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Mathematics

1 answer:

PtichkaEL [24]2 years ago

8 0

Answer:
1. x + 24 = 3x
24 = 3x - x
24 = 2x
12 = x

3x
3 (12)
36

2. 10x - 27 = 7x
10x - 7x = 27
3x = 27
x = 9

7x
7 (9)
63

3. 5x + 1 = 6x - 13
5x - 6x = -13 - 1
-x = -14
x = 14

5x + 1
5 (14) + 1
71

4. 6x + 3 = 4x + 39
6x - 4x = 39 - 3
2x = 36
x = 18

6x + 3
6 (18) + 3
111

1. B
2. A
3. H
4. E

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In the right ΔABC, AN is the altitude to the hypotenuse. Find BN, AN, and AC, if AB=2√5 in and NC= 1 in.

kipiarov [429]

Answer:

$BN=4\ \text{in}$

$AN=2\ \text{in}$

$AC=\sqrt{5}\ \text{in}$

Step-by-step explanation:

Let $BN=x$

$BC=c$

$NC=y=1\ \text{in}$

$AB=a=2\sqrt{5}\ \text{in}$

$AC=b$

We have the relation

$\dfrac{BC}{AB}=\dfrac{AB}{BN}\\\Rightarrow \dfrac{c}{a}=\dfrac{a}{x}\\\Rightarrow c=\dfrac{a^2}{x}\\\Rightarrow x+1=\dfrac{a^2}{x}\\\Rightarrow x^2+x=20\\\Rightarrow x^2+x-20=0\\\Rightarrow x=\frac{-1\pm \sqrt{1^2-4\times 1\times \left(-20\right)}}{2\times 1}\\\Rightarrow x=4,-5$