If triangle LMN ~ triangle PON, what is MN?

The plate is rotated 90° about the origin in the counterclockwise direction. In the image trapezoid, what are the coordinates of

Jet001 [13]

Answer:

The coordinates of the endpoints of the side congruent to side EF is:

E'(-8,-4) and F'(-5,-7).

Step-by-step explanation:

" when point M (h, k) is rotated about the origin O through 90° in anticlockwise direction or we can say counter clockwise. The new position of point M (h, k) will become M' (-k, h) "

We are given a trapezoid such that the vertices of trapezoid are:

E(-4,8) , F(-7,5) , G(-4,3) , H(-2,5)

Then the new coordinates after the given transformation is:

E(-4,8) → E'(-8,-4)

F(-7,5) → F'(-5,-7)

G(-4,3) → G'(-3,-4)

H(-2,5) → H'(-5,-2)

Hence the coordinates of the endpoints of the side congruent to side EF is:

E'(-8,-4) and F'(-5,-7).

4 0

3 years ago

2. Water is leaking from a faucet at a constant rate of 1/3 gallon per minute.

Cloud [144]

Answer:

$W = \frac{1}{3}t$

20 gallons of water is leaked after an hour.

Step-by-step explanation:

Water is leaking at a constant rate of 1/3 gallon per minute.

a) We have to write a linear equation in two variables that show the amount of water, w, in gallons, that is leaked from the faucet after t minutes.

So, the equation is $W = \frac{1}{3}t$ ......... (1) (Answer)

b) Now, if t = 1 hour i.e. 60 minutes, then from equation (1) we can write

$W = \frac{1}{3}\times 60 = 20$ gallons.

Therefore, 20 gallons of water is leaked after an hour. (Answer)

5 0

3 years ago

Solve the solution of the equations 10x-3y=3 and 2x+y=9

forsale [732]

Answer:

x=1.875 y=-0.875

Step-by-step explanation:

10x-3y=3 10x-3y=3

3(2x+y)=(9)3 +6x+3y=27

1/16(16x)=(30)1/16 = x=1.875

10x-3y=3 10x-3y=3

-5(2x+y)=(9)-5 -10x-5y=4

1/-8(-8y)=(7)1/-8 = y=-0.875

4 0

3 years ago

The area of a rectangle is 56 cm. the length is 2 less than x and the width is 5 less than twice of x. solve for x

Nostrana [21]

Answer:

$x=\frac{9+\sqrt{449}}{4}$

Step-by-step explanation:

The area of a rectangle is:

$A=l\cdot w$

First let's write both the length and the width in terms of x:

$l=x-2$

How we obtained the answer:

The question states the length is "2 less than x". In this case, "less" is a keyword that represents subtraction. Therefore, "2 less than x" is "x-2".

$w=2x-5$

How we obtained the answer:

The question states the width is "5 less than twice of x". First, start by figuring out what "twice of x" is. The keyword is "twice" which represents multiplication. Therefore, "twice of x" can be written as "2x". Then, using the same keyword from before ("less"), "5 less than..." represents "2x-5".

Given:

Area = 56 cm

$l=x-2$

$w=2x-5$

Find:

x

$A=l\cdot w$

$56=(x-2)(2x-5)$

FOIL (Firsts, outsides, insides, lasts):

$56=2x^2-4x-5x+10\\56=2x^2-9x+10$

Subtract 10 from both sides:

$46=2x^2-9x$

Subtract 46 from both sides (forms a quadratic equation):

$0=2x^2-9x-46$

Use the quadratic formula:

${x = \frac{{ - b \pm \sqrt {b^2 - 4ac} }}{{2a}}}$ where $0=ax^2+bx+c$

Therefore:

$x=\frac{9\pm\sqrt{81-4(2)(-46)}}{2(2)}\\x=\frac{9\pm\sqrt{81+368}}{4}\\\\x=\frac{9\pm\sqrt{449}}{4}$

The answer is:

$x=\frac{9+\sqrt{449}}{4}$

This is because if we used subtraction, we would get a negative value, and we cannot have a negative length/width.

4 0

2 years ago

An analyst at Umbrella Corporation studied the relationship between the sales (in millions of dollars) of a product (Y) and popu

Sunny_sXe [5.5K]

Answer:

OPTION A: The company can be 95% confident, based on the method used to calculate the interval, that the true increase in mean sales for each additional 1 million persons in the marketing district is between $453,000 and $1,060,000.

Step-by-step explanation:

Note that the slope here is the increase in sales (in millions of dollars) per every 1 million increase in population. Hence, as this is a confidence interval for the slope, then

OPTION A: The company can be 95% confident, based on the method used to calculate the interval, that the true increase in mean sales for each additional 1 million persons in the marketing district is between $453,000 and $1,060,000.

5 0

4 years ago