Answer:
The number of boys, x = 12
Step-by-step explanation:
Given that the sum of the ages of the boys in a class = 84 years
The number of boys = x
A new boy aged 8 years 1 month is added and the average age increases by 1 month
We have
Average age = 84/x = y
Age of new boy = 8 years 1 month = [tex]8\frac{1}{12} \ year[/tex]
New average = y + 1/12 = [tex](8\frac{1}{12}+84) /(x + 1)[/tex] which gives;
84/x + 1/12 = [tex](8\frac{1}{12} + 84) /(x + 1)[/tex]
[tex]\dfrac{x +1008}{12 \cdot x} = \dfrac{1105}{12 \cdot x+ 12}[/tex]
(x + 1008)×(12·x + 12) = 1105× 12·x
12·x² -1152·x + 12096 = 0
x² -96·x + 1008 = 0
(x - 84)×(x - 12) = 0
Therefore, x = 12 or 84,
The number of boys are 12 or 84
For there to bee 84 boys, their average age would be one year each
Given that they are boys not babies, then there are only 12 boys.
There are 30 students in a class. 10 students have a pet dog, 13 students have a pet cat, and 7 students have a pet fish. 4 students have both a pet dog and a pet cat, 6 students have a pet cat and a pet fish, 2 students have a pet dog and a pet fish. 1 student has all three. How many of the 30 students have pets?
Answer:
9 students have pets
Step-by-step explanation:
From the above question, we are given the following information
Total number of students = 30
Let Pet Dog = D
Pet Cat = C
Pet Fish = F
Number is students that have pet dog
(D) = 10 students
Number of students that have pet cat (C) = 13 students
Number of students that have pet fish (F) = 7 students
Number of students that have Pet dog and cat ( D and C) = 4 students
Number of students that have Pet cat and fish (C and F) = 6 students
Number of student that has pet dog and pet fish (D and F) = 2 students
1 student has all three = ( D and F and C)
Number of student that have a pet Dog only
= n(D) - [n( D and C) + n( D and F) - n(D and C and F)]
= 10 -( 4+ 2 -1)
= 10 - 5
= 5
Number of student that have Pet cat only
= n(C) -[ n( D and C) + n( C and F) - n( D and C and F)]
= 13 -( 4 + 6 - 1)
= 13 - 9
= 4
Number is student that have a pet fish only
= n(F) - [n (C and F) + n( D and F) - n( D and C and F)]
= 7 - [6 + 2 - 1]
= 7 - 7
= 0
The number of students that have pets is calculated as:
(Number of students that have dogs only + Number of student that have cats only + Number of students that have fish only)
= 5 + 4 + 0
= 9
Therefore only 9 students have pets.
Two planes make a 1750 mile flight, one flying 75 miles per hour faster than the other. The quicker plane makes the trip 3 hours faster. How long did it take the slower plane to complete the flight?
Answer:
The slower plane is flying at 175 miles per hour and complete the trip in 10 hours
The faster plane is flying at 250 Miles per hour and complete the trip in 7 hours
Step-by-step explanation:
Let s= speed of the slower plane s+75= speed of the faster plane
The time it takes the slower plane to make the flight = 1750/s
The time it takes the faster plane to make the flight is=1750/(s+75)
The difference in these two times is 3 hours
1750/s - 1750/(s+7)=3
{(s+75) / (s+75) * (1750/s)} - {(s/s) * (1750/s+75)} =3
(1750s+131250 / s^2+75s) - (1750s/s^2+75s) =3
1750s+131,250-1750s / s^2+75d =3
131,250 / s^2+75s = 3
Cross product
131,250=3(s^2+75s)
131,250=3s^2+225s
43,750=s^2+75s
s^2+75s-43,750=0
Solve the quadratic equation
x= -b +or- √b^2-4ac / 2a
a=1
b=75
c= -43750
x= -b +or- √b^2-4ac / 2a
= -75 +or- √(75)^2 - (4)(1)(-43750) / (2)(1)
= -75 +or- √(5625) - (-175,000) / 2
= -75 +or- √180625) / 2
= -75 +or- 425 / 2
x= -75 + 425/2 OR -75- 425/2
=350/2 OR -500/2
x=175 OR -250
We will ignore the negative sign because the planes are not flying Backward
The slower plane is flying at 175 miles per hour and complete the trip in 1750/175= 10 hours
The faster plane is flying at 250 Miles per hour and complete the trip in 1750/250= 7 hours
Sharon is making a large batch of soup. The soup reaches a height of 25 in a cylindrical pot whose diameter is 30cm. To store the soup for later, she'll pour it into ice cube molds where each cube has edges that are 7cm, end text long.
Complete question :
Sharon is making a large batch of soup. The soup reaches a height of 25 in a cylindrical pot whose diameter is 30cm. To store the soup for later, she'll pour it into ice cube molds where each cube has edges that are 7cm long. How many whole cubes can Sharon make?
Answer:
About 51 ice cubes
Step-by-step explanation:
Given the following :
Height (h) of cylindrical pot = 25
Diameter = 30cm
Edge of ice cube = 7cm long
Volume of cylinder (v) = πr^2h
V = π * (30/2)^2 * 25
V = π * 15^2 * 25
V = 17671.458cm^3
Therefore, the soup occupies 17673.75cm^3
Volume of cubes to store the soup for later:
The volume of a cube is given by the formula:
V = a^3
Where a is the length of it's edge
V = 7^3
V = 343cm^3
Number of cubes required to store soup:
(Volume of cylinder / Volume of ice cube)
17671.458cm^3 / 343cm^3
= 51.520287
This is about 51 whole cubes
What is the equation of a circle with center (0, 5) and radius 8
Answer:
See below.
Step-by-step explanation:
Recall that the equation for a circle is:
[tex](x-h)^2+(y-k)^2=r^2[/tex]
Where (h,k) is the center and r is the radius.
We know the center is (0,5) and the radius is 8. Plug in the numbers:
[tex](x-(0))^2+(y-(5))^2=(8)^2[/tex]
We can remove the parentheses on the left. Therefore, the equation will be:
[tex]x^2+(y-5)^2=64[/tex]
Answer:
( x) ^2 + ( y-5) ^2 = 64
Step-by-step explanation:
The equation of a circle can be written as
( x-h) ^2 + ( y-k) ^2 = r^2 where ( h,k) is the center and r is the radius
( x-0) ^2 + ( y-5) ^2 = 8^2
( x) ^2 + ( y-5) ^2 = 64
Suppose that you pick a bit string from the set of all bit strings of length ten. Find the probability that a) the bit string has exactly two 1s; b) the bit string begins and ends with 0; c) the bit string has the sum of its digits equal to seven; d) the bit string has more 0s than 1s; e) the bit string has exactly two 1s, given that the string begins with a 1.
Answer:
45/10241/415/128193/5129/512Step-by-step explanation:
There are 2^10 = 1024 bit strings of length 10.
a) There are 10C2 = 45 ways to have exactly two 1-bits in 10 bits
p(2 1-bits) = 45/1024
__
b) Of the four (4) possibilities for beginning and ending bits (00, 01, 11, 10), exactly one (1) of those is 00.
p(b0=0 & b9=0) = 1/4
__
c) There are 10C7 = 120 ways to have seven 1-bits in the bit string.
p(7 1-bits) = 120/1024 = 15/128
__
d) ∑10Ck {for k=0 to 4} = 386 is the total of the number of ways to have 0, 1, 2, 3, or 4 1-bits in the string. If there are more than that, there won't be more 0-bits than 1-bits
p(more 0 bits) = 386/1024 = 193/512
__
e) The string will have two 1-bits if it starts with 1 and there is a single 1-bit among the other 9 bits. There are 9 ways that can happen, among the 512 ways to have 9 remaining bits.
p(2 1-bits | first is a 1-bit) = 9/512
Agrid shows the positions of a subway stop and your house. The
subway stop is located at (-7,8) and your house is located at (6,4).
What is the distance, to the nearest unit, between your house and
the subway stop?
Answer: about 13u
Step-by-step explanation:
Distance can be calculated as [tex]\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
[tex]\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\\\\\sqrt{(6-(-7))^2+(4-8)^2}\\\\\\\sqrt{(13)^2+(-4)^2}\\\\\\\sqrt{185}\\\\13[/tex]
Hope it helps <3
Please help I really need to get it right
Answer:
Alternate interior angles.
17x + 6 = 18x - 1.
x = 7.
Step-by-step explanation:
According to the diagram below, the angles are alternate interior angles.
Since they are alternate interior angles, they are congruent. So, 17x + 6 = 18x - 1.
17x + 6 = 18x - 1
18x - 1 = 17x + 6
x = 7
Hope this helps!
The lines graphed below are perpendicular. The slop of the red line is -1/3. What is the slope of the green line
Answer:
Option C. 3
Step-by-step explanation:
Let M1 be the slope of the red line
Let M2 be the slope of the green line
From the question:
Slope of red line (M1) = – 1/3
Slope of green line (M2) =.?
The slopes of perpendicular lines are related as follow:
M1 = –1 / M2
With the above formula, the slope of the green line (M2) can be obtained as illustrated below:
Slope of red line (M1) = – 1/3
Slope of green line (M2) =.?
M1 = –1 / M2
– 1/3 = –1 / M2
Cross multiply
– 1 × M2 = – 1 × 3
– 1 × M2 = – 3
Divide both side by –1
M2 = – 3/ –1
M2= 3
Therefore, the slope of the green line is 3.
Use special right triangles to solve for the exact value of x. 4 16 9
Answer:
16
Step-by-step explanation:
I took the test and that's the answer.
Answer:
16
Step-by-step explanation:
CHECK THE ATTACHMENT FOR THE FIQURE OF THE QUESTION;
✓The given figure is a special right triangle and it's a 30° 60° 90° angle.
The length of its side have the ratio of
1: √3: 2 i.e adjacent, opposite, Hypotenuse
✓ it has an Hypotenuse which is double in value to the adjacent.
✓ the adjacent ( shortest sides) = 8 unit,
Then the Hypotenuse= ( 2×8)= 16 units
A small manufacturing company makes $125 on each stereo sound bar produces, and $100 profit on each flat screen TV makes. Each sound bar and TV must be processed by cutting machine (A), A fitting machine (B), and a polishing machine (C). each sound bar must be processed on machine A for one hour, Machine B for one hour machine C for four hours. each TV must be processed on machine A for two hours, machine B for one hour, machine C for one hour. Machine A is available for 16 hours, machine B for nine, machine C for 24. Using the information in the problem, right the constraints. Let X represent the number of sound bars made, and Y represent the number of TVs
Constraint Equations : [tex]X + 2Y \leq 16 , X + Y \leq 9 , 4X + Y \leq 24[/tex]
Time required for producing sound bar 'X' = 1 hour of machine A , 1 hour of machine B , 4 hour of machine C
Time required for producing flat screen TV 'Y' = 2 hours of machine A, 1 hour of machine B, 1 hour of machine C
So, constraint for machine A (needed for sound bar & flat screen TV) : [tex]1X + 2Y \leq 16[/tex]
Similarly, constraint for machine B (needed for X & Y) : [tex]1X + 1Y \leq 9[/tex]
Also, constraint for machine C = [tex]4X + 1Y \leq 24[/tex]
More for reference : https://brainly.com/question/9405925?referrer=searchResults
What is the equation of the graphed line in standard form? y = 2x + 6 12x+y=6 12x−y=−6 −2x+y=6
Answer:
THe standard form of equation for a line is -2x+y=6
Step-by-step explanation:
THe standard equation has a form of Ax+ By=C, where A, B and C are constants.
12x-y=-6 is not a standard form of a line equation, because the value near you is negative, but should be positive. It would be this form if we would change it a little bit to the form:
-12x=y=6
If b = 1/2x −1/y, then what is an expression for 2/b in terms of x and y?
Answer:
2/xy
Step-by-step explanation:
you have to do the math but im not very sure on this
The diagram shows two shapes A and B. Prove that both of them have equal perimeter.
Answer:
see explanation
Step-by-step explanation:
Calculate the perimeters by summing the measures of the sides.
Left figure ( starting with base and summing clockwise )
x + 5 + (x - 6) + (y - 5) + 6 + y ( brackets are the measure of the indents )
= x + 5 + x - 6 + y - 5 + 6 + y
= 2x + 2y
Right figure ( starting with base and summing clockwise )
x + 2 + (x - 3) + (y - 2) + 3 + y
= x + 2 + x - 3 + y - 2 + 3 + y
= 2x + 2y
Both figures have perimeters of 2x + 2y cm
The average age of 15 students is 16 years. If teacher’s age is included the average increases
by 1. Find teacher’s age
31
because 15 +16 :31
[tex]. = y1 = \times [/tex]
Sales of a popular toy were about 20 million in 2000 and growing about 5% each year. At this growth rate, the function f(x) = 20(1.05)^x gives the annual number of toys sold in million in the xth year after 2000. Using this model, in about what year will the annual sales surpass 37 million?
===========================
Work Shown:
Plug in f(x) = 37. Solve for x. Use logarithms.
f(x) = 20(1.05)^x
37 = 20(1.05)^x
20(1.05)^x = 37
1.05^x = 37/20
1.05^x = 1.85
log( 1.05^x ) = log( 1.85 )
x*log( 1.05 ) = log( 1.85 )
x = log( 1.85 )/log( 1.05 )
x = 12.6088044498867
Round up to the nearest whole number to get x = 13.
In the year 2013, sales exceed 37 million.
John needs to find out the probability that he will sell all his cars by the end of the
year. He takes a sample of the customers that come in to see if they will buy a car.
How many customers should he sample to get an accurate probability?
a) 3 customers
b) 10 customers
c) 100 customers
d) 1000 customers
Answer:
c) 100
Step-by-step explanation:
This is the best choice because the number is not too low or too high. He will get an accurate probability.
2 concentric circles have radii 2cm and 3cm respectively, calculate the ratio of their areas
Answer:For the first circle the radius is 2cm and for the second circle the radius is 3cm,by taking the ratio of their areas:
πr^2:πR^2
π cancels out and we are left with only r^2:R^2
r=2cm and R=3cm
Therefore r^2:R^2=2^2:3^2
=4:9
The answer is 4:9
Step-by-step explanation:
The people who responded to a survey reported that they had either brown, green, blue, or hazel eyes. The results of the survey are shown in the table. A 2-column table has 4 rows. The first column is labeled Eye Color with entries brown, green, blue, hazel. The second column is labeled Number of People with entries 20, 6, 17, 7. What is the probability that a person chosen at random from this group has brown or green eyes? StartFraction 3 Over 25 EndFraction StartFraction 7 Over 25 EndFraction StartFraction 13 Over 25 EndFraction StartFraction 17 Over 25 EndFraction
Answer:
13/25
Step-by-step explanation:
The total number of people is 20 + 6 + 17 + 7 = 50.
Of these, the number that have brown or green eyes is 20 + 6 = 26.
So the probability is 26/50, which reduces to 13/25.
The probability that a person chosen at random from this group has brown or green eyes is; 13/25
How to find the probability?From the given data values, we can deduce that;
Total number of people = 20 + 6 + 17 + 7 = 50.
Now, the total number of people that have brown or green eyes is;
Total(brown or green eyes) = 20 + 6 = 26.
Thus, the probability that a person chosen at random from this group has brown or green eyes is;
P(brown or green eyes) = 26/50 = 13/25.
Read more about Probability at; https://brainly.com/question/251701
#SPJ2
Select all the correct answers. Which statements are correct interpretations of the logarithmic function f(x) = 7 log2 x, with respect to the context? The password is weakest if it uses a single symbol for all 7 characters. The strength of the password increases with a decrease in the number of symbols. The password is stronger with an increase in the number of symbols. The password is strongest if a single symbol is used for all 7 characters. There are 2 possible symbol options per character to produce a password of strength of 7 bits. There are 7 possible symbol options per character to produce a password of strength of 7 bits.
Answer:
The password is weakest if it uses a single symbol for all 7 characters.
The strength of password increases with an increase in the number of symbols.
There are 7 possible symbol options per character to produce a password of strength of 7 bits.
Step-by-step explanation:
The password strength is determined by the usage of symbols and upper case and lower case letters along with a numeric character. The strength of password increases when different symbols are used. It is considered as weak password if only single symbol is used for all the 7 characters. The strong passwords are not easy to break and decode.
Answer:
The three correct options are:
The password is weakest if it uses a single symbol for all 7 characters.
The password is stronger with an increase in the number of symbols.
There are 2 possible symbol options per character to produce a password of strength of 7 bits.
What is 37 ÷ 100 × 9 =
Answer: 3.33
Step-by-step explanation:
Multiplication and division should be solved left to right.
[tex]37/100*9\\\\Divide(100)\\\\0.37*9\\\\Multiply(9)\\\\3.33[/tex]
Hope it helps <3
Answer:
=37/100×9=.
=divide 37 by 100
=0.37 ×9
=3.33
Jennifer wants to see if the color of the testing room causes test anxiety. She asks 100 participants to come to a modified classroom, and as they walk in, she asks each person to choose either a testing cubicle painted bright red or a testing cubicle painted off white. On the basis of their choices, participants spend 20 minutes in one or the other cubicle solving challenging math problems. Then, they complete a survey asking them questions about how anxious they were during the math test. What's wrong with Jennifer's experiment?
Answer: Jennifer didn't randomly assign participants to the control and experimental group.
Step-by-step explanation: In the scenario discussed above, Jennifer failed to perform a random assignment of the participants who took part in the survey, that is the experimental group, those who receive the treatment and the control group, those who don't. Random assignment is required in other to address the issue of bias in our experiment. She was supposed to perform a random assignment of the participants to the two groups instead of asking them to make a choice.
At Camp Sunshine, 4 kids went home sick. Of the remaining campers, 18 kids went hiking and the other 41 kids spent the day swimming. How many kids started the day at Camp Sunshine?
Answer:
63 kids
Step-by-step explanation:
We can add up the number of students who went home sick, hiked, and swam to find the total amount of people.
[tex]4+18+41 = 63[/tex]
Therefore, 63 kids started their day at Camp Sunshine.
I get that feeling I oversimplified this one, let me know if I did. I'm not sure if this is right.
Answer:
63 kids
Step-by-step explanation:
We know that there are some kids who went home sick, some went hiking and some went swimming.
The total number of kids that started the day at Camp Sunshine can be found by adding the number who went home sick, went hiking and went swimming.
sick + hiking + swimming
4 went home sick, 18 went hiking and 41 went swimming.
4+ 18 + 41
Add the numbers together
22+ 41
63
63 kids started the day at Camp Sunshine.
Solve for x. (x+2)/3+(2x-4)/4=3
Answer:
x=4
Step-by-step explanation:
First you need to factor the equation. You can do this by multiplying the numbers by eachother so they have a denominatior of 12.
You would come out to have this...
((x+2)*4)/12 + ((2x-4)*3)/4=3
At this point you can combine the numerators over the common denominator.
((x+2)*4+(2x-4)*3)/12=3
You can now rewrite the equation into factored form.
5x-2/6=3
Multiply both sides of the equation by 6.
5x-2=18
move the terms not containing x to the right
5x=20
and divide by 5
x=4
Mr. Conner is placing stone tiles to make a patio. Each tile is 1 square foot. The drawing shows the dimensions of his patio.
This question is incomplete
Complete Question
Mr. Conner is placing stone tiles to make a patio. Each tile is 1 square foot. The drawing shows the dimensions of his patio. A quadrilateral is broken into a triangle and rectangle. The triangle has a base of 20 feet and a height of 6 feet. The rectangle has a base of 20 feet and a height of 12 feet. How many total stone tiles will Mr. Connor need for the patio?
Answer:
300 tiles
Step-by-step explanation:
From the above question, we know that the patio is a combination of a triangle and a rectangle.
Step 1
Find the area of the shape
a) Area of the Triangle = 1/2 × Base × Height
Base = 20 feet
Height = 6 feet
Area = 1/2 × 20 × 6
Area = 60 square feet
b) Area of the rectangle
= Length × Breadth.
The rectangle has a
Base = Breadth = 20 feet
Height = Length = 12 feet
Area = 20 × 12 = 240 square feet.
Total Area of the patio
= Area of Triangle + Area of square
= 60 square feet + 240 square feet
= 300 square feet
Step 2
We are told that each stone tile = 1 square foot.
Hence, if the total area of the patio = 300 square feet, the number of stone tiles that would be used is
1 square foot = 1 stone tile
300 square feet = 300 stone tiles.
Therefore,the total stone tiles that Mr. Connor will need for the patio is 300 stone tiles.
Answer:
The answer is 300
Step-by-step explanation:
The amount that two groups of students spent on snacks in one day is shown in the dot plots below. Which statements about the measures of center are true? Select three choices. The mean for Group A is less than the mean for Group B. The median for Group A is less than the median for Group B. The mode for Group A is less than the mode for Group B. The median for Group A is 2. The median for Group B is 3.
Answer:
The mean for Group A is less than the mean for Group B. The median for Group A is less than the median for Group B.The mode for Group A is less than the mode for Group B.Step-by-step explanation:
First, we can find the measures of center for each group.
Group A
Mode: 1
Median: (1 + 2) / 2 = 3 / 2 = 1.5
Mean: (1 * 5 + 2 * 4 + 3) / 10 = (5 + 8 + 3) / 10 = 16 / 10 = 1.6
Group B
Mode: 3
Median: 92 + 3) / 2 = 5 / 2 = 2.5
Mean: (1 * 3 + 2 * 2 + 3 * 4 + 5) / 10 = (3 + 4 + 12 + 5) / 10 = 24 / 10 = 2.4
From here, we can see that...
The mean for Group A is less than the mean for Group B. The median for Group A is less than the median for Group B.The mode for Group A is less than the mode for Group B.Hope this helps!
Answer:
ABC
Step-by-step explanation:
Solve the proportion for X.
5/2.5=
X/2
1
4
5.5
6.25
Answer:
[tex]\large \boxed{X = 4}[/tex]
Step-by-step explanation:
5/2.5 = X/2
To solve a proportion, use the following equation:
(numerator * opposite denominator) = (numerator * opposite denominator)
Substitute in given numbers
(5 * 2) = (X * 2.5)
Multiply to simplify
10 = 2.5X
Divide both sides of this equation by 2.5
[tex]\large \boxed{X = 4}[/tex]
Hope this helps :)
There are 30 names in a hat. If two names are picked without repalcement, which expression shows the probability that Jack and Jill will be picked?
Step-by-step explanation:
The probability that either Jack or Jill will be selected on the first draw is 2/30.
The probability that the other person will be selected on the second draw is 1/29.
The probability of both events is (2/30) (1/29), which simplifies to 1/435.
A metal cube
of
side 4.4cm was melted
and the molten material used to make a Sphere
Find to 3 significant figures the radius of
the
sphere [take It - 22/7].
Answer: 2.73 cm
Step-by-step explanation:
Given that :
Side (a) of cube = 4.4cm
Volume of a cube (V) = a^3
V = 4.4^3
V = 85.184cm^3
Therefore, volume of the sphere made = 85.184cm^3
Volume of sphere = 4/3 πr^3
Where r = radius
85.184 = (4/3)*(22/7)*r^3
85.184 = (88/21)*r^3
85.184 = 4.1905 * r^3
r^3 = 85.184 / 4.1905
r^3 = 20.327884
Take the cube root of both sides
r = 2.73 cm
Find the perimeter of parallelogram AFCB.
A. 14
B. 12
C. 28
D. 24
Answer:
C.28
Step-by-step explanation:
It gives you 2 sides.
One of them is 8.
The other one is 12 but the 12 is divided by 2 which is 6.
Since it is a parallelogram there is the same measurements on the opposite sides.
So finally you get 6+6+8+8= 28
The perimeter of parallelogram AFCB is C. 28
How do you calculate a perimeter?
With the purpose to discover the perimeter or distance around the rectangle, we want to add up all four side lengths. this can be performed efficiently by using truly including the duration and the width, after which multiplying this sum by means of when you consider that there are of every facet length.
What is perimeter for instance?The Perimeter is the gap around the item. for instance, your own home has a fenced backyard. the perimeter is the length of the fence. If the yard is 50 toes × 50 feet your fence is 2 hundred feet long.
Learn more about Perimeter here https://brainly.com/question/397857
#SPJ2
The linear function f (x) and g(x) are represented on the graph where g(x) is a tranfomation of f(x) I need help with part A part B and Part C
Answer:
see below
Step-by-step explanation:
Part A
We can shift f(x) to the left or we can shift f(x) up to make it become g(x)
Part B
y = f(x + k) k > 0 moves it left
Using the point ( 2,8) for f(x) and ( 0,8) for g(x)
k is 2 units
g(x) = f(x+2)
y = f(x) + k k > 0 moves it up
Using the point ( 0,-2) for f(x) and ( 0,8) for g(x)
The difference between -2 and 8 is 10
k = 10
g(x) = f(x) + 10
Part C
for the shift to the left g(x) = f(x+2)
for the shift up g(x) = f(x) + 10