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2 years ago

What is the expression (x-3)(x^2-3x-10) as a polynomial in standard form?

1 answer:

5 0

A polynomial in standard form only means that you put it in order of descending x values. Multiplying out those 2 factors gives us $x^3-3x^2-10x-3x^2+9x+30$ . Combining like terms and we have $x^3-6x^2-x+30$ . That's in standard form.

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Determine the point of intersection between the lines with equations x+3y=5 and 3x−2y=26.

Zolol [24]

Answer:

the ans is :

Step-by-step explanation:

First, it would be helpful to draw a quick sketch of the lines. It helps to visualize the problem.

To find the intersection point, we need to find the point where x and y are the same value in both equations.

The line equations:

6x+2y=26 ................... 1

2x+3y=18 ................... 2

Can be rearranged to the common line equation form: y = mx + c

y = 13 - 3x ................... 3

y = 6 - 2/3 x ................. 4

At the intersection point, y will be equal for both equations. So, we can set 3 equal to 4 and solve for x.

13- 3x = 6 - 2/3 x

13 = 6 + 3x - 2/3x ....... add 3x to both sides

13 = 6 + 2 1/3x ........ simplify

7 = 2 1/3 x ........ subtract 13 from both sides

7 = 7/3 x ......... multiply both sides by 3/7

3 = x

To calculate the y-coordinate substitute x = 3 into 3.

y = 13 - 3x

y = 13 - 3(3)

y = 4

To check your answer, substitute the values for x and y into the other equation, 4.

The point of intersection is (3,4).

If you drew a sketch of the problem, you should be able to see that this point of intersection makes sense.

4 0

3 years ago

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1 of 3

Nonamiya [84]

Answer:

y = -1/2x + 3.5

Step-by-step explanation:

The gradients of perpendicular lines multiply to make -1. The gradient of the line given is 2, so 2 multiplied by something gives us -1. 2 × -1/2 = -1. The gradient of the perpendicular line is -1/2

y = -1/2x + c

Now we can substitute x = 1 and y = 3 into the equation:

3 = -1/2(1) + c
3 = -1/2 + c
c = 3 + 1/2
c = 3 1/2 or 3.5 or 7/2

The equation of the line is y = -1/2x + 3.5

Hope this helps!

3 0

2 years ago

Factor the expression using the GCF. The expression 18a-12 factored is

Dafna1 [17]

Answer: 6(3a-2)

Step-by-step explanation:

The greatest common factor (GCF) of 18a and -12 is 6. Therefore,

18a-12=6()=6(3a-2)

3 0

2 years ago

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Rabies is a viral disease of mammals transmitted through the bite of a rabid animal. The virus infects the central nervous syste

lisabon 2012 [21]

Answer:

(a) The value of x is 0.30.

(b) The probability that a reported case of rabies is not a raccoon is 0.45.

Step-by-step explanation:

Denote the events as follows:

R = reported case of rabies is a raccoon

F = reported case of rabies is a fox

B = reported case of rabies is a bat

O = reported case of rabies is a some other animal.

The data provided is:

P (R) = 0.55

P (F) = 0.11

P (B) = 0.04

P (O) = x.

(a)

A property of a probability distribution is that the sum of all individual properties is 1.

That is, $\sum P(X)=1$

Compute the value of x as follows:

$\sum P(X)=1\\P(R)+P(F)+P(B)+P(O)=1\\0.55+0.11+0.04+x=1\\0.70+x=1\\x=1-0.70\\x=0.30$

Thus, the value of x is 0.30.

(b)

The probability of the complement of an event is the probability of its not happening.

$P(A^{c})=1-P(A)$

Compute the probability that a reported case of rabies is not a raccoon as follows:

$P(R^{c})=1-P(R)\\=1-0.55\\=0.45$

Thus, the probability that a reported case of rabies is not a raccoon is 0.45.

(c)

Compute the probability that a reported case of rabies is either a bat or a fox as follows:

$P(B\cup F)=P(B)+P(F)\\=0.11+0.04\\=0.15$

Thus, the probability that a reported case of rabies is either a bat or a fox is 0.15.

4 0

3 years ago

A softball team is ordering pizza to eat after their tournament. They plan to order cheese pizzas that cost $6 each and four-top

Softa [21]

Answer:

Step-by-step explanation:

Well $1o each than 10×4=40 and 40 +6=46

7 0

2 years ago

Read 2 more answers