16. WILL MARK BRAINLIEST!! HELP!

Mathematics

1 answer:

Komok [63]3 years ago

8 0

Step-by-step explanation:

$\frac{3}{2x + 5} + \frac{5}{x - 5} \\ \\ = \frac{3(x - 5) + 5(2x + 5)}{(2x + 5)(x - 5)} \\ \\ = \frac{3x - 15 + 10x + 25}{(2x + 5)(x - 5)} \\ \\ = \frac{3x + 10x + 25- 15 }{2 {x}^{2} - 10x + 5x - 25 } \\ \\ = \frac{13x + 10 }{2 {x}^{2} - 5x - 25 } \\ \\$

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Translating a sentence into a multi-step equation

Kryger [21]

Answer:7x-4= 3

Step-by-step explanation:

4 less than the product of 7 and a number is equal to 3.

The answer is 7x-4= 3 beacuse:

(a. whenever you have something less than , the first number in the sentence (in this cacse 4) goes after the second number (in this case 7) with a subtraction sign in the middle. (imagine this equation looking like 7-4 <u>for now)</u>.Thats a little trick i use whenever i have to write "something less than something"

(b. okay so now we know it has to be 7 times somethig -4=3, but now we just need to write the "product of 7 and a number" in proper form. in other words, whenever you get somethig times a number, it is always going to be that number with an x right next to it. so thats why i made it 7x.

(c. "equals 3" is easy because you just turn it into an "=3".

(d. Now put it together. "4 less than the product of 7 and a number is equal to 3." becomes 7x-4=3.

Hope this helps :)) Also brainliest would be appreciated, worked pretty hard on this ! :D

5 0

1 year ago

Looking at the top of tower A and base of tower B from points C and D, we find that ∠ACD = 60°, ∠ADC = 75° and ∠ADB = 30°. Let t

katrin2010 [14]

Answer:

$\text{Exact: }AB=25\sqrt{6},\\\text{Rounded: }AB\approx 61.24$

Step-by-step explanation:

We can use the Law of Sines to find segment AD, which happens to be a leg of $\triangle ACD$ and the hypotenuse of $\triangle ADB$ .

The Law of Sines states that the ratio of any angle of a triangle and its opposite side is maintained through the triangle:

$\frac{a}{\sin \alpha}=\frac{b}{\sin \beta}=\frac{c}{\sin \gamma}$

Since we're given the length of CD, we want to find the measure of the angle opposite to CD, which is $\angle CAD$ . The sum of the interior angles in a triangle is equal to 180 degrees. Thus, we have:

$\angle CAD+\angle ACD+\angle CDA=180^{\circ},\\\angle CAD+60^{\circ}+75^{\circ}=180^{\circ},\\\angle CAD=180^{\circ}-75^{\circ}-60^{\circ},\\\angle CAD=45^{\circ}$

Now use this value in the Law of Sines to find AD:

$\frac{AD}{\sin 60^{\circ}}=\frac{100}{\sin 45^{\circ}},\\\\AD=\sin 60^{\circ}\cdot \frac{100}{\sin 45^{\circ}}$

Recall that $\sin 45^{\circ}=\frac{\sqrt{2}}{2}$ and $\sin 60^{\circ}=\frac{\sqrt{3}}{2}$ :

$AD=\frac{\frac{\sqrt{3}}{2}\cdot 100}{\frac{\sqrt{2}}{2}},\\\\AD=\frac{50\sqrt{3}}{\frac{\sqrt{2}}{2}},\\\\AD=50\sqrt{3}\cdot \frac{2}{\sqrt{2}},\\\\AD=\frac{100\sqrt{3}}{\sqrt{2}}\cdot\frac{ \sqrt{2}}{\sqrt{2}}=\frac{100\sqrt{6}}{2}={50\sqrt{6}}$

Now that we have the length of AD, we can find the length of AB. The right triangle $\triangle ADB$ is a 30-60-90 triangle. In all 30-60-90 triangles, the side lengths are in the ratio $x:x\sqrt{3}:2x$ , where $x$ is the side opposite to the 30 degree angle and $2x$ is the length of the hypotenuse.

Since AD is the hypotenuse, it must represent $2x$ in this ratio and since AB is the side opposite to the 30 degree angle, it must represent $x$ in this ratio (Derive from basic trig for a right triangle and $\sin 30^{\circ}=\frac{1}{2}$ ).