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valina [46]
3 years ago
11

In the following exercises, find the greatest common factor.15y3, 21y2, 30y

Mathematics
1 answer:
Lelechka [254]3 years ago
6 0

Answer:

<h2>3y</h2>

Step-by-step explanation:

each term has at least y^1

each term's coeficient is a factor of 3

3y(5y^2, 7y, 10)

<h2>3y is the GCF</h2>
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Describe the graph of y=3/4x-12 as compared to the graph of y=1/x
Eddi Din [679]

Answer:

Parent function is compressed by a factor of 3/4 and shifted to right by 3 units.

Step-by-step explanation:

We are asked to describe the transformation of function y=\frac{3}{4x-12} as compared to the graph of y=\frac{1}{x}.

We can write our transformed function as:

y=\frac{3}{4(x-3)}

y=\frac{3}{4}*\frac{1}{(x-3)}

Now let us compare our transformed function with parent function.

Let us see rules of transformation.  

f(x-a)\rightarrow\text{Graph shifted to the right by a units},

f(x+a)\rightarrow\text{Graph shifted to the left by a units},

Scaling of a function: a*f(x)

If a>1 , so function is stretched vertically.

If 0<a<1 , so function is compressed vertically.

As our parent function is multiplied by a scale factor of 3/4 and 3/4 is less than 1, so our parent function is compressed vertically by a factor of 3/4.

As 3 is being subtracted from x, so our parent function is shifted to right by 3 units or a horizontal shift to right by 3 units.

Therefore, our parent graph is compressed by a factor of 3/4 and shifted to right by 3 units to get our new graph.

5 0
3 years ago
A pyramid has a regular hexagonal base with side links of four and a slant height of six. Find the total area of the pyramid
vova2212 [387]

Area of the Base = 6 * side^2 / 4 * tan (180/6)

Area of the Base = 6 * 16 / 4 * 0.57735

Area of the Base = 96 / 2.3094

Area of the Base = 41.5692387633


Area of 1 Face = 2 * 6 = 12

Area of 6 Faces = 72


Total Area = 41.5692387633 + 72

Total Area = 113.5692387633

7 0
3 years ago
34. For the following exercises, given each set of information, find a linear equation satisfying the conditions, if possible.
skad [1K]

Answer:

The linear equation for the line which passes through the points given as (-1,4) and (5,2), is written in the point-slope form as $y=\frac{1}{3} x-\frac{13}{3}$.

Step-by-step explanation:

A condition is given that a line passes through the points whose coordinates are (-1,4) and (5,2).

It is asked to find the linear equation which satisfies the given condition.

Step 1 of 3

Determine the slope of the line.

The points through which the line passes are given as (-1,4) and (5,2). Next, the formula for the slope is given as,

$m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}$

Substitute 2&4 for $y_{2}$ and $y_{1}$ respectively, and $5 \&-1$ for $x_{2}$ and $x_{1}$ respectively in the above formula. Then simplify to get the slope as follows,

m=\frac{2-4}{5-(-1)}$\\ $m=\frac{-2}{6}$\\ $m=-\frac{1}{3}$

Step 2 of 3

Write the linear equation in point-slope form.

A linear equation in point slope form is given as,

$y-y_{1}=m\left(x-x_{1}\right)$

Substitute $-\frac{1}{3}$ for m,-1 for $x_{1}$, and 4 for $y_{1}$ in the above equation and simplify using the distributive property as follows,

y-4=-\frac{1}{3}(x-(-1))$\\ $y-4=-\frac{1}{3}(x+1)$\\ $y-4=-\frac{1}{3} x-\frac{1}{3}$

Step 3 of 3

Simplify the equation further.

Add 4 on each side of the equation $y-4=\frac{1}{3} x-\frac{1}{3}$, and simplify as follows,

y-4+4=\frac{1}{3} x-\frac{1}{3}+4$\\ $y=\frac{1}{3} x-\frac{1+12}{3}$\\ $y=\frac{1}{3} x-\frac{13}{3}$

This is the required linear equation.

5 0
1 year ago
How much does mike earn at fresh foods if he works 20 hours? 40 hours? 60 hours? He gets pay $10 per the hour
Taya2010 [7]

This is pretty easy math.

All we have to do here is multiply the hours times the constant (10$ an hour)

20*10=200$

40*10=400$

60*10=600$

All together he makes 1,200$.

-Seth


6 0
3 years ago
Read 2 more answers
.Help Please! <br><br> Is this a monomial, binomial, trinomial, or<br> polynomial? Explain
zhenek [66]

Answer:

Polynomial

Step-by-step explanation:

=> x³ - 4x² + 1 + 3x² + x

=> x³ - x² + x - 1

This is a polynomial expression, as, there are 4 terms in the equation, <em>v</em><em>iz</em><em>.</em><em>,</em><em> </em>x³, x², x and -1.

<em>Hope</em><em> </em><em>it</em><em> </em><em>helps</em><em>.</em>

4 0
2 years ago
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