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ivolga24 [154]
4 years ago
11

1.The coordinates of the vertices of △RST are R(−4, −1) , S(−1, −1) , and T(−4, −2) .

Mathematics
1 answer:
Tju [1.3M]4 years ago
8 0

RS points east; R'S' points north, so there has been a rotation 90° CCW.

After that rotation, point S would be at (1, -1). It is actually at (1, 1), so has been shifted 2 units upward.

A sequence that does the desired mapping is

  • c. rotation of 90° CCW about the origin
  • b. translation 2 units up

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What is the point-slope form of a line with slope 3 that contains the point (2,1)?
Serjik [45]

Answer:

A) y-1=3(x-2)

Step-by-step explanation:

Point-slope formula.

y-y_1=m(x-x_1)

Given.

Slope (m) = 3

Points (x, y) = (2, 1)

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3 years ago
What is a prime factor?
iren [92.7K]
Prime factors are factors of a number that are, themselves, prime numbers. There are many methods to find the prime factors of a number, but one of the most common is to use a prime factor tree.
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According to the Mortgage Bankers Association, 8% of U.S. mortgages were delinquent in 2011. A delinquent mortgage is one that h
shepuryov [24]

Answer:

The probability that exactly one of these mortgages is delinquent is 0.357.

Step-by-step explanation:

We are given that according to the Mortgage Bankers Association, 8% of U.S. mortgages were delinquent in 2011. A delinquent mortgage is one that has missed at least one payment but has not yet gone to foreclosure.

A random sample of eight mortgages was selected.

The above situation can be represented through Binomial distribution;

P(X=r) = \binom{n}{r}p^{r} (1-p)^{n-r} ; x = 0,1,2,3,.....

where, n = number of trials (samples) taken = 8 mortgages

            r = number of success = exactly one

           p = probability of success which in our question is % of U.S.

                  mortgages those were delinquent in 2011, i.e; 8%

<em>LET X = Number of U.S. mortgages those were delinquent in 2011</em>

So, it means X ~ Binom(n=8, p=0.08)

Now, Probability that exactly one of these mortgages is delinquent is given by = P(X = 1)

                 P(X = 1)  = \binom{8}{1}\times 0.08^{1} \times (1-0.08)^{8-1}

                               = 8 \times 0.08 \times 0.92^{7}

                               = 0.357

<u><em>Hence, the probability that exactly one of these mortgages is delinquent is 0.357.</em></u>

4 0
3 years ago
Draw the graphs of the equations x – y = 1 and 2x + y = 8. Shade the area bounded by these two lines and y-axis. Also, determine
NikAS [45]

Answer:

Using Geometry to answer the question would be the simplest:

Step-by-step explanation:

Remembering the formula for the area of a triangle which is A=\frac12bh. One can then tackle the question by doing the following:

Step 1 Find the y-intercepts

The y-intercepts are found by substituting in x=0.

Which gives you this when you plug it into both equations:

-y=1\\y=-1\\y=8

So the y-intercepts for the graphs are (0,-1)\\, and (0,8) respectively.

Now one has to use elimination to solve the problems by adding up the equations we get:

x-y=1\\2x+y=8\\3x=9\\x=3

Now to solve for the y component substitute:

2(3)+y=8\\y=2

Therefore, the graphs intersect at the following:

(3,2)

Now we have our triangle which is accompanied by the graph.

now to solve it we must figure out how long the base is:

b=8-(-1)\\b=9

The height must also be accounted for which is the following:

h=3

Now the formula can be used:

A=\frac12bh=\frac12(9)(3)=\frac{27}2\ \text{units}^2

7 0
3 years ago
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A rectangle has dimensions 7 ft x 12 ft. Which of the dimensions describe a rectangle that is similar to this rectangle?
kotegsom [21]

Answer:

C) 21 ft x 36 ft

Step-by-step explanation:

Because 7 * 3 = 21 ft & 12 * 3 = 36 ft

7 0
3 years ago
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