Find the diagonal of the box using the Pythagorean Theorem.

Given:

The total admission price for a group of 4 adults and 10 children is $57.

The total admission price for a group of 3 adults and 7 children is $41.

To find:

The admission prices for an adult and for a children.

Solution:

Let the price of an adult be x and price of children be y.

According to the question,

[tex]4x+10y=57[/tex]         ...(i)

[tex]3x+7y=41[/tex]      ...(ii)

Multiply equation (i) by 3.

[tex]12x+30y=171[/tex]         ...(iii)

Multiply equation (i) by 4.

[tex]12x+28y=164[/tex]      ...(iv)

Subtract (iv) from (iii).

[tex]12x+30y-12x-28y=171-164[/tex]

[tex]2y=7[/tex]

Divide both sides by 2.

[tex]y=3.5[/tex]

Put y=3.5 in (i).

[tex]4x+10(3.5)=57[/tex]

[tex]4x+35=57[/tex]

[tex]4x=57-35[/tex]

[tex]4x=22[/tex]

Divide both sides by 4.

[tex]x=5.5[/tex]

Therefore, the price for an adult is $5.5 and price for a child is $3.5.

Answer:

120°

Step-by-step explanation:

[tex]m\angle S = 180\degree - 2\times 30\degree \\\\

m\angle S = 180\degree - 60\degree \\\\

\huge\purple {\boxed{m\angle S = 120\degree}} [/tex]

Answer:

53

Step-by-step explanation:

move 82 down next to (2x-8)

if 82+2x-8 is 180, x is 53

Answer:

2x-8=98

2x=106

×=53 is the right answer

Answer:

f(-5)= -2

f(0) =  3

f(3) = 6

Step-by-step explanation:

f(x) = x + 3

f(-5) = -5 + 3

= -2

f(0) = 0 + 3

=3

f(3) = 3 + 3

=6

Answer:

216$

Step-by-step explanation:

Answer:

41.2%

Step-by-step explanation:

[tex]Percentage\ change = (\frac{Final\ Price\ - Initial\ Price}{Final\ Price})100\\\\Percentage\ change=(\frac{238-140}{238})100\\\\Percentage\ change=(\frac{98}{238})100\\\\Percentage\ change=(0.412)100\\Percentage\ change=41.2\\[/tex]

So the percentage increase was 41.2%

Answer:  k = 3

Step-by-step explanation:

1

Combine multiplied terms into a single fraction

4

.

5

+

1

.

5

Answer:

Thr33

Step-by-step explanation:

3

Answer:

D. Every rational number is also an integer

Step-by-step explanation:

Some rational numbers are integers, but not all of them

Answer:

C

Step-by-step explanation:

The terms with the same variable are like terms.

9514 1404 393

Answer:

  C.  greater than 180°

Step-by-step explanation:

Arcs are classified as "major" or "minor" depending on whether they are more or less than half a circle. A major arc is more than half a circle so is greater than 180°.

Answer:

A

Step-by-step explanation:

Answer:

The answer is choices C.

Step-by-step explanation:

Let's solve your inequality step-by-step.

2x+8<3x−4

Step 1: Subtract 3x from both sides.

2x+8−3x<3x−4−3x

−x+8<−4

Step 2: Subtract 8 from both sides.

−x+8−8<−4−8

−x<−12

Step 3: Divide both sides by -1.

−x/-1<−12/-1

x>12

Answer:

(f - g)(x) = -x² + 3x + 5

General Formulas and Concepts:

Pre-Algebra

Algebra I

Step-by-step explanation:

Step 1: Define

f(x) = 3x + 5

g(x) = x²

(f - g)(x) is f(x) - g(x)

Step 2: Find (f - g)(x)

Answer:12x^3y^5

Step-by-step explanation:

Answer:

[tex]\huge\boxed{12x^3y^5}[/tex]

Step-by-step explanation:

[tex]4x^2y^3\times3xy^2=(4\cdot3)(x^2\cdot x)(y^3\cdot y^2)=12x^{2+1}y^{3+2}=12x^3y^5[/tex]

Answer:

189 cm²

Step-by-step explanation:

The area (A) of a rhombus is calculated as

A = [tex]\frac{1}{2}[/tex] × product of diagonals

   = [tex]\frac{1}{2}[/tex] × 18 × 21 = 9 × 21 = 189 cm²

Answer:

$19.2

Step-by-step explanation:

The school mascot is rectangular in nature.

Perimeter P = 2(L+W)

L is the length = 4feet

W is the width = 12 feet

Perimeter = 2(4+12)

Perimeter = 2(16)

Perimeter  = 32 feet

Convert to inches

12in = 1feet

x = 32 feet

Cross multiply

x = 12 * 32

x = 384in

Hence the perimeter of the school mascot is 384in

If it is to be completely framed using a single row of square tiles each 2inches on an edge

2 inches = 1 tiles

384inches = y tiles

Cross multiply

2y = 384

y = 384/2

y = 192 tiles

The number of tiles needed is 192 tiles

Get the cost of 192tiles

If the tiles are $0.10 each. 192 tiles will cost 192 * 0.1 = $19.2

Hence the cost of the tiles needed is $19.2

Answer:

​​

Step-by-step explanation:

Subtract 7y7y from both sides.

-4x=18-7y−4x=18−7y

2 Divide both sides by -4−4.

x=-\frac{18-7y}{4}x=−

​4

​

​18−7y

Answer:

We conclude that the volume of a regular octahedron will be:

Step-by-step explanation:

Given

The length of one of the side or edge of a regular octahedron = a = 4 cm

To determine

The volume of a regular octahedron = V

Using the formula to determine the volume of a regular octahedron

[tex]V\:=\:\frac{\sqrt{2}}{3}a^3[/tex]

substituting a = 4 in the volume equation

[tex]V=\frac{\sqrt{2}\cdot \:4^3}{3}[/tex]

[tex]V=\frac{64\sqrt{2}}{3}[/tex]         ∵ 4³ = 64

[tex]\:\:V\:\approx \:30.17[/tex] cm

Therefore, we conclude that the volume of a regular octahedron will be:

Answer:

C, "The small crowd of protesters had turned into an angry mob".

Step-by-step explanation:

A and B are 1st person point of view because of "we" and "our". D is 2nd person point of view because of "your".

Answer:

c. The small crowd of protesters had turned into an angry mob.

Point of view is a way the voice sounds.

1st person uses: I, we, she, he, her, my. (it sounds like you are in their head.)

2nd person uses: you, your. (it sounds like the narrator is talking directly to you.)

3rd person uses: they, them he, her. (it sounds like someone is watching the story happening and is telling it from an outside point of view.

1st: My friends and I can't wait until Christmas.

2nd: You and your friends can't wait until Christmas.

3rd: Macy and her friends can't wait until Christmas.

Answer:

x=10

Step-by-step explanation:

[tex]9x-9=81\\9x=90\\x=10[/tex]

Answer:

joe mama

Step-by-step explanation:

Answer:

An Echo

Step-by-step explanation:

Answer:

Step-by-step explanation:

you have alternate angles, which are equal

6z-91=71

6z=71+91=162

z=162/6=27

z=27

y=180-27=153

Answer:

about 1437

about 2144

Step-by-step explanation:

i looked it up on google :)

Answer:

8

Step-by-step explanation:

The y-intercept represents when she starts riding her bike while the x-intercept is the the time it takes her to get to her school.

The complete question shows us a table with time travelled being on the x-axis while distance remaining is on the y-axis.

We see from the table that at 0 minutes travelled, the distance remaining is 5500 ft. Thus, the y-intercept represents when she starts riding her bike at 0 minutes and 5500 ft left to cover.

We see also from the table that after 8 minutes covered, she has 0 ft left to travel. Thus, the x-intercept is the the time it takes her to get to her school which is 8 minutes.

Read more about Intercepts at; https://brainly.com/question/3951754

#SPJ2

Answer:

First of all i just did this in school! <3 And second of all I WILL HELPP!!

Step-by-step explanation:

its luxuryyyyy!!!!!!!!!

Answer:

B is the answer

Step-by-step explanation:

Rigid motion they don't change shape or size just move around.

Answer:

25%

Step-by-step explanation:

Answer:

plz make it brainlisted

Step-by-step explanation:

Since the total is 300 and the ratio is 4:1,

Let us suppose the number of adults be 4x and children be x;

According to the question,

4x+x=300

or,5x=300

or,x=(300/5)

or,x=60

So, 60 students attended the show.

Answer:

75

Step-by-step explanation:

4:1 children meaning 1/4 of the population of 300 is 75