Answer:
Step-by-step explanation:
Complete the square to do this. This one is a bit of a pain because of the 7 as our linear term, but a little hard work never killed anyone!
The rules for completing the square are very strict and cannot be strayed from. The first rule is that the leading coefficient HAS to be a positive 1; ours is a positive 6 so we have to factor it out. Let's do that first then we can get to rule number 2.
Set the quadratic equal to 0, then move the constant over to the other side. This is not a rule, per se, but I teach it this way to avoid unnecessary confusion in an already confusing process.
[tex]6x^2+7x=-2[/tex] and to factor out the 6:
[tex]6(x^2+\frac{7}{6}x)=-2[/tex]
Now for rule #2: take half the linear term, square it, and add it to both sides. Our linear term is 7/6. Half of that is 7/12, and 7/12 squared is 49/144. BUT we cannot forget about that 6 hanging around out front, refusing to be ignored. It is a multiplier, so when we add 49/144 inside the parenthesis on the left, we have to add 6(49/144) to the right, giving us:
[tex]6(x^2+\frac{7}{6}x+\frac{49}{144})=-2+\frac{294}{144}[/tex]
We will rewrite now by simplifying. The left side can be written into a perfect square binomial (which is why we did this in the first place) and the right side can be added. The left side becomes
[tex]6(x+\frac{7}{12})^2[/tex]
The 7/12 comes from the square root of 49/144, and the x comes from the square root of x-squared. The right side requires a common denominator:
[tex]-2+\frac{294}{144}=-\frac{288}{144}+\frac{294}{144}=\frac{6}{144}=\frac{1}{24}[/tex]
So now we have
[tex]6(x+\frac{7}{12})^2=\frac{1}{24}[/tex]
Put evertyhing back onto the left side and set it back to equal y and you're done!
[tex]y=6(x+\frac{7}{12})^2-\frac{1}{24}[/tex]
Because the vertex form of a quadratic does not allow us to stray from the format "x -", we have to interpret our h coordinate as "x - (-7/12))" which is movement to the left. This gives us a vertex of
[tex](-\frac{7}{12},-\frac{1}{24})[/tex]
If you substitute the x- and y-values of the point for x and y in the equations, will both equations be true?
Answer:
Yes, both equations should be true.
A circular oil spill continues to increase in size. The radius of the oil spill, in miles, is given by the function r(t) = 0.5 + 2t, where t is the time in hours. The area of the circular region is given by the function A(r) = πr2, where r is the radius of the circle at time t.
Explain how to write a composite function to find the area of the region at time t.
Answer:
The area at time t is given by [tex]A(t) =\pi (4t^2+2t+0.25).[/tex]
Step-by-step explanation:
We know the radius [tex]r(t)[/tex] of the oil spill as a function of time, and we know the area [tex]A(r)[/tex] as a function of radius, and we want the area at time t. In other words we are looking for area as a function of time [tex]A(t)[/tex]
We find [tex]A(t)[/tex] by putting [tex]r(t)[/tex] into [tex]A(r)[/tex] as a substitute to r:
[tex]A(t) = A(r(t))= \pi r(t)^2 =\pi (0.5 + 2t)^2={\pi (4t^2+2t+0.25).}[/tex]
[tex]\boxed{A(t) =\pi (4t^2+2t+0.25).}[/tex]
Which is our answer.
To find the composite function for the area of the oil spill over time, replace 'r' in A(r) = πr2 with the function r(t). The function becomes A(t) = π(0.5 + 2t)2.
Explanation:In order to find the function that represents the area of the oil spill over time, we need to write a composite function. This means we plug the function r(t) into A(r). Since r(t) = 0.5 + 2t, you can replace every instance of 'r' in A(r) = πr2 with (0.5 + 2t) to get the area as a function of time 't'. So, the composite function becomes A(t) = π(0.5 + 2t)2. Now we have a composite function that represents the area of the oil spill, denoted by A(t), as a function of time. The function is: A(t) = π(0.5 + 2t)2.
Learn more about Composite Functions here:https://brainly.com/question/30143914
#SPJ12
after the booster club sold 40 hotdogs at a football game, it had $90 in profit. after the next football game, it has sold a total of 80 hotdogs and had a total of $210 in profit. which equation models the total profit, y, based on the number of hotdogs sold, x?
Answer:
The required equation models the total profit, y, based on the number of hot dogs sold, x is y = 3 x - 30.
Step-by-step explanation:
Let x = total number of hot dogs sold
y = total profit from total sales of hot dogs
The given situation can be written as: y = m x + C ......[A]
Now, Profit for 40 hot dogs = $90 profit
So, here this can be written as:
90 = 40 m + C ......[1]
Profit for 80 hot dogs = $210 profit
So, here this can be written as:
210 = 80 m + C ......[2]
Now, solving both the equations, we get:
Subtracting [1] and [2], we get
210 - 90 = 80 m + C - (40 m + C)
or, 120 = 40 m
or, m = 120/40 = 3
or, m = 3
Solving for the value of C , we get: C = - 30
Putting the value of m back in the equation : y = m x + C
y = 3 x -30
Hence, the required equation models the total profit, y, based on the number of hot dogs sold, x is y = 3 x - 30.
kendra takes bread to her two frends' shouses every week. She takes 3 times the amount to Judy as she does lynn. combined, she takes them 12 loafs. how much does she give judy?
Answer:
9 loaves
Step-by-step explanation:
Judy get 3/4 of the bread, so ...
(3/4) · 12 loaves = 9 loaves
Final answer:
In order to find out how much bread Kendra gives Judy, we can set up a system of equations.
Explanation:
In order to find out how much bread Kendra gives Judy, we can set up a system of equations based on the information given. Let's say Kendra gives Lynn x loaves of bread. According to the problem, Kendra gives Judy 3 times the amount she gives Lynn, so Judy receives 3x loaves of bread. Together, they receive 12 loaves of bread, so x + 3x = 12. Simplifying the equation, we get 4x = 12. Dividing both sides by 4, we find x = 3. Therefore, Kendra gives Judy 3x = 3(3) = 9 loaves of bread.
Susie works out in the gym three times a week. Her heartbeat
increased to 94 beats per minute during one workout. If she
maintained this rate for 25 minutes, how many times did her heart
beat during the 25-minute workout?
Answer:
Step-by-step explanation:
94 beats per minute during one workout.
If the rate was maintained for 25 minutes, the heart beats = 94×25
= 2350 beats
You decide to put $2,000 in a savings account to save for a $3,000 downpayment on a new car. If the account has an interest rate of 4% per year and is compounded monthly, how long does it take until you have $3,000 without depositing any additional funds?
121.862 years
12.1862 years
10.155 years
1.0155 years
It takes 10.155 years until you have $3,000 ⇒ 3rd
Step-by-step explanation:
The formula for compound interest, including principal sum is:
[tex]A=P(1+\frac{r}{n})^{nt}[/tex] , where
A is the future value of the investment/loan, including interestP is the principal investment amount r is the annual interest rate (decimal)n is the number of times that interest is compounded per unit tt is the time the money is invested or borrowed for∵ You decide to put $2,000 in a savings account
∴ P = 2000
∵ You want to save for $3,000
∴ A = 3000
∵ The account has an interest rate of 4% per year and is
compounded monthly
∴ r = 4% = 4 ÷ 100 = 0.04
∴ n = 12 ⇒ compounded monthly
- Substitute all of these values in the formula above to find t
∵ [tex]3000=2000(1+\frac{0.04}{12})^{12t}[/tex]
- Divide both sides by 2000
∴ [tex]1.5=(1+\frac{1}{300})^{12t}[/tex]
∴ [tex]1.5=(1\frac{1}{300})^{12t}[/tex]
- Change the mixed number to an improper fraction
∴ [tex](1.5)=(\frac{301}{300})^{12t}[/tex]
- Insert ㏒ for both sides
∴ [tex]log(1.5)=log(\frac{301}{300})^{12t}[/tex]
- Remember [tex]log(a)^{n}=nlog(a)[/tex]
∴ [tex]log(1.5)=(12t)log(\frac{301}{300})[/tex]
- Divide both sides by [tex]log(\frac{301}{300})[/tex]
∴ 121.84 = 12 t
- Divide both sides by 12
∴ 10.155 = t
It takes 10.155 years until you have $3,000
Learn more:
You can learn more about the compound interest in brainly.com/question/4361464
#LearnwithBrainly
Eric uses 1 3/4 cups of granola for every 1/3 cup of chocolate chips when making a snack mix. Enter the number of
cups of granola Eric uses for 1 cup of chocolate chips
Answer:
Step-by-step explanation:
Set this up as a proportion with granola on the top and chocolate chips on the bottom:
[tex]\frac{g}{cc}:\frac{1.75}{\frac{1}{3} }=\frac{x}{1}[/tex] and cross multiply to solve for x:
1/3x = 1.75 Multiply both sides by 3 to get
x = 5.25
This means for every 1 cup of chocolate chips, he needs 5 1/4 cups of granola.
Are the numbers (2,3)(1,5)(2,7) a function ?
Firstly they are not numbers, they are ordered pairs or points with a form [tex](x,f(x))[/tex] yes they probably lie on a function graph but that would be rather impossible to find out. The function may be linear, exponential, logarithmic etc. we can't tell. All we can tell is that if these ordered pairs [tex]P_{1,2,3}[/tex] lie on a function graph [tex]P_{1,2,3}\in G_f[/tex] where [tex]G_f=\{(x,f(x)):\forall x\in D_f\wedge f(x)\in T_f\}[/tex] where D is definition set of function defined x's and T a transformation set of f(x)'s for this function. So yes they may lie on some lambda function but they themselves are nothing but an ordered pairs with no meaningful connection.
Hope this helps.
Answer:
no
Step-by-step explanation:
there are two coordinates with the same x value
PLEASE HELP ME ASAP NEED THIS FOREAL!! picture shown below
Rewrite as a simplified fraction.
0.67 where 7 repeats forever
Answer:
[tex]\frac{61}{90}[/tex]
Step-by-step explanation:
We require to create 2 equations with the repeated value 7 after the decimal point
Let x = 0.6777777... ← multiply both sides by 10 and 100
10x = 6.777...... → (1)
100x = 67.777..... → (2)
Subtract (1) from (2) thus eliminating the repeating value
90x = 61 ( divide both sides by 60 )
x = [tex]\frac{61}{90}[/tex]
The decimal 0.67 with the repeating 7 can be written as the simplified fraction 2/3.
Rewriting as a simplified fraction 0.67 where 7 repeats foreverTo rewrite the decimal 0.67 with the repeating 7 as a simplified fraction, we can use the concept of infinite geometric series.
Let x = 0.677777...
Multiply both sides of the equation by 10 to shift the decimal point:
10x = 6.777777...
Now, subtract the original equation from the shifted equation to eliminate the repeating 7s:
10x - x = 6.777777... - 0.677777...
Simplifying, we get:
9x = 6
Divide both sides of the equation by 9 to solve for x:
x = 6/9
The fraction 6/9 can be further simplified by dividing both the numerator and denominator by their greatest common divisor, which is 3:
x = (6/3) / (9/3)
x = 2/3
Therefore, the decimal 0.67 with the repeating 7 can be written as the simplified fraction 2/3.
Learn more about fraction at https://brainly.com/question/78672
#SPJ6
Please help me ASAP I really need help 15 points
Answer:
45,2316
Step-by-step explanation:
You have to move the numbers to their new respective places as told by the description of the new place
the average annual income, /, in dollars, of a lawyer with an age of x years is modeled with with the following function: I=-425x^2+45,500x-650,000 what is the youngest age for which the average income of a lawyer is $250,000?
Answer:
26 years of age.
Step-by-step explanation:
The average annual income, I, in dollars, of a lawyer with an age of x years is modeled with with the following function:
I = - 425x² + 45500x - 650000 .......... (1)
If the average annual income of the lawyer at the age of x years is $250000, then from the equation (1) we can write
- 425x² + 45500x - 650000 = 250000
⇒ - 425x² + 45500x - 900000 = 0
⇒ - 17x² + 1820x - 36000 = 0
Now, using the quadratic formula,
[tex]x = \frac{- 1820 \pm \sqrt{(1820)^{2} - 4(-17)(- 36000) } }{2(- 17)} = \frac{-1820 + 929.73}{- 34} = 26[/tex] years (Approximate)
{We have neglected the other root as we need the youngest age}(Answer)
Answer: 27
Step-by-step explanation:
Other answer is wrong
During the basketball season, Shane scored 53 points. He scored 3 fewer points than two times the number Jason did. How many points did Jason score?
Answer:
23 points
Step-by-step explanation:
If he shane scored 3 fewer points, then that means double of Jason's score is 56. divide 56 by two to get Jason's real score, which is 23.
Solve this system of linear equations. Separate
the x- and y-values with a comma.
- 14x = -1 - 9y
17x = 7 +9y
NEED HELP ASAP!!
Step-by-step explanation:
making x subject in eq 1
x= (-1-9y)/-14
substituting the value of x in eq 2
17(-1-9y/-14)=7+9y
(-17-153y)/-14=7+9y
-17-153y=-98-126y
-17+98=153y-126y
81=27y
y=3
substituting this value of y in eq 1
-14x=-1-9(3)
-14x=-28
x=2
(x,y) = (2,3)
Bruce bought two books.One book costs $4.00 more than three times the other.Together, the two books cost him $72.
Write the statement using symbolic language
The given statement written in symbolic language is x = 3y + 4 and x + y = 72 where "x" is the cost of one book and "y" is the cost of another book
Solution:
Given that Bruce bought two books
One book costs $ 4.00 more than three times the other
Let the two books be denoted as Book A and book B
Let "x" be the cost of book A
Let "y" be the cost of Book B
From given,
One book costs $ 4.00 more than three times the other
Let Cost of book A = $ 4.00 more than three times the other book B
x = 4 + 3 times cost of Book B
x = 4 + 3y
x = 3y + 4 --- (i)
Also given that Together, the two books cost him $72
cost of book A + cost of Book B = 72
x + y = 72 ------- (ii)
Therefore the given statement written in symbolic language is:
x = 3y + 4 and x + y = 72
plz help ill rate you
Answer:
The only correct statement is the first one
because the product of a number greater than 1 and another positive number always makes the second number greater than its original value
:)
Find the value of x that makes A || B.
Answer:
x = 90.
Step-by-step explanation:
< 1 and < 4 are corresponding angles and are congruent if line a is parallel to line b. So:
3x - 160 = x + 20
2x = 180
x = 90.
PLZ HELP ME!!!!! I will give u 5 stars and a thank u. and i will friend u.
( I DO NOT NEED HELP ON PART ONE JUST ON PART TWO I PUT PART ONE IN TO HELP YOU ANSWER PART TWO)
It cost $0.50 to download an individual song and $4 to downlad an album. Jada has $15 to spend downloading music.
PART ONE:
EXAMPLE: individual songs, numbers of albums...
6,3
22,1
30,0
PART 2:
Create a graph to show a visual representation of the solutions for the answers to the problem above. With albums as the y axis and songs on the x axis. Upload a photo of your graph and with a short summary for your explanantion.
Answer:
Graph is attached below.
The graph illustrates the music that Jada may have downloaded with the $15 (s)he spent. The x-axis represents the number songs and the y-axis represents the number of albums. The data shows what combination of music she may have downloaded. The number of songs and albums have a negative correlation because if more money is spent on one variable, there is less money available to spend on the other.
Step-by-step explanation:
How to create a graph:
Using the data from part 1, plot the points (6, 3) (22, 1) and (30, 0) onto the graph. Label the x and y axis as the question asks. The axis should have arrows at the end. Include a title for the graph.
Do not connect the points because this indicates that all the space between the points are possible. Connecting the points includes decimal numbers and you can't buy part of a song or album, only a whole song or album.
Find the volume of a right circular cone that has a height of 5.7 ft and a base with a
radius of 15.6 ft. Round your answer to the nearest tenth of a cubic foot.
Answer:
56652.3 ft^3
Step-by-step explanation:
The formula for the volume of a right circular cone is V=13pi*r^2*h where r is the radius of the base.
So V=13pi*(15.6)^2*(5.7)=56652.3
Given the following points, write the equation of the line that goes through them. ( -12,56), (0,8), and (8,-24).
Answer:
[tex]y=-4x+8[/tex]
Step-by-step explanation:
step 1
Find the slope
The formula to calculate the slope between two points is equal to
[tex]m=\frac{y2-y1}{x2-x1}[/tex]
take two points from the data
(0,8), and (8,-24).
substitute
[tex]m=\frac{-24-8}{8-0}[/tex]
[tex]m=\frac{-32}{8}[/tex]
[tex]m=-4[/tex]
step 2
Find the equation of he line in slope intercept form
[tex]y=mx+b[/tex]
we have
[tex]m=-4[/tex]
[tex]b=8[/tex] ----> the y-intercept is given
substitute
[tex]y=-4x+8[/tex]
Julia exercises at the gym. For every 333 minutes she spends running, she spends 555 minutes lifting weights.
Question is Incomplete, Complete question is given below.
Julia exercises at the gym. For every 3 minutes she spends running, she spends 5 minutes lifting weights.
Which of the following could be how Julia spends time at the gym?
A Run for 10 mins and lifting weights for 12 mins.
B Run for 15 minutes and lift weights for 25 mins.
C Run for 20 mins and lift weights for 30 mins.
D Run for 24 mins and lift weights for 48 mins.
E Run for 30 mins and lift weights for 50 mins.
Answer:
B Run for 15 minutes and lift weights for 25 mins.
E Run for 30 mins and lift weights for 50 mins.
Step-by-step explanation:
Given:
Julia Spend s 3 minute for running and weight lifts for 5 mins.
We need to find which choices are correct match for the given data.
Hence we will check each.
A Run for 10 mins and lifting weights for 12 mins.
Since given that she runs for 3 mins and in the above choice the given date is she is running for 10 mins it is neither 3 nor multiple of 3.
Hence this is Choice is Incorrect.
B Run for 15 minutes and lift weights for 25 mins.
Now Given in choice is that she runs for 15 minutes and in given data she runs for 3 minutes hence 15 is multiple of 3 and is multiplied by 5 also given lift weights for 25 mins and in given data she lift weights for 5 mins since 25 is multiple of 5 and is multiplied by 5.
Hence the above Choice is Correct.
C Run for 20 mins and lift weights for 30 mins.
Since given that she runs for 3 mins and in the above choice the given date is she is running for 20 mins it is neither 3 nor multiple of 3.
Hence this is Choice is Incorrect.
D Run for 24 mins and lift weights for 48 mins.
Now Given in choice is that she runs for 24 minutes and in given data she runs for 3 minutes hence 24 is multiple of 3 and is multiplied by 8 also given lift weights for 48 mins and in given data she lift weights for 5 mins and 48 is not the multiple of 5.
Hence this is Choice is Incorrect.
E Run for 30 mins and lift weights for 50 mins.
Now Given in choice is that she runs for 30 minutes and in given data she runs for 3 minutes hence 30 is multiple of 3 and is multiplied by 10 also given lift weights for 50 mins and in given data she lift weights for 5 mins since 50 is multiple of 5 and is multiplied by 10.
Hence the above Choice is Correct.
there are N apples in a sack and 3 of the apples are ripe how many are not ripe
The number of unripe apples in a sack, given that there are N total apples and 3 are ripe, is calculated by subtracting 3 from N (N - 3).
Explanation:The question posed is asking for a basic subtraction calculation within the context of ripe and unripe apples.
Given that there are N apples in total and 3 of them are ripe, we need to find out how many are not ripe.
The number of not ripe apples is N - 3, where N is the total number of apples in the sack.
To solve this, we subtract the number of ripe apples from the total number of apples:
Subtract the number of ripe apples (3) from the total apples (N).The result gives you the number of unripe apples, which is N - 3.For example, if a sack has 10 apples and 3 are ripe, then there would be 10 - 3 = 7 unripe apples.
23.6-2×3÷2 what is the answer to this question
Answer:
20. 3
Step-by-step explanation:
23.6 - 2 × 3 ÷ 2 = 23.6 - 3
= 20.3
Brent has a shopping bag with 8 similar size containers of yogurt: 2 strawberry, 3 cherry, and 3 raspberry. If he randomly takes 2 yogurt containers from the bag
without replacement, what is the probability that neither will be strawberry yogurt?
Answer:[tex]\frac{15}{28}[/tex]
Step-by-step explanation:
Number of strawberry = 2
Number of cherry = 3
Number of = 3
Total number = 8
Brent randomly takes 2 yogurt containers from the bag
without replacement ,we are to find the probability that hat neither will be strawberry yogurt.
Let r represent raspberry and c represents Cherry ,then Bent selection could be :
{ rr , cc , rc , cr}
Calculating this , we have
([tex]\frac{3}{8}[/tex] x [tex]\frac{2}{7}[/tex] ) + ([tex]\frac{3}{8}[/tex] x [tex]\frac{2}{7}[/tex] ) + ([tex]\frac{3}{8}[/tex] x [tex]\frac{3}{7}[/tex] ) + ([tex]\frac{3}{8}[/tex] x [tex]\frac{3}{7}[/tex] )
= [tex]\frac{30}{56}[/tex]
= 15/28
Therefore , the probability that neither will be strawberry yogurt= 15/28
What is the remainder of 28,254 divided by 52?
Answer:
18
Step-by-step explanation:
Finding the remainder of 28254 divided by 52.
Steps1. Use calculator to divide 28254 by 52:
28254/52= 543.346...2. Take whole part of the quotient and multiply by divisor:
543*52= 282363. Subtract this number from the initial dividend:
28254 - 28236 = 18This is the remainder: 18
Final answer:
The remainder when 28,254 is divided by 52 is 9. This is found by dividing the number step by step until no more digits can be brought down, leaving the remainder.
Explanation:
The student is asking for the remainder when 28,254 is divided by 52. To solve this, we perform the division process until we reach a point where we cannot divide any further without going into decimals. The number that is left over at this point is the remainder. Below is a step-by-step explanation of the process.
Begin dividing 28,254 by 52.52 goes into 282 five times (since 52 x 5 = 260), with a remainder of 22.Bring down the next digit, 4, to make 224.52 goes into 224 four times (since 52 x 4 = 208), with a remainder of 16.Bring down the final digit, 5, to make 165.52 goes into 165 three times (since 52 x 3 = 156), with a remainder of 9.Since there are no more digits to bring down, we have our final remainder.The remainder when 28,254 is divided by 52 is 9.
How do I figure out when to use add and when to use subtract ? Please and thank you !
*I'm not sure what you mean when to add and subtract but I hope this helps!
Answer:
Triangle1: 13
Triangle2: 25
Triangle3: 17
Step-by-step explanation:
*Pythagorean Theorem Formula: a²+b²=c² where c is the hypotenuse (the side opposite of the right angle)
Triangle1:
1. Plug in the values into the Pythagorean Theorem Formula and simplify as shown below.
5²+12²=c²
25+144=c²
169=c²
c=√169
c=13
Triangle2:
1. Plug in the values into the Pythagorean Theorem Formula and simplify as shown below.
15²+20²=c²
225+400=c²
625=c²
c=√625
c=25
Triangle3:
1. Plug in the values into the Pythagorean Theorem Formula and simplify as shown below.
8²+15²=c²
64+225=c²
289=c²
c=√289
c=17
Given AFGH is a cyclic quadrilateral, find the value below:
Answer:
238°
Step-by-step explanation:
In a cyclic quadrilateral, the pair of opposite angles add up to 180 degrees.
So, the angle "21x - 2" and the angle "38x + 5" add up to 180.
So, we can write an equation and solve for x first:
[tex]21x-2+38x+5=180\\59x+3=180\\59x=180-3\\59x=177\\x=3[/tex]
x = 3
Now, Arc FGH is DOUBLE of Angle A. Angle A is "38x + 5". We know x, so angle A is:
Angle A = 38x + 5 = 38(3) + 5 = 119
Thus, Arc FGH = 2 * 119 = 238°
Solve and share these questions
After a heavy snowfall, George shovels 12 2/4 square yards of snow off his driveway in 1 1/2 hours. At this rate, how many square yards of driveway would he shovel in 5 1/2 hours?
George shovels at a rate of 8.33 square yards per hour. In 5 1/2 hours, he will shovel approximately 45.815 square yards of his driveway.
Explanation:The student asked about how many square yards of driveway George would shovel in 5 1/2 hours after shoveling 12 2/4 square yards in 1 1/2 hours. To find this, we first need to calculate the rate at which George is shoveling.
George shovels 12 2/4 square yards in 1 1/2 hours. Simplifying these fractions, we have 12.5 square yards in 1.5 hours. The rate is therefore 12.5 ÷ 1.5 yards per hour = 8.33 square yards per hour.
Next, we multiply this rate by the total time George will be shoveling to find how much he would shovel in 5 1/2 hours:
8.33 yards/hour × 5.5 hours = 45.815 square yards
So, George will shovel approximately 45.815 square yards of his driveway in 5 1/2 hours.
Final answer:
To find out how many square yards of driveway George would shovel in 5 1/2 hours, we can set up a ratio using the given information and multiply the rate by the time.
Explanation:
To find out how many square yards of driveway George would shovel in 5 1/2 hours, we can set up a ratio using the given information. In 1 1/2 hours, he shovels 12 2/4 square yards of snow. We can write this as a fraction: 12 2/4 / 1 1/2. To simplify this fraction, we can convert the mixed numbers to improper fractions: 50/4 / 3/2.
To divide fractions, we multiply the first fraction by the reciprocal of the second fraction: (50/4) × (2/3). Multiplying the numerators and denominators, we get (50 × 2) / (4 × 3) = 100/12.
So, in 1 1/2 hours, George shovels 100/12 square yards of snow. To find out how many square yards he would shovel in 5 1/2 hours, we can multiply this rate by 5 1/2: (100/12) × (5 1/2). Multiplying the numerators and denominators, we get (100 × 11) / (12 × 2) = 1100/24. Simplifying this fraction, we get 275/6.
Therefore, George would shovel approximately 275/6 square yards of driveway in 5 1/2 hours.
Given that (-2,-2) is on the graph of f(x), find
the corresponding point for the function
f(x) +5.
Answer:
(-2, 3)
Step-by-step explanation:
f(x) +5 means 5 is added to the y-value that is output from the function. The given point indicates the function output is -2, so when 5 is added, the result is +3. The point (-2, 3) is on the graph of f(x)+5.