The lengths of two sides of a right triangle are 12 inches and 15 inches. What is the difference between the two possible
lengths of the third side of the triangle? Round your answer to the nearest tenth.
10.2 inches
24.0 inches
28.2 inches
30.0 inches

Angle BCA

Step-by-step explanation:

You can see this due to the angle having the name amount of congruent angle marks.

Answer:

The pairs are (13,15) and (-15,-13).

Step-by-step explanation:

If n is an odd integer, the very next odd integer will be n+2.

n+1 is even (so we aren't using this number)

The sum of the squares of (n) and (n+2) is 394.

This means

(n)^2+(n+2)^2=394

n^2+(n+2)(n+2)=394

n^2+n^2+4n+4=394               since (a+b)(a+b)=a^2+2ab+b^2

Combine like terms:

2n^2+4n+4=394

Subtract 394 on both sides:

2n^2+4n-390=0

Divide both sides by 2:

n^2+2n-195=0

Now we need to find two numbers that multiply to be -195 and add up to be 2.

15 and -13 since 15(-13)=-195 and 15+(-13)=2

So the factored form is

(n+15)(n-13)=0

This means we have n+15=0 and n-13=0 to solve.

n+15=0

Subtract 15 on both sides:

n=-15

n-13=0

Add 13 on both sides:

n=13

So if n=13 , then n+2=15.

If n=-15, then n+2=-13.

Let's check both results

(n,n+2)=(13,15)

13^2+15^2=169+225=394.  So (13,15) looks good!

(n,n+2)=(-15,-13)

(-15)^2+(-13)^2=225+169=394.  So (-15,-13) looks good!

Answer:

f(n + 1) = f(n) + 2

Step-by-step explanation:

A recursive formula gives any term in the sequence from the previous term.

the n th term of an arithmetic sequence is

f(n) = f(1) + (n - 1)d ← d is the common difference

Given

f(1) = 6 and

f(4) = 12, then

f(1) + 3d = 12, that is

6 + 3d = 12 ( subtract 6 from both sides )

3d = 6 ( divide both sides by 3 )

d = 2

To obtain a term in the sequence add 2 to the previous term, hence

f(n + 1) = f(n) + 2 ← recursive formula

Answer:

c

Step-by-step explanation:

its c

Answer:

-5/4

Step-by-step explanation:

The average rate of change of f from x=0 to x=4 is_____.

This means we are being asked to evaluate [tex]\frac{f(4)-f(0)}{4-0}[/tex].

To do this we will need to find f(0) and f(4).

f(0) means what y-coordinate corresponds to x=0 on the curve.  Find x=0, the curve is above there, go straight up and see  y=5 there.  This means f(0)=5.

f(4) means what y-coordinate corresponds to x=4 on the curve. Find x=4, then curve is above there, go straight up and see y=0 there.  This means f(4)=0.

So we have:

[tex]\frac{f(4)-f(0)}{4-0}=\frac{0-5}{4-0}=\frac{-5}{4}[/tex].

166

27 + 42 + 21 + 76 = 166

Answer:

9 : 16

Step-by-step explanation:

Given 2 similar figures with linear ratio = a : b, then

area ratio = a² : b² and

volume ratio = a³ : b³

Here the volume ratio = 27 : 64, hence

linear ratio = [tex]\sqrt[3]{27}[/tex] : [tex]\sqrt[3]{64}[/tex] = 3 : 4

Hence area ratio = 3² : 4² = 9 : 16

Answer:

8.8.8.

Step-by-step explanation:

8.8.8  = 8^3  = 512    Perfect cube.

8+8+8 =24

9.9.9.9 = 6561

9+9+9+9+9 = 45.

None of the others are perfect cubes.

Answer:A 8.8.8

Step-by-step explanation:i did the quiz

Answer:

T10= -21

Step-by-step explanation:

If Sn=n^2+3 then t10=?

Sn= n²+5

put n=1, 2

S1= T1 =  (1)²+5

=1+5 =6

S2= n²+5

S2=(2)²+5

S2=4+5

S2=9

T2 = S2 - S1

T2 = 9-6

T2=3

T10 = a+(n-1)d

where a = 6, d = -3, n=10

T10= 6+(10-1)*-3

T10=6+(9)*-3

T10=6+(-27)

T10=6-27

T10= -21

Therefore T10= -21 ....

Step-by-step explanation:

In a standard deck of 52 cards, there are 2 red aces, 2 red Queens, and 13 spades.  That leaves 35 cards for everything else.

For the game to be fair, the cost must equal the expected value.  The expected value is the sum of each outcome times its probability.

C = (12) (13/52) + (20) (2/52) + (38) (2/52) + (0) (35/52)

C = 68/13

C ≈ 5.2308

Answer:

Yes you are right.

The answer is .45 or 45/100 which reduces to 9/20.

Step-by-step explanation:

[tex]\frac{4x}{15}=\frac{3}{25}[/tex]

Your first step is to cross multiply:

[tex]15(3)=25(4x)[/tex]

Simplify both sides:

[tex]45=100x[/tex]  You got this! You go!

Divide both sides by 100:

[tex]\frac{45}{100}=x[/tex]

You wrote 45/100 as .45 which is correct!

Nice.

All except combine like terms. Since you only have 1 variable.

Hope this helps.

r3t40

Answer:

4 ≤ x

4

●→

Step-by-step explanation:

There is no illustration, it looks something like this.

Answer: A. y=(1/2)^x+6

Step-by-step explanation: If this is the graph you’re talking about-

When “a” is less than one, the graph increases exponentially to the left. The smaller the value of a, the steeper the slope of the line.

There is a vertical shift up 6 as well

Answer:

A

Step-by-step explanation:

Calculate the midpoint using the midpoint formula

[ 0.5(x₁ + x₂ ), 0.5(y₁ + y₂ ) ]

with (x₁, y₁ ) = (- 1, 5) and (x₂, y₂ ) = (5, 5)

midpoint = [ 0.5(- 1 + 5), 0.5(5 + 5) ]

              = [ 0.5(4), 0.5(10) ] = (2, 5 ) → A

Answer:

The answer would be A 2,5

Step-by-step explanation:

Answer:

Triangle APB is an isosceles triangle ⇒ 3rd answer

Step-by-step explanation:

* Lets explain the how to solve the problem

- ABCD is a square

∴ AB = BC = CD = AD

∴ m∠A = m∠∠B = m∠C = m∠D = 90°

- DPC is equilateral triangle

∴ DP = PC = DC

∴ m∠DPC = m∠PCD = m∠CDP = 60°

- In the Δs APD , BPC

∵ AD = BC ⇒ sides of the square

∵ PD = PC ⇒ sides of equilateral triangle

∵ m∠ADB = m∠BCP = 30° (90° - 60° = 30) ⇒ including angles

∴ Δs APD , BPC are congregant ⇒ SAS

- From congruent

∴ AP = BP

∴ Triangle APB is an isosceles triangle

Answer:

It's 53.

Step-by-step explanation:

Let the number be xy so the digits are x and y, so:

x + y = 8...........(1)

Reversing the 2 digits we have the number 10y + x and this equals

10x + y - 18 so we have the equation:-

10x + y - 18 = 10y + x

9x - 9y = 18

x - y = 2...........(2)   Adding equations (1) and (2) we have:

2x = 10

x = 5

and y = 8 - 5 = 3.

So the original number is  53.

We can check this  as follows

Original number is 53 so the reverse is 35 .

53 - 35 = 18  which checks out.

Answer:

x= -3.75

Step-by-step explanation:

Answer:

x = -15/4

Step-by-step explanation:

7(x+6)=3(x+9)

Distribute

7x+42 = 3x+27

Subtract 3x from each side

7x-3x+42 = 3x-3x+27

4x +42 = 27

Subtract 42 from each side

4x+42-42 = 27-42

4x =-15

Divide each side by 4

4x/4 =-15/4

x = -15/4

Answer:

7/11

Step-by-step explanation:

Two events are disjoint events if they cannot occur at the same time. It is given that A and B are disjointed events, so A and B cannot occur at the same time i.e. the intersection of two disjoint events will be 0.

For two disjoint events A and B:

P(A or B) = P(A) + P(B)

P(A) is given to be 4/11 and P(B) is given to be 3/11. Using these values in the equation, we get:

P(A or B) = [tex]\frac{4}{11}+\frac{3}{11} = \frac{3+4}{11}=\frac{7}{11}[/tex]

Answer:

The GCF of both the terms is 8....

Step-by-step explanation:

Given:

What is the greatest common factor of 8x and 40y.

The GCF of 8x and 40y is 8.

We will use the method of prime factorization to find the greatest common factor.

The prime factorization of 8x is:

8x = 2*2*2*x

The prime factorization of 40y is:

40y = 2*2*2*5*y

Therefore the common factors in both the terms are 2*2*2 which becomes 8

Thus the GCF of both the terms is 8....

Answer:

8

Step-by-step explanation:

Answer:

Step-by-step explanation:

AC is a midsegment of the trapezoid DFBE.

The formula of a midsegment of trapezoid is:

[tex]m=\dfrac{a+b}{2}[/tex]

a, b - bases of a triangle

We have

a = x, b = 4.4, m = 5.5

Substitute:

[tex]5.5=\dfrac{x+4.4}{2}[/tex]          multiply both sides by 2

[tex]11=x+4.4[/tex]       subtract 4.4 from both sides

[tex]6.6=x\to x=6.6[/tex]

Answer:

[tex]x < 10[/tex]

Step-by-step explanation:

[tex]2x - 8 < 12 \\ 2x - 8 + 8 < 12 + 8 \\( 2x < 20) \div 2 = x < 10[/tex]

x<10 is the solution to the inequality 2x - 8 < 12

To solve the inequality 2x - 8 < 12, you can follow these steps:

Add 8 to both sides of the inequality:

2x - 8 + 8 < 12 + 8

This simplifies to:

2x < 20

Divide both sides of the inequality by 2:

(2x)/2 < 20/2

This simplifies to:

x < 10

Therefore, the solution to the inequality 2x - 8 < 12 is x < 10.

Learn more about inequalities here:

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Answer:

[tex]\frac{-11}{25}+\frac{-27}{25}i[/tex] given you are asked to simplify

[tex]\frac{-3+5i}{-3-4i}[/tex]

Step-by-step explanation:

You have to multiply the numerator and denominator by the denominator's conjugate.

The conjugate of a+bi is a-bi.

When you multiply conjugates, you just have to multiply first and last.

(a+bi)(a-bi)

a^2-abi+abi-b^2i^2

a^2+0         -b^2(-1)

a^2+-b^2(-1)

a^2+b^2

See no need to use the whole foil method; the middle terms cancel.

So we are multiplying top and bottom of your fraction by (-3+4i):

[tex]\frac{-3+5i}{-3-4i} \cdot \frac{-3+4i}{-3+4i}=\frac{(-3+5i)(-3-4i)}{(-3-4i)(-3+4i)}[/tex]

So you will have to use the complete foil method for the numerator. Let's do that:

(-3+5i)(-3+4i)

First: (-3)(-3)=9

Outer::  (-3)(4i)=-12i

Inner: (5i)(-3)=-15i

Last: (5i)(4i)=20i^2=20(-1)=-20

--------------------------------------------Combine like terms:

9-20-12i-15i

Simplify:

-11-27i

Now the bottom (-3-4i)(-3+4i):

F(OI)L (we are skipping OI)

First:-3(-3)=9

Last: -4i(4i)=-16i^2=-16(-1)=16

---------------------------------------------Combine like terms:

9+16=25

So our answer is [tex]\frac{-11-27i}{25}{/tex] unless you want to seprate the fraction too:

[tex]\frac{-11}{25}+\frac{-27}{25}i[/tex]

Answer:

x = -1255

Step-by-step explanation:

336+x/5=85

Subtract 336 from each side

336-336 +x/5=85-336

x/5 =-251

Multiply each side by 5

x/5 * 5 = -251 *5

x = -1255

Check the picture below.

Answer:

[tex](d + 8m)^2[/tex]

Step-by-step explanation:

[tex]d^2 + 16dm + 64 m^2  = (d + 8m)^2[/tex]

d^2 + 16dm + 64m^2

64m^2 + 16dm + d^2

Note: This polynomial is already in lowest terms. It cannot be factored. Are you sure that you posted the entire, correct problem?

Answer:

It is C. Multiply each side by negative one over five , subtract 25 from each side.

Hope this helped you! :3

Answer:

D;Multiply each side by −5, add 25 to each side

Step-by-step explanation:

-1/5 (x − 25) = 7

To solve this equation, we will first multiply both-side of the equation by -5

-5 × -1/5(x-25) =7 × 5

(At the left-hand side of this equation, the  5 we multiplied will cancel the 5 at the denominator, leaving us with just '1' since negative multiply by negative is positive), Hence our equation becomes;

(x - 25) = 35

x - 25 = 35

Then the next thing to do is to add 25 to both-side of the equation in other to get the value of your x

x -25 + 25 = 35 + 25

x=60

Therefore,  option D is the correct sequence of operation to follow to enable you solve the equation.

Answer:

Either A or B.

Step-by-step explanation:

When shifting to the left you are adding to x.

Example: x^2 shifted to the left by 3. (x+3)^2

For this case we have that, by definition of horizontal translation of functions we have to:

We assume h> 0:

To graph[tex]y = f (x-h),[/tex] the graph moves, h units to the right.

To graph[tex]y = f (x + h)[/tex], the graph moves, h units to the left.

If we have the following function:

[tex]f (x) = x ^ 2 + 3x + 2[/tex]and move 2 units to the left, then:

[tex]f (x + 2) = g (x) = (x + 2) ^ 2 + 3 (x + 2) +2[/tex]

ANswer:

Option B

Answer: y=-ax(x-500)(x-1000)^2

Step-by-step explanation:

The behavior of the x-intercept of a graph is given by the multiplicity of the zero

The required polynomial for the coaster is, y = -a·x·(x - 500)·(x - 1000)²

Reason:

The question relates to the introduction of characteristics to the graph of a polynomial through knowledge of the effect of parameters of a polynomial

Known parameter:

Parent function is, y = a·x·(x - 1000)

The polynomial crosses the x-axis when (x - 500) is a factor of the polynomial, therefore, we have;

y = a·x·(x - 500)·(x - 1000)

Given that the graph is to initially rise, the leading coefficient is negative, therefore, we have;

y = -a·x·(x - 500)·(x - 1000)

For the polynomial to come in smoothly to stop at y = 0, when x = 1,000 we have that a turning point of the polynomial will be located at x = 1,000, this is given by introduction of a bump on the x-axis at x = 1,000 with a factor of (x - 1,000)²

Therefore, the required polynomial is y = -a·x·(x - 500)·(x - 1000)²

The height of the above polynomial is progressively smaller as x tends towards 1,000, given that the factors, (x - 500), and (x - 1,000), becomes smaller.

Learn more about the graph of polynomial functions here:

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Answer:

98.518 repeating prercent

Step-by-step explanation:

2 out of 135 can also be written as 2/135

2 divided by 135 is 0.014814814814

that number is the percentage of failures

100% in decimal form is 1.00

1.00 subtracted by the percentage of failures is the percentage of successes

which is .98518518518, 518 repeating move the decimal over 2 and you got the percentage 98.518 repeating

Answer:

The lectures cost is $7.33 per hour

Step-by-step explanation:

* Lets explain how to solve the problem

- For the level 3 course the examination hours cost twice as much

 as workshop hours

- The workshop hours cost twice as much as lecture hours

- There are examination hours , workshop hours and lecture hours

- There are 3 hr for examination, 24 hr for workshops and 12 hr

  for lectures

* Let the cost of the lecture hours is $x per hour

∴ The cost of the lecture hours is x per hour

∵ The cost of workshop hours is twice the cost of lecture hours

∴ The cost of the workshop hours is 2(x) = 2x per hour

∵ The cost of examination hours is twice the cost of workshop hours

∵ The cost of the workshop hours is 2x

∴ The cost of examination hours is 2(2x) = 4x per hour

- The cost of the level 3 is the sum of the costs of the lecture hours,

  workshop hours and examination hours

∵ There is 12 hours for lectures

∵ There is 24 hours for workshops

∵ There is 3 hours for examination

∵ The total cost of level 3 = 12(x) + 24(2x) + 3(4x)

∴ The total cost of level 3 = 12 x + 48 x + 12 x

∵ The total cost of level 3 = $528

∴ 12 x + 48 x + 12 x = 528

∴ 72 x = 528 ⇒ divide both sides by 72

∴ x = 7.33

∵ x is the cost of the lecture hours per hour

∴ The lectures cost is $7.33 per hour