MATHEMATICS HIGH SCHOOL

If a polynomial P(x) has P(-2)=0, then which of the following can you conclude?P(x) has a factor (x+2)

P(x) has a constant term of -2

P(x) has an x-intercept of -2

Both P(x) has a factor (x+2) and P(x) has an x-intercept of -2

Answers

Answer 1
Answer:

Answer: Both P(x) has a factor (x+2) and P(x) has an x-intercept of -2

Explanation: if a polynomial has a factor (x-a) it means its form can be written as:

(x-a)*(rest of polynomial)=0

and thus "a" is a root because the entire expression becomes 0 when x=a. In this case a=-2

An x-intercept is a point on the curve intersecting the x axis with coordinates (a, 0) where a is one of the roots. As shown above x=-2 will make the expression 0, so y=0 for x=-2. In other words there is a point (-2,0), which means -2 is the x-intercept.

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Question Simplify. 1+32⋅2−5

Given Δ ABC ≅ Δ EFG, What is the value of x? A. x= 45 °
B. x= 50 °
C. x= 85 °
D. x= 135 °

Answers

Answer:  The correct option is (A) 45.

Step-by-step explanation:  We are given that triangles ABC and EFG are congruent to each other, where

m\angle A=50^\circ,m\angle G=85^\circ,m\angle B=x^\circ.

We are to find the value of x.

We know that the corresponding angles of congruent triangles have equal measures.

So, m∠A = m∠E, m∠B = m∠F and m∠C = m∠G.

Also, since the sum of three angles of a triangle is 180 degrees, so from triangle ABC, we get

m\angle A+m\angle B+m\angle C=180^\circ\n\n\Rightarrow 50^\circ+85^\circ+x^\circ=180^\circ\n\n\Rightarrow 135^\circ+x^\circ=180^circ\n\n\Rightarrow x^\circ=180^\circ-135^\circ\n\n\Rightarrow x^\circ=45^\circ\n\n\Rightarrow x=45.

Thus, the required value of x is 45.

Option (A) is CORRECT.

Answer:

A.   x = 45

Step-by-step explanation:

m<C = m<G = 85°

m<A + m<B + m<C = 180°

50° + x° + 85° = 180°

x = 45

Consider the following set of equations: Equation C: y = 2x + 8
Equation D: y = 2x + 2

Which of the following best describes the solution to the given set of equations?

No solution
One solution
Two solutions
Infinite solutions

Answers

No solution because both equations have 2x on the same side.

Answer:

No Solution

Step-by-step explanation:

No Solution because they both have the same slopes but different y- intercept.

Hope this helped!

Factor by grouping:4-12r+9r^2

i know the answer is (2-3r)^2

Can anyone explain to me how it is?

Answers

(x-y)^2=x^2-2xy+y^2\n---------------------------\n\n4-12r+9r^2=2^2-2\cdot2\cdot3r+(3r)^2=(2-3r)^2

other\ method:\n\n4-12r+9r^2=4-6r-6r+9r^2=2(2-3r)-3r(2-3r)\n\n=(2-3r)(2-3r)=(2-3r)^2
Because:
(a-b)^2=a^2+2ab+b^2

(03.06 LC)Choose the equation below that represents the line that passes through the point (2, 4) and
has a slope of 3. (5 points)
O y + 2 - 3(x + 4)
Oy+4= 3(x + 2)
Oy - 4 - 3(x - 2)
Oy - 2 - 3(x - 4)

Answers

Answer:

i think B

Step-by-step explanation:

but im not sure

either way, Hope it helps

Function f(x) is represented on the graph. Which statement identifies the effect of replacing f(x) with 1/2f(x) on the graph? A)The curve would remain the same size but would be flipped upside down. B)The curve would remain the same size but would shift to the left. C)The curve would be narrower, but the vertex would be in the same position. D)The curve would be wider, but the vertex would be in the same position.

Answers

Answer:

Option (D)

Step-by-step explanation:

If a function f(x) is represented on a graph and we follow the transformation as,

f(x) → k.f(x)

1). If k ≥ 1, graph of the parent function f(x) will be stretched vertically by a factor k.

That means the transformed graph will be narrower.

2). If 0 < k < 1, graph will be vertically compressed or the transformed function will show a wider graph.

Following this rule,

f(x) → (1)/(2).f(x) shows k = (1)/(2) [Since 0 < (1)/(2) < 1]

Therefore, transformed form will be wider.

Option (D) will be the answer.

Solve for x. -ax+4b>9

Answers

-ax+4b>9
-ax>9-4b
-x>(9-4b)/a
x<-(9-4b)/a
x<(4b-9)/a

Answer: x<-(9-4b)/a              or            x<(4b-9)/a
Let's solve for a.(−a)(x)+4b>9Step 1: Add -4b to both sides.  −ax+4b+−4b>9+−4b                                                                 −ax>−4b+9
Step 2: Divide both sides by -x.       −ax−x>−4b+9−x                                                                  a<4b−9x
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