Simplify each of the following:
a) root25 + root50 - root24 + root49

b) root2(2root8 – 3root32 + 4roor50)
Show your work

Answer:

Step-by-step explanation:

Can't see all the graphs, but the graph of [tex]y=-x^2[/tex] is an upside down parabola with the vertex at the origin.

4x - 5y = -12

-x + 5y = 18

Add the equations together:

4x + -x = 3x

-5y + 5y = 0

-12 + 18 = 6

So now you have:

3x = 6

Divide both sides by 3:

X = 2

Now you have the value of x, replace x with 2 in one of the equations and solve for y:

4(2) -5y = -12

8 -5y = -12

Subtract 8 from both sides:

-5y = -20

Divide both sides by -5:

Y = 4

The solution is x = 2 and y = 4 which is written as (2,4)

Answer:

7/16 mile

Step-by-step explanation:

Distance of the loop = 7/8 mile

Distance of Water fountain = 1/2 of the Distance of the loop

= 1/2 of 7/8

Ibrahim stopped to get a drink of water at the water fountain. How far did Ibrahim run?

= 1/2 of 7/8

= 1/2 * 7/8

= (1 * 7) / (2 * 8)

= 7/16

Ibrahim ran 7/16 mile to drink water at the water fountain around the loop

Answer:

the second option : w should be 25 units

Step-by-step explanation:

the area of the rectangle is length×width = L×W

the perimeter of a rectangle = 2L + 2W

now, we know that the perimeter is 100 units.

and we have to find the best length of W, that will then define L (to keep the 100 units of perimeter) and maximizes the area of the rectangle.

in other words, what is the maximum area of a rectangle with perimeter of 100 (and what are the corresponding side lengths)?

now, w = 625 is impossible. that side alone would be bigger than the whole perimeter.

W = 0 would render the whole rectangle to a flat line with L = 50 because of

100 = 2L + 2W = 2L + 0 = 2L

L = 50

and A = L×W = 50×0 = 0

an area of 0 is for sure not the largest possible area.

w = 50 would cause L = 0

100 = 2L + 2W = 2L + 2×50 = 2L + 100

0 = 2L

L = 0

and with L = 0 the same thing happens as with W = 0 : a flat line with 0 area.

so, the only remaining useful answer is W = 25

100 = 2L + 2W = 2L + 2×25 = 2L + 50

50 = 2L

L = 25

A = L×W = 25×25 = 625 units²

and indeed, the maximum area for a given perimeter is achieved by arranging the sides to create a square.

Answer:

read explanation

Step-by-step explanation:

since y=2/5x-3 we substitute x=10 in making it y=2/5*10-3

following PAMDAS we do multiplication first so 2/5*10=4.

so y=4-3 and then we subtract and get y=1. Hope this helps:> if you need more explanation message me. If not give this a heart for helping. Good luck.

the answer would be 5 because 5*5 or 5 squared (5^2) is equal to 25, hope this helps!

Answer:

3/(n + 3)

Step-by-step explanation:

The given probability that Sara wins a raffle draw, P = n/(n + 3)

Given that the sum of all probabilities is 1, we get

The probability that Sara does not win, Q = 1 - P

Therefore;

Q = 1 - n/(n + 3) = (n + 3) - n/((n + 3) = 3/(n + 3)

The probability that Sara does not win, Q = 3/(n + 3)

Answer: See below

Step-by-step explanation:

This relates to the usage of water displacement.

------------------------------------------------------------------------

EXTRA (Only for advanced purposes, if you do not understand, it is totally fine)

Refer to the attachment below to finish the question.

Assuming the water levels are integer,

Then, we do the fourth step which is subtraction

Hope this helps!! :)

Please let me know if you have any quesitons

Answer:

Volume=Area × height

=35×7

volume = {245} m³

OAmalOHopeO

Answer:

Since the area of the triangle(base) is known we now multiply it to the height so we can get the volume.

7 x 35 = 245 m3 is your answer

You can picture it too:

(sorry my drawing is bad with the marker)

9514 1404 393

Answer:

  ₹1442

Step-by-step explanation:

The new price will be 1+3% = 1.03 times the old price.

  ₹1400 × 1.03 = ₹1442

Answer:

[tex]{ \boxed{ \bf{ \frac{dy}{dx} = v \frac{du}{dx} + u \frac{dv}{dx} }}}[/tex]

u = ( x + 1 )

v = ( 2x + 5 )²

[tex]{ \tt{ \frac{dy}{dx} = {(2x + 5) {}^{4} .(1) + (x + 1).(2)(2x + 5) {}^{3} } }} \\ = { \tt{ {(2x + 5)}^{3} ((2x + 5) +(2x + 2) }} \\ = { \tt{ \frac{dy}{dx} = {(2x + 5)}^{3}(4x + 7) }}[/tex]

Answer:sadwer

Step-by-step explanation:

Answer:

2y = 8

Step-by-step explanation:

4x+3y = 17

- ( 4x+y = 9)

----------------------

Distribute the minus sign

4x+3y = 17

-  4x -y =- 9

----------------------

  0x +2y = 8

Answer:

2y = 8

Step-by-step explanation:

4x+3y=17

-4x-y=9

_______

0+2y=8

2y=8

Answer:

Height = 12in

Surface area = 320in²

Step-by-step explanation:

Given

Length of the square base = 8in

Volume of the prism = 768 cubic inches

Using the formula;

Volume of the prism = Base area * Height of prism

768 = 8² * H

768 = 64H

H = 768/64

H = 12in

Hence the height of the prism is 12in

Get the surface area

Surface area = 2l² + 2lh

Surface area = 2(8)² + 2 (8)(12)

Surface area = 128  + 192

Surface area = 320in²

Hence the Surface area of the prism is 320in²

Answer:

The answers are options A and C.

They are (-2,0) and (0,0).

Step-by-step explanation:

x-intercept

(-2,0) and (0,0)

Answer:

Step-by-step explanation:

Answer:

No

Step-by-step explanation:

Kilogram is the unit of weight. Kilogram is the measure of how much matter or the mass an object has in it. Kilogram is the bigger unit of measurement while gram and milligram are the smaller units to measure the weight of any object.

We know,

1 kilogram = 1000 gram x 1

So, 1000 gram is equal to 1 kilogram

That means, 39,000 gram is equal to 39 kilogram.

In the question it is asked whether 1000 pillows times 300 is equal to 39 kilogram sofa or not.

The answer is not correct, because we do not know the weight of the 1000 pillows.

And also, 1000 x 300 will give you 300,000 and not 39 kilogram or 39,000 grams.

Answer:

The maximum  volume is 35316.4 in^3.

Step-by-step explanation:

Length + width + height is less than equal to 62 inches

Height = width = W

Let the length is L .

[tex]L + W + W = 62 \\\\L= 62 - 2 W\\\\Volume, V = L W H\\\\V = (62 - 2 W)\times W \times W\\\\V = 62 W^2 - 2 W^3\\\\\frac{dV}{dW}=124 W - 6 W^2\\\\So, \frac{dV}{dW} =0\\\\124 = 6 W\\\\W = 20.67 inches[/tex]

So, the maximum volume is

[tex]V =124\times 20.67\times 20.67 - 2 \times 20.67^3\\\\V =52978.86 - 17662.46 = 35316.4 inch^3[/tex]

Answer:

A

Step-by-step explanation:

The zero of the function is where the y-value is zero.

then it's -5

Total amount she wants to raise = $3200

Amount she'll get for each kilometer = $35

So, number of kilometers she need to run

= Total amount she wants to raise/Amount she'll get for each kilometer

= $3200/$35

= 91.42....

Since her sponser is will donate only for whole kilometers she'll have to run 92 km.

Answer:

65 and 25

Step-by-step explanation:

90=(5x+10)+(6x-41)

121=11x

11=x

Going back to the angles:

5(11)+10

=55+10

=65 this is the first angle

6(11)-41

=66-41

25 this is the second angle

Answer:

Step-by-step explanation:

            Statements                               Reasons

1. m∠A = 6x - 10                              1. Given

2. m∠B = 2x                                    2. Given

3. m∠C = 8x - 2                               3. Given

4. m∠A + m∠B + m∠C = 180°         4. Triangle sum theorem

5. (6x - 10) + (2x) + (8x - 2) = 180°   5. Substitution

6. 16x - 12 = 180                              6. Algebra

7. 6x = 192                                       7. Addition property of equality

8. x = 12                                           8. Division property of equality  

Answer:

A.

Step-by-step explanation:

3x + x - 13 + 4 - 6x = 12

we try to combine the elements with the same power of x (including the ones without any x) :

3x + x - 6x

-13 + 4

so, we get

-2x - 9 = 12

-2x = 21

x = -21/2

Answer:

A

Step-by-step explanation:

group the like terms

3x+x-6x-13+4=12

-2x=12+9

divide both sides by -2

-2x/-2=21/-2

x= -21/2

hope it helps