Answers
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.
Related Questions
the length of a rectangular sing is 5 time its width. if the sign perimeter is 24 inches. what is the sign area ?
Answers
Answer:
20 in²
Step-by-step explanation:
Assuming that the width of the sign is x, then from the question, we're told that the length is 5 times it's width, so
b = x inches
l = 5x inches
Again, we're told that the perimeter of the sign is 24 inches, and we know already that the perimeter of a rectangle is given as
Perimeter = 2(l + b), substituting this, we have
24 = 2(5x + x)
24 = 10x + 2x
24 = 12x
x = 24 / 12
x = 2 inches.
Since x is the width of the rectangle, and it's 2 inches, we use it to find the length of the sign.
l = 5 * 2
l = 10 inches.
Then, we are asked to find the area of the sign. Area of a rectangle is given as
A = l * b, so if we substitute, we have
Area = 10 * 2
Area = 20 square inches
Evaluate h(t)=50-t/5
h(35)=
Answers
You just put in 35 in for t. 35/5 = 7, 50 - 7 = 43.
Helppppppppppppppppppp ASAP
Answers
Answer:
-2, 1, 3
Step-by-step explanation:
The product of three positive integers is 300. If one of them is 5, what is the
least possible value of the sum of the other two?
Answers
Answer and Step-by-step explanation:
So, we are told that 3 positive integers multiply to be 300, and that one of the integers is 5.
First, we divide 300 by 5.
The result is 60.
Now, we take different (reasonable) numbers that add to 16:
10 and 6
12 and 4
We can see here that 10 and 6 are the integers because they add up to 16 and multiplies to 60.
#teamtrees #WAP (Water And Plant)
Evaluate. Write your answer as a fractionin simplest form. 2 1/6 - (-8/3) + (-4 7/9)=
Answers
Answer: 1/20
Step-by-step explanation:
Your value to live in a quiet apartment is $400. The neighbor living above your apartment makes noise using her treadmill every day. She values running at $500. Your neighbor has the right to run in her apartment. If the proper conditions are met, what does the Coase Theorem suggest is the likely outcome in this case
Answers
Answer:
continuation
Step-by-step explanation:
Since you value a quiet apartment at $400, which is less than $500, you might offer $400 for your neighbor to stop, but she values running higher, so she would likely refuse, resulting in the continuation of what's happening.
The correct statement to the given query is "The neighbor pays you $401 to continue running".
Coase's theorem predicts that throughout the face of such an external cost, contracting groups or two entities would be prepared to arrange as well as achieve a satisfactory solution.Because of this, one's neighbor would then compensate them at minimum the worth of their condominium so that he would rather start operating upon the treadmills.Learn more about Coase theorem here:
https://brainly.com/question/2898855
Monica went shopping for holiday presents. She bought boxes of chocolates and boxes of ornaments for her
coworkers. Boxes of chocolate cost $10 each and boxes of ornaments cost $12 each. She buys a total of 14
boxes and spends $156. How many boxes of chocolates and how many boxes of ornaments does she buy?
Use C for number of chocolate boxes and for number of ornament boxes.
Answers
and 8 boxes of ornaments
6*10=60 & 8*12=96
so you would add them and get
60+96=156
An equation is a mathematical statement that is made up of two expressions connected by an equal sign.
The number of chocolate boxes is 6.
The number of ornament boxes is 8.
What is an equation?An equation is a mathematical statement that is made up of two expressions connected by an equal sign.
Example:
2x + 4y = 9 is an equation.
2x = 5 is an equation.
We have,
Number of chocolate boxes = C
Number of ornaments boxes = B
The total cost of 14 boxes = $156
Cost of one box of chocolate = $10
Cost of one box of ornaments = $!2
Now,
C + B = 14 ______(1)
10C + 12B = 156 _______(2)
From (1) we get,
C = 14 - B ______(3)
Putting (3) in (2) we get,
10 (14 - B) + 12B = 156
140 - 10B + 12B = 156
140 + 2B = 156
2B = 156 - 140
2B = 16
B = 16/2
B = 8
Now,
C = 14 - B
C = 14 - 8
C = 6
Thus,
The number of chocolate boxes is 6.
The number of ornament boxes is 8.
Learn more about equations here:
https://brainly.com/question/17194269
#SPJ2
Find the equation of a line that contains the points (5.-7) and (-5,5). Write the equation in slope-intercept form, using
fractions when required.
Answers
Answer:
.
Step-by-step explanation:
The science club went on a two-day field trip. The first day the members paid $62 for transportation plus $15 per ticket to the planetarium. The second day they paid $95 for transportation plus $12 per ticket to the geology museum. Write an expression to represent the total cost for two days for the n members of the club.
Answers
Answer:
(62 + 15n) + (95 + 12n)
Get that hundo!
At ShopRite, chicken sells for $3.75 per pound. How much would it cost to buy 2.25 pounds of chicken?
Answers
Answer: 8.4375 U.S. dollars2
Step-by-step explanation:
Answer:
$8.44
Step-by-step explanation:
From the question it self we know that 1 pound of chicken costs $3.75. In order to solve this question we just need to find out how much 1 pound does fit into 2.25 pounds and then multiple the result by $3.75. We can find that out by dividing 2.25 by 1, and we get 2.25. Then we do the following....
2.25 x $3.75 = $8.4375
We got $8.4375 as an answer but we have to remember that when we are talking about money and we have to round to the nearest cent (which is equal to 1 hundredth of a dollar). So now we just have to round to the nearest hundredth, and we get $8.44 as our answer.
what is the area of the trapezoid?
Answers
Answer:
use formula=1/2×sum of parallel sides ×height
Answer:
A=64ft^2
Step-by-step explanation:
hope this helps
take care
PLZ HELP! WILL GIVE BRAINLIEST!! PLZ SOLVE QUICK!!
Find the value of x by filling in the blanks in the provided statement - reason solution.
I NEED THE WHOLE STATEMENT REASON CHART FILLED OUT!! THANK YOU SO MUCH IF YOU HELP!
Answers
Answer:
1. m<UTV=m<STR Vertical angles
2. m<R+ m<S+m<T. Triangles must add up to 180°
3. 3x+2x+85°=180°. Substitution
4. X=19. Algebra
Step-by-step explanation:
So basically we look at angle UTV and it equals to 85 degrees. We have to find another angle that equals 85 degrees and to do this we have to find a vertical angle congruent angle which here is angle RTS and this equals 85 degrees.
Next just use sum of angles in triangle from RTS.
Then substitute the values from angle RTS.
3x + 2x + 85 = 180
Solve for x.
I have attachtched a picture of what it should look like:
(2,-3), slope = 4
What is the answer
Answers
We are given:
The line passes through (2,-3)
Slope of the line = 4
Finding the equation of the line:
We know that the general form of the slope-intercept form is:
y = mx + b [where m is the slope and b is the y-intercept]
y = 4x + b [since slope = 4]
Finding the y-intercept:
Now, we are given that the line passes through the points: (2,-3)
which can be written as: x = 2 and y = -3
Since the line passes through these points, these values must satisfy the equation
So,
y = 4x + b
-3 = 2(4) + b
-3 = 8 + b
b = -11 [subtracting 8 from both sides]
Hence, the y-intercept is -11
Equation of the line:
We wrote the equation of the line as:
y = 4x + b (where b is the y-intercept)
now that we know the value of b,
y = 4x - 11
Therefore, the equation of the line is: y = 4x - 11
Michelle and her roommate rent an apartment for $798 a month. Each of them pays half. Because there are about 4 weeks in a month, Michelle estimates her share of the rent is about $100 a week. Is that a good estimate?
Yes
No, it is much high
Not, it is much low
Answers
Answer:
yes
Step-by-step explanation:
half of $798 is $399. $100 a week × 4 = $400. 400 is very close to 399, so yes it would be a food estimate. Hope this helps! :)
A farmer wants to fence a rectangular habitat for goats. The length (y) of the habitat has to be at least 80 feet. The farmer currently has 310 feet of fencing available to use on the habitat. The system of inequalities below models this problem situation, where x represents the width of the habitat (in feet) and y represents the length of the habitat (in feet). y≥80 2x+2y≤310 Which of the following is a true statement? a. If the farmer makes a rectangular habitat with a length of 60 feet, the width needs to be 80 feet. b. The farmer can make a habitat that is 75 feet long and 60 feet wide. c. The farmer does not have enough fencing to enclose a rectangular habitat that is 80 feet long. d. The farmer can make a habitat that is 40 feet wide and 100 feet long.
Answers
Answer:
d. The farmer can make a habitat that is 40 feet wide and 100 feet long.
Step-by-step explanation:
The attached graph shows the inequalities and the various answer choices. The existence of the doubly-shaded area shows that answer choice C is false.
The appropriate choice is ...
d. The farmer can make a habitat that is 40 feet wide and 100 feet long.
Rewrite the following equation in exponential form.
log49 (7)=1/2
Answers
Answer:
49^1/2 =7
Step-by-step explanation:
log49(7)=1/2
in exponential form
49^1/2 =7
Find all values of X which make the equation below true | 3x + 5 | = 8
Answers
Answer:
x= -13/1,1
3x+5=8
-(3x+5)=8
x=1
x=-13/3
x=-13/3,1
Answer:
x and equal 1 or -13/3
Step-by-step explanation:
this is an absolute value equation so the equation can either equal 8 or -8. if you set up two equations that are 3x+5=8 and 3x+5 = -8 and just isolate the x, you get 1 and -13/3.
HELP PLEASE ASAP WILL GIVE BRAINLEIST
Answers
Answer:
PN = 10
Step-by-step explanation:
Base angles converse theorem states that a triangle with two congruent angles is isosceles. The sides opposite to the two congruent angles are the congruent sides. The side between the two congruent angles is the base.
In this problem, it is given that <P = <O, hence ΔNOP is isosceles, because of base angles theorem. OP is the base, and hence NO is one of the congruent sides and therefore has to be congruent to PN. Which means that PN is 10.
Why did the feudal system rely on a high degree of local independence?
Answers
Answer:Feudalism helped protect communities from the violence and warfare that broke out after the fall of Rome and the collapse of strong central government in Western Europe. Feudalism secured Western Europe's society and kept out powerful invaders. Feudalism helped restore trade. Lords repaired bridges and roads.
Step-by-step explanation:
Under typical conditions, 1 [tex]\frac{1}{2}[/tex] feet of snow will melt in 2 inches of water. How many inches of water will it take to melt 1 [tex]\frac{3}{4}[/tex] feet of snow?
Answers
Answer:
2[tex]\frac{1}{3}[/tex]inches
Step-by-step explanation:
First, I would try to get the mixed numbers into improper fractions. Then, I try to make them have the same denominator so it is easier.
1[tex]\frac{1}{2}[/tex]feet --- 2 inches
[tex]\frac{3}{2}[/tex]feet --- 2 inches
[tex]\frac{6}{4}[/tex]feet --- 2 inches
1[tex]\frac{3}{4}[/tex]feet --- ? inches
[tex]\frac{7}{4}[/tex]feet --- ? inches
[tex]\frac{7}{4}[/tex]feet --- [tex]\frac{7}{6}[/tex] × 2 inches
= 2[tex]\frac{1}{3}[/tex]inches
Nancy paid six dollars for two cans of soup. Determine the cost per can.
Answers
Answer:
3 dollars
Step-by-step explanation:
6 / 2 = 3
Answer:
3$ per can
Step-by-step explanation:
6$ divided by 2 cans of soup equals $3 per can :)
Solve for
m
.
−
5
m
=
−
35
m =
Answers
Answer: 7
Step-by-step explanation: -35 / -5 = 7
Answer:
The answer is 7. I did the lesson and 7 was the correct answer
Step-by-step explanation:
Regina spent $45.50 over 6 1/2 months on music downloads. If she spent the same amount of money each month, how much money did Regina spend per month on music downloads? Choose the equation that can be used to represent the situation?
Answers
Answer:
It should be B, -45.50÷6.5=−7
Step-by-step explanation:
It should be B, -45.50÷6.5=−7
Answer:
Regina spent $7.00 every month.
An equation you can use is 45.50 / 6.50.
Step-by-step explanation:
P.S Can I have brainliest?
I need a story problem to match the equation 36÷5=7 Remainder 1
Answers
Answer: sarah has 36 cookies but she has 5 friends. she doesnt know how much cookies go to her friends. Write a equation to solve the problem
Step-by-step explanation:
Find the equation of the line through point (-3, 8) and perpendicular to y = x + 14. Use a forward slash (i.e. "M) for
fractions (e.g. 1/2 for 3).
Answers
Answer:
y+x = 5
Step-by-step explanation:
Given the equation y = x + 14
Get the slope first
The slope m = 1
Since the required equation is perpendicular to the line, the required slope will be M = -1/1 = -1
Get the required equation using the equation y-y0 = m(x-x0)
(x0, y0) = (-3, 8)
y - 8 = -1(x-(-3))
y-8 = -(x+3)
y-8 = -x-3
y+x = -3+8
y+x = 5
Hence the required equation of the line is y+x = 5
A package states that there are 60 calories in 12 crackers
Answers
Answer: 5 calories = 1 cracker
Step-by-step explanation:
60:12 = 5:1
60 calories and 12 crackers = 5 calories and 1 cracker
write and equation of the line that passes through 2,2 and is parallel to the line y=7x
Answers
Answer:
y = 7x+2
Step-by-step explanation:
(2x + y = 14
5x - y = 28
Which ordered pair represents the solution
Answers
Answer:
D (6,2)
Step-by-step explanation:
2x6+2=14 2x6= 12 12+2= 14
5x6-2=28 5x6=30 30-2=28
) Which expressions are equivalent to 26? Choose ALL that apply.
6.6.6.6.6.6
2.2.2.2.2.2
2.6
4.16
12.12
8.8
Answers
Answer:
2x2x2x2x2x2
4 x 16
8 x 8
Step-by-step explanation:
All equal to 64.
2^6=64
Marita always listen to her favourite radio station when she drives her car
Everymoarning she listen to her radio