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3 years ago

What is the area of the cross section if the length is 12 cm and the width is 10 cm?

Mathematics

1 answer:

VARVARA [1.3K]3 years ago

6 0

Answer:

120 cm²

Step-by-step explanation:

From the question;

Length is 12 cm
Width is 10 cm

We are required to determine the area of the cross section;

Note that the cross section is the plane of a solid that remains constant through the solid.
In this case, the cross section is a rectangle whose dimensions are 12 cm by 10 cm.

But Area of a rectangle = Length × Width

Therefore;

Area of cross section = 12 cm × 10 cm

= 120 cm²

Thus, area of the cross section is 120 cm²

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Find all roots: x^3 + 7x^2 + 12x = 0 Show all work and check your answer.

Aliun [14]

The three roots of x^3 + 7x^2 + 12x = 0 is 0,-3 and -4

Solution:

We have been given a cubic polynomial.

$x^{3}+7 x^{2}+12 x=0$

We need to find the three roots of the given polynomial.

Since it is a cubic polynomial, we can start by taking ‘x’ common from the equation.

This gives us:

$x^{3}+7 x^{2}+12 x=0$

$x\left(x^{2}+7 x+12\right)=0$ ----- eqn 1

So, from the above eq1 we can find the first root of the polynomial, which will be:

x = 0

Now, we need to find the remaining two roots which are taken from the remaining part of the equation which is:

$x^{2}+7 x+12=0$

we have to use the quadratic equation to solve this polynomial. The quadratic formula is:

$x=\frac{-b \pm \sqrt{b^{2}-4 a c}}{2 a}$

Now, a = 1, b = 7 and c = 12

By substituting the values of a,b and c in the quadratic equation we get;

$\begin{array}{l}{x=\frac{-7 \pm \sqrt{7^{2}-4 \times 1 \times 12}}{2 \times 1}} \\\\{x=\frac{-7 \pm \sqrt{1}}{2}}\end{array}$

Therefore, the two roots are:

$\begin{array}{l}{x=\frac{-7+\sqrt{1}}{2}=\frac{-7+1}{2}=\frac{-6}{2}} \\\\ {x=-3}\end{array}$

And,

$\begin{array}{c}{x=\frac{-7-\sqrt{1}}{2}} \\\\ {x=-4}\end{array}$

Hence, the three roots of the given cubic polynomial is 0, -3 and -4

4 0

3 years ago

How does the graph of y=|x|+ 4 compare to the graph of the parent function y=|x|?

neonofarm [45]

Answer:

Please check the explanation and attached graph.

Step-by-step explanation:

Given the parent function

y = |x|

In order to translate the absolute function y = |x| vertically, we can use the function

g(x) = f(x) + h

when h > 0, the graph of g(x) translated h units up.

Given that the image function

y=|x|+4

It is clear that h = 4. Since 4 > 0, thus the graph y=|x|+4 translated '4' units up.

The graph of both parent and translated function is attache below.

In the graph,

The blue line represents the parent function y=|x|.

The red line represents the image function y=|x| + 4.

It is clear from the graph that the y=|x| + 4 translated '4' units up.

Please check the attached graph.

3 0

2 years ago

What is 0.000000025 written in exponent form plz hurry

Evgesh-ka [11]

Answer:2.5×10^-5. (And i think u meant in Scientific Notation)

Step-by-step explanation//Give thanks(and or Brainliest) if helpful (≧▽≦)//

4 0

3 years ago

Type the correct answer in each box. Use numerals instead of words. If necessary, use / for the fraction bar(s). Consider the gi

STatiana [176]

Answer:

To determine the inverse of the given function, change f(x) to y, switch x and y and solve for y and $f^{-1}(x)= \frac{ln\ x+4}{2}$

Step-by-step explanation:

Data provided in the question

f(x) = e^2x - 4

Now

to find the inverse let

So,

y = e^2x - 4

Now

Replace x and y

Therefore

x = e^2y - 4

Now compute the value of y

So,

x + 4 = e^2y

Now take ln on both sides:

The equation is

ln(x+4) = ln(e^2y)

ln(x+4) = 2y

y = ln(x+4) ÷ 2

$f^{-1}(x)= \frac{ln\ x+4}{2}$

Therefore, To determine the inverse of the given function, change f(x) to y, switch x and y and solve for y and $f^{-1}(x)= \frac{ln\ x+4}{2}$

5 0

3 years ago

If BTS=GHD BS=25 TS=14 BT=31 GD=4x-11 S=56 B=21 and H=(7y+5) find the values of x and y

77julia77 [94]

Given:

Consider the completer question is "If ∆BTS≅∆GHD, BS=25, TS=14, BT=31, GD=4x-11, m∠S=56, m∠B=21 and m∠H=(7y+5), find the values of x and y.

To find:

The values of x and y.

Solution:

We have,

$\Delta BTS\cong \Delta GHD$ (Given)

$BS=GD$ (CPCTC)

$25=4x-11$

$25+11=4x$

$36=4x$

Divide both sides by 4.

$9=x$

In ∆BTS,

$\angle B+\angle T+\angle S=180^\circ$ (Angle sum property)

$21^\circ+\angle T+56^\circ=180^\circ$

$77^\circ+\angle T=180^\circ$

$\angle T=180^\circ-77^\circ$

$\angle T=103^\circ$

Now,

$\angle T=\angle H$ (CPCTC)

$103=7y+5$

$103-5=7y$

$98=7y$

Divide both sides by 7.

$14=y$

Therefore, the value of x is 9 and value of y is 14.

3 0

3 years ago