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3 years ago

Lines AB and CD intersect at E, mLAED = 110,

Mathematics

2 answers:

IgorC [24]3 years ago

7 0

Answer:

x = 10, y = 20

Step-by-step explanation:

Form a system of equations:

From the picture at the bottom you can see that vertical angles are equal, so:

$3x + 2y = 70$

Then, since the angles all together will add up to 360, you can do

$3x+2y+9x+y+70+9x+y=360$

$21x+4y+70=360$

subtract 70 from both sides

$21x + 4y = 290$

With the equation 3x + 2y = 70, multiply both sides by 2

$6x+4y=140$

Subtract the two equations:

$15x=150\\x=10$

Plug this into one of the original equations

$30+2y=70\\2y = 40\\y=20$

lakkis [162]3 years ago

5 0

Answer:

45,698,09864,58586,96403

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Several students were asked how many blocks they walk from home to school each day. The results are shown in the line plot. How

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Answer:

25 students.

Step-by-step explanation:

A line plot is a simple graph that shows relationship among the values in a data using a number line.

From the line plot, each dot represents a student. While the number on the line shows the number of blocks walk each day by each student.

It can be deduced from the line plot that;

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3 years ago

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Step-by-step explanation:

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3 years ago

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dimulka [17.4K]

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3 years ago

If tan ⁡x=12/5, and 0°

Charra [1.4K]

The value of sin(2x) is $\frac{120}{169}$

Explanation:

Given that $tan x =\frac{12}{5}$

The formula for $sin(2x)$ is $\sin (2 x)=2 \sin x \cos x$

Since, $\tan x=\frac{o p p}{a d j}$

Also, it is given that $tan x =\frac{12}{5}$

Thus, $opp=12$ and $adj=5$

To find the hypotenuse, let us use the pythagoras theorem,

$\begin{aligned}h y p &=\sqrt{12^{2}+5^{2}} \\&=\sqrt{144+25} \\&=\sqrt{169} \\&=13\end{aligned}$

Now, we can find the value of sin x and cos x.

$\sin x=\frac{\text { opp }}{h y p}=\frac{12}{13}$

$\cos x=\frac{a d j}{h y p}=\frac{5}{13}$

Now, substituting these values in the formula for sin 2x, we get,

$\begin{aligned}\sin (2 x) &=2 \sin x \cos x \\&=2\left(\frac{12}{13}\right)\left(\frac{5}{13}\right) \\&=\frac{120}{169}\end{aligned}$

Thus, the value of sin(2x) is $\frac{120}{169}$

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3 years ago

There were 20 gallons of gasoline in your car's gas tank. You used 4 gallons and 1 quart. How much gasoline remains in the tank?

Naya [18.7K]

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3 years ago

Read 2 more answers