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3 years ago

What are the coordinates of the image rectangle for a scale factor of 3 if the center of dilation is the origin?

Mathematics

1 answer:

Ksju [112]3 years ago

7 0

Answer: Choice B)

Explanation:

You mentioned there isn't a diagram to go with this, but I'm assuming that this problem is referring to a previous problem you posted. In that problem, it mentions that point W is at (1,-2). If we apply the scale factor 3, then we're tripling each coordinate. That means x = 1 becomes x = 3, and y = -2 becomes y = -6

We can write it like this:

(1,-2) ---> 3*(1, -2) = (3*1, 3*(-2) ) = (3, -6)

Only choice B has W'(3,-6) so this is likely the final answer.

If we apply this dilation to every point, then that effectively makes quadrilateral W'X'Y'Z' to be three times longer and taller than compared to quadrilateral WXYZ. In other words, its side lengths are 3 times longer.

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Solve the following system of equations <br> x^2+2y^2=59<br> 2x^2+y^2=43

aivan3 [116]

Answer: x = (-3,3), y = (-5,5)

Step-by-step explanation:

Add both of the equations together, for $3x^{2}+3y^{2} = 102$ . Now we can divide both sides by 3, getting $x^2+y^2=34$ . we subtract the first equation from our equation we just got, getting $y^2=25$ y= (5,-5). once we plug that in, we get $50+x^2 = 59$ , $x^2 = 9$ x = (-3,3)

8 0

3 years ago

A recent study suggested that 70% of all eligible voters will vote in the next presidential election. Suppose 20 eligible voters

natita [175]

Answer:

0.0479 = 4.79% probability that fewer than 11 of them will vote

Step-by-step explanation:

For each voter, there are only two possible outcomes. Either they will vote, or they will not. The probability of a voter voting is independent of any other voter, which means that the binomial probability distribution is used to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

In which $C_{n,x}$ is the number of different combinations of x objects from a set of n elements, given by the following formula.

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

And p is the probability of X happening.

70% of all eligible voters will vote in the next presidential election.

This means that $p = 0.7$

20 eligible voters were randomly selected from the population of all eligible voters.

This means that $n = 20$

What is the probability that fewer than 11 of them will vote?

This is:

$P(X < 11) = P(X = 10) + P(X = 9) + P(X = 8) + P(X = 7) + P(X = 6) + P(X = 5) + P(X = 4) + P(X = 3) + P(X = 2) + P(X = 1) + P(X = 0)$

In which

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

$P(X = 10) = C_{20,10}.(0.7)^{10}.(0.3)^{10} = 0.0308$

$P(X = 9) = C_{20,9}.(0.7)^{9}.(0.3)^{11} = 0.0120$

$P(X = 8) = C_{20,8}.(0.7)^{8}.(0.3)^{12} = 0.0039$

$P(X = 7) = C_{20,7}.(0.7)^{7}.(0.3)^{13} = 0.0010$

$P(X = 6) = C_{20,10}.(0.7)^{6}.(0.3)^{12} = 0.0002$

$P(X = 5) = C_{20,5}.(0.7)^{5}.(0.3)^{15} \approx 0$

The probability of 5 or less voting is very close to 0, so they will not affect the outcome. Then

$P(X < 11) = P(X = 10) + P(X = 9) + P(X = 8) + P(X = 7) + P(X = 6) + P(X = 5) + P(X = 4) + P(X = 3) + P(X = 2) + P(X = 1) + P(X = 0) = 0.0308 + 0.0120 + 0.0039 + 0.0010 + 0.0002 = 0.0479$

0.0479 = 4.79% probability that fewer than 11 of them will vote

8 0

3 years ago

The hypotenuse of a right triangle is 17 cm long. If one of the remaining two sides is 8 cm in length, then the length of the ot

VashaNatasha [74]

don't know

Mark as brainlist

mate

8 0

3 years ago

Read 2 more answers

The tires on Eric's car have a diameter of 18 inches. Rounded to the nearest whole number, how many rotations per second does ea

Step2247 [10]

Answer:

Step-by-step explanation:

We need to figure out how far Eric's car takes him in 1 rotation based on the diameter of his tire in feet. If the diameter of the tire is 18", then it is 1.5'. The circumference will tell us the distance 1 rotation of his tires will take him:

C = 3.1415(1.5) so

C = 4.71225 feet is how far he goes in 1 rotation. If he travels 88 feet in 1 second, we can figure the number of rotations by dividing 88 by 4.71225 to give us the unit rate (or, rotations per second his car makes). This quotient is 18.67 feet per sec, which rounds to 19, choice B.

4 0

3 years ago

The area of a rectangular patio is 384 square feet.

Usimov [2.4K]

the ratio of the length and width = 3:2

Step-by-step explanation:

let the length be =x

width be = $\frac{2x}{3}$

area of a rectangle = length X width

so, x X $\frac{2x}{3}$ = 384

or, $x^{2}$ X 2/3 = 384

or, $x^{2}$ = (384 X 3)/2

= 576

or, x = 24 ( taking square root)

hence, length is 24

width is = 24 X (2/3)

=16

so the ratio of length and width = 24 : 16

= 3:2

3 0

3 years ago