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2 years ago

Simplify (ab2 + 10 + a) – (6ab2 - 2ab + 8). I want it with steps please

Mathematics

1 answer:

lara [203]2 years ago

4 0

<h3>Answer:</h3>

-5ab² + 2ab + a + 2

<h3>Solution:</h3>

➙ ( ab² + 10 + a ) - ( 6ab² - 2ab + 8 )

➙ ab² + 10 + a - 6ab² + 2ab - 8

➙ ab² - 6ab² + a + 2ab + 10 - 8

➙ -5ab² + 2ab + a + 2

➲ More information:

Polynomial s in two variables are algebraic expressions consisting of terms in the form of a x n y m .
When adding or subtracting terms that have exactly the same same variable, we either add or subtract the coefficients .

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Mhanifa please help! Find the coordinates of the circumcenter of the triangle with the vertices A(4, 12), B(14, 6), and C(-6, 2)

melamori03 [73]

Answer:

(4.5, 1.5)

Step-by-step explanation:

Given vertices of a triangle:

A(4, 12), B(14, 6), and C(-6, 2)

Let the circumcenter is point M(x, y)

We know that the circumcenter is equidistant from each of the vertices.

Use distance formula:

AM = √(x - 4)² + (y - 12)²
BM = √(x - 14)² + (y - 6)²
CM = √(x + 6)² + (y - 2)²

All three distances are equal:

AM = BM = CM ⇒ AM² = BM² = CM² ⇒
(x - 4)² + (y - 12)² = (x - 14)² + (y - 6)² = (x + 6)² + (y - 2)²

Square of each:

AM² = x² - 8x + 16 + y² - 24y + 144 = x² + y² - 8x - 24y + 160
BM² = x² - 28x + 196 + y² - 12y + 36 = x² + y² - 28x - 12y + 232
CM² = x² + 12x + 36 + y² - 4y + 4 = x² + y² + 12x - 4y + 40

Comparing the squares, we get following system:

-8x- 24y + 160 = -28x - 12y + 232 ⇒ 20x - 12y = 72 ⇒ 5x - 3y = 18
- 8x - 24y + 160 = 12x - 4y + 40 ⇒ 20x + 20y = 120 ⇒ x + y = 6

Solve by substitution, x = 6 - y:

5(6 - y) - 3y = 18
30 - 8y = 18
8y = 12
y = 1.5

Find x:

x = 6 - 1.5 = 4.5

So the circumcenter is M(4.5, 1.5)

7 0

3 years ago

A climber on Mt Everest is 6000 meters from the start of his trail and at elevation 8000 meters above sea level. At x meters fro

sergeinik [125]

Answer:

h'(x) = 0.6 and Δx = 1 and 2

h(6001) = h(6000) + h'(6000)(1) = 8000 +0.6 = 8,000.6

h(6002) = h(6000) + h'(6000)(2) = 8000 + 0.6 (2) =8000 +1.2 = 8001.2

Explanation below:

Step-by-step explanation:

Based on the information given we have that when the climber is 6000 meters from the start, his elevation is 8000 meters above sea level.

We know that the function for elevation is given by h(x) where x is the number of meters from the start.

Therefore, h(6000) = 8000.

We also know that the derivative of a function tells us the reason of change at some point (or how fast a function is changing near that point). For this problem we have that h'(x) = 0.6. (meaning that the elevation increases in 0.6 meters for every meter they hike further nearby the 6000 meters)

We need to use the derivative at a point to estimate values of the function at nearby points

We're going to use h'(x)= 0.6. Δx= 1

h(6001) = h(6000) + h'(6000)(1) = 8000 +0.6 = 8,000.6

Therefore h (6001) = 8,000.6

Now for h'(x)= 0.6. Δx= 1

h(6002) = h(6000) + h'(6000)(2) = 8000 + 0.6 (2) =8000 +1.2 = 8001.2

Therefore h(6002) = 8001.2

6 0

3 years ago

Find the surface area of the cylinder in terms of pi.

Ilia_Sergeevich [38]

Hello!

To find the surface area of a cylinder you use the equation

$SA = 2 \pi rh+2 \pi r^{2}$

SA is surface area
r is radius
h is height

Put in the values you know

$SA = 2 \pi 9 * 3 + 2 \pi 9^{2}$

Square the number

$SA = 2 \pi 9 * 3 + 2 \pi 81$

Times the 9 and 3

$SA = 2 \pi 27 + 2 \pi 81$

Multiply the 2 and 27

$SA = 54 \pi + 2 \pi 81$

Multiply the 2 and 81

$SA = 54 \pi + 162 \pi$

Add

$SA = 216 \pi$

The answer is $216 \pi$

Hope this helps!

8 0

3 years ago

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Which statement is true?

lisov135 [29]

No statements are true

3 0

3 years ago

What is the y-intercept? y-3=1\2(x+2)

Margaret [11]

Y-3=1/2(x+2)

To find the y-intercept, we must first get the equation in slope intercept form. Start off by distributing 1/2 into the parentheses.

y-3= 1/2x+1
Add 3 to both sides

y= 1/2x+4

The slope is whatever is in front of x, in this case, 1/2. The y-intercept is the number after that which would be 4

6 0

3 years ago