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2 years ago

Triangle PQR is formed by the three squares A, B, and C:

Mathematics

2 answers:

Svetradugi [14.3K]2 years ago

8 0

Answer:

A. $PR^2=PQ^2+QR^2$

Because $25=9+16$

Step-by-step explanation:

We are given that

Area of square A= $9$ square units

Are of square B= $16$ square units

Area of square C= $25$ square units

We have to find the relationship between sides of triangle PQR.

Side of square= $\sqrt{Area\;of\;square}$

Using the formula

Side of square A= $\sqrt{9}$ =3 units

Side of square B= $\sqrt{16}=4$ units

Side of square C= $\sqrt{25}=5$ units

Pythagoras theorem

$(hypotenuse)^2=(Base)^2+(Perpendicular\;side)^2$

Using Pythagoras theorem

$PR^2=PQ^2+QR^2$

$5^2=3^2+4^2$

$25=9+16$

Option A is true

Levart [38]2 years ago

3 0

The first choice if ()2 means to the power of two if not then it is none of them.

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On February 1, 1977, John deposited $2250 into a savings account paying 5.76% interest, compounded quarterly. If he hasn't made

Travka [436]

John's effective annual rate is about
(1 +.0576/4)^4 -1 ≈ 5.8856%
According to the "rule of 72", John's money will have doubled in
72/5.8856 = 12.23 years

John's balance will be $4500 in 1989.

_____
Since you're only concerned with the year (not the month), you don't actually need to determine the effective annual rate. The given rate of 5.76% will tell you 72/5.76 = 12.5 years. The actual doubling time is closer to 12.12 years, so using the effective rate gives results that are closer, but "good enough" is good enough in this case.

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3 years ago

Let x be the amount of time (in minutes) that a particular San Francisco commuter must wait for a BART train. Suppose that the d

babymother [125]

Answer:

a) P (x is less than 11 minutes) = 0.55

P (x is more than 14 minutes) = 0.3

b) P (x is between 8 and 13 minutes) = 0.25

c) P(x < c) =0.8 is 0.05 x c = 0.8

Step-by-step explanation:

a) P (x is less than 11 minutes) = 11 x 0.05

= 0.55

P (x is more than 14 minutes) = 0.05 x (20 - 14)

= 0.05 x 6

= 0.3

b) P (x is between 8 and 13 minutes) = 0.05 x (13 -8)

= 0.05 x 5

= 0.25

c) P(x < c) =0.8

The area between 0 and c is 0.8

Hence,

0.05 x c = 0.8

3 0

2 years ago

Read 2 more answers

At the local grocery store, q 16-ounce bottle of Apple juice costs $3.20. What is the cost of the Apple juice per ounce?

galben [10]

16q= 3.20
÷16 on both sides
and you get .20 cents per ounce.

6 0

2 years ago

On a snow day, Mason created two snowmen in his backyard. Snowman A was built to a height of 51 inches and Snowman B was built t

mr_godi [17]

Answer:

A ( t ) = -4t + 51

B ( t ) = -2t + 29

t < 11 hours ... [ 0 , 11 ]

Step-by-step explanation:

Given:-

- The height of snowman A, Ao = 51 in

- The height of snowman B, Bo = 29 in

Solution:-

- The day Mason made two snowmans ( A and B ) with their respective heights ( A(t) and B(t) ) will be considered as the initial value of the following ordinary differential equation.

- To construct two first order Linear ODEs we will consider the rate of change in heights of each snowman from the following day.

- The rate of change of snowman A's height ( A ) is:

$\frac{d h_a}{dt} = -4$

- The rate of change of snowman B's height ( B ) is:

$\frac{d h_b}{dt} = -2$

Where,

t: The time in hours from the start of melting process.

- We will separate the variables and integrate both of the ODEs as follows:

$\int {} \, dA= -4 * \int {} \, dt + c\\\\A ( t ) = -4t + c$

$\int {} \, dB= -2 * \int {} \, dt + c\\\\B ( t ) = -2t + c$

- Evaluate the constant of integration ( c ) for each solution to ODE using the initial values given: A ( 0 ) = Ao = 51 in and B ( 0 ) = Bo = 29 in:

$A ( 0 ) = -4(0) + c = 51\\\\c = 51$

$B ( 0 ) = -2(0) + c = 29\\\\c = 29$

- The solution to the differential equations are as follows:

A ( t ) = -4t + 51

B ( t ) = -2t + 29

- To determine the time domain over which the snowman A height A ( t ) is greater than snowman B height B ( t ). We will set up an inequality as follows:

A ( t ) > B ( t )

-4t + 51 > -2t + 29

2t < 22

t < 11 hours

- The time domain over which snowman A' height is greater than snowman B' height is given by the following notation:

Answer: [ 0 , 11 ]

8 0

2 years ago

Here is a list of five numbers.98^53 98^64 98^73 98^88 98^91Find the lowest common multiple of these five numbers.

tekilochka [14]

Answer:

98^91

Step-by-step explanation:

Since the base of all the numbers is 98,

the LCM is simply the one with the greatest exponent

example

98^53 * 98^38 = 98^91

3 0

2 years ago