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3 years ago

This is the question

Mathematics

2 answers:

vlabodo [156]3 years ago

6 0

Answer:

$=\left(9a-8\right)\left(a+1\right)$

Step-by-step explanation:

$9a^2+a-8\\\mathrm{Break\:the\:expression\:into\:groups}\\=\left(9a^2-8a\right)+\left(9a-8\right)\\\mathrm{Factor\:out\:}a\mathrm{\:from\:}9a^2-8a\mathrm{:\quad }a\left(9a-8\right)\\9a^2-8a\\\mathrm{Apply\:exponent\:rule}:\quad \:a^{b+c}=a^ba^c\\a^2=aa\\=9aa-8a\\\mathrm{Factor\:out\:common\:term\:}a\\=a\left(9a-8\right)\\=a\left(9a-8\right)+\left(9a-8\right)\\\mathrm{Factor\:out\:common\:term\:}9a-8\\=\left(9a-8\right)\left(a+1\right)$

Eva8 [605]3 years ago

3 0

So the right answer is (9a-8)(a+1)

Look at the attached picture

Hope it will help you

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Problem:

Molodets [167]

Answer:

We know that:

a, b > 0

a < b

With this, we want to prove that a^2 < b^2

Well, we start with:

a < b

If we multiply both sides by a, we get:

a*a < b*a

a^2 < b*a

now let's go back to the initial inequality.

a < b

if we now multiply both sides by b, we get:

a*b < b*b

a*b < b^2

Then we have the two inequalities:

a^2 < b*a

a*b < b^2

a*b = b*a

Then we can rewrite this as:

a^2 < b*a < b^2

This means that:

a^2 < b^2

b) Now we know that a.b > 0, and a^2 < b^2

With this, we want to prove that a < b

So let's start with:

a^2 < b^2

only with this, we can know that a*b will be between these two numbers.

Then:

a^2 < a*b < b^2

Now just divide all the sides by a or b.

if we divide all of them by a, we get:

a^2/a < a*b/a < b^2/a

a < b < b^2/a

In the first part, we have a < b, this is what we wanted to get.

Another way can be:

a^2 < b^2

divide both sides by a^2

1 < b^2/a^2

Let's apply the square root in both sides:

√1 < √( b^2/a^2)

1 < b/a

Now we multiply both sides by a:

a < b

7 0

3 years ago

How do I answer this?

12345 [234]

Answer:

Step-by-step explanation:

area of trapezium ABCD

=(16.5+12)/2 \times 15

=(28.5)/2 \times 15

=213.75 cm^2

$\frac{PQ}{DC} =\frac{8}{12} =\frac{2}{3}$

Area of PQRS

=213.75 \times (\frac{2}{3} )^2\\=213.75 \times\frac{4}{9} \\=95 ~cm^2

area of green portion=213.75-95=118.75 cm²

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2 years ago

The volume of a cone with a radius of 4 feet and a height of 12 feet

Nitella [24]

Answer:

150.8

Step-by-step explanation:

Hope it helps.

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3 years ago

Help me with this math question please I'm giving away brainliests

aleksklad [387]

Answer:

Step-by-step explanation:

Given function in the question is,

$f(x)=\frac{-2x^2-4x}{4x+8}$

$=\frac{-2x(x+2)}{4(x+2)}$

$=-\frac{1}{2}x$ If $x\neq -2$

Given function is not defined at x = -2

At x = -2,

$f(-2)=\frac{1}{2}(2)$

$=1$

Therefore, there is a hole in the graph at (-2, 1).

Graph of the function 'f' will be a straight line with a hole at (-2, 1).

Horizontal asymptote → None

Vertical asymptote → None

x-intercept → No x-intercept [Line passes through origin (0,0)]

y-intercept → No y-intercept [Line passes through origin (0,0)]

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4 years ago

The midpoint of a segment is (4,3) and one endpoint is (10,8). Find the coordinates of the other endpoint.

Anastaziya [24]

9514 1404 393

Answer:

(-2, -2)

Step-by-step explanation:

The midpoint M is calculated from end points A and B as ...

M = (A +B)/2

Solving for end point B, we get ...

2M = A +B . . . . . . multiply by 2

B = 2M -A . . . . . . subtract A

Then the other end point is ...

B = 2(4, 3) -(10, 8) = (2·4 -10, 2·3 -8) = (8-10, 6-8)

B = (-2, -2)

The other end point has coordinates (-2, -2).

4 0

3 years ago