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3 years ago

10

X2 + 16x – 2 = 11

1 answer:

lord [1]3 years ago

6 0

Answer:

(x+8)^2=77 and x=negative 8±√77

Step-by-step explanation:

After watching a video, I got it right on Khan

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Which are true statements about a translation?

jeka94

a} The image is congruent to the pre-image.

c} The image could be moved left or right.

d} The image could be moved up or down.

6 0

3 years ago

an influencer had 400 subscribers in January. The number of subscribers have grown by a factor of 1.5 every month since then. wr

goblinko [34]

Answer:

y=400(1.5)^4

Step-by-step explanation:

5 0

3 years ago

A piece of cardboard is 15 inches by 30 inches. A square is to be cut from each corner and the sides folded up to make an open-t

solmaris [256]

Answer:

Maximum volume = 649.519 cubic inches

Step-by-step explanation:

A rectangular piece of cardboard of side 15 inches by 30 inches is cut in such that a square is cut from each corner. Let x be the side of this square cut. When it was folded to make the box the height of box becomes x, length becomes (30-2x) and the width becomes (15-2x).

Volume is given by

V = $V = Length\times Width\times Height\\V = (30 - 2x)(15-2x)x= 4x^3-90x^2+450x\\So,\\V(x) = 4x^3-90x^2+450x$

First, we differentiate V(x) with respect to x, to get,

$\frac{d(V(x))}{dx} = \frac{d(4x^3-12x^2+9x)}{dx} = 12x^2 - 180x +450$

Equating the first derivative to zero, we get,

$\frac{d(V(x))}{dx} = 0\\\\12x^2 - 180x +450 = 0$

Solving, with the help of quadratic formula, we get,

$x = \displaystyle\frac{5(3+\sqrt{3})}{2}, \frac{5(3-\sqrt{3})}{2}$ ,

Again differentiation V(x), with respect to x, we get,

$\frac{d^2(V(x))}{dx^2} = 24x - 180$

At x =

$\displaystyle\frac{5(3-\sqrt{3})}{2}$ ,

$\frac{d^2(V(x))}{dx^2} < 0$

Thus, by double derivative test, the maxima occurs at

x = $\displaystyle\frac{5(3-\sqrt{3})}{2}$ for V(x).

Thus, largest volume the box can have occurs when $x = \displaystyle\frac{5(3-\sqrt{3})}{2}}$ .

Maximum volume =

$V(\displaystyle\frac{5(3-\sqrt{3})}{2}) = (30 - 2x)(15-2x)x = 649.5191\text{ cubic inches}$

8 0

3 years ago

What does the fundamental theorem of algebra and its corollary tell you about the roots of the polynomial equation p(x)=0 where

denis23 [38]

Answer:

A polynomial with complex coefficients of degree n has n complex roots, counted with multiplicity.

Step-by-step explanation:

We are given a polynomial p(x) in the question with degree n.

The degree n means the n is the highest power of variable in the given polynomial.

The equation:

$p(x) = 0$

Fundamental theorem of Algebra

The Fundamental theorem of Algebra states that a a polynomial of degree n will have n roots of the equation.

This can further be explained as:

A polynomial with complex coefficients of degree n has n complex roots, counted with multiplicity.

3 0

3 years ago

The dimensions of a room are 4.2m by 6m. On a plan, the longer side is equal to 4 cm. What is the length of the shorter side on

Fiesta28 [93]

Answer: Length of shorter side is 2.8 cm.

Explanation:

Since we have given that

Dimensions of a room are given by

$4.2\ m\times 6\ m$

On a plan, the longer side = 4 cm

As we know that the ratio of original room is equal to ratio of plan room

So,

$\frac{4.2}{6}=\frac{x}{4}\\\\4.2\times 4=6x\\\\16.8=6x\\\\\frac{16.8}{6}=x\\\\2.8=x$

So, length of shorter side is 2.8 cm.

7 0

3 years ago

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