Which equation represents the general form a circle with a center at (–2, –3) and a diameter of 8 units?
A.) x^2+y^2+4x+6y-51=0
B.) x^2+y^2-4x-6y-51=0
C.) x^2+y^2+4x+6y-3=0
D.) x^2+y^2-4x-6y-3=0
Answers
Standard Form of a Circle.
[tex](x - h)^2 + (y - k)^2 = r^2[/tex]
To use the standard form of a circle, we need to know the center of the circle and the radius of the circle. Our center is at (-2, -3), which is (h, k). Our radius is half of the diameter, which the diameter is 8 so 8 / 2 = 4. So we have a radius of 4.
In our Standard Form of a Circle, the h = -2 and the k = -3 and the 4 = r
Now we can turn this into the general form of a circle.
Insert our point (-2, -3) and our radius of 4 into the standard form of a circle equation and transform it into the general form.
[tex](x - h)^2 + (y - k)^2 = r^2[/tex]
[tex](x - (-2))^2 + (y - (-3))^2 =4^2[/tex]
[tex](x + 2)^2 + (y + 3)^2 = 4^2[/tex]
[tex](x + 2)^2 + (y + 3)^2 = 16[/tex]
Expand (x + 2)^2
[tex]x^2 + 4x + 4 + (y + 3)^2 = 16[/tex]
Expand (y + 3)^2
[tex]x^2 + 4x + 4 + y^2 + 6y + 9 = 16[/tex]
Move the 16 over to the left side by adding a - 16
[tex]x^2 + 4x + 4 + y^2 + 6y + 9 - 16 = 16 - 16[/tex]
[tex]x^2 + 4x + 4 + y^2 + 6y + 9 - 16 = 0[/tex]
Now arrange and combine like terms
[tex]x^2 + 4x + 4 + y^2 + 6y + 9 - 16 = 0[/tex]
Gathering all constant values
[tex]x^2 + 4x + y^2 + 6y + 9 -16 + 4 = 0[/tex]
Gathering all x and y values
[tex]x^2 + 4x + y^2 + 6y + 9 - 16 + 4 = 0[/tex]
[tex]x^2 + y^2 + 4x + 6y + 9 - 16 + 4 = 0[/tex]
Combining all constant terms
[tex]x^2 + y^2 + 4x + 6y + 9 - 16 + 4 = 0[/tex]
[tex]x^2 + y^2 + 4x + 6y - 3 = 0[/tex]
There is nothing else to combine so we have the general form of a circle, which is [tex]x^2 + y^2 + 4x + 6y - 3 = 0[/tex] so the answer is C
Answer: C
[tex]x^2 + y^2 + 4x + 6y - 3 = 0[/tex]
To find the equation, we will form the general equation of a circle and then will find the equation that matches the equation we formed.
General equation of a circleThe general equation of a circle is given as
[tex](x-h)^2+(y-k)^2 = R^2[/tex]
where, the (h, k) are the coordinates of the center of the circle, and R is the radius of the circle.
The correct option is c.
Given to uscircle with a center at (–2, –3) diameter of 8 unitsTo findthe equation of the circle that represents the general form of a circle with a center at (–2, –3) and a diameter of 8 units.
Radius of the CircleGiven that the diameter of the circle is 8 units. therefore,
[tex]\rm{ Radius\ of\ the\ circle =\dfrac{Diameter}{2} = \dfrac{8}{2}[/tex]
Equation of a circleThe equation of the circle that represents the general form of a circle with a center at (–2, –3) and a radius of 4 units can be found by substituting the values in the equation of a circle:
[tex](x-h)^2+(y-k)^2 = R^2[/tex]
Substituting the values,
[tex][x-(-2)]^2+[y-(-3)]^2 = 4^2\\\\ (x+2)^2+(y+3)^2 = 16[/tex]
[tex](x+2)^2+(y+3)^2 = 16\\\\ (x^2 + 4 + 4x)+(y^2+9+6y) = 16\\\\ x^2 + 4 + 4x+y^2+9+6y = 16\\\\ x^2 + 4x+y^2+6y = 16-4-9\\\\ x^2 + 4x+y^2+6y = 3\\\\ x^2 + 4x+y^2+6y -3 = 0[/tex]
Therefore, the equation which will be in the above form will be the equation we want. As we can see the above equation is similar to option c.
VerificationTo verify that we will plot the graph. The image given below represents the general form of a circle with a center at (–2, –3) and a diameter of 8 units.
Hence, the correct option is c.
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Related Questions
whats the distance between (-8,-7) (8,-4)
Answers
Distance formula: [tex] \sqrt{ (x_{2} - x_{1})^{2} + ( y_{2} - y_{1})^{2} } [/tex]
Plug in your values for [tex] x_{2}, x_{1}, y_{2}, y_{1}[/tex] using (-8, -7) and (8, -4) and solve.
[tex] \sqrt{(8 - (-8))^{2}+(-4 - (-7))^{2}} [/tex]
[tex] \sqrt{(8+8)^{2}+(-4+7)^{2}} [/tex]
[tex] \sqrt{(16)^{2}+(3)^{2}} [/tex]
[tex] \sqrt{256+9} [/tex]
[tex] \sqrt{265} [/tex] ≈ [tex] 16.28[/tex]
Answer:
Approximately 16.28 units.
A 2 liter drink costs $0.10 per deciliter. How much does the drink cost?
Answers
0.1*20=2
2 dollars
The price of drink is given as 0.10 dollars per deciliter.
It says to find the cost of 2 liters of drink.
We need to convert the units from liters to deciliters.
We know 1 liter = 10 deciliters.
then 2 liters = 20 deciliters.
So we need to find the cost of 20 deciliters of drink at rate of 0.10 dollars per deciliter.
1 deciliter of drink cost = 0.10 dollars.
20 deciliter of drink would cost = 20 x 0.10 dollars = 2.00 dollars.
Hence, 2 liters of drink would cost 2 dollars.
226Ra has a half-life of 1599 years. How much is left after 1000 years if the initial amount was 10 g?
Answers
how many rootes are in f(x)=(x^2-3x+1)^2
2
5
6
9
Answers
What the complement of 54.6 degree
Answers
x + 54.6° = 90°
x = 90° - 54.6°.
What is the volume of the figure below if a = 3.9 units, b = 5.7 units, and c = 3 units?
A. 157.95 cubic units
B. 351.351 cubic units
C. 124.605 cubic units
D. 113.49 cubic units
Answers
45.63 * 2 = 91.26
a x b x c = 3.9 * 5.7 * 3 = 66.69
66.69 + 91.26 = 157.95 cubic units
Final answer:
The volume of the parallelepiped with sides of lengths a = 3.9 units, b = 5.7 units, and c = 3 units is given by the formula V = a × b × c. After performing the calculation, the volume comes out to be 66.87 cubic units.
Explanation:
To find the volume of the parallelepiped with edges of lengths a, b, and c, you can multiply the length of each edge together. The volume (V) of a parallelepiped (a three-dimensional figure formed by six parallelograms) is given by the product of the lengths of its three dimensions. In this case, the formula to calculate the volume is V = a × b × c.
By plugging in the values provided:
a = 3.9 units
b = 5.7 units
c = 3 units
We get:
V = 3.9 units × 5.7 units × 3 units
Doing the multiplication:
V = 66.87 cubic units
Therefore, the volume of the figure is 66.87 cubic units.
Assume that when adults with smartphones are randomly selected, 48% use them in meetings or classes. If 55 adult smartphone users are randomly selected, find the probability that at least 22 of them use their smartphones in meetings or classes.
Answers
Success Rate = p = 0.48
Sample Size = n = 55
Number of success = x = 22
We are to find [tex]P(X \geq 22)[/tex] i.e. that probability that atleast 22 adults use the smartphone in meetings or class.
The probability can be calculated using the Binomial Calculators and it comes out to be 0.907.
This means there is 0.907 or 90.7% probability that there are atleast 22 adults among the 55 selected adults who use cell phones in meeting or class.
2x - y + 3z = -9
x + 3y - z = 10
3x + y - z = 8
find the ordered triple
Answers
Evaluate the integral. (use c for the constant of integration.) 7 ln(x)/ x sqrt(5 + (ln(x))^2) dx
Answers
[tex] \int\limits { \dfrac{7ln(x)}{x \sqrt{5+ln(x)^2}}} \, dx [/tex].
Substitute [tex]u=ln(x)^2+5[/tex] and differentiate.
[tex]dx= \dfrac{x}{2ln(x)}du[/tex]
[tex] \dfrac{7}{2} \int\limits { \dfrac{1}{ \sqrt{u}}} \, du [/tex]
[tex]\int\limits { \dfrac{1}{ \sqrt{u}}} \, du = 2 \sqrt{u} [/tex]
[tex] \dfrac{7}{2} \int\limits { \dfrac{1}{ \sqrt{u}} } \, du = 7 \sqrt{ln(x)^2+5}+C [/tex]
The expression for the integral [tex]\int\frac{7ln(x)}{x\sqrt{5+(ln(x))^2} } dx[/tex] after the evaluation is [tex]\text{I}=7\sqrt{5+(ln(x))^2} +C[/tex].
Given an integral expression:
[tex]\text{I}=\int\frac{7ln(x)}{x\sqrt{5+(ln(x))^2} } dx[/tex]
This can be written as:
[tex]\text{I}=7\int\frac{ln(x)}{x\sqrt{5+(ln(x))^2} } dx[/tex]
It is required to find the integral value.
Let u = 5 + (ln (x))²
Differentiate.
[tex]du=2ln(x)*\frac{1}{x} dx[/tex]
Or [tex]\frac{du}{2} =\frac{lnx}{x} dx[/tex]
Substitute the values.
[tex]\text{I}=7\int\frac{1}{\sqrt{u} } \frac{du}{2}[/tex]
[tex]\text{I}=\frac{7}{2} \int\frac{1}{\sqrt{u} }du[/tex]
[tex]\text{I}=\frac{7}{2} (2\sqrt{u} )+C[/tex]
Substitute back the value of u.
[tex]\text{I}=7\sqrt{5+(ln(x))^2} +C[/tex]
Hence the value of the integral is [tex]\text{I}=7\sqrt{5+(ln(x))^2} +C[/tex].
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PLEASE HELPS NEED THIS DONE BEFORE 3 O CLOCK
1)Jerome noticed the following house numbers on his street:
305, 318, 331, 344
The house numbers follow a pattern. Which expression can be used to determine the nthnth house number on his street?
A) 292 +13n
B) 292n
C) 292n + 13
D) 13(n + 292)
2) A polynomial expression is shown below.
(mx+8)(2x−4)
The expression is simplified to:
−6x2+28x−32-6x2+28x-32
What is the value of m?
A) 3
B) 4
C) -3
D) -4
3) What is the domain of the function shown below? (PICTURE AT BOTTOM)
A) 2
B) −8 ≤ x <3and 4 ≤ x <8
C) −8 ≤ x < 8
D) −7 ≤ x ≤ 7
Answers
A) 292 + 13*2 = 318 . . . . a good candidate
B) 292*2 = 584 (nope)
C) 292*2 + 13 = 597 (nope)
D) 13(2 + 292) = 3822 (nope)
The appropriate choice is ...
A) 292 +13n
2)The squared term in the product is 2mx^2. The squared term in the given expression is -6x^2. Comparing the coefficients, we have
2m = -6
m = -3
The appropriate choice for the value of m is ...
C) -3
3) The end point of one segment matches up with the beginning of the next except in the region 3 ≤ x < 4.
The appropriate choice is ...
B) -8 ≤ x < 3 and 4 ≤ x < 8
Answer:
Jerome noticed the following house numbers on his street:
Answer 292 +13n
A polynomial expression is shown below. What is the value of m?
Answer -3
What is the domain of the function shown below
Answer −8 ≤ x <3and 4 ≤ x <8
You were just approved for a $32,000 car loan at an APR of 1.99% for 60 months. As you make payments over time: your payment is , the amount of interest you will pay each month , and the amount of principal you pay each month .
Answers
What it Means...
If you borrow $32,000 at 1.99% for 5 years, your monthly payment will be $560.75.
The payments do not change over time. The loan amortizes over the repayment period, meaning the proportion of interest paid vs. principal repaid changes each month. As the loan amortizes, the amount of monthly interest paid decreases while the amount of principal paid increases.
Loan Amount: $32,000Term (years): 5 (60 Months)
Annual Interest Rate (%): 1.99% Monthly Payment = $560.75
Check out upload files
Amortization Schedule
Suppose a shipment of 140 electronic components contains 3 defective components. to determine whether the shipment should be accepted, a quality-control engineer randomly selects 3 of the components and tests them. if 1 or more of the components is defective, the shipment is rejected. what is the probability that the shipment is rejected?
Answers
To find the probability that a shipment of 140 electronic components, with 3 defects, is rejected upon testing 3 components, calculate the complement (all non-defective) and subtract from 1.
Explanation:The question involves determining the probability that a shipment containing 140 electronic components, with 3 being defective, is rejected based on a quality-control test of 3 components. To solve, consider the complementary probability - the chance all selected components are non-defective. First, calculate the probability of picking 3 non-defective components: (137/140) * (136/139) * (135/138). Then, subtract this probability from 1 to find the probability of the shipment being rejected.
1 - [(137/140) * (136/139) * (135/138)] equals the probability the shipment is rejected. After performing the calculations, you find that the shipment's rejection probability is determined by the presence of at least one defective component in the tested sample.
what is the answer please
Answers
Use The Pythagorean theorem. It’s a^2+b^2=c^2. Plug in 11 and 60. The equation would be 11^2+60^2=c^2. Simplify to get 121+3600=c^2. Simplify again to get 3721=c^2. Sqaure root each side to get c=61. The answer is the last one, c=61.
I hope this helps!
For which k will the graph of f(x)=x^2−kx+k^2 cross the x-axis twice?
Answers
b=-k, a=1, c=k²
b²-4ac=k²-4k²=-3k²
-3k² will never be larger than 0.
Complete the square to form a perfect square trinomial x^2-14x+
Answers
Explanation:
1) Divide the coefficient of x by 2:
14 / 2 = 7
2) so you have to add 7^2 = 49
x^2 - 14x + 49
3) that trinomial is equivalent to:
=> (x - 7)^2
4) prove that using the formula (a - b)^2 = a^2 - 2ab + b^2
(x - 7)^2 = x^2 - 14x + 49
Then you have to add 49 to complete the square. and form a perfect square trinomial.
if x2 = 49 the only possible answer for x is 7
Answers
x^2 = 49
Take the square root of both sides:
Answer: x = 7 or x = -7
While the equation x² = 49 suggests that x = 7, it also has a negative solution, x = -7. Both solutions can be verified by substitution into the original equation, proving they are correct through resulting identities.
The equation x² = 49 has two solutions in the realm of real numbers, not just x = 7. To find the values of x that satisfy the equation, we take the square root of both sides. Since the square root of a number has both a positive and a negative value, the solutions are x = 7 and x = -7. To verify these solutions, we can substitute them back into the original equation to confirm that they work, demonstrating identities such as 7² = 49 and (-7)² = 49.
I WILL GIVE U BRAINLY!!!
Which substance has been changed most over time from its original plant material?
A.
peat
B.
anthracite coal
C.
bituminous coal
D.
lignite
Answers
.
...
How much would $500 invested at 7% interest compounded annually be worth after 5 years?
Answers
7%= 7/100=0.07
A=500(0.07+1)^5
A=701.28
tickets for a football match are sold at $30 for adults and $15 for children a company bought 28 tickets if x of these tickets were for adults, write in terms of x a. the number of tickets for children b. the amount spent on tickets for adults c. the amount spent on tickets ...
Answers
The number of tickets for children is represented by '28-x' and the amount spent on tickets for adults is '$30x'. The amount spent on tickets for children is '$15*(28-x)'.
Explanation:We will use the concept of algebraic expressions to solve this question. If we represent the number of adult tickets as x, we know that the total number of tickets is 28. Hence, the number of children tickets can be represented as 28-x. The cost of a ticket for adults is $30, so the amount spent on adult tickets can be represented as $30x. Similarly, as the cost of a ticket for children is $15, the amount spent on children tickets can be represented as $15*(28-x).
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The number of ticket for children is (28 - x), the amount spent on tickets for adults would be $30x, and the total amount spent on tickets would be $30x + $15(28 - x).
Explanation:If a company bought 28 tickets and x of these tickets were for adults, then:
a. The number of tickets for children would be 28 - x. This is because from the total number of tickets purchased, we subtract the number of adult tickets to find the number of children's tickets.
b. The amount spent on tickets for adults would be $30x. This is because each adult ticket costs $30 and there are x number of adults.
c. To find out the total amount spent by the company, we will multiply the number of adult tickets by the price of an adult ticket ($30x) and add this to the product of the number of children tickets (28 - x) and the price of a child's ticket ($15). Therefore, the total spent would be $30x + $15(28 - x).
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The hypotenuse of a right triangle is 8 centimeters long. One of the legs of the triangle is 7 centimeters. What is the length of the triangle's other leg?
Answers
Answer:
3.87 centimeters
Step-by-step explanation:
sorry its took 3 years lol :)
Answer:
3.87 centimeters
Step-by-step explanation:
Got it right on Imagine math.
Treys online music club charges a monthly rate of $20 plus $0.80 per song download. Debs online music club charges a monthly rate of $21 plus $0.60 per song download. For what number of songs will the monthly charge be the same for both clubs? How much will it cost?
Answers
We have then:
x: number of songs.
y: total charge
For Treys online music club:
[tex]y = 0.80x + 20 [/tex]
For Debs online music club:
[tex]y = 0.60x + 21 [/tex]
Equaling both equations we have:
[tex]0.80x + 20 = 0.60x + 21 [/tex]
Clearing x we have:
[tex]0.80x - 0.60x = 21 - 20 0.20x = 1 x = 1 / 0.20 x = 5 songs[/tex]
Substituting the value of x for any of the equations we have:
[tex]y = 0.60 (5) + 21 y = 3 + 21 y = 24 $[/tex]
Answer:
The monthly charge will be the same for 5 songs in both clubs.
the cost will be $ 24
Answer:
For 5 songs the monthly charge be the same for both clubs.
It will cost $ 24.
Step-by-step explanation:
Let, for x songs, the monthly charges are same for both clubs,
Given,
For Treys online music club,
Monthly rate = $ 20,
Additional Charges for a song = $ 0.80,
⇒ Additional Charges for x song = $ 0.80x,
Thus, the total monthly charges for x songs = Monthly rate + Additional Charges for x song
= 20 + 0.80x
Now, for Debs online music club,
Monthly rate = $ 21,
Additional Charges for a song = $ 0.60,
⇒ Additional Charges for x song = $ 0.60x,
Thus, the total monthly charges for x songs = Monthly rate + Additional Charges for x song
= 21 + 0.60x
Hence, we can write,
[tex]20 + 0.80x = 21 + 0.60x[/tex]
[tex]0.80x - 0.60x = 21 - 20[/tex]
[tex]0.20x = 1[/tex]
[tex]\implies x = \frac{1}{0.20}=5[/tex]
Hence, for 5 songs the monthly charge be the same for both clubs.
Also, the cost for 5 songs = 20 + 0.80 × 5 = 20 + 4 = $ 24
PLZZZZZZ HELPPPP
Solve the system of equations using the substitution method.
{2x+8y=4x=−3y+5 Enter your answers in the boxes.
Answers
x = -3y + 5
plug in the value of x, from the second equation, into the first
2(-3y + 5) + 8y = 4
-6y + 10 + 8y = 4
combine like terms
2y + 10 = 4
subtract 10
2y = -6
divide both sides by 2
y = -3
then, plug what you got for y into one of the equations
x = -3y + 5
x = -3(-3) + 5
x = 9 + 5
x = 14
Hope this helps! And yes, it's correct!
The method of substitution is a three step method to solve the equations. In this method , one equation for one of the variables is solved and in the first step.
The outcome is then substituted to the second equation in the second step for solving the equation.The value is re-substituted to the original equation to find the outcome in the third step.
On solving the equations by substitution method we get x=14 and y=-3
Calculation:Given equations:
[tex]\rm 2x+8y = 4[/tex] (1)
[tex]\rm x=-3y+5[/tex] (2)
On substituting [tex]x=-3y+5[/tex] in equation 1:
[tex]\begin{aligned}\rm 2(-3y+5)+8y&=4\\\\-6y+10+8y&=4\\\\2y+10&=4\\\\2y&=4-10\\\\ 2y &= -6\\\\y&=\dfrac{-6}{2}\\\\y&=-3\end[/tex]
Substituting [tex]\rm y=-3[/tex] in equation 2:
[tex]\rm x&=-3y+5\\\\x&=-3(-3)+5\\\\x=9+5\\\\x=14[/tex]
Therefore the values of x and y for the given equations is 14 and -3 respectively.
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Determine if the functions are even, odd or neither. f(x) = -5x4 - 2 and g(x) = x3 + 2x
Answers
the rule: if f(-x)=f(x), then the function f(x) is even, if f(-x)=-f(x) then the function is odd.
1. f(x)=-5x⁴-2;
if to substitute x→(-x), then f(-x)=-5*(-x)⁴-2; ⇔ f(-x)=-5x⁴-2, in other words f(x)=f(-x), it means that this function is even.
2. f(x)=x³+2x.
if to substitute x→(-x), then f(-x)=(-x)³+2*(-x); ⇔ f(-x)=-(x³+2x), in other words f(-x)=-f(x), it means that this function is odd.
J is 25 more than 3 help???
Answers
Write the explicit formula for the geometric sequence.
64, 32, 16, 8, ...
A) an = 8 · 4n-1
B) an = 8 · 2n-1
C) an = 32 · 0.5n-1
D) an = 64 · 0.5n-1
Answers
Answer:
D) [tex]a_{n}[/tex][tex]=64[/tex]×[tex]0.5^{n-1}[/tex]
Step-by-step explanation:
The answer is D because it is the only answer that has an=64 and a decimal, 64 is your first term and the sequence is getting smaller
AND OR
Answer:
D) [tex]a_{n}[/tex][tex]=64[/tex]×[tex]0.5^{n-1}[/tex]
Step-by-step explanation:
Explicit Formula: an = a1 · dn-1
a1 = 64, d = 0.5
an = 64 · 0.5n-1
The formula for the volume of a cube is V(s) = s3 where s is the side length of the cube. In which quadrant(s) is the graph of the function V(s)?
Answers
However, when talking about the volume of a figure, a cube specifically, so that there is a physical sense, it must be fulfilled:
s> 0
Thus:
V (s)> 0
Thus, the function V (s) = s3 belongs to the first quadrant.
Answer:
the graph of the function V (s) is in the first quadrant.
Answer:
The answer is A: Quadrant 1
Step-by-step explanation:
On Edge :)
Robin randomly selects a number between 1 and 20. What is the probability that the number selected is the square of a natural number?
Answers
The probability that the number selected is the square of a natural number will be 0.20.
What is probability?Its basic premise is that something will almost certainly happen. The percentage of favorable events to the total number of occurrences.
Robin randomly selects a number between 1 and 20.
Then the total number of the events will be
Total events = 20 {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20}
The probability that the number selected is the square of a natural number will be
We know that natural numbers 1, 2, 3, 4, 5, and so on.
Then the square of the natural numbers will be
1, 4, 9, 16, 25, ....
Favorable event = 3 {1, 4, 9, 16}
Then the probability will be
P = 4 / 20
P = 1/5
P = 0.20
The probability that the number selected is the square of a natural number will be 0.20.
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the sum of two numbera is 122. the second number is 18 less than three times the first number. find the numbers. help please!
Answers
x + y = 122
y = 3*x - 18
by substitution:
x + (3x - 18) = 122
now you simplify:
4x - 18 = 122
4x = 140
x = 35
to find y, you can use the first equation
35 + y = 122
y = 87
Find the inverse of this 3x3 matrix. [1 5 2]
[ 1 1 7]
[0 -3 7]
Answers
M = [1 5 2 ]
[1 1 7 ]
[0 -3 7 ]
We apply the Gauss-Jordan elimination method (Procedure and result shown in the image below)
Answer:
A
Step-by-step explanation:
⎡−25 26 −33⎤
⎥ 4 −4 5 ⎥
⎥ 3 −3 4 ⎦
Cheryl paid $3 for each pin in her collection. She bought 32 pins in March and 56 pins in April.
How much did Cheryl spend on pins in April?
A.
What is the total amount of money Cheryl spent buying pins?
B.
How many pins did Cheryl add to her collection in March and April?
C.
What is the total cost of the pins that Cheryl bought in April?
D.
What is the difference between the number of pins bought in March and April?
Answers
B) She added 88 pins in total to her collection
C) She spent $168 in April
D) The difference is 24 pins
If you want me to explain the answers, just let me know :)
$3×(32 +56)
= $3×88
= $264
B. From part A, 88 pins.
C. $3×56 = $168
D. 56 -32 = 24
Cheryl bought 24 more pins in April than in March.
(Sometimes, "the difference of M and A" is intended to be strictly interpreted as "M - A". If that is the intent here, then the answer would be -24. More commonly, this wording is interpreted in common English to mean the value that results when the smaller number is subtracted from the larger one.)