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3 years ago

Equation A: y = 2x + 4

Mathematics

1 answer:

Ymorist [56]3 years ago

6 0

2x+4=3x+1 they've substituted y =2x+4 into the second eq.

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In a right triangle ABC, CD is an altitude, such that AD=BC. Find AC, if AB=3 cm, and CD= root 2 cm.

Nata [24]

Given CD is an altitude such that AD=BC , AB=3 cm and CD= √2 cm.

Let AD=x, Since given AB=3

AD+DB=3

x+DB = 3

DB = 3-x

Since ΔBCD is rght angle triangle, let's apply Pythagoras theorem

$BC^{2} = DB^{2} +CD^{2}$

$BC^{2} = (3-x)^{2} +(\sqrt{2} )^{2}$

$BC^{2} =(3-x)^{2} +2$

Since given AD=BC,let us plugin BC=x in above step.

$x^{2} =(3-x)^{2} +2$

$x^{2} =9-6x+x^{2} +2$

6x=11

x= $\frac{11}{6}$

Now we know AD=x= $\frac{11}{6}$ and given CD=√2.

Let us apply Pythagoras theorem for ΔACD

$AC^{2} =AD^{2} +DC^{2}$

$AC^{2} = (\frac{11}{6} )^{2} +(\sqrt{2} )^{2}$

$AC^{2} =\frac{193}{36}$

$AC=\sqrt{\frac{193}{36} }$ = 2.315cm

3 0

3 years ago

Help please :))<br>10 points

DaniilM [7]

Answer:

54 -3n²

Step-by-step explanation:

The square of a number (n) is represented by n². Three times that value is represented by 3n².

The relation "a is subtracted from b" is represented as ...

b - a

When 3n² is subtracted from 54, the appropriate representation is ...

54 -3n²

6 0

3 years ago

1.9996 by 2 significant numbers

Svetradugi [14.3K]

1.9 or rounding with 2.0

8 0

3 years ago

Find the value of 8!

lukranit [14]

Answer: B

Step-by-step explanation: 8! = (8*7*6*5*4*3*2*1) = 40,320

8 0

3 years ago

Read 2 more answers

Joey invest $900 at 4% simple interest for 2 years but he wants to know how much money he will have after only 18 months. Determ

malfutka [58]

Well, bearing in mind that, a year has 12 months, so 18 months is really just 18/12 of a year, or 3/2 a year, then

$\bf \qquad \textit{Simple Interest Earned Amount}\\\\
A=P(1+rt)\qquad 
\begin{cases}
A=\textit{accumulated amount}\\
P=\textit{original amount deposited}\to& \$900\\
r=rate\to 4\%\to \frac{4}{100}\to &0.04\\
t=years\to \frac{18}{12}\to &\frac{3}{2}
\end{cases}
\\\\\\
A=900\left( 1+0.04\cdot \frac{3}{2} \right)$

4 0

3 years ago