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3 years ago

A square is shown below. Which expression can be used to find the area, in square units, of the shaded triangle in the square?

Mathematics

1 answer:

AlexFokin [52]3 years ago

6 0

The area of a square would me multiplying the width times the length and then multiplying by one half would be like splitting the square in half so your answer would be that last one right there. 6*6= area then multiply by 1/2 = half of area Hope this helps! :D

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Tell whether the angles are adjacent or vertical. Then find the value of x.

Nimfa-mama [501]

Answer:

adjacent, x=15

Step-by-step explanation:

the angels are connected so they are adjacent, the red box shows that it is a 90 degree angle so adding both angels together means 90=6x so x=15

8 0

3 years ago

12 out of 15 students play in the school band. In a class of 45 students, how many do NOT play in the band? |

jek_recluse [69]

Answer:36

becuse if you maltiply 15 by 3 it makes 45 and you can maltiply 12 by 3 and you will get your answer

3 0

3 years ago

<img src="https://tex.z-dn.net/?f=prove%20that%5C%20%20%5Ctextless%20%5C%20br%20%2F%5C%20%20%5Ctextgreater%20%5C%20%5Cfrac%20%7B

inysia [295]

$\large \bigstar \frak{ } \large\underline{\sf{Solution-}}$

Consider, LHS

$\begin{gathered}\rm \: \dfrac { \tan \theta + \sec \theta - 1 } { \tan \theta - \sec \theta + 1 } \\ \end{gathered}$

We know,

$\begin{gathered}\boxed{\sf{ \:\rm \: {sec}^{2}x - {tan}^{2}x = 1 \: \: }} \\ \end{gathered} \\ \\ \text{So, using this identity, we get} \\ \\ \begin{gathered}\rm \: = \:\dfrac { \tan \theta + \sec \theta - ( {sec}^{2}\theta - {tan}^{2}\theta )} { \tan \theta - \sec \theta + 1 } \\ \end{gathered}$

We know,

$\begin{gathered}\boxed{\sf{ \:\rm \: {x}^{2} - {y}^{2} = (x + y)(x - y) \: \: }} \\ \end{gathered} \\$

So, using this identity, we get

$\begin{gathered}\rm \: = \:\dfrac { \tan \theta + \sec \theta - (sec\theta + tan\theta )(sec\theta - tan\theta )} { \tan \theta - \sec \theta + 1 } \\ \end{gathered}$

can be rewritten as

$\begin{gathered}\rm\:=\:\dfrac {(\sec \theta + tan\theta ) - (sec\theta + tan\theta )(sec\theta -tan\theta )} { \tan \theta - \sec \theta + 1 } \\ \end{gathered} \\ \\ \\\begin{gathered}\rm \: = \:\dfrac {(\sec \theta + tan\theta ) \: \cancel{(1 - sec\theta + tan\theta )}} { \cancel{ \tan \theta - \sec \theta + 1} } \\ \end{gathered} \\ \\ \\\begin{gathered}\rm \: = \:sec\theta + tan\theta \\\end{gathered} \\ \\ \\\begin{gathered}\rm \: = \:\dfrac{1}{cos\theta } + \dfrac{sin\theta }{cos\theta } \\ \end{gathered} \\ \\ \\\begin{gathered}\rm \: = \:\dfrac{1 + sin\theta }{cos\theta } \\ \end{gathered}$

<h2>Hence,</h2>

$\begin{gathered} \\ \rm\implies \:\boxed{\sf{ \:\rm \: \dfrac { \tan \theta + \sec \theta - 1 } { \tan \theta - \sec \theta + 1 } = \:\dfrac{1 + sin\theta }{cos\theta } \: \: }} \\ \\ \end{gathered}$

$\rule{190pt}{2pt}$

5 0

2 years ago

Write an expression for the calculation 84 divided into sevenths added to 9 divided into thirds

VladimirAG [237]

The answer:
_______________
$\frac{84}{7}$ + $\frac{9}{3}$ .

6 0

3 years ago

Which ordered pair is the solution to the system of equations?

Virty [35]

-1*/x+3y=12
<span>-4x+3y=-3

-x-3y= -12
-4x+3y= -3
+-------------------
-5x= -15
x=3

</span><span>x+3y=12
</span><span>
3+3y=12

3y=9 y=3

(x,y)=(3,3)</span>

5 0

3 years ago

Read 2 more answers