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3 years ago

A rectangular box is created by cutting out squares of equal sides

Mathematics

1 answer:

stiks02 [169]3 years ago

5 0

Well, the box will have 7in long 4 in wide and 2 in high

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The length of a rectangle is the width minus 8 units. The area of the rectangle is 9 units. What is the length, in units, of the

frez [133]

Length of rectangle is 1 unit

<u>Solution: </u>

Given that

Length of a rectangle is width minus 8 units.

Area of rectangle = 9 square units

Need to calculate the length of rectangle.

Let us assume width of rectangle = x

As Length is width minus 8,

Length of the rectangle = x – 8

$\text{ Area of rectangle }=\text{ width of rectangle }\times \text{ Length of the rectangle }$

$\text{ Area of rectangle }= x\times (x-8)$

$\text { Area of rectangle }=\left(x^{2}-8 x\right)$

As given that area of rectangle = 9 square units

$\begin{array}{l}{\Rightarrow x^{2}-8 x=9} \\\\ {\Rightarrow x^{2}-8 x-9=0}\end{array}$

On solving above quadratic equation for x, we get

$\begin{array}{l}{\Rightarrow x^{2}-9 x+x-9=0} \\\\ {\Rightarrow x(x-9)+1(x-9)=0} \\\\ {\Rightarrow (x-9)(x+1)=0}\end{array}$

When $x-9 =9, x = 9$

When $x + 1 = 0, x = -1$

As width cannot be negative, so considering x = 9

$\text{ Length of rectangle }= x-8 = 9-8 = 1 \text{ unit }$

Hence, Length of rectangle is 1 unit.

5 0

3 years ago

Which of the following terms best describes three points that all lie in a straight line?A. CollinearB. CongruentC. EqualD. Midp

Ket [755]

Answer:

A. Collinear

Step-by-step explanation:

three points that all lie in a straight line

A. Collinear- means along the same line

B. Congruent - means the same

C. Equal = means the same

D. Midpoint= means the middle

8 0

3 years ago

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The length of a side of a triangle is 26 in. A line, parallel to the given side ,divides the triangle into 2 parts of equal area

Ugo [173]

Answer:

13 $\sqrt{2}$

7 0

3 years ago

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What is the equation of the line that passes through the point (8,1) and has a slope of 3/4

iris [78.8K]

Answer:

believe the answer is

$y = \frac{3}{4} x - 5$

Step-by-step explanation:

Hope this helps!

3 0

3 years ago

Find the angle between the given vector in degrees. u=<6, 4>, v=<7, 5> HELPPPPPPPPPP

Paladinen [302]

Recall that

$\vec a\cdot\vec b=\|\vec a\|\|\vec b\|\cos\theta$

where $\theta$ is the angle between the vectors $\vec a,\vec b$ whose magnitudes are $\|\vec a\|,\|\vec b\|$ , respectively.

We have

$\langle6,4\rangle\cdot\langle7,5\rangle=\sqrt{6^2+4^2}\sqrt{7^2+5^2}\cos\theta$

$\cos\theta=\dfrac{31}{\sqrt{962}}\implies\theta\approx88.2^\circ$

7 0

3 years ago