A farmer was dividing up his one-eighth of an acre of land between his 6 children. Since each child got the same amount of land, what fraction of the acre did each get?

Answer:

x=2/9

Step-by-step explanation:

x^3=8/729

Hence,

x= cube root of (8/729)

x=cube root of 8

  cube root of 729

x=2

   9

Answer: decimal form : x=0.10475656

Step-by-step explanation:

Take roots of both sides and solve

Answer:

Both functions must be linear. The y-intercepts of f(x) and g(x) must be opposites.

Step-by-step explanation:

First we need to solve.

h(x) = 10[tex]x^{2}[/tex] + 12[tex]x[/tex] - 16

It seems tricky at first but we know a couple things. When we add the factors of h(x) together we get j(x) = 7[tex]x[/tex] so we know that when we multiply 2 numbers together it should equal 10 but add up to 7.

Lets write the possible combinations of 10:

1 x 10 = 10

2 x 5 = 10

5 x 2 = 10

10 x 1 = 10

Now which combination will add or subtract to 7?

1 - 10 = 9    1 + 10 = 11  

2 - 5 = -7    2 + 5 = 7   We can stop here!

2 and 5 are in our factor, so let's write it down.

(2x      ) (5x        )     We know there will one + and one - because the -16. If we had two + it would be positive 16, and is we had two - it would also be positive 16 because a    - x - = +

Now the last number is 16. Let's find the possible combinations of 16.

1 x 16 = 16

2 x 8 = 16

4 x 4 = 16  We will stop here because we end up repeating posibilities.

Here is where we think critically. Whichever combination we choose has to be multiplied by 2 and 5 and end up equaling 12. I think 16 is too high so let's try 2 and 8.

2x * 2 = 4x     5x * 8 = 40x    Now one is positive and the other is negative. Let's try each combination.

4x - 40x = -36x   -4x + 40x = 36x     Neither of those are 12x. So let's Try 4 and 4.

2x * 4 = 8x       5x * 4 = 20x  One will be positive and the other will be negative. Let's try each combination.

8x - 20x = -12x    -8x + 20x = 12x There is our combination!  Remeber when you mutiply together you have to multiply the opposite factor. Here are the combinations:

(Ax + B )(Cx + D) = (Ax*Cx) + (Ax*D) + (B*Cx) + (B*D)

(Ax - B )(Cx + D) = (Ax*Cx) + (Ax*D) - (B*Cx) - (B*D)

(Ax + B )(Cx - D) = (Ax*Cx) - (Ax*D) + (B*Cx) - (B*D)

(Ax - B )(Cx - D) = (Ax*Cx) - (Ax*D) - (B*Cx) + (B*D)

So we have:

(2x + 4) (5x - 4)

Let's prove is and multiply it back out.

2x*5x - 2x*4 + 4*5x - 4*4

10[tex]x^{2}[/tex] - 8[tex]x[/tex] + 20

10[tex]x^{2}[/tex] + 12[tex]x[/tex] - 16  So we got it right!

Now let's see if they really add up to 7x.

(2x + 4) (5x - 4)  which we now need to add together

2x + 4 + 5x - 4   Rearrange

2x + 5x + 4 - 4   Combine like terms

7x + 0  or 7x  It works!

So our original functions are f(x) = 2x + 4   and g(x) = 5x - 4

Now to answer the question. Select 2 options.

Both functions must be linear. Yes, because an equation with only an [tex]x[/tex] will be a straight line, if we graph both functions they are both straight lines.

Both functions must be quadratic. No, because a quadratic equation is any equation that can be rearranged in standard form as [tex]ax^{2} + bx +c = 0[/tex] Neither f(x) or g(x) can be rearranged to fit that.

Both functions must have a y-intercept of 0. No, to find the y intercept we set x to 0 and solve for y.

2x + 4 = y                    5x - 4 = y

2(0) + 4 = y                  5(0) - 4 = y

0 + 4 = y                        0 - 4 = y

y = 4                                y = -4

Neither are 0.  

The rate of change of either f(x) or g(x) must be 0. Let's find the rate of change for each equation.

We need an interval so we have to find one. Let's use 1 and 2 for x, but we have to solve for y to get the coordinate.

f(x[tex]_{1}[/tex]) = 2x + 4       f(x[tex]_{2}[/tex]) = 2x + 4         g(x1) = 5x - 4        g(x2) = 5x - 4

x[tex]_{1}[/tex] = 1                     x[tex]_{2}[/tex] = 2                      x

y[tex]_{1}[/tex] = 2(1) + 4           y[tex]_{2}[/tex] = 2(2) + 4           y

y[tex]_{1}[/tex] = 2 + 4              y[tex]_{2}[/tex] = 4 + 4                y

y[tex]_{1}[/tex] = 6                    y[tex]_{2}[/tex] = 8                      y

( 1 , 6 )                  ( 2 , 8 )                     ( 1 , 1 )                   ( 2 , 6 )

Rate of change formula is:

[tex]\frac{y_{2} - y_{1} }{x_{2} - x_{1} }[/tex]

Now we just plug in for each function.

f(x) = 2x + 4                                      g(x) = 5x - 4

[tex]\frac{y_{2} - y_{1} }{x_{2} - x_{1} }[/tex] = [tex]\frac{8 - 6}{2 - 1}[/tex] = [tex]\frac{2}{1}[/tex] = 2                            

You can see the rate of change is not 0 for either function.

The y-intercepts of f(x) and g(x) must be opposites. Yes, we solved for the y intercepts earlier.

To find the y intercept we set x to 0 and solve for y.

2x + 4 = y                    5x - 4 = y

2(0) + 4 = y                  5(0) - 4 = y

0 + 4 = y                      0 - 4 = y

y = 4                             y = - 4

4 and - 4 are opposites, so this statement is also true.

Answer:

Putting the value in x = 2 , y =4 in 2x - 2y we get,

2 × 2 - 4× 2= 4-8 = -4

Putting the value in z = 3 in z - 5 we get,

z - 5 = 3 - 5 = -2

Answer:

D. X=2

Step-by-step explanation:

Answer:

X=2

Step-by-step explanation:

Answer:

B. 50 times greater

Step-by-step explanation:

Given;

size of phytoplankton = 2 × 10⁻⁶ in

size of sand grain = 1 × 10⁻⁴ in

Determine how many times longer the grain of sand is than the phytoplankton.

Divide the sand size by the phytoplankton size, to find out how much greater the sand is.

This can be done by equating it as follows;

2 × 10⁻⁶ (y)  = 1 × 10⁻⁴

[tex]y = \frac{1*10^{-4}}{2*10^{-6}} \\\\y = 50[/tex]

Therefore, the grain of sand is 50 times greater than the phytoplankton

B. 50 times greater

Answer:

7.0 seconds

Step-by-step explanation:

i did the test but how i know this is bc 3 divided by 21 is 7

NOT 9

DON'T USE 9 AS THE ANSWER

Answer:

7.0 seconds

Step-by-step explanation:

Answer:

$0.43

Step-by-step explanation:

Preston adopted a cat from a rescue shelter

He needs to buy food for his new cat so he compared the price of cat litter at different stores

Preston gets the best deal at fluffy felines pet shop

They sell 20 pound jug litter for $8.60

Therefore the cost of the cat litter per pound can be calculated as follows

= 8.60/20

= 0.43

Hence the cost of the cat litter per pound is $0.43

Answer:

113 square feet

Step-by-step explanation:

Since the shape of the mosaic that the architect would be using is circular is shape, the formula to apply to solve this question is area of a circle.

The formula for the area of a circle = πr²

In the above question,Area if a circle = πr²

radius of the circle = r = 6 feet

πr² = π × 6²

113.09733553 square feet

Approximately to the next whole number ≈ 113 square feet.

Therefore, the number in square feet of tiles needed for the mosaic is 113 square feet

Answer:

a.  L.B. = 20.5

b.  U.B. = 21.5

Step-by-step explanation:

Length is measured 21 cm correct to 2 significant figures

a.  Lower bound of 21

  =  20.5 < 21

  = 20.5

b. Upper bound of 21

   = 21 < 21.5

   = 21.5

Answer:

x = 1

y = 1

Step-by-step explanation:

Given:

Add up the two equations side-by-side, this will cancel y/b and 1/b:

Subtract the  two equations side-by-side, this will cancel x/a and 1/a:

Answer:

x = 1, y = 1

Step-by-step explanation:

[tex] \frac{x}{a} + \frac{y}{b} = \frac{1}{a} + \frac{1}{b} .....(1) \\ \frac{x}{a} - \frac{y}{b} = \frac{1}{a} - \frac{1}{b} .....(2) \\ \\ let \: \: \frac{1}{a} = m, \:\:\&\: \: \frac{1}{b} = n \\ so \: equatin \: (1) \: reduces \: to: \: \\ \\ so \: equatin \: (1) \: reduces \: to: \: \\ mx + ny = m + n....(3)\\ and \: equatin \: (2) \: reduces \: to: \: \\ mx - ny = m - n....(4) \\ adding \: equations \: (3) \: (4) \\ mx + ny = m + n \\ mx - ny = m - n \\ - - - - - - - - - - \\ 2mx = 2m \\ x = \frac{2m}{2m} \\ \huge \red{ \boxed{x = 1}} \\ substituting \: x = 1 \: in \: equatin \: (3) \\ m \times 1 + ny \: = m + n \\ m + ny \: = m + n \\ ny = m + n - m \\ ny = n \\ y = \frac{n}{n} \\ \huge \purple{ \boxed{y = 1}}[/tex]

Answer:

point A: 2

point B: -3

your friend is incorrect

Step-by-step explanation:

Answer:

point A: 2

point B: -3

your friend is incorrect

Step-by-step explanation:

Answer:

________________________

I believe that it's 114 degrees.

________________________

Answer:

114

Step-by-step explanation:

angle Bcd=180-66=114 degrees

the two angles are supplementary equal to 180 degrees

Answer:

-5

Step-by-step explanation:

We are given the expression:

[tex]\frac{1}{4} [-5+5(-3)][/tex]

and asked to evaluate.

We must solve this expression according to PEMDAS: Parentheses, Exponents, Multiplication, Division, Addition and Subtraction.

Solve inside the brackets first. Multiply 5 and -3.

5 * -3= -15

[tex]\frac{1}{4} [-5+-15][/tex]

Add -5 and -15.

-5+-15= -20

[tex]\frac{1}{4} [-20][/tex]

Finally, multiply 1/4 and -20, or divide -20 by 4.

1/4 * -20 = -5      OR       -20/4= -5

[tex]-5[/tex]

When evaluated, the expression 1/4 [ -5 +5(-3)] is equal to -5.

Answer:

A: Domain: {9, 8, 7, -5} Range: {1, -3, 5, 3}

Step-by-step explanation:

C = {(9, 1) (8, -3) (7, 5) (-5, 3)}

The domain is the inputs

Domain: { -5,7,8,9}

The range is the output

Range{ -3,1,3,5}

This is a functions since there is no input that goes to multiple outputs

Answer:

y= 1-x

Step-by-step explanation:

● (a^2x)/a^(x-y) = a

This means that:

● 2x-(x-y) = 1

● 2x - x +y = 1

● x + y = 1

Substract x from both sides

● x+y -x = 1-x

● y = 1-x

Answer:

The measure of ∠TSU = 65°

Step-by-step explanation:

Since RST is a right-angled triangle and RS and ST connect to form a right angle, ∠RST = 90°. Also, since RS and ST connect to form a right angle, ∠RST = ∠RSU + ∠TSU.

We make ∠TSU subject of the formula. So,

∠TSU = ∠RST - ∠RSU

Given that angle ∠RSU = 25° and ∠RST = 90°, substituting these values into he expression for ∠TSU, we have

∠TSU = ∠RST - ∠RSU

∠TSU = 90° - 25°

∠TSU = 65°

So, ∠TSU = 65°

The measure of ∠TSU = 65°

Answer:

65

Step-by-step explanation:

you know it forms a right angle because of the marking on it

so take 90 because thats the degree of a right angle, and subtract 25 from it and you will get your other side

90-25=x

65=x

check by adding both angles

65+25=90

Answer:

division property of equality.

Step-by-step explanation:

Answer:

x = - 1, x = 1, x = 2

Step-by-step explanation:

The coefficients of the polynomial sum to zero, that is

- 1 + 2 + 1 - 2 = 0

This indicates that x = 1 is a zero

let x = - 1, then

- (- 1)³ + 2(- 1)² + (- 1) - 2 = 1 + 2 - 1 - 2 = 0

Thus x = - 1 is a zero

let x = 2

- (2)³ + 2(2)² + 2 - 2 = - 8 + 8 + 2 - 2 = 0

Thus x = 2 is a zero

The 3 zeros are x = - 1, x = 1, x = 2

Answer:  703

Step-by-step explanation:

This situation is the same as,

7,030 / 10  = 703

Answer:

y=-2x-3

Step-by-step explanation:

y-y1=m(x-x1)

gronala bars:18

energy drinks:9

Step-by-step explanation:

$0.50 •18= $9

$2.00•9=$18

$9+$18=$27

Answer:

It was not my intention to post that answer, as it does not solve the question, but hope it helps somehow.  

Step-by-step explanation:

[tex]$\text{b)} \frac{\sin(a)}{\sin(a)-\cos(a)} - \frac{\cos(a)}{\cos(a)-\sin(a)} = \frac{1+\cot^2 (a)}{1-\cot^2 (a)} $[/tex]

You want to verify this identity.

[tex]$\frac{\sin(a)(\cos(a)-\sin(a))}{(\sin(a)-\cos(a))(\cos(a)-\sin(a))} - \frac{\cos(a)(\sin(a)-\cos(a))}{(\sin(a)-\cos(a))(\cos(a)-\sin(a))} = \frac{1+\cot^2 (a)}{1-\cot^2 (a)} $[/tex]

The common denominator is

[tex](\sin(a)-\cos(a))(\cos(a)-\sin(a))= \boxed{2\cos (a)\sin(a)-\cos ^2(a)-\sin ^2(a)}[/tex]

Solving the first and second numerator:

[tex]\sin(a)(\cos(a)-\sin(a))=\sin(a)\cos(a)-\sin^2(a)[/tex]

[tex]\cos(a)(\sin(a)-\cos(a))= \cos(a)\sin(a)-\cos^2(a)[/tex]

Now we have

[tex]$\frac{ \sin(a)\cos(a)-\sin^2(a) -(\cos(a)\sin(a)-\cos^2(a))}{2\cos (a)\sin(a)-\cos ^2(a)-\sin ^2(a)}$[/tex]

[tex]$\frac{ -\sin^2(a) +\cos^2(a)}{2\cos (a)\sin(a)-\cos ^2(a)-\sin ^2(a)}$[/tex]

Once

[tex]-\sin^2(a) +\cos^2(a) = \cos(2a)[/tex]

[tex]2\cos (a)\sin(a) = \sin(2a)[/tex]

Also, consider the identity:

[tex]\boxed{\sin^2(a)+\cos^2(a)=1}[/tex]

[tex]$\frac{ -\sin^2(a) +\cos^2(a)}{2\cos (a)\sin(a)-\cos ^2(a)-\sin ^2(a)}=\boxed{\frac{ \cos(2a)}{\sin(2a)-1}}$[/tex]

That last claim is true.

Answer:

-2(3v - 6) = 0

-6v + 12 = 0

-6v = -12

v = -12/-6

v = 2 answer

Step-by-step explanation:

Answer:

h=8cm

Step-by-step explanation:

V= πr^2h/3

Where

V=volume of a cone

π=pi= 3.14

r= radius=4cm

h= height = ?

V= πr^2h/3

134= 3.14*4*4*h/3

134= 50.24h/3

Divide both sides by 50.24

h/3= 134 / 50.24

h/3= 2.67

Cross product

h= 2.67*3

h= 8.01

Approximately h= 8cm

The best estimate of the cone's height is 8cm

Answer:

Herbs are small plants that have a fleshy or juicy stem when they are young. The stems of some herbs develop hard, woody tissue when they grow old. Most herbs are perennials. This means that the tops of the plants die each growing season, but the roots remain alive and produce new plants year after year.

Step-by-step explanation:

Answer:

[tex]x=15/2=7.5[/tex]

Step-by-step explanation:

So we have the function:

[tex]f(x)=2x+1[/tex]

And we want to find x such that:

[tex]f(x)=16[/tex]

To do so, substitute 16 for f(x):

[tex]f(x)=2x+1\\16=2x+1[/tex]

Subtract 1 from both sides. The right side cancels:

[tex](16)-1=(2x+1)-1\\2x=15[/tex]

Divide both sides by 2. The left side cancels:

[tex](2x)/2=(15)/2\\x=15/2=7.5[/tex]

The value of x is 7.5

Answer:

[tex]x=\frac{15}{2}[/tex]

Step-by-step explanation:

We are given the value of f(x). Insert this value into the original equation:

[tex]f(x)=16\\\\16=2x+1[/tex]

Solve for x. Subtract 1 from both sides:

[tex]16-1=2x+1-1\\\\15=2x[/tex]

Divide both sides by 2 to isolate x:

[tex]\frac{15}{2} =\frac{2x}{2} \\\\\frac{15}{2}=x[/tex]

When f(x) equals 16, x is equal to [tex]\frac{15}{2}[/tex]

Answer:

y=3b + 6 ................ . ..

The answer is 3b + 6 in Khan Accademy

Step-by-step explanation:

Seven more than twice a number is 47. Let's break down this sentence into numbers so you can see what's going on.

"Seven more than twice a number" - This tells you that there is a number, let's call it y, that is 7 more than twice a different number, lets call this x. So in equation form this is y = 7 + 2x. Hmm this seems a little tricky, how do we find the answer? Well if we keep reading, it tells you that the number that is 7 more than twice another number is 47, so we now know that y = 47. So let's redo our equation by substituting y for the number 47:

47 = 7 + 2x

Now we have a workable equation. We need to solve for x. So let's rewrite this equation without changing it, just putting it in different order. Now we have 2x + 7 = 47. So how do we solve for x? First, we subtract 7 from both sides. Remember, when solving for x, anything you do to one side you must do to the other. So now we get this:

2x + 7 = 47 simplifies to 2x = 40

Now if we divide both sides by 2 to get x all by itself, we get x = 20. That is your answer. You can check it by substituting 20 for s in your original equation of 2x + 7 = 47, then you get 2(20) + 7 = 47. It works! Hope this helps!

40

2 + 10 = 24

2(2 + 10) = 2×12 = 24

3 + 6 = 27

3(3 + 6) = 3×9 = 27

7 + 2 = 63

7(7 + 2) = 7×9 = 63

5 + 3 = 40

5(5 + 3) = 5×8 = 40

Answer:

Width= 12 yards

Length= 24 yards

Step-by-step explanation:

Perimeter of a rectangle= 2(length + width)

Let

w= width

Twice as long as it is wide

Length= 2w

Perimeter of the rectangle= 72 yards

Perimeter of a rectangle= 2(length + width)

72 = 2(2w + w)

72 = 4w + 2w

72 = 6w

Divide both sides by 6

72/6 = w

12= w

w=12

Therefore,

Width= 12 yards

Length= 2w

=2(12)

=24 yards