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2 years ago

Determine the value of x in the diagram? A.32 B.10 C.20 D.16

Mathematics

2 answers:

Gnesinka [82]2 years ago

6 0

Answer:

B. 10

Step-by-step explanation:

These are vertical angles meaning they are also equal.

$4x-12=2x+8\\2x-12=8\\2x=20\\x=10$

alex41 [277]2 years ago

6 0

Answer:

The choice B. 10

Step-by-step explanation:

4x -12=2x+8 —> Opposite angles

4x -2x =8+12

2x = 20

x =20/2

x= 10

I hope I helped you^_^

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What is the equation of the line that passes through the points (-1, 1.5) and (0.5, 0.5)

Step2247 [10]

The slope-point formula:

$y-y_1=m(x-x_1)\\\\m=\dfrac{y_2-y_1}{x_2-x_1}$

We have:

$(-1,\ 1.5)\to x_1=-1,\ y_1=1.5\\(0.5,\ 0.5)\to x_2=0.5,\ y_2=0.5$

Substitute:

$m=\dfrac{0.5-1.5}{0.5-(-1)}=\dfrac{-1}{1.5}=-\dfrac{1}{\frac{3}{2}}=-\dfrac{2}{3}\\\\y-1.5=-\dfrac{2}{3}(x-(-1))\\\\y-1.5=-\dfrac{2}{3}x-\dfrac{2}{3}\\\\y-\dfrac{3}{2}=-\dfrac{2}{3}x-\dfrac{2}{3}\ \ \ |+\dfrac{3}{2}\\\\y=-\dfrac{2}{3}x-\dfrac{2}{3}+\dfrac{3}{2}\\\\y=-\dfrac{2}{3}x-\dfrac{2\cdot2}{3\cdot2}+\dfrac{3\cdot3}{2\cdot3}\\\\y=-\dfrac{2}{3}x-\dfrac{4}{6}+\dfrac{9}{6}\\\\y=-\dfrac{2}{3}x+\dfrac{5}{6}$

6 0

3 years ago

This robotic arm is made up of two cylinders with equal volume and two triangular prism hands. The volume of each hand is

BaLLatris [955]

Answer:

$\frac{r}{3\pi h+r}$

Step-by-step explanation:

Since the height isn't given, we assume it to be "h" (of cylinders). And the answer will be in terms of "r" and "h".

The area of 1 arm is given, so the area of 2 arms would be:

$A_{arm}=2*(\frac{1}{2}r*\frac{1}{3}r*2r)=\frac{2r^3}{3}$

Now, area of 2 cylinders would be the formula:

$A_{cyl}=2*(\pi r^2 h)=2\pi r^2 h$

So, total area is A_arm PLUS A_cyl. The fractional area the arms are would be gotten by taking expression A_arm divided by A_total.

Shown below:

$\frac{A_{arm}}{A_{total}}=\frac{\frac{2r^3}{3}}{2\pi r^2 h + \frac{2r^3}{3}}$

We simplify further:

$\frac{\frac{2r^3}{3}}{2\pi r^2 h + \frac{2r^3}{3}}\\=\frac{\frac{2r^3}{3}}{2r^2(\pi h + \frac{r}{3})}\\=\frac{r}{3(\pi h + \frac{r}{3})}\\=\frac{r}{3\pi h+r}$