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vlada-n [284]
3 years ago
15

Translate the sentence into an equation, then solve the

Mathematics
1 answer:
Oduvanchick [21]3 years ago
4 0

Answer:

The equation is: \frac{x-7}{5} = 13 and the number is 72.

Step-by-step explanation:

We have to use mathematical notation to convert the given statement into an equation. As we don't know the exact value of number, we have to use a variable in place of the number.

Let x be the required number then

"A number decreased by 7"

x-7

"and then  divided by 5"

\frac{x-7}{5}

" is 13."

\frac{x-7}{5} = 13

For solving, multiplying both sides of equation by "5"

\frac{x-7}{5} * 5 = 13*5\\x-7 = 65

Adding 7 on both sides of equation

x-7+7 = 65+7\\x = 72

Hence,

The equation is: \frac{x-7}{5} = 13 and the number is 72.

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If angle 1 is 140°, then find the measure of the other angles.
Vlad [161]
<h2><u>Angles</u></h2>

<h3>If angle 1 is 140°, then find the measure of the other angles.</h3>

  • ∠2 = <u>40°</u>
  • ∠3 = <u>40°</u>
  • ∠4 = <u>140°</u>
  • ∠5 = <u>140°</u>
  • ∠6 = <u>40°</u>
  • ∠7 = <u>40°</u>
  • ∠8 = <u>140°</u>

<u>Explanation:</u>

  • The relationship between ∠1 and ∠2 are <u>supplementary angles</u>, so when you <u>add up their measurements, it will become 180°</u>. Simply subtract 180 and 140 to get the measure of ∠2. As well as ∠3, they're <u>linear pairs</u>. And they are also <u>supplementary</u>. To determine the measure of ∠6 and ∠7, notice the <u>relationship</u> between ∠2 and ∠6. As you noticed, it is <u>corresponding angles</u>. So they <u>have the same measurement</u>. If <u>∠2 = 40°</u>, then <u>∠6 = 40°</u>. As well as ∠7, because the relationship between ∠6 and ∠7 are <u>vertical pairs</u>. So the angle measurement of ∠7 is also <u>40°</u>.

  • Meanwhile, the relationship between ∠1 and ∠4 are <u>vertical pairs</u>. It means they also <u>have the same measurement</u>. So ∠4 = <u>140°</u>. The relationship between ∠1 and ∠5 are <u>corresponding angles</u>, so they also <u>have the same measurement</u>. If <u>∠1 = 140°</u>, then <u>∠5 = 140°</u>. The relationship between ∠1 and ∠8 are <u>alternate exterior angles</u>, and they also <u>have the same measurement</u>. <u>If ∠1 = 140°</u>, then <u>∠8 = 140°</u>.

Wxndy~~

8 0
2 years ago
For what value of x is AABC - ADEF?<br> HELP PLEASE!!
NeX [460]

Answer:

A) x = 12

Step-by-step explanation:

4x-6 = 42

4 = 48

x = 12

7x+10 = 94

7x = 82

x = 12

7 0
3 years ago
Round 287.9412 to the nearest tenth. Do not write extra zeros.
goldenfox [79]
Salutations!

<span>Round 287.9412 to the nearest tenth. 

Lets solve this!

To round to the nearest tenth, you need to know the tenth place--------

In the number, 287.9412, nine is in the tenth place. You need also make sure whether the number next to 9 is greater than 5 or not. 

</span><span>287.9412 =287.941=287.94=287.9=288=290

Thus, your answer is 290.

Hope I helped.
</span>
3 0
3 years ago
Read 2 more answers
Find a particular solution to the nonhomogeneous differential equation y′′+4y=cos(2x)+sin(2x).
I am Lyosha [343]
Take the homogeneous part and find the roots to the characteristic equation:

y''+4y=0\implies r^2+4=0\implies r=\pm2i

This means the characteristic solution is y_c=C_1\cos2x+C_2\sin2x.

Since the characteristic solution already contains both functions on the RHS of the ODE, you could try finding a solution via the method of undetermined coefficients of the form y_p=ax\cos2x+bx\sin2x. Finding the second derivative involves quite a few applications of the product rule, so I'll resort to a different method via variation of parameters.

With y_1=\cos2x and y_2=\sin2x, you're looking for a particular solution of the form y_p=u_1y_1+u_2y_2. The functions u_i satisfy

u_1=\displaystyle-\int\frac{y_2(\cos2x+\sin2x)}{W(y_1,y_2)}\,\mathrm dx
u_2=\displaystyle\int\frac{y_1(\cos2x+\sin2x)}{W(y_1,y_2)}\,\mathrm dx

where W(y_1,y_2) is the Wronskian determinant of the two characteristic solutions.

W(\cos2x,\sin2x)=\begin{bmatrix}\cos2x&\sin2x\\-2\cos2x&2\sin2x\end{vmatrix}=2

So you have

u_1=\displaystyle-\frac12\int(\sin2x(\cos2x+\sin2x))\,\mathrm dx
u_1=-\dfrac x4+\dfrac18\cos^22x+\dfrac1{16}\sin4x

u_2=\displaystyle\frac12\int(\cos2x(\cos2x+\sin2x))\,\mathrm dx
u_2=\dfrac x4-\dfrac18\cos^22x+\dfrac1{16}\sin4x

So you end up with a solution

u_1y_1+u_2y_2=\dfrac18\cos2x-\dfrac14x\cos2x+\dfrac14x\sin2x

but since \cos2x is already accounted for in the characteristic solution, the particular solution is then

y_p=-\dfrac14x\cos2x+\dfrac14x\sin2x

so that the general solution is

y=C_1\cos2x+C_2\sin2x-\dfrac14x\cos2x+\dfrac14x\sin2x
7 0
3 years ago
What do u add to 5 5/8 to make 9 ?
mixas84 [53]

Answer:

5+5=9and mark me as brainlestttt

8 0
2 years ago
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