Tickets to see a movie cost $5 for children and $8 for adults. The equation 5x + 8y = 80 represents the number of children (x) and adults (y) who can see the movie with $80.
If no adults see the movie, how many children can see the movie with $80?

Angle 8 and angle 5 are vertical angles

4 triangles can be created with 3 points on a line.

20 triangles can be created with 6 points on a line.

30 triangles can be created with 7 points on a line.

Combination has to do with selection.

Note that a triangle has 3 vertices. If there are 4 points on a line, the number of triangles it is possible to create is derived using the combination formula shown as:

[tex]nC_r=\frac{n!}{(n-r)!r!}[/tex]

[tex]4C_3 = \frac{4!}{(4-3)!3!}\\4C_3 =\frac{4\times3!}{3!}\\4C_3=4triangles[/tex]

This means that 4 triangles can be created with 3 points on a line.

For a line with 6 points:

[tex]6C_3 = \frac{6\times 5\times 4\times 3!}{(6-3)!3!}\\6C_3 =\frac{6\times5\times 4\times3!}{3!3!}\\4C_3=20triangles[/tex]

This shows that 20 triangles can be created with 6 points on a line.

For a line with 7 points:

[tex]7C_3 = \frac{7\times 6\times 5\times 4!}{(7-3)!3!}\\4C_3 =\frac{7\times6\times 5\times4!}{4!3!}\\4C_3=30triangles[/tex]

This shows that 30 triangles can be created with 7 points on a line.

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Answer:

hsoabajakahaknanaKambaKla

Answer:

1) = 90=acute angle   2)103=acute angle

Step-by-step explanation:

Answer:

1.) x = 90 (Right angle)

2.) x = 103 (Obtuse angle)

Step-by-step explanation:

[tex]1.)\\x+48+42=180\\x+90=180\\x=90\\\\2.)\\x+45+32=180\\x+77=180\\x=103[/tex]

Answer:

4500 cm²

Step-by-step explanation:

10 mm = 1 cm

So 450 × 10

= 4500 cm²

Answer:

g(

x

2

−

3

)

=

2

x

2

−

7

Step-by-step explanation:

brainliest

Answer:

34 hours

Step-by-step explanation:

Lets call M the number of hours that Maddie volunteered. Ryan volunteered 1 + 3×M hours, and altogether they volunteered 45 hours, so:

1 + 3×M + M = 45

1 + 4M = 45 Subtract 1 in both sides

4M = 44 Divide both sides by 4

M = 11 hours

So Maddie volunteered 11 hours, and Ryan volunteered

1 + 3×11 = 34 hours

Answer: The answer is 18x + 26

Step-by-step explanation:

What I did was simplify the Expression of (3x+8)+6(2.5x-3) then combine the terms and last evaluate the Expression.

Answer:

35 / 9.99 = can buy 4 rounded

paragraph: To find how many pairs of shorts we can buy, we must divide our total money with the cost. We are diving because we need to find how many times 35 can go into 9.99 to find our number. 35 / 9.99 = 3.5035035035035. Our answer must be rounded now because shorts are in whole numbers and can't be in decimals. Take the tenth place of the decimal and round it to the nearest number. 5 is closer to 10 than 0 so we just round it to 4 and there is our answer.

10- 9

11- 5

12- 1

13- 10

14- 3

15- 7

16- 3

17- 3

18- 6

Step-by-step explanation:

4a)

the principle of similar triangles : they have the same angles.

and we do not forget : the sum of all angles in a triangle is always 180 degrees.

a = 180 - 65 - 45 = 70 degrees

b = 65 degrees

c = 70 degrees

b)

same principles.

x = 58 degrees

y = 52 degrees

z = 180 - 58 - 52 = 70 degrees

c)

same principles.

plus the fact that complementary angles around a point on one side of a line are also together 180 degrees.

x = 85 degrees

y = 180 - 40 - 85 = 55 degrees

z = 180 - 85 = 95 degrees

d)

again same principles.

y = 2x (as these 2 angles correspond to each other among the 2 similar triangles).

the angle POQ is again complementary with 87 degrees,

POQ = 180 - 87 = 93 degrees

x + y + 93 = x + 2x + 93 = 180

3x = 87

x = 29 degrees

y = 2x = 2×29 = 58 degrees

The value of the function if the independent variable is equal to -1 is -2

Given the function p(x) = x^3 - 1

The input variable "x" is the independent variable. If the independent variable is equal to -1, the value of the function will be expressed as:

P(-1) = (-1)^3 - 1

P(-2) = -1 -1

P(-2) = -2

Hence the value of the function if the independent variable is equal to -1 is -2

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Answer:b- 4,000

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

It is B because

4000-800=3200

then

3200+800=4000

so he answer is B.4000  

Answer:

[tex]{ \rm{ \sqrt{32} = \sqrt{2 \times 16} }} \\ \\ = { \rm{ \sqrt{2 \times 4 \times 4} }} \\ \\ = { \rm{ \sqrt{2} \times( \sqrt{4}) {}^{2} }} \\ \\ = { \rm{ \sqrt{2} \times 4 }} \\ \\ = { \rm{4 \sqrt{2} }} \\ \\ { \rm{ \sqrt{32} = 5.656854....}} \\ \\ { \boxed{ \rm{ \sqrt{32} = 5.66 \: }}}[/tex]

9514 1404 393

Answer:

  5.66

Step-by-step explanation:

For an integer x = s² +r, where s and r are also integers, a first approximation of the square root of x will be ...

  y = √x ≈ s +r/(2s+1)

An iterative improvement on the estimate can be had by ...

  y' = s + r/(s +y)

Here, this means a first estimate can be obtained as ...

  32 = 5² +7   ⇒   s = 5, r = 7

  √32 ≈ y1 = s +r/(2s +1) = 5 7/11

Then an iterative improvement will be ...

  y2 = s +r/(s +y1) = 5 +7/(10 7/11) = 5 77/117 ≈ 5.658 ≈ 5.66

_____

Additional comment

The above iterator will add about 1 decimal place for each iteration. The Babylonian method will roughly double the number of good decimal places with each iteration. For an approximate root of p/q, the next iteration using that method would be ...

  p'/q' = (x·q² +p²)/(2pq)

Then our above estimate of 5 7/11 for the root of 32 would be refined to ...

  p'/q' = (32·11² +62²)/(2·11·62) = 7716/1364 = 5 224/341 ≈ 5.65689.... This compares favorably to the first digits of the actual root: 5.65685....

Answer:

-18/29

Step-by-step explanation:

54 ÷ 3 = 18 - numerator

84 ÷ 3 = 29 - denominator

-54/84 = -18/29

Answer:

423

Step-by-step explanation:

123423

The constant speed for the given distance and time is 123/2 miles/hour.

Given that, Andrea drove [tex]20\frac{1}{2}[/tex] miles in 1/3 of an hour at constant speed.

The speed formula can be defined as the rate at which an object covers some distance. Speed can be measured as the distance travelled by a body in a given period of time. The SI unit of speed is m/s.

Here, [tex]20\frac{1}{2} = \frac{41}{2}[/tex]

Now, speed = Distance ÷ Time

= 41/2 ÷ 1/3

Change division to multiplication and reciprocal the fraction

That is, 41/2 × 3/1

= 123/2 miles/hour

Therefore, the constant speed for the given distance and time is 123/2 miles/hour.

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#SPJ2

Answer:

1/5

Step-by-step explanation:

[tex]\lim_{x->4} \frac{x-4}{x^{2}-3x-4 } \\= \lim_{x->4} \frac{x-4}{(x+1)*(x-4) } \\\\= \lim_{x->4} \frac{1}{(x+1) } \\\\\\[/tex]

lim x->4   plug in x=4

1/(x+1) = 1/(4+1) = 1/5

Answer:

x= 3/7 i.d.k if this is correct I did it in my brain

Answer:

Your answer should be C

Step-by-step explanation:

Answer:

3x - 2y = -18

Step-by-step explanation:

3x - 2y = -18 and (-2, 6)

(3)(-2) - (2)(6) = -6 - 12 = -18

Answer:

y = 150º

Step-by-step explanation:

The sum of internal angles of a triangle must be 180º and the sum of y + (x-20) forms a straight line which is also 180º, so:

2x + x + (x - 20) = 180

4x - 20 = 180

4x = 200

x = 50

x - 20 = 50 - 20

x - 20 = 30

y = 180 - 30

y = 150º

Answer:

60%

Step-by-step explanation:

You could make a fraction to help solve for the answer. The denominator is 25 because you add 4 + 15 + 6. The numerator is 15, because it is the number of roses. 15/25 as a percent is 60% because you just times both the numerator and denominator by 4.

Answer:

[tex]12x^{2} -11x-5[/tex]

Step-by-step explanation:

1) Distribute

[tex]4x(3x-1)-2(3x+1)-(x+3)\\12x^{2} -4x-2(3x+1)-(x+3)[/tex]

2) Distribute

[tex]12x^{2} -4x-2(3x+1)-(x+3)\\12x^{2} -4x-6x-2-(x+3)[/tex]

3) Distribute

[tex]12x^{2} -4x-6x-2(x+3)\\12x^{2} -4x-6x-2-x-3[/tex]

4) Subtract the numbers

[tex]12x^{2} -4x-6x-2-x-3\\12x^{2} -4x-6x-5-x[/tex]

5) Combine like terms

[tex]12x^{2} -4x-6x-5-x\\12x^{2} -11x-5[/tex]

→ You will pay $ 89.7.

The tip value is based on the bill value. Hence, to find the total payment you have to multiply 78 by 1.15 (this includes the tip, 1.15).

[tex]\Large \text {$Total = 78 \times 1.15 = 89.7 $}[/tex]

Or you can first find how many 15% is from $78:

[tex]\Large \text {$0.15 \times 78 = 11.7$}[/tex]

And then add this to $78:

[tex]\Large \text {$78 +11.7 = 89.7$}[/tex]

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Answer:

$89.70

Step-by-step explanation:

15/100=0.15

78 * 0.15 =89.70

Multiply to get the answer:

Convert to scientific notation and find the ratio of the second number by the first:

Divide:

Answer:

5 houses

Step-by-step explanation:

She needs to visit 5 houses as 20 divided by 4 is 5