Answers
Answer:
The third: [tex]\bold{\dfrac{x+5}{x+15}}[/tex]Step-by-step explanation:
[tex]x^2+19x+70\ \implies a=1\,,\ b=19\,,\ c=70\\\\x=\frac{-19\pm\sqrt{19^2-4\cdot1\cdot70}}{2\cdot1}=\frac{-19\pm\sqrt{361-280}}{2}=\frac{-19\pm9}{2}\ \Rightarrow\ x_1=-14\,,\ x_2=-5\\\\x^2+19x+70=(x+14)(x+5)\\\\\\x^2-225=x^2-(15)^2=(x-15)(x+15)\\\\\\x^2-5x-150\ \implies a=1\,,\ b=-5\,,\ c=-150\\\\x=\frac{-(-5)\pm\sqrt{(-5)^2-4\cdot1\cdot(-150)}}{2\cdot1}=\frac{5\pm\sqrt{25+600}}{2}=\frac{5\pm25}{2}\ \Rightarrow\ x_1=-10\,,\ x_2=15\\\\x^2-5x-150=(x+10)(x-15)[/tex]
[tex]x^2+24x+140\ \implies a=1\,,\ b=24\,,\ c=140\\\\x=\frac{-24\pm\sqrt{24^2-4\cdot1\cdot140}}{2\cdot1}=\frac{-24\pm\sqrt{576-560}}{2}=\frac{-24\pm4}{2}\ \Rightarrow\ x_1=-14\,,\ x_2=-10\\\\x^2-5x-150=(x+14)(x+10)[/tex]
[tex]\dfrac{x^2+19x+70}{x^2-225}\,\cdot\,\dfrac{x^2-5x-150}{x^2+24x+140}=\dfrac{(x+14)(x+5)}{(x-15)(x+15)}\cdot\dfrac{(x+10)(x-15)}{(x+14)(x+10)}=\\\\\\=\dfrac{(x+14)(x+5)}{(x-15)(x+15)}\cdot\dfrac{x-15}{x+14}=\dfrac{x+5}{x+15}\cdot\dfrac11=\boxed{\dfrac{x+5}{x+15}}[/tex]
Answer:
The answer is option 3.
Step-by-step explanation:
First, you have to factorize the expressions :
[tex] \frac{ {x}^{2} + 19x + 70 }{ {x}^{2} - 225 } \times \frac{ {x}^{2} - 5x - 150}{ {x}^{2}24x + 140 } [/tex]
[tex] = \frac{(x + 5)(x + 14)}{(x + 15)(x - 15)} \times \frac{(x - 15)(x + 10)}{(x + 10)(x + 14)} [/tex]
Next, you have to cut out the common terms like (x + 14), (x - 15) and (x + 10):
[tex] \frac{(x + 5)(x + 14)}{(x + 15)(x - 15)} \times \frac{(x - 15)(x + 10)}{(x + 10)(x + 14)} [/tex]
[tex] = \frac{x + 5}{x + 15} [/tex]
Related Questions
I NEED SOMEONES HELP HELP ME PLEACE
Answers
Answer:
He needs to paint 12 inches in height
and 42 inches in width
Which of the following is a factor of x3+ 6x2 + 5x – 12?
A.X + 1
B. x - 3
C. x + 2
D. x + 4
Answers
1,3,4 that is the answer
Answer:
The answer is option D.Step-by-step explanation:
x³ + 6x² + 5x - 12
A factor of the polynomial is the value of x when substituted into the expression will make it zero
Choosing x + 4
x = - 4
We have
(- 4)³ + 6(- 4)² + 5(- 4) - 12
-64 + 96 - 20 - 12 = 0
Since the result is zero
x + 4 is a factor of the polynomial
Hope this helps you
In the figure, OM is perpendicular to AB. Prove that M is the the midpoint of AB.
Answers
we know by looking at the picture that m is the midpoint of AB since O to M doted lines had half into two equal parts.so M is in the midpoints of AB.
Step-by-step explanation:
to prove: M is the midpoint of AB
given: OM is perpendicular to AB
construction: joint AO and BO
proof: in the given fig,
OA and OB are joined
In Δ AOM and ΔBOM
AO = BO ( two sides of Δ AOB )
OM = OM ( common )
∴ Δ AOM ≅ Δ BOM ( by SAS rule )
∴ AM = BM ( by CPCT ) -------- 1
∴ M is the midpoint of AB ( from 1 )
⇒hence proved
HOPE THIS HELPED and PLEASE MAKE ME AS THE BRAINLIEST
Subtract -134 from the sum of 38 and -87.
Answers
Answer:
[tex]\boxed{85}[/tex]
Step-by-step explanation:
Sum of 38 and -87:
=> 38 + (-87)
=> 38 - 87
=> -49
Subtraction of -134 from -49:
=> -49 - (-134)
=> -49 + 134
=> 85
please help!!!!! idk how to do this
Answers
Answer:
30 seconds.
Step-by-step explanation:
So, we have the equation:
[tex]h(t)=-16t^2+h[/tex]
Where t is the time in seconds and h is the initial height.
A barometer falls from a weather balloon at a height of 14,400 feet. In other words, the initial height is 14,400. Substitute for h:
[tex]h(t)=-16t^2+14400[/tex]
We need to find when the barometer hits the ground. Ground level is 0 feet. Therefore, we can substitute h(t) for 0 and solve for the equation (solve for t) in order to find how long (in seconds) it took for the barometer to fall:
[tex]0=-16t^2+14400\\-14400=-16t^2\\900=t^2\\t=\pm\sqrt{900} \\\text{Time cannot be negative.}\\t=\sqrt{900}\\ t=30 \text{ seconds}[/tex]
Therefore, it took 30 seconds for the barometer to hit the ground when it fell at a height of 14,400 feet.
Edit: Spelling.
Lines m and n are parallel. Which of the other 5 named angles have a measure of 110°?
Press the hotspot for all that apply.
Answers
2 bcoz vertically opp
the one in front of 3, I can't see that number maybe 4
because corresponding angles
yea that's all
Which transformations can be used to carry ABCD onto itself? The point of rotation is (3, 2). Check all that apply. A. Reflection across the line y = 2 B. Rotation of 180 C. Rotation of 90 D. Translation two units up
Answers
Answer: rotate 180 degrees and reflection across the line y=2
Step-by-step explan
Answer:
Step-by-step explanation:
10 pts
A 25-foot ladder is placed against a building and the top of the ladder makes a 32° angle with the
building. How many feet away from the building is the base of the ladder? Write only the number
rounded to the nearest tenth of a foot.
Answers
Answer:
13.2 ft
Step-by-step explanation:
We are given a ladder, a building, and an angle. Let's construct a right triangle (see attachment).
In this right triangle, we know that the hypotenuse (the ladder) is 25 feet, while the angle made between the top of the ladder and the building is 32°. Since we want to find the number of feet between the building and the base of the ladder, we will use the trigonometric function sine, which is opposite divided by hypotenuse.
Here, the opposite side is the value we want to find, while the hypotenuse is the length of the ladder.
We have:
sin(32°) = opposite / hypotenuse = x / 25
x = 25 * sin(32°) ≈ 13.2 ft
The answer is thus 13.2 ft.
~ an aesthetics lover
Find mQPR. If mQPS=40,mRPS=8x+7,mQPR=9x+16
Answers
Explanation:
QPR + RPS = QPS
9x + 16 + 8x + 7 = 40
17x + 23 = 40
17x = 17
x = 1
Since QPR = 9x + 16
And x = 1
9(1) + 16 = 9 + 16 = 25
Suppose your car has hhh liters of engine oil in the morning. During the day, some oil may have leaked, you may have added more oil, or both. The oil level in the evening is ggg liters.
Answers
Answer:
g = (h+a) - l
None of them
Step-by-step explanation:
Suppose your car has h liters of engine oil in the morning. During the day, some oil may have leaked, you may have added more oil, or both. The oil level in the evening is g liters. Which of the following expressions always represents how far away the new oil level is from the previous oil level? H+G lGl none of them
Let
h = liters of oil in the morning
l= liters that has leaked
a= liters that were added during the day
g= amount of liters at the end of the evening
Total liters of oil in the evening= (litres of oil in the morning + litres of oil added during the day) - litres of oil that leaked
Substituting each variable into the formula, we have
g = (h+a) - l
On a pice of paper graph Y + 2 > -3x - 3
Answers
Answer:
Copy this onto a piece of graph paper
Step-by-step explanation:
when graphing you want to make sure that the slope is correct and the y-intercept is the same
HELPPPP The equation 2x = 3y – 5 when written in slope-intercept form is: y = 2x – 5. y = -2x + 5. y = 2x + 5. None of these choices are correct.
Answers
Answer:
Y= 2/3x +(5/3)
Step-by-step explanation:
First, have to get Y alone on one side 3y=2x+5
Second, have to get read of the 3 with the Y so divide each side by three.
What are the coordinates of the vertex of the function f(x)=x2+ 10x-3?
O (-5. -28)
(-5, 28)
O (5,-28)
(5.28)
Answers
Answer:
(-5,-28)
Step-by-step explanation:
Use the vertex form y=a(x-h)^2
a=1
h=-5
k=-28
vertex=(h,k)
Answer: A. (-5, -28)
Step-by-step explanation:
f(x) = x² + 10x - 3
a=1 b=10
The axis of symmetry is the x-coordinate of the vertex:
[tex]AOS: x=\dfrac{-b}{2a}\quad =\dfrac{-(10)}{2(1)}=-5[/tex]
Input x = -5 into the original equation to find the y-coordinate of the vertex:
f(-5) = (-5)² + 10(-5) - 3
= 25 -50 -3
= -28
x, y coordinate of the vertex is: (-5, -28)
find the zeros or x-intercepts (values of r and s) of a quadratic relation y=x^2-5x+6 by factoring using the sum and product method
Answers
Answer:
[tex] y = x^2 -5x +6[/tex]
And for this case we want to find the zeros or x interceps r and s so we want to rewrite the function on this way:
[tex] y = (x-r) (x-s)[/tex]
The reason why we have two zeros is because the degree of the polynomial is 2. If we find two numbers that adding we got -5 and multiplied 6 we solve the problem. For this case the solution is r =3, s =2
[tex] y=(x -2)) (x-3)[/tex]
Step-by-step explanation:
For this problem we have the following polynomial given:
[tex] y = x^2 -5x +6[/tex]
And for this case we want to find the zeros or x interceps r and s so we want to rewrite the function on this way:
[tex] y = (x-r) (x-s)[/tex]
The reason why we have two zeros is because the degree of the polynomial is 2. If we find two numbers that adding we got -5 and multiplied 6 we solve the problem. For this case the solution is r =3, s =2
[tex] y=(x -2)) (x-3)[/tex]
There are 5 orange bumper cars and 3 green bumper cars that are being tested
for safety for a ride at an amusement park. Two bumper cars are tested at
random, one at a time, without retesting the same car.
Find the probability that both cars are orange.
Enter the correct answer in the box.
Answers
Answer:
5/14
Step-by-step explanation:
I assume after testing the 1st car, it is not placed back into the pool.
So, 1st test orange is 5/8
2nd test orange is 4/7.
Both had to be true, so 5/8 x 4/7 = 5/14
URGENT!!!!!!
Identify the sequence graphed below and the average rate of change from n = 0 to n = 3 . (2, 10) (3, 5) (4, 2.5) (5, 1.25)
A) a_n=8(1/2)^(n-2); average rate of change is -3
B) a_n=10(1/2)^(n-2); average rate of change is -(35/3)
C) a_n=8(1/2); average rate of change is 3
D) a_n=10(1/2)^(n-2); average rate of change is 35/3
Answers
Answer: Choice B
a_n = 10(1/2)^(n-2) is the nth term
average rate of change = -35/3
=======================================================
Explanation:
Each time x increases by 1, y is cut in half. For instance, going from (2,10) to (3,5) shows this.
If we want to go in reverse, decreasing x by 1 will double the y value. So (1,20) is another point and (0,40) is another. We'll be using (0,40) and (3,5) because we want the average rate of change from x = 0 to x = 3. I'm using x in place of n here.
Use the slope formula to find the slope of the line through (0,40) and (3,5)
m = (y2-y1)/(x2-x1)
m = (5-40)/(3-0)
m = -35/3
The negative slope means the line goes downhill as you read it from left to right. The average rate of change from n = 0 to n = 3 is -35/3
The nth term of this geometric sequence is 20(1/2)^(n-1) since 20 is the first term (corresponds to n = 1) and 1/2 is the common ratio. Your teacher has done a bit of algebraic manipulation to change the n-1 into n-2. This means the 20 has to change to 10 to counterbalance.
In other words, 20(1/2)^(n-1) is equivalent to 10(1/2)^(n-2) when n starts at n = 1.
The functions f(x) and g(x) are shown on the graph.
f(x) = x2
What is g(x)?
A. g(x) = -x2 + 2
B. g(x) = -X2 - 2
C. g(x) = (-x)2 - 2
D. g(x) = (-x)2 + 2
Answers
B. [tex]-x^2-2[/tex].
Hope this helps.
Answer:
i think its g(x)=-x^2-2
Step-by-step explanation:
Consider the points P(5,5,1) and Q(13,13,3).
a. Find PQ with right arrow and state your answer in two forms: (a,b,c) and ai+bj+ck.
b. Find the magnitude of PQ with right arrow.
c. Find two unit vectors parallel to PQ with right arrow.
Answers
Answer:
a) [tex]\overrightarrow{PQ} = (8,8, 2)[/tex] or [tex]\overrightarrow{PQ} = 8\,i + 8\,j + 2\,k[/tex], b) The magnitude of segment PQ is approximately 11.489, c) The two unit vectors associated to PQ are, respectively: [tex]\vec v_{1} = (0.696,0.696, 0.174)[/tex] and [tex]\vec v_{2} = (-0.696,-0.696, -0.174)[/tex]
Step-by-step explanation:
a) The vectorial form of segment PQ is determined as follows:
[tex]\overrightarrow {PQ} = \vec Q - \vec P[/tex]
Where [tex]\vec Q[/tex] and [tex]\vec P[/tex] are the respective locations of points Q and P with respect to origin. If [tex]\vec Q = (13,13,3)[/tex] and [tex]\vec P = (5,5,1)[/tex], then:
[tex]\overrightarrow{PQ} = (13,13,3)-(5,5,1)[/tex]
[tex]\overrightarrow {PQ} = (13-5, 13-5, 3 - 1)[/tex]
[tex]\overrightarrow{PQ} = (8,8, 2)[/tex]
Another form of the previous solution is [tex]\overrightarrow{PQ} = 8\,i + 8\,j + 2\,k[/tex].
b) The magnitude of the segment PQ is determined with the help of Pythagorean Theorem in terms of rectangular components:
[tex]\|\overrightarrow{PQ}\| =\sqrt{PQ_{x}^{2}+PQ_{y}^{2}+PQ_{z}^{2}}[/tex]
[tex]\|\overrightarrow{PQ}\| = \sqrt{8^{2}+8^{2}+2^{2}}[/tex]
[tex]\|\overrightarrow{PQ}\|\approx 11.489[/tex]
The magnitude of segment PQ is approximately 11.489.
c) There are two unit vectors associated to PQ, one parallel and another antiparallel. That is:
[tex]\vec v_{1} = \vec u_{PQ}[/tex] (parallel) and [tex]\vec v_{2} = -\vec u_{PQ}[/tex] (antiparallel)
The unit vector is defined by the following equation:
[tex]\vec u_{PQ} = \frac{\overrightarrow{PQ}}{\|\overrightarrow{PQ}\|}[/tex]
Given that [tex]\overrightarrow{PQ} = (8,8, 2)[/tex] and [tex]\|\overrightarrow{PQ}\|\approx 11.489[/tex], the unit vector is:
[tex]\vec u_{PQ} = \frac{(8,8,2)}{11.489}[/tex]
[tex]\vec u_{PQ} = \left(\frac{8}{11.489},\frac{8}{11,489},\frac{2}{11.489} \right)[/tex]
[tex]\vec u_{PQ} = \left(0.696, 0.696,0.174\right)[/tex]
The two unit vectors associated to PQ are, respectively:
[tex]\vec v_{1} = (0.696,0.696, 0.174)[/tex] and [tex]\vec v_{2} = (-0.696,-0.696, -0.174)[/tex]
Zach tried to solve an equation step by step. 34=z−1234+12=z−12+12Step 154=zStep 2\begin{aligned} \dfrac34&=z-\dfrac12\\\\ \dfrac34+\dfrac12&=z-\dfrac12+\dfrac12&\green{\text{Step } 1}\\\\ \dfrac54&=z&\blue{\text{Step } 2} \end{aligned} 4 3 4 3 + 2 1 4 5 =z− 2 1 =z− 2 1 + 2 1 =z Step 1 Step 2 Find Zach's mistake. Choose 1 answer: Choose 1 answer:
Answers
Question:
Zach tries to solve an equation step by step;
[tex]\frac{3}{4} = z - \frac{1}{2}[/tex]
Step 1:
[tex]\frac{3}{4} + \frac{1}{2} = z - \frac{1}{2} + \frac{1}{2}[/tex]
Step 2:
[tex]\frac{3}{4} + \frac{1}{2} = z[/tex]
[tex]\frac{5}{4} = z[/tex]
Find Zach's mistake;
Answer:
Zach didn't make any mistake
Step-by-step explanation:
Given: the steps above
At step 1, he applied addition property of equality by adding [tex]\frac{1}{2}[/tex] to both sides of the equation
Step 2 is a result of step 1 and he rightly added the fractions
Further Explanation;
[tex]\frac{3}{4} = z - \frac{1}{2}[/tex]
Add [tex]\frac{1}{2}[/tex] to both sides
[tex]\frac{3}{4} + \frac{1}{2} = z - \frac{1}{2} + \frac{1}{2}[/tex]
[tex]\frac{3}{4} + \frac{1}{2} = z[/tex]
Take LCM of fractions at the left hand side
[tex]\frac{3 + 2}{4} = z[/tex]
[tex]\frac{5}{4} = z[/tex]
Reorder
[tex]z = \frac{5}{4}[/tex]
Analyzing the steps one after the other, we can conclude that Zach didn't make any mistake;
Answer:
C: Zach did not make a mistake
Step-by-step explanation:
SO IT NOT CONFUSING
+
GOT IT ON KHAN
(p.s. can u give me brainliest?)
WILL MARK BRAINLIEST! Match each pair of angles with the correct angle relationship(s). Explain your reasoning for each.
Answers
Answer:
∠AOB and ∠COD are vertical angles
∠DOE and ∠COD are complementary, adjacent
∠AOB and ∠AOD are supplementary, adjacent.
Step-by-step explanation:
Let's start with ∠AOB and ∠COD.
Looking at this, we can see they are the same angles formed by two lines that intersected. These are vertical angles as they are opposite each other.
∠DOE and ∠COD together form the angle ∠EOC, which is a right angle. Complementary angles are any of two that add up to 90°, so these two angles are complementary. They are also adjacent because they are right next to each other.
∠AOB and ∠AOD together form the angle ∠BOD, which has a measure of 180°. Supplementary angles are any of two that add up to 180°, so ∠AOB and ∠AOD are supplementary. They are also adjacent as they are touching/right next to each other.
I hope this helped!
describe the end behavior f(x)=5x^4+3x^2-1.
Answers
PLEASE HELP A store is having a sale on chocolate chips and walnuts. For 5 pounds of chocolate chips and 3 pounds of walnuts, the total cost is $21. For 2 pounds of
chocolate chips and 6 pounds of walnuts, the total cost is $24. Find the cost for each pound of chocolate chips and each pound of walnuts.
Answers
Answer:
Chocolate Chips cost $2.25 and Walnuts cost $3.25 per pound each
Step-by-step explanatChocion:
Let x = cost of pounds of chocolate chip cookies and y = cost of pounds of walnuts.
From the question, we get 5x+3y = 21 and 2x+6y = 24. To solve the equation, we use substitution. From the first equation, we get y = (21-5x)/3. We substitute the y into the second equation to get 2x + 6(21-5x)/3 = 24. This turns out to be 2x+(42-10x) = 24. Adding like terms you should get 42-8x = 24. Solving for x, x = $2.25 per pound. Plugging this into the first equation, we get 5(2.25)+3y = 21. Solving for y, we get $3.25 per pound of walnuts. If we plug in the numbers into the 2 equations, we will get the right total.
pls help !!!! i do not know or understand this at all
Answers
Answer:
(3, -3)
Step-by-step explanation:
Given functions:
f(x)= x² - 5x + 3and
f(x)= -3Solution is the Intersect which is found by equalizing the two functions:
x² - 5x + 3= -3Solving for x:
x² - 5x + 6=0x² - 2x -(3x -6) =0x(x-2) - 3(x-2)=0(x-2)(x-3)= 0x= 2 and x= 3As both values of x for the first function reveal f(x) = -3, the pairs are:
(2, -3) and (3, -3)Convert 50 degrees into radians (NEED ASAP)
Answers
Answer:
0.872665
Step-by-step explanation:
Radians = (π / 180) x Degrees
If we put 50 Degrees into our formula we get: (π / 180) x 50 = 0.872664625997165
50 Degrees is not the only number of degrees we have converted to radians. To convert another number of degrees, simply use same formula.
^_^ ^_^
PLEASE HURRY! Use the diagram to answer the question. What is the measure of ∠A? Enter the correct value. Do not enter the degree symbol. (This is from Primavera. I've tried 60.07, and it is not correct.)
Answers
Answer: 60.1
Step-by-step explanation: If you did 13/15 and then took sin-1 and got 60.07356513, you did everything right.
But sometimes they want the answer rounded to one decimal point.
So try 60.1
what is the value of the exponent expression below?
Answers
Answer:
6Option C is the correct option.
Step-by-step explanation:
[tex] {36}^{ \frac{1}{2} } [/tex]
Write the number in exponential form with a base of 6
[tex] =( {6}^{2}) \: ^{ \frac{1}{2} } [/tex]
Simplify the expression by multiplying the exponents
[tex] = 6[/tex]
Hope this helps..
Best regards!!
Find the value of x.
Answers
Answer:
x = 84°Step-by-step explanation:
A radius to the tangent point always forms a right angle with the tangent.
m∠OAB = m∠OCB = 90°
[tex]m\angle AOC=\stackrel{\big{\frown}}{ADC}=96^o[/tex]
The sum of the angles in the quadrilateral is 360°, so:
x = 360° - 2•90° - 96° = 84°
if m∠2= 137 and m∠P= 22, what is m∠O? answers are 43,21,65,115
Answers
Answer:
21
Step-by-step explanation:
since it is a triangle subtract 180 by 137 and 22
180-(137+22) or 180-132-22
hope this helps
Answer:
21
Step-by-step explanation:
We khow that the sum of a triangle's angles sizes is 180°
137+22 = 159°substract the sum of the two khown angles from 180°
180°-159° = 21 °so m<0 = 21°
Sarah has a bag of green and yellow marbles. The number of yellow marbles is 2 less than double the number of green marbles. If you let g be the variable for the green marbles and y be the variable for the yellow marbles, which equation represents the relationship between yellow and green marbles? Sarah has a total of 16 marbles. Which equation represents the total number of marbles she has?Sarah has a bag of green and yellow marbles. The number of yellow marbles is 2 less than double the number of green marbles. If you let g be the variable for the green marbles and y be the variable for the yellow marbles, which equation represents the relationship between yellow and green marbles? Sarah has a total of 16 marbles. Which equation represents the total number of marbles she has?
Answers
Answer:
[tex]y = 2g - 2[/tex]
[tex]y + g = 16[/tex]
Step-by-step explanation:
Given
Let g represent the green marbles
Let y represent the y marbles
Required
Determine the relationship between both marbles
The question says that y is 2 less than twice of g
This implies that: [tex]y = 2g - 2[/tex]
The question further states that, Sarah has a total of 16 marbles;
This implies that [tex]y + g = 16[/tex]
So, the system of equation that defines the relationship between y and g are:
y = 2g - 2
y + g = 16
Answer:
edge 2021
Step-by-step explanation:
If you let g be the variable for the green marbles and y be the variable for the yellow marbles, which equation represents the relationship between yellow and green marbles?
✔ y = 2g - 2
Sarah has a total of 16 marbles. Which equation represents the total number of marbles she has?
✔ y + g = 16
Donut Haven fries donuts in batches of $20$, but sells them in boxes of $13$. If Donut Haven fries just enough batches of $20$ to pack $44$ full boxes of $13$ donuts, how many donuts will be left over?
Answers
Answer:
The number of doughnuts left over are 8 doughnuts
Step-by-step explanation:
The information given are;
The number of doughnuts fried per batch = 20 doughnuts
The number of doughnuts contained in a pack = 13 doughnuts
The number of doughnut batches just fried = 20 batches
The number of packs filled = 44 packs
The number of packs filled with the fried = 44 packs
The number of doughnuts per pack = 13 doughnuts
The number of doughnuts in the pack = The number of packs filled with the fried × The number of doughnuts per pack
The number of doughnuts in the pack = 44 × 13 = 572 doughnuts
Given that the number of batches of doughnuts fried = X batches and the amount of left over = Y doughnuts, where each batch contains 20 doughnuts, we have;
Number of doughnuts fried = Number of batches of doughnuts fried × Number of doughnuts per batch
Number of doughnuts fried = X × 20 =20×X doughnuts
Therefore we have;
Number of doughnuts fried = The number of doughnuts in the pack + The number of doughnuts left over
Which gives;
20×X = 572 + Y where Y < 20
Checking we have multiples of 20 are 560, 580
Given that 520 is the next multiple of 20 after 572, we have;
The number of doughnuts fried = 580 and the number of left over = 580 - 572 = 8 doughnuts.