Hey there!
We are given two functions - one is Exponential while the another one is Linear.
[tex] \large{ \begin{cases} f(x) = {4}^{x} - 8 \\ g(x) = 5x + 6 \end{cases}}[/tex]
1. Operation of Function
(f+g)(x) is a factored form of f(x)+g(x). We can common factor out x. Therefore:[tex] \large{(f + g)(x) = f(x) + g(x)}[/tex]
2. Substitution
Next, we substitute f(x) = 4^x+8 and g(x) = 5x+6.[tex] \large{(f + g)(x) = ( {4}^{x} - 8) + (5x + 6)}[/tex]
3. Evaluate/Simplify
Cancel out the brackets and combine like terms.[tex] \large{(f + g)(x) = {4}^{x} - 8 + 5x + 6} \\ \large{(f + g)(x) = {4}^{x} + 5x - 8 + 6} \\ \large{(f + g)(x) = {4}^{x} + 5x - 2}[/tex]
4. Final Answer
(f+g)(x) = 4^x+5x-2the product of ten and the sum of two and a number is five times the number. find the number
Answer:
-4
Step-by-step explanation:
10(2+n)=5n
20+10n=5n
20=-5n
-4=n
The number is n = -4.
What is the product of ten and the sum of two and a number is five times the number?Given: the product of ten and the sum of two and a number exists five times the number.
Let x be the unknown number:
The product of 5 and the sum of two and the number = 10(2+n)
five times the number = 5n
10(2+n) = 5n
Expand 10(2+n) = 20+10n
20+10n = 5n
Subtract 20 from both sides
20+10n-20 = 5n-20
Simplify
10n = 5n-20
Subtract 5n from both sides
10n-5n = 5n-20-5n
Simplify
5n = -20
Divide both sides by 5
[tex]$\frac{5 n}{5}=\frac{-20}{5}[/tex]
n = -4
Therefore, the correct answer is n = -4.
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Find the distance from the vertices of AABC to the corresponding vertices of the other three triangles, and enter them in the table. For AJKL-
you'll need to use the distance formula da (01 – 12) + (y1 - y2) . Verify your calculations using the tools available in GeoGebra.
Answer:
See explanation
Step-by-step explanation:
The question is incomplete, as the vertices of the triangle are not given.
A general explanation is as follows;
To calculate distance between two points, we use:
[tex]d = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}[/tex]
Take for instance;
[tex]A = (1,4)[/tex]
[tex]B = (3,-2)[/tex]
Distance AB is:
[tex]AB = \sqrt{(1 - 3)^2 + (4 - -2)^2}[/tex]
[tex]AB = \sqrt{(- 2)^2 + (4 +2)^2}[/tex]
[tex]AB = \sqrt{(- 2)^2 + (6)^2}[/tex]
Evaluate the exponents
[tex]AB = \sqrt{4 + 36}[/tex]
[tex]AB = \sqrt{40}[/tex]
[tex]AB = 6.32[/tex]
Answer:
for edmentum
Step-by-step explanation:
A rectangular vegetable garden will have a width that is 3 feet less than the length, and an area of 54square feet. If x represents the length, then the length can be found by solving the equation: x(x-3)=54 What is the length, x, of the garden? The length is blank feet.
Answer: 9 feet
Step-by-step explanation:
From the information given, we have already been given the equation which is x(x-3)=54. Therefore we will find the value of x which will be:
x(x-3)=54
x² - 3x - 54
x² - 9x + 6x - 54
x(x - 9) + 6(x - 9)
Therefore,
(x - 9) = 0
x = 0 + 9
x = 9
The length is 9 feet
The width will be:
x - 3 = 9 - 3 = 6 feet
The graph below is the graph of a function.
10
- 10
10
- 10
True
B. False
Answer:
hgfyjtdjtrxgfyfguktfkgh
Step-by-step explanation:
hgfytrdutrc
John runs a computer software store. Yesterday he counted 125 people who walked by the store, 58 of whom came into the store. Of the 58, only 21 bought something in the store. (Round your answers to two decimal places.)
(a) Estimate the probability that a person who walks by the store will enter the store.
(b) Estimate the probability that a person who walks into the store will buy something.
(c) Estimate the probability that a person who walks by the store will come in and buy something.
(d) Estimate the probability that a person who comes into the store will buy nothing.
Answer:
a) 0.46 = 46% probability that a person who walks by the store will enter the store.
b) 0.36 = 36% probability that a person who walks into the store will buy something.
c) 0.17 = 17% probability that a person who walks by the store will come in and buy something.
d) 0.64 = 64% probability that a person who comes into the store will buy nothing.
Step-by-step explanation:
A probability is the number of desired outcomes divided by the number of total outcomes.
(a) Estimate the probability that a person who walks by the store will enter the store.
58 out of 125. So
[tex]p = \frac{58}{125} = 0.46[/tex]
0.46 = 46% probability that a person who walks by the store will enter the store.
(b) Estimate the probability that a person who walks into the store will buy something.
58 walked, 21 bought. So
[tex]p = \frac{21}{58} = 0.36[/tex]
0.36 = 36% probability that a person who walks into the store will buy something.
(c) Estimate the probability that a person who walks by the store will come in and buy something.
21 came in and bought out of 125 that walked by. So
[tex]p = \frac{21}{125} = 0.17[/tex]
0.17 = 17% probability that a person who walks by the store will come in and buy something.
(d) Estimate the probability that a person who comes into the store will buy nothing.
0.36 probability that a person buys something, so 1 - 0.36 = 0.64 = 64% probability that a person who comes into the store will buy nothing.
Please kindly help
According to a newspaper article 15% more home remodeling was done in 1985 than in 1984. Professionals performed 75% of all remodeling. If $80.4 billion was spent on residential remodeling in 1985 what was the value of the work done by professionals in 1985?
(1) $ 8.4 billion
(2) $12.06 billion
(3) $20.1 billion
(4) $60 billion
(5) $60.3 billion
Answer:
(3) $20.1 billion
Step-by-step explanation:
hope it help
Answer:
(5) $60.3 billion
Step-by-step explanation:
7 women can bake 100 cookies in 14 days. How many would it take for 4 women to bake 240 cookies?
Answer:
it would take 30 and a half days to make 240 cookies
IF A=[2,4] and B=[0,3] then BUA=?
Answer:
it equal:
answer is : [0234]
If one table and two lamps cost $88, and two
tables and three lamps cost $153, how much
does a lamp cost?
Answer:
One lamp is equal to 23 dollars
One table is equal to 42 dollars.
Step-by-step explanation:
We can solve this by first organizing what we have.
1 table (t) + 2 lamps (l) = 88.
2 tables (t) + 3 lamps (l) = 153.
_____________
===============
1t + 2l = 88
2t + 3l = 153
===============
-------------------------
If we multiply both sides by 2 on the first equation of
1t + 2l = 88
we could get
2t + 4l = 176.
If that is true, we can subtract the second equation of
2t + 3l = 153 from the new equation to get the price of a lamp.
2t + 4l = 176
- 2t + 3l = 153
____________
= 0t + l = 23
One lamp is equal to 23.
We can check this by plugging it into an equation.
1 + 2(23) = 88
1t + 46 = 88
1t + 46 - 46 = 88 - 46
1t = 42
If one table equals 42, we can put this back into the second equation to check.
2 (42) + 3 (23) = 153
84 + 69 = 153
That is correct.
Another way to solve is to put this like a system of equations in a graph, by replacing "t" by "x" for example, and "l" by y.
Then you could put it into a graphing calculator and solve by looking for the place where the two lines converge or meet.
Since we put "x" for "t", that means that whatever the x-value is on the solution point, that is the cost of a table, and the y-value is the cost of the lamps.
Another way to solve, is to find the unit rate first by subtracting the first equation from the second equation.
2t + 3l = 153
- 1t + 2l = 88
____________
= t + l = 65
If t + l = 65, we can rearrange that equation to be something like t = 65 - l.
That means "t" is equal to 65 bucks minus a lamp.
We put this back into the first equation of
1t + 2l = 88
and replace "t" with the previous expression.
1(65 - l) + 2l = 88
Simplify/distributive property
65 - l + 2l = 88
65 - 65 - l + 2l = 88 - 65
-l + 2l = 23
l = 23
One lamp is equal to 23 bucks.
Confirmed :)
A lamp cost $23
Let the cost of a table be represented by x
Let the cost of a lamp be represented by y.
Since one table and two lamps cost $88, this can be represented as:
x + 2y = 88 ........ equation i
Since two tables and three lamps cost $153, this can be represented as:
2x + 3y = 153 ........ equation ii
Therefore, the equations are:
x + 2y = 88 ....... i
2x + 3y = 153 ....... ii
From equation i,
x + 2y = 88
x = 88 - 2y ...... iii
Put the value of x into equation ii
2x + 3y = 153
2(88 - 2y) + 3y = 153
176 - 4y + 3y = 153
Collect like terms
-4y + 3y = 153 - 176
-y = -23
y = 23
Therefore, a lamp cost $23
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In a survey, 250 adults and children were asked whether they know how to
swim. The survey data are shown in the relative frequency table.
Can swim
Cannot swim
Total
0.34
Adults
Children
0.06
0.48
0.12
Total
What percentage of the people surveyed can swim?
O A. 18%
B. 82%
C. 48%
D. 34%
Answer:
B - 82%
Step-by-step explanation:
.34+.48
The percentage of people who can swim is 82%.
Option B is the correct answer.
What is a percentage?
The percentage means the required value out of 100.
It is calculated by dividing the required value by the total value and multiplying it by 100.
The percentage change is also calculated using the same method.
In percentage change, we find the difference between the values given.
Example:
Required percentage value = a
total value = b
Percentage = a/b x 100
We have,
The relative frequency table shows the proportion of people in each group who can and cannot swim.
To find the percentage of people who can swim, we need to add up the proportion of adults who can swim (0.34) and the proportion of children who can swim (0.48).
Percentage of people who can swim
= (0.34 + 0.48) x 100%
= 82%
Therefore,
The percentage of people who can swim is 82%.
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Divide: (2n3+4n−9)÷(n+2).
Answer:
2n+2
_____
9 2n
Sameer bought 8kg 500g mango and 5kg 250g apples and Anil bought 7kg 800g Guava and 4kg 625g Banana. Who bought more fruits? And by how much?.
Answer:
Below.
Step-by-step explanation:
Sameer:-
Number of mango's = total weight / weight of 1 mango
= 5 kg / 500g
= 5000/500
= 10.
Number of apples: = 5000/250 = 20.
Total number of fruit = 30.
Anil :-
Number of guava = total weight / weight of 1 guava
= 7 kg / 800g
= 7000/800
= 9.
Number of banana: = 4000/625 = 6.
Total number of fruit = 15.
Sameer bought the most fruit, 15 more than Anil.
Note: in Anil's case I rounded the values to the nearest whole number.
simplify 3 / 8 (–2 / 7 +(–3 / 8 ×2 / 5)
Answer:
so the answer is 0.16339
Help please I don’t get may I please have help with this
Answer:
[tex]1)\:2\frac{2}{3} ft[/tex]
[tex]2)\:4[/tex]
[tex]3)\:\frac{20}{3} ft^{2}[/tex]
[tex]4)\:10\frac{2}{3} ft^{2}[/tex]
------------------------
hope it helps...
have a great day!!
Stuck on this question
Answer:
9262
Step-by-step explanation:
just plug in 22 for n and calculate
How do I find the image after it’s been rotated 270 degrees about the point (-2,-1)?
Answer: (-1, 2)
Step-by-step explanation:
It's a counter-clockwise rotation, that means (x, y) changes to (y, -x).
(-2, -1) ⇒ (-1, -(-2)) ⇒ (-1, 2)
If it's a clockwise rotation, then (x, y) will change to (-y, x)
(-2, -1) ⇒ (-(-1), -2) ⇒ (1, -2)
A file that is 266 megabytes is being downloaded . 14.4 % is completed , how many megabytes have been downloaded round to the tenth
Answer:
38.3 megabytes
Step-by-step explanation:
Find how many megabytes have been downloaded by multiplying 266 by 0.144:
266(0.144)
= 38.304
Round this to the nearest tenth:
= 38.3
So, 38.3 megabytes have been downloaded
the value of (-15/23)+(+30/-46) is ---------.
[tex] \frac{ - 15}{23} + \frac{30}{ - 46} \\ = \frac{ - 15}{23} + \frac{(2) \times (15)}{(2) \times ( - 23)} \\ = \frac{ - 15}{23} + \frac{15}{ - 23} \\ = \frac{ - 15}{23} - \frac{15}{23} \\ = \frac{ -3 0}{23} \\ = - 1.3[/tex]
Match the y coordinate with coo responding pairs of x
Sam works at a shoe store. He earns $300 every week plus $15 for every pair of shoes that he sells. How many pairs of shoes would he need to sell to make $500 in a week?
Answer:
300 + 15x = 500
15x = 200
x = 200/15
x=13.333
14 pair of shoes
Step-by-step explanation:
Previous Question Question 17 of 20 Next Question Based on the regression model, the expected daily production volume with 112 factory workers is 118,846 units. The human resource department noted that 123,415 units were produced on the most recent day on which there were 112 factory workers. What is the residual of this data point
Answer:
4,569 units
Step-by-step explanation:
Given :
Measured value = 123,415 units
Expected value = 118,846 units
Residual is the difference between the measured and expected value :
Residual = Measured value - Expected value
Residual = 123,415 units - 118,846 units
Residual = 4,569 units
The answer to this 6th grade summer school math question is
Answer 7.84
If JKL - PNM. then M = L and the sides NP and
KJ are proportional.
True
Or
False???
Answer:
True
Step-by-step explanation:
In similarity triangles, corresponding angles are congruent and corresponding sides are in proportion.
An art history professor assigns letter grades on a test according to the following scheme. A: Top 13% of scores B: Scores below the top 13% and above the bottom 56% C: Scores below the top 44% and above the bottom 21% D: Scores below the top 79% and above the bottom 9% F: Bottom 9% of scores Scores on the test are normally distributed with a mean of 79.7 and a standard deviation of 8.4. Find the numerical limits for a B grade. Round your answers to the nearest whole number, if necessary.
Answer:
The numerical limits for a B grade are 81 and 89, that is, a score between 81 and 89 gets a B grade.
Step-by-step explanation:
Normal Probability Distribution:
Problems of normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
Scores on the test are normally distributed with a mean of 79.7 and a standard deviation of 8.4.
This means that [tex]\mu = 79.7, \sigma = 8.4[/tex]
B: Scores below the top 13% and above the bottom 56%
So between the 56th percentile and the 100 - 13 = 87th percentile.
56th percentile:
X when Z has a p-value of 0.56, so X when Z = 0.15. Then
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]0.15 = \frac{X - 79.7}{8.4}[/tex]
[tex]X - 79.7 = 0.15*8.4[/tex]
[tex]X = 81[/tex]
87th percentile:
X when Z has a p-value of 0.87, so X when Z = 1.13.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]1.13 = \frac{X - 79.7}{8.4}[/tex]
[tex]X - 79.7 = 1.13*8.4[/tex]
[tex]X = 89[/tex]
The numerical limits for a B grade are 81 and 89, that is, a score between 81 and 89 gets a B grade.
Suppose that the consensus forecast of security analysts of your favorite company is that earnings next year will be $5.00 per share. The company plows back 50% of its earnings and if the Chief Financial Officer (CFO) estimates that the company's return on equity (ROE) is 16%. Assuming the plowback ratio and the ROE are expected to remain constant forever:
If you believe that the company's required rate of return is 10%, what is your estimate of the price of the company's stock?
Answer:
$250
Step-by-step explanation:
according to the constant dividend growth model
price = d1 / (r - g)
d1 = next dividend to be paid
r = cost of equity
g = growth rate
Sustainable growth rate is the rate of growth a company can afford in the long term
sustainable growth rate = plowback rate x ROE
b = plowback rate. It is the portion of earnings that is not paid out as dividends
g = 0.50 x 0.16 = 0.08 = 8%
5 / (10% - 8%)
5 / 2%
5 / 0.02 = $250
A printing machine 600 books in 3 hours. How many books will the machine print in 5
Answer:
1, 000 hrs
Step-by-step explanation:
The machine prints,
in 3 hrs = 600 books
in 1 hr = 600/ 3 hrs = 200 hrs.
in 5 hrs = 200 × 5
= 1, 000 hrs
The printing machine will print 1000 books in 5 hours.
Let's calculate how many books the printing machine will print in 5 hours based on the given information.
To do this, we'll use the concept of rates and proportions.
Given that the printing machine can print 600 books in 3 hours, we can set up a rate equation as follows:
Rate of printing = Number of books / Time taken
Let "x" be the number of books the machine will print in 5 hours. We can set up the proportion:
600 books / 3 hours = x books / 5 hours
To solve for "x," we cross-multiply:
3 * x = 600 * 5
Now, let's solve for "x":
3x = 3000
x = 3000 / 3
x = 1000
So, the printing machine will print 1000 books in 5 hours.
Given: Printing machine prints 600 books in 3 hours.
Let the number of books the machine will print in 5 hours be "x."
Using the rate formula, we can set up the proportion:
600 books / 3 hours = x books / 5 hours
Cross-multiplying:
3 * x = 600 * 5
Solving for "x":
3x = 3000
x = 3000 / 3
x = 1000
Hence, the printing machine will print 1000 books in 5 hours.
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help me with 2 excersise , thanks a lot
Answer: I do not know what you mean, but you could do burpees, and sit ups.
On Monday, Ray had $153.75 in his bank account. On Tuesday, he withdrew $71.00 from his account. After depositing #292.50 on Wednesday, how much money did Ray have in his account
Answer:
$375.25
Step-by-step explanation:
[tex]===========================================[/tex]
Withdrew- taking out money (-)
Deposit- putting in money (+)
[tex]===========================================[/tex]
Ray started off with 153.75. He withdraws (-) 71.
[tex]153.75-71=82.75[/tex]
Then he deposits (+) 292.5.
[tex]82.75+292.5=375.25[/tex]
That's your answer!
I hope this helps ❤
Find the values of x and y that make these triangles congruent by the HL theorem
Answer:
x = 3, y = 2Step-by-step explanation:
As due to congruency,
x + 3 = 3y
[By putting the values of x = 3 and y = 2]
=> 3 + 3 = 3 × 2
=> 6 = 6
and,
x = y + 1
[By putting the values of x = 3 and y = 2]
=> 3 = 2 + 1
=> 3 = 3
Hence, proved
On a coordinate plane, points (0.5, 2), (4, 16), and (6.5, 26) are plotted.
Natalie made a graph showing these ordered pairs representing a proportional relationship.
(0.5, 2), (4, 16), (6.5, 26)
Which ordered pair would be on the same line as Natalie’s ordered pairs?
(3.5, 12)
(2, 4)
(8, 32)
(12, 36)
Answer:
(8,32)
Step-by-step explanation:
(8,32) because when graphed (8,32) lands on the same line as the other.
Answer:
C
Step-by-step explanation:
got it right on edge 2021