Which functions are continuous at x= -2? Select all that apply.

Answer:

± 1/2,±1, ±2,± 5/2, ±4 ,±5 , ±10, ± 20

Step-by-step explanation:

We can use the rational root theorem to find all the possible roots

2x^3+5x^2-8x-20=0  

Let the constant term  be called p and the leading term be called q.  Then the possible roots are the positive and negative roots of the factors of p/q

p = 20

q = 2

Factors of p: 1,2,4,5,10,20

Factors of q: 1,2

Possible roots

    1 ,2,4,5,10,20

±   --------------------------------------------------------

      1,2

So we get

±1, ±2, ±4 ,±5 , ±10 ± 20 ± 1/2± 2/2,±4/2,± 5/2,± 10/2,± 20/2

Simplifying

±1, ±2, ±4 ,±5 , ±10, ± 20, ± 1/2,± 1,±2,± 5/2,± 5,± 10

Eliminating repeats

±1, ±2, ±4 ,±5 , ±10, ± 20 ,± 1/2,± 5/2

Putting them in numerical order

± 1/2,±1, ±2,± 5/2, ±4 ,±5 , ±10, ± 20

Answer:

Its Option 1

Step-by-step explanation:

The possible rational roots will have a numerator that divides 20 (the last number) and a denominator that divides 2 (the coefficient of x^3).

For example 20/2, 10/2 and -1/2  =  10, 5 and -1/2.

The correct answer is the first option.

I think the answer is A, but I could be wrong. I think the answer is A, because it is the only equation that is linear. In mathematics a geometric sequence  is a sequence of numbers where each term after the first is found by multiplying the previous one by a fixed, non-zero number, meaning when you graph it the line should be linear. Of all of these A is the only that is Linear the others are not. The slope of line A is 2 and the Y-intercept is 3.

Since we are given that ABC is congruent to JKL, then AB has to be equal to JK

therefore --- [tex]14x+7=5x+34[/tex]

Subtract 7 from both sides

[tex]14x=5x+27[/tex]

Subtract 5x from each side

[tex]9x=27[/tex]

Divide 9 on each side

[tex]x=3[/tex]

Since, We are asked to find the length of AB and JK

plug in 3 for x

[tex]5(3)+34=15+34=49[/tex]

Answer:

B

(x-2) is a factor since remainder is 0.

Step-by-step explanation:

We divide (x-2) into the polynomial [tex]-4x^4+6x^3+8x^2-6x-4[/tex] through long division or synthetic. We choose long division and look for what will multiply with (x-2) to make the polynomial [tex]-4x^4+6x^3+8x^2-6x-4[/tex] .

[tex](x-2)(-4x^3)=-4x^4+8x^3[/tex]

We subtract this from the original [tex]-4x^4-(-4x^4)+6x^3-(8x^3)+8x^2-6x-4[/tex].

This leaves [tex]-2x^3+8x^2-6x-4[/tex]. We repeat the step above.

[tex](x-2)(-2x^2)=-2x^3+4x^2[/tex].

We subtract this from [tex]-2x^3-(-2x^3)+8x^2-(4x^2)-6x-4=4x^2-6x-4[/tex]. We repeat the step above.

[tex](x-2)(4x)=4x^2-8x[/tex].

We subtract this from [tex]4x^2-(4x^2)-6x-(-8x)-4=2x-4[/tex]. We repeat the step above.

[tex](x-2)(2)=2x-4[/tex].

We subtract this from [tex]2x-(2x)-4-(4)=0[/tex]. There is no remainder. This means (x-2) is a factor.

The remainder R when the polynomial p(x) = -4x4 + 6x3 + 8x2 - 6x - 4 is divided by (x - 2) is 0, indicating that (x - 2) is indeed a factor of p(x).

To find the remainder R when the polynomial p(x) = -4x4 + 6x3 + 8x2 - 6x - 4 is divided by (x - 2), we can use the Remainder Theorem. The Remainder Theorem states that the remainder of the division of a polynomial p(x) by a linear term (x - a) is equal to p(a). Therefore, to find R, simply calculate p(2).

p(2) = -4(2)4 + 6(2)3 + 8(2)2 - 6(2) - 4

p(2) = -4(16) + 6(8) + 8(4) - 12 - 4

p(2) = -64 + 48 + 32 - 12 - 4

p(2) = 0

Since the remainder is 0, this means that (x - 2) is a factor of p(x).

The correct answer is therefore R = 0, and yes, (x - 2) is a factor of p(x).

Answer:

12 dogs

Step-by-step explanation:

Let d = dogs

c = cats

d = 3c

c+d = 16

Substitute d =3c into the second equation

c+3c = 16

Combine like terms

4c = 16

Divide by 4

4c/4 = 16/4

c = 4

There are 4 cats

We still need to find the number of dogs

d = 3c

d = 3*4

   = 12

There are 12 dogs

Answer:

cats = 4; dogs = 12

Step-by-step explanation:

There are 3 times more dogs than cats.

There are 16 dogs and cats in all.

Let:

dogs = d ; cats = c

Set the system of equations:

d + c = 16

3c = d

Plug in 3c for d (as d = 3c) in the first equation

(3c) + c = 16

Simplify. Combine like terms:

(3c + c) = 16

4c = 16

Isolate the variable. Note the equal sign, what you do to one side, you do to the other. Divide 4 from both sides

(4c)/4 = (16)/4

c = 16/4

c = 4

Plug in 4 for c in one of the equations.

d + c = 16

d + (4) = 16

Isolate the variable. Note the equal sign, what you do to one side, you do to the other. Subtract 4 from both sides

d + 4 (-4) = 16 (-4)

d = 16 - 4

d = 12

Answers: c = 4; d = 12

~

Answer:

320.

Step-by-step explanation:

1,000 - the 680 that have been completed gives you 320.

Answer:

He will make 16.50 per hour after his raise.

Step-by-step explanation:

15 x .10 = 1.50

15.00 + 1.50 = 16.50

Answer: 13 units

The x value goes from x = 21 to x = 9, which is an x distance of 12 units (21-9 = 12)

The y distance is 5 units (16-11 = 5)

We have a right triangle with legs of 12 and 5. The hypotenuse is x

Use the pythagorean theorem to find x

a^2 + b^2 = c^2

5^2 + 12^2 = x^2

25 + 144 = x^2

169 = x^2

x^2 = 169

x = sqrt(169)

x = 13

The hypotenuse of this right triangle is 13 units, so this is the distance between the two points.

Answer:

x > 5

Step-by-step explanation:

isolate x by subtracting 7 from both sides

x > 12 - 7

x > 5

The point-slope form of line:

[tex]y-y_1=m(x-x_1)\\\\m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]

We have the points (-5, -6) and (2, 8). Substitute:

[tex]m=\dfrac{8-(-6)}{2-(-5)}=\dfrac{8+6}{2+5}=\dfrac{14}{7}=2\\\\y-(-6)=2(x-(-5))\\\\\boxed{y+6=2(x+5)}[/tex]

Answer:

B

Step-by-step explanation:

Let [tex]r[/tex] be the radius of one sphere.

Since radius is r,  the height of the cylinder will be [tex]4r[/tex]

Also, the cylinder has the same radius as the sphere: [tex]r[/tex]

Plugging in the values we get: [tex]V=\pi (r)^{2}(4r)=4\pi r^3[/tex]

Ratio of volume of 1 sphere to volume of cylinder is:

[tex]\frac{\frac{4}{3}\pi r^3}{4\pi r^3}=\frac{\frac{4}{3}}{4}=\frac{4}{3}*\frac{1}{4}=\frac{1}{3}[/tex]

The ratio is 1:3

Answer choice B is right.

Rectangle is the closed shaped polygon with 4 sides. Opposite sides of the rectangle are equal. when the length and the width of the sandbox are doubled the percent of change in the perimeter is 100 percent and the percent of change in the area is 300 percent.

Given-

The length of the sandbox is 10.

The width of the sandbox is 6.

a) The percent of change in the perimeter.

The perimeter of the rectangle is the twice of the sum of its side.The perimeter P of the sandbox is,

[tex]P =2\times (10+6)[/tex]

[tex]P =2\times (16)[/tex]

[tex]P=32[/tex]

When the length and the width of the sandbox are doubled the perimeter [tex]P_d[/tex] of the box is,

[tex]P_d=2\times(20+12)[/tex]

[tex]P_d=2\times(32)[/tex]

[tex]P_d=64[/tex]

Percentage [tex]\DeltaP[/tex][tex]\Delta P[/tex] change in the perimeter,

[tex]\Delta P=\dfrac{64-32}{32}\times 100[/tex]

[tex]\Delta P=100[/tex]

b) The percent of change in the area.

The area of the rectangle is the product of its side.The area A of the sandbox is,

[tex]A = (10\times6)[/tex]

[tex]A=60[/tex]

When the length and the width of the sandbox are doubled the area [tex]A_d[/tex] of the box is,

[tex]A_d=20\times12[/tex]

[tex]P_d=240[/tex]

Percentage [tex]\DeltaP[/tex][tex]\Delta A[/tex] change in the area,

[tex]\Delta A=\dfrac{240-60}{60}\times 100[/tex]

[tex]\Delta P=300[/tex]

Thus when the length and the width of the sandbox are doubled the percent of change in the perimeter is 100 percent and the percent of change in the area is 300 percent.

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Answer:

The game costs 32 dollars total, we know this because if you divid 32 by 4 its 8 and . if you multiply 8 times 3 its 24

Step-by-step explanation:

The total cost of the game is $32, calculated using the concept of fractions in mathematics where the given $24 was considered as three-fourths of the total game cost.

The subject of the question involves the concept of fractions in mathematics. Here the information provided states that $24, which Ivanna has saved, represents three-fourths (or 3/4) of the total cost of the game. To find out the total cost of the game, we will consider the $24 as three parts, and we need to find out the value of one part (or one-fourth). So, we divide $24 by 3, which gives us $8. This $8 is one-fourth of the total game cost. Now, to get the total cost, we will multiply this one-fourth value ($8) by 4. So, the total cost of the game is $8 * 4 = $32.

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Answer:

b

Step-by-step explanation:

B// 8pi x-24pi

Question:

line x + 2y = 0 is end side of angle θ

and cos θ < 0

Answer: sin θ = √5/5

Step-by-step explanation:

cos θ < 0 means x < 0

Line is y = -x/2, slope -1/2

Line intersects unit circle when x^2+y^2=1

x^2 + (-x/2)^2 = 1

x^2 + x^2/4 = 1

5x^2/4 = 1

x = -√(4/5) = -2√(1/5) = -2√5/5

y = √5/5

x^2 = 4/5, y^2 = 1/5

sin θ is y value at intersection of line and unit circle, √5/5

In this exercise we have to use the given equation and thus calculate the intersection value:

[tex]sin (\theta) = \sqrt{5/5}[/tex]

So knowing that you were informed:

Line x + 2y = 0 is end side of angle θ and  cos θ < 0 means x < 0.  Line is y = -x/2, slope -1/2 and the  Line intersects unit circle when :

[tex]x^2+y^2=1\\x^2 + (-x/2)^2 = 1\\x^2 + x^2/4 = 1\\5x^2/4 = 1\\x = -\sqrt{4/5} = -2\sqrt{1/5} = -2\sqrt{5/5}\\y = \sqrt{5/5}\\x^2 = 4/5, y^2 = 1/5[/tex]

[tex]sin(\theta)[/tex]  is y value at intersection of line and unit circle, [tex]\sqrt{5/5}[/tex]

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Answer:

A. the graph flip over the x - axis...

Option b) the graph flips over the line y=x

When you multiply two function together, you will get a third function as the result,  and that third function as the result, and that third function will be the product of the two original functions . when we multiply the function by -1 ,it becomes y=-f(x)  . Then the coordinates becomes (x, -f(x))

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Answer: Choice D) approaches y = -4

"x increases without bound" is another way of saying "x heads off to positive infinity". Visually, you follow the graph curve going to the right. As the graph shows, the curve steadily gets closer to the horizontal line y = -4, but it never actually gets there. This line is the horizontal asymptote.

We can first find the probability of the first person picking Brand A, which would be:

9/6+9

=9/15

=3/5

We can then find the probability of the second person choosing brand A:

(9-1)/(6+9-1)

=8/14

To find the probability they both select Brand A, we could multiply them together:

3/5 x 8/14

=12/35

Therefore the answer would be 12/35.

Hope it helps!

Answer:

2 and 6

Step-by-step explanation:

Corresponding angles are the angles that occupy the same relative position at each intersection.  

1 and 5

2 and 6

4 and 8

3 and 7

Answer:

P ( blue ) =  1/4

P ( white ) =  5/12

P ( red ) = 1/3

P ( not red ) =  2/3

Step-by-step explanation:

To find the probability of a marble being chosen,  it is the number of that color over the total

We need to find the total number of marbles

4 red+ 5 white+3 blue = 12 marbles

P ( blue ) = 3 blue / 12 total = 3/12 = 1/4

P ( white ) = 5 white / 12 total = 5/12

P ( red ) = 4 red/ 12 total = 4/12 = 1/3

How man marbles are not red

total marbles - red marbles = 12-4 = 8

8 marbles are not red

P ( not red ) = 8 not red / 12 total = 8/12 = 2/3

Answer:

C

Step-by-step explanation:

The measure of an exterior angle of a triangle is equal to the sum of the measures of the two remote interior angles.

The measure of an exterior angle of a triangle is equal to the sum of the measure of the two opposite interior angles.

A triangle is a three-sided closed-plane figure formed by joining three noncolinear points. Based on the side property triangles are of three types they are Equilateral triangle, Scalene triangle, and Isosceles triangle.

We know the sum of all the interior angles in a triangle is 180°.

We also know that the measure of an exterior angle of a triangle is the sum of the measure of two opposite interior angles.

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Answer:

A difference of squares has the following form [tex]a^2-b^2[/tex]. Any two perfect squares connected by subtraction can be factored.

It factors to (a+b)(a-b).

Step-by-step explanation:

A binomial is an expression with only terms where at least one is a term with a variable. When we can factor for difference of squares, we can have two variable terms or just one with a constant.

A difference of squares has the following form [tex]a^2-b^2[/tex]. Any two perfect squares connected by subtraction can be factored.

It factors to (a+b)(a-b).

Answer:

Warning:

I think that these are correct, but don't make this your official source :)

7. B

8. D

9. B

I hope this helps :)

Answer:

∠A=40°

Step-by-step explanation:

Equation 1: ∠A+∠B+∠C=180°

Equation 2: ∠B/2+∠C/2+110°=180°

2(Equation 2): ∠B+∠C+220°=360°

                                 ∠B+∠C=140°

Equation 1 - 2(Equation 2): ∠A=40°

Therefore, ∠A=40°

Answer:

2/3 - 1/4

=> taking L.C.M of the denominators we get,

=> 8/12-3/12

=> 5/12 is left with her,, ;)

HOPE THIS HELPS YOU...;)

Answer: Choice B (1,-2)

note: I'm assuming there is a "less than or equal to" sign as part of the given inequality, rather than a simple "less than" sign (without the "or equal to" part)

============================================

Work Shown:

Plug in x = -2 and y = 4 from the point (x,y) = (-2, 4). Then simplify. If you get a true statement, then this is a solution point

[tex]y - 4x \le -6[/tex]

[tex]4 - 4*(-2) \le -6[/tex]

[tex]4 + 8 \le -6[/tex]

[tex]12 \le -6[/tex]

This statement is false. The value 12 is not to the left of -6 on the number line, nor is 12 equal to -6. So (x,y) = (-2,4) is not a solution

-------------

Plug in x = 1 and y = -2

[tex]y - 4x \le -6[/tex]

[tex]-2 - 4*(1) \le -6[/tex]

[tex]-2 - 4 \le -6[/tex]

[tex]-6 \le -6[/tex]

This statement is true, but only if the inequality sign is a "less than or equal to" sign. Otherwise, the statement is false because -6 cannot be smaller than itself.

-------------

Plug in x = 1 and y = 3

[tex]y - 4x \le -6[/tex]

[tex]3 - 4*(1) \le -6[/tex]

[tex]3 - 4 \le -6[/tex]

[tex]-1 \le -6[/tex]

Like choice A, this is false. So (x,y) = (1,3) is not a solution

-------------

Plug in x = 2 and y = 3

[tex]y - 4x \le -6[/tex]

[tex]3 - 4*(2) \le -6[/tex]

[tex]3 - 8 \le -6[/tex]

[tex]-5 \le -6[/tex]

We end up with another false statement. So (x,y) = (2,3) isn't a solution either.

Answer:

It is 15% off

Step-by-step explanation:

30.00-(15%×30.00)= 25.5

Answer:

$68.32

Step-by-step explanation:

Is 9.76 = x

And the value needed is 8 * this amount, then it can be shown with 8x

8x = 9.76 * 8

8x = 78.08

So the total price is $78.08

To find the money needed, simply subtract the saved money from this amount:

78.08 - 9.76 = 68.32

So she needs $68.32!

Isabelle needs $78.08 to buy the bicycle, which is 8 times her current savings of $9.76.

Isabelle's current savings stands at $9.76. But she needs to have 8 times this amount in order to buy the bicycle. Mathematically speaking, you find how much she needs by multiplying her current savings by 8. So, $9.76 x 8 equals $78.08. Therefore, Isabelle needs a total sum of $78.08 to buy the bicycle.

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