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erma4kov [3.2K]
3 years ago
12

Find the greatest common factor of each set of numbers 12 54

Mathematics
1 answer:
max2010maxim [7]3 years ago
4 0
I hope this helps you

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Can someone please explain how to do these?
Pani-rosa [81]

Answer:

<u>First question answer:</u> The limit is 69

<u>Second question answer:</u> The limit is 5


Step-by-step explanation:

For the first limit, plug in x=8 in the expression (9x-3), that's the answer for linear equations and limits.

So we have:

9x-3\\9(8)-3\\72-3\\69

The answer is 69


For the second limit, if we do same thing as the first, we will get division by 0. Also indeterminate form, 0 divided by 0. Thus we would think that the limit does not exist. But if we do some algebra, we can easily simplify it and thus plug in the value x=1 into the simplified expression to get the correct answer. Shown below:

\frac{x^2+8x-9}{x^2-1}\\\frac{(x+9)(x-1)}{(x-1)(x+1)}\\\frac{x+9}{x+1}

<em>Now putting 1 in x gives us the limit:</em>

\frac{x+9}{x+1}\\\frac{1+9}{1+1}=\frac{10}{2}=5

So the answer is 5

3 0
3 years ago
A triangle has an angle that measures 10°. The other two angles are in a ratio of 3:14. What
ivann1987 [24]

Step-by-step explanation:

<h3>Need to FinD :</h3>

  • We have to find the measures of other two angles of triangle.

\red{\frak{Given}} \begin{cases} & \sf{The\ measure\ of\ one\ angle\ of\ traingle\ is\ {\pmb{\sf{10^{\circ}}}}.} \\ & \sf{The\ other\ two\ angles\ are\ in\ the\ ratio\ of\ {\pmb{\sf{3\ :\ 14}}}.} \end{cases}

We know that,

  • The other two angles of triangle are in the ratio of 3 : 14. So, let us consider the other two angles of the triangle be 3x and 14x.

Angle sum property,

  • The angle sum property of triangle states that the sum of interior angles of triangle is 180°. By using this property, we'll find the other two angles of the triangle.

\rule{200}{3}

\sf \dashrightarrow {10^{\circ}\ +\ 3x\ +\ 14x\ =\ 180^{\circ}} \\ \\ \\ \sf \dashrightarrow {10^{\circ}\ +\ 17x\ =\ 180^{\circ}} \\ \\ \\ \sf \dashrightarrow {17x\ =\ 180^{\circ}\ -\ 10^{\circ}} \\ \\ \\ \sf \dashrightarrow {17x\ =\ 170^{\circ}} \\ \\ \\ \sf \dashrightarrow {x\ =\ \dfrac{\cancel{170^{\circ}}}{\cancel{17}}} \\ \\ \\ \dashrightarrow {\underbrace{\boxed{\pink{\frak{x\ =\ 10^{\circ}.}}}}_{\sf \blue {\tiny{Value\ of\ x}}}}

∴ Hence, the value of x is 10°. Now, let us find out the other two angles of the triangle.

\rule{200}{3}

Second AnglE :

  • 3x
  • 3 × 10
  • 30°

∴ Hence, the measure of the second angle of triangle is 30°. Now, let us find out the third angle of triangle.

\rule{200}{3}

Third AnglE :

  • 14x
  • 14 × 10
  • 140°

∴ Hence, the measure of the third angle of the triangle is 140°.

5 0
2 years ago
-8x-27=-7\left(1+2x\right)+2x
Darina [25.2K]

Answer:

x=5

Step-by-step explanation:

-8x-27=-7\left(1+2x\right)+2x

Expand:

-8x-27=-7\times 1-7\times 2x+2x

-8x-27=-7-12x

Add 27 to both sides:

-8x-27+27=-7-12x+27

-8x=-12x+20

Add 12x to both sides:

-8x+12x=-12x+20+12x

4x=20

Divide both sides by 4:

\frac{4x}{4}=\frac{20}{4}

x=5

5 0
3 years ago
2y^4 x 5y^3 please can you help me
Morgarella [4.7K]

Answer:

20y^7. this is because the exponents are added together because the variable attached to the coefficient are the same therefor the coefficients are multiplied, and the exponents are added together.

8 0
2 years ago
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kotykmax [81]
The answer is x=70 degrees
5 0
3 years ago
Read 2 more answers
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