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olya-2409 [2.1K]

3 years ago

12

Find the area of the triangle.

1 answer:

Thepotemich [5.8K]3 years ago

3 0

Answer:

$270 \:m^2$

Step-by-step explanation:

The area of the triangle.

$bh\frac{1}{2}$

$b \times h \times \frac{1}{2}$

$20 \times 27 \times \frac{1}{2}$

$540 \times 1/2$

$=270$

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1) State the area of the given trapezoid.

Ber [7]

Answer:

The answer would be 26

Step-by-step explanation:

First I divided the shape to make a rectangle and a right angle triangle, then i calculated the shape of the rectangle which came out to be 20. After that I calculated the area of the right angle triangle which is 6. So The answer would be 6 + 20 = 26

5 0

2 years ago

As a result of the installation of a muffler, the noise level of an engine was reduced from 89 to 72 decibels. Find the percent

Jobisdone [24]

Answer:

Step-by-step explanation:

Using the formula

Initial -final/initial =%/100

89-72/89 =%/100

17/89 =%/100

Making %subject of the formula

% =17*100/89

So % =1700/89

%= 19.101

Therefore rounding off the answer we have

X=19%

4 0

3 years ago

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mr_godi [17]

Answer:

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Step-by-step explanation:

there's only ten cubes

3 0

2 years ago

The first side of a triangle is 3 inches shorter than the second side, and 2 inches longer than the third side. How long is each

ziro4ka [17]

Answer:

the length of the first side of the triangle is $\frac{28}{3}\ in$

the length of the second side of the triangle is $\frac{37}{3}\ in$

the length of the third side of the triangle is $\frac{19}{3}\ in$

Step-by-step explanation:

Let

x-----> the length of the first side of a triangle

y----> the length of the second side of a triangle

z---> the length of the third side of a triangle

we know that

$x=y-3$

$y=x+3$ -----> equation A

$x=z+3$

$z=x-3$ -----> equation B

The perimeter of the triangle is equal to

$P=x+y+z$

$P=28\ in$

so

$28=x+y+z$ -----> equation C

substitute equation A and equation B in equation C

$28=x+(x+3)+(x-3)$

solve for x

$28=3x$

$x=\frac{28}{3}\ in$

Find the value of each side

the first side of a triangle is x

$x=\frac{28}{3}\ in$

the second side of a triangle is y

$y=\frac{28}{3}+3=\frac{37}{3}\ in$

the third side of a triangle is z

$z=\frac{28}{3}-3=\frac{19}{3}\ in$

7 0

3 years ago

Write the equation of the quadratic function that passes through the points (-1, 1), (1, 5), and (2,10).

Serjik [45]

Answer:

$\displaystyle f(x)=x^2+2x+2$

Step-by-step explanation:

<u>System Of Linear Equations </u>

In this problem, we'll need to solve a 3x3 system of linear equations because we have three unknowns and three conditions.

We are required to find the equation of the quadratic function that passes through the points (-1, 1), (1, 5), and (2,10)

The general quadratic function can be written as

$\displaystyle f(x)=ax^2+bx+c$

We need to find the values of a,b, and c. Let's use the first condition, i.e. f(-1)=1

$\displaystyle f(-1)=a(-1)^2+b(-1)+c$

$\displaystyle f(-1)=a-b+c$

$\displaystyle a-b+c=1.....[eq\ 1]$

Now we use the second condition f(1)=5

$\displaystyle f(1)=a(1)^2+b(1)+c$

$\displaystyle f(1)=a+b+c$

$\displaystyle a+b+c=5.......[eq\ 2]$

Finally, we use the third condition f(2)=10

$\displaystyle f(2)=a(2)^2+b(2)+c$

$\displaystyle f(2)=4a+2b+c$

$\displaystyle 4a+2b+c=10....[eq\ 3]$

We put together eq 1, eq 2, and eq 3 to form the system

$\displaystyle \left\{\begin{matrix}a-b+c=1\\ a+b+c=5\\ 4a+2b+c=10\end{matrix}\right.$

Adding the first two equations we have

$\displaystyle 2a+2c=6$

$\displaystyle a+c=3$

And also

$\displaystyle b=2$

Using the above equation and the value of b in the third equation, we have

$\displaystyle \left\{\begin{matrix}a+c=3\\ 4a+c=6\end{matrix}\right.$

Subtracting the first equation from the second

$\displaystyle 3a=3$

$\displaystyle a=1$

And therefore

$\displaystyle c=2$

Now we have all the values, the quadratic function is

$\displaystyle \boxed{f(x)=x^2+2x+2}$

6 0

2 years ago