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dedylja [7]
3 years ago
12

ABCD is a rectangle. If AC = 5x + 2 and BD = x + 22, find the value of x.

Mathematics
1 answer:
alexgriva [62]3 years ago
6 0
AC and BD are diagonals so they are congruent to each other and you can set the expressions equal

5x+2=x+22
Then, you need to subtract 2 from both sides to get 5x=x+20

Next, you subtract x from both sides to get 4x=20

Finally, you divide both sides by 4 to get a final answer of x=5

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If 1200 cm2 of material is available to make a box with a square base and an open top, find the largest possible volume of the b
Colt1911 [192]

Answer:

The largest possible volume V is ;

V = l^2 × h

V = 20^2 × 10 = 4000cm^3

Step-by-step explanation:

Given

Volume of a box = length × breadth × height= l×b×h

In this case the box have a square base. i.e l=b

Volume V = l^2 × h

The surface area of a square box

S = 2(lb+lh+bh)

S = 2(l^2 + lh + lh) since l=b

S = 2(l^2 + 2lh)

Given that the box is open top.

S = l^2 + 4lh

And Surface Area of the box is 1200cm^2

1200 = l^2 + 4lh ....1

Making h the subject of formula

h = (1200 - l^2)/4l .....2

Volume is given as

V = l^2 × h

V = l^2 ×(1200 - l^2)/4l

V = (1200l - l^3)/4

the maximum point is at dV/dl = 0

dV/dl = (1200 - 3l^2)/4

dV/dl = (1200 - 3l^2)/4 = 0

3l^2= 1200

l^2 = 1200/3 = 400

l = √400

I = 20cm

Since,

h = (1200 - l^2)/4l

h = (1200 - 20^2)/4×20

h = (800)/80

h = 10cm

The largest possible volume V is ;

V = l^2 × h

V = 20^2 × 10 = 4000cm^3

4 0
3 years ago
Y = 7x - 15<br> y = 4x - 12
elena-14-01-66 [18.8K]

Answer:

Step-by-step explanation:

7x - 15 = 4x - 12

3x - 15 = -12

3x = 3

x = 1

y = 7(1) - 15

y = 7 - 15

y = -8

(1, -8)

3 0
3 years ago
A. One player places 1 red, 5 green and 3 blue tiles in Bag A, and 6 red, 4 green, and 2 blue in Bag B. What is the probability
cupoosta [38]

Answer:

\frac{8}{27} is the probability that a player draws out two tiles of the same color assuming they are drawing one tile from each bag.

Step-by-step explanation:

In each bag there are red, green, and blue tiles, meaning that no matter which color is pulled out first there is always some probability that the second tile will be the same color. So, we can set up three possible outcomes:

Red: The player pulls out a red tile first. This has a \frac{1}{9} probability of happening. Then in order to succeed for the problem, the next tile also needs to be red which has a \frac{6}{12} probability attached to it. \frac{1}{9} × \frac{6}{12}=\frac{1}{18} probability of happening.

Green: There is a \frac{5}{9} probability of the player pulling out a green tile first. In this case we want to calculate the probability of the second tile being green, which would be \frac{4}{12}. \frac{5}{9}×\frac{4}{12}=\frac{5}{27}.

Blue: There is a \frac{3}{9} probability of the first tile being blue in which case we are hoping for the second tile to be blue as well. The probability of the second tile being blue is \frac{2}{12} on its own, and them both being blue is  \frac{3}{9}×\frac{2}{12}=\frac{1}{18}

Adding \frac{1}{18}+\frac{1}{18}+\frac{5}{27} we get the answer \frac{8}{27}.

4 0
3 years ago
I AM BEGGING YOU PLEASE IF YOU HAVE A HEART AWNSER FOR 50 POINTS AND BRILLIANT!!!
dangina [55]
5. Yes 1,2, or 3 hours
6. No, because the distance will never change and there aren't multiple values
7. Yes, yes or no (a person could be colorblind)
8. Yes, yes or no (a person could be colorblind)
9. Yes: Rap, country, pop, classical, etc
4 0
3 years ago
Read 2 more answers
The roots of the quadratic equation $z^2 + bz + c = 0$ are $-7 + 2i$ and $-7 - 2i$. What is $b+c$?
Alexxx [7]

Answer:

67

Step-by-step explanation: Given the quadratic equation $z^2 + bz + c = 0$, Vieta's formulas tell us the sum of the roots is $-b$, and the product of the roots is $c$. Thus,

\[-b = (-7 + 2i) + (-7 - 2i) = -14,\]so $b = 14.$

Also,

\[c = (-7 + 2i)(-7 - 2i) = (-7)^2 - (2i)^2 = 49 + 4 = 53.\]Therefore, we have $b+c = \boxed{67}$.

There are many other solutions to this problem. You might have started with the factored form $(z - (-7 + 2i))(z - (-7 - 2i)),$ or even thought about the quadratic formula.

This is the aops answer :)

8 0
2 years ago
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