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3 years ago

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Find the number which when divided by 4 and increased by 12 is the same as when it is divided by 3 and decreased by 5

1 answer:

MatroZZZ [7]3 years ago

5 0

Step-by-step explanation:

Let's make the number we're finding to be $a$ . So, it says that it will be divided by 4 and then added by 12 if we want this in algebraic expression it will be $\frac{a}{4} +12\\$ . It's also telling us that that expression is the same thing as our number divided by 3 and subtracted by 5. If we want an expression out of it it well be $\frac{a}{3} -5\\$ . Since they are the same, we have the equation below.

$\frac{a}{4} +12 = \frac{a}{3} -5\\$

All we have to do now is to find $a$ .

$\frac{a}{4} +12 = \frac{a}{3} -5 \\ \frac{a +48}{4} = \frac{a -15}{3} \\ (3)(a +48) = (a - 15)(4) \\ 3a +144 = 4a -60 \\ (60 -3a) + 3a +144 = 4a -60 +(60 -3a) \\ a = 204$

<h3>Answer:</h3>

Our number must be $204$ . I think

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PLEASE HELP Given: △KLM LM=12, m∠K=60°, m∠M=45° Find: Perimeter of △KLM.

worty [1.4K]

We have to find the perimeter of the triangle KLM.

We have been given that the length of the side LM=12, $m\angleK=60^\circ$ , and $m\angle M= 45^\circ$

Refer the attached image.

In a triangle sum of three angles should be $180^\circ$ .

So,

$m\angle K+m\angle L+m\angle M=180^\circ$

Plugging the values of angle K and angle M, we get:

$60^\circ+m\angle L+45^\circ=180^\circ$

So,

$m\angle L=180^\circ-105^\circ=75^\circ$

Now, that we have the measure of angle L, we will apply sine rule to find the length of the sides KL and KM.

Using the sine law for the triangle KLM, we get:

$\frac{sin K}{LM}=\frac{sin L}{KM}=\frac{sin M}{KL}$

Refer the image. Plugging the value of the sides of the triangle KLM and the angles of the triangle KLM, we get:

$\frac {sin 60^\circ}{12}=\frac{sin 75^\circ}{y}=\frac{sin 45^\circ}{x}$

Now using,

$\frac {sin 60^\circ}{12}=\frac{sin 75^\circ}{y}$

We get the value of 'y'

$y=\frac{sin 75^\circ}{sin 60^\circ} \times 12=\frac{0.9659}{0.866} \times 12=13.38$

So the length of the side KM is 13.38 units.

Now using,

$\frac {sin 60^\circ}{12}=\frac{sin 45^\circ}{x}$

We get the value of 'x'

$x=\frac{sin 45^\circ}{sin 60^\circ} \times 12=\frac{0.707}{0.866} \times 12=9.79$

So the length of the side KL is 9.79 units.

Now, to find the perimeter of the triangle KLM we need to sum up the length of the sides of the triangle KLM.

The perimeter of the triangle KLM $= KL+ LM + KM = 9.79 + 12 + 13.38 = 35.17$ units

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Can somebody help me with this. Will Mark brainliest.

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Answer:

The maesure of D will be 23 hope this help :')

Step-by-step explanation:

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