Find the values of x and y that maximize the objective function

Answer: 16 times

Step-by-step explanation:

So in this situation, an equation helps!

634 = 38x

Where 634 is the number of gallons of gas she has; 38x is how much she needs to mow her lawn each time.

Now simply divide!

If we round we get x= 16.68 however this is not the correct answer because you can't mow 68/100 of a lawn! So even though 0.68 is greater than 0.5, we would round down to 16.

Answer:

p(x) is a function, and a polynomial of degree 3, then

By remainder theorem and factor theorem,

p(0) = p(1) = p (-1) = 0 if and only if

x = 0, 1, -1 are zeroes if and only if

p(x) = k(x - 0)(x - 1)(x + 1) = k(x)(x^2 - 1) = k(x^3 - x) = kx^3 - kx

p(2) = k(2)^3 - k(2) = 6

8k - 2k = 6

6k = 6

k = 1

Thus p(x) = x(x - 1)(x + 1) = x(x^2 - 1) = x^3 - x

p(-x) = (-x)^3 - (-x) = x^3 + x

-p(x) = -(x^3 - x) = -x^3 + x

As you can see, p(x) does not equal to -p(x), unless x = 0, 1, -1,

because p(0) = -p(0) = 0, p(-1) = - p(1) = 0, p(1) = -p(-1) = 0

p(x) = x(x - 1)(x + 1)

If x < -1, then x < 0, x - 1 < 0, x + 1 < 0

That means p(x) < 0

If -1 < x < 0, then x < 0, -2 < x - 1 < -1 < 0, 0 < x + 1 < 1

That means p(x) > 0

If 0 < x < 1, then x > 0, -1 < x - 1 < 0, 0 < 1 < x + 1 < 2

That means p(x) < 0

If x > 1, then x > 0, x - 1 > 0, x + 1 > 2 > 0

That means p(x) > 0

Thus p(x) < 0 if x < -1 or 0 < x < 1

When the spacecraft launched, it was 254 miles away from the Earth and its distance away from the Earth is increasing at a rate of 270 miles per hour.

The equation that represents the distance of the space craft is known as a linear equation. A linear equation is an equation that has only one variable that is raised to the power of one.

A linear equation increases or decreases at a constant rate. When drawn on a graph, a linear equation is a straight curve that slopes either upward or downward.

A linear equation usually has this form y = mx + b

Where:

D = 254 + 270t

Where:

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Answer: 242 square ft

Step-by-step explanation:

Divide the polygon into 2 pieces so you have 2 rectangles. Then find the area of both rectangles.

Answer:

Step-by-step explanation:

The domain is the set of x-coordinates.

The domain of the function f(x) is:

Answer:

A. yes the y-intercept is 2

B. the graph is a straight line

C. The Slope of the Line is 1/2

D. The line Does Not pass through the origin

Step-by-step explanation:

A. the y-intercept is when x=0... y=([tex]\frac{-1}{2}[/tex]*0)+2

B. It is a straight line because x is raised to the 1st power and not another number

C. Although the slope of the equation is [tex]\frac{-1}{2}[/tex]... the slope is still 1/2

D. The line Does Not pass through the origin

origin= (0,0)

x=0 --> y=([tex]\frac{-1}{2}[/tex]*0)+2=

y=0---> 0=([tex]\frac{-1}{2}[/tex]*x)+2

[tex]\frac{-x}{2}[/tex]=2---> x=-4

Answer:

The first two statements are true.

Click "The y-intercept of the line is 2" and "The graph is a straight line"

Step-by-step explanation:

The most important thing to know for this question is the equation of a line, y=mx+c, where m is the slope of the line and c is the y-intercept (where the lines crosses the y-axis).

Our formula is y= - [tex]\frac{1}{2}[/tex]x+2, which means the y-intercept is 2. Therefore, the first statement is true.

The equation follows the general equation for a straight line, so the second statement is true.

Our formula is y= - [tex]\frac{1}{2}[/tex]x+2, which means the slope is -  [tex]\frac{1}{2}[/tex], not  [tex]\frac{1}{2}[/tex]. Therefore, the third statement is not true.

For a line to pass through the origin (0,0), it's y-intercept must be 0, but we already know the y-intercept here is 2. Therefore, the fourth statement is not true.

To see if the line passes through (0, -2), we must sub these values into the equation and see if it makes sense

y= - [tex]\frac{1}{2}[/tex]x+2?

-2=- [tex]\frac{1}{2}[/tex](0)+2?

-2 = 2? This is not true, so the last statement is also not true.

Based on the amount invested, and the interest, the amount after 3 years would be $567.86

The interest is compounded monthly  so you must convert it to a monthly rate:

= 4.25% / 12 months

= 4.25/12%

Number of periods:

= 3 years x 12 months

= 36 months

The future value of this amount is:

= Amount x ( 1 + rate) ^ number of periods

= 500 x ( 1 + 4.25/12%)³⁶

= $567.86

In conclusion, the amount would be $567.86

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The solution of the equation ( x - 7 ) × 2 = 36  is x = 25

The equation is

( x - 7 ) × 2 = 36

To solve this equation we have to rearrange the terms and do the arithmetic operations

The arithmetic operation is a branch of mathematics. The basic arithmetic operations are addition, subtraction, division and multiplication.

Move the 2 to the right hand side of the equation

x - 7 = 36 / 2

Divide the term

x - 7 = 18

Move the 7 to the right hand side of the equation

x = 18 + 7

Add the term

x = 25

Hence, the solution of the equation ( x - 7 ) × 2 = 36  is x = 25

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An equation is a collection of variables and constants with the value of x which will make the equation 7+3(x - 1)=5x+-2(x+1) to be true is 1/2.

There are many different ways to define an equation. The definition of an equation in algebra is a mathematical statement that demonstrates the equality of 2 mathematical expressions.

As per the given equation,

7+3(x - 1)=5x+-2(x+1)

7 + 3x - 3 = 5x + 2x + 2

3x + 4 = 7x + 2

7x + 2 = 3x + 4

7x - 3x = 4 - 2

4x = 2

x = 1/2

Hence "The value of x which will make the equation 7+3(x - 1)=5x+-2(x+1) to be true is 1/2".

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The time taken by thunder to travel a distance of 5 miles is 25 seconds.

Let d denote the distance and t the time.

Distance varies linearly with time, implying that distance is proportional to time.

Distance ∝ Time

d ∝ t

When the proportionality symbol is removed;

d = kt or k = d/t

Where k is the constant of proportionality.

In the equation, d = 2 and t = 10 are substituted.

k = 2/10 = 1/5

Therefore,

The following is a direct variation formula for the correlation between time and distance: d = (1/5)t

Now, for the distance of 5 miles, the time taken by the thunder is-

5 = (1/5)t

t = 5 × 5

t = 25 seconds.

Thus, the time taken by thunder to travel a distance of 5 miles is 25 seconds.

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use the cross multiplication method :)

The distributive property for the product of 27x34 will give a value of 918.

It should be noted that distributive property simply means that one can distribute the contents of the parentheses into the other so that one can get the answer.

The distributive property is illustrated as:

a × (b + c) = a×b + a×c

In this case, using distributive property to find the product 27x34 will be:

=27x(30+4)

= 27 × 30 + 27 × 4

= 810 + 108

= 918

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Answer:

11) 7d + 28 and 7(d+4)

12) y^2 + 3y and y(y+3)

Step-by-step explanation:

It is not possible to create a complex number in which b = 0, as it would be equivalent to a real number.

The general format of a complex number is given as follows:

z = a + bi.

The meaning of the parameters a and b are given as follows:

If the coefficient b has a value of zero, then the complex number is written as follows:

z = a + 0i.

z = a.

Which is equivalent to a real number, that is, the number would have only a real component, hence it is not possible to find an imaginary number with b = 0.

Basically, any real number can be represented as a complex number with imaginary part 0, but then the number would not be complex.

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Answer:

down below

Step-by-step explanation:

You can use a number line to show the subtraction between two integers by plotting the first night number and then move backwards, (left) however many spaces you are subtracting by. It is a visual representation of subtraction.

Hope this helps! :)

Using the exponential distribution, there is a 0.263 probability that a truck will be loaded in 20 minutes or more.

The exponential probability distribution, with mean m, is described by the following probability mass function:

[tex]f(x) = \mu e^{-\mu x}[/tex]

[tex]\mu = \frac{1}{m}[/tex] is the decay parameter.

The probability that x is lower or equal to a is given by:

[tex]P(X \leq x) = \int\limits^a_0 {f(x)} \, dx[/tex]

The integral has the following solution:

[tex]P(X \leq x) = 1 - e^{-\mu x}[/tex]

Hence the probability of finding a value higher than x is given by:

[tex]P(X > x) = 1 - P(X \leq x) = 1 - (1 - e^{-\mu x}) = e^{-\mu x}[/tex]

In the context of this problem, the mean and the decay parameter are given, respectively, by:

[tex]m = 15, \mu = \frac{1}{15} = 0.0667[/tex]

Hence the probability that a truck will be loaded in 20 minutes or more is:

[tex]P(X > 20) = e^{-0.0667 \times 20} = 0.263[/tex]

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Let x = pounds of raisins

Let y = pounds of walnuts

The first linear equation for the system is representing COST

The second linear equation for the system is representing WEIGHT

Hence the two-equation for each constraint are

27 ft. can be used to represent the water's surface if the platform is 15 ft. above the pool surface and the pool has a depth of 12 ft.

As Sadie stands on a platform that is 15 ft. above the pool surface. The pool has a depth of 12 ft. then, and the total height of the water surface is, the total hight,

The total height = distance between pool surface to platform + the depth of the pool

∵ The total height =  15 ft. + 12 ft.= 27 ft.

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Answer:

Plot the point (6, 2). From there, move 3 units up and then 4 units to the left. You will be at (2, 5). Plot that point, and then draw a line through (6, 2) and (2, 5).

Answer:

y = 0.57143x - 4

Step-by-step explanation:

Simply subtract the lowest value from the highest value in the data set to determine the range.

Find the biggest observed value of a variable (the maximum) and subtract the smallest observed value to determine the range (the minimum). The data points between the distribution's two extremes are not taken into account by the range; just these two values are.

Because of its sensitivity to extreme values, it is frequently employed as a supplement to other measures of dispersion rather than as the single measure.

To help find the quartiles for bigger data sets, you can utilise the cumulative relative frequency distribution or, even better, the fundamental statistics algorithms found in spreadsheets or statistical applications that provide results more quickly.

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The expression will be written in monomial standard form as -64x⁶a³.

A monomial may be defined as an expression which consists of only one term. If we are to write an expression in monomial standard form, then we will have to form an expression consisting of numbers and variable along with their powers. The variable containing the maximum power will be written first and so on. In the question we have to write monomial standard form of third power of (-4ax³). This can be written as

(-4ax³)³ and on further expanding

-64a³x⁶, but in standard from we write the variable having maximum power first, so we rearrange the terms, and we get

-64x⁶a³ which is the required answer.

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Answer:

D)

Step-by-step explanation:

Alternate interior angles: Alternate interior angles are formed inside the two parallel lines, when intersected by transversal and are equal to its alternate pairs.

AB // CD, BC is transversal

∠2 = ∠4   {Alternate interior angles}

∠2 = 35

The product of 3.7x x 6x = (3.7 x 6) x (x x x) = 22.2x².

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(i) cosФ = 4/7 and sinФ is negative → It lies in the 4th quadrant 304.8° and the suitable graph is not provided here.

(ii) secФ = -13/5 and tanФ is negative  → It lies in the IInd quadrant 112.6° and the suitable graph is J.

(iii) sinФ = 7/10 and cotФ is positive  → It lies in Ist quadrant =44.4° and the suitable graph is I.

(iv) tan0 = 3/4 and sin0 is negative  → It lies in the IIIrd quadrant 216.9° and the suitable graph is not provided here.

What is quadrant?

(i) cosФ = 4/7 and sinФ is negative

Ф=cos^(-1)(4/7)= 55.2°

It lies in 4th quadrant (360-55.2)°=304.8°

A suitable graph is not provided here.

(ii) secФ = -13/5 and tanФ is negative.

Ф=sec^(-1)(-13/5)=67.4°

It lies in IInd quadrant (180-67.4°)=112.6°

A suitable graph is J.

(iii) sinФ = 7/10 and cotФ is positive.

Ф=sin^(-1)(7/10)=44.4°

It lies in Ist quadrant =44.4°

A suitable graph is I.

(iv) tan0 = 3/4 and sin0 is negative.

Ф=tan^(-1)(3/4)=36.9°

It lies in IIIrd quadrant (180+36.9)=216.9°

A suitable graph is not provided here.

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The value of f(3) for the given expression is 8.

What is evaluation of an expression?
In mathematics, an expression that incorporates variables, constants, and algebraic operations is known as an algebraic expression (addition, subtraction, etc.). Finding the value of an algebraic expression when a specified integer is used to replace a variable is known as evaluating the expression. We use the given number to replace the expression's variable before applying the order of operations to simplify the expression. The concept of algebraic expressions is the use of letters or alphabets to represent numbers without providing their precise values. We learned how to express an unknown value using letters like x, y, and z in the fundamentals of algebra. Here, we refer to these letters as variables. Variables and constants can both be used in an algebraic expression. A coefficient is any value that is added before a variable and then multiplied by it.

Given, the expression is 5(x - 1) - 2
Let y = f(x) = 5(x - 1) - 2 = 5x - 5 - 2 = 5x - 7
Therefore, f(3) using the equation above is: f(3) = 5(3) - 7 = 8
Thus, the value of f(3) or y at x = 3 for the given expression is 8.

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STEP 1

Interpret question to make sense geometrically.

We have circular shapes, thus, we are dealing with circles and these circles have their area, however, we seek the angle with which when used to cut the circle will give us an area of 220 sq cm.

Note that this is a fraction of the total area of the circle.

This will be illustrated diagrammatically below

Area of a sector is given as:

STEP 2

Find unknown

The ci