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2 years ago

Find the coefficient of x2 in (3x2 – 5) (4 + 4x2), expand using algebraic expressions and answer

Mathematics

1 answer:

Scilla [17]2 years ago

7 0

Answer:

- 8

Step-by-step explanation:

Given

(3x² - 5)(4 + 4x²)

Each term in the second factor is multiplied by each term in the first factor, that is

3x²(4 + 4x²) - 5 (4 + 4x²) ← distribute both parenthesis

= 12x² + 12 $x^{4}$ - 20 - 20x² ← collect like terms

= 12 $x^{4}$ - 8x² - 20

The coefficient of the x² term is - 8

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Solve the following inequality: –1 + 6(–1 – 3x) > –39 – 2x.

insens350 [35]

<span>–1 + 6(–1 – 3x) > –39 – 2x.
</span>-1-6-18x>-39-2x
-7-18x>-39-2x
-18x>-32-2x
-16x>-32
x<2

B. x<2

7 0

2 years ago

Read 2 more answers

A veterinarian needs to know an animal's weight in kilograms.If 20 pounds is about 9 kilograms and dog weighs 30 pounds,use a ra

Lesechka [4]

Answer:

Using the ratio table the dogs weight is:

30 pounds = 13.5 kilograms

Step-by-step explanation:

For this case we have the following conversion:

20 pounds = 9 kilograms

To use the table what we must do is find another relationship that allows us to find the weight in kilograms for 30 pounds.

For example, half the weight in pounds is half the weight in kilograms.

Therefore, the given conversion is:

10 pounds = 4.5 kilograms

So, for 30 pounds, we multiply this last ratio obtained by three on both sides:

30 pounds = 13.5 kilograms

Then, the table is:

Pounds 10 20 30

7 0

2 years ago

F⃗ (x,y)=−yi⃗ +xj⃗ f→(x,y)=−yi→+xj→ and cc is the line segment from point p=(5,0)p=(5,0) to q=(0,2)q=(0,2). (a) find a vector pa

DerKrebs [107]

a. Parameterize $C$ by

$\vec r(t)=(1-t)(5\,\vec\imath)+t(2\,\vec\jmath)=(5-5t)\,\vec\imath+2t\,\vec\jmath$

with $0\le t\le1$ .

b/c. The line integral of $\vec F(x,y)=-y\,\vec\imath+x\,\vec\jmath$ over $C$ is

$\displaystyle\int_C\vec F(x,y)\cdot\mathrm d\vec r=\int_0^1\vec F(x(t),y(t))\cdot\frac{\mathrm d\vec r(t)}{\mathrm dt}\,\mathrm dt$

$=\displaystyle\int_0^1(-2t\,\vec\imath+(5-5t)\,\vec\jmath)\cdot(-5\,\vec\imath+2\,\vec\jmath)\,\mathrm dt$

$=\displaystyle\int_0^1(10t+(10-10t))\,\mathrm dt$

$=\displaystyle10\int_0^1\mathrm dt=\boxed{10}$

d. Notice that we can write the line integral as

$\displaystyle\int_C\vecF\cdot\mathrm d\vec r=\int_C(-y\,\mathrm dx+x\,\mathrm dy)$

By Green's theorem, the line integral is equivalent to

$\displaystyle\iint_D\left(\frac{\partial x}{\partial x}-\frac{\partial(-y)}{\partial y}\right)\,\mathrm dx\,\mathrm dy=2\iint_D\mathrm dx\,\mathrm dy$

where $D$ is the triangle bounded by $C$ , and this integral is simply twice the area of $D$ . $D$ is a right triangle with legs 2 and 5, so its area is 5 and the integral's value is 10.

4 0

2 years ago

Which pairs of angles in the figure below are vertical angles?

ch4aika [34]

Answer: Option A and Option C.

Step-by-step explanation:

For this exercise it is important to know the definition of "Vertical Angles".

When two lines intersect or cross, there are a pair of angles that share the same vertex and they are opposite each other. This pair of angles are known as "Vertical angles".

By definition, Vertical angles are congruent, which means that the have the equal measure.

In this case, you can observe in the picture provided in the exercise that the line TI and the line WN intersect each other at the point S.

You can identify that the pair of angles that are opposite to each other and share the same vertex are the shown below:

$\angle ISN$ and $\angle TSW$

$\angle TSN$ and $\angle ISW$

6 0

2 years ago

Mike's closing costs will add up to 4 percent and he'll make a down payment of 20 percent on a house that costs $210,000. Over t

postnew [5]

<span>For the question "Mike's closing costs will add up to 4 percent and he'll make a down payment of 20 percent on a house that costs $210,000. Over the life of his loan, he will pay $197,040.76 in monthly payments. What is the total cost of his house?" To obtain the total cost of the house, we first obtain the amount he paid as the closing costs and the down payment he paid which we will add to the total amount paid in monthly payments. Closing cost = 4% of $210,000 = 0.04 x 210,000 = $8,400 Down payment = 20% of $210,000 = 0.2 x 210,000 = $42,000 Total monthly payments = $197,040.76 Total cost of the house = $8,400 + $42,000 + $197,040.76 = $247,440.76</span>

7 0

2 years ago