Answer:
x = 4
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightEquality Properties
Multiplication Property of Equality Division Property of Equality Addition Property of Equality Subtract Property of EqualityStep-by-step explanation:
Step 1: Define
5 - 7(2 - x) = 31 - 4(2x - 5)
Step 2: Solve for x
Distribute: 5 - 14 + 7x = 31 - 8x + 20Subtract/Add: -9 + 7x = -8x + 51Add 8x on both sides: -9 + 15x = 51Add 9 to both sides: 15x = 60Divide 15 on both sides: x = 4Step 3: Check
Plug in x into the original equation to verify it's a solution.
Substitute in x: 5 - 7(2 - 4) = 31 - 4(2(4) - 5)(Parenthesis) Multiply: 5 - 7(2 - 4) = 31 - 4(8 - 5)(Parenthesis) Subtract: 5 - 7(-2) = 31 - 4(3)Multiply: 5 + 14 = 31 - 12Add/Subtract: 19 = 19Here we see that 19 does indeed equal 19.
∴ x = 4 is the solution to the equation.
Eight people went to a movie and three of them purchased a drink. Write an expression you could use to solve for the total cost if the tickets are $12 each and the drinks are $2.50 each.
Answer:
The expression : 12x + 2.50y
Total cost = $103.5
Step-by-step explanation:
The number of people that went to the movie = x
Number of people that bought drinks = y
Total cost = 12x + 2.50y
Eight people went to a movie and three of them purchased a drink
Total cost = 12 × 8 + 2.50 × 3
Total cost = 96 + 7.5
Total cost = $103.5
work out (5 x 10^3) x (9 x 10^7)
Step-by-step explanation:
5×10³) × (9×10^7)
= 45 × 10^10
= 4.5 × 10¹¹
Answer:
(5*10^3)*(9*10^7)=4.5*10^11
Step-by-step explanation:
5*10^3=5*1000=5000
9*10^7=9*10000000=90000000
5000*90000000=5*1000*9*10000000=5*9*10000000000=45*10000000000=450000000000, or 45 with 10 0's, or 10^10
45*10^10 is not simplified, as we need a number less then 10, so we divide 10 from 45, and add 1 to the exponent, getting 4.5*10^11
A store pays $100 for a barbecue grill and marks the price up by 7%. What is the amount
of the mark-up?
Answer:
$7
multiply .07 times 100
9 million people own dogs in Florida
with 3 million additional people getting
dogs each year. If 13 million people
have cats and an additional 1 million
people get cats each year, in how
many years would the number of
people with cats equal the number of
people with dogs.
Answer:
2 years
Step-by-step explanation:
the answer is 2 years because if right now florida has 9 million dogs and each year 3 million are gained in 2 years there will be 15 million dogs. if there are 13 million cats in Florida right now and 1 million and gained every year. in 2 years there will be 15 million cats.
A single card is drawn at random from a standard 52 card deck.
Work out the following probabilities in their simplest form:
P(8)
=
P(not 8)
=
Answer:
Step-by-step explanation:
P(8)
There are 4 eights in a standard deck (no jokers) So the probability is 4/52 = 1/13 = 0.0769
P( ~ 8)
48 cards in a standard deck are not 8
P( ~8) = 12/13 = 0.9231
Hi. I need help with these questions (see image)
Please show workings.
Answer a and b
Answer:
see explanation
Step-by-step explanation:
Using the chain rule along with standard derivatives
Given
y = f(g(x)) , then
[tex]\frac{dy}{dx}[/tex] = f'(g(x)) × g'(x)
[tex]\frac{d}{dx}[/tex] (sinx) = cosx , [tex]\frac{d}{dx}[/tex] (cosx) = - sinx
(a)
y = sin x²
[tex]\frac{dy}{dx}[/tex] = cos x² × [tex]\frac{d}{dx}[/tex] (x² )
= cos x² × 2x
= 2xcosx²
(b)
y = cos4x³
[tex]\frac{dy}{dx}[/tex] = - sin4x³ × [tex]\frac{d}{dx}[/tex] (4x³ )
= - sin4x³ × 12x²
= - 12x²sin4x³
1. Doug invested $2,500 into a Certificate of Deposit earning 6.5% interest. How long will it take to
double Doug's investment?
Answer:
Step-by-step explanation:
14.5 years
Use the equation below to find v, if u =21, a= 12, and t = 2.
v=utat
Step-by-step explanation:
We have v = u + at = (21) + (12)(2) = 45.
Answer:
v= 1008
v=21*2*12*2
Step-by-step explanation:
The Paint Factory has 500 different colors of interior paint from which to choose. Generate an equivalent expression using prime factorization for the number 500.
a)2 x 2 x 5 x 25
b)4 x 5 x 25
c)2 x 2 x 5 x 5 x 5
please hurry
Answer:
The answer is C.
Step-by-step explanation:
The simplest form is C.
Answer:
c)2 x 2 x 5 x 5 x 5
[tex]500 \\ \frac{500}{5} = 100 \\ \frac{100}{5} = 20 \\ \frac{20}{2} = 10 \\ \frac{10}{2} = 5 \\ \frac{5}{5} = 1\\ [/tex]
Rewrite the denominators
2 x 2 x 5 x 5 x 5
Kareem heats a beaker of water to a boil. Then he records that the water temperature decreases from 100°C to 19°C in 5 and 2/5 minutes.
What was the change in temperature each minute? Enter your answer in the box.
Answer:
Step-by-step explanation:
2/5min=24 sec
5 min=300 sec
total=324 seconds
the water decreased 100-19=81 degrees
81/324=0.25 degrees/second
the change in temperature was 0.25 degrees per second
we will multiply by 60
15 degrees per minute
Questions related on indices. ( I need a full explanations of how the answer is found. )
Answer:
(a) m = 10
(b) n = 160
Step-by-step explanation:
To rewrite the expression in the manner indicated, write an equation that sets the given expression equal to the desired expression. Then solve for the variable value. The distributive property and the usual rules of exponents apply.
The rules of exponents you can use here are ...
(a^b)(a^c) = a^(b+c)
(a^b)^c = a^(bc)
a^0 = 1
__
(a) 2^101 +2^103 = m×2^100
2^(101-100) +2^(103-100) = m × 2^(100-100) . . . . . . . multiply by 2^(-100)
2^1 +2^3 = m
2 + 8 = m
m = 10
__
(b) 2^101 +2^103 = n×4^48
2^101 +2^103 = n×(2^2)^48 . . . . . substitute 4 = 2^2
2^101 +2^103 = n×2^96 . . . . . . . . simplify
2^5 +2^7 = n . . . . . . . . . . . . . . . . . as above, multiply by 2^(-96)
32 +128 = n
n = 160
_____
Additional comment
The rules of exponents tell you that ...
(m × 2^100) × 2^-100 = m × 2^(100 -100) = m × 2^0 = m
This is effectively the same as dividing by 2^100. You're doing the same thing you would do to solve any linear equation: divide by the coefficient of the variable.
PLEASE HELP!!!PLEASE HELP!!!PLEASE HELP!!!PLEASE HELP!!!PLEASE HELP!!!PLEASE HELP!!!PLEASE HELP!!V
Answer:
12+12+14+15+16+18+20+23=130
130÷8=16.25
aanswer=16
you move 89 as its anomalous
too higher than the other numbers
Why does no one answer my questions?
Answer:
Which one do you need help with
calculate the cost of 15 articles at 1.95 each
Answer:
29.25
Step-by-step explanation:
15x1.95= 29.25
Hope this helps :)
if 1 article = 1.95
then if u want to find how much 15 articles = to
you just have to multiply 1.95 * 15 which is equal to 29.25
hope this helps
:)
solve the linear equation
9x-2x+6=4x+3x+11-5
Answer:
Undefined
Step-by-step explanation:
0=0
Answer:
0
Step-by-step explanation:
Combine the like terms 9x-2x = 7x
Subtract the numbers 11-5 = 6
Combine the like terms again 4x+3x = 7x
Subtract 6 from both sides of the equation 6-6 = 0 6-6 = 0
Simplify 7x = 7x
Result 0
A triangle has sides with lengths of 16 millimeters, 20 millimeters, and 25 millimeters. Is it a
right triangle?
Answer:
No
Step-by-step explanation:
If it is a right triangle, then the Pythagorean theorem must work.
a^2 + b^2 = c^2 (a and b are the shorter sides and c is the longest)
16^2 + 20^2 = 25^2
256 + 400 = 625
656 = 625
This is not true
Hope this helps!
An archeologist has found a fossilized leg bone of some unknown mammal. Based on the size of the bone, she determines that it should have contained about 100 g of carbon-14 when the animal was alive. Knowing that the half-life of carbon-14 is 5730 years, write an equation that will model how much carbon-14 is left in the bone now after "t" years.
Answer:
Therefore, required equation is N = 100 x [tex]2^{- \frac{t}{5730 }[/tex]
Step-by-step explanation:
According to the question it is given that
Amount of carbon atom when animal was alive is [tex]N_0[/tex] = 100g
Half life of C-14 is 5730 years
Let 'N' be the amount of carbon atom present after 't' time
since the differential equation of decay process of radioactive atom is
[tex]\frac{dN}{dt} = \lambda N[/tex] where, λ is the decay constant
on solving this we get
[tex]N = N_0 e^{-\lambda t}[/tex]
on further solving and substituting [tex]\lambda = \frac{ln2}{T_{1/2}}[/tex] we get
[tex]N = N_0 2^{- \frac{t}{T_{1/2}} }[/tex]
on substituting the value of [tex]N_0[/tex] = 100g and [tex]T_{1/2}[/tex] = 5730 we get
N = 100 x [tex]2^{- \frac{t}{5730 }[/tex]
A c ompany purchased 3,128 bottles of water.Each departments needs 55 bottles.Which compatible numbers provide a better estimate for the number of departments that can get the bottles needed 3,000 divided 60 or 3,000 divided 50? Explain.Then make the estimate.
Answer:
3,000 divided 60 are the compatible numbers, and the estimate is 50.
Step-by-step explanation:
Compatible numbers can be described as numbers which are close in value to the actual numbers and can easily be added, subtracted, multiplied, or divided mentally.
From the question, 3,000 divided 60 are the compatible numbers that provide a better estimate for the number of departments that can get the bottles because 55 can be rounded up to 60.
The estimate will therefore be as follows:
Estimate = 3,000 / 60 = 50
I need some help please
Answer:
a) -10
b) 7
Step-by-step explanation:
a) [tex]2(x + 3) = x - 4[/tex]
[tex] = > 2x + 6 = x - 4[/tex]
[tex] = > 2x - x = - 4 - 6[/tex]
[tex] = > x = - 10[/tex]
b) [tex]4(5x - 2) = 2(9x + 3)[/tex]
[tex] = > 20x -8 = 18x + 6[/tex]
[tex] = > 20x - 18x = 8 + 6[/tex]
[tex] = > 2x = 14[/tex]
[tex] = > x = \frac{14}{2} = 7[/tex]
Answer:
a)-10 b)7
Step-by-step explanation:
a)2 ( x + 3 ) = x - 4
2x+6=x-4
2x+6-x=-4
x+6=-4
x=-4-6
x=-10
b)4 ( 5 x - 2 ) = 2 ( 9 x + 3 )
20x-8=2(9x+3)
20x-8=18x+6
20x-8-18x=6
2x-8=6
2x=6+8
2x=14
x=14/2
x=7
Word problem:
(I only need the answer and explanation no need statements PLS HELP )
The weight of Jack is 30kg 500g. The weight of Dereck is 28kg 700g. What is their total weight? Also, find the difference of their weight?
Answer:
Below.
Step-by-step explanation:
30 kg 500g + 28kg 700g
= 58kg + 1200g
= 59kg 200g.
Difference
= 30 kg 500g - 28kg 700g
= 2kg + 500 - 700
= 2kg - 200g
= 1kg 800g.
What is the equation of the line whose y-intercept is 3 and slope is 1?
O y=x-3
O y=x+3
O y= 3x+1
Answer:
y = x + 3
Step-by-step explanation:
y = mx + b
m is the slope
b is the y intercept
if m = 1 and b = 3 then
y = x + 3
What classes should I take as a freshman in high school
math, science, social studies,elcteives, English,
Answer:
Depends on what you what to do in the future. But u should take math, science and english (those are the main important classes)
Step-by-step explanation:
Which expression is equivalent to 5(4x + 5)
Answer:
5(4x+5)=20x+25
Step-by-step explanation:
Which of the following numbers is irrational?
A)5/8
B)2/3
C) √12
D-√36
Answer:
A) 5/8
Step-by-step explanation:
5 and 8 are irrational as a fraction
Answer:
5/8 i TOOK THE EXAM REVIEW
Step-by-step explanation:
Which is shorter? 3/6 of a minute or 2/6 of an hour?
Answer:
3/6 of a minute
Step-by-step explanation:
3/6 can also be simplified to 1/2. So, 1/2 of a minute is 30 seconds. 2/6 can be simplified to 1/3. So, 1/3 of an hour is 20 minutes. 30 seconds is very much shorter than 20 minutes. Thus, 3/6 of a minute is shorter than 2/6 fo an hour.
Courtney needs to find 2,495 ÷ 48. In which place should she write the first digit of the quotient?
A. Ones
B. tens
C. Hundreds
D. Thousands
Javier wants to put in a home theater. The area of the space for the screen is 20 ft. by 16 ft. What is the largest home theater screen he can purchase if the size is determined by the length of the diagonal?
Group of answer choices
15 feet
20 feet
25 feet
30 feet
Answer:
25
Step-by-step explanation:
PLEASE HELP!!! i will give 5 stars and a thanks
Answer:
i DONT KNOW HOPEFULLY U DO GOOD
Step-by-step explanation:
What is the solution of the system of equations?
{3x−12y=−72x+2y=1
Answer:
i think 9
Step-by-step explanation:
i not sureURGENT PLZ HELP!
Find the value of x so that the points
(x, 2) and (-5, 8) lie on a line with a slope
of -1.
9514 1404 393
Answer:
x = 1
Step-by-step explanation:
The slope formula can be useful here.
m = (y2 -y1)/(x2 -x1)
-1 = (8 -2)/(-5 -x)
5 + x = 6 . . . . . . . . multiply by (-5-x)
x = 1 . . . . . . . . subtract 5