8) There are 2116 students in a school .In how many equal rows and columns can they be arranged for a drill display?

Step-by-step explanation:

Hey, there!!!

Let me simply explain you about it.

We generally use the distance formula to get the points.

let the point R be (x,y)

As it an equilateral triangle it must have equal distance.

now,

let's find the distance of PQ,

we have, distance formulae is;

[tex]pq = \sqrt{( {x2 - x1)}^{2} + ( {y2 - y1)}^{2} } [/tex]

[tex]or \: \sqrt{( {5 + 3)}^{2} + ( {2 - 2)}^{2} } [/tex]

By simplifying it we get,

[tex] 8[/tex]

Now,

again finding the distance between PR,

[tex] pr = \sqrt{( {x2 - x1}^{2} + ( {y2 - y1)}^{2} } [/tex]

or,

[tex] \sqrt{( {x + 3)}^{2} + ( {y - 2)}^{2} } [/tex]

By simplifying it we get,

[tex] = \sqrt{ {x}^{2} + {y}^{2} + 6x - 4y + 13 } [/tex]

now, finding the distance of QR,

[tex]qr = \sqrt{( {x - 5)}^{2} + ( {y - 2)}^{2} } [/tex]

or, by simplification we get,

[tex] \sqrt{ {x}^{2} + {y}^{2} - 10x - 4y + 29 } [/tex]

now, equating PR and QR,

[tex] \sqrt{ {x}^{2} + {y}^{2} + 6x - 4y + 13} = \sqrt{ {x}^{2} + {y}^{2} - 10x - 4y + 29 } [/tex]

we cancelled the root ,

[tex] {x}^{2} + {y}^{2} + 6x - 4y + 13 = {x}^{2} + {y}^{2} -10x - 4y + 29[/tex]

or, cancelling all like terms, we get,

6x+13= -10x+29

16x=16

x=16/16

Therefore, x= 1.

now,

equating, PR and PQ,

[tex] \sqrt{ {x}^{2} + {y}^{2} + 6x - 4y + 13 } = 8} [/tex]

cancel the roots,

[tex] {x}^{2} + {y}^{2} + 6x - 4y + 13 = 8[/tex]

now,

(1)^2+ y^2+6×1-4y+13=8

or, 1+y^2+6-4y+13=8

y^2-4y+13+6+1=8

or, y(y-4)+20=8

or, y(y-4)= -12

either, or,

y= -12 y=8

Therefore, y= (8,-12)

by rounding off both values, we get,

x= 1

y=(8,-12)

So, i think it's (1,8) is your answer..

Hope it helps...

Answer:

1,8.9

Step-by-step explanation:

Step-by-step explanation:

For example:

Ex: 2:3 :: 6:9

In this question, the means are 3 and 6.

The extremes are 2 and 9.

We use this method to find whether the two ratios are equal or not.

We multiply the means and the extremes, and if there products are same, then these two ratios are proportional.

If these two ratios are proportional, their "means" = "extremes"

=> Means = Extremes

=> 3 x 6 = 2 x 9

=> 18 = 18

So, these two ratios are proportional.

Hope this helps you.

Answer:

A=45cm^2

Step-by-step explanation:

A= h/2(b1 + b2) for trapezoid

A=(5/2(6+12))cm^2

A=(2.5(18))cm^2

A=45cm^2

Answer:

See below.

Step-by-step explanation:

There is an infinite n umber of systems of equations that has (1, 4) as its solution. Are you given choices? Try x = 1 and y = 4 in each equation of the choices. The set of two equations that are true when those values of x and y are used is the answer.

Answer:

Two solutions: -0.12 and 1.75.

Step-by-step explanation:

The quadratic formula is:

[tex]\begin{array}{*{20}c} {\frac{{ - b \pm \sqrt {b^2 - 4ac} }}{{2a}}} \end{array}[/tex]. Assuming that the x² term is a, the x term is b, and the constant is c, we can plug the values into the equation.

[tex]\begin{array}{*{20}c}{\frac{{ - 8 \pm \sqrt {8^2 - 4\cdot-4.9\cdot1} }}{{2\cdot-4.9}}} \end{array}[/tex]

[tex]\begin{array}{*{20}c}{\frac{{ - 8 \pm \sqrt {64 + 19.6} }}{{-9.8}}} \end{array}[/tex]

[tex]\begin{array}{*{20}c}{\frac{{ - 8 \pm \sqrt {83.6} }}{{-9.8}}} \end{array}[/tex]

[tex]\begin{array}{*{20}c}{\frac{{ - 8 \pm \sqrt {9.14} }}{{-9.8}}} \end{array}[/tex]

[tex]\frac{-8 + 9.14}{-9.8} = -0.12[/tex]

[tex]\frac{-8-9.14}{-9.8} =1.75[/tex]

Hope this helped!

Answer:

[tex]\frac{9}{100}[/tex]

Step-by-step explanation:

Given:

Number of red balls, n(R) = 3

Number of green balls, n(G) = 9

Number of yellow balls, n(Y) = 2

Number of orange balls, n(O) = 2

Number of purple balls, n(P) = 4

Two balls are drawn one at a time with replacement.

To find:

Probability of drawing a green ball and an orange ball ?

Solution:

Total number of balls, n(Total) = 3 + 9 + 2 + 2 + 4 = 20

Formula for probability of an event E is given as:

[tex]P(E) = \dfrac{\text{Number of favorable cases}}{\text {Total number of cases}}[/tex]

Probability that a green ball is drawn at first:

[tex]P(Green) = \dfrac{\text{Number of Green balls}}{\text {Total number of Balls}}[/tex]

[tex]P(Green) = \dfrac{9}{20}[/tex]

Now, the ball is replaced , so total number of balls remain the same i.e. 20.[tex]P(Orange) = \dfrac{\text{Number of Orange balls}}{\text {Total number of Balls}}[/tex]

[tex]P(Orange) = \dfrac{2}{20} = \dfrac{1}{10}[/tex]

[tex]P(Green\ then\ orange) = P(Green) \times P(Orange)\\\Rightarrow P(Green\ then\ orange) = \dfrac{9}{10} \times \dfrac{1}{10}\\\Rightarrow P(Green\ then\ orange) = \bold{ \dfrac{9}{100} }[/tex]

Answer:

C

Step-by-step explanation:

you multiply each dot by the fraction of hours it is under. you add everything up and you should get 66/8 which is equivalent to 8 and 1/4

Answer:

Is c

Step-by-step explanation:

For plato Users

Answer:

The answer is A

Step-by-step explanation:

This shows a mirroring effect over the vertical y axis.

Choices B and C are a translation (aka shifting)

Choice D is a reflection but over the horizontal x axis.

Answer:

New depth of the milk will be 4 cm.

Step-by-step explanation:

If the carton (shaded side) is standing vertically, milk in the box will acquire the dimensions of the box.

Length of the cuboid formed by the the milk = 8 cm

Width = 5 cm

Height = 12 cm

Volume of the cuboid formed by the milk in the carton = Length × width × height

V = 8 × 5 × 12

  = 480 cm³

If the carton is turned so that the carton stands on the shaded face,

Volume of the milk remains unchanged but the dimensions of the cuboid formed by the milk inside the carton will get changed.

Length = 15 cm

Width = 8 cm

Height = h cm

Then volume of the cuboid = Length × width × height

V = 15 × 8 × h

480 = 120h

h = [tex]\frac{480}{120}[/tex]

h = 4 cm

Therefore, new depth of the milk will be 4 cm.

Answer:

see below

Step-by-step explanation:

This is in slope intercept form

y = mx+ b  where m is the slope and b is the y intercept

32 is the slope

Parallel lines have the same slope so 32 would be the slope of  the parallel line

Perpendicular lines have slopes that multiply to -1

m*32 = -1

m = -1/32

The slope of the perpendicular line is -1/32

Answer:

[tex]\huge\boxed{p = 3}[/tex]

Step-by-step explanation:

7p + 7 = 37 - 3p (They both are equal)

7p + 3p = 37-7

10p = 30

Dividing both sides by 10

p = 3

Answer:

p=3

Step-by-step explanation:

7p+7=37-3p

7p[+3p]+7=37-3p[+3p]

10p+7=37

10p+7[-7]=37[-7]

10p=30

10p/10=30/10

p=3

I hope this helps!

Answer:

12

Step-by-step explanation:

1 inch = 20 miles

240 miles ÷ 20 miles =

12 inches

Answer:

12 inches

Step-by-step explanation:

Hey there!

Well to solve the given question we need to use fractions,

if 1 inch is 20 milles, we can set up the following.

[tex]\frac{1}{20} = \frac{x}{240}[/tex]

Cross multiply

240 = 20x

Divide both sides by 20

x = 12

So it is 12 inches in the map.

Hope this helps :)

Answer:

9 tables

12 stools

Step-by-step explanation:

x= number of tables

x+3= number of stools

4x+3(x+3)=72

4x+3x+9=72

4x+3x=72-9

7x=63

x=9

So he built 9 tables and 12 stools

(9x4=36, 3X12=36, 36+36=72) CHECK

1. (a) 0 = x² + 4x - 12 (Switch Sides)

x² + 4x - 12 = 0 (Factor Expression)

(x - 2)(x + 6) = 0 (Apply the Zero Factor Principle)

x = 2, and x = - 6

x - intercept : (2, 0) and ( - 6, 0)

(b) y = (0)² + 4(0) - 12 (Simplify)

y = 0 + 4 * 0 - 12 = 0 + 0 - 12 = - 12

y - intercept : (0, - 12)

(c) Our vertex belongs to an upward facing parabola, and hence it will be a minimum, of ( - 2, - 16).

2. Seth's solution is not accurate. He did the calculations accurately, and ended up with x = 3 and x = - 2. However he forgot to substitute those values back into the equations y = x² + 3x - 5 and y = 4x + 1, solving for the y values. Instead of being ( - 2, 0) and (3, 0) it should have been (3, 13), ( - 2, - 7)...

y = (3)² + 3(3) - 5 = 9 + 9 - 5 = 18 - 5 = 13,

y = 4( - 2) + 1 = - 8 + 1 = - 7

Hence we get the solutions (3, 13) and ( - 2, - 7).

nCr(20, 2) = 190 ways of selecting 2 from 20

nCr(10, 1)    =   10 ways of selecting 1 from 10

To find the over all probability of winning,

Calculate the Harmonic Mean (19) and divide by 2

Equivalent to

1/ (1//190 + 1/10) =9.5

So the probability is 1/9.5 = 2/19.

Answer:

500

Step-by-step explanation:

A = the unknown number that we need to find

A x 13/100 = 65

=> A x 13 = 6500

=> A = 6500 / 13

=> A = 500

13% of 500 is 65.

Let's check whether the answer is correct or not.

=> 500 x 13/100

=> 5 x 13

=> 65.

So, the number whose 13% is 65 is 500

Answer:

Step-by-step explanation:

Let the number be x,

Then,

13% of x =65

Or, 13/100 of x =65

Or,x=6500/13

:.x=500

Answer:

Hey there!

Pythagorean Theorem

a^2+b^2=c^2

10^2+36^2=c^2

100+1296=c^2

1396=37.4.

Um... did you make a typo?

Let me know if you did, because then I can edit my answer.

Answer:

1.75 seconds

Step-by-step explanation:

Lets apply the quadratic formula-

- 8 +_ (sqrt of 64 + 19.6)

__________________

-9.8

-8 +_  9.1433

__________________

-9.8

x = 1.74931972 ( since x can only be positive in real life situations like when throwing a ball)

x = 1.75 rounded in seconds

Answer:

Step-by-step explanation:

h(t)= -8±√8^2-4(-4.9)(1)/2(-4.9)

h(t)=-8±√64-19.6/ -9.8

h(t)=-8±√44.4 / -9.8

h(t)=-8±6.6633325/ -9.8

h(t)= 0.14

The height will be 0.14

The time will be 2.02 seconds per meter

Hope that helps.

Answer:

When V is composed with r, the composite function is StartFraction 1 Over 48 EndFraction pi t Superscript 6

V(r(6)) shows that the volume is 972π inches cubed when the radius increases to 6 inches.

Step-by-step explanation:

Answer:

1 and 3 on edge

Step-by-step explanation:

Answer:

1/4

1/3

Step-by-step explanation:

If one number is odd, then the other number must also be odd in order for the sum to be even.  There are 3 odd numbers per dice, so the probability is (3/6)² = 1/4.

If one number is 6, the other number must be 1 or 2 for the product to be at most 15.  The probability is 2/6 = 1/3.

Answer:

1:4

Step-by-step explanation:

so we are comparing the arc lengths to get the ratio of DE:BC

[tex] \beta \div 360 \times 2 \times \pi \times r[/tex]

to get arc length BC as

[tex] \beta \times \pi \times r \div 90[/tex]

and for DE as

[tex] \beta \times \pi \times r \div 360[/tex]

so divide DE by BC where beta pi r will cancel out. and you remain with 1/4 Wich will translate to 1:4

Answer:

b

Step-by-step explanation:

Answer:

d) it has to be greater than 150 and 250

Step-by-step explanation:

It  says in the question it is greater than 150. So the number will be between 150 and 250.

Mark it as Brainliest pls

Hope it helps!!!

Answer:

=√100

= 10

=√49

= 7

=√144

= 12

=√9

=3

Answer:

Step-by-step explanation:

So we know that there are 213 oranges and Theresa fills each bag with 3 oranges, so we can represent each bag as 3x. She keeps filling until she reaches 51 oranges.

First. let's write this as an equation, She is starting with 213 oranges and filling x bags with 3 oranges to the point she has less than 51 oranges.

213 - 3x < 51

Now add 3x to both sides,

213 - 3x + 3x < 51 + 3x

213 < 51 + 3x

Now we subtract 51 from both sides,

213 - 51 < 51 - 51 + 3x

162 < 3x

Now we divide both sides by 3,

162/3 < 3x/3

We find the answer,

54 < x

x > 54 bags

Answer:

-2> -3

Step-by-step explanation:

when in the minuses, the lower the number, the bigger it really is!

Answer:

-2> -3

Step-by-step explanation:

Answer:

5/2 OR 2.5

Step-by-step explanation:

( x + 2y ) = 7 , ( x - 2y ) = 5

x = 7 - 2y , x = 5 + 2y

substitute the two eqns together:

7 - 2y = 5 + 2y

7 - 5 = 2y + 2y

2 = 4y

y = 1/2

when y = 1/2 ,

5y = 5(1/2)

= 5/2 OR 2.5

Answer:

[tex](B.) y= 1/2x -3/2[/tex]

Step-by-step explanation:

[tex](-3, -3) = (x_1,y_1)\\m = 1/2\\\\y-y_1=m(x-x_1)\\\\y -(-3)=\frac{1}{2} (x -(-3)\\\\y+3 = \frac{1}{2}(x+3)\\\\ y+3 = \frac{1}{2} x+\frac{3}{2}\\\\ y = \frac{1}{2} x +\frac{3}{2} -3\\\\y = \frac{1}{2} x - \frac{3}{2}[/tex]

Answer:

[tex]\Large \boxed{\mathrm{Option \ B}}[/tex]

Step-by-step explanation:

y = mx + b

(slope intercept form of a line)

m = slope

b = y-intercept

y = 1/2x + b

Only three options have a slope of 1/2.

y= 1/2x + 3/2

y= 1/2x - 3/2

y= 1/2x - 1/2

The line crosses the point (-3, -3), x = -3 and y = -3.

-3= 1/2(-3) + 3/2

-3= -3/2 + 3/2

-3 = 0

This is false.

-3= 1/2(-3) - 3/2

-3 = -3/2 - 3/2

-3 = -6/2

-3 = -3

This is true.

-3= 1/2(-3) - 1/2

-3 = -3/2 - 1/2

-3 = -2

This is false.

Answer: what table? u need to add an attachment

Step-by-step explanation:

The table containing whole number express 2.8 as the sum or difference.

To express 2.8 as the sum or difference of whole numbers.

There are three different ways to do it:

1. As a sum of whole numbers:

  2 + 0.8 = 2.8

2. As a difference of whole numbers:

  4 - 1.2 = 2.8

3. Another way as a sum of whole numbers:

  1 + 1.8 = 2.8

The table will be:

Representation             Whole Number 1        Whole Number 2      Result

          1                                      2                               0.8                       2.8

          2                                      4                               1.2                       2.8

          3                                      1                               1.8                        2.8

As each row represents a different way to represent the number 2.8 using whole numbers.

Learn more about Whole number here:

https://brainly.com/question/29766862

#SPJ3

Answer:

The value of k is 16, the angle of OLN and MNL is 72° .

Step-by-step explanation:

Given that alternate interior angles are the same. So we can assume that ∠OLN and ∠MNL have the same angle. In order to find k, we have to let ∠OLN = ∠MNL :

[tex]4k + 8 = 5k - 8[/tex]

[tex]5k - 4k = 8 + 8[/tex]

[tex]k = 16[/tex]

Next, we have to find the angle of OLN and MNL :

[tex]OLN = 4k + 8 = 4(16) + 8 = 72[/tex]

[tex]MNL = 5k - 8 = 5(16) - 8 = 72[/tex]

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▹ Answer

Y = 1

▹ Step-by-Step Explanation

[tex]\frac{10}{2} = \frac{5}{y} \\\\10/5 = 2\\2/2 = 1\\\\Y =1[/tex]

Hope this helps!

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