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3 years ago

I don’t know how to solve the equation

Mathematics

1 answer:

Artemon [7]3 years ago

8 0

To solve this equation we have to factor.
We are looking for 2 numbers with a sum of -3, and multiplied they have to be -28. These numbers are -7 and 4.

So:
${x}^{2} - 3x - 28 = 0$
$(x - 7)(x + 4) = 0$
$x - 7 = 0 \: \: \: \: x + 4 = 0$
$x = 7 \: \: \: \: x = - 4$

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2 years ago

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3 years ago

Thomas needs to buy a cardboard sheet that will allow him to make his 224 in 3 box. To help construct the box, he decided to cut

Slav-nsk [51]

Answer:

Part 1; The volume of the box Thomas wants to make is 224 = 2·w² + 12·w

Part 2; The zeros for the equation of the function, are w = -14, or w = 8

Part 3

The width of the box is 8 inch

The length of the box, is 14 inches

The height of the box, is given as 2 inches

Part 4

Please find attached the graph of the function

Step-by-step explanation:

Part 1

The volume of the box Thomas wants to make, V = 224 in.³

The dimensions he cuts out from the length and width = 2 in² each

The length of the box = 6 inches + The width of the box

Let l represent the length of the box and let w represent the width of the box, we have;

l = 6 + w

The height of the box, h = The length of the cut out square = 2 inches

The volume of the box, V = Length, l × Width, w × Height, h

∴ V = l × w × h

l = 6 + w, h = 2

∴ V = (6 + w) × w × 2

V = 2·w² + 12·w,

The equation of the volume of the box, V = 2·w² + 12·w, where, V = 224

∴ 224 = 2·w² + 12·w

Part 2

The zeros of the equation for the volume of the box, V = 2·w² + 12·w, where, V = 224 are found as follows;

V = 224 = 2·w² + 12·w

∴ 2·w² + 12·w - 224 = 0

Dividing by 2 gives;

(2·w² + 12·w - 224)/2 = w² + 6·w - 112 = 0

∴ (w + 14) × (w - 8) = 0

The zeros for the equation of the function, are w = -14, or w = 8

Part 3

We reject the value, w = -14, therefore, the width of the box, w = 8 inch

The length of the box, l = 6 + w

∴ l = 6 + 8 = 14

The length of the box, l = 8 inches

The height of the box, h, is given as h = 2 inches

Part 4

The graph of the function created with MS Excel is attached

4 0

3 years ago

Evaluate k to the 6th power times p to the -7 power when k is 2 and p is -1

Solnce55 [7]

$\bf ~~~~~~~~~~~~\textit{negative exponents}
\\\\
a^{-n} \implies \cfrac{1}{a^n}
\qquad \qquad
\cfrac{1}{a^n}\implies a^{-n}
\qquad \qquad a^n\implies \cfrac{1}{a^{-n}}
\\\\[-0.35em]
\rule{34em}{0.25pt}\\\\
k^6p^{-7}~~
\begin{cases}
k=2\\
p=-1
\end{cases}\implies (2)^6(-1)^{-7}\implies \cfrac{2^6}{(-1)^7}\implies \cfrac{64}{-1}\implies -64$

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3 years ago