Justify each step in solving the equation 6x = 3(x+4) by writing a reason for each statement.
Answers
6x = 3x +12 minus 3x
6x- 3x = 3x +12 - 3x
3x = 12 division with 3
3x/3 = 12/3
x=4
Related Questions
you can use similar triangles to find the height of a tree. Triangle ABC is similar to triangle DEC. what is the height of the tree?
please explain it too ^_^
Answers
AC/DC = BC/EC =AB/DE = k
BC= 9ft + 6ft = 15
BC/EC= k
15/6=k
Now that we know the k we can find the height of the tree that's equal to AB:
AB/DE= k
AB/4=15/6
6AB= 15 x 4
AB= 60/6 = 10
The height of the tree is 10ft
The height of the tree is 10 feet.
What is a triangle?A triangle is a three-sided closed-plane figure formed by joining three noncolinear points. Based on the side property triangles are of three types they are Equilateral triangle, Scalene triangle, and Isosceles triangle.
We know the ratios of the lengths of the corresponding sides are equal when two figures are similar, if triangle ABC and triangle DEC are similar, then we may write,
AC/DC = BC/EC = AB/DE = k
BC= 9ft + 6ft = 15
BC/EC= k
15/6=k
Now from this value of 'K' we can determine the height of the tree which is,
AB/DE = k
AB/4 = 15/6
6AB = 15 x 4
AB = 60/6 = 10
The height of the tree is 10ft.
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Set up an equation that can be used to solve the problem. Solve the equation and determine the desired value.
At a boating and sports store, the cost of renting a personal watercraft is $53 per half hour, which includes a 6% sales tax. Determine the cost of a half hour rental before tax.
The equation is ?. The cost of a half hour rental is $? Per half hour.
Type an equation using x as the variable.
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[tex]y = 53x[/tex]
y= 53(1)
[tex]y = 53[/tex]
do any of the points below fall on the linear equation shown. Please show work
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Example: Determine whether (2,0) lies on the graph of the given line.
Subst. 2 for x: y = (9/5)(2-273) + 32 = -455.8. This is not equal to the given ordinate (0), so NO, (2,0) does NOT lie on the graph of the given function.
4(x+8)-4=34-2x steps
Answers
write the answer as a decimal fraction 14/100=? /10+? /100=?
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To write the fraction 14/100 as a decimal fraction, divide the numerator by the denominator. The result is 0.14. Additionally, dividing any number by 100 will result in moving the decimal two places to the left.
Explanation:To write the fraction 14/100 as a decimal fraction, divide the numerator (14) by the denominator (100). 14 divided by 100 is equal to 0.14.
To find an expression as a decimal fraction, you can first convert the fractions to a decimal by dividing the numerator by the denominator.
For example, 10/100 is equal to 0.10 (10 divided by 100) and ?/100 is equal to ? (dividing any number by 100 will result in moving the decimal two places to the left).
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What is the smallest power of 10 that would exceed 987,654,321,098,765,432?
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A baker used 4 cups of flour to make 5 batches of brownies. He used_of a cup of flour to make 1 batch of brownies
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First of all, Let x = the mystery amount of flour
To create my equation, I put cups of flour over the amount batches in a formation, kind of like a fraction.
cups
-----------
batches
Next, I fill in the values.
cups 4
----------- = ---------
batches 5
The 4/5 represents the first ratio of flour/batches.
cups 4 x
----------- = --------- = ---------
batches 5 1
Since we do not know that amount of flour it took to make one batch, we put x in it's place.
Now it's time to cross multiply. It's exactly like it sounds! Multiply diagonally.
Multiply 5 and 'x'. Multiply 4 and 1.
You end up with a eqaution that looks like:
5x = 4
As you would for any solve-by-x equation, divide the five on both sides.
5x= 4
- -
5 5
4/5 = Four-Fifths
5/5 cancels itself out and poofs into thin air.
You end with x = 4/5
This is the answer.
The baker used 4/5 cups of flour to make 1 batch of brownies :)
Find the outlier in the data: 38, 38, 18, 28, 36, 30, 39, 32. How does the outlier affect the mean? If necessary, round to the nearest tenth. 43; raises it by 1.5. 18; lowers it by 2. 43; lowers it by 1.5. 18; raises it by 2.
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and it lowers the mean by about 2
Please help me!! This is due by 11.59pm. Please show how you got the answer. I got $270.
Answers
Noah currently has an account balance of $2,976.45. He opened the account 11 years ago with a deposit of $1,963.45. If the interest compounds quarterly, what is the interest rate on the account?
Answers
Acct. balance A (11)= $2,976.45
Pricipal=$1,963.45
Compounded (n)=quarterly (4)
rate=r
Compound interest formula: A (t)=p (1+r/n)^nt
What we need toi find:
If the interest compounds quarterly, what is the interest rate on the account? Find r.
A (t)=p (1+r/n)^nt
2976.45=1963.45 (1+r/4)^(4×11)
2976.45=1963.45 (1+r/4)^44
2976.45/1963.45=1963.45/1963.45 (1+r/4)^44
1.5159=(1+r/4)^44
(1.5159)^(1/44)=((1+r/4)^44)^(1/44)
1.0095=1+r/4
1.0095-1=1-1+r/4
.0095=r/4
.0095(4)=r/4 (4)
.038=r
Rate = 3.8%
Answer:
The interest rate is 3.79% or 3.8%
Step-by-step explanation:
The formula to find how much money A we have at the end of t years if we start with a principal or amount of money P today and the interest is compounded n times in the years is:
A=P(1+ r/n)^(nt) (1)
Here A = $2,976.45 the final amount
t = 11 years
P = $1,963.45.
and n = 4 because the interest is compounded quarterly or 4 times in the year.
We the need to simplify the interest rate r in (1) so:
A=P(1+ r/n)^(nt) (1)
A/P = (1+ r/n)^(nt)
(A/P)^(1/nt) = (1+ r/n)
(A/P)^(1/nt) - 1 = r/n
((A/P)^(1/nt) - 1 ) * n = r
r = ((A/P)^(1/nt) - 1 ) * n
We replace values and solve doing parenthesis exponents first
r = ((2,976.45/1,963.45.)^(1/(4*11)) - 1 ) * 4
r= ((1.51^(1/44)) -1)*4
((1.51^(1/44)) -1)*4
r= (1.009499443 - 1)*4
r= 0.009499443 *4 = 0.037997773
That expressed in percentage multiplying by 100 is 3.79% or 3.8% interest
The figure shows the letter T and four of its transformed images—A, B, C, and D. (See image.)
Which of the four images was formed by a reflection of the letter T?
A) A
B) B
C) C
D) D
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I believe it is
Benjamin solved the equation 3+/2=10 and justified each step as shown. Identify Benjamin’s error and fix his mistake.
3+x/2=10 GIVEN
x/2=7 MULTIPLICATION PROPERTY OF EQUALITY
x=14 SUBTRACTION PROPERTY OF EQUALITY
Answers
3 + x / 2 = 10
Multiply 2 on both sides.
3 + x = 20
Subtract 3 from both sides.
x = 17.
What he did wrong:
He subtracted the three on both sides before he multiplied the two. This will make him get the incorrect answer because he did it in the wrong order.
Hope this helps!
Dr. McDonald thinks that his group of earth science students is particularly special (in a good way), and he is interested in knowing if their class average falls within the boundaries of the average score for the larger group of students who have taken earth science over the past 20 years. Because he has kept good records, he knows the means and standard deviations for both his group of 36 students and the larger group of 1,000 past enrollees. Here are the data he has, and the values for which you will need to compute the z-test
Answers
A recipe requires 1/4 lb of onions to make 3 servingsof soup. Mark has 1 1/2 lb of onions. How many servings can mark make?
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We know that if you have 1/4 Ib of onions, that will make 3 servings. If we make a unit rate table, you'll end up with 18 servings when you have 1 1/2 Ibs of onions.
He would be able to make 18 servings. Hope this helps.
May.
What is 23/35 simplified?
Answers
*But if you do 1/1, it will be 1; so this won't work properly.
So the answer is 23/35.
A pet store has 9 puppies and 48 kittens.
What is the ratio of kittens to puppies?
Enter your answer in simplest fractional form in the box.
Answers
answer
ratio of kittens to puppies = 16/3
hope it helps
The ratio of kittens to puppies is [tex]\dfrac{16}{3}[/tex].
Given:
The number of puppies is 9.
The number of kittens is 48.
To find:
The ratio of kittens to puppies.
Explanation:
The ratio of kittens to puppies is the fraction of the number of kittens and the number of puppies. So,
[tex]\text{Ratio}=\dfrac{\text{Number of kittens}}{\text{Number of puppies}}[/tex]
[tex]\text{Ratio}=\dfrac{48}{9}[/tex]
[tex]\text{Ratio}=\dfrac{16}{3}[/tex]
Therefore, the ratio of kittens to puppies is [tex]\dfrac{16}{3}[/tex].
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Find the value of x (5x) (3x+12
Answers
The value that shows the expansion of the given algebraic expression is 6.
What is the solution to the algebraic expression.
An algebraic expression is a mathematical expression that has the variables, coefficients, and its arithmetic operators
In the complete question attached below, we are to find the value of x.
We can see that the angles are alternate angles.
So, 5x = (3x + 12).Combine like terms, we have:
5x - 3x = 12
2x = 12
x = 12/2
x = 6
Therefore, the value of x is = 6.
What is the sum of the geometric sequence −4, 24, −144, … if there are 7 terms?-159,964
−26,661
26,661
159,963
Answers
mutiply -144 by -6, then 864 by -6, then -5184 by -6. then 31104 by -6 to get -186624
so we have -4, 24, -144, 864, -5184, 31104, -186624 as the seven terms in the geometric sequence, now we just need to add these together and getting the final answer of -159,964
Answ
-159,964
Step-by-step explan
I got it right on the test
How do you write 1/10 in percent
Answers
10/100 = 0.10
0.10 = 10%
10% is your answer
hope this helps
You put $550 in an account that earns 4.4% simple interest per year. How much interest do you earn in 6 month
$1.21
$12.10
$121.00
$145.20
Answers
24.2/12=2.016 $ in month
2.016*6=12.10 $
A farmer had 1,000 horses and cows. After selling some of them, he had 550 horses and 350 cows left. How many horses and cows did he sell altogether?
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is 5 factor of the number 38 yes or no
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Simplify this algebrtic expression
Z-4/4+8
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brainliest answer plz:)
What number goes on top and how do you solve it.
Answers
See, 7 = 3+4, 8 = 5 +3, etc.
So, the top would be 16 + 17.
16 + 17 = 33
So 33 goes on top.
A soccer field has an area of 7/8 square miles. The length of the field is 2/5 miles. What is the width of the soccer field?
Answers
Answer: The answer is 35/16 miles
Step-by-step explanation: I have my ways ;>
ShopRite has jeans on sale for 3/10 off .Save more has jeans on sale for 33% off for has a better sale on jeans?explain.
Answers
Save more jeans are 33% off
4. Grace works from 10 to 20 hours per week while attending college. She earns $9.00 per hour. Her roommate Frances also has a job. Her pay for t hours each week is given by the function f(t)= 10t, where 5
Answers
Part A:
Given that Grace's time is rounded to the nearest quarter of an hour. The domain for Grace is given by {10, 10.25, 10.50, 10.75, - - -, 19.75, 20}.
The range for grace is given by {9(10), 9(10.25), 9(10.50), 9(10.75), - - -, 9(19.75), 9(20)} = {90, 92.25, 94.5, 96.75, - - -, 177.75, 180}
The domain for Frances is given by: 5 ≤ t ≤ 15.
The range for Frances is given by: 10(5) ≤ f(t) ≤ 10(15) = 50 ≤ f(t) ≤ 150.
Part B:
Grace earns $9 per hour and $80 to $180 per week while Frances earns $10 per hour and $50 to $150 per week.
Giving who ever answers correctly over 30 points.
1: Solve for x.
x - 3/8 = - 5/8
a: x=1/4
b: x= -1/4
c: x= -1
2: Solve for x.
2x = 15 + x
a: x= -15
b: x= 15
c: x= 15/2
3: Solve for x.
x + 5 = 2x
a: x=3
b: x= -5
c: x= 5
Answers
The first one would be b,
second is b
third is c.
Hope this helps!
Number 2 is b
Number 3 is c
If d = 20 and C = 20π
If d = 26 and C = 26π
If r = 12 and C = π
If r = 18 and C = 14π
If r = 6 and C = 12π
If r = 50 and C = 100π
^Matches w
then d = 1
then d = 100
then d = 12
then d = 14
then r = 10
then r = 13
What goes w what!
Answers
If d = 26 and C = 26π, then r = 13.
If r = 1/2 and C = π, then d = 1.
If r = 7 and C = 14π, then d = 14.
If r = 6 and C = 12π, then d = 12.
If r = 50 and C = 100π, then d = 100.
*Note, r= 1/2×d or d=2×r
I need help Simplifying!!!!!!!!!!
2x−(x+6)
Answers
[tex]2x+(-1)(x+6)=2x+(-1)*x+(-1)*6=2x-x-6[/tex]
Now combine like terms:
[tex]2x-x-6=x-6[/tex]
The first step is to multiply every term inside the parentheses by -1.
2x - x - 6
Now combine like terms.
x - 6
Done.