Step-by-step explanation:
(f + g)(x) = f(x) + g(x) = (4x² + 1) + (x² - 5) = 5x² - 4. (D)
Answer:
D. 5x^2-4
Step-by-step explanation:
We are asked to find (f+g)(x), which is really just the sum of the two functions.
(f+g)(x)=f(x)+g(x)
We know the the functions are:
• f(x)= 4x^2+1
• g(x)=x^2-5
Substitute the functions in.
(f+g)(x)=(4x^2+1)+(x^2-5)
Add the functions by combining like terms. For this equation, the like terms are those with x^2 and the constants.
(f+g)(x)= (4x^2+x^2)+(1-5)
Add the terms with x^2
(f+g)(x)=(5x^2)+(1-5)
Add the constants or terms without variables.
(f+g)(x)=(5x^2)+(-4) = 5x^2-4
The sum of the functions is D. 5x^2-4
3. Determine whether the set of numbers can be the measures of the sides of a triangle. If so, classify the triangle as acute, obtuse, or right. 16, 30, 33
Answer:
all of them are acute
.......
Answer:
yes. it will be an acute.
What type of triangle is this?
Options:
-SSS
-SAS
-AAS
-ASA
-HL
-Not Possible
Answer:
ASA
Step-by-step explanation:
As two lines are parallel, alternate interior angles will be congruent and the side between them is common.
So, ASA congruent
In the figure above, the circle with center O is inscribed in square ABC
Line segment AO intersects the circle at P. What is the length of AP?
Step-by-step explanation:
Line AP = Line AO - Line PO = sqrt2 - 1.
Given the side lengths 9.5 cm, 7.5 cm, and 10 cm, can they form a triangle and if so, what type of triangle?
Answer:
this number 6
Step-by-step explanation:
yes self 4
Answer:
yes
Step-by-step explanation:
because if you add correctly you will get the answer
HELLP HELP PLSSSSSSSSSS
HELP
Help with quadratic! Really struggling with this
Answer:
Step-by-step explanation:
The equation
[tex]G(h)=-3h^2+24h+47[/tex]
represents the grade you are going to earn which is represented by G(h) where h in the equation is the hours you study the week before.
Part A) Is totally up to you because in the question it asks What's the best possible grade you can earn with your current study habits lets say if you study around 4 hours the week before the test. Which means the value of h should be 4 because h represents hours in the equation.
so ,
[tex]G(h)=-3h^2+24h+47\\G(4)=-3(4)^2+24(4)+47\\G(4)=-48+96+47\\G(4)=95\\[/tex]
So if you studied for 4 hours the week before the test you are going to score 95 marks which would be an A* grade.
Part B) In this part it asks you the maximum amount of study time you will need to have to earn that grade which means how many maximum hours you would need to earn a total of 95 marks which is 4.
Part C) The y-intercept is the constant in the equation in this case +47 is y-intercept and in the context of the problem it denotes that if you studied for 0 hours you would still earn 47 marks on the test, which would result you failing the test.
Part D) How many hours would you need to complete and still earn a zero would be:
[tex]G(h)=-3h^2+24h+47\\-3h^2+24h+47=0[/tex]
because it says still earn a zero which means the grade is zero so now we solve the equation.
[tex]-3h^2+24h+47=0\\3h^2-24h-47=0\\[/tex]
using the quadratic formula we get two values for h which are
h = 9.627 and h = -1.627 so eventually hours can never be in negative its impossible you can't study for -1.627 so our answer is 9.627 hours and you would still earn a zero after studying approximately 9.6 hours.
Part E) The grade that you will earn if you studied for 5 hours is:
[tex]G(h)=-3h^2+24h+47\\G(5)=-3(5)^2+24(5)+47\\G(5)= -75+120+47\\G(5)=92\\[/tex]
You would earn 92 marks which would result in an A* grade
Answer:
(A) 95
(B) h=4
(C) 47, represents 0 hours of study
(D) h=9.63
(E) 92
Step-by-step explanation:
(A) They are asking for the maximum of the graph of the equation which can be found using the vertex formula:
[tex]max= c-\frac{b^2}{4a}[/tex]
where 'a' is the coefficient of the first term, 'b' is the coefficient of the second term and 'c' is the third term.
So we have:
[tex]max=47-\frac{(24)^2}{4(-3)} = 95[/tex]
(B) To find the hours of study required to get 95 we need to set the equation equal to 95:
[tex]-3h^2+24h+47=95[/tex]
which can be rewritten as:
[tex]-3h^2+24h+47-95=0[/tex]
or
[tex]-3h^2+24h-48=0[/tex]
When we solve for 'h' we get h = 4
Therefore, studying 4 hours gives us a grade of 95, which is the maximum score from the equation.
(C) The function G(h) is our y and h is our x values. To find the y intercept, x (which is h in the equation) must be set to 0 and solved for y. This is because the y intercept is at the point where x =0.
So we have:
[tex]G(h)=-3(0)+24(0)+47\\ =0+0+47\\ =47[/tex]
This is when h=0 and therefore is represents the grade when 0 hours of studying is done.
(D) To find how many hours of study can still produce a grade of 0, we need to set the function equal to 0 and solve for h.
[tex]-3h^2+24h+47=0\\[/tex]
This gives us two results when solved quadratically:
[tex]h=-1.63[/tex] and [tex]h=9.63[/tex]
Obviously, time cannot be negative so the answer is 9.63 hours.
(E) If we study for 5 hours, h should be equal to 5.
So substituting 5 for h we get:
[tex]-3(5)^2+24(5)+47=92[/tex]
So 5 hours of study affords us a grade of 92.
Hope that explains it.
HELP ME! HELP! PLEASE HELP ME!!!
Answer:
Step-by-step explanation:
The answer is 12 units
how to graph g(x) = 3f(x) when f(x) = x
Step-by-step explanation:
f(x) = x
g(x) =3x
point if intersection
f(x) =g(x)
x = 3x
Find (f/g)(x)
f(x)=√ x^2-1
g(x)√ x-1
A. √ x+1
B. √ x-1
C.√ -x^2/-x+1
D.√ 1/x+1
Answer:
option A is the Answer
Step-by-step explanation:
hope it helps
What is 820 milliliters equal to in liters?
Answer:
0.82 L
Step-by-step explanation:
Answer: 0.82 liters
Step-by-step explanation:
Match each set of numbers with their least common multiple.
Answer:
25 and 8) = 200
(32,24 and 18) =288
(22 and 4)=44
(14 and 12) = 84
(9,8 and 7)= 504
(27,12 and 36) =108
Answer:
top down: 200, 288, 44, 84, 504, 108
Step-by-step explanation:
The least common multiple (LCM) can be figured a couple of ways.
a) factor the numbers, then form the product of unique factors (to their highest powers)
b) divide the product of the numbers by their greatest common factor (GCF). Factoring or Euclid's method can be used to find the GCF.
When there are more than two numbers, the LCM can be figured for two of them, then for that result and the next number, and so on.
__
25 and 8 have no common factors, so their LCM is their product: 200
__
32 and 24 have 8 as their GCF, so their LCM is 32·24/8 = 96. 96 and 18 have 6 as their GCF, so their LCM is 96·18/6 = 288
__
22 and 4 have 2 as their GCF, so their LCM is 22·4/2 = 44
__
14 and 12 have 2 as their GCF, so their LCM is 14·12/2 = 84
__
9, 8, 7 have no common factors, so their LCM is their product: 9·8·7 = 504
__
27 and 12 have 3 as their GCF, so their LCM is 27·12/3 = 108. 108 is a multiple of 36, so their LCM is 108.
pls ANSWERRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRR
Hi there!
[tex]\large\boxed{ 9.4m}[/tex]
Find the perimeter using the formula:
P = 2l + 2w
It is given that the dimensions are 2.8 × 1.9 so plug these number into the equation:
P = 2(2.8) + 2(1.9)
P = 5.6 + 3.8
P = 9.4m
Using Newton-Raphs
f (x) = 2x3 + x2 - x + 1 accurate to within 10-4
Answer:
2x3+x2−x+1x
Step-by-step explanation:
Let's solve for f.
fx=2x3+x2−x+1
Step 1: Divide both sides by x.
fx=2x3+x2−x+1x
fx=2x3+x2−x1x
Answer:
9514 1404 393
Answer:
-1.2338
Step-by-step explanation:
The graph shows the one real root is about -1.234. The Newton's method iterator is ...
new x = x - f(x)/f'(x) . . . . . where f'(x) is the derivative of f(x)
Many graphing calculators provide a derivative function, so the iteration equation can be evaluated more or less directly by the calculator. In the attached, we have shown a table with three iterations of the root. After the second iteration, the root is good to 4 decimal places.
x ≈ -1.2338
Need help!!!!!!!!!!!!!
Answer:
25 units (cant see what it says on the side :/ ) per hour
Step-by-step explanation:
hope this helps <3
Josh buys cucumbers that cost $0.62 per pound. He pays $2.79 for the cucumbers. How many pounds of cucumbers does Josh have?
Answer:
Josh bought 4.5 pounds of cucumbers.
Step-by-step explanation:
2.79 divided by the cost per pound, .62, is 4.5. Therefore he bought 4.5 pounds of cucumbers
Will give brailyest!!!!
what makes farming possible in Central Asia's dry climate?
a. annual floods.
b. irritation systems
c. seasonal droughts
d. tropical storms
Answer:
I think its a
Step-by-step explanation:
Answer: B
Step-by-step explanation: EDGE 2021
Subtract.
8/9-1/3
Need help!
Answer:
5/9
Step-by-step explanation:
the common denominator is 9.
multiply 1/3 by 3
8/9 minus 3/9
5/9
Tim worked 23 hours and earned $6.50 per hour. Round the number of hours Tim worked to the nearest ten and round his hourly pay to the nearest dollar to estimate how much he will be paid.
Step-by-step explanation:
23=20. $6.50=$7
20x7=$140
Answer:
first step is 20. Second step is 7.00$. He will make 140.00$ an hour.
Step-by-step explanation:
A rectangle has a length of x+ 4 centimeters and a width of x centamentere the perimeter of the rectangle is 28cm what is the value of x
Answer: The perimeter of the rectangle is 28 centimeters.
Step-by-step explanation: I hope this helps-
Answer:
x=10
Step-by-step explanation:
x+4+x=24
2x=20
x=10
A university dean is interested in determining the proportion of students who receive some sort of financial aid. Rather than examining the records for all the students, the dean who randomly selects 76 students and finds that 58 out of 76 are receiving financial aid. Calculate the standard error of your estimate. 3.7061
Answer:
Standard error (S.E) = 0.048 ≅ 0.05
Step-by-step explanation:
Explanation:-
Given sample size 'n'=76
Given the dean who randomly selects 76 students and finds that 58 out of 76 are receiving financial aid.
Sample proportion
[tex]p = \frac{x}{n} = \frac{58}{76} = 0.7631[/tex]
The standard error is determined by
[tex]S.E = \sqrt{\frac{p(1-p)}{n} }[/tex]
[tex]S.E = \sqrt{\frac{0.763(0.2369}{76} }[/tex]
Standard error is 0.048 ≅ 0.05
Hot dogs come in packs of 12. Buns come in packs of 16. What is the fewest number of hot dogs or buns you can buy to have the same number of each?
IF CORRECT I WILL GIVE BRAINLIEST!!
Answer is not 9. IDK THE ANSWER. The last few problems everybody is saying it is 9.
Please help me do this problem!
Screenshot below!
Answer:
2
Step-by-step explanation: I'm not very smart, nor do I understand this, so it's probably wrong but I'm just trying to help
QUICK HELP HURRY MAKRIMG PIEPLE AS BRIANLDIT
Answer:
36
Step-by-step explanation:
Answer:
36
Step-by-step explanation:
which type of plate boundary is illustrated in each of the following figures below
Answer:
SEXXXXXXXZZZZZz
Step-by-step explanation:
AJ is writing a report about Calvin Coolidge. He's including information about the former president's early days. Should he quote directly from a biography of Coolidge or paraphrase the information? Why?️
Pls help me answer this question for my homework
Answer:
4
Step-by-step explanation:
2 goes to both A and B which makes it not a function because if I remember right the domain isnt allowed to repeat.
What is the opposite of the opposite of -1.4?
Answer:
1.4
Step-by-step explanation:
when we add -1.4 and 1.4 we get zero so its the opposite
Find the value of X algebraically. Show your work.
Answer: 21
Step-by-step explanation:
We know 9x - 56 is equal to 6x + 7
So:
9x - 56 = 6x + 7
Add 56 to each side
9x = 6x + 63
Subtract 6x from each side
3x = 63
Now divide each side by 3
x = 21
Solve the system.
2x + 3y -
2z =
-7
2
x – 2y + 4z = 15
2y + z = = 1
Enter your answer as an ordered triple.
([?],[ ], [ ]
Enter
Answer:
(1, -1, 3)
Step-by-step explanation:
Given system of linear equations is,
2x + 3y - 2z = -7 ---------- (1)
x - 2y + 4z = 15 ------- (2)
2y + z = 1 ------------ (3)
Equation (2) multiplied by 2 then subtracted from equation (1),
(2x + 3y - 2z) - 2(x - 2y + 4z) = -7 - 30
(2x - 2x) + (3y + 4y) + (-2z - 8z) = -37
7y - 10z = -37 ------ (4)
Equation (3) multiplied by 10 then added to equation (4),
(20y + 10z) + (7y - 10z) = 10 - 37
27y = -27
y = -1
From equation (3),
2(-1) + z = 1
-2 + z = 1
z = 3
From equation (2),
x - 2(-1) + 4(3) = 15
x + 2 + 12 = 15
x + 14 = 15
x = 1
What is 31/26 simplified?
Answer:
it cant be simplified
Step-by-step explanation:
Answer:
1 5/26 i used a calculator
2) For 9 cows, 13 kg 500 g of food supplement are required every day.
In the same proportion, how much will be needed for 12 cows?
Answer:
18 kg
Step-by-step explanation:
We can use a proportion.
First, 13 kg 500 g = 13 kg + 500 g = 13 kg + 0.5 kg = 13.5 kg
Proportion:
9 cows is to 13.5 kg as 12 cows is to x
9/13.5 = 12/x
Cross multiply.
9x = 13.5 * 12
Divide both sides by 3.
3x = 4.5 * 12
Divide both sides by 3.
x = 1.5 * 12
x = 18
Answer: 18 kg