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3 years ago

Factor the following trinomials . x2 + 2x - 35 x2 - x - 12

2 answers:

6 0

X2-2x-35=0x2-7x+5x-35=0x(x-7)+5(x-7)=0(x-7)(x+5)=0x-7=0 or x+5=0x=7 or x=-5 Check: x=7 ,LHS = 49-14-35 =0 =RHS x=-5, LHS = 25+10-35 =0=RHSAns: x=7 or x=-5

x2−x−12=0

NNADVOKAT [17]3 years ago

5 0

(x + 7) • (x - 5)= Answerx^2+2x-35
What multiplies to -35 and adds up to 3?
-5+7=2
-5*7=-35
NEXT
 x^2 - 5x + 7x - 35

Add up the first 2 terms, pulling out like factors :
x • (x-5)

Add up the last 2 terms, pulling out common factors :
7 • (x-5)
Add up the four terms of step 4 :
(x+7) • (x-5)

___________________________________________________________

(x + 3) • (x - 4)=Answer
x^2-x-12
What multiplies up to -12 and adds to -1?
-4+3=-1
-4*3=-12

x^2 - 4x + 3x - 12

Add up the first 2 terms, pulling out like factors :
x • (x-4)

Add up the last 2 terms, pulling out common factors :
3 • (x-4)
Add up the four terms
(x+3) • (x-4)

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First, let's rewrite both of these dimensions in the same units.

Knowing that:

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Then the dimensions of the space can be rewritten from:

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to:

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So, if we enlarge our original picture by a scale factor K, the new dimensions of the picture will be:

K*46cm by K*32cm

Now we just need to find a value of K such that:

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K*32cm is something near to 200cm

First, we can solve the equation:

K*46cm = 300cm

solving this for K we get:

K = 300cm/46cm = 6.5

While if we solve the equation:

K*32cm = 200cm

we get:

K = 200cm/32cm = 6.25

So we got two possible scale factors.

Which one we should take?

Notice that if we wanted to use the larger one (K = 6.5) for the 32cm side. the new length would be:

32cm*6.5 = 208cm

This is larger than the 200cm of space that we have

Then we can not select the larger option, we can only take the other value:

K = 6.25

Then we can conclude that a reasonable scale factor to use is K = 6.25

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3 years ago

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Answer:

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Step-by-step explanation:

Width of the sign made by Darius initially = 2 feet

Length of the sign = 2 feet 6 inches

Dimension of the flyer are 10 inches by 8 inches. Since, in original sign the measure of length is greater, therefore, the length of flyer is 10 inches and its width is 8 inches.

In order to find the scale factor we must convert the lengths and widths to same units. Lets convert the length and width of sign into inches.

Since, 1 feet = 12 inches

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Now we can find the scale factor by either comparing the lengths or widths of both the designs. Scale factor will be equal to the ratio of corresponding lengths/widths.

So, the scale factor would be:

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= 10 inches : 30 inches

= 1 : 3

= $\frac{1}{3}$

This shows, the length of flyer is $\frac{1}{3}$ times as that of the sign. So, the scale factor that Darius must use is $\frac{1}{3}$ . The length and width of the flyer are $\frac{1}{3}$ as that of the sign.

The same scale factor would result if we would have used the ratio of widths instead of the lengths.

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Therefore, Darius must type the scale factor of $\frac{1}{3}$ in his computer to get the size of the flyer.

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