Answer:
a) A-B = { 1 , 3, 5 }
b) The remainder is 50
c) f + g)(x) = x⁴+ 5x³
d) [tex]\frac{dy}{dx} = \frac{2x- y^3(3x^2)) }{ 1- x^3 3y^2}[/tex]
Step-by-step explanation:
Step(I):-
1) a)
Let A = { 1, 3, 5, 7 } and B = { 7 , 14 , 21 }
A - B = {1,3,5,7} - { 7,14,21}
A - B = { 1 , 3, 5}
b)
Given f (x)=3x³−11x−48
x-1 ) 3 x³ - 11x -48 (- 3x²-3x -2
-3x³ +3x²
3x²-11x-48
-3x²+9x
2x -48
-2x +2
50
The remainder is 50
c) Given f(x) = x³ and g(x) = x + 5
(f. g)(x) = f(x) .g(x) = x³ . (x+5) = x³(x) + 5 x³ = x⁴+ 5x³
d)
Given function y = 3 + x²+x³y³ ...(I)
By using derivative formulas
y = xⁿ
[tex]\frac{dy}{dx} = n x^{n-1}[/tex]
Apply d/dx ( UV) = U V¹ + V U¹
Differentiating equation (I) with respective to 'x' , we get
[tex]\frac{dy}{dx} = 0 + 2x + ( x^3 3y^2(\frac{dy}{dx} )+ y^3(3x^2))[/tex]
[tex]\frac{dy}{dx} - ( x^3 3y^2(\frac{dy}{dx} )= 2x- y^3(3x^2))[/tex]
[tex]\frac{dy}{dx} = \frac{2x- y^3(3x^2)) }{ 1- x^3 3y^2}[/tex]
14. The area of a rectangle is 375 square inches and it’s perimeter is 80 inches. Find both the length and width.
Answer:
Length [tex]=25[/tex] inches
Width [tex]= 15[/tex] inches
Step-by-step explanation:
Let [tex]l[/tex] = length of rectangle, [tex]w[/tex] = width of rectangle
Given the area and the perimeter of the rectangle, we can write:
[tex]lw = 375[/tex]
[tex]2l+2w=80[/tex]
So:
[tex]l+w = 80\div2[/tex]
[tex]=40[/tex]
[tex]l=40-w[/tex]
Now, we can use substitution to find the value of [tex]w[/tex]:
[tex]lw = 375[/tex]
[tex](40-w)w = 375[/tex]
[tex]40w-w^2 = 375[/tex]
[tex]375+w^2-40w = 0[/tex] (Quadratic equation)
[tex](w-15)(w-25) = 0[/tex]
∴ [tex]w = 15, 25[/tex]
We can use substitution again to find the value of [tex]l[/tex]
[tex]lw = 375[/tex]
[tex]l=375\div w[/tex]
[tex]=25,15[/tex]
∵ Length usually refers to the longer side of a rectangle, ∴ length [tex]=25[/tex] inches and width [tex]=15[/tex] inches.
Hope this helps :)
1. Luis wants to buy Jordans for 75.23. He saves 10.27 per month. Write an equation to solve how many months he'll need to save. Use x for the variable and do not have any spaces.
2. Jovie earns $8.25 for the hours that she is at work. This week she earned $288.75. Write an equation to solve how many hours she worked. Use x for the variable and do not have any spaces. Pls help :(
Answer:
Chicken nugget
Step-by-step explanation:
Which statement can you conclude is true from the given information?
Answer:
angle IJA is a right angle
!!! time sensitive please answer !!!
consider the sequence below. 3, 1, 1/3, 1/9
select the explicit function which defines the sequence
A. f(n) = 1/3 • 2^(n-1)
B. f(n) = 2 • (1/3)^(n-1)
C. f(n) = 3 • (1/3)^(n-1)
D. f(n) = 1/3 • 3^(n-1)
What do you divide by 90 to get 30?
Answer:
3
Step-by-step explanation:
3 times 30 = 90 then divide 90 and 30 you get 3
6(x−2)=−18
x=?
Anybody know what X is equal to?
If you know a little bit about this question, thank you for your help.
(If the answer is right, this person will be the smartest.)
HEYYYYYYYYYYYY ONCE AGAIN THIS IS ONLY 3 OF 30 PlS HELPPP
Answer:
the 3rd one im pretty sure
Step-by-step explanation:
Answer:
the 3rd one <3
Step-by-step explanation:
Car X travels 186 miles and 3 hours right the equation of the line that describes the relationship between distance and time
Answer:
Y=62x
Step-by-step explanation:
The equation of the line that describes the relationship between distance and time is (y = 62x) and this can be determined by using the definition of speed.
Given :
Car X travels 186 miles and 3 hours.
The following steps can be used to determine the equation of the line that describes the relationship between distance and time:
Step 1 - Let the total distance covered by car X be 'y' and the total time taken by car to cover that distance be 'x'.
Step 2 - The speed is given by the ratio of distance to time.
[tex]\rm Speed = \dfrac{Distance }{Time}[/tex]
Step 3 - Now, put the value of distance and time in the above equation.
[tex]\rm Speed = \dfrac{y}{x}[/tex] ---- (1)
Step 4 - According to the given data the speed is given by:
[tex]\rm Speed = \dfrac{186}{3} = 62\; miles/hour[/tex]
Step 5 - Now, put the value of speed in equation (1).
[tex]\dfrac{y}{x}= 62[/tex]
y = 62x
The equation of the line that describes the relationship between distance and time is (y = 62x).
For more information, refer to the line given below:
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Felipe sold t-shirts and hats at a festival. He made a $5 profit for each t-shirt he sold. He also made a profit of $40 from selling hats. If he made a total profit
$125, how many t-shirts did he sell?
Answer:
He sold 17 shirts at the festival.
The total number of t-shirts Felipe sold is 17 t-shirts.
Consider that the number of t-shirts Felipe sold be "x".
Since He made a profit of $5 for each t-shirt sold. Therefore, his profit from selling t-shirts is 5x. also made a profit of $40 from selling hats.
His total profit is given as $125.
So we can write the following equation:
5x + 40 = 125
Subtracting 40 from both sides;
5x = 85
Dividing both sides by 5, we get:
x = 17
Therefore, Felipe sold 17 t-shirts.
Learn more about equations here;
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Convert 45°C to Fahrenheit.
Answer:
113 degrees Fahrenheit
Step-by-step explanation:
If Tim has 2/3 pizza to share with 6 friends how much does he friend get
Answer:
Each friend gets 1/9th of the pizza.
Step-by-step explanation:
Assuming Tim does not have any pizza, you would multiply 2/3 by 3 to get 6/9. 6/9 divided by 6 is 1/9.
Which of the following is equivalent to 75/100? A 2/3 B 10/15 C 25/50 D 15/20
Answer:
D. 15/20
Step-by-step explanation: Because if it is 100 divide by 5 then it equals 20 and since 75% is 3/4 then 15/20 is your answer.
Answer:
D 15/20
Step-by-step explanation:
35 points plz help
Evaluate −4(14)6x for x=13.
Enter your answer as a fraction in simplest form in the box.
Answer:
-15228
Step-by-step explanation:
Given the expression :
-4(14)6x for X = 13
To evaluate ; simply substitute 13 for X in the equation :
-14(14)6(13)
-14 * 14 * 6 * 13 = - 15228
Estimate 32% of 19.
Answer: 6.08.
Explanation: 32% × 19 = 6.08.
A gas tank holds exactly 13 gallons. If the tank is 2/3 empty, how many gallons remain in the tank? (Round your answer to the nearest tenth)
Group of answer choices-
4.3
5.5
6.5
8.7
patricia has 45.82 in her checking account. How much does she have in her account after she makes a deposit of 120.75 and a withdraw of 185.90
Answer:
-19.43
Step-by-step explanation:
You got to add 120.75 to 45.82 then you subtract it from 185.90
comment if this helps :)
Which equation should you solve to find x?
If 47 divided by a power of 10 to get 0.047 what power of 10 was it divided by
Answer:
0.01
Step-by-step explanation:
cause 47 x 0.01 + 0.047
The power of 10 that you would dived it by would be 1,000.
Because here we have 3 option 10, 100, and 1,000. So what we would do is divide each one to that main number "47"
47 ÷ 10 = 4.747 ÷ 100 = 0.4747 ÷ 1,000 = 0.047Learn more at https://brainly.com/
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Eight friends go to the movies. The price for each ticket is
$7.99. One person thinks the total for all eight people will
be around $50.00.
Is this a reasonable estimate? Why?
OA. Yes, a reasonable estimate is around 5- $10 = $50.
B. No, a reasonable estimate is around 5 $8 = $40.
C. No, a reasonable estimate is around 8 $8 = $64.
OD. No, a reasonable estimate is around 8-$9 = $72.
Answer:The answer is C....
Step-by-step explanation:
Answer:
C
Step-by-step explanation:
determine if the 2 triangles are similar or not. if they are similar choose the correct similarity theorem below.
A
B
C
D
2 L = _____ ml can someone help? :((
Answer:
2000
Step-by-step explanation:
Answer:
2000 ml
Step-by-step explanation:
if f = 3, g = -4 and h = -5
[3-h]+13
Karim Corp. requires a minimum $8,600 cash balance. Loans taken to meet this requirement cost 1% interest per month (paid monthly). Any excess cash is used to repay loans at month-end. The cash balance on July 1 is $9,000, and the company has no outstanding loans. Forecasted cash receipts (other than for loans received) and forecasted cash payments (other than for loan or interest payments) follow.
Answer:
Step-by-step explanation:
Karim Corp. requires a minimum $8,600 cash balance. Loans taken to meet this requirement cost 1% interest per month (paid monthly). Any excess cash is used to repay loans at month-end. The cash balance on July 1 is $9,000, and the company has no outstanding loans. Forecasted cash receipts (other than for loans received) and forecasted cash payments (other than for loan or interest payments) follow. Cash receipts Cash payments July $ 24,600 28,900 August $32,600 30,600 September $ 40,600 32,600 Prepare a cash budget for July, August, and September. (Negative balances and Loan repayment amounts (if any) should be indicated with minus sign. Round your final answers to the nearest whole dollar.) KARIM CORP. Cash Budget For July, August, and September July August $ 9,000 September Beginning cash balance Total cash available Preliminary cash balance Ending cash balance Loan balance $ 0 Loan balance - Beginning of month Additional loan (loan repayment) Loan balance - End of month
What is the missing numbers to this equation please
? - (? × ?)=90
Answer:
-0(10 x 9)=90
Suppose you deposit $2,500 in a savings account that pays you 5% interest per year.
a. How many years will it take for you to double your money?
b. How many years will it take for your account to reach $8,000?
Answer:A=4 Years B=6 years
Step-by-step explanation:
A physicist examines 23 sedimentary samples for mercury concentration. The mean mercury concentration for the sample data is 0.036 cc/cubic meter with a standard deviation of 0.012. Determine the 80% confidence interval for the population mean mercury concentration. Assume the population is approximately normal. Step 1 of 2: Find the critical value that should be used in constructing the confidence interval. Round your answer to three decimal places.
Answer:
The 80% confidence interval is [tex]0.0328 < \mu < 0.0392[/tex]
Step-by-step explanation:
From the question we are told that
The sample size is n = 23
The sample mean is [tex]\= x = 0.036 \ cc/m^3[/tex]
The standard deviation is [tex]\sigma = 0.012[/tex]
From the question we are told the confidence level is 80% , hence the level of significance is
[tex]\alpha = (100 - 80 ) \%[/tex]
=> [tex]\alpha = 0.20[/tex]
Generally from the normal distribution table the critical value of [tex]\frac{\alpha }{2}[/tex] is
[tex]Z_{\frac{\alpha }{2} } = 1.282[/tex]
Generally the margin of error is mathematically represented as
[tex]E = 1.282 * \frac{0.012 }{\sqrt{23} }[/tex]
=> [tex]E = 0.00321 [/tex]
Generally 80% confidence interval is mathematically represented as
[tex]0.036 -0.00321 < \mu < 0.036 + 0.00321[/tex]
=> [tex]0.0328 < \mu < 0.0392[/tex]
If P(A or B) = 0.8, P(A) = 0.3, and P(A and B)= 0.15, find P(B).
P(B) =
(Simplify your answer. Type an integer or a decimal.)
9514 1404 393
Answer:
P(B) = 0.65
Step-by-step explanation:
The appropriate formula is ...
P(A or B) = P(A) +P(B) -P(A and B)
Then P(B) is ...
P(B) = P(A or B) +P(A and B) -P(A)
P(B) = 0.8 +0.15 -0.3
P(B) = 0.65
Solve the system using substitution.
y - 3x = 1
2y - x = 12
([?], [])
Answer:
(2, 5)
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightEquality Properties
Algebra I
Solving systems of equations using substitution/eliminationStep-by-step explanation:
Step 1: Define Systems
y - 3x = 1
2y - x = 12
Step 2: Rewrite Systems
y - 3x = 1
Add 3x on both sides: y = 3x + 1Step 3: Redefine Systems
y = 3x + 1
2y - x = 12
Step 4: Solve for x
Substitution
Substitute in y: 2(3x + 1) - x = 12Distribute 2: 6x + 2 - x = 12Combine like terms: 5x + 2 = 12Isolate x term: 5x = 10Isolate x: x = 2Step 5: Solve for y
Define equation: 2y - x = 12Substitute in x: 2y - 2 = 12Isolate y term: 2y = 10Isolate y: y = 5Kesha it’s plain to rent a van for a trip to Mt.rainier two of her friends each went to the same type of van from the same car rental company last week
Answer:
a
Step-by-step explanation:
Which statements describe one of the transformations performed on f(x) =x^2 to create g(x)=2x^2+5?
A: A translation of 5 units to the right
B: A vertical stretch with a scale factor of 1/2
C: A vertical stretch with a scale factor of 2
D: A translation of 5 units up
Answer:
do u know the answer ik it's five units up but that it
Answer: a vertical stretch with a scale factor of 2. and a translation of 5 units up.
Step-by-step explanation: