Solve each of the following equations by first using the distributive property to rewrite one or both of the two sides of the equation.
(A) 2(5t+9)=36-7(t-2)+t
(B) 47+s=8(s+2)-s+13
Answers
Answer:
A) t = 2
B) s = 3
Step-by-step explanation:
(A) 2(5t+9)=36-7(t-2)+t
Expand 2(5t + 9) using distributive law[tex]2(5t + 9) = 2 \cdot 5t + 2 \cdot 9 = 10t + 18[/tex]
Expand -7(t-2) using distributive law
[tex]7(t-2) = -7 \cdot t - (-7) \cdot 2 = -7t + 14[/tex]
simplify [tex]36-7\left(t-2\right)+t[/tex]
[tex]36-7\left(t-2\right)+t = 36-7t+14+t = -6t+50[/tex]
Set lhs = rhs
[tex]10t+18=-6t+50[/tex]
Subtract 18 from both sides
[tex]0t+18-18=-6t+50-18[/tex]
Simplify
[tex]10t=-6t+32[/tex]
Add 6t to both sides
[tex]0t+6t=-6t+32+6t[/tex]
Simplify
[tex]16t=32[/tex]Divide by 16 both sides
[tex]\dfrac{16t}{16}=\dfrac{32}{16}[/tex]
==> t = 2 (answer A)
(B) 47+s=8(s+2)-s+13
8(s+2) = 8s + 16RHS becomes 8s + 16 - s + 13==> 7s + 29We get
47 + s = 7s + 29Subtract s from both sides
⇒ 47 = 7s - s + 29
⇒ 47 = 6s + 29Subtract 29 from both sides
47 - 29 = 6s
18 = 6sDivide both sides by 6
⇒ 18/6 = 6s/6
⇒ 3 = s
or s = 3
Related Questions
Tessa returned a book to the library 16 days
late. If she was charged $0.35 per day,
what was the total fine?
Answers
Answer:
5.60
Step-by-step explanation:
Answer: $5.60
Step-by-step explanation:
Given:
Tessa did not return her book for 16 daysThe fee per day was $0.35We must find:
The total cost after 16 daysLet t = total cost.
We will multiply 0.35 by 16 to get the answer.
t = 5.60Find the equation for the line graph below
Answers
given two points P = (2,4) and
Q = (9, -1).
The slope of a line passing through the two
points P = (x1, yi) and Q = (x2, y2)
У2 - У
is given by m =
X2 ー X1
We have that x1 = 2, y, = 4, x2 = 9,
У2 = -1.
Plug the given values into the formula for Slope:
m =
(-1) - (4
(9) - (2)
=
-5
7
5
=-+
Now, the y-intercept is b = y, - m • xj (or b = y2 - m • x2, the result is the same).
6=4-(-)・0=
38
7
Finally, the equation of the line can be written
in the form y = mx + b.
y=
5
38
i have no question x = 2. apples
Answers
Answer:
ok
Step-by-step explanation:
................................................
In the phrase rise over run
what does rise indicate
Answers
Answer:
how far a line goes up
Step-by-step explanation:
rise/run gives the slope of the line
Suppose that the weather forecast indicates a 10% chance that cold weather will reduce the citrus grower’s profit from $100,000 to $85,000 and a 10% chance that cold weather will reduce the profit to $75,000. Should the grower spend $5000 to protect the citrus fruit against the possible bad weather?
Answers
Answer:
We can think in this situation as:
There is 10% (or a probability equal to 0.1) where the citrus grower's profit will be reduced by $15,000
There is 10% (or a probability equal to 0.1) where the citrus grower's profit will be reduced by $25,000
And in the remaining 80% (or a probability equal to 0.8), the profit does not change.
Then the expected value for the total profit can be written as:
EV = $100,000 + ( 0.1*(-$15,000) + 0.1*(-$25,000) + 0.8*$0)
= $96,000
In the case where the citrus grower spends $5000 to protect the fruits against possible bad weather, there is a 100% that is profit will not change, but he must pay $5,000
Then his profit will be:
P = $100,000 - $5,000 = $95,000
So in this case, the profit is $1000 less than the expected profit in the prior case. So the scenario where he does not buy the protection has a larger expected profit, which may mean that is better to not buy it (in a straight mathematical point of view)
One also could think that the values are really close together, so buying the protection does not mean a big change, and increases the security
(4x3−12x2−5)−(−8x2+4x+3)=
find the difference
Answers
Answer:
4x³ - 4x² - 4x - 8
General Formulas and Concepts:
Pre-Algebra
Distributive PropertyAlgebra I
Combining Like TermsStep-by-step explanation:
Step 1: Define expression
(4x³ - 12x² - 5) - (-8x² + 4x + 3)
Step 2: Simplify
Distribute negative: 4x³ - 12x² - 5 + 8x² - 4x - 3Combine like terms (x²): 4x³ - 4x² - 5 - 4x - 3Combine like terms (Z): 4x³ - 4x² - 4x - 8Colin buys a tv
for £800.
It depreciates at a rate of 4% per year.
How much will it be worth in 3 years?
Give your answer to the nearest penny where appropriate.
Answers
The amount of the tv in 3 years which depreciates at a rate of 4% per year is £708 .
Compound interest is interest calculated on the principal and the interest accrued in previous periods. It differs from simple interest where interest is not added to the principal when calculating interest for the next period. In mathematics, compound interest is usually represented by C.I.If the interest is compounded annually, then amount is given by [tex]A=P(1+\frac{r}{100} )^t[/tex] where " A " = Amount , " R " = annual interest rate , "T" = number of years , " P" is principal amount .
We have given principal amount = £800 , rate = 4% and time = 3 years .
Putting above values in equation (1) , we get
[tex]A=800(1-\frac{4}{100} )^3\\A= 800(1 -0.04)^3\\A=800(0.96)^3\\A=800\times 0.88\\A= \£707.78[/tex]
Note that the minus sign is due to depreciation .
On rounding off , amount will be £708 .
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39 decreased by a number p
Answers
Answer:
mm
Step-by-step explanation:
I don't know sooorryy
2y − 7x + 4x2 + 3y + 7x
A 4x2 − 14x + 5y
B 4x2 − 14x
C 4x2 + 14x + 5y
D 4x2 + 5y
Answers
Answer:
5y + 8
Step-by-step explanation:
unless you forgot your parentheses are the (2y-7x+4x)(2+3y+7x) then your answer would be different
Step 3: Estimate the Volume of Each Regularly Shaped Ball
Estimate the volume of each ball. Use the formula
4
V== πr³
where Vis the volume and r is the radius. Record the
volumes in Table A of your Student Guide.
What is the estimated volume of the table tennis ball
cm³
What is the estimated volume of the golf ball?
cm³
Answers
estimated Volume of tennis ball by given data = 38.808 .
estimated Volume of golf ball by given data = 33.523 .
WHAT IS SPHERE ? HOW TO FIND ITS VOLUME ?In terms of geometry, a sphere is described as a collection of points that are spaced apart by a specific amount. The supplied point is referred to as the sphere's center, and the given distance from the sphere's center to the collection of points that make up the sphere is referred to as the sphere's radius.
Many everyday things, including balls and globes, are spheres. Finding a sphere's radius and entering it into the straightforward formula V = [tex]\frac{4}{3}[/tex]π [tex]r^{3}[/tex] will allow you to determine its volume.
CALCULATIONGiven: The radius of the tennis ball is 2.1cm and the radius of the golf ball is 2.0cm. the formula is V=4πr(to the 3rd power) /3 .
To find: Volume of tennis ball and golf ball .
Formula used: V = [tex]\frac{4}{3}[/tex]π [tex]r^{3}[/tex] .
pi(π) =[tex]\frac{22}{7}[/tex] .
We are given that
Radius of the tennis ball = 2.1 cm
radius of the golf ball =2.0 cm.
We need to find the volume of each ball
So , plugging the given values of radius in above formula
Volume of the tennis = [tex]\frac{4 * 22 * (2.1)^{3} }{3 * 7}[/tex] = 38.808 [tex]cm^{3}[/tex]
On simplification we get, volume of tennis ball = 38.808 [tex]cm^{3}[/tex]
Volume of the golf ball= [tex]\frac{4 * 22 * (2.0)^{3} }{ 3*7}[/tex] = 33.523[tex]cm^{3}[/tex]
On simplification we get, volume of golf ball = 33.523[tex]cm^{3}[/tex]
∴ The volume of tennis ball = 38.808[tex]cm^{3}[/tex]
Volume of golf ball = 33.523[tex]cm^{3}[/tex]
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If a person makes $5.00 in 10 minutes, how much can she make in1.5 hours?
Please help due today!!!!!!!
Answers
Answer:
$45
Step-by-step explanation:
A ball is launched upwards from a height of 4 feet. The ball’s height as a function of time, in seconds, is modeled by the function h(t)= -16t^2 +80t +4. What is the time interval in which the ball has a height greater than 100 feet?
Answers
Answer:
Between 2 & 3 seconds. Or we can write it as 2<t<3
Step-by-step explanation:
t = elapsed time in seconds
h(t) = height of the ball at time t
So we just need to replace h(t) with 100 and start to solve. In the end, the answer will be t=2, or t=3 or we can write it as 2<t<3. You can check it by plugging in the number into the equation.
Look at this triangle.
B
13 cm
A
8 cm
Work out length BC.
Answers
Using the Pythagorean theorem:
BC = sqrt(13^2 - 8^2)
BC - sqrt(169 - 64)
BC = sqrt(105)
The exact dimension is sqrt105
If it needs be be in decimal format, sqrt(105) = 10.24695
7= -10s-3 Solve the equation
Answers
Answer:
s = 1
Step-by-step explanation:
7 = -10s - 3
=> 7 + 3 = 10s
=> 10 = 10s
=> 10/10 = s
=> 1 = s
Answer: s= -1
Step-by-step explanation:
Your bedroom wall is 150 inches wide. You want to hang two posters, each 27 inches across, with an equal space between each poster and the wall edges.
How many inches of space should you leave between the wall edge and each poster?
Answers
Answer:
32
Step-by-step explanation:
let the space be x
x + 27 + x + 27 + x = 150
3x + 54 = 150
3x = 96
x= 32
let m>0. match each inequality with its graph. Explain your reasoning.
Answers
Answer:
a. C
b. A
c. B
d. D
Step-by-step explanation:
[tex]a.\ \ \frac{x}{m} < -1 \Longleftrightarrow x < -m[/tex]
Then
The graph that represents the inequality is C.
[tex]b.\ \ \frac{x}{m} > 1 \Longleftrightarrow x > m[/tex]
Then
The graph that represents the inequality is A.
[tex]c.\ \ \frac{x}{m} < 1 \Longleftrightarrow x < m[/tex]
Then
The graph that represents the inequality is B
[tex]d.\ \ -\frac{x}{m} < 1 \Longleftrightarrow -x < m \Longleftrightarrow x > -m[/tex]
Then
The graph that represents the inequality is D.
[tex]f(x) = - 2(x - 4) ^2 + 6[/tex]
what is the vertex of this function ?
Answers
Answer:
x = 4
Step-by-step explanation:
x = 4 is the vertex of the function.
This is a negative quadratic equation and the vertex is the zero of the function. We set (x - 4) equal to 0 and solve.
x - 4 = 0
x = 4
which formula represents a substance that contains covalent bonds 1) LiCl 2)CaCl2 3)K2O 4)CO2
Answers
Answer:
It is CO2 Number 4
Step-by-step explanation:
Answer:
Step-by-step explanation:
What is the Decimal equivalent for fraction 4/8
Answers
Answer:
I hope this helps you
Step-by-step explanation:
4/8 = 0.5
A rectangle has a length of 3 1/4 feet and a width of 1 1/3 feet. What is the area of the rectangle?
Answers
Answer:
the answer is simple 4 1/3
Step-by-step explanation:
you can support me with brainliest
Answer:
13/3 or 4 1/3
Step-by-step explanation:
area of rectangle = length * width
3 1/4 feet as an improper fraction is 13/4
1 1/3 feet as an improper fraction is 4/3
length * width
13/4 * 4/3
= 13/3 or 4 1/3
identify the k-value that makes the relationship shown in the table below proportional.
Answers
Answer:
The value of k that makes the relationship shown in the table below proportional is [tex]\mathbf{\frac{1}{2}}[/tex]
Step-by-step explanation:
The relation is proportional if [tex]y=kx \:or\:k=\frac{y}{x}[/tex]
Putting values of x and y to find k.
For x =2 and y =1 k is: [tex]k=\frac{y}{x}=\frac{1}{2}[/tex]
For x =4 and y =2 k is: [tex]k=\frac{y}{x}=\frac{2}{4} =\frac{1}{2}[/tex]
For x =6 and y = 3 k is: [tex]k=\frac{y}{x}=\frac{3}{6} =\frac{1}{2}[/tex]
For x = 8 and y = 4 k is: [tex]k=\frac{y}{x}=\frac{4}{8} =\frac{1}{2}[/tex]
For x =10 and y = 5 k is: [tex]k=\frac{y}{x}=\frac{5}{10} =\frac{1}{2}[/tex]
So, The value of k that makes the relationship shown in the table below proportional is [tex]\mathbf{\frac{1}{2}}[/tex]
What is the approximate area of the circle shown below?
Answers
Answer:
do you have a picture to go with it's?
You are facing North. Turn 90 degrees left. Turn 180 degrees right. Reverse the direction. Turn 90
degree left Reverse the direction. In which direction are you facing now?
E. East
F. West
G. North
H. South
Answers
Answer:
i believe that it's north
Morgan is visiting a city and wants to take a taxi. The driver tells Morgan that they charge per kilometer and
shows this table describing their cost:
Answers
The amount it would cost Morgan to travel 13 km is £32.5
Calculating CostFrom the question, we are to calculate how much it would cost Morgan to travel 13 km
From the given table, we have that
The cost of traveling 5 km is £12.50
and
The cost of traveling 10 km is £25
First, we will determine the cost of traveling 1 km
If the cost of traveling 5 km is £12.50
Then,
The cost of traveling 1 km will be £12.50/5
£12.50/5 = £2.5
The cost of traveling 1 km is £2.5
Now,
If the cost of traveling 1 km is £2.5
Then,
The cost of traveling 13 km will be 13 × £2.5
13 × £2.5 = £32.5
Hence, the amount it would cost Morgan to travel 13 km is £32.5
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Which set of ordered pairs does not represents a fraction
Answers
please help me asap
Answers
Answer:
2 5/18
Step-by-step explanation:
It's the last choice
Is × = 12 a solution to the equation 6 + × 19?
A. no, because 6 + 12 = 19 is not true
B. yes, because 6 + 12 = 19 is true
C. no, because 6 + 12 = 19 is true
D. yes, because 6 + 12 = 19 is not true
Answers
It equals 18 so it is not true
QUESTION 4 of 10: It is estimated that 32 patrons will attend an event for every $100 spent in advertising. If tickets cost $75, how much can a
promoter expect to increase sales if he spends $25,000 in advertising?
Answers
Answer:
$575000Step-by-step explanation:
Spend on advertising = $25000
32 patrons per $100
Number of patrons:
25000/100×32 = 8000Sales amount:
8000×$75 = $600000Increase in sales excluding advertisement cost:
$600000 - $25000 = $575000Answer:
$600,000
Step-by-step explanation:
$25,000 / 100 then 250 x 32 then 8,000 x 75 to get $600,000
Each dairy cow in the U.S. produces an average
of 25 quarts of milk per day. Given that there are
quarts in a gallon, how many gallons of milk does a
cow produce?
Answers
a cow produces about 6 gallons of milk per day
Luke made 25% of his free throws over the season if he shot 200 free throws how many did he make?
Answers
Based on the number of throws Luke had and the percentage he made, the number he made was 50 throws.
Number of Free Throws MadeThere were 200 free throws in the season and Luke was able to make about 25% of them.
The formula to find this is therefore:
= Number of free throws x Percentage made
Solving gives:
= 200 x 25%
= 50 throws
In conclusion, Luke made 50 throws.
Find out more about proportions at https://brainly.com/question/6788689.