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2 years ago

Find the value of c so that the polynomial p is divisible by (x+2)

Mathematics

1 answer:

alexandr1967 [171]2 years ago

3 0

Answer:

The value of c is 8.

Step-by-step explanation:

When a function is divisible by a factor, it will get 0 value. So, you have to substitute x = -2 into p(x) and equals to 0 :

$p(x) = 4 {x}^{3} + c {x}^{2} + x + 2$

$p( - 2) = 4 {( - 2)}^{3} + c {( - 2)}^{2} + ( - 2) + 2$

$4( - 8) + 4c - 2 + 2 = 0$

$- 32 + 4c = 0$

$4c = 32$

$c = 32 \div 4$

$c = 8$

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The angle between the two altitudes of a parallelogram through the vertex of an obtuse angle of the parallelogram is 60°. Find t

Galina-37 [17]

Answer:

∠A = ∠C = 60°

∠B = ∠D = 120°

Step-by-step explanation:

In quad. DPBQ, by angle sum property we have

∠PDQ + ∠DPB + ∠B + ∠BQD = 360°

60° + 90° + ∠B + 90° = 360°

∠B = 360° – 240°

Therefore, ∠B = 120°

But ∠B = ∠D = 120° opposite angles of parallelogram

As, AB || CD opposite sides of a parallelogram

∠B + ∠C = 180° sum of adjacent interior angles is 180°

120° + ∠C = 180°

∠C = 180° – 120° = 60°

Hence ∠A = ∠C = 60° Opposite angles of parallelogram are equal

7 0

2 years ago

Marla bought 12 books for $27.60. What is the price per book?

Ilia_Sergeevich [38]

Answer: $2.30

Step-by-step explanation:

Because if we do $27.60 divided by 12 we get 2.3 which then means 1 book cost $2.30

HOPE THIS HELPS ^^

7 0

2 years ago

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The width of a rectangle is 1 units less than the length. The area of the rectangle is 72 units. What is the width, in units, of

nalin [4]

A = l × w. Substitute 72 into A and fill in the rest of the equation.

w = l - 1. Plug l - 1 into w

72 = l × (l - 1). Multiply l by (l - 1)

72 = l^2 - l. Subtract 72 from each side.

0 = l^2 - l - 72. Factor.

0 = (l + 8) (l - 9). Set each term equal to zero.

(l + 8) = 0. Subtract 8 from each side.

l = -8. Length cant be a negative number so let's try the other term.

(l - 9) = 0. Add 9 to each side.

l = 9. The length is 9.

Earlier we stated that the width is one less than the length, therefore, the width is 9 - 1 = 8.

The width is 8 units.

8 0

2 years ago

Can somebody help me with (a) and (b)? Thanks! :D

Pachacha [2.7K]

Answer:

PART A:

Line m: 1/2x + 6

Line n: 1/2x - 3

PART B:

The slope is the same in both lines

6 0

2 years ago

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Sanjay graphs a quadratic function that has x-intercepts of –3 and 7. Which functions could he have graphed?

kykrilka [37]

we will select each options and find zeros

(a)

$g(x)=x^2-4x-21$

for finding x-intercept , we can set g(x)=0

and then we can solve for x

$g(x)=x^2-4x-21=0$

now, we can factor it

$(x-7)(x+3)=0$

we get

$x=7,x=-3$

so, this is TRUE

(b)

$g(x)=(x-3)(x+7)$

we can set it to 0

and then we can solve for x

$g(x)=(x-3)(x+7)=0$

we get

$x=3,x=-7$

so, this is FALSE

(c)

$g(x)=3x^2-12x-63$

we can set it to 0

and then we can solve for x

$g(x)=3x^2-12x-63 =0$

$3(x^2-4x-21) =0$

$3(x-7)(x+3) =0$

$x=-3,x=7$

so, this is TRUE

(d)

$g(x)=-(x+3)(x-7)$

now, we can set it to 0

and then we can solve for x

$g(x)=-(x+3)(x-7)=0$

$x=-3,x=7$

so, this is TRUE

(e)

we have

$g(x)=x^2+4x-21$

now, we can set it to 0

and then we can solve for x

$g(x)=x^2+4x-21=0$

$(x+7)(x-3)=0$

$x=-7,x=3$

so, this is FALSE

5 0

2 years ago

Read 2 more answers