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vesna_86 [32]
3 years ago
5

Lia has $24. Lia and her brother together have a total of $45. The solution of the equation 24 + x = 45 is the amount of money,

x, that Lia's brother has. How much money does Lia's brother have?
Mathematics
2 answers:
sp2606 [1]3 years ago
8 0

Answer:

x=21

Step-by-step explanation:

45-24=21

Julli [10]3 years ago
6 0

Answer:

21$

Step-by-step explanation:

24+x=45

-24      -24

x=21$

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Answer:

so x+y=77

1/2x-1/3y=6

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The height of a building is
eduard

Answer:

10 feet

Step-by-step explanation:

This is a problem of scale

where scale is

actual height of any object/ height of that object on drawing

given

actual height = 24 feet

this is represented 1/2 inch on drawing

thus

scale = actual height/ height on drawing = 24 feet/1/2 inch = 24*2 feet/ 1 inch

scale = 48 feet / 1 inch

given actual  height of a building = 480 feet

let the height on drawing be x inch

thus

48 feet / 1 inch = 480 feet/ x inch

=> x inch/ 1 inch = 480 feet / 48 feet

=> x = 10 feet

Thus,  the  height of  building on the drawing is 10 feet

6 0
2 years ago
if 48% of the students at a certain college are female and there are 2,400 female students, what is the total amount of students
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7 0
3 years ago
Select the correct answer.
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5 0
3 years ago
If cos theta= -8/17 and theta is in quadrant 3, what is cos2 theta and tan2 theta
Karo-lina-s [1.5K]
\bf cos(\theta)=\cfrac{adjacent}{hypotenuse}\qquad  
\begin{array}{llll}
\textit{now, hypotenuse is always positive}\\
\textit{since it's just the radius}
\end{array}
\\\\\\
thus\qquad cos(\theta)=\cfrac{-8}{17}\cfrac{\leftarrow adjacent=a}{\leftarrow  hypotenuse=c}

since the hypotenuse is just the radius unit, is never negative, so the - in front of 8/17 is likely the numerator's, or the adjacent's side

now, let us use the pythagorean theorem, to find the opposite side, or "b"

\bf c^2=a^2+b^2\implies \pm\sqrt{c^2-a^2}=b\qquad 
\begin{cases}
c=hypotenuse\\
a=adjacent\\
b=opposite
\end{cases}
\\\\\\
\pm\sqrt{17^2-(-8)^2}=b\implies \pm\sqrt{225}=b\implies \pm 15=b

so... which is it then? +15 or -15? since the root gives us both, well
angle θ, we know is on the 3rd quadrant, on the 3rd quadrant, both, the adjacent(x) and the opposite(y) sides are negative, that means,  -15 = b

so, now we know, a = -8, b = -15, and c = 17
let us plug those fellows in the double-angle identities then

\bf \textit{Double Angle Identities}
\\ \quad \\
sin(2\theta)=2sin(\theta)cos(\theta)
\\ \quad \\
cos(2\theta)=
\begin{cases}
cos^2(\theta)-sin^2(\theta)\\
\boxed{1-2sin^2(\theta)}\\
2cos^2(\theta)-1
\end{cases}
\\ \quad \\
tan(2\theta)=\cfrac{2tan(\theta)}{1-tan^2(\theta)}\\\\
-----------------------------\\\\
cos(2\theta)=1-2sin^2(\theta)\implies cos(2\theta)=1-2\left( \cfrac{-15}{17} \right)^2
\\\\\\
cos(2\theta)=1-\cfrac{450}{289}\implies cos(2\theta)=-\cfrac{161}{289}




\bf tan(2\theta)=\cfrac{2tan(\theta)}{1-tan^2(\theta)}\implies tan(2\theta)=\cfrac{2\left( \frac{-15}{-8} \right)}{1-\left( \frac{-15}{-8} \right)^2}
\\\\\\
tan(2\theta)=\cfrac{\frac{15}{4}}{1-\frac{225}{64}}\implies tan(2\theta)=\cfrac{\frac{15}{4}}{-\frac{161}{64}}
\\\\\\
tan(2\theta)=\cfrac{15}{4}\cdot \cfrac{-64}{161}\implies tan(2\theta)=-\cfrac{240}{161}
6 0
3 years ago
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