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4 years ago

Find the missing length . Leave your answers in simplest radical form

Mathematics

1 answer:

Iteru [2.4K]4 years ago

7 0

We have the triangle 30° - 60° - 90°.

The lenght of the sides are in proportion: $1:2:\sqrt3\to a:2a:a\sqrt3$ .

$a=y\\2a=x\\a\sqrt3=5\qquad\text{multiply both sides by}\ \sqrt3\\\\3a=5\sqrt3\qquad\text{divide both sides by 3}\\\\a=\dfrac{5\sqrt3}{3}\\\\2a=2\cdot\dfrac{5\sqrt3}{3}=\dfrac{10\sqrt3}{3}$

Answer:

$x=\dfrac{10\sqrt3}{3}\\\\y=\dfrac{5\sqrt3}{3}$

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Help me with question a please ! With full workings !

frosja888 [35]

A)

$\bf \textit{distance between 2 points}\\ \quad \\
\begin{array}{lllll}
&x_1&y_1&x_2&y_2\\
% (a,b)
Q&({{ 0}}\quad ,&{{ 2}})\quad 
% (c,d)
P&({{ 0.5}}\quad ,&{{ 0}})
\end{array}\qquad 
% distance value
d = \sqrt{({{ x_2}}-{{ x_1}})^2 + ({{ y_2}}-{{ y_1}})^2}$

$\bf QP=\sqrt{(0.5-0)^2+(0-2)^2}\implies QP=\sqrt{0.5^2+2^2}
\\\\\\
QP=\sqrt{\left( \frac{1}{2} \right)^2+4}\implies QP=\sqrt{ \frac{1^2}{2^2}+4}\implies QP=\sqrt{\frac{1}{4}+4}
\\\\\\
QP=\sqrt{\frac{17}{4}}\implies QP=\cfrac{\sqrt{17}}{\sqrt{4}}\implies QP=\cfrac{\sqrt{17}}{2}$

b)

since QR=QP, that means that QO is an angle bisector, and thus the segments it makes at the bottom of RO and OP, are also equal, thus RO=OP

thus, since the point P is 0.5 units away from the 0, point R is also 0.5 units away from 0 as well, however, is on the negative side, thus R (-0.5, 0)

c)

what's the equation of a line that passes through the points (-0.5, 0) and (0,2)?

$\bf \begin{array}{lllll}
&x_1&y_1&x_2&y_2\\
% (a,b)
Q&({{ 0}}\quad ,&{{ 2}})\quad 
% (c,d)
R&({{ -0.5}}\quad ,&{{ 0}})
\end{array}
\\\\\\
% slope = m
slope = {{ m}}= \cfrac{rise}{run} \implies 
\cfrac{{{ y_2}}-{{ y_1}}}{{{ x_2}}-{{ x_1}}}\implies \cfrac{0-2}{-0.5-0}\implies \cfrac{-2}{-0.5}$

$\bf m=\cfrac{\frac{-2}{1}}{-\frac{1}{2}}\implies \cfrac{-2}{1}\cdot \cfrac{2}{-1}\implies 4
\\\\\\
% point-slope intercept
y-{{ y_1}}={{ m}}(x-{{ x_1}})\implies y-2=4(x-0)\implies y=4x+2\\
\left. \qquad \right. \uparrow\\
\textit{point-slope form}$

7 0

3 years ago

Find the rate of change:

AURORKA [14]

It takes 2 gallons of gas for each 50 Mike's you drive so rate of change is 25 miles per gallon

7 0

3 years ago

Two more than four times a number is -18 ((I have to solve it too!!))

vivado [14]

4 x -5= -20 and -20 + 2 = -18

The number is -5

5 0

4 years ago

(2k + 3k) + ( 9k - 7k + 8)

tamaranim1 [39]

(2k + 3k) + (9k - 7k + 8)
(5k) + (2k + 8)
7k+8

7k + 8 is the answer

5 0

4 years ago

Read 2 more answers

Write a linear function f with the values f(0)=-1 and f(2)=-5

Darya [45]

Answer:

f(x) = - 2x - 1

Step-by-step explanation:

Let the linear function f(x) is given by f(x) = ax + b where a and b are unknown constants.

Given that f(0) = -1 and f(2) = -5

Hence, a(0) + b = - 1, ⇒ b = - 1

Again from the condition given

a(2) + b = -5, ⇒ 2a - 1 = - 5, ⇒ 2a = - 4, ⇒ a = - 2.

Therefore, the linear function is f(x) = - 2x - 1 (Answer)

5 0

3 years ago