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guajiro [1.7K]
3 years ago
14

In the diagram, two parallel lines are intersected by a transversal. What are the measurements of angles 1, 2, 4, 5, 6, 7, and 8

?

Mathematics
1 answer:
larisa86 [58]3 years ago
8 0

Answer:

Step-by-step explanation:

1  6  8          55 degrees

2  4  5  7      125 degrees

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Determine which of the indicated column vectors are eigenvectors of the given matrix
gladu [14]
]Eigenvectors are found by the equation (A-\lambda I) \vec{v} = 0$ implying that \det(A-\lambda I) = 0. We then can write:

A-\lambda I = \left [ \begin{array}{cc} 4-\lambda & 2 \\ 5 & 1-\lambda \end{array}\right ] 

And:

\det(A-\lambda I) = (4-\lambda)(1-\lambda) - 10 = 0 

Gives us the characteristic polynomial:

\lambda^2 - 5 \lambda -6 = 0 \implies \lambda_1 = -1, \lambda_2 = 6

So, solving for each eigenvector subspace:

\left [ \begin{array}{cc} 4 & 2 \\ 5 & 1 \end{array} \right ] \left [ \begin{array}{c} x \\ y \end{array} \right ] = \left [ \begin{array}{c} -x \\ -y \end{array} \right ]

Gives us the system of equations:

4x + 2y = -x \newline 5x + y = - y 

Producing the subspace along the line y = -\frac{5}{2} x

We can see then that 3 is the answer. 



7 0
3 years ago
Suppose the probability of an IRS audit is 1.5 percent for U.S. taxpayers who file form 1040 and who earned $100,000 or more.
sp2606 [1]

Answer:

(A) The odds that the taxpayer will be audited is approximately 0.015.

(B) The odds against these taxpayer being audited is approximately 65.67.

Step-by-step explanation:

The complete question is:

Suppose the probability of an IRS audit is 1.5 percent for U.S. taxpayers who file form 1040 and who earned $100,000 or more.

A. What are the odds that the taxpayer will be audited?

B. What are the odds against such tax payer being audited?

Solution:

The proportion of U.S. taxpayers who were audited is:

P (A) = 0.015

Then the proportion of U.S. taxpayers who were not audited will be:

P (A') = 1 - P (A)

        = 1 - 0.015

        = 0.985

(A)

Compute the  odds that the taxpayer will be audited as follows:

\text{Odds of being Audited}=\frac{P(A)}{P(A')}

                                    =\frac{0.015}{0.985}\\\\=\frac{3}{197}\\\\=0.015228\\\\\approx 0.015

Thus, the odds that the taxpayer will be audited is approximately 0.015.

(B)

Compute the odds against these taxpayer being audited as follows:

\text{Odds against Audited}=\frac{P(A')}{P(A)}

                                    =\frac{0.985}{0.015}\\\\=\frac{3}{197}\\\\=65.666667\\\\\approx 65.67

Thus, the odds against these taxpayer being audited is approximately 65.67.

8 0
3 years ago
Simplify y-2/3/y+1/5
liberstina [14]

Answer:

\frac{15y-10}{15y-3}

Step-by-step explanation:

First at all, we need to use a=\frac{a}{1} to convert this expression into a fraction, like:

y-\frac{2}{3} to convert into \frac{y}{1} -\frac{2}{3}.

Expand the fraction to get the least common denominator, like

\frac{3y}{3*1}-\frac{2}{3}

Write all numerators above the common denominator, like this:

\frac{3y-2}{3}

The bottom one used the same way to became simplest form, like this:

y+\frac{1}{5}

\frac{y}{1} +\frac{1}{5}

\frac{5y}{5*1}+\frac{1}{5}

\frac{5y+1}{5}

And it became like this:

\frac{3y-2}{3}/\frac{5y+1}{5}

Now, we are going to simplify this complex fraction. We can use cross- multiply method to simplify this fraction.

\frac{3y-2}{3}*\frac{5y+1}{5}

3y-2(5) and 5y-1(3)

and it will becomes like this in function form:

\frac{3y-2(5)}{5y+1(3)}

Then, we should distribute 5 through the parenthesis

\frac{15y-10}{5y+1(3)}

\frac{15y-10}{15y+3}

And.... Here we go. That is the answer.

7 0
3 years ago
Please help me!!!!!!!!!
nalin [4]

(y+20)=1(x+10); First, we can find the slope by using the equation y2-y1/x2-x1.

-9+20/1+10 (Accounting for double negatives).

11/11 = 1

The slope of the equation is 1, now we just need to pick a set of points from which we derived the slope from (doesn't matter which) as y1 and x1 in the point-slope equation. (y-y1)=m(x-x1)

Your final answer can either be (y+20)=1(x+10) or (y+9)=1(x-1) but in the context of this question it is (y+20)=1(x+10)

8 0
3 years ago
Express the set of real numbers between but not including 2 and 5 as follows.
Mashcka [7]
2 < x < 5

i think this is the answer
7 0
3 years ago
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