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3 years ago

Find the value of a3 + 3b2 when a = 2 and b = -2

Mathematics

1 answer:

FrozenT [24]3 years ago

5 0

Given:

a = 2 and b = -2.

To find:

The value of $a^3+3b^2$ .

Solution:

We need to find the value of expression $a^3+3b^2$ at a = 2 and b = -2.

Substituting a = 2 and b=-2 in $a^3+3b^2$ , we get

$(2)^3+3(-2)^2$

$=8+3(4)$

$=8+12$

$=20$

Therefore, the value of expression $a^3+3b^2$ at a = 2 and b = -2 is 20.

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Pleaseeeee helpppppp!!

Sergio [31]

Answer: The equation of the circle as specified is (x+5)² + (y -1)² = 25

Step-by-step explanation: Use the Pythagorean Theorem to calculate the length of the radius from the coordinates given for the triangle location: A(-1,4), B(-1,1) and C(-5,1)

subtract y-values of A & B 4-1=3 AB = 3

subtract x-values of B &C -5-(-1) =4 BC=4 3² + 4² = 9 + 16 = 25

√25 = 5 AC = 5 That is the radiuus of the circle.

The sides of the triangle are AB=3, BC=4, AC=5.

Use the equation for a circle:

( x - h )² + ( y - k )² = r², where ( h, k ) is the center and r is the radius.

Use the coordinates of C, (-5, 1) as h and k in the equation

Substituting those values, we have (x -[-5])² + (y -[1])² = 5²

Simplify: (x+5)² + (y -1)² = 25

A graph of the circle is attached. The radius is AC, between the center C (-5,1) and A( -1,4) on the circumference. (Sorry, I still need to learn how to create line segments!)

8 0

3 years ago

Solve the system of equations 4x+5y=-1 and -5x-8y=10 by combining the equations.

Flura [38]

The solutions to the given system of equations are x = 6 and y = -5

<h3>Simultaneous linear equations</h3>

From the question, we are to solve the given system of equations

The given system of equation is

4x+5y=-1

-5x-8y=10

Multiply the <u>first equation</u> by 5 and the <u>second equation</u> by 4

5× (4x+5y=-1)

4× (-5x-8y=10)

20x + 25y = -5

-20x - 32y = 40

------------------------

0x + (-7y) = 35

-7y = 35

y = 35/-7

y = -5

Substitute the value of y into the first equation to find x

4x + 5y = -1

4x + 5(-5) = -1

4x -25 = -1

4x = -1 +25

4x = 24

x = 24/4

x = 6

Hence, the solutions to the given system of equations are x = 6 and y = -5

Learn more on Simultaneous linear equation here: brainly.com/question/12647791

#SPJ1

3 0

2 years ago

I’m not very sure how to simplify the two bottom rows, can someone help me?

love history [14]

Answer:

The simplification is done below.

Step-by-step explanation:

$(\sin(\frac{\pi}{6})\cos(\frac{\pi}{4}) - \sin(\frac{\pi}{4})\cos(\frac{\pi}{6}))^{2}$

= $(\frac{1}{2} \times \frac{1}{\sqrt{2}} - \frac{1}{\sqrt{2}} \times \frac{\sqrt{3}}{2})^{2}$

= $((\frac{1}{2\sqrt{2}}) \times (1 - \sqrt{3}))^{2}$

= $0.125 \times (1 - (2 \times \sqrt{3}) +3)$

5 0

3 years ago

PLEASE HELP ME WITH THIS!!!!!

nadezda [96]

For the given experiment of spinning a spinner and drawing a card, we will see that:

A) Yes, the events are independent.
B) P(3 and A) = 1/16
C) P(5 and C) = 0
D) P(4) = 1/4
P(B or C) = 1/2
E) P(3 and not D) = 3/16

<h3>What are independent events?</h3>

We say that two events are independent if the outcome of one does not affect the outcome of the other.

In this case, the outcome of the spinner clearly does not affect the outcome of the card draw, so the events are independent.

<h3>How to get the probabilities?</h3>

B) First we want to get the probability of getting 3 and A.

The probability of getting a 3 when drawing a card is given by the quotient between the numbers of card with the number 3 (only one) and the total number of cards, so we have:

p = 1/4

Similar for the case of the spinner, the letter A appears twice, and there are a total of 8 letters, then the probability is:

q = 2/8 = 1/4

The joint probability is the product of the two individual probabilities, we have:

P(3 and A) = p*q = 1/4*1/4 = 1/16

C) The probability of getting a 5 and the letter C is 0, because there is no card with the number 5.

D) P(4) is the probability of drawing the card with the number 4, this is:

p = 1/4

P(B or C) is the probability of spinning the letter B or C. There are 2 B's and 2 C's, and a total of 8 letters, so the probability is:

q = (2 + 2)/8 = 1/2

E) P(1 and not D) is equal to: P(1 and A or B or C).

P(1) is 1/4.

P(A or B or C) is 6 over 8 (because there are 6 cards that are either an A, a B, or a C)

Then the joint probability is:

P(1 and not D) = (1/4)*(6/8) = 3/16

If you want to learn more about probability, you can read:

brainly.com/question/251701

8 0

2 years ago

The side length of the cube is 5 cm. Find the volume of the cube.

lidiya [134]

Answer:

125 cm³

General Formulas and Concepts:

<u>Pre-Algebra</u>

Order of Operations: BPEMDAS

Brackets
Parenthesis
Exponents
Multiplication
Division
Addition
Subtraction

Left to Right<u> </u>

<u>Geometry</u>

Volume of a Cube Formula: V = a³

<em>a</em> is a side length

Step-by-step explanation:

<u>Step 1: Define</u>

<em>Identify variables</em>

<em>a</em> = 5 cm

<u>Step 2: Find Volume</u>

Substitute in variables [Volume of a Cube Formula]: V = (5 cm)³
Evaluate exponents: V = 125 cm³

5 0

3 years ago

Read 2 more answers