MATHEMATICS HIGH SCHOOL

Find the product. a 4(3a 2 - 2a + 1)

Answers

Answer 1

Answer:

Answer:

The product of $a^(4)(3a^(2)-2a+1)$ is $3a^(6)-2a^(5)+a^(4)$ .

Step-by-step explanation:

As given the expression in the question be as follow .

$= a^(4)(3a^(2)-2a+1)$

First open the bracket

$= a^(4)* 3a^(2)-a^(4)* 2a+a^(4)* 1$

Now by using the property of exponent .

$x^(a)* x^(b)= x^(a+b)$

$= 3a^(2+4)-2a^(4+1)+a^(4)$

$= 3a^(6)-2a^(5)+a^(4)$

Therefore the product of $a^(4)(3a^(2)-2a+1)$ is $3a^(6)-2a^(5)+a^(4)$ .

Answer 2

Answer:

a^4(3a^2 - 2a + 1)

= 3a^6 - 2a^5 + a^4

hope that helps

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Jenny makes food for her hummingbird feeders. The food is made up of 1 part sugar and 4 parts water. She uses 34 3 4 cup of sugar to make the hummingbird food. How much water should Jenny use?

Answers

I am assuming that the 34 3 4 cup of sugar means 34 3/4.

Given:
Ratio of sugar to water is 1:4

34 3/4 sugar to quantity of water.

First, we need to convert the mixed fraction into an improper fraction.

34 3/4 = ((34*4)+3)/4 = 139/4

1:4 = 139/4:x
x = 4*139/4
x = 139

Jenny should use 139 cups of water for the 34 3/4 cups of sugar.

Answer:

1 part sugar : 4 parts water

3/4 cup of sugar.

1/4 = 3/4 : x

x = 4 * 3/4

x = 12/4

x = 3 part water

Step-by-step explanation:

Find the distance between the points (11, 4) and (10, 5). 1 2

Answers

I hope this helps you

Answer:

Hi, I'm on this assignment. :)

√2

Step-by-step explanation:

(x(2) - x(1))^2 + (y(2) - y(1))^2

(10 - 11)^2 + (5 - 4)^2

(-1)^2 + (1)^2

1 + 1

√2

The answer options are

2√2

2 <--

I just purchased a swimming pool with the dimensions of 15 feet across and 42 inches deep. Yes it is a circle. I need to know how many gallons of water it will hold. I am having a tanker brought out and need to know how much they need to bring because they charge by the gallon to bring it out.

Answers

When the pool is full to the rim, you'll have a cylinder of water. The diameter
of the cylinder is 15-ft, and the height of the cylinder is 42 inches.

Here are the tools you'll need:

-- Volume of a cylinder = (pi) (radius squared) (height)
-- Radius = 1/2 diameter = 7.5 feet
-- Keep everything in the same units. Depending on which unit
you prefer, 7.5 feet = 90 inches, and 42 inches = 3.5 feet.

I like inches and cubic inches, because I remember that
1 gallon = exactly 231 cubic inches.

Volume of the cylinder = (pi) (radius squared) (height)

Volume = (pi) (90 squared) (42) = (pi) (8,100) (42) = 1,068,769.8 cubic inches

1,068,769.8 / 231 = 4,626.7 gallons
===================================
Slightly easier:

about 7.48 gallons = 1 cubic foot

Volume = (pi) (7.5-ft squared) (3.5-ft) = 618.5 cubic feet

(618.6 cubic-ft) x (7.48 gallons per cubic-ft) = 4,627.1 gallons

The results are not identical, but don't panic. They are equal
to within about 51 ounces (0.009 percent). The tanker will either
spill or evaporate more than that during the process of the delivery.

By the way ... you'd be wise not to install the pool on the second floor.
That much water weighs a little over 19.3 tons !

What is 1/3 the sum of 7 and 11?

Answers

Add 11 and 7

11 + 7

18

Mulitply 1/3 and 18

1/3 * 18

6

1/3 the sum of 7 and 11 is 6.

X^2+5x-104=0 solve quadratic equations

Answers

$x^2+5x-104=0\n\na=1;\ b=5;\ c=-104\n\n\Delta=b^2-4ac;\ if\ \Delta > 0\ then\ x_1=(-b-\sqrt\Delta)/(2a);\ x_2=(-b+\sqrt\Delta)/(2a)\n\n\Delta=5^2-4\cdot1\cdot(-104)=25+416=441;\ \sqrt\Delta=√(441)=21\n\nx_1=(-5-21)/(2\cdot1)=(-26)/(2)=-13;\ x_2=(-5+21)/(2\cdot1)=(16)/(2)=8\n\nAnswer:x=-13\ or\ x=8.$

You first have to factor and get (x-8)(x+13)=o and set them equal to zero x-8=0 x=8 x+13=0 x=-13

For the values a = 2.9 which is a leg of a right triangle, and value c = 4.2, which is the hypotenuse, find the length of the other leg, b, to the nearest tenth.A. 2.9

B. 3.0

C. 2.8

D. 1.3

Answers

Given:
a = 2.9
c = 4.2
b = ?

Right triangle. Use Pythagorean Theorem.
a² + b² = c²
b² = c² - a²
b² = 4.2² - 2.9²
b² = 17.64 - 8.41
b² = 9.23
b = √9.23
b = 3.04 Choice B.

The length of the other leg is 3.0

The right one is B) 3.0, as you know $a^(2) + b^(2) = c^2$ due to Pythagoras' theorem. So $b= √(c^2 - a^2)$ . Put the right numbers into the formula and you get 3.0. That is B.

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