How many planes exist that pass through points A, B,
and C?
O
1
2
3

Answer:

A = 36 cm^2

Step-by-step explanation:

The perimeter of a square is given by

P =4s

24 = 4s

Divide by 4

24/4 = 4s/4

6 =s

The area of a square is

A =s^2

A = 6^2

A = 36 cm^2

Answer:

(x + 2) , (x + 3) are factors

Step-by-step explanation:

Given

x² + 5x + 6

Consider the factors of the constant term (+ 6) which sum to give the coefficient of the x- term (+ 5)

The factors are + 2  and + 3, since

2 × 3 = 6 and 2 + 3 = 5 , thus

x² + 5x + 6 = (x + 2)(x + 3)

Answer:

refer to the pic attached

Answer:

velocity of recoil velocity of cannon  is -9.6 m/sec

Step-by-step explanation:

according to law of conservation of momentum

total momentum of isolated system of body remains constant.

momentum  = mass of body* velocity of body.

__________________________________

in the problem the system is

shell + cannon

momentum of shell = 8*600 = 4800 Kg-m/sec

let the velocity of cannon be x m/sec

momentum of cannon = 500*x = 500x Kg-m/sec

initially the system of body is in rest (before the shell is fired) hence, total momentum of the system i is 0

applying  conservation of momentum

total momentum before shell fired = total momentum after the shell is fired

0 = momentum of shell + momentum of cannon

4800 + 500x = 0

x = -4800/500 = -9.6

Thus, velocity of recoil velocity of cannon  is -9.6 m/sec

here negative sign implies that direction of velocity of cannon is opposite to that of velocity of shell.

Answer: y=12x+8

Step-by-step explanation:

The relationship between y, the total cost of the popcorn and movie tickets, and x, the number of movie tickets that are purchased will be y = 12x + 8.

Determine the known quantities and designate the unknown quantity as a variable while trying to set up or construct a linear equation to fit a real-world application.

In other words, an equation is a set of variables that are constrained through a situation or case.

Let's suppose the cost of popcorn is P and the cost of movie tickets is M then

P + 4M = 56

P + 6M = 80

Given that P =$8 hence by putting it to the equation 1

8 + 4M = 56

4M = 48

M = 12 now

Let x number of movie have watch then

y = 12x + 8 will be the formation of the equation.

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Answer:

30w-51

Step-by-step explanation:

6+8(4w-7)-(2w+1)

Distribute

6 + 32w-56 -2w-1

Combine like terms

32w-2w  +6-56 -1

30w-51

Answer:W=1.7

Step-by-step explanation: Simplifying

0 = 6 + 8(4w + -7) + -1(2w + 1)

Reorder the terms:

0 = 6 + 8(-7 + 4w) + -1(2w + 1)

0 = 6 + (-7 * 8 + 4w * 8) + -1(2w + 1)

0 = 6 + (-56 + 32w) + -1(2w + 1)

Reorder the terms:

0 = 6 + -56 + 32w + -1(1 + 2w)

0 = 6 + -56 + 32w + (1 * -1 + 2w * -1)

0 = 6 + -56 + 32w + (-1 + -2w)

Reorder the terms:

0 = 6 + -56 + -1 + 32w + -2w

Combine like terms: 6 + -56 = -50

0 = -50 + -1 + 32w + -2w

Combine like terms: -50 + -1 = -51

0 = -51 + 32w + -2w

Combine like terms: 32w + -2w = 30w

0 = -51 + 30w

Solving

0 = -51 + 30w

Solving for variable 'w'.

Move all terms containing w to the left, all other terms to the right.

Add '-30w' to each side of the equation.

0 + -30w = -51 + 30w + -30w

Remove the zero:

-30w = -51 + 30w + -30w

Combine like terms: 30w + -30w = 0

-30w = -51 + 0

-30w = -51

Divide each side by '-30'.

w = 1.7

Simplifying

w = 1.7

Answer:

Difference : 4th option

Step-by-step explanation:

The first thing we want to do here is to factor the expression x² + 3x + 2. This will help us if it is similar to the factored expression " ( x + 2 )( x + 1 ). " The denominators will be the same, and hence we can combine the fractions.

x² + 3x + 2 - Break the expression into groups,

( x² + x ) + ( 2x + 2 ) - Factor x from x² + x and 2 from 2x + 2,

x( x + 1 ) + 2( x + 2 ) - Group,

( x + 2 )( x + 1 )

This is the same as the denominator of the other fraction, and therefore we can combine the fractions.

x - 1 / ( x + 2 )( x + 1 )

As you can see this is not any of the options present, as we have not expanded ( x + 2 )( x + 1 ). Remember previously that ( x + 2 )( x + 1 ) = x² + 3x + 2. Hence our solution is x - 1 / x² + 3x + 2, or option d.

Answer:

Sum equation: [tex]d + 0.05d[/tex]

Product equation: [tex]1.05d[/tex]

Step-by-step explanation:

If we have an increase in 5% of d, that means that 5% of d ([tex]0.05\cdot d[/tex]) will be the total amount of money added to it.

However, we need to still count the original price of d, if we increase it by 5%!

So we add d to 0.05d.

[tex]d + 0.05d[/tex] is the sum equation.

Now, we can create the product equation for d by expanding the coefficients for the previous equation,  [tex]d + 0.05d[/tex].

[tex]1d + 0.05d[/tex]

We can add like terms here: [tex]1 + 0.05 = 1.05[/tex]! So we can just multiply this by d for our product equation.

[tex]1.05d[/tex]

Hope this helped!

Answer:

248.96.

Step-by-step explanation:

We write  it as:

(2 + 0.2)^7 = 2^7 + 7*2^6*0.2 + 7C2*2^5*(0.2)^2 + 7C3*2^4(*(0.2)^3

= 128 + 89.6 + 26.88 + 4.48

= 248.96.

Answer:

[tex]\dfrac{7}{10}[/tex]

Step-by-step explanation:

Given that

Number of batteries that do not have a charge = 14

Total number of batteries = 20

To find:

Experimental probability that the next battery checked does not have a charge = ?

Solution:

First of all, let us learn about the definition of experimental probability.

Probability is the chances of happening of an event.

Formula for probability of happening of an event E is given as:

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

Here we have to find the probability of checking a battery that has no charge.

So, number of favorable cases = Number of batteries that do not have a charge = 14

AND

Total Number of cases = Total number of batteries to be checked = 20

So, the required probability is:

[tex]\dfrac{14}{20} = \bold{\dfrac{7}{10}}[/tex]

Answer:

C D E

Step-by-step explanation:

Edg

Out of the given options, options C, D and E are a difference of squares.

Difference of Squares, two terms that are squared and separated by a subtraction sign.

Given are, options,

D) (y squared minus x y)(y squared + x y) = (y²-xy)(y²+xy) = y⁴-(xy)²

E) (64 y squared + x squared)(negative x squared + 64 y squared) = (64y²+x²)(64y²-x²) = (64y)⁴-x⁴

C) (3 + x z)(negative 3 + x z) = (3+xz)(3-xz) = 3²-(xz)²

Hence, out of the given options, options C, D and E are a difference of squares.

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Answer:

SI=PRT/100

=10000*5*42/12*100

=1750

SI=1750

TOTAL AMOUNT=PRINCIPLE+SI

=10000+1750

=101750

Answer:

Tolerance

Step-by-step explanation:

Value in this situation doesn't make sense and you can search up the definition of tolerance on the web to verify.

Also, this doesn't seem like a math related question so you should have answered this in English or something.  

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:

4 1/4 <_ 2K

Step-by-step explanation:

The inequality that represents the situation is k ≥ 2.125 hours.

Inequality is the statement where two algebraic expressions are equated using an inequality operator, <, >, <> etc.

Karissa takes k time to complete the project.

Oliver takes ≤ 2k

The time spent by Oliver is 4 1/4 = 17/4 = 4.25 hours

2k ≥ 4.25

k ≥ 2.125 hours

Therefore, the inequality that represents the situation is k ≥ 2.125 hours.

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Answer: He can use 3 x 5 = 15 and 15 + 3.

Step-by-step explanation:

Since a small car is $3, and the large car is 5x the price of the small car, he can use the equation 3 x 5 = 15, because the small car is $3, and the large car is 5x the price. You can use 15 + 3 = 18, because the small car is $3, so you also have to add that.

Here to help!

The equation is x + 5x = 18 , where x is the cost of small toy car and the total cost of the two cars = $ 18

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the total cost of the two cars be A

Now , the equation will be

Let the cost of the small toy car be = x

The cost of small toy car = $ 3

The cost of the large car = 5 x cost of small toy car

Substituting the values in the equation , we get

The cost of the large car = 5 x 3

The cost of the large car = $ 15

So , the cost of two cars = x + 5x

Substituting the values in the equation , we get

The total cost of the two cars A = 15 + 3

The total cost of the two cars A = $ 18

Therefore , the value of A is $ 18

Hence , the equation is A = x + 5x

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Answer:  is 762 meters

Step-by-step explanation:

One foot is equal to 0.3048 meters so multiply 2500 by 0.3048 to find how many meters there are.

2500 * 0.3048 = 762

Answer:762.5 meters

Step-by-step explanation:

1 foot =0.305 m

Hence,0.305×2500=762.5 metres as the answer.

Answer:

First. 115°

Second. 65°

Third. 65°

Fourth. 7

Fifth. 425.25

First

angle DAB = angle ADC (since this is an isosceles trapezoid)

Second

In a trapezoid adjacent angle are supplmentary (that is their sum is 180°)

180-115 is 65°

Third

(Same reason as second)

Fourth

The side 3x+4 is same as the opposite side

So 3x + 4 = 25

on solving you get x = 7 in

Fifth

[tex]area \: = \frac{1}{2} \times length \: of \: the \: perpendicular \: (b1 + b2)[/tex]

area = 1/2 × 13.5 (20+43)

area = 1/2 × 13.5 × 63

Thus area is 425.25

Answer:

Step-by-step explanation:

1)As ABCD is isosceles trapezium,

∠ADC= ∠DAB

∠ADC = 115°

2) AD //BC

∠ADC + ∠DCB = 180°   {co interior angles}

115 + ∠DCB = 180

 ∠DCB = 180 - 115

 ∠DCB = 65°

3) As ABCD is isosceles trapezium,

∠CBA = ∠DCB

∠CBA = 65°

4) As ABCD is isosceles trapezium, non parallel sides are congruent.

AB = DC

3x + 4 = 25 in

3x = 25 - 4

3x = 21

x = 21/3

x = 7 in

5) height = 13.5 in

a= 43 in

b= 20 in

Area of trapezium = [tex]\frac{(a+b)*h}{2}\\[/tex]

                   [tex]= \frac{(43 +20)*13.5}{2}\\\\=\frac{63*13.5}{2}\\\\\\= 425.25 in^{2}[/tex]

Answer:

C = 207.55 + 223.07x

Step-by-step explanation:

Given the following :

Cost of community college:

Enrollment fee = 207.55

Fee per credit hour = 223.07

Attending the community College for 'x' credit hours can be represented by:

Total cost = C

[Enrollment fee + (fee per credit hour * number of credit hours)]

Number of credit hours = x

C = [207.55 + (223.07 * x)]

C = 207.55 + 223.07x

Therefore, the total cost 'C' of attending the community college for 'x' credit hour:

C = 207.55 + 223.07x

Answer:

41 inches

Step-by-step explanation:

Let the point at the top of the door on the left be x

Wx + xH = 45

Let the point at the top of the door  on the right be c

Yc + cZ = 37

We know the door is

xH +  plus the width of the tile

The width of the tile is Yc

xH + Yc

On the right door

cZ +  the height of the tile

cZ + Wx

Add the two doors together

xH + Yc + cZ + Wx = 2 times the height of the door

Rewriting

xH +  Wx +  Yc + cZ = 2 times the height of the door

45+ 37 = 2 times the door height

82 = 2 times the door height

Divide by 2

41 = door height

Answer:

[tex]D)\ x + y = 109\\(1.5)x + (3.5)y = 227.50[/tex]

Step-by-step explanation:

Let the items sold with price $1.5 = [tex]x[/tex]

Let the items sold with price $3.5 = [tex]y[/tex]

Initially, total number of items = 150

Items left at the end of the day = 41

So, number of items sold throughout the day = Total number of items - Number of items left

Number of Items sold = 150 - 41 = 109

So, the first equation can be written as:

[tex]\bold{x+y = 109} ....... (1)[/tex]

Now, let us calculate the sales done by each item.

Sales from item with price $1.5 = Number of items sold [tex]\times[/tex] price of each item

= (1.5)[tex]x[/tex]

Sales from item with price $3.5 = Number of items sold [tex]\times[/tex] price of each item

= (3.5)[tex]y[/tex]

Total sales = [tex]\bold{(1.5)x+(3.5)y = 227.50} ....... (2)[/tex]

So, the correct answer is:

[tex]D)\ x + y = 109\\(1.5)x + (3.5)y = 227.50[/tex]

Answer: it would be 40/2 or 20, but im not sure.

Step-by-step explanation: so what I did was: 100 1/4 - 60 1/2: 100 - 60 = 40 and then I subtracted 1-1 which is 0 then 4-2 which is 2, and got 40/2 or just simplify which will be equal to 20

area of circle =22/7×4=12.56

Answer:

Picture below

Step-by-step explanation:

● 5/2 is 2.5 so just divide the space between 3 by 2

● for 1/3 divide the space between 0 and by 3

[tex]3x-1=81x\\78x=-1\\x=-\dfrac{1}{78}[/tex]

Answer:

[tex]\large \boxed{\displaystyle x=- \frac{1}{78}}[/tex]

Step-by-step explanation:

[tex]3x-1=81x[/tex]

Subtract 3x from both sides of the equation.

[tex]-1=78x[/tex]

Divide both sides of the equation by 78.

[tex]\displaystyle \frac{-1}{78} =x[/tex]

Answer:

2¹ + 3¹, 2³ - 2¹, 3²

Step-by-step explanation:

2³ - 2¹ = 8 - 2 = 6

2¹ + 3¹ = 2 + 3 = 5

3² = 9

Answer:

A. the product of complex conjugates is a difference of two squares and is always a real number

Step-by-step explanation:

Given a complex number z1 = x+iy where x is the real part and y is the imaginary part.

The conjugate of a complex number is the negative form of the complex number z1 above i.e z2= x-iy (The conjugate is gotten by mere changing of the plus sign in between the terms to a minus sign.

Taking the product of the complex number and its conjugate will give;

z1z2 = (x+iy)(x-iy)

z1z2 = x(x) - ixy + ixy - i²y²

z1z2 = x² - i²y²

.since i² = -1

z1z2 = x²-(-1)y²

z1z2 = x²+y²

The product gave a real function x²+y² since there is no presence of complex number 'i'

It can also be seen that the product of the complex numbers z1z2 is like taking the difference of two square. An example of difference of two square is that of two values a and b which is (a+b)(a-b).

From the above solution, it can be concluded that the product of complex conjugates is a difference of two squares and is always a real number.

Answer:

1) 27.89

2) 20

Step-by-step explanation:

#1)

9.5x + 75 --> 340

340 - 75 --> 265

265 / 9.5 = 27.89

#2)

120 / 6 =

20 minutes