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4 years ago

Find the value of x in each case.

Mathematics

2 answers:

velikii [3]4 years ago

3 0

Answer:

x=11

Step-by-step explanation:

Due to angles DCA and CAB being Alternate Interior Angles, we know that they will be equal. This means that

$DCA=33$ °

Next, we can find the measure of the angle DCE.

Angles BCE and BCA are supplementary. This means that they will add together to be 180°

This means that 180-BCE=BCA

Which means $BCA=180-5x$

As all of the angles in a triangle must add together to be 180 degrees, we can set up the following equation

$33+180-5x+2x=180\\213-3x=180\\3x=33\\x=11$

dsp734 years ago

3 0

Answer:

x=11°

Step-by-step explanation:

If you do the math right you get 33=3x which then makes x=11

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an inlet pipe and a hose together can fill the pond in 10 hours. The inlet pipe alone can complete the job in one hour less time

Annette [7]

Answer:

The hose pipe can fill the pond in 21.465 hours.

The inlet pipe can fill the pond in 20.465 hours.

Step-by-step explanation:

Given that, a inlet pipe and a hose pipe together can fill the pond in 10 hours.

The inlet pipe alone can fill the pond in one hour less time than the hose pipe can fill the pond.

Let the hose pipe can complete the job in x hours.

Then the inlet pipe can fill the pond in (x-1) hours.

The rate of filling of hose pipe is $=\frac{1}{x}$

The rate of filling of inlet pipe is $=\frac{1}{x-1}$

The rate of filling of both pipes is = $\frac 1{10}$

According to the problem,

$\frac{1}{x}+\frac{1}{x-1}=\frac{1}{10}$

$\Rightarrow \frac{x-1+x}{x(x-1)}=\frac1{10}$ [ simplifying the fraction]

$\Rightarrow \frac{2x-1}{x^2-x}=\frac1{10}$

$\Rightarrow 10(2x-1)= x^2-x$ [ Multiplying 10(x²-x) both sides]

$\Rightarrow x^2-x= 20x-10$

$\Rightarrow x^2-x-20x+10=0$ [ simplifying ]

$\Rightarrow x^2-21x+10=0$

$\Rightarrow x=\frac{-(-21)\pm\sqrt{(-21)^2-4.1.10}}{2.1}$ [ applying quadratic formula]

$\Rightarrow x=\frac{21\pm21.93}{2.1}$

⇒ x= 21.465, -0.465

x= - 0.465 does not possible, since time can not be negative.

∴x=21.465

The hose pipe can fill the pond in 21.465 hours.

The inlet pipe can fill the pond in (21.465-1)=20.465 hours.

3 0

3 years ago

Yasmine is serving ice cream at her birthday party and she got 19 1/2 pints of ice cream and she going to serve her guest 3/4 of

lilavasa [31]

Answer:

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Step-by-step explanation:

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8 0

3 years ago

A study examined the alertness benefits of higher caffeine intake. In the study, the researchers investigated the link between d

Katyanochek1 [597]

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Step-by-step explanation:

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3 0

3 years ago

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Black_prince [1.1K]

$\qquad \qquad\huge \underline{\boxed{\sf Answer}}$

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3 0

2 years ago

Read 2 more answers

Anyone feel like helping me??

Digiron [165]

The angles of a triangle add up to 180 degrees

65 + 3x - 10 + 2x = 180
5x + 55 = 180
5x = 180 - 55
5x = 125
x = 125/5
x = 25 <====

m < B = 3x - 10 = 3(25) - 10 = 75 - 10 = 65 <== B is 65 degrees
m < C = 2x......= 2(25) = 50 <== C is 50

8 0

3 years ago