Solution:
Given that,
[tex]f(x) = 2x^2 + 5\sqrt{x + 2}[/tex]
We have to find f(2)
To find f(2), plug in x = 2 in given f(x) and solve to get the answer
Plug in x = 2 in f(x)
[tex]f(2) = 2(2)^2 + 5 \sqrt{2+2}\\\\f(2) = 2 \times 4 + 5\sqrt{4}\\\\Simplify\\\\f(2) = 8 + 5 \times 2\\\\f(2) = 8 + 10\\\\f(2) = 18[/tex]
Thus the value of f(2) is 18
what is the distance between S( -9, 8) & T(8 , -6) ?
Answer:
Exact Form:
√485
Decimal Form:
22.02271554…
Step-by-step explanation:
Union employees vote for a representative to negotiate on behalf of all workers. This representative negotiates 3%
increase in wages, but requires workers to contribute 15% of their $10,000/year health insurance rather than 10% last year. What is the net
gain or loss each worker (on average) receives or pays if the average worker makes $39,000 per year when both issues are factored?
a) $500 loss
b) $670 gain
c) $1,170 gain
d) $3,000 gain
Answer:
670$ gain
Step-by-step explanation:
After accounting for both the wage increase and the increased health insurance contribution, on average, each worker experiences a net gain of $670 annually.
Explanation:The first step is to calculate the increase in wages due to the 3% increase in salary. This is calculated as follows: 3% of $39,000 is $1,170.
Next, we need to calculate the additional amount contributed toward health insurance, which has increased from 10% to 15%. This represents an increase of 5%. Thus, the added cost of health insurance is 5% of $10,000, which equals $500.
Finally, we can calculate the net change for the worker. This is achieved by subtracting the increase in health insurance contributions from the increase in wages. So, $1,170 - $500 equals $670 gain.
Hence, the correct option is (b), $670 gain.
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the pizza restaurant has a special offer today 3 pizzas for $25. the soccer team is ordering pizza. if each player eats 1/4 pizza, how many players will 3 pizzas serve?
Answer:
The 3 pizzas will serve 12 players
A = {1, 3, 5, 7, 9)
B = {2, 4, 6, 8, 10)
C = {1, 5, 6, 7,9}
A U (B n C)= ?
Answer:
{1, 3, 5, 6, 7, 9}
Step-by-step explanation:
A u (B n C)
First we look at
(B n C)
n indicates intersects. Intersects means the common. The common number in B and C, we have
{6}
Now A u {6}
u means union. That is, joining both sets together, hence, we have
{1, 3, 5, 6, 7, 9}
A u (B n C} gives {1, 3, 5, 6, 7, 9}
Which statement is NOT TRUE about the two points (6, 9) and (6, −9) on a coordinate plane?
A) the -coordinates are the same
B) the -coordinates are the same
C) same distance from zero on the -axis
D) same distance but opposite sides of zero on the -axis
Answer:
The y-coordinates are the same
Step-by-step explanation:
1) fifteen of 31 measurements are below 10cm and 12 measurements are above 11cm. Find the median if the other four measurements are 10.1, 10.4, 10.7 and 10.9cm.
2) the man and the median of a set of nine measurements are both 12. If seven of the measurements are 7, 9, 11, 13, 14, 17 and 19, find the other two measurements.
Pls show full working out ty ;)
Answer:
1) 10.1
2) 6 and 12
Step-by-step explanation:
1) median position: (31+1)/2 = 16th
15 are below 10, so 16th would be the first one to be greater than/equal to 10.
Which is 10.1
2) median = 12 of 9 values
So 5th value is 12
7,9,11,12,13,14,17,19 are the 8 values
To find the last measurement, use mean = 12
Mean = 12
Sum = 12×9 = 108
7+9+11+12+13+14+17+19+x = 108
102 + x = 108
x = 6
Final answer:
To determine the median of a data set with an odd number of measurements, find the middle value in the ordered list. In the first question, the median is 10.1cm. In the second question, the two missing measurements needed to maintain the given mean and median are 6 and 12.
Explanation:
To find the median of a given data set, one must first order the measurements from the smallest to the largest. Once the data are sorted, the median will be the middle value if there is an odd number of measurements. If there is an even number of measurements, the median will be the average of the two middle values.
We have 31 measurements with 15 being below 10cm and 12 above 11cm. The remaining four measurements are 10.1cm, 10.4cm, 10.7cm, and 10.9cm. Because there are 31 measurements (an odd number), the median will be the 16th value when sorted. The first 15 values are below 10cm, thus the 16th value is the first value above 10cm, which is 10.1cm. Therefore, the median is 10.1cm.
The mean and median of the data set are both 12. We are given seven of the measurements, and we need to find the remaining two that will keep the mean and the median at 12. To maintain the median at 12 for a set of nine measurements, the fifth datum must be 12. Among the given values, 13 is the smallest number that is bigger than 12, thus the two unknown values must be either less than or equal to 12 to not affect the median. To find these two unknown values we use the concept of mean, which is the sum of all the measurements divided by the number of measurements. Our equation to find the sum of the nine measurements is 7 + 9 + 11 + 13 + 14 + 17 + 19 + x + y = 9×12 (since the mean is 12). This simplifies to 90 + x + y = 108. Therefore, x + y = 18. Since we already have a 13 and we need a median of 12, one of the unknowns must be 12 to be the middle value and the other must be 6 to fulfill the equation x + y = 18. So the two unknown measurements are 6 and 12.
The mixed number 6 7/8 is equal to which improper fraction?
A.) 55/8
B.)13/8
C.)48/8
D.)42/8
Answer:
A.) 55/8
Step-by-step explanation:
To make 6 7/8 an improper fraction, multiply the whole number by the denominator and add the result to the numerator.
That’s
6 x 8 = 48
48 + 7 = 55
Also, the denominator of the mixed number still remains the denominator of the improper fraction.
That’s
55/8
The mixed number 6 7/8 is equal to the improper fraction 55/8, making option A correct.
Explanation:To convert a mixed number to an improper fraction, you multiply the whole number by the denominator of the fraction and then add the numerator of the fraction. The mixed number 6 7/8 can be converted to an improper fraction by following this method: Multiply 6 (the whole number) by 8 (the denominator) to get 48, and then add 7 (the numerator) to get 55. Therefore, 6 7/8 as an improper fraction is 55/8, which makes option A correct.
Triangle ABC is similar to triangle YBX. Find the value of n. The figure is not drawn to scale.
Answer:
16
Step-by-step explanation:
Set up a proportion: 27/12=36/n
Solve algebraically: 27n=432
n=16
Therefore, 16
15% of 20 is ____ find the percentage of the number
Answer:
3
Step-by-step explanation:
x 15
------ = -----
20 100
20x5 is 100
What times 5 is 15? 3
Which shows two triangles that are congruent by the sss congruence theorem?
Answer: Triangles can be similar or congruent. Similar triangles will have congruent angles but sides of different lengths. Congruent triangles will have completely matching angles and sides. Their interior angles and sides will be congruent. Testing to see if triangles are congruent involves three postulates, abbreviated SAS, ASA, and SSS.
Step-by-step explanation:
Answer:
D is the correct answer if you have this pic in your question then its this one pls like if its right thanks
Step-by-step explanation:
Cherie was building a fort with her friend jaylah . Cherie built a fort that was 181 inches tall and jaylah built a fort that was 62 inches taller than cheries fort. How tall was jaylah fort?
Height of Jaylah's fort = 243 inches
Step-by-step explanation:
Step 1:
Height of Cherie's fort = 181 inches
Height of Jaylah's fort = 62 inches taller than Cherie's fort
We need to find the actual height of Jaylah's fort
Step 2 :
Since we are given that Jaylah's fort is 62 inches taller than Cherie's fort the actual height of Jaylah's fort can be determined by adding the height of Jaylah's fort to that of Cherie's fort.
Hence
Height of Jaylah's fort = 181 + 62 = 243 inches
Step 3 :
Answer :
Height of Jaylah's fort = 243 inches
what value of a makes the equation true?
a+29=-63
I need help!!
Answer:
a = -92
Step-by-step explanation:
Step 1: Subtract 29 from both sides
a + 29 = -63
a + 29 - 29 = -63 - 29
a = -92
Answer: a = -92
Answer:
-92
Step-by-step explanation:
a + 29 = -63
- 29 = -29
a = -63 - 29
a = -92
how can you get 3 1/2x alone on the left side of the equation 3 1/2 x + 215 = 495? what is the resulting equation?
Answer:3 1/2x = 280
Step-by-step explanation: Subtract 215 from both sides.
Answer:
subtract 215 from both sides
x = 80
Step-by-step explanation:
to get the 3 1/2 x alone subtract 215 from both sides.
this moves it to the other side.
495-215 =280
3 1/2 x = 280
divide both sides by 3 1/2
this will solve for x
x = 80
Solve -(6)^x-1 +5=(2/3)^2-x
Answer:
6^x=x+32/9
Step-by-step explanation:
pls help!!
solve
question22
Answer:
19
Step-by-step explanation:
(x+2)/3 - (x+1)/5 = (x-3)/4 - 1
[5(x+2) - 3(x+1)]/15 = [(x-3) - 4]/4
(2x+7)/15 = (x-7)/4
4(2x+7) = 15(x-7)
8x+28 = 15x-105
7x = 133
x = 19
An amount of $4000 was deposted in a bank of 7% compounded quarterly for 2 years. The rate the increased to 10% and was compounded quarterly for the next 2 years. If no money was
balance at the end of this time?
The balance was $=
(Round to the nearest cant as needed)
Answer:
$5599.20
Step-by-step explanation:
The quarterly interest rate for the first two years was ...
7%/4 = 0.0175
So, the multiplier each quarter for those 8 quarters was 1+0.0175 = 1.0175. At the end of the first 8 quarters, the account value had been multiplied by ...
1.0175^8
For the next 8 quarters, the quarterly interest rate was 10%/4 = 0.025. So at the end of those 8 quarters, the balance had been multiplied by ...
1.025^8
Then the balance at the end of 4 years was ...
$4000(1.0175^8)(1.025^8) ≈ $5599.20
The balance was $5599.20.
Select the correct answer.
Which situation indicates that an Investor shouldn't sell his or her stocks?
A.
The price of the stock shows a negative trend, and the current stock price is lower than the Investor's purchase price.
B.
The price of the stock shows a negative trend, and the current stock price is higher than the Investor's purchase price.
C. The price of the stock shows a positive trend, and the current stock price is lower than the investor's purchase price.
D. The price of the stock shows a positive trend, and the current stock price is the same as the investor's purchase price.
Answer: C
Example:
Bob bought stocks in a local company for $10. Now the stocks are showing a positive trend. Joe comes in and offers bob $5 for the stock. Bob says no because that would provide no good for him considering he is gaining money because of the positive trend, and he would not earn any money for the stock because he bought it for $5 more then Joe offered him.
We can actually infer that the situation that indicates that an investor shouldn't sell his or her stocks is: C. The price of the stock shows a positive trend, and the current stock price is lower than the investor's purchase price.
Who is an investor?An investor refers to an individual whose takes the responsibility of releasing capital to a venture or business with an expectation of getting financial returns in future.
We can then see here that option C gives us a clear example of a situation that indicates that an investor shouldn't sell his or her stocks.
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What plus what equals 4 but multiplies to equal -5?
zahra earns $80 each day plus a 6% commission on her sale at an appliance store. on friday zahra has $900in sales.how much does zahra earn on friday including commission
Solution:
Given that,
zahra earns $80 each day plus a 6% commission on her sale at an appliance store
zahra has $900 in sales
Find the commission amount
commission amount = 6 % of 900
[tex]commission\ amount = \frac{6}{100} \times 900\\\\commission\ amount = 54[/tex]
Zara earnings including commission amount = 80 + 54 = 134
Thus Zara earned $ 134 on friday including commission
Find the area of this figure. Show your work or explain your logic.
Answer:500 units square
Step-by-step explanation:Area= length times width
The length is 20 the down arrows are 5+10+5=20 so that's the width
20 times 20=400
2 boxes on the sides are 5 times =50
400+50+50=500
how to do inverse of functions
Answer:
Step-by-step explanation:
First, replace f(x) with y
Replace every x with a y and replace every y with an x .
Solve the equation from Step 2 for y .
Replace y with f−1(x) f − 1 ( x ) .
Verify your work by checking that (f∘f−1)(x)=x ( f ∘ f − 1 ) ( x ) = x and (f−1∘f)(x)=x ( f − 1 ∘ f ) ( x ) = x are both true.
Final answer:
To find the inverse of a function, you reverse the original operation, whether it's an exponential with its natural log, a square with a square root, or logarithms with their exponential counterpart. These inverses, like ln(e^x) = x, demonstrate how they 'undo' each other. The inverse log can be used to find the original number from its logarithm.
Explanation:
Understanding Inverse Functions
To find the inverse of a function, you essentially want to reverse the original operation. For example, an exponential function and its inverse, the natural logarithm (ln), undo each other. If you have an equation y = ex, taking the natural logarithm of both sides would give you ln(y) = x, which effectively isolates x. This demonstrates that ln(ex) = x and eln(x) = x, showing how these functions are inverses of each other.
Similarly, other function pairs such as sine and arcsine, or a power function and its corresponding root function, act as inverse operations. For instance, if you have a2 = c2 - b2, as in the Pythagorean Theorem, you would take the square root of both sides to find a. This 'undoes' the square, showing that (√()2) is the inverse function of squaring.
When it comes to logarithms, the process of finding an inverse is similar. If you take a logarithm of a number, you can find the original number by taking the inverse log or calculating 10to the power of the logarithm. If you have log10(x) = y, then 10y = x.
Use the distributive property to write and equivalent expression: 6(y+5)
Answer:
6y+30
Step-by-step explanation:
1) distributive property is basically multiplying the number outside of the parenthesis with each number/variable inside
so
6*y+6*5
6y+30
hope this helps
Answer:
6y+30
Step-by-step explanation:
(6*y)+(5*6)
what is equivalent to [tex](3^6)3[/tex]
A. 3^2
B 3^9
C 3^3
D 3^18
ILL GIVE ALL 20 POINTS
For this case we must indicate an expression equivalent to:
[tex](3 ^ 6) ^ 3[/tex]
For properties of powers we have to:
[tex](a ^ n) ^ m = a ^ {n * m}[/tex]
So, the above expression can be rewritten as:
[tex](3 ^ 6) ^ 3 = 3^{6*3} = 3^{18}[/tex]
Thus, the resulting expression is: [tex]3^{ 18}[/tex]
Answer:
[tex]3^{ 18}[/tex]
Option D
expand the brackets
1.
[tex]3(2x + 5)[/tex]
2.
[tex]7(p + 3q)[/tex]
3.
[tex]3m(n - 2m)[/tex]
[tex]1)\ 3(2x + 5) = 6x + 15\\\\2)\ 7(p + 3q) = 7p + 21q\\\\3)\ 3m(n - 2m) = 3mn - 6m^2\\\\[/tex]
Solution:
Given that,
We have to expand the brackets
Use distributive property,
a(b + c) = ab + bc
Multiply the number in front of parenthesis with each term inside the parenthesis and then add them together
1)
[tex]3(2x + 5) = 3 \times 2x + 3 \times 5\\\\3(2x + 5) = 6x+15[/tex]
-------------------------------------------------
2)
[tex]7(p + 3q) = 7 \times p + 7 \times 3q\\\\7(p + 3q) =7p + 21q[/tex]
----------------------------------------------------
3)
[tex]3m(n-2m) = 3m \times n - 3m \times 2m\\\\3m(n-2m) = 3mn - 6m^2[/tex]
Thus the given expressions are expanded using distributive property
is 1/7 greater than -5? Or is it less than?
Answer: Greater than
Step-by-step explanation:
1/7, no matter how small, is a positive number, and a positive number is always greater than a negative number, as visualized on a number line.
A vegetable garden and a surrounding path are shaped like a square that together is 12 ft wide. The path is 1 foot wide. Find the total area of the vegetable garden and path.
Answer:
144 square feet
Step-by-step explanation:
The 12-foot width apparently includes the garden and path, so the desired area is that of a 12-foot square:
A = s² = (12 ft)² = 144 ft²
The area of the garden and path is 144 square feet.
I need help please and thank you
Answer:
c = 13
Step-by-step explanation:
2 ways of going about in this problem
1. If you have done enough Pythagorean theorem problems, you might be able to memorize some common right triangle side lengths, such as 3-4-5 or
5-12-13
2. actually using Pythagorean theorem
[tex]a^2+b^2=c^2[/tex], where c is hypotenuse
c = [tex]\sqrt{5^2+12^2}[/tex]
c = [tex]\sqrt{169}[/tex] = 13
Janets family wants to save for a four year college education for her. After some research they estimate that the total will cost about $78,000 how much should her family save if she is 12 years old in plans to go to college in 6 years?
Janet's family should save $13,000 per year for the next 6 years to achieve their goal of $78,000 for her college education.
To calculate this, we divide the total cost by the number of years until Janet starts college.
Total cost for a four-year college education: $78,000.
Number of years until college: 6 years.
Annual savings required: Total cost / Number of years
= $78,000 / 6 years
= $13,000 per year.
(ii) The value V of a Porsche 718 Cayman that is tyears old can be modeled by
V(t) = 420,000(0.965)
(a) What would be worth the car's worth in 2 years?
(b) I how may years will the car be worth $325,000?
Answer:
Part A: What would be worth the car's worth in 2 years?
V(2) = $ 391,114.50
Part B. In how many years will the car be worth $325,000?
t = 7.2 years (rounding to the next tenth) or approximately 7 years, 2 months and 12 days
Step-by-step explanation:
Part A: What would be worth the car's worth in 2 years?
If V(t) = 420,000(0.965) ^t, therefore:
V(2) = 420,000(0.965)²
V(2) = 420,000 * 0.931225
V(2) = $ 391,114.50
Part B. In how many years will the car be worth $325,000?
If V(t) = 420,000(0.965) ^t, therefore:
325,000 = 420,000(0.965) ^t
325,000/420,000 = (0.965) ^t
0.7738 = 0.965^t
t = log 0.965(0.7738)
t = log 0.7738/log 0.965
t = 7.2 years (rounding to the next tenth) or approximately 7 years, 2 months and 12 days
0.2 years = 0.2 * 12 = 2.4 months
Savannah drove 716 miles on Monday. She drove another 572 miles one Tuesday. About how many more miles did she drive on Monday than Tuesday?
Final answer:
Savannah drove 144 more miles on Monday than she did on Tuesday, calculated by subtracting Tuesday's mileage from Monday's.
Explanation:
The student is asking how many more miles Savannah drove on Monday than Tuesday. To calculate this, we simply subtract the number of miles driven on Tuesday from the number of miles driven on Monday.
Miles driven on Monday: 716 miles
Miles driven on Tuesday: 572 miles
To find the difference in miles, we use the following equation:
716 miles (Monday) - 572 miles (Tuesday) = 144 miles
Therefore, Savannah drove 144 more miles on Monday than on Tuesday.