Answer:
x = 3
Explanation:
4x = 2x +6
2x = 6
x = 3
Answer:
Two
Step-by-step explanation:
x² + 4 = 4x + 1
x² - 4x + 3 = 0
x² - 3x - x + 3 = 0
x(x - 3) - (x - 3) = 0
(x - 3)(x - 1) = 0
x = 1, 3
y = 4(1) + 1 = 5
y = 4(3) + 1 = 13
Two solutions: (1,5) (3,13)
The formula for the nth term of a geometric sequence:
a₁ - the first term, r - the common ratio
![54, a_2, a_3, 128 \\ \\ a_1=54 \\ a_4=128 \\ \\ a_n=a_1 \times r^{n-1} \\ a_4=a_1 \times r^3 \\ 128=54 \times r^3 \\ \frac{128}{54}=r^3 \\ \frac{128 \div 2}{54 \div 2}=r^3 \\ \frac{64}{27}=r^3 \\ \sqrt[3]{\frac{64}{27}}=\sqrt[3]{r^3} \\ \frac{\sqrt[3]{64}}{\sqrt[3]{27}}=r \\ r=\frac{4}{3}](https://tex.z-dn.net/?f=54%2C%20a_2%2C%20a_3%2C%20128%20%5C%5C%20%5C%5C%0Aa_1%3D54%20%5C%5C%0Aa_4%3D128%20%5C%5C%20%5C%5C%0Aa_n%3Da_1%20%5Ctimes%20r%5E%7Bn-1%7D%20%5C%5C%0Aa_4%3Da_1%20%5Ctimes%20r%5E3%20%5C%5C%0A128%3D54%20%5Ctimes%20r%5E3%20%5C%5C%0A%5Cfrac%7B128%7D%7B54%7D%3Dr%5E3%20%5C%5C%20%5Cfrac%7B128%20%5Cdiv%202%7D%7B54%20%5Cdiv%202%7D%3Dr%5E3%20%5C%5C%0A%5Cfrac%7B64%7D%7B27%7D%3Dr%5E3%20%5C%5C%0A%5Csqrt%5B3%5D%7B%5Cfrac%7B64%7D%7B27%7D%7D%3D%5Csqrt%5B3%5D%7Br%5E3%7D%20%5C%5C%0A%5Cfrac%7B%5Csqrt%5B3%5D%7B64%7D%7D%7B%5Csqrt%5B3%5D%7B27%7D%7D%3Dr%20%5C%5C%0Ar%3D%5Cfrac%7B4%7D%7B3%7D)
In triangle ABC,
AC = 12/ (sin30) = 12 / (1/2) = 24
DC = 24-x
DB = DC tan 30 = (24-x) tan30 <span>=(24−x)/</span><span>√3
</span>
In triangle ADB using Pythagorean Theorem<span><span>x2</span>+((24−x)/<span>√3</span><span>)2</span>=<span>12^2</span></span><span><span>x2</span>+(24−x<span>)^2</span>/3=<span>12^2</span></span><span>3<span>x2</span>+(24−x<span>)^2</span>=432</span><span>4<span>x2</span>−48x+576=432</span><span>4<span>x2</span>−48x+144=0</span><span><span><span>x2</span>−12x+36=0
x1 = x2 =6
AD = AC - DC = 24- (24-x) = 6</span></span>
Answer:
2:3
Step-by-step explanation:
16/24=1/3
Hope this helps you!!!!!!!! :D
