MATHEMATICS HIGH SCHOOL

4. The admission fee at a play is $2.50 for each child and $4.00 for each adult. On opening night, the 1000 seat auditorium was sold out! When all the money was counted, they had $3400. How many adults attended the opening night's show? A.100

B.400

C.500

D.600

Answers

Answer 1

Answer:

600 adults and 400 children attended the opening night's show

Let x represent the number of children and y represent the number of adult.

Since 1000 seat auditorium was sold out!, hence:

x + y = 1000 (1)

they had $3400. Hence:

2.5x + 4y = 3400 (2)

Solving equations 1 and 2 simultaneously gives:

x = 400, y = 600

600 adults and 400 children attended the opening night's show.

Find out more on equation at: brainly.com/question/2972832

Answer 2

Answer: Answer is D. 600 adults

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Stonehenge II in Hunt, Texas, is a scale model of the ancient construction in Wiltshire, England.The scale of the model to the original is 3 to 5 . the Alter Stone of the original construction is 4.9 meters tall. write and solve a porportion to find the height of the model of the Alter Stone

Answers

Let the height of the model of the Alter Stone be h.
Then, 3/5 = h/4.9
h = (3 x 4.9)/5 = 2.94

Therefore, the height of the Alter Stone is 2.94 meters

What is the total amount that First Consumer Bank will receive after lending Jane $7,000 for three years at an interest rate of 5 percent, compounded annually?

Answers

Answer: $8103.375

Step-by-step explanation:

The compound amount after x years is given by :-

$A=P(1+r)^x$ , where p is the principal amount , r is the rate of interest .

Given: The principal amount = $7,000

The rate of interest per year = 5 % = 0.05

Time in years = 3

Then, the compound amount is given by :_

$A=7,000(1+0.05)^3\n\n\Rightarrow\ A=7,000(1.05)^3\n\n\Rightarrow\ A=\$8103.375$

take you amount and add 1 with the interest in brackets. close the brackets and square your year, then calculate.

formula:
7000(1+5%) multiplied by the year
=8103.38

Factor completely 2x2 + 9x + 4.(2x + 2)(x + 2)

(2x + 1)(x + 4)

(2x + 4)(x + 1)

(2x + 2)(x + 4)

Answers

Answer:

(2x + 4) ( x +1 ) are factors .

Step-by-step explanation:

Given : 2x² + 9x + 4.

To find : Factor.

Solution : We have given that 2x² + 9x + 4.

On factoring 2x² + 8x + 1x + 4.

Taking common 2x from first two terms and 1 from last two terms .

2x ( x +4 ) +1 (x +4 ).

On grouping

(2x + 4) ( x +1 ).

Therefore , (2x + 4) ( x +1 ) are factors .

The factored form of the polynomial 2x² + 9x + 4 is (2x + 1)(x + 4).

Hence the correct answer is 3rd.

Given is a polynomial 2x² + 9x + 4, we need to factorize it.

To factorize the polynomial 2x² + 9x + 4, we can use the factoring method.

Step 1: Multiply the coefficient of the quadratic term (2) with the constant term (4). In this case, 2 × 4 = 8.

Step 2: Find two numbers that multiply to give 8 and add up to the coefficient of the linear term (9).

In this case, the numbers are 1 and 8 because 1 × 8 = 8 and 1 + 8 = 9.

Step 3: Rewrite the middle term (9x) using the two numbers found in step 2. This will split the middle term into two parts.

2x² + 1x + 8x + 4

Step 4: Group the terms in pairs and factor out the greatest common factor from each pair.

(2x² + 1x) + (8x + 4)

Step 5: Factor out the greatest common factor from each pair.

x(2x + 1) + 4(2x + 1)

Step 6: Notice that we now have a common binomial factor, (2x + 1). Factor out this common binomial.

(2x + 1)(x + 4)

Therefore, the factored form of the polynomial 2x² + 9x + 4 is (2x + 1)(x + 4).

Hence the correct answer is 3rd.

Learn more about Factorization click;

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Can i know the steps to this answer?

Answers

(cos²Ф - 1) / sin Ф * 1/sin Ф=
1(cos²Ф-1) / (sin Ф* sinФ)=
(cos²Ф-1) / sin² Ф=

--------------------------------------------------------------
Fundamental relation of trigonometry:
sin²Ф + cos²Ф=1 ⇒ sin²Ф=1-cos²Ф ⇒-sin²Ф=cos²Ф-1
--------------------------------------------------------------

-sin²Ф/sin²Ф=1

Answer: (cos²Ф - 1) / sin Ф * 1/sin Ф=-1

A piece of wire 7/8 meter long broke into two pieces.one piece was 1/4 meter long. How is the other piece

Answers

Answer:

The second piece is 5/8 meters.

Step-by-step explanation:

To find the length of the second piece of wire, subtract the length of the first piece of wire from the total.

7/8 - 1/4

Get a common denominator:

7/8 - (1/4) *2/2

7/8 - 2/8

5/8

The second piece is 5/8 meters.

A welder needs apiece of half-inch pipe18 3/4 in. Long. she has a piece the is 28 1/8 in. Long. how much must she cut off from the longer piece?

Answers

I got 9 and 3/8 because you would subtract 18 3/4 from 28 1/8

Final answer:

The welder needs to cut off 9 3/8 inches from the longer piece.

Explanation:

To determine how much the welder needs to cut off from the longer piece of pipe, we need to find the difference between the lengths of the two pieces.

Given that the longer piece is 28 1/8 inches and the desired length is 18 3/4 inches, we can subtract the desired length from the longer piece's length:

28 1/8 - 18 3/4 = 9 3/8

Therefore, the welder needs to cut off 9 3/8 inches from the longer piece of pipe.