Write 0.0000000642 in scientific notation.

Considering that the diagonal divided the area of the rectangle in two equal parts, Dan is not correct, as both will have to cut the same amount of grass.

It is the number of square units inside of the rectangle, and for a rectangle of length l and width w it is given by:

A = lw.

The diagonal divides the area of the triangle exactly in the middle, hence  Dan is not correct, as both will have to cut the same amount of grass.

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Answer:

4(5x-2)= 6(x+8)

20x-8=6x+48

20x-6x=48+8

14x=56

\(x = \frac{56}{14} \)

x=4

Step-by-step explanation:

hope this helps you!!

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Answer:

x = 4

Step-by-step explanation:

\(\frac{5x-2}{6}=\frac{x+8}{4} < == cross\ multiply\\\\4(5x-2)=6(x+8) < ==distribute\\\\4(5x)+4(-2)=6(x)+6(8)\\\\20x-8=6x+48 < ==subtract\ 6x\ from\ both\ sides\\-6x\ \ \ \ -6x\\\\14x-8=48 < == add\ 8\ to\both\ sides\\\ \ \ +8 \ \ \ \ \ \ \ +8\\\\14x=56 < ==divide\ both\ sides\ by\ 14\\/14 \ \ \ /14\\\\x=4 < ==final\ answer\)

Check your answer:

\(\frac{5x-2}{6}=\frac{x+8}{4}\\\\\frac{5(4)-2}{6}=\frac{4+8}{4}\\\\\frac{20-2}{6}=\frac{12}{4}\\\\\frac{18}{6}=\frac{12}{4}\\\\3=3\)

This statement is correct

Hope this helps!

Answer:

\(m=2\)

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Algebra I

Step-by-step explanation:

Step 1: Define

Find points from graph.

Point (0, 3)

Point (-3, -3)

Step 2: Find slope m

Simply plug in the 2 coordinates into the slope formula to find slope m.

Answer:

a. x=5

b. x=4

Step-by-step explanation:

-5+6=1 because if it's not a normal equation it has a negative

Answer:

1

Step-by-step explanation:

When adding a negative and a positive number, subtract the biggest number from the smallest (ignore the signs), so :

\(6-5=1\)

After you have your answer, keep the symbol of the bigger number (pay attention to the signs now). Since positive 6 is greater than negative 5, keep the positive. Add this symbol to the answer, making the answer positive.

\(-5+6=1\)

Answer:

If it is using pi as 3.14, it is 56.52.

If it is just the pi symbol, it is 18π.

Step-by-step explanation:

We do 9 x 3.14 = 28.26 and then you multiply that by 2 to get 56.52.

We do 9 x π = 9π. Then multiply by 2 to get 18π.

Step-by-step explanation:

.......................

a. The dimensions that maximize the area of the pen are 33 meters by 100 meters.

b. The dimensions of each rectangular pen that minimize the amount of fence used are 10sqrt(2) meters by 10sqrt(2) meters.

a. To maximize the area of the rectangular pen, we need to find the dimensions that use up all 200 meters of fencing, except for the side that is against the barn. Let the length of the pen be x and the width be y. Then we have:

Perimeter of the pen = 2x + y = 200 - x (since one side is against the barn)

Simplifying this equation, we get:

3x + y = 200

Area of the pen = xy

Now we can express y in terms of x using the equation above:

y = 200 - 3x

Substituting this into the expression for area, we get:

A(x) = x(200 - 3x) = 200x - 3x^2

To maximize the area, we need to find the value of x that makes A(x) as large as possible. We can do this by taking the derivative of A(x) with respect to x and setting it equal to 0:

A'(x) = 200 - 6x

200 - 6x = 0

x = 33.33

Since we can't have a fractional length, we choose x = 33 meters (rounded to the nearest meter). Then y = 200 - 3x = 100 meters.

b. Let the dimensions of each rectangular pen be x and y. Then we have:

Area of each pen = xy = 100

Perimeter of each pen = 2x + 2y

We want to minimize the amount of fence used, which is equal to the total perimeter of all four pens. So, we need to find the dimensions that minimize the total perimeter subject to the constraint that the area of each pen is 100. We can use Lagrange multipliers to solve this problem:

L(x, y, λ) = 2x + 2y + λ(xy - 100)

Taking the partial derivatives with respect to x, y, and λ, we get:

∂L/∂x = 2 + λy = 0

∂L/∂y = 2 + λx = 0

∂L/∂λ = xy - 100 = 0

Solving these equations simultaneously, we get:

x = y = sqrt(200/λ)

xy = 100

Substituting the first equation into the second equation, we get:

sqrt(200/λ)^2 = 100

λ = 2

Substituting λ = 2 back into the first equation, we get:

x = y = sqrt(200/λ) = 10sqrt(2)

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Answer:

10x + 21

Step-by-step explanation:

5x + 2x-9 + 3x + 30 = 10x + 21

9514 1404 393

Answer:

  f(x) = x^2 +2x -8

Step-by-step explanation:

If p and q are zeros of a quadratic, its factored form is ...

  f(x) = (x -p)(x -q)

For your zeros, the factored form is ...

  f(x) = (x +4)(x -2)

Expanded using the distributive property, this is ...

  f(x) = x(x -2) +4(x -2) = x^2 -2x +4x -8

  f(x) = x^2 +2x -8

The point (x, y) is located in Quadrant III when x > 0 and y < 0. It does not belong to any other quadrant.

In a Cartesian coordinate system, the x-axis represents the horizontal axis, and the y-axis represents the vertical axis. The quadrants are divided based on the signs of the x and y coordinates.

Quadrant I is located in the upper right portion of the coordinate plane, where both x and y are positive. Quadrant II is in the upper left portion, where x is negative and y is positive. Quadrant III is in the lower left portion, where both x and y are negative. Quadrant IV is in the lower right portion, where x is positive and y is negative.    

Given the condition x > 0 and y < 0, we know that x is positive (greater than 0) and y is negative (less than 0). Therefore, the point (x, y) satisfies the conditions for being located in Quadrant III. It does not fulfill the criteria for any other quadrant since either the x-coordinate or the y-coordinate is not consistent with their signs in the other quadrants.

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After solving the equation 2 x² the value of x is equal to 1   \(\sqrt{1/2}\)

we are asked to find x in 2x² = 1

⇒ 2x² = 1

⇒ x² = 1/2

⇒ x = \(\sqrt{1/2}\)

So, x is equal to  \(\sqrt{1/2}\)

To solve linear equations, utilize the steps that are provided below.

Lets take an example of solve z for 7z – (3z – 4) = 12

Here is no multiplication or division, so this will be easy to solve

⇒ 7z – (3z – 4) = 12

⇒ 7z – 3z + 4 = 12

⇒ 4z = 12 – 4

⇒ 4z = 8

⇒ z = 8/4

⇒ z = 2

See, that was so simple, using the mentioned methods, every linear equation can be solved easily.

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Answer:

0.6 miles per minute

Step-by-step explanation:

3/5 = 0.6/1 = 0.6

Answer:

0.6 miles or 3168 feet

Explanation:

In 5 minutes, you hike 3 miles, so in 1 minute you hike 3/5 miles or 0.6 miles.

A local variable is defined inside the body of the function and is not accessible outside of the function.

A local varible is a type of variable that we declare inside a block or a function, unlike the gloabal variable. They can be used only by the statements that are inside the function or the block of the code. Local variables are not known to functions outside their own.

Thus,

A local variable is defined inside the body of the function and is not accessible outside of the function.

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The two values that makes the given equation false are 3 and 5.

These integer solutions are false since the only solution for the given equation is 4.

Given equation is,

11 = 2x + 3

We have to find the integer values which makes the equation false.

Since, this is a linear solution, there can be one, none or infinite number of solutions.

Rearranging the equation,

11 - 3 = 2x

8 = 2x

4 = x

So any number not equal to 4 is not a solution for the given equation.

Two integers can be 3 and 5.

Hence the integers which is not a solutions are 3 and 5.

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Answer:

help with what?

Step-by-step explanation:

The farm for sale measures 1120 acres.  

How many acres are equivalent to one square mile?

1 square mile= 640 acres.

To convert square miles to acres, we need to know that there are 640 acres in one square mile.

Given that the farm for sale measures one and three-quarter square miles, we can calculate the number of acres as follows:

1 and 3/4 square miles = 1.75 square miles  

Number of acres = 1.75 square miles * 640 acres/square mile

Number of acres = 1120 acres

Therefore, the farm for sale measures 1120 acres.

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From the unit conversion, the mass of

1 cubic foot of western red cedar with

density of about 380 kilometers per cubic meter is equals to the 1,246.7192 km.

We have a wood of western red cedar tree. Density of wood of western red cedar tree, d = 380 kilometres per cubic meter. We have to determine the mass of 1 cubic foot of western red cedar.

That is volume of wood of western red cedar tree, V = 1 foot³

Let m be the mass of wood of western red cedar. As we know, density is defined as the ratio of mass of substance to the volume of substance. Mathematically,

\(d = \frac{m}{V}\)

But before substitution, we use unit conversion formula from foot to meters. So, 3.28084 foot = 1 meter

then 1 foot³ = 3.28084 m³

Substitute all known values in above formula, \( 380 km/m³= \frac{m}{3.28084 m³}\)

=> m = 380 km/m³ (3.28084 m³)

=> m = 1,246.7192 km

Hence, required value is 1,246.7192 km.

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The X value corresponding to z = -2.25 is X = 56.

A z score is a statistical indicator that shows how far a raw score is from a distribution's mean. Give the z-score formula. The z-score is calculated using the formula z = (x -μ)/σ.

To find the corresponding X value for a given z-score, we use the formula:

X = µ + (z * σ)

Given µ = 65, σ = 4, and z = -2.25, we can calculate the X value:

X = 65 + (-2.25 * 4)

X = 65 - 9

X = 56

Therefore, the X value corresponding to z = -2.25 is X = 56.

The correct answer is b. X = 56.

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Answer:

b) because it's in descending exponent order

Step-by-step explanation:

a) To find the average temperature between t1 = 6 and t2 = 12 hours, we need to calculate the definite integral of T(t) from t1 to t2 and divide it by the time interval (t2 - t1).

∫[t1, t2] T(t) dt = ∫[6, 12] (20 - 5cos(t)) dt

= [20t - 5sin(t)] [6, 12]

= [(20*12 - 5sin(12)) - (20*6 - 5sin(6))] / (12-6)

= [240 - 5sin(12) - 120 + 5sin(6)] / 6

= (120 - 2.5sin(12) + 2.5sin(6)) / 3

Therefore, the average temperature between t1 = 6 and t2 = 12 hours is (120 - 2.5sin(12) + 2.5sin(6)) / 3 degrees Celsius.

b) To find the time at which the average temperature occurs, we need to find the maximum value of T(t) in the interval [t1, t2]. The maximum value of cos(t) is 1, which occurs when t = 0. Therefore, the maximum value of T(t) is:

Tmax = 20 - 5cos(0) = 25 degrees Celsius.

The average temperature occurs at the time when T(t) equals Tmax. Solving for t in the equation T(t) = Tmax:

T(t) = Tmax

20 - 5cos(t) = 25

cos(t) = -1

t = π + k*2π, where k is an integer.

Since we are only interested in the time between t1 = 6 and t2 = 12, we need to choose the value of k that gives a solution in this interval. We have:

π + 2π = 3π > 12, which is outside the interval.

π + 4π = 5π > 12, which is outside the interval.

π - 2π = -π < 6, which is outside the interval.

π - 4π = -3π < 6, which is outside the interval.

Therefore, there is no time in the interval [6, 12] when the average temperature occurs at its maximum value.

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Answer: 4 months

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

Answer:

it's A

Step-by-step explanation:

if you look at Ait showa that the dot is at 4 and goes down to -2

A B C is the correct condition for the researcher to calculate the mean.

When a researcher collects a simple random sample of grade-point averages of statistics students, the sample mean can be treated as a value from a population having a normal distribution under the following conditions:

A. The researcher collects more than 30 samples.

B. If the population of statistics students has a normal distribution.

C. If the population of grade-point averages has a normal distribution.

Hence, options A, B, and C are correct. In order to estimate P(at least 5)

with n = 13 and p = 0.5, the following formula should be used:μ = np = (13)

(0.5) = 6.5σ = sqrt(npq) = sqrt(13 × 0.5 × 0.5) = 1.802P(at least 5) = P(X ≥

5.5)Using continuity correction, P(X ≥ 5.5) is equivalent to:P(Z ≥ (5.5 -

6.5)/1.802)P(Z ≥ -0.555) = 0.2918 (rounded to 4 decimal places)Therefore,

P(at least 5) = 0.2918 (rounded to 3 decimal places).Thus, the correct

choice is option A: P(at least 5) = 0.292 (rounded to 3 decimal places).

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Equation employing the slope-intercept method for two points

The slope-intercept version of the equation may be used to calculate the two-point Y-intercept.

The shape of a point-slope is\(\mathbf{Y-Y_{1} = m(X-X_{1})}.\)

Steps to find the y-intercept with two ordered pairs?

Determine the slope using two points.

\(Slope = \frac{Y_{2}-Y_{1}}{X_{2}-X_{1}} = \frac{Rise}{Run} = \frac{\bigtriangleup Y}{\bigtriangleup X}\)

As an illustration, two points are (3, 5) and (6, 11)

Slope = \(\frac{Y_{2}-Y_{1}}{X_{2}-X_{1}} = \frac{11 - 5}{6 - 3} = \frac{6}{3} = 2\)

In the slope-intercept form of the equation, substitute the slope(m).

\(\\y = mx+b \\y = 2x+b\)

Either point may be substituted in the equation. You may either use (3,5) or (6,11).

\(\\y = 2x+b \\5 = 2(3)+b\)

Find the answer to the equation for b, the line's y-intercept.

\(\\5 \ \ \ = 2(3) + b \\5 \ \ \ = 6 + b \\\underline{-6\ = -6 \ \ \ \ \ \ \ } \\-1 = b\)

Substitute b,  into the equation.

\(\\y = 2x + b \\y = 2x - 1\)

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Answer:

13.86

Step-by-step explanation:

\(8^2+x^2=16^2\\64+x^2=256\\x^2=192\\\sqrt{x^2} =\sqrt{192} \\x=13.86\)

Answer:

80 cups of water will be needed.

Step-by-step explanation:

Let the equation that represents the amount of lemonade mix (y) and the cups of water needed (x) for second recipe is,

y = mx

Here, m = rate of change (amount of water required for a cup of lemonade mix)

m = \(\frac{y_2-y_1}{x_2-x_1}\)

m = \(\frac{65-50}{13-10}\) = 5

Therefore, equation will be,

y = 5x

If x = 16,

y = 5×(16)

y = 80 cups

Therefore, 80 cups of water will be needed to prepare 16 cups of lemonade mix.