written as a power of 5 the Answer is D. 5*4

chloe is sorting items at a thrift store. She finds a box of tiny blocks that has 1,344 written on the outside. She can see that each layer in the box has 64 blocks. How many layers of blocks are there?

Answers

There is 21 layers in the box.

Answer: There are 21 layers of blocks.

Step-by-step explanation:

Since we have given that

Number of blocks in a box = 1344

Number of blocks in each layer = 64

We need to find the number of layer of blocks.

So, the number of layer of blocks is given by

[tex]\dfrac{1344}{64}\\\\=21[/tex]

Hence, there are 21 layers of blocks.

A soccer ball is kicked into the air from the ground. If the ball reaches a maximum height of 25 ft and spends a total of 2.5 s in the air, which equation models the height of the ball correctly? Assume that acceleration due to gravity is –16 ft/s2.

Answers

Hello,

g=9.81m/s²= 9.81/0.3048 =32.18.. ft/s² rounded to 32

h=-g/2*t²+vt+h0
if t=0,h=0 ==>h0=0

==>h=-16*t²+vt
50 ft in 2.5s ==> 25 ft in 1.25s

25=-16*1.25²+v*1.25
==>v=50/1.25=40

Equation h=-16t²+40*t

Solve for x: 1/4(4x+15)=24

Answers

t's solve your equation step-by-step.14(4x+15)=24Step 1: Simplify both sides of the equation.14(4x+15)=24(14)(4x)+(14)(15)=24(Distribute)x+15/4=24Step 2: Subtract 15/4 from both sides.x+15/4−15/4=24−154x=81/4

Solve for A. R = x(A + B) A = (R - B)/x A = (B - Rx)/x A = (R - Bx)/x

Answers

R = x(A + B)...distribute
R = Ax + Bx.....subtract Bx
R - Bx = Ax...divide both sides by x
(R - Bx) / x = A <==

In the given equation of the provided problem, the solution for A is A =  [tex]\frac{R - xB}{x}[/tex].

Mathematically, an equation is a statement that asserts the equivalency of two expressions. It consists of two hands, the left-hand side( LHS) and the right-hand side( RHS), separated by an equal sign( =). The LHS and RHS can be numbers, variables, constants, or further complex fine expressions.

To solve for A in each of the given equations, we'll isolate the variable A on one side of the equation. Let's go through each equation:

R = x(A + B)

To solve for A, we'll start by expanding the expression on the right side:

R = xA + xB

R - xB = xA

Divide both sides of the equation by x to solve for A:

A = [tex]\frac{R - xB}{x}[/tex].

Therefore, the solution for A is A =  [tex]\frac{R - xB}{x}[/tex].

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Fine the missing coordinate of the ordered pair

Answers

[tex]\bf 6x+7y-6=0\qquad \qquad (\stackrel{x}{-2}~,~\stackrel{y}{?}) \\\\\\ \textit{if x = -2 then }\implies 6(-2)+7y-6=0\implies -12+7y-6=0 \\\\\\ 7y-18=0\implies 7y=18\implies y=\cfrac{18}{7}[/tex]

Specify 3 fractions with different denominators that have an LCD of 24

Answers

1/3, 1/4, 1/8 The answer given is not the only possible answer. You need to come up with 3 different fractions so that the LCD (least common denominator) So first, determine the prime factors of 24. 24 = 2 * 2 * 2 * 3 Now you want some denominators that will need all of those prime factors. For the above list of 3, 4, 8, only the 3 and 8 are important, since one of them uses the prime factor of 3 and the other uses 3 prime factors of 2, so the LCD for those 2 numbers is 24. The 3rd denominator could be almost anything that uses some combination of prime factors 2,2,2,3 such as 1/2, 1/4, 1/6, 1/12, etc. I just happened to pick 1/4. The only real restriction is that none of the denominators can use any extra prime factors. If they did. then the resulting LCD would not be equal to 24.

Solve the system using the elimination method.

2x + 2y + 5z =−1

2x − y + z =2

2x + 4y − 3z =14

What x,y, and z?

Answers

Multiplying the first equation by -1 and adding it to the third, we get 2y-8z=15 and by multiplying the first equation by -1 and adding it to the second equation, we get -3y-4z=3

Using the two equations, we have 
2y-8z=15
-3y-4z=3

Multiplying the second equation by -2 and adding it to the third, we have 8y=9 and y = 9/8 by dividing both sides by 8. Plugging it back into
-3y-4z=3, we have -27/8-4z=3 and by adding 27/8 to both sides, we have -4z=51/8 and by dividing both sides by -4 we get z=-51/32.

Plugging it into 2x − y + z =2, we get 2x-9/8+5(-51/32)=2, we get x=151/64 by adding -(5(-51/32)) to both sides as well as adding 9/8 to both.

50 POINTS!!! DO NOT ANSWER JUST FOR THE POINTS!!! IF YOU DO, IF YOU DO ALL OF YOUR EARNED POINTS WILL BE TAKEN~~~~~~~~~~~~~~~
Find this a bit complicated. Please explain and show work with steps.

Suppose f(x)=–x²–4x+4. Compute the following:

A. f(–5)+f(5)=

B. f(–5)–f(5)=

Answers

A. f(-5) = -(-5)^2-4(-5)+4 = -1

  f(5) = -(5)^2-4(5)+4 = -41

-1 + -41 = -42

B. -1 - -41 = 40

1/3 (9x+3)=3x+1 what does x equal

Answers

Distribute on the left
3x+1=3x+1

Since the equations are equivalent, x can be any number and the equation will be true.

Final answer: Infinitely many solutions

Select the expression that has a quitiont greater than 1. Explain your reasoning.

4 2/3 divided by 5 1/4= 3 1/8 divided by 2 2/5=
1 6/7 divided by 2 1/3= 5 3/4 divided by 7 3/8=

Answers

The answer is 3 1/8 divided by 2 2/5. What I did was turn all of them into improper fractions then divided (which is basically cross-multiply). By doing so, you would have 14/3 divided by 21/4 which equals 0.8888888 or 8/9 in fraction form, 25/8 divided by 12/5 which equals 1.30208333 or 1 29/96, 13/7 divided by 7/3 which equals 0.79591836 or 39/49, and 23/4 divided by 59/8 which equals 0.77966101 or 46/59

Final answer:

To find the expression with a quotient greater than 1, we convert the mixed numbers into improper fractions and perform the division for each expression. The expression that gives a quotient greater than 1 is 5 3/4 divided by 7 3/8.

Explanation:

To find the expression that has a quotient greater than 1, we need to divide the given fractions. Let's examine each expression:

4 2/3 divided by 5 1/4: To divide mixed numbers, we convert them into improper fractions and then perform the division. In this case, the quotient is less than 1.

3 1/8 divided by 2 2/5: Similar to the first expression, we convert the mixed numbers into improper fractions and divide. The quotient is also less than 1.

1 6/7 divided by 2 1/3: Again, convert the mixed numbers into improper fractions and perform the division. The quotient is less than 1.

5 3/4 divided by 7 3/8: Convert the mixed numbers into improper fractions and divide. The quotient is greater than 1, so this is the expression we're looking for.

Therefore, the expression with a quotient greater than 1 is 5 3/4 divided by 7 3/8.

An urn contains 8 red balls, 8 white balls, and 8 blue balls, and a sample of 5 balls is drawn at random without replacement. Compute the probility that all of the balls in the sample are the same color.

Answers

(8/24)*(7/23)*(6/22)*(5/21)*(4/20)

If Logx (1 / 8) = - 3 / 2, then x is equal to

A. - 4

B. 4

C. 1 / 4

D. 10

Answers

answer is C 1/4

 see attached picture, it is not exact but with rounding it comes out correct.

Kendra and her horse completed the barrel racing course in 15.839 seconds. What is this number rounded to the nearest tenth? :explain how you decided

Answers

the answer is 15.84.

To find the nearest tenth, you go to the 3rd place after the decimal and decide: if the value is 5 or greater, go to the second place after the decimal and round up one. If it does not, the value of the second decimal stays the same.
15.839 rounded to the nearest tenth would be 15.8. It would be that because when you look at the number to the right when it is below five you leave the number your rounding alone, but when the number to the right is higher you would add one to the number that you are rounding. Easy. 

What's S divided by 8=2 ?.....Answer needed ASAP.

Answers

16 ÷ 8 = 2
S = 16
Hope it helps :)
S/8 = 2

S/8 * 8 = 2 * 8

S = 2 * 8

S = 16

hope this helps

A principal of $1,000 is invested in an account paying an annual interest rate of 4% using the formula A=P(1+r/n) ^nt
find the amount in the account after 2 years if the account is compounded annually

Answers

 If $1000 is invested now with simple interest of 8% per year. Find the new amount after two years.P = $1000, t = 2 years, r = 0.08.A = 1000(1+0.08(2)) = 1000(1.16) = 1160

Point Q is the midpoint of segment PR. If PQ= (15x-2) and QR= (5x+3) find the value of Q.

Answers

is that the measure or linear equation
check the picture below.

so, the distance to Q, or one can say Q's length is the same as PQ's. or QR's for that matter.

Point C(3.6, -0.4) divides in the ratio 3 : 2. If the coordinates of A are (-6, 5), the coordinates of point B are . If point D divides in the ratio 4 : 5, the coordinates of point D are

Answers

Given:
A has coordinates (-6,5)
C has coordinates (3.6,-0.4).
C divides AB in the ratio 3:2.

Refer to the diagram shown below.
The coordinates of B are determined by
[tex] \frac{3.6-(-6)}{x-(-6)} = \frac{3}{3+2} \\ \frac{9.6}{x+6} = \frac{3}{5} \\ 3(x+6) = 48 \\ 3x +18=48 \\ x=30/3=10[/tex]
Also,
[tex] \frac{5-(-0.4)}{5-y} = \frac{3}{5} \\ 3(5-y) = 27 \\ 15-3y=27 \\ y= \frac{12}{-3} =-4[/tex]

Answer:
The coordinates of B are (10,-4).

Now, we know the coordinates of line segment AB as A (-6, 5) and B (10,-4).
D (x,y) divides AB in the ratio 4:5.
Therefore
[tex] \frac{x-(-6)}{10-(-6)} = \frac{4}{4+5} \\ \frac{x+6}{16} = \frac{4}{9} \\ 9(x+6)=64 \\ 9x+54=64 \\ x=1.11[/tex]
Also,
[tex] \frac{5-y}{5-(-4)} = \frac{4}{9} \\ 5-y = 4 \\ y = 1[/tex]

Answer:
The coordinates of D are (1.11, 1)

Answer:

I just had to do this problem and,

B is (10, -4) and D is (58/9, -2)

Step-by-step explanation:

93 times the sixth power of ten

Answers

93 x 6^10

93 x 60466176 = 5623354368
hope this helps

The motorcycle engine on a kawasaki ninja 1000 has a displacement of 1043 cubic-centimeters (cm3). in order to calculate its engine displacement in cubic-inches (in3) what unit conversion factor would you use to multiply the given displacement

Answers

1 in3 / (2.54)3 cm3      this is the answer

[tex]\boxed{\boxed{ \ 0.061 \frac{inch^3}{cm^3}\ }}[/tex]

Further explanation

We will calculate the unit conversion factor used to convert its engine displacement from cubic-centimeters to cubic-inches.

The relationships between inch and cm are as follows:

[tex]\boxed{ \ 1 \ inch = 2.54 \ cm\ }[/tex]

Inches and cm represent units of length.

Made into fractions, 1 inch as the denominator and 2.54 cm as the numerator.

[tex]\boxed{ \ \frac{1 \ inch}{2.54 \ cm} \ }[/tex]

As a unit conversion factor of volume, the numerator and the denominator in cubic.

[tex]\boxed{ \ \frac{(1 \ inch)^3}{(2.54 \ cm)^3} \ }[/tex]

[tex]\boxed{ \ \frac{1 \ inch^3}{16.387 \ cm^3} \ }[/tex]

Thus, we get the unit conversion factor

[tex]\boxed{\boxed{ \ 0.061 \frac{inch^3}{cm^3}\ }}[/tex]

Let's use this unit conversion factor to calculate its engine displacement in new units.

[tex]\boxed{= 1,043 \ cm^3 \times 0.061 \ \frac{inch^3}{cm^3}}[/tex]

Note for cm³ units that have been crossed out.

The conversion result is [tex] \ \boxed{ \ 63.623 \ inch^3\ }[/tex]

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Keywords: the motorcycle engine, Kawasaki Ninja 1000, 1043 cubic-centimeters (cm³), to calculate, its engine displacement, in cubic-inches (in³), what unit conversion factor

The temperature in Minneapolis changed from -7°F at 6 AM to 7°F at noon. how much did the temperature increase?

Answers

that would be 7 - (-7)  = 7 + 7 = 14 degrees F
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