Is 2mn and mn^2 like terms?

The endpoints of are A(2, 2) and B(3, 8). is dilated by a scale factor of 3.5 with the origin as the center of dilation to give

goldfiish [28.3K]

Answer:

The given line segment whose end points are A(2,2) and B(3,8).

Distance AB is given by distance formula , which is

if we have to find distance between two points (a,b) and (p,q) is

= $\sqrt{(p-a)^2+(q-b)^2}$

AB= $\sqrt{(3-2)^2+(8-2)^2}=\sqrt{1+36}=\sqrt{37}$ = 6.08 (approx)

Line segment AB is dilated by a factor of 3.5 to get New line segment CD.

Coordinate of C = (3.5 ×2, 3.5×2)= (7,7)

Coordinate of D = (3.5×3, 3.5×8)=(10.5,28)

CD = AB × 3.5

CD = √37× 3.5

= 6.08 × 3.5

= 21.28 unit(approx)

2. Slope of line joining two points (p,q) and (a,b) is given by

m= $\frac{q-b}{p-a}$

m= $\frac{8-2}{3-2}=6$

As the two lines are coincident , so their slopes are equal.

Slope of line AB=Slope of line CD = 6

6 0

3 years ago

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Solving quadratic equation using the completing method.<br>(a).x^2+6x+1=0

irina1246 [14]

Answer:

$x = -3 + 2\sqrt2 \ , \ x = -3 - 2\sqrt2$

Step-by-step explanation:

x² + 6x + 1 = 0

a = 1 , b = 6 , c = 1

$x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}\\\\x = \frac{-6 \pm \sqrt{36-4}}{2}\\\\x=\frac{-6 \pm \sqrt{32}}{2}\\\\x= \frac{-6 \pm \sqrt{16 \times 2}}{2}\\\\x = \frac{-6 +4\sqrt2 }{2}\\\\x = -3 + 2\sqrt2 \ , \ x = -3 - 2\sqrt2$

7 0

3 years ago

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If 90 percent of automobiles in Orange County have both headlights working, what is the probability that in a sample of eight au

Alex17521 [72]

Answer:

$P(X \geq 7) = P(X=7) +P(X=8)$

And we can find the individual probabilities using the probability mass function

$P(X=7)=(8C7)(0.9)^7 (1-0.9)^{8-7}=0.3826$

$P(X=8)=(8C8)(0.9)^8 (1-0.9)^{8-8}=0.4305$

And replacing we got:

$P(X \geq 7) = P(X=7) +P(X=8)=0.3826 +0.4305=0.8131$

Step-by-step explanation:

Previous concepts

The binomial distribution is a "DISCRETE probability distribution that summarizes the probability that a value will take one of two independent values under a given set of parameters. The assumptions for the binomial distribution are that there is only one outcome for each trial, each trial has the same probability of success, and each trial is mutually exclusive, or independent of each other".

Solution to the problem

Let X the random variable of interest "number of automobiles with both headligths working", on this case we now that:

$X \sim Binom(n=8, p=0.9)$

The probability mass function for the Binomial distribution is given as:

$P(X)=(nCx)(p)^x (1-p)^{n-x}$

Where (nCx) means combinatory and it's given by this formula:

$nCx=\frac{n!}{(n-x)! x!}$

And for this case we want to find this probability:

$P(X \geq 7) = P(X=7) +P(X=8)$

And we can find the individual probabilities using the probability mass function

$P(X=7)=(8C7)(0.9)^7 (1-0.9)^{8-7}=0.3826$

$P(X=8)=(8C8)(0.9)^8 (1-0.9)^{8-8}=0.4305$

And replacing we got:

$P(X \geq 7) = P(X=7) +P(X=8)=0.3826 +0.4305=0.8131$

3 0

2 years ago

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65% of the workers are women. If 980 people work for the company who

rosijanka [135]

637 is the answer because our value is 980 we all know the unknown value with x for the step above 980 and 100% and 65% is the result in a pair of a simple equations

8 0

3 years ago

How fast should the ant walk to go around the rectangle in 4 minutes if the sides are 12 inches and 16 inches

Bess [88]

14 inches per minute.

4 0

3 years ago

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