Francis surveyed a random sample of 70 students at Franklin High School about their favorite season. Of the students surveyed, 18 chose fall as their favorite season. There are 1816 students at Franklin High School.

Answer:

9x + 8.

Step-by-step explanation:

2(x - 3) + 7(x + 2)

= 2x - 6 + 7x + 14

= 2x + 7x - 6 + 14

= 9x + 8.

Hope this helps!

Answer:

-8y +7x

Step-by-step explanation:

(–3y – x) – (5y – 8x)Distribute

-3y -x -5y +8x

Combine like terms

-3y-5y -x+8x

-8y +7x

Answer:

SSS

Step-by-step explanation:

I think it would be SSS (side, side, side)... let me know if I'm wrong and I'll try again:)

Check out the diagram below. I've marked the angles and sides that are congruent. Notice how the marked sides are not between the marked angles for either triangle. So we're dealing with AAS instead of ASA. The order is important. If we wanted to use ASA, then we would have to know DE = TU, both of those sides are between the marked angles.

Answer: Choice B) The conjecture is valid given the focus is on proportional equivalence of two sectors.

This is another way of saying "the two pie slices are the same percentage in area". By this, I mean the percentage of the entire cake. For instance, the shaded slice could be 20% of the entire circle area, for each circle.

It's probably easier to see this is the angle was 90 degrees (split the cake into 4 equal slices, only shade one slice). Or probably even easier if you cut the cake into two slices and only shade one slice (to form a central angle of 180 degrees). For the first example, the slice would be 25% of the whole area, while the second slice is 50%.

Choice C is close, but the two sectors are not the same area. This is because the bottom circle has a larger radius, and therefore its sector area is larger.

Answer:

3x - y = - 7

Step-by-step explanation:

The equation of a line in point- slope form is

y - b = m(x - a)

where m is the slope and (a, b) a point on the line

Here m = 3 and (a, b) = (- 2, 1) , thus

y - 1 = 3(x + 2) ← distribute

y - 1 = 3x + 6 ( subtract 6 from both sides )

y  - 7 = 3x ( subtract y from both sides )

- 7 = 3x - y, that is

3x - y = - 7 ← in standard form

Answer:

276

Step-by-step explanation:

∆y = 2y3

∆2 = 2(2)3 = 16

∆5 = 2(5)3 = 250

∆2 + ∆5 = 250 + 16 = 276

Answer:

The correct options are;

A. 120

B. 34

Step-by-step explanation:

The given parameters are;

Required to find how many of the permutations of 1, 2, 3, 4, 5, 6, have 1, 2, 3 arranged one after the other in the given order

Requirement to arrange 6 digits, 1, 2, 3, 4, 5, 6 in the order such that 1, 2, and 3 always appear in turn, they are as follows

When the first digit is 1, and the 2nd digit is 2 the number of ways of selecting the other  digits is 24

Arrangement,                                              Number of ways

1, 2, 3, 4, 5, 6,                                               24

1, 4, 2,                                                            18

1, 4, 5, 2,                                                        12

1, 4, 5, 6, 2,                                                     6

4, 1, 2,                                                             18

4, 1, 5, 2,                                                         12

4, 1, 5, 6,                                                         6

4, 5, 1, 2,                                                         12

4, 5, 1, 4, 2                                                      6

4, 6, 5,                                                            6

Total = 24 + 18 + 12 + 6 + 18 + 12 + 6 + 12 + 6 + 6 = 120 ways

The correct option is A. 120

2. The dimensions of the original rectangle = L by W

The dimensions of the lager rectangle = 1.5·L by 2·W

1.5·L × 2·W = 30

Given that L > W

∴ L×W = 30/(1.5 × 2) = 30/3 = 10

The possible integers that have a product of 10 are;

1 × 10 and 5 × 2

Therefore, since L > W, The dimensions of the larger rectangle are either 15 by 2 or 7.5 by 4

Which gives the perimeters as 2*(15 + 2) = 34 or 2*(7.5 + 4) = 23

Therefore, the largest possible rectangle is 34

The correct option is B. 34.

Answer:

The correct options are;

A. 120

B. 34

Step-by-step explanation:

The given parameters are;

Required to find how many of the permutations of 1, 2, 3, 4, 5, 6, have 1, 2, 3 arranged one after the other in the given order

Requirement to arrange 6 digits, 1, 2, 3, 4, 5, 6 in the order such that 1, 2, and 3 always appear in turn, they are as follows

When the first digit is 1, and the 2nd digit is 2 the number of ways of selecting the other  digits is 24

Arrangement,                                              Number of ways

1, 2, 3, 4, 5, 6,                                               24

1, 4, 2,                                                            18

1, 4, 5, 2,                                                        12

1, 4, 5, 6, 2,                                                     6

4, 1, 2,                                                             18

4, 1, 5, 2,                                                         12

4, 1, 5, 6,                                                         6

4, 5, 1, 2,                                                         12

4, 5, 1, 4, 2                                                      6

4, 6, 5,                                                            6

Total = 24 + 18 + 12 + 6 + 18 + 12 + 6 + 12 + 6 + 6 = 120 ways

The correct option is A. 120

2. The dimensions of the original rectangle = L by W

The dimensions of the lager rectangle = 1.5·L by 2·W

1.5·L × 2·W = 30

Given that L > W

∴ L×W = 30/(1.5 × 2) = 30/3 = 10

The possible integers that have a product of 10 are;

1 × 10 and 5 × 2

Therefore, since L > W, The dimensions of the larger rectangle are either 15 by 2 or 7.5 by 4

Which gives the perimeters as 2*(15 + 2) = 34 or 2*(7.5 + 4) = 23

Therefore, the largest possible rectangle is 34

The correct option is B. 34.

Answer:

tan 50 = (51+10)/x where x is the distance of the boat

x = 51.2 m  

Boat is in an unsafe area

Step-by-step explanation:

<3

Answer: If point B is on the same line and the same distance from points A and C,  the location is (-1.5, 4,5)

Step-by-step explanation: For point B to be the same distance from the other two points, it must be halfway between them.

for the x-value, find the number that is halfway between 0 and -3. That is -1.5

For the y-value, find the number that is halfway between 4 and 5. That is 4.5

The coordinate for point B is (-1.5, 4.5)

Answer:

add the y coordinates of the two lines and divide by 2

Step-by-step explanation:

½[0+(-12)]

½[0-12]

½[-12)

y co-ordinate of the midpoint is -6

6.

[tex]y^2\sqrt[8]{8}[/tex]

Step-by-step explanation:

[tex]\sqrt[8]{8*y*y*y*y*y*y*y*y*y*y*y*y*y*y*y*y}[/tex]

Since there are eight y's in two groups we can take them out which turns into

[tex]y^2\sqrt[8]{8}[/tex]

:)

3.

Problem 3:

We are given the following complex number and I'm assuming we want to simplify it:

[tex]\dfrac{5+i}{6+i}[/tex]

Using the complex arithmetic rule (research about this if you're not familiar with it, it's very helpful):

[tex]=\dfrac{(5\times6+1)+(6-5)i}{6^2+1^2}[/tex]

[tex]=\dfrac{31+i}{37}[/tex]

Simplifying gives us:

[tex]=\dfrac{31}{37}+\dfrac{1}{37}i[/tex]

Problem 6:

You seem to have done this problem correctly

[tex]\sqrt[8]{8y^{16}}[/tex]

Expanding gives us:

[tex]=\sqrt[8]{y^{16}}\times\sqrt[8]{8}[/tex]

[tex]=y^2\sqrt[8]{8}[/tex]

This can't be simplified further as the 8th root of 8 gives us an irrational number

Let me know if you need any clarifications or extra help, thanks!

The number 3.14159265 produces an irrational number when added to 1/2.

The sum of any rational number and any irrational number will be always an irrational number.

An irrational number is a type of real number which cannot be represented as a simple fraction.

A number that can be represented as the quotient p/q of two integers such that q ≠ 0 is called a rational number.

According to the given question

We have a rational number 1/2.

Since, 0.373737373.... is a rational number because it is recurring and its behavior it known that 37 is repeating.

And we know that when any rational number is added with a rational number it with number we will get always a rational number.

⇒ 0.3737373737... + [tex]\frac{1}{2}[/tex] = rational number.

3.14159265... is an irrational number because its behavior is not known and it is not terminating.

So, when we add 1/2 to 3.14159265.. we get a irrational number.

√16 = 4 is a rational number. And it can be written as [tex]\frac{4}{1}[/tex].

So, [tex]\frac{4}{1} + \frac{1}{2} = \frac{9}{2}[/tex] which is a rational number.

-4/7 is a rational number. And when we add 1/2 to -4/7 we get a rational number.

i.e. [tex]\frac{-4}{7} + \frac{1}{2} = \frac{-1}{14}[/tex] which is rational number.

Hence, the number 3.14159265 produces an irrational number when added to 1/2.

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The answer would be x =7/5 because you would need to multiply everything by two. Then you would add 4+3 and you would end up with 5x = 7. After that, you need to divided both answers by five

Please Mark brainliest

Answer:

The answer is x=7/5

Step-by-step explanation:

because you have to multiply everything by 2 the add 4+3 and you end up with 5x=7 then divide both sides by 5

Answer:

216 cubic inches

Step-by-step explanation:

We want to simplify:

102 * 4 - 3(8 * 8 * 1)

We will apply BODMAS:

Solving the Bracket first:

102 * 4 - 3(64)

102 * 4 - 192

=> 408 - 192

= 216 cubic inches

He will need 216 cubic inches of packing foam.

Answer:

y = ∛(x+3) + 3

Step-by-step explanation:

I plugged each equation into a graphing calculator.

Answer:

(squareroot2^2) times 27 (1/2)

Step-by-step explanation:

Answer:3z^2/9

Step-by-step explanation:

Answer:

(-6, 0) and (2, 0)

Step-by-step explanation:

To find the x-intercepts, we can factor the expression:

f(x) = x² + 4x - 12

2 factors of -12 that add up to 4 are 6 and -2

(x + 6)(x - 2)

Set each factor equal to 0 and solve for x:

x + 6 = 0

x = -6

x - 2 = 0

x = 2

So, the x intercepts are (-6, 0) and (2, 0)

Answer:

It's the first option, (-6, 0) (2, 0)

Step-by-step explanation:

100% on Edge

Answer: x + y = 16. 0.10 x + 0.25 y = 2.95. x + y = 16.

Step-by-step explanation:

You know that there are 16 coins in all, so x + y has to equal 16 (x being dimes and y being quarters) but you also know that whatever compilation of dimes and quarters is equal to $2.95.

Hope this helped you! Feel free to ask any further questions!

The system of equations which represents the number of dimes and quarters that Hamid has are x+y=16 and 0.10x+0.25y=2.95.

Equation is relationship between two or more variables that are expressed in equal to form. Equation of two variables look like ax+by=c. It is of many types like linear equation, quadratic equation, cubic equation, etc.

Suppose  the number of dimes be x and the number of quarters be y.

According to question there are 16 coins, so

x+y=16-----1

1 dime=$0.10

1 quarter=$0.25

According to question Hamid has $2,95 ,so

0.10x+0.25y=2.95.

Hence the system which represents the number of dimes and quarters that Hamid has are x+y=16 and 0.10x+0.25y=2.95.

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Answer:

(x-4)²+4

Step-by-step explanation:

Answer:

[tex](x-4)^2+4[/tex]

Step-by-step explanation:

[tex]x^2 - 8x + 20\\**********************************\\\frac{8}{2} =( 4 )^2 = 16 \\\\20 - 16 = 4\\**********************************\\x^2 - 8x + 16 + 4\\(x-4)^2+4[/tex]

Answer:

$180

Step-by-step explanation:

100%=x

35%=$63

63 x 100=6300/35=$180

Answer:

96.92

Step-by-step explanation:

If the backpack was 35% off  you will  still pay 100 -35 or 65%

Let x be the original price

x * 65% = 63

Change to decimal form

x * .65 = 63

Divide each side by .64

x*.65/.65 = 63/.65

x =96.92

Answer:

B

Step-by-step explanation:

you can FOIL or set up a box that is 3 x 3 (which is what I recommend) to solve it.

The product of the given polynomials is [tex]16x^4 +16x^3 -12x^2-32x-16[/tex]. The correct option is- B. [tex]16x^4 +16x^3 -12x^2-32x-16[/tex]

From the question, we are to determine the product of the given polynomials

The given polynomials are

(8x^2-4x-8) (2x^2+3x+2)

Their product can be determined as follows

[tex](8x^2-4x-8) (2x^2+3x+2)[/tex]

[tex](8x^2) (2x^2+3x+2)-4x(2x^2+3x+2)-8 (2x^2+3x+2)[/tex]

Clear the brackets

[tex]16x^4 +24x^3+16x^2 -8x^3-12x^2-8x-16x^2-24x-16[/tex]

Now, collect like terms

[tex]16x^4 +24x^3 -8x^3-12x^2+16x^2-16x^2-8x-24x-16[/tex]

Simplifying

[tex]16x^4 +16x^3 -12x^2-32x-16[/tex]

Hence, the product of the given polynomials is [tex]16x^4 +16x^3 -12x^2-32x-16[/tex]. The correct option is- B. [tex]16x^4 +16x^3 -12x^2-32x-16[/tex]

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Answer:

Step-by-step explanation:

Let the three numbers be a-d, a, a+d being a series in AP.

The sum of the three numbers is 24 = a-d+ a+ a+d = 3a

Thus a = 8.

Now a-d-1, a-2, a+d form a GP. It means, the common ratios should be equal or the middle term should be the Geometric Mean of the first and third terms, or

(a-d-1)(a+d) = (a-2)^2 or

(8-d-1)(8+d) = (8-2)^2, or

(7-d)(8+d) = 36, or

56 -8d +7d -d^2 = 36, or

56 -8d +7d -d^2 - 36 = 0, or

d^2 +d -20 = 0

(d+5)(d-4) = 0

Thus d = -5 or 4

So the AP is 13,8,3 or 4,8,12

Check: 13,8,3 in AP becomes (13–1), (8–2), 3 = 12, 6, 3 which is a GP with r = (1/2)

4,8,12 in AP becomes (4–1), (8–2), 12 = 3, 6, 12 which is a GP with r =2

Answer: [tex]10\frac{2}{3}\pi[/tex]

Step-by-step explanation:

Do you really need it? If so, reply, if not, mark brainliest.

Answer:

the value of n will be the range

Step-by-step explanation:

lets just give an example of (9,n) and you had to find the value its actually simple

9 is the domain

n is the range

a part of ordered pair function

got it?

Answer:

Factors: 5x, 3x²y⁵   Not Factor: 10x⁴y³

Step-by-step explanation:

5x is a factor because 15x²y⁶= 5x•3xy⁶

3x²y⁵ is a factor because 15x²y⁶ = 3x²y⁵•5y

10x⁴y³ isn't a factor because 15:10=1.5 isn't integer

Answer:

The answer is

Step-by-step explanation:

Equation of a line is y = mx + c

where

m is the slope

c is the y intercept

12x - 5y = 2

5y = 12x - 2

Divide both sides by 5

y = 12/5x - 1/5

Comparing with the above formula

Slope / m = 12/5

Since the lines are parallel their slope are also the same.

Slope the parallel line = 12/5

Equation of the line using point (2,3) is

[tex]y - 3 = \frac{12}{5} (x - 2) [/tex]

Multiply through by 5

That's

5y - 15 = 12(x - 2)

5y - 15 = 12x - 24

We have the final answer as

Hope this helps you

Answer:

5 units apart.

Step-by-step explanation:

You can figure this out by:

a- You can count the squares in between the two points.

                                               OR

b- You would find the absolute value of both the x  values and add them together to see the overall length from each other that they are.

So when you complete either one of these tactics you would get an answer of  5 units apart.

Answer:

13

Step-by-step explanation:

We have:

8a^2 + 2b^2 = 10

Dividing both sides by 2,

=> 4a^2 + b^2 = 5

or (2a)^2 + b^2 = 5

We also have ab = 2

=> (2a + b)^2

= (2a)^2 + 2(2a)(b) + b^2

= (2a)^2 + b^2 + 4ab

= 5 + 4(2)

= 5 + 8

= 13

Answer:

f(x) = x2 – 10x + 21

Step-by-step explanation:

I got it because you substract and add the last part

Answer: -1/1

Step-by-step explanation: The fraction, -1/1 or just -1, passes through the transactional point through the slope of the line, y=3x+5.