Answer:
4 pairs
Step-by-step explanation:
You want the number of pairs of integers (m, n) such that m > n and m² -n² = 96.
Difference of squaresThe difference of squares is factored as ...
m² -n² = (m -n)(m +n)
In order for the difference to be 96, these factors must be factors of 96.
Factors of 96The prime factorization of 96 is ...
96 = 2^5 · 3
The number of divisors of 96 is the product of the exponents of these factors, each increased by 1:
(5+1)(1+1) = 12
That is, there are 12/2 = 6 factor pairs ab such that a<b. They are ...
96 = 1·96 = 2·48 = 3·32 = 4·24 = 6·16 = 8·12
SolutionThe values of m and n relate to the values of 'a' and 'b' by ...
m = (a+b)/2
n = (b-a)/2
In order for m and n to be integers, the values of 'a' and 'b' must both have the same parity. That is, they must both be even, or both be odd. This eliminates the factor pairs 1·96 and 3·32, leaving 4 (a, b) pairs, hence 4 (m, n) pairs. Possible ordered pairs are ...
(m, n) ∈ {(25, 23), (14, 10), (11, 5), (10, 2)} . . . . . 4 pairs
CAN SOMEONE DO THE ESSAY PART
The two triangles in the first figure is congruent by the ASA (angle-side-angle) axiom of congruency.
First diagram:
In ΔABC and ΔDEF we have :
∠C = ∠F
∠B = ∠E
BC = FE
∴ΔABC ≅ ΔDEF (by ASA axiom of congruency)
Second diagram:
In ΔABC and ΔDEF we have :
AB = XZ
BC = ZY
CA = XY
∴ΔABC ≅ ΔXYZ (by SSS axiom of congruency)
Third diagram:
In ΔKLM and TSU we have :
KL = TS
∠K = ∠U
∠M = ∠S
∴ΔKLM ≅ ΔTSU (by AAS axiom of congruency)
Fourth diagram:
In ΔABC and XYZ we have :
AB = YZ
BC = ZX
∠C = ∠Z
∴ΔABC ≅ ΔXYZ (by SAS axiom of congruency)
Fifth diagram:
No the two triangles are not congruent , they are similar.
AAA axiom is not for congruency, it is for similar triangles.
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HELP HELP HELP
(2^4x+4) / (2^x+1)
Answer:
[tex]2^{3x+3}[/tex]
Step-by-step explanation:
to divide exponents with the same base you just subtract them
(4x+4)-(X+1)
4x+4-x-1
3x+3
Hopes this helps please mark brainliest
Answer:
frac{16x+4}{2^{x}+1 =
Step-by-step explanation:
Evaluate the exponent! hope this helped
Find the component form of the vector that translates (3, − 2) to ′(− 1, 4)
The vector that translates P to P' is (-4 , 6)
What is a translation?A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction either in it’s range(involving values of y) or in it’s domain(involving values of x).
The points are given;
[tex]{P = (3, -2)}\\{P' = (-1, 4)}[/tex]
The translation rule is calculated as:
{(x,y) = P' - P}
So, we have:
{(x,y) =(− 1, 4) - (3, − 2)}
Combine the terms;
{(x,y) = (-1 -3 , 4 + 2)}
{(x,y) = (-4 , 6)}
Express as vectors;
(x, y) = (-4 , 6)
Hence, the vector that translates P to P' is (-4 , 6)
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A movie theater has a seating capacity of 183. The theater charges $5.00 for children, $7.00 for students,
and $12.00 of adults. There are half as many adults as there are children. If the total ticket sales was $
1316, How many children, students, and adults attended?
children attended.
Using simplification, if the total ticket sales was $1316, then 70 children, 78 students and 35 students attended.
From the given question,
We know that the capacity of movie theater is 183.
The theater charges $5.00 for children, $7.00 for students and $12.00 of adults.
There are half as many adults as there are children.
If the total ticket sales was $1316, then we have to find how many children, students, and adults attended.
Let the number of children that attended = x
Since, there are half as many adults as children.
Therefore number of adults = 1/2x =0.5x
We know there are total of 183 tickets
Therefore number of students = 183 - x - 0.5x
number of students = 183 - 1.5x
Each children ticket costs = $5
Then the price of children tickets = 5x
Similarly for adults each ticket costs = $12
So total cost of adult ticket = 12×0.5x = $6x
Now the cost of student tickets = 7(183 - 1.5x)
As given that
Total cost of all tickets = $1316
So the expression should be
5x + 6x + 7(183 -1.5x) = 1316
Simplifying
11x + 1281 - 10.5x = 1316
Subtract 1281 on both side
11x + 1281 - 10.5x-1281 = 1316-1281
Simplifying
0.5x = 35
Divide by 0.5 on both side we get
x = 70 children
Now finding the number of adults
= 0.5x
= 0.5×70
= 35 adults
Now finding the number of students
= 183 - 1.5x
= 183 - 1.5×70
= 183 - 105
= 78 students
Hence, If the total ticket sales was $1316, then 70 children, 78 students and 35 students attended.
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HELP!! 25 POINTS
Simplify the expression to a + bi form:
√36+ √-75+ √1-√-108
Answer: 7-i√3
Step-by-step explanation:
√36+ √-75+ √1-√-108
6 + √75i + 1 - √108i
7 + 5i√3 - 6i√3
7-i√3
Solve for x
-2x+6y=13
A web designer charges a $200 fee plus $50 per hour to build a website. Which equation represents the total cost, y, to a customer based on the number of hours, x, it takes to buld the website?
Answer: 50x+200=y
Step-by-step explanation:
This is the answer because the number of hours is not provided leaving us to multiply 50 by x, 200 is the flat fee so we will know to automatically add that to our first step and since y is the total this will form the equation, 50x+200=y.
Use the Law of Detachment to draw a conclusion from the two given statements.
If two angles are complementary, then the sum of their measures is 90°.
The Law of detachment states that if m then n and m is true then q is true.
If two angles are complementary, then the two angles' sum is 90 degrees.
This is m∠E + m∠F = 90.
Option C is the correct answer
What is the law of detachment?The Law of detachment states that if m then n and m is true then q is true.
We have,
If two angles are complementary, then the sum of their measures is 90°.
This is in the form of,
If M then N and if M is true then N must be true.
So,
If two angles are complementary, then the two angles' sum is 90 degrees.
If the two angles are m∠E and m∠F.
m∠E + m∠F = 90
Thus,
If two angles are complementary, then the two angles' sum is 90 degrees.
This is m∠E + m∠F = 90.
Option C is the correct answer
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What is an equation of the line that passes through the point (3,-1)(3,−1) and is parallel to the line 5x+3y=6
Answer: y=-5/3x+4
Step-by-step explanation:
Since the line is parrallel that means that the gradient is the same
We can reorder 5x+3y=6 into 3y=-5x+6 but in order to find the gradient the number infront of y must be 1 so...
3y=-5x+6
y=-5/3x+2
Now we know that the gradient is -5/3
To find th y-intercept we just subsitute the points it passes through (3, -1) into the equation
y=-5/3x+c
-1=-5/3(3)+c
-1=-5+c
4=c
One fifth of a number plus three times the number is equal to twice the number plus 42 . What is the number
The value of the number is 35
What are algebraic expression?Algebraic expressions are the idea of expressing numbers using letters or alphabets without specifying their actual values.These letters are called variables. An algebraic expression can be a combination of both variables and constants. Any value that is placed before and multiplied by a variable is a coefficient.
If the number is represented by x then,
1x/5+3x= 2x+42
making the left hand side a single fraction, then,
(x+15x)/5= 2x+42
16x/5= 2x+42
multiply both sides by 5
16x= 10x+210
collect like terms
16x-10x= 210
6x= 210
x=35
therefore the value of the number is 35
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Solve the equation by factoring.
(x+2)(x + 7) = 0
A) (-2,-7)
C) (5,-8)
B) -5,5)
D) (6, 3)
Step-by-step explanation:
(x+2)(x+7) = 0
It is already factorised.
So, x = (-2,-7)
So, option A is correct
10. Which segment below is perpendicular to line AB? How do you know?
Answer:
Line CE
Step-by-step explanation:
We know that lines are perpendicular when their intersections form 90° angles (see below diagram). ∠E is a 90° angle, so line CE is perpendicular to line DF. Assuming that line DF is parallel to line AB, we now know that line CE is also perpendicular to line AB.
What is the converse of the conditional statement "If the streetlights are on, then the sun has gone down."?
O If the sun has gone down, then the street lights are on.
O If the streetlights are not on, then the sun has gone down.
O If the streetlights are not on, then the sun has not gone down.
If the sun has not gone down, then the streetlights are on.
The converse of the conditional statement "If the streetlights are on, then the sun has gone down" is If the sun has not gone down, then the streetlights are on and is denoted as option D.
What is Converse of the conditional statement?This is referred to as the type of sentence which is formed when the hypothesis and the conclusion are interchanged.
In this scenario, "If the streetlights are on, then the sun has gone down" when interchanged will be If the sun has not gone down, then the streetlights are on which therefore makes option D the correct choice.
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10 pionts!!!!
if f(x)=6x+5, find f(1)
Answer:
11
Step-by-step explanation:
Plug in 1 to the function:
f(x) = 6x + 5
f(1) = 6(1) + 5
f(1) = 6 + 5
f(1) = 11
Which expression is a difference of a number and a product?
OA. 7-5x
OB. 5+x-3
C. 5(x-3)
OD. 3+5x
⇒Option A is an expression of a difference 7 and 5x which is the product of 5 and x.
⇒Option A is the answer.
wer:
Find the slope of the line that passes through the given points.
(-3, 7.2) and (2,-2.3)
Answer:
Step-by-step explanation:
this slope of a line question is such a common question. I feel like math teachers all over don't understand how to teach this subject. Just so you know, I answer a question like this about 10 times a day when I am on here. It's like one of the most common questions.
Here is my copy and paste answer for this...
point P1 (-3,7.2) in the form (x1,y1)
point P2(2,-2.3) in the form (x2,y2)
slope = m
m = (y2-y1) / (x2-x1)
m = (-2.3-7.2) / (2-(-3))
notice all the minus signs and how i'm being very careful to keep close track of them. Also, who ever has written this question is intentionally trying to trip you up by putting in all the minus signs, there is no need for so many minus signs to teach this well. Anyway...
m = -8.5 / 5
m = - 1.7
the problem question ends there , but there is a common place this question is supposed to take you. to the point slope formula. but for another question.
The slope of (-3, 7.2) and (2, -2.3) is -1.9.
Consider,
(x1, y1) = (-3, 7.2)
(x2, y2) = (2, -2.3)
slope = (y2 - y1)/(x2-x1)
slope = ((-2.3) - (7.2))/((2) - (-3))
slope = (-9.5)/(5)
slope = -1.9
Therefore, the slope of the given points (-3, 7.2) and (2, -2.3) is -1.9.
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The perimeter of a rectangle is 150 inches. The width is 12 inches. Find the length.
Answer:
63 inches
Step-by-step explanation:
The perimeter of a rectangle is found by adding all of the side lengths. Since both pairs of opposite sides have the same length, an equation for the perimeter can be written like this:
[tex]P=2w+2l[/tex]
Where w and l represent the width and length.
Since we are asked to find the length, rewrite the equation in terms of l:
[tex]l=\frac{P-2w}{2}[/tex]
We know the values for P and w, so plug those in:
[tex]l=\frac{150-2(12)}{2}[/tex]
Now simplify!
[tex]l=\frac{126}{2}=63[/tex]
Answer:
l = 63 in
Step-by-step explanation: If the P=150 in W=12 in so .... using the formula P=2 (l + w) you get L= P/2 - W = 150/2 - 12 = 63 in. I hope this helps!
Please I need help please
The measure of missing angles in the diagram is angle 1 = 88°, angle 2 = 42° and angle 3 = 113° .
In the question ,
a figure is given ,
the labelled diagram is show below .
we can see that the angle ACB and angle ECD are vertically opposite angles ,
we know that, the vertically opposite angles are equal ,
So, angle ACB = m∠2 = 42°
In triangle ABC
By Angle Sum Property Of Triangle ,
angle A + angle B [tex]+[/tex] angle C [tex]=[/tex] 180°
50° + m∠1 + 42° [tex]=[/tex] 180°
92° + m∠1 = 180°
m∠1 = 180° - 92°
m∠1 = 88°
In triangle CDE ,
By Angle Sum Property Of Triangle
angle C + angle D [tex]+[/tex] angle E [tex]=[/tex] 180°
42° + m∠3 + 25° [tex]=[/tex] 180°
m∠3 + 67° = 180°
m∠3 = 180° - 67°
m∠3 = 113°
Therefore , The measure of angle 1 = 88°, angle 2 = 42° and angle 3 = 113° .
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Joel types 180 words in 4 minutes.
How many words per minute
can he type?
Answer:
45 words
Hope this helps :)
Step-by-step explanation:
We know that he can type 180 wprds in 4 minutes.
So to find how man words he types per minute which is 1 minute, then we need to divide 180 by 4.
1. Divide.
45
4| 180
- 16↓
20
- 20
0
2. Answer.
Joel can type 45 words per minute.
3. Check.
45
× 4
180 ✓
There is one negative solution and two nonreal solutions to the equation x3 + 87 = 7x2 + x. What are the solutions?
3, 5 + 2i, 5 – 2i
3, –5 + 2i, –5 – 2i
–3, 5 + 2i, 5 – 2i
–3, –5 + 2i, –5 – 2i
The solutions to the expression x³ + 87 = 7x² + x are given as follows:
–3, 5 + 2i, 5 – 2i.
How to obtain the solutions to the equation?The equation is defined as follows:
x³ + 87 = 7x² + x.
In standard format, it is given by:
x³ - 7x² - x + 87 = 0.
It has one negative solution, hence from the options it is:
x = -3.
The verification is:
(-3)³ - 7(3)² - (-3) + 87 = 0.
Considering the linear factor (x + 3), the function can be written as follows:
x³ - 7x² - x + 87 = (x + 3)(ax² + bx + c).
As the product of a linear function and a quadratic function results in a cubic function.
Expanding the right side of the equality, we have that:
ax³ + (b + 3a)x² + (3b + c)x + 3c = x³ - 7x² - x + 87.
Hence the coefficients of the quadratic equation are given as follows:
a = 1.b + 3a = -7 -> b = -10.c = 87/3 = 29.Hence the equation is:
x² - 10x + 29 = 0.
And the solutions, using a quadratic equation calculator, are given as follows:
x = 5 + 2i.x = 5 - 2i.Which means that the third option is correct.
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Jamar bought 22 chicken wings for $48.40. How much would it cost for 6 wings?
Answer: $13.2
Step-by-step explanation:
You can use proportions to find the cost(x):
[tex]\frac{22}{48.40} =\frac{6}{x} \\\\22x=6*48.4\\\\22x=290.4\\\\x=13.2[/tex]
find the missing side of the right triangle.
Answer:
Step-by-step explanation:
48
Answer:
51
Step-by-step explanation:
Pythagorean theorem
a^2+b^2=c^2
45^2+24^2
2025+576
2601=c^2
square root both sides
51=c
Hopes this helps please mark brainliest
HELP ME PLSS THIS IS DUE NOW
Franchising is a popular way to grow. Subway has about 42,000 franchisees that pay 12. 5% of their annual store revenue ($417,000 average) to subway. About how much does subway collect in franchise fees?.
Total amount that Subway collect in franchise fees = $2,189,250,000
Total number of subway franchisees = 42,000
Average annual store revenue = $417,000
Total paying percentage of franchisees = 12.5%
12.5% of average revenue = (417000×12.5)÷100
= $52,125
Total subway collection in franchise fee= total number of franchisees×amount of fees per franchisees
= 42,000×52,125
= $2,189,250,000
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Since subways has about 42000 franchisees and about $417000 average revenue is earned. Therefore, the total amount that Subway collect in franchise fees is $2,189,250,000.
Subways Franchise operate 16 submarine sandwich shop and they expanded quickly with its long time slogan "East Fresh".
Franchisor gives a franchisee the authority to do business in the franchisor's trade name using its business system it is called franchising.
Subways franchises pay 12.5% every week (gross sales minus the sales tax), 8% goes toward the franchise royalties and 45% gores towards advertising.
The company has the lowest start-up costs compared to many other fast food franchises but does take more royalty and advertising money.
The franchise fee:
A franchise owner pay 12.5% of gross sales minus tax every week. They must pay even if they are losing money.8% of that 12.5% goes toward the franchise royalties and 4.5% is for advertising.Now, according to the question:
Total number of subway franchisees = 42,000
Average annual store revenue = $417,000
Total paying percentage of franchisees = 12.5%
∴ At 12.5% of average revenue = (417000 × 12.5) ÷ 100
= $52,125
Total subway collection in franchise fee
= total number of franchisees × amount of fees per franchises
= 42,000×52,125
= $2,189,250,000
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The sum of three times a number and 2 less than 4 times that same number is 15. Which of the followin
equations could be used to find the value of the number, n? Explain how you arrived at your choice.
Answer:
11
Step-by-step explanation:
Three times an unknown number
= 3(n)
Added to
Two less than four times the same unknown number
= 4 - 2(n)
Total
= 3(n) + 4 - 2(n) = 15
= 3n + 4 - 2n = 15
Collect like terms
= 3n - 2n = 15 - 4
n = 11
In the formula A = r², find A when ris
14 centimeters.
Step-by-step explanation:
A = r², find A when r is 14 centimeters.
A = (14)²
A = 196 cm²
Two squares are similar. The
perimeter of the smaller square is p
46 cm. The perimeter of the larger
square is doubled the perimeter of
smaller square. Find the side
length (in cm) of the
larger square.
Answer:23
Step-by-step explanation:
Divide 46 by 4 so u know the length of the side of the smaller square
the answer is 11.5 so them you multiply It by 2 and you get 23cm
hope this helps
Simplify
a9/a5
a^4
1/a^4
4
a^14
Answer:
36a^10
Step-by-step explanation:
Please do the one you understand anything is helpful!
Answer:
1. 30 years old
2. 7 years old
3. 5 hours
Step-by-step explanation:
We can solve all of these problems using algebraic equations.
1. In this question, we will use variable x to represent the age of Mrs. Olsen's daughter.
In 10 years, x - 20 = 2x. That means that in 10 years, Mrs. Olsen will be 40 years old. That means she is 30 right now.
2. In this question, we will use variable x to represent the age of Alyssa.
If, in 30 years, their total age is 88, their current total is 28. Tyler is 3 times as old as Alyssa, so Tyler is 21 and Alyssa is 7.
3. Ryan leaves home at 50 mph. That means, in an hour Ryan will be 50 miles away from home. At that point, Jacob leaves home at a speed of 60 mph, so the gap between them closes by 10 miles each hour. That means that Jacob will take 5 hours to catch up, counting from when he left (how far is this workplace jeez?!?!?!?).
We could also represent this with a graph.
Hour 1: R = 50, J = 0 (Jacob leaves after this hour so it doesn't count for the answer)
Hour 2: R = 100, J = 60
Hour 3: R = 150, J = 120
Hour 4: R = 200, J = 180
Hour 5: R = 250, J = 240
Hour 6: R = 300, J = 300
after begging his parents for 3 years, jason is finally going to clown college! on the first day, his juggling instructor divides a box of bean bags equally among the 16 clowns in jason's class. each clown gets 6 bean bags. which equation can you use to find the number of bean bags b in the instructor's box?
The equation that can be used to determine the number of bean bags in the instructor's box is b = 17 x 4.
Given,
In the question:
His juggling instructor divides a box of bean bags equally among the 16 clowns in Jason's class. each clown gets 6 bean bags.
Now, According to the question:
The equation that can be used to determine the number of bean bags in the instructor's box is b = 16 x 6.
The number of bean bags in the instructor's box is 96.
What is multiplication?
Multiplication is a mathematical operation that can be used to determine the product of two or more numbers. The sign used to represent multiplication is ×.
Hence, The equation that can be used to determine the number of bean bags in the instructor's box is b = 17 x 4.
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