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Zinaida [17]
1 year ago
13

Trapezoid $RSTU$ is a cross section of a lampshade. The diagonals of $RSTU$ are congruent, and the measure of $\angle S$ is $112

\degree$ . What is the measure of $\angle U$ ?
Mathematics
1 answer:
Alexxandr [17]1 year ago
3 0

Answer:

112°

Step-by-step explanation:

Given that the diagonals of trapezoid RSTU are congruent, it is an Isosceles Trapezoid.

One of the properties of an Isosceles Trapezoid is that the base angles are equal.

Therefore if the measure of angle S=112°, the measure of Angle U will also be 112°.

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Which statements about the local maximums and minimums for the given function are true? Choose three options.
Nostrana [21]

Answer:

Over the interval [2, 4], the local minimum is –8.

Over the interval [3, 5], the local minimum is –8.

Over the interval [1, 4], the local maximum is 0.

Step-by-step explanation:

The true statements are:

Over the interval [2, 4], the local minimum is –8.

Over the interval [3, 5], the local minimum is –8.

Over the interval [1, 4], the local maximum is 0.  

Lets discuss each option one by one:

Over the interval [1, 3], the local minimum is 0

This is a false statement. Look at the graph. The minimum point given is (3.4,-8). Therefore the local minimum is -8 not 0

Over the interval [2, 4], the local minimum is –8.

This statement is true because the given minimum point is(3.4, -8). Thus the  local minimum is -8 which is true

Over the interval [3, 5], the local minimum is –8.

According to the given minimum point, the local minimum  is -8 which is true

Over the interval [1, 4], the local maximum is 0.

Look at the graph. The maximum point given is (2,0). Thus this statement is true because local maximum is 0.

Over the interval [3, 5], the local maximum is 0.

This is a false statement because there is no maximum point

8 0
1 year ago
Read 2 more answers
A fitted multiple regression equation is Y = 28 + 5X1 - 4X2 + 7X3 + 2X4. When X1 increases 2 units and X2 increases 2 units as w
ad-work [718]

Answer:

A. Increase by 2

Step-by-step explanation:

Given that a  fitted multiple regression equation is

Y = 28 + 5X_1 -4X_2 + 7X_3 + 2X_4

This is a multiple regression line with dependent variable y and independent variables x1, x2, x3 and x4

The coefficients of independent variables represent the slope.

In other words the coefficients represent the rate of change of y when xi is changed by 1 unit.

Given that x3 and x4 remain unchanged and x1 increases by 2 and x2 by 2 units

Since slope of x1 is 5, we find for one unit change in x1 we can have 5 units change in y

i.e. for 2 units change in x1, we expect 10 units change in Y

Similarly for 2 units change in x2, we expect -2(4) units change in Y

Put together we have

10-8 =2 change in y

Since positive 2, there is an increase by 2

A. Increase by 2

5 0
1 year ago
sam lives in Massachusetts and wants to buy a television that costs $2000. the sales tax in Maine is only 5% which is less than
nexus9112 [7]
2000(1.0625)dave vs sam 2000(1.05)+30
2125 dave vs. sam 2,100+30
2125 dave vs. sam 2130
dave is correct, because it costs five dollars less in massachusetts than in Maine
3 0
2 years ago
 If the trapezoid below is reflected across the x-axis, what are the coordinates of B'?
Grace [21]
The x-coordinate remains the same as the x-coordinate of point B.
The y-coordinate becomes the additive inverse of the y-coordinate of point B.

Answer: B. (3, -8)

9 0
1 year ago
Read 2 more answers
Logan starts an IRA (Individual Retirement Account) at the age of 28 28 to save for retirement. He deposits $400 $ ⁢ 400 each mo
Valentin [98]

Answer:

A) Total amount deposited over the length of investment = $177600

B) Interest accrued upon retirement = $1,043,678.01

Step-by-step explanation:

From the question, we can see that he started the savings at the age of 28 and ended when he retired at the age of 65. Thus, number of years = 65 - 28 = 37 years

We are told he deposited $400 each month and that upon retirement it had grown to $1,161,278.01.

Since he deposited $400 each month, in a year which has 12 months, he deposited;

Amount deposited each year = 12 × 400 = $4800

Now, it took 37 years before he retired which was the point at which he stopped the deposit.

Thus;

Total Amount deposited upon retirement = Amount deposited each year × number of years he deposited.

Thus;

Total amount deposited over the length of investment upon retirement = 4800 × 37 = $177600

Now,we have seen that his retirement savings reads $1,161,278.01.

Thus is way more than the deposits he made throughout his work years.

This means there was interest on the money.

Interest = $1,161,278.01 - $177600

Interest = $1,043,678.01

8 0
1 year ago
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