how many ordered pairs ( m , n ) of positive integers, such that m > n , have the property that their squares differ by 96 ?

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

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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Answer: 7-i√3

Step-by-step explanation:

√36+ √-75+ √1-√-108

6 + √75i + 1 - √108i

7 + 5i√3 - 6i√3

7-i√3

Step-by-step explanation:

A = r², find A when r is 14 centimeters.

A = (14)²

A = 196 cm²

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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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

⇒Option A is an expression of a difference 7 and 5x which is the product of 5 and x.

⇒Option A is the  answer.

The vector that translates P to P' is (-4 , 6)

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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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.

The value of the number is 35

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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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]

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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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

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

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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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

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

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.

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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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:

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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Step-by-step explanation:

(x+2)(x+7) = 0

It is already factorised.

So, x = (-2,-7)

So, option A is correct

The solutions to the expression x³ + 87 = 7x² + x are given as follows:

–3, 5 + 2i, 5 – 2i.

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:

Hence the equation is:

x² - 10x + 29 = 0.

And the solutions, using a quadratic equation calculator, are given as follows:

Which means that the third option is correct.

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Answer:

36a^10

Step-by-step explanation:

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

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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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!

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

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 ✓

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.

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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