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What is the area of the rectangle? shoe your work! do not round anything until the very end and round your final answer to the t

weeeeeb [17]

Answer:

The area of the rectangle is 42 units^2

Step-by-step explanation:

we know that

The area of rectangle is equal to

$A=LW$

In this problem

AB=DC

BC=AD

see the attached figure with letters to better understand the problem

we have that

$L=BC\\W=AB$

the formula to calculate the distance between two points is equal to

$d=\sqrt{(y2-y1)^{2}+(x2-x1)^{2}}$

we have the points

$A(2,-1),B(5,2),C(12,-5),D(9,-8)$

Find out the distance BC

we have

$B(5,2),C(12,-5)$

substitute in the formula

$d=\sqrt{(-5-2)^{2}+(12-5)^{2}}$

$d=\sqrt{(-7)^{2}+(7)^{2}}$

$d_B_C=\sqrt{98}\ units$

Find out the distance AB

we have

$A(2,-1),B(5,2)$

substitute in the formula

$d=\sqrt{(2+1)^{2}+(5-2)^{2}}$

$d=\sqrt{(3)^{2}+(3)^{2}}$

$d_A_B=\sqrt{18}\ units$

Find out the area

$A=(L)(W)$

we have

$L=d_B_C=\sqrt{98}\ units$

$W=d_A_B=\sqrt{18}\ units$

substitute

$A=(\sqrt{98})(\sqrt{18})=42.0\ units^2$

4 0

3 years ago

Roll a die 10 sided die 3 times. What is the probability that the sequence is strictly increasing or decreasing?

snow_lady [41]

Answer:

The probability of obtaining a sequence which is neither strictly increasing nor decreasing in 0.76.

Step-by-step explanation:

We have 10 possible outcomes on a single throw.

So, outcomes in 3 throws = $10^{3} =1000$ outcomes.

Let x be the number of strictly increasing arrangements.

Let y be the number of strictly decreasing arrangements.

Let z be the number of outcomes that are neither strictly decreasing nor strictly increasing

So, we have $x+y+z=1000$

If we look at a strictly increasing arrangement from the other/opposite side, it will look like a strictly decreasing arrangement.

So, x = y

Hence, we can say the final equation will be :

$2x+z=1000$

And for strictly increasing arrangements ,all 3 numbers will be different and it can be done in 10C3 ways.

10C3= $\frac{10!}{3!7!}$ = 120 ways

So, $2x=2\times120=240$

Thus $z=1000-240=760$

So, the probability is = $\frac{760}{1000} = 0.76$

Therefore, the probability of obtaining a sequence which is neither strictly increasing nor decreasing in 0.76.

4 0

3 years ago

use elimination to solve. For a production of sweeney Todd in Las Vegas, orchestra seats cost $42 and mezzanine seats cost $25.

lidiya [134]

They bought 8 orchestra seats and 6 mezzanine seats.

Step-by-step explanation:

Cost of one orchestra seat = $42

Cost of one mezzanine seat = $25

No. of people = 14

Amount spent = $486

Let,

x be the number of orchestra seats

y be the number of mezzanine seats

According to given statement;

x+y=14 Eqn 1

42x+25y=486 Eqn 2

Multiplying Eqn 1 by 25;

$25(x+y=14)\\25x+25y=350\ \ \ \ Eqn\ 3$

Subtracting Eqn 3 from Eqn 2 to eliminate y;

$(42x+25y)-(25x+25y)=486-350\\42x+25y-25x-25y=136\\17x=136$

Dividing both sides by 17

$\frac{17x}{17}=\frac{136}{17}\\x=8$

Putting x=8 in Eqn 1

$8+y=14\\y=14-8\\y=6$

They bought 8 orchestra seats and 6 mezzanine seats.

Keywords: linear equation, elimination method

Learn more about elimination method at:

#LearnwithBrainly

5 0

3 years ago

What is the area of the paper used to wrap a can of soup if the can is 11 cm tall and has a diameter of 7.5 cm. Show all formula

Dimas [21]

Notice that a can is a cylinder, which is basically two circles and one rectangle. Now, the question wants area of this rectangle.

You know the width of the rectangle (or the paper), which is 11cm. How do you find the length then?

Notice that the length of the rectangle is also the circumference of the circles. From here, use C = πd where C is circumference and d is diameter. The d is given, which is 7.5 cm. Depending on the question, π can be 3.14, 22/7 or the actual pi.

multiply π and 7.5cm and you get the circumference. Multiply this to 11cm and you get area of the rectangle.

6 0

3 years ago

517x82= what is the anser

erma4kov [3.2K]

Answer:

The answer is 42394

7 0

3 years ago

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