2. Tiangle ABC has vertices A(3, 3), B(2,-4), and c(0, 0). This triangle is rotated 90

Find the coordinates of the circumcenter for triangle DEF with coordinates D(1,3) E(8,3) and F(1,-5) show your work

nikklg [1K]

One leg is horizontal, on the line y=3. Another leg is vertical, on the line x=1. The point where these intersect, D(1, 3) is the vertex of a right angle. Any right triangle inscribed in a circle has its hypotenuse as the diameter of the circle.

Since the triangle is a right triangle, the circumcenter is the midpoint of the hypotenuse: ((8, 3) + (1, -5))/2 = (4.5, -1).

6 0

3 years ago

Help Please!<br> Find the value of x for which ABCD must be a parallelogram.

Pepsi [2]

Answer:

2

Step-by-step explanation:

We know that the opposite sides of a parallelogram are equal so:

25x+1=7x+37

18x=36

x=2

4 0

2 years ago

Min-Jee is planting two rectangular flower beds. One bed is 2.78 feet by 4.81 feet, and the other bed is 2.78 feet by 5.61 feet.

shusha [124]

Answer: $(2.78+4.81)(2.78+5.61)$

Step-by-step explanation:

<h3> The complete exercise is attached.</h3><h3></h3>

The area of a rectangle can be calculated with this formula:

$A=lw$

Where "l" is the lenght and "w" is the width.

Then, you can notice that it can be obtained by multiplying the dimensions of the rectangle.

Knowing this, you can determine that the total area of the two flowers bed can be obtained by adding the products of their dimensions.

Since one of the rectangular flower bed is 2.78 feet by 4.81 feet and the other bed 2.78 feet by 5.61 feet, you can write the following expression to find the total area (in square feet)of the two beds:

$2.78*4.81 +2.78*5.61$

If you factor out 2.78:

$2.78(4.81 +5.61)$ or $(4.81 +5.61)2.78$

Therefore, the expression that does not represent the total area in square feet of the two beds, is:

$(2.78+4.81)(2.78+5.61)$

6 0

3 years ago

Read 2 more answers

A random sample of 10 parking meters in a resort community showed the following incomes for a day. Assume the incomes are normal

GenaCL600 [577]

Answer:

A 95% confidence interval for the true mean is [$3.39, $6.01].

Step-by-step explanation:

We are given that a random sample of 10 parking meters in a resort community showed the following incomes for a day;

Incomes (X): $3.60, $4.50, $2.80, $6.30, $2.60, $5.20, $6.75, $4.25, $8.00, $3.00.

Firstly, the pivotal quantity for finding the confidence interval for the population mean is given by;

P.Q. = $\frac{\bar X-\mu}{\frac{s}{\sqrt{n} } }$ ~ $t_n_-_1$

where, $\bar X$ = sample mean income = $\frac{\sum X}{n}$ = $4.70

s = sample standard deviation = $\sqrt{\frac{\sum (X-\bar X)^{2} }{n-1} }$ = $1.83

n = sample of parking meters = 10

$\mu$ = population mean

<em>Here for constructing a 95% confidence interval we have used a One-sample t-test statistics because we don't know about population standard deviation.</em>

<u>So, 95% confidence interval for the population mean, </u> $\mu$ <u> is ;</u>

P(-2.262 < $t_9$ < 2.262) = 0.95 {As the critical value of t at 9 degrees of

freedom are -2.262 & 2.262 with P = 2.5%}

P(-2.262 < $\frac{\bar X-\mu}{\frac{s}{\sqrt{n} } }$ < 2.262) = 0.95

P( $-2.262 \times {\frac{s}{\sqrt{n} } }$ < ${\bar X-\mu$ < $2.262 \times {\frac{s}{\sqrt{n} } }$ ) = 0.95

P( $\bar X-2.262 \times {\frac{s}{\sqrt{n} } }$ < $\mu$ < $\bar X+2.262 \times {\frac{s}{\sqrt{n} } }$ ) = 0.95

<u>95% confidence interval for</u> $\mu$ = [ $\bar X-2.262 \times {\frac{s}{\sqrt{n} } }$ , $\bar X+2.262 \times {\frac{s}{\sqrt{n} } }$ ]

= [ $4.70-2.262 \times {\frac{1.83}{\sqrt{10} } }$ , $4.70+ 2.262 \times {\frac{1.83}{\sqrt{10} } }$ ]

= [$3.39, $6.01]

Therefore, a 95% confidence interval for the true mean is [$3.39, $6.01].

The interpretation of the above result is that we are 95% confident that the true mean will lie between incomes of $3.39 and $6.01.

Also, the margin of error = $2.262 \times {\frac{s}{\sqrt{n} } }$

= $2.262 \times {\frac{1.83}{\sqrt{10} } }$ = <u>1.31</u>

4 0

3 years ago

Can I Get A Little Help Here?

Musya8 [376]

Hey there :)

We know the formula for simple interest is
I = prt
{ The picture includes what each stands for }

Lehena:
Initial amount = $100
Interest rate = 2.5% = $\frac{2.5}{100} = 0.025$
Time = 3 years
I = ( 100 )( 0.025 )( 3 )
= 7.5$

Total = $100 + $7.5 = $107.5

Marty:
Initial amount = $100
Interest rate = 2% = $\frac{2}{100} = 0.02$
Time = 3 years
I = ( 100 )( 0.02 )( 3 )
= $6

Total = $100 + $6 = $106

How much more than Marty did Lehena receive?
= Total Amount of Lehena - Total Amount of Marty
= 107.5 - 106
= $1.5

Your answer will be option B) $1.50

7 0

3 years ago