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3 years ago

The remainder after diving x^4+3x^3-8x^2+5x-9 by x+5 is ____.

Mathematics

1 answer:

raketka [301]3 years ago

6 0

Use the polynomial remainder theorem. It says that a polynomial $f(x)$ has remainder $f(c)$ upon division by $x-c$ .

Here we have

$f(x)=x^4+3x^3-8x^2+5x-9$

and $c=-5$ , so the remainder is

$f(-5)=(-5)^4+3(-5)^3-8(-5)^2+5(-5)-9=\boxed{16}$

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Find the length of a square whose diagonal is 15cm

Vladimir [108]

2a^2 = 225
So a^2 = 225/2

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2 years ago

2. XYZW is a parallelogram with diagonals XZ and YW that intersect at point A.

sergeinik [125]

Answer:

AW=10

Step-by-step explanation:

In a parallelogram opposite sides are congruent meaning XA and AZ are congruent. YA and AW are congruent. So...

Solving for XA and AZ

XA=AZ

3m=5m-4

-2m=-4

m=2

If YW=10m then 10 x 2 = 20

20 divided by 2 = 10

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2 years ago

One container is filled with mixture that is 25% acid. A second container is filled with a mixture that is 55% acid. The second

algol13

Answer:

Therefore the third container contains $\frac{735}{17}\%$ = 43.23 % acid.

Step-by-step explanation:

Given that, One container is filled with the mixture that 25% acid. 55% acid is contain by second container.

Let the volume of first container be x cubic unit.

Since the volume of second container is 55% larger than the first.

Then the volume of the second container is

$= (V\times \frac{100+55}{100})$ cubic unit.

$=\frac{155}{100}V$ cubic unit.

The amount of acid in first container is

$=V\times \frac{25}{100}$ cubic unit.

$=\frac{25}{100}V$ cubic unit.

The amount of acid in second container is

$=(\frac{155}{100}V \times \frac{55}{100})$ cubic unit.

$=\frac{8525}{10000}V$ cubic unit.

Total amount of acid $=(\frac{25}{100}V+\frac{8525}{10000}V)$ cubic unit.

$=(\frac{2500+8525}{10000}V)$ cubic unit.

$=(\frac{11025}{10000}V)$ cubic unit.

Total volume of mixture $=(V+\frac{155}{100}V)$ cubic unit.

$=\frac{100+155}{100}V$ cubic unit.

$=\frac{255}{100}V$ cubic unit.

The amount of acid in the mixture is

$=\frac{\textrm{The volume of acid}}{\textrm{The amount of mixture}}\times 100 \%$

$=\frac {\frac{11025}{10000}V}{\frac{255}{100}V}\times 100\%$

$=\frac{735}{17}\%$

Therefore the third container contains $\frac{735}{17}\%$ acid.

5 0

3 years ago

The diagram shows the graph of y = 2x + c, where c is a constant find the value of K.

mote1985 [20]

Answer:

$k=\frac{13}{2}$

Step-by-step explanation:

The equation $y=2x+c$ is a <em>linear equation</em>. By definition, the independent term on this equation (that is, the number that is not being multiplied by $x$ ) is the <em>y-intercept</em>, which is a fancy way of saying "the point where the line crosses the y-axis".

By looking at the equation, we know that our y-intercept is <em>c. </em>By looking at the graph, we can see that the y-intercept is -3. Therefore, $c=-3$ and we get the complete version of our linear equation:

$y=2x-3$

Now, looking at the graph we can see that the point $(k,10)$ lies on the line of the equation, which means that the point is a solution to our equation. All we have to do is replace $x$ and $y$ by the values of the given point (which are $k$ and $10$ , respectively), and then solve for $k$ :