On a boat tour there are half as many children as there are adults. There are 30 people on the tour. How many children are there?

Answer/Step-by-step explanation:

1. 7x + 2 = 5x + 22 (alternate interior angles are congruent)

Collect like terms

7x - 5x = -2 + 22

2x = 20

2x/2 = 20/2

x = 10

2. 13x - 6 = 10x + 24 (alternate interior angles are congruent)

Collect like terms

13x - 10x = 6 + 24

3x = 30

3x/3 = 30/3

x = 10

3. (12x + 26)° + 46° = 180° (same side interior angles are supplementary)

12x + 26 + 46 = 180

12x + 72 = 180

12x + 72 - 72 = 180 - 72

12x = 108

12x/12 = 108/12

x = 9

4. (5x + 5)° + 135° = 180° (same side interior angles are supplementary)

5x + 5 + 135 = 180

5x + 140 = 180

5x + 140 - 140 = 180 - 140

5x = 40

5x/5 = 40/5

x = 8

Answer:

No, similar triangles cannot contain a pair of parallel lines. Yes, because || . Yes, because ∠QUR ≅ ∠TUS (vertical angles) and ∠R ≅ ∠S (alternate interior angles).

Step-by-step explanation:

Yes, because ∠QUR ≅ ∠TUS (vertical angles) and ∠R ≅ ∠S (alternate interior angles).

Two triangles are similar if they have the same ratio of corresponding sides and equal pair of corresponding angles.

Both triangles are similar as,

∠QUR ≅ ∠TUS (vertical angles)

∠R ≅ ∠S (alternate interior angles).

So, By AA similarity criteria triangles are similar.

Learn more about similarity here:

https://brainly.com/question/17170212

#SPJ5

Answer:

[tex]\frac{x - 20}{ x^2 + x - 20} = \frac{5}{9(x-4)}+\frac{4}{(x+5)}[/tex]

Step-by-step explanation:

Given

[tex]\frac{x - 20}{ x^2 + x - 20}[/tex]

Required

Decompose into partial fraction

Start by factorizing the denominator:

[tex]x^2 + x - 20 =x^2 + 5x -4x- 20[/tex]

[tex]x^2 + x - 20 =x(x + 5)-4(x+5)[/tex]

[tex]x^2 + x - 20 =(x-4)(x+5)[/tex]

So, we have:

[tex]\frac{x - 20}{ x^2 + x - 20} = \frac{A}{x-4}+\frac{B}{x+5}[/tex]

Take LCM

[tex]\frac{x - 20}{ x^2 + x - 20} = \frac{A(x+5)+B(x-4)}{(x-4)(x+5)}[/tex]

Cancel out the denominator

[tex]x - 20 = A(x+5)+B(x-4)}[/tex]

Open brackets

[tex]x - 20 = Ax+5A+Bx-4B[/tex]

Collect Like Terms

[tex]x - 20 = Ax+Bx+5A-4B[/tex]

[tex]x - 20 = (A+B)x+5A-4B[/tex]

By comparison;

[tex](A +B)x = x[/tex] ==>[tex]A + B = 1[/tex]

[tex]5A - 4B = 1[/tex]

Make A the subject in [tex]A + B = 1[/tex]

[tex]A = 1 - B[/tex]

Substitute 1 - B for A in [tex]5A - 4B = 1[/tex]

[tex]5(1-B) -4B = 1[/tex]

[tex]5-5B -4B = 1[/tex]

[tex]5-9B = 1[/tex]

Collect Like Terms

[tex]-9B = 1 - 5[/tex]

[tex]-9B = - 4[/tex]

[tex]B = \frac{4}{9}[/tex]

[tex]A = 1 - B[/tex]

[tex]A = 1 - \frac{4}{9}[/tex]

[tex]A = \frac{9-4}{9}[/tex]

[tex]A = \frac{5}{9}[/tex]

So:

[tex]\frac{x - 20}{ x^2 + x - 20} = \frac{A}{x-4}+\frac{B}{x+5}[/tex]

[tex]\frac{x - 20}{ x^2 + x - 20} = \frac{5}{9(x-4)}+\frac{4}{(x+5)}[/tex]

Answer:12

Step-by-step explanation:

Answer:

12

Step-by-step explanation:

Answer:

160 cans for 5 pounds of aluminum

Step-by-step explanation:

Answer:

C. Get it by itself

Step-by-step explanation:

When solving for a variable, whether it be an inequality, a factor, or an algebraic expression. Getting the specified variable by itself is the most effective and best way to get that answer to your question. The other two answers here do not make any sense whatsoever.

Answer:

A. 29.1020

Step-by-step explanation:

Rewrite it:

29°6'6"

29° + 6(1/60)° + 6(1/3600)°

Simplify:

29° + 0.1° + 0.002°

= 29.102

So, the correct answer is A, 29.1020

117°

same side interior angles theorem

Answer:

-1/8   <----- FRACTION

Step-by-step explanation:

Answer and Step-by-step explanation:

31 degrees on the top would be equal to the angle in between x and 600ft, by the interior angles theorem.

That means we can solve for y using the trigonometric function of tangent.

[tex]tan(31) = \frac{y}{600}[/tex]

Multiply by 600 to both sides, then use a calculator to solve.

600(tan(31)) = x

x = 360.5163714

x ≈ 360.5 is the answer.

Answer:$1312.5

Step-by-step explanation:

1500x1.875=2812.5

2812.5-1500=1312.5

Answer:

224 feet^3

Step-by-step explanation:

Cube -> Volume = 4×7×7 = 196 feet^3

Prism -> Volume = 2×7×2 = 28 feet^3

196+28=224

Answer:

B = 68

Step-by-step explanation:

(6-2)×180 = 720

69+108+135+204+b+2b=720

516+3b=720

3b=720-516

3b=204

b= 68

Step-by-step explanation:

4+12x=7

12x=7-4

12x=3

X=3/12

X=0.25

Answer:

Assuming that you mean 1/6, the answer would be 3 .

Step-by-step explanation:

1/6 x 18 is equal to three.

Answer:

-2

Step-by-step explanation:

Integers can be positive or negative.

Answer:

in 136 miles=7 gallons

?=42 gallon

= 136=7

?=42

cross multiply

136×42=5,712

=5,712÷7=816

Answer:

816 miles

Step-by-step explanation:

136miles/7 g =19.43

19.43 x 42 ≅ 816.06

or

136/7 = X/42

solve for X

42/7 =6, then 136 x6= 816

x = 816 miles

Answer:

5 for $4.45

Step-by-step explanation:

Answer:

Step-by-step explanation:

[tex]\text{By the Pythagorean Theorem the hypotenuse of a right triangle squared is equal to the sum of the squared sides.}\\ \\ h^2=x^2+y^2\\ \\ 33^2=31^2+x^2\\ \\ x^2=33^2-31^2\\ \\ x^2=128\\ \\ x=\sqrt{128}\\ \\ x\approx 11.3m[/tex]

Answer:

the sencond and the last one

Answer:

125 • 125

Step-by-step explanation:

5⁶ = 5 × 5 × 5 × 5 × 5 × 5 = 15,625

125 • 125 = 15,625

They give the same result so both expressions are equivalent to each other.

Answer:

Option (C)

Step-by-step explanation:

Given inequalities are,

81 > x and x > 68

Therefore, 81 > x > 68 is the inequality representing the solution area for x.

Out of x = 88, 85 and 80,

x = 80 will lie between the range of x = 68 and x = 81.

Therefore, Option (C) will be the correct option.

9514 1404 393

Answer:

  neither

Step-by-step explanation:

A polynomial consisting of even-degree terms only is even.

A polynomial consisting of odd-degree terms only is odd.

The given f(x) polynomial has both even- and odd-degree terms, so is neither.

Answer:

11 / 20

Step-by-step explanation:

16 / 20 - 1×5 / 4×5

16 / 20 - 5 / 20

16 - 5 / 20

= 11 / 20

Answer:

4 different odd integers:  25, 45, 55, 85

Step-by-step explanation:

SLOPE INTERCEPT FORM: y = 7x −23

Answer: 420

Step-by-step explanation:

I took the test and got it right lol

Answer:

27 feet

Step-by-step explanation:

There are 3 feet in 1 yard. 9×3=27

Answer:

-6xy-18x

Step-by-step explanation:

To solve -2x(3y+9), multiply -2x by 3y and 9.

Solve

Answer:

-24 i think

Step-by-step explanation:

Answer:

$77,886

Step-by-step explanation:

We solve this question by proportions, using a rule of three.

The table states that:

$201.6 in 2006 is worth $232.957 in 2013.

We want to find:

The value of $90,000 in 2013 in 2006:

$201.6 - $232.957

x - $90000

Applying cross multiplication

[tex]232957x = 201.6*90000[/tex]

[tex]x = \frac{201.6*90000}{232957}[/tex]

[tex]x = 77886[/tex]

$77,886 is the answer