Archimedes drained the water in his tub. 62.562.562, point, 5 liters of water were drained each minute, and the tub was completely drained after 888 minutes.

[tex] \dfrac{126}{21} = \dfrac{2 \times 3 \times 3 \times 7}{3 \times 7} = 6[/tex]

Answer: 6

Answer:

2.72

Step-by-step explanation:

the other one copied my answer from another website.

Explanation:

Move all the terms containing a to the left side of the equation

-0.5a+4.96=3.6

Subtract 4.96 from right side

-0.5a=3.6-4.96

Would be

-0.5a=-1.36

Divide each term by -0.5 and simplify

a= 2.72

Answer: Wheres the table

Step-by-step explanation:

Answer:

Step-by-step explanation:

40

Answer:

A is a solution because it is in the shaded area.

Step-by-step explanation:

Answer:

The value of 9f(3) is 1683.

Step-by-step explanation:

This is a compound function, so let's call it [tex]g[/tex], where it is equal to:

[tex]g = 9*f(3)[/tex]

To solve it, we need to find [tex]f(3)[/tex] and apply it on the expression above, this is done below:

[tex]f(3) = 4*(3)^3 + 8*(3)^2 - 2*3 + 13\\f(3) = 4*27 + 8*9 - 6 + 13\\f(3) = 108 + 72 + 7\\f(3) = 187\\[/tex]

Applying it on [tex]g[/tex] we have:

[tex]g = 9*187 =1683[/tex]

Answer:

1,863

Step-by-step explanation:

First thing to do here is to substitute 3 for the value of x

f(3) =4)3)^3 + 8(3)^2 -2(3) + 13

= 4(27) + 8(9) -6 + 13

= 108 + 72 + 7 = 207

we now multiply this result by 9

= 9 * 207 = 1,863

Answer:

6

Step-by-step explanation:

Since they have the same x - value, just find the distance between the y - values.

6

Answer:

The inverse of the function is [tex]g (x)=-5x-4[/tex].

Step-by-step explanation:

The function provided is:

[tex]f^{-1}(x)=-\frac{1}{5}\ x-\frac{4}{5}[/tex]

Let us assume that:

[tex]y=f^{-1}(x)[/tex]

Then the equation will be:

[tex]y=\frac{-x-4}{5}[/tex]

To compute the inverse of the function substitute x as y and y as x.

[tex]x=\frac{-y-4}{5}[/tex]

Now solve for y as follows:

[tex]x=\frac{-y-4}{5}[/tex]

[tex]5x=-y-4[/tex]

[tex]y=-5x-4[/tex]

Thus, the inverse of the function is [tex]g (x)=-5x-4[/tex].

Answer:

The answer is "-5x-4"

Step-by-step explanation:

Given:

[tex]\bold{f^{-1} (x)=(-\frac{1x}{5}-\frac{4}{5})}[/tex]

solve the above equation:

[tex]\to f^{-1}(x)= \frac{-x-4}{5}\\\\\to f^{-1}(x)= -\frac{x+4}{5}\\[/tex]

Let

[tex]y= f^{-1} x= -(\frac{x+4}{5})\\\\[/tex]

inverse the above function:

[tex]\to x= -(\frac{y+4}{5})\\\\\to 5x= -(y+4)\\\\\to 5x= -y-4\\\\\to\boxed {y=-5x-4}\\\\[/tex]

Answer:

its the fourth one on edg

Step-by-step explanation:

Answer:

The last option :)

Step-by-step explanation:

Answer: Slope of 2.

Step-by-step explanation:

Start at where the line meets on the y-axis, -7. Then work your way upwards until you see the line align with a value of x, like (1,-5). Then you see a trend of it going up 2 units and over 1. 2/1 or 2 is your slope.

Answer:

Eva swam 400 meters in 1/5 hour. Her average swimming speed was 2000 meters per hour.

Step-by-step explanation:

Eva swam 2/3*600 meters in 1/5 hour. 2/3*600=400. She swam 400 meters in  1/5 hour, which means she swims 5*400 meters in a whole hour. Eva swims 2000 meters per hour.

Answer: [tex]726 cm^{2}[/tex]

Step-by-step explanation:

surface area(SA)= [tex]6s^{2}[/tex]

= [tex]6*(11)^{2}[/tex]

= [tex]6*121[/tex]

= [tex]726 cm^{2}[/tex]

s= the length of the side of the cube

Answer:

a). A = -2x² + 200x

b). Widths = 40 feet and 60 feet

Step-by-step explanation:

It is given that length of the fencing material = 200 feet

a). Peg wants to cover the vegetable garden from three sides with the given fencing material.

If length of the garden = l

and width of the garden = x

l + x + x = 200

l + 2x = 200

l = (200 - 2x) feet

Therefore, area of the garden = Length × width

A = [tex](200-2x)\times x[/tex]

A = -2x² + 200x

b). Foe A = 4800 square feet,

4800 = -2x² + 200x

2x² - 200x + 4800 = 0

x² - 100x + 2400 = 0

x² - 60x - 40x + 2400 = 0

x(x - 60) - 40(x - 60) = 0

(x - 60)(x - 40) = 0

x = 40, 60 feet

Therefore, widths of Peg's garden will be 40 feet and 60 feet.

Answer:

(6, 1)

Step-by-step explanation:

Answer:

centre = (6, 1 )

Step-by-step explanation:

The equation of a circle in standard form is

(x - h)² + (y - k)² = r²

where (h, k) are the coordinates of the centre and r is the radius

Given

x² + y² - 12x - 2y + 12 = 0

Collect the x and y terms together and subtract 12 from both sides

x² - 12x + y² - 2y = - 12

To obtain the equation in standard form use completing the square

add ( half the coefficient of the x/ y term )² to both sides

x² + 2(- 6)x + 36 + y² + 2(- 1)y + 1 = - 12 + 36 + 1

(x - 6)² + (y - 1)² = 25 ← in standard form

with centre = (6, 1 ) and radius = [tex]\sqrt{25}[/tex] = 5

Answer:

b & e

Step-by-step explanation:

The statements that are true of the given function are f(0)=3/2 and f(4)=7/2. This can be obtained by finding the function and checking the values of given in the question.

Given, f(-1/2)= -2

f(0)= 3/2

f(1)= -1

f(2)= 1

f(4)= 7/2

The function is of the form, f(x)= mx +b

where m is the slope of the line and b is the cutting point with the y axis.

For x=0, the value of the function is f(0)=3/2

⇒b=3/2   and m=1/2

∴ The function is f(x) = (1/2)x + 3/2

f(-1/2) = (1/2)(-1/2) + 3/2 =5/4

f(0) = (1/2)(0) + 3/2 = 3/2

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

f(2) = (1/2)(2) + 3/2 = 5/2

f(4) = (1/2)(4) + 3/2 = 7/2

Hence the statements that are true of the given function are f(0)=3/2 and f(4)=7/2.

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Answer:

Rina is 1/4 feet taller than Ryan

Step-by-step explanation:

(height of Rina)-(height of Ryan)

6x+3/8-(5x+1/8)

6x+3/8-5x-1/8

x+3-1/8

x+2/8

x+1/4

Answer:

[tex]33\%[/tex]

Step-by-step explanation:

To work out the percentage of the circle shaded blue, we first must work out the area of the whole circle.

Area of the whole circle = [tex]\pi r^2[/tex]

[tex]r=4+3+3\\\pi * (4+3+3)^2=\pi*10^2=100\pi[/tex]

Now we need to work out the area of the blue 2d torus, by finding out the area of the blue circle, then subtracting the area of the innermost white circle.

Blue shaded area = [tex]\pi(r_{0}{^2}-r_{1}{^2})[/tex]

[tex]r_0=4+3\\r_1 = 4\\\pi ((4+3)^2-(4)^2)= \pi (7^2-4^2)=33 \pi[/tex]

Now we have the total areas of each, we can work out the fraction of blue to non blue by dividing the blue area by the total area, and then working out the percentage by multiplying by 100.

[tex]\frac{33\pi}{100\pi}*100=\frac{33\pi}{\pi}=33\%[/tex]

Answer:

(8-5)/(7-2)= 3/5

Step-by-step explanation:

proper fraction

Answer:

The slope is 3/8

The y intercept is 75/8

Step-by-step explanation:

The slope is found by

m= (y2-y1)/(x2-x1)

   = (9-6)/(-1- -9)

   = (9-6)/(-1+9)

    =3/8

The y intercept is found by

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

y = 3/8 x+b

9 = 3/8(-1) +b

Getting a common denominator

72/8 = -3/8 +b

Add 3/8 to each side

75/8 = b

The y intercept is 75/8

Answer:

3/8, 9 3/8

Step-by-step explanation:

y= mx+b

m=(y2-y1)/(x2-x1)

L (-9, 6) and M(-1, 9)

slope is:

y- intercept is:

Answer:

X= 24

Step-by-step explanation:

Y was multiplied by 3 to equal 30, so same rules are applied and you multiply 8 by 3

Answer:

28 or 24 im not sure which

Answer:

-14 >x

Step-by-step explanation:

x-2>2x+12

Subtract x from each side

x-2-x > 2x+12-x

-2 > x+12

Subtract 12 from each side

-2-12 > x

-14 >x

Answer:

A

Step-by-step explanation:

Answer:

y = 8.5x

Step-by-step explanation:

A proportional relation in one in which change of value of y with respect to change of value of x remains proportional. It can be represented by equation

y = kx, where k is constant of proportionality

________________________________________________

Let  the  relation be

y = kx

but we have a as 3 and b as 25.5

thus

substituting value of and a and b in y = kx , we have

25.5 = k*3

=> k = 25.5/3 = 8.5

Thus, equation which can represent this relation is y = 8.5x

Answer:

7-x

Step-by-step explanation:

49 - x^2 is a perfect square so

it factors to :(7+x)(7-x)

since there is a negative in 49 - x^2, it would make sense that the answer would be a negative to get that negative answer in the first place (negative times a positive equals a negative)

Forgive me for my lame explanation :')

The range of the graph is  -∞ ∠ y ∠ 5, which is option a.

The range of a function is the set of numbers that the function can produce. In other words, it is the set of y-values that you get when you plug all of the possible x-values into the function.

In the given graph

Red line shows the value of y when we put the value of x.

and the line goes down towards negative y upto infinity and on another side at constant value 5 when put x any value.

that means y lies between negative infinity ( -∞ ) and 5

Hence, The range of the graph is  -∞ ∠ y ∠ 5.

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Answer:

f⁻¹(f(6.022)) = 6.022

f⁻¹(-10) + f(-6) = -6 + -10 = -16

Step-by-step explanation:

f⁻¹(f(x)) = x

so  f⁻¹(f(6.022)) = 6.022

inverse function flips y and x coordinates so look at table where f(x)=-10 and read x so f⁻¹(-10) = -6

f⁻¹(-10) + f(-6) = -6 + -10 = -16

Answer:

hope this helps you

Answer:

(C) ¹/₂

Step-by-step explanation:

Given;

A standard number cube with the numbers 1 through 6 = 1, 2, 3, 4, 5, 6

The probability of rolling a number less than 4 = 3, 2, 1

The probability of rolling 3, P(3) = ¹/₆

The probability of rolling 2, P(2) = ¹/₆

The probability of rolling 1, P(1) = ¹/₆

Probability of rolling a number less than = P(3) or P(2) or P(1)

                                                                   = ¹/₆ + ¹/₆ + ¹/₆

                                                                   = ³/₆

                                                                   = ¹/₂

Therefore, the probability of rolling a number less than 4 is ¹/₂

Option (C) ¹/₂

Answer:

[tex]\dfrac{2s^3+136}{s}[/tex]

Step-by-step explanation:

Let the side length of the square base =s feet

Let the height of the box = h

Given that the volume of the box = [tex]34$ ft^3[/tex]

Volume of the box =[tex]s^2h[/tex]

Then:

[tex]s^2h=34$ ft^3\\$Divide both sides by s^2\\h=\dfrac{34}{s^2}[/tex]

Surface Area of a Rectangular Prism =2(lb+bh+lh)

Since we have a square base, l=b=s feet

Therefore:

Surface Area of our closed box[tex]= 2(s^2+sh+sh)[/tex]

[tex]S$urface Area= 2s^2+4sh\\Recall: h=\dfrac{34}{s^2}\\$Surface Area= 2s^2+4s\left(\dfrac{34}{s^2}\right)\\=2s^2+\dfrac{136}{s}\\$Surface Area in terms of length only=\dfrac{2s^3+136}{s}[/tex]

Answer:

The volume  is  191.3 [tex]cm^3[/tex]

Step-by-step explanation:

Recall that the formula for the volume of a pyramid is given by the formula:

[tex]Volume=\frac{B\,*H}{3}[/tex]

where B is the area of the pyramid's base, and H its height. So, in our case, the base is a square of length 7.5 cm, which gives 56.25 cm^2

Now, we use this value and the height 10.2 cm to find the volume:

[tex]Volume=\frac{B\,*H}{3}\\Volume=\frac{56.25\,*10.2}{3}\\Volume=191.25\,\,cm^3[/tex]

which rounded to the nearest tenth is: 191.3 [tex]cm^3[/tex]

Answer:

191.3

Step-by-step explanation:

Answer:

4^3

11>6

y>2

13-x

Step-by-step explanation:

4 is to the third power

11 is greater than 6 which means u use this sign >

y is greater than 2

13 subtract x