what's the square footage of 12'3" * 18'4"

Answer:

C. 35

Step-by-step explanation:

x^2 + 12^2 = (x + 2)^2

x^2 + 144 = x^2 + 4x + 4

144 = 4x + 4

4x = 140

x = 35

Answer:

C

Step-by-step explanation:

Since this is a right triangle, we can use the Pythagorean Theorem (a² + b² = c², in this case a = x, b = 12 and c = x + 2) to solve for x.

x² + 12² = (x + 2)²

x² + 144 = x² + 4x + 4

144 = 4x + 4

140 = 4x

x = 35

Answer:

[tex]\Huge \boxed{\mathrm{61.22 \ m}}[/tex]

Step-by-step explanation:

A stone is thrown downward straightly with the velocity of 20 m/s and it reaches the ground at the velocity of 40 m/s. What will be the height of building? (Question)

The initial velocity ⇒ 20 m/s

The final velocity ⇒ 40 m/s

We can apply a formula to solve for the height of the building.

[tex](V_f)2 - (V_i)^2 =2gh[/tex]

[tex]V_f = \sf final \ velocity \ (m/s)[/tex]

[tex]V_i = \sf initial \ velocity \ (m /s)[/tex]

[tex]g = \sf acceleration \ due \ to \ gravity \ (m/s^2 )[/tex]

[tex]h = \sf height \ (m)[/tex]

Plugging in the values.

Acceleration due to gravity is 9.8 m/s².

[tex](40)^2 - (20)^2 =2(9.8)h[/tex]

Solve for [tex]h[/tex].

[tex]1600 - 400 =19.6h[/tex]

[tex]1200 =19.6h[/tex]

[tex]\displaystyle h=\frac{1200}{19.6}[/tex]

[tex]h= 61.22449[/tex]

The height of the building is 61.22 meters.

Answer:

3

= 15/5

= [tex]\sqrt[3]{27}[/tex]

= 1.5*2

= 3/1

= 3*1

= 3¹

= 1/3⁻¹

= 3⁴ / 3³

= 3⁵ * 3⁻⁴

Answer:

0.25%

Step-by-step explanation:

Rate of commission

= (commission*100)/cost of land

=( 20000*100)/8000000

= 2000000/8000000

=2/8

= 0.25%

Answer:The first issue one most notice is the words “at least” We are trying to find the probability of at least 2 girls.

The five possible outcomes for girls are 0,1,2,3,4. The odds of 1 girl out of 4 is .25 and the odds of 1 boy out of 4 is .25 (same as the odds of 3 out of 4 girls). Therefore the odds of 1 OR 3 girls must be .5 because 1 girl and 3 girls each has a .25 probability. If the probability of (1 OR 3 girls) equals .5, then the probability of 2 girls must be a different number.

The probability of 2 or more girls, is the sum of the probability of 4 girls (.06125)(—-.5 to the 4th power—— ), plus the probability of 3 girls (.25)——(the same as the probability of 1 boy)—- plus the probability of 2 girls. Since we know the probability of zero boys is .0625 (again, .5 to the 4th power) and the probability of 1 boy is .25 (the same as the probability of 3 girls )———then the probability of 2 girls is ((1 minus (the sum of the probability of 0 OR 1 boys) plus the (sum of the probability of 3 or 4 girls)), or 1-((.0625+.25)+(.0625+.25)), or .375. We had to derive the probability of two from the other known probabilities. Therefore .375+.25+.0625=.6875 is the probability of both AT LEAST 2 girls and also NO MORE than 2 boys. Notice this adds up to 1.375 because the probability of the central number 2 (i.e., .375) appears on both sides.

Answer:

5x-4y = -32

Step-by-step explanation:

First write the equation in point slope form

y-y1 = m(x-x1)

y - -2 = 5/4 ( x- -8)

y+2 = 5/4 (x+8)

Multiply each side by 4 to clear the fraction

4( y+2 )= 4*5/4 (x+8)

4y +8 = 5(x+8)

4y+8 = 5x+40

Subtract 4y from each side

8 = 5x-4y +40

Subtract 40 from each side

-32 = 5x-4y

5x-4y = -32

Answer:

The answer is

Step-by-step explanation:

To write an equation of a line given a point and slope use the formula

y - y1 = m( x - x1)

where

m is the slope

( x1 , y1) is the point

From the question

slope = 5/4

point (-8 , -2)

So the equation of the line is

Multiply through by 4

4y + 8 = 5( x + 8)

4y + 8 = 5x + 40

5x - 4y = 8 - 40

We have the final answer as

Hope this helps you

Answer:

461.58 in²

Step-by-step explanation:

The surface area (A) is calculated as

A = area of base + area of curved surface

   = πr² + πrl ( r is the radius of base and l is slant height )

    = 3.14 × 7² + 3.14 × 7 × 14

    = 3.14 × 49 + 3.14 × 98

    = 3.14(49 + 98)

    = 3.14 ×147

     = 461.58 in²

Answer:

y =( -1/2 )x + 2

Step-by-step explanation:

first step is to determine the slope of the line ( which is the rise over the run) or symbolically slope is defined as m= ∆x / ∆y, so plugging those values we get...

m= ∆x / ∆y = (-1 - 0) / (4 - 2) = -1 / 2

so next is to find the zero( y-intercept) of the function by ....

y = mx + b

y = ( -1/2)x + b (since m is equal to -1/2)

2 = ( -1/2)0 + b

2= b

Answer:

6000 metres is equal to 6 kilograms

Answer:$60,000

Step-by-step explanation:

If he bought it for $50,000 and then spent $5,000 on repairs then he spent a total of $55,000. For a profit of $5,000 he would need to sell it for $60,000 Because

60,000 - 55,000 = 5,000

Answer:

Hope this helps you.

Step-by-step explanation:

I plugged in x for t, but it is the same graph.

Answer:

Here for the comments .

Step-by-step explanation:

Answer:

47

Step-by-step explanation:

Using the follwing property

[tex]x^{2} -y^2=(x+y)(x-y)[/tex]

in which x=24 and y=23

so

[tex]24^2-23^2=(24-23)(24+23)\\=1(47)\\=47[/tex]

Answer:

47

Step-by-step explanation:

Lets say 24 is x and 23 is y.

the equation would be x^2 - y^2

this is = to (x-y)(x+y)

substitute the numbers in

(24-23)(24+23)

which simplifies to

(1)(47)

which equals 47

Answer:

1. 98.7 km

2. 303.5 degree

Step-by-step explanation:

Using the alternate angle, the angle at B will be 50 + 10 = 60 degree.

To calculate the length AC of the returning journey, use cosine formula to calculate it.

To find the bearing of the returning journey, use sine rule to calculate it.

Please find the attached file for the solution

Answer:

Step-by-step explanation:

If he were to find the mean then he would need to add all the numbers up and divide by the number of numbers. The answer of this would 69.1

If you find the median you would need to put the numbers in order,

2, 38, 75, 80, 88, 90, 92, 92, 95, then find the middle which would be 88.

So the better option would be finding the median. I think that this would be the best way to get the the most favorable measure of center.

I hope this helps.

Answer:

3.5 hours

Step-by-step explanation:

Paul:

Mary:

Since the distance is same, we have:

Answer: Paul's travel took 3.5 hours

Answer:

See explanation

Step-by-step explanation:

a) 15:20 - 12:35 = 14:80 - 12:35 = 2 hours and 45 minutes

b) 13:05 - 10:15 = 12:65 - 10:15 = 2 hours and 50 minutes

c) 6:50 - 4:30 = 2 hours and 20 minutes

d) 1:15pm - 9:55am = 13:15 - 9:55 = 12:75 - 9:55 = 3 hours and 20 minutes

Answer:

a) 15:20 - 12:35 = 14:80 - 12:35 = 2 hours and 45 minutes

b) 13:05 - 10:15 = 12:65 - 10:15 = 2 hours and 50 minutes

c) 6:50 - 4:30 = 2 hours and 20 minutes

d) 1:15pm - 9:55am = 13:15 - 9:55 = 12:75 - 9:55 = 3 hours and 20 minutes

Step-by-step explanation:

Answer:

The two inequalities that show the solution to these equations are n ≥ 55 and y ≥ 6

Step-by-step explanation:

We are given two inequalities that we have to solve. We can solve these inequalities as if we are solving for the variable.

n/5 ≥ 11

Multiply by 5 on both sides.

n ≥ 55

Now, let's do the second one.

-3y ≤ -18

Divide by -3 on both sides. When we divide by a negative in inequalities, then the sign is going to flip to its other side. So, this sign (≤) becomes this sign (≥)

y ≥ 6

Answer:

one

Step-by-step explanation:

Zero has one square root which is 0.

Negative numbers don't have real square roots since a square is either positive or 0.

To get the area simply multiply the length by the width.

(3x^2+5x+10)(x^2-3x-1) = 3x^4 - 4x^3 - 8x^2 - 35x - 10

Answer:

the answer is A

Step-by-step explanation:

got it right on edge

Answer:

115

Step-by-step explanation:

5 - 4(30)

5 - 120

115

Answer:

-115

Step-by-step explanation:

Since anything in between those two lines (absolute value) always comes out positive and the five inside there is already positive, we don't need to worry about it.

First let's look at what's inside the parenthesis.

5 - 4(32 - 2)

= 5 - 4(30)

Next, we'd multiply. (I'm going by PEMDAS)

5 - 120

Now that we've done that we just need to subtract. Generally, 120-5=115, so, we just need to make it negative.

Hope this helps!! <3 :)

Answer:

X = 1

Step-by-step explanation:

To solve the system of equation by susbtitution:

3x + y = 9

y = –4x + 10

We can follow the steps thus:

Substitute the value of y in the first equation:

As in the second equation y = -4x + 10 we can substitute in the first equation as follows:

3x + y = 9

3x + -4x + 10 = 9

Combine like terms:

3x + -4x + 10 = 9

Like therms are the therms with X (3x - 4x = -1x):

-1x + 10 = 9

Apply the subtraction property of equality:

-1x + 10 = 9

As 10 is suming, it passes to subtracting the 9:

-1x  = 9 - 10

-1x = -1

Apply the division property of equality:

-1x = -1

Dividing in -1:

x = -1 / -1

Answer:

b

Step-by-step explanation:

The value of x in this system of equations is 1.

3x + y = 9

y = –4x + 10

Substitute the value of y in the first equation:

Combine like terms:

Apply the subtraction property of equality:

Apply the division property of equality:

3x + (–4x + 10) = 9

–x + 10 = 9

–x = –1

x = 1

What is the value of y?

y =  

Answer:

15 lawns

Step-by-step explanation:

The Xbox costs $400 and his parents gave him $100. He needs to earn $300 more. $20 each lawn so $100 for 5 lawns. 5 lawns times three.

Xbox cost =400

Daniel's money =100

Xbox cost - Daniel money=300

yard cost =20

therefore 400 -100 /20

Daniel's need 15 yards to get the xbox

A) Here, We'll use "Pythagoras Theorem" which tells:

a² + b² = c²

So, PR² = PQ² + QR²

PR² = 14² + 9²

PR² = 196 + 81

PR = √277

In short, Your Answer would be 16.64 Feet

B) Again, Use the Pythagoras Theorem,  

c² - a² = b²

18² - 14² = b²

b² = 324 - 196

b = √128

b = 11.31

In short, Your Answer would be 11.31 Feet

Part A: Using the Pythagorean Theorem. a^2 + b^2 = c^2

PQ^2 + QR^2 = PR^2  (The rods make a right triangle, where PR would be the hypotenuse, and QR and PQ would be legs a and b.)

14^2 + 9^2 = PR^2

196 + 81 = PR^2

Square root of 277 = PR 

16.64 = PR

So, the hypotenuse would be equal to 16.64 ft.

Part B: Using the Pythagorean Theorem. a^2 + b^2 = c^2

PR^2 - PQ^2 = QR^2 (Trying to find the height of QR this time, not the hypotenuse, since we know what it is already. Subtracting the value of leg a from the hypotenuse will give us the value of leg b, QR.)

18^2 - 14^2 = QR^2

324 - 196 = QR^2

Square root of 128 = QR

So, the new height of QR would be 11.31 ft.

Answer:

x = 3

y = -1

Step-by-step explanation:

Based on the fact that our have two variables and two equations, I'm going to assume you are trying to find the values of x and y.

For these two equations, let's first find the value of x using the equation elimination method.

We're going to eliminate the y variable by multiplying the first equation by 2 and then adding that new equation to the second equation.

7x - y = 22 ==> 14x - 2y = 44

4x + 2y + (14x - 2y) = 10 + (44)

18x + 0y = 54

x = 3

Now we plug the value of x back into one of the equations to find the value of y.

7x - y = 22

7(3) - y = 22

-y = 22 - 21

y = -1

So our values are as follows:

x = 3

y = -1

Cheers.

Answer:

10 ships

Step-by-step explanation:

did it on Khan and

There can be many ways to solve this problem. Here, we will do this by thinking about units.

Let's say that Astrid can build

x

ships

xshipsx, start text, s, h, i, p, s, end text if she receives deliveries of wood for the maximum possible number of days, which is

100

days

100days100, start text, d, a, y, s, end text. How can we relate these two quantities with an equation?

100

days

⋅

y

ships

day

=

x

ships

100days⋅y

day

ships

​

=xships

​

So in order to find the number of ships

x

xx, we need to figure out the value of

y

yy, which is the rate of ships per day.

Hint #22 / 4

Notice what other information we are given:

40

tons

ship

40

ship

tons

​

40, start fraction, start text, t, o, n, s, end text, divided by, start text, s, h, i, p, end text, end fraction

300

sailors

ship

300

ship

sailors

​

300, start fraction, start text, s, a, i, l, o, r, s, end text, divided by, start text, s, h, i, p, end text, end fraction

4

tons

day

4

day

tons

​

4, start fraction, start text, t, o, n, s, end text, divided by, start text, d, a, y, end text, end fraction

2100

sailors

2100sailors2100, start text, s, a, i, l, o, r, s, end text

Which of these quantities can help us calculate a rate whose units are

ships

day

day

ships

​

start fraction, start text, s, h, i, p, s, end text, divided by, start text, d, a, y, end text, end fraction?

Hint #33 / 4

We can combine the following quantities:

4

tons

day

40

tons

ship

=

4

40

tons

day

⋅

ships

ton

=

0.1

ships

day

​

=

40

ship

tons

​

4

day

tons

​

​

=

40

4

​

day

tons

​

⋅

ton

ships

​

=0.1

day

ships

​

​

Now we can plug that in the original equation:

100

days

⋅

0.1

ships

day

=

x

ships

10

ships

=

x

ships

100days⋅0.1

day

ships

​

10ships

​

=xships

=xships

​

Hint #44 / 4

In conclusion, assuming Astrid receives the maximum possible amount of wood, she can build

10

1010 ships.

Answer:

what's the fraction though?

Answer:

Step-by-step explanation:

a. The slope of the perpendicular line is the negative reciprocal of the slope of the given line, so is ...

  m = -1/(5/6) = -6/5

Then the point-slope form of the desired line through (-3, 6) can be written as ...

  y = m(x -h) +k . . . . . line with slope m through (h, k)

  y = (-6/5)(x +3) +6

  y = -6/5x +12/5 . . . equation of line B

__

b. The distance from point P to the intersection point (X) can be found from the formula for the distance from a point to a line.

When the line's equation is written in general form, ax+by+c=0, the distance from point (x, y) to the line is ...

  d = |ax +by +c|/√(a² +b²)

The equation of line A can be written in general form as ...

  y = 5/6x -5/2

  6y = 5x -15

  5x -6y -15 = 0

Then the distance from P to the line is ...

  d = |5(-3) -6(6) -15|/√(5² +(-6)²) = 66/√61

The length of segment PX is (66√61)/61.

__

c. To find the midpoint, we need to know the point of intersection, X. We find that by solving the simultaneous equations ...

  y = 5/6x -5/2

  y = -6/5x +12/5

Equating y-values gives ...

  5/6x -5/2 = -6/5x +12/5

Adding 6/5x +5/2 gives ...

  x(5/6+6/5) = 12/5 +5/2

  x(61/30) = 49/10

  x = (49/10)(30/61) = 147/61

  y = 5/6(147/61) -5/2 = -30/61

Then the point of intersection of the lines is X = (147/61, -30/61).

So, the midpoint of PX is ...

  M = (P +X)/2

  M = ((-3, 6) +(147/61, -30/61))/2

  M = (-18/61, 168/61)

Answer:

Domain: 0 ≤ x < 9

Range: 0 < y ≤ 3

Step-by-step explanation:

The domain is the set of all values used for x-coordinates of all points on the curve.

The range is the set of all values used for y-coordinates of all points on the curve.

Look at the graph. The leftmost point is (0, 3). That point is included in the graph since there is no open circle there.

So far we know this:

Domain goes from 0 to ...

Range goes from 3 to ...

Now we look at the rightmost point. It is (9, 0), but there is an open circle on it, so that point itself is not included in the domain or range.

Now we know this:

Domain goes from 0 to just less than 9.

Range goes from 3 to to just more than 0.

Domain: 0 ≤ x < 9

Range: 0 < y ≤ 3