solve by graphing
y=2x
y= -1/2x+5



Sorry that the photos blurry

The minimum value on the interval [-11, 5] is -19, and the maximum value is 28.

In mathematics, a linear function is a function that expresses the relationship between two variables, x and y, in the form of y = mx + b, where m denotes the slope of the line and b the y-intercept. A linear function has a graph that is either a straight line passing through the origin if b = 0 or a point (0, b) if b 0.

A number of applications can benefit from linear functions because of their numerous beneficial characteristics. One of these characteristics is that they are always continuous, i.e., their graphs are seamless and devoid of gaps. They are the best candidates for simulating actual scenarios when two variables have a continuous relationship because of this characteristic.

According to question:

The function f(a) = Va + 3 is a linear function, and all linear functions have a minimum and maximum value that occur at either endpoint of the interval. In this case, the interval is [-11, 5].

To find the minimum value, we evaluate the function at -11:

f(-11) = V(-11) + 3 = -22 + 3 = -19

To find the maximum value, we evaluate the function at 5:

f(5) = V5 + 3 = 25 + 3 = 28

Therefore, the minimum value on the interval [-11, 5] is -19, and the maximum value is 28.

Minimum: -19

Maximum: 28

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Since the y-intercept of the estimated line of best fit is at (0, b), the appropriate value of b is 360.

The appropriate slope of the estimated line of best fit is -30

In Mathematics, the y-intercept is also referred to as an initial value and the y-intercept of any graph such as a linear function, generally occur at the point where the value of "x" is equal to zero (x = 0). Therefore, the y-intercept is at (0, 360).

In Mathematics, the slope of any straight line can be determined by using this mathematical equation;

Slope (m) = (Change in y-axis, Δy)/(Change in x-axis, Δx)

Slope (m) = (y₂ - y₁)/(x₂ - x₁)

Based on the information provided, we can logically deduce the following data points on the line:

Substituting the given points into the slope formula, we have the following;

Slope, m = (y₂ - y₁)/(x₂ - x₁)

Slope, m = (360 - 0)/(0 - 12)

Slope, m = -30.

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The expression of the given composite functions is; (f ∘ g)(x) = 75x² - 150x + 78

We are given the functions as;

f(x) = 3x²+3

g(x) = 5x - 5

We know that the expression of the composite function (f ∘ g)(x) is;

(f ∘ g)(x) = f(g(x)

Thus;

f(g(x) = 3(5x - 5)² + 3

= 3(25x² - 50x + 25) + 3

= 75x² - 150x + 75 + 3

= 75x² - 150x + 78

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Answer:

(f + g)(x) = 3x² + x + 1

Step-by-step explanation:

[tex]\displaystyle{(f+g)(x) = f(x)+g(x)}[/tex]

Substitute f(x) = 3x² - 1 and g(x) = x + 2 in:

[tex]\displaystyle{f(x)+g(x) = (3x^2-1)+(x+2)}\\\\\displaystyle{f(x)+g(x)=3x^2-1+x+2}\\\\\displaystyle{f(x)+g(x) = 3x^2+x+1}\\\\\displaystyle{\therefore (f+g)(x) = 3x^2+x+1}[/tex]

The horizontal velocity of a bullet right before it hits the ground is 10 m/s.

The horizontal velocity of a bullet remains constant throughout its flight, as it is only affected by gravity. This means that the horizontal velocity of the bullet right before it hits the ground will be the same as the initial horizontal velocity when it was fired.

In this case, the bullet was fired at an angle of 60 degrees above the horizontal, but the horizontal velocity remains constant, so it will still be 10 m/s right before it hits the ground. To determine the vertical velocity, we would need to know the time of flight and use the equations of motion to calculate the vertical acceleration due to gravity.

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The mean net worth of the 42 national corporations is approximately 31.5 million dollars. The modal class is the class with the highest frequency, which is the class with class limits of 10-15 and a frequency of 14.

To find the mean, we add up all the net worth values and divide by the total number of corporations. However, since we only have the frequency of each class, not the actual net worth values, we need to estimate the mean using the midpoint of each class and the frequency as the weight. The midpoint of a class is calculated by averaging the lower and upper-class limits.

In this case, the midpoint for a class with class limits of 10-15 is 12.5 million dollars and the midpoint for a class with class limits of 40-45 is 42.5 million dollars. By multiplying the midpoint of each class by its frequency and summing up the results, we can estimate the mean net worth of the corporations.

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Complete Question:

Net Worth of Corporations These data represent the net worth (in millions of dollars) of 42 national corporations. Find the mean and modal class for the data.

Class limits     Frequency

10-15                   14

16-21                   2

22-27                 4

28-33                 8

34-39                 3

40-45                 11

Thresholding is the simplest method of image segmentation. It is a non-linear operation that converts a gray-scale image into a binary image where the two levels are allowed to pixels that are below or above the specified threshold value.

In other words, if the pixel value is greater than a threshold value, it is assigned one value (maybe white), or else it is assigned another value (maybe black). In OpenCV, we use cv2.threshold() function.

cv2.threshold(src, thresh, maxval, type[, dst])

This function put fixed-level thresholding to a single-channel array. The function is used to get a binary image out of a grayscale image or for removing noise, that is, filtering out pixels with too small or too large values.

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Answer: Based on the information given, it seems like the crow is unable to break open the walnut in its current location without it being stolen. To overcome this problem, the best solution would be for the crow to fly away to another location where it can safely break open the walnut. With a take-off speed of 19 feet per second, the crow should be able to quickly reach a new location where it can safely open the walnut.

Step-by-step explanation:

The functions are 1. f(x) = x⁴ and g(x) = cos (x), 2. f(x) = cos x and g(x) = cos x and 3. f(x) = cos (x) and g(x) = x⁴.

A function is a relation from a set A to a set B where the elements in set A only maps to one and only one image in set B. No elements in set A has more than one image in set B.

The composition of two functions f(x)  and g(x) can be defined as the new function h(x) such that h(x) = f(g(x)).

1. cos^4 (x) = f(g(x))

cos⁴ (x) can be written as (cos x)⁴

f(g(x)) = (cos x)⁴

Let g(x) = cos (x)

f(g(x)) = (g(x))⁴

Substitute x in place of g(x).

So, f(x) = x⁴

2. cos(cos(x)) = f(g(x))

Let g(x) be cos x

f(g(x)) = cos (g(x))

Substitute x in place of g(x),

f(x) = cos x

3. cos (x⁴) = f(g(x))

Let g(x) = x⁴

f(g(x)) = cos (g(x))

Substitute x in place of g(x),

f(x) = cos (x)

Hence each of the functions is found from the composition of functions.

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1. To compute the probability that we have picked exactly n cards, we need to consider the number of ways to pick n cards out of 52 such that all 4 shades are represented, and divide that by the total number of possible n-card combinations from the deck of 52.

The number of ways to pick n cards such that all 4 shades are represented is given by the number of combinations of n items taken 4 at a time, with repetition allowed (denoted as C(n-1,3) or C(n+3-1,n)). This is because there are 4 shades, and we need to pick one card from each shade.

The total number of possible n-card combinations from the deck of 52 is given by C (52, n).

Therefore, the probability that we have picked exactly n cards is given by:

P(n) = C(n-1,3) / C(52, n)

2. To verify that the probability sums up to 1, we need to take the summation over all possible values of n, from n=4 to n=52:

P = sum(P(n)) from n=4 to n=52

If P is equal to 1, then the probability of picking exactly n cards over all possible values of n adds up to 1, which means that the event of picking all 4 shades is certain to occur at some point.

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The function is differentiable at these two x-values, the x-values at which the function is differentiable is (-1, 1/3).

The x-values at which the function is differentiable can be found by taking of the function and setting it equal to 0. The derivative of the function y = x3 + 2x2 - 5x + 8 is 3x2 + 4x - 5. Setting this equal to 0 and solving for x yields x = -1 and x = 1/3. So, the x-values at which the function is differentiable is (-1, 1/3).

In order to find the derivative of the function, the power rule was used. The power rule states that the derivative of a function f(x) = xn is f'(x) = nxn-1. Applying this to the function y = x3 + 2x2 - 5x + 8, the derivative is 3x2 + 4x - 5. Next, setting this equal to 0 and solving for x yields two solutions: x = -1 and x = 1/3. Since the function is differentiable at these two x-values, the x-values at which the function is differentiable is (-1, 1/3).

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The solution of the equation -3(x+7)=7 is x=-7.

How to solve an algebric expression:

An algebraic expression is a mathematical phrase that contains numbers and/or variables. Though it cannot be solved because it does not contain an equals sign (=), it can be simplified. You can, however, solve algebraic equations, which contain algebraic expressions separated by an equals sign.

-3(x+7)=0

Now I need to find the value of x by sorting the variables. This expression has an x ​​variable, so find the value of the variable.

The formula is:

-3(x+7) =0

give:

-3(x+7) =0

(divide both sides of the equation by the coefficient of the variable)

x+7=0

(reorder variables on the left side of the expression)

x=-7

The answer is x= -7.

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The direction of vector a1 is found as: Ф = 75° with the x -axis, measured counterclockwise from that axis.

The stated vector is (-7.765,28.978)

Angle made is estimated by the formula:

Ф = tan ⁻¹ (y/x)

In which,

y = 28.978

x = -7.765

Put the given values;

Ф = tan ⁻¹ ( 28.978/-7.765)

Ф = - 74.99

Ф = 75°

So, the direction of the vector a1 is found as: Ф = 75° with the x -axis, measured counterclockwise from that x-axis.

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The complete question is-

let the direction of a vector be the angle that the vector makes with the x -axis, measured counterclockwise from that axis. find the direction of the vector a1 -  (-7.765, 28.978)

The equation of the line is y = -2/3x + 1

From the question, we have the following parameters that can be used in our computation:

The graph

On the graph, we have the following highlights

The graph intersect the y-axis at y = 1

This means that the intercept c is 1

Also, as x changes by 1, the y values changes by -2/3

This mean sthat the slope is -2/3

So, we have

y = mx + c

This gives

y = -2/3x + 1

Hence, the equation is y = -2/3x + 1

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The value of x must be less than 50.

Triangle is a three sided polygon which has three vertices. The three sides are connected with each other end to end at a point which forms the angles of the triangle.

In a triangle, the sum of the lengths of any two sides must be greater than the length of the third side.

Given that the two sides have lengths 5^2 and 5^2, we can write the inequality:

x < 5^2 + 5^2

Now, we can evaluate the expressions 5^2 and 5^2:

5^2 = 25

So, x < 25 + 25 = 50.

Therefore, the value of x must be less than 50.

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Answer:30

Step-by-step explanation:

64-4=60

60/2 = 30

The value of the variable x is 72 degrees

A supplementary angle is simply defined as a  pair of angles that sum up to 180 degrees.

The properties of supplementary angles includes;

From the information given, we have that;

108 degress + x = straight line

But we know that angles on a straight line is 180

Then,

108 + x = 180

collect like terms

x = 180 - 108

subtract the values

x = 72 degrees

Hence, the value is  72 degrees

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Answer:

Step-by-step explanation:

The cost of the labor per hour will be $35.

What is an expression?

Expression in maths is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication, and division.

Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols, which can also be used to indicate the logical syntax's order of operations and other features.

Given that Ella needed to get her computer fixed. She took it to the repair store. The technician at the store worked on the computer for 4 hours and charged her $85 for parts. The total was $225.

The expression will be formed as below to get the value of x.

4x+85 =225

x =35

Therefore, the cost of the labor per hour will be $35.

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The effect of scaling on a hexagon by the scale factor of 6 is discussed above.

In geometry -

Given is a model of the hexagon that is made by using a scale factor of 6.

If the initial length is equivalent to {a}. Then, after the scaling by the scale factor of {K}, the length becomes {Ka}. So, we can write the perimeter of the hexagon, before and after the scaling as -

P{i} = P{before scaling} = 6 x side = 6a

P{i} = 6a                                                             ... Eq { 1 }

P{f} = P{after scaling} = 6 x 6a = 36a

P{f} = 36a                                                           ... Eq { 2 }

The total of the internal angles of the hexagon will remain 720° only.

Therefore, the effect of scaling on a hexagon by the scale factor of 6 is discussed above.

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The additive inverse of an integer n can be expressed mathematically as Vn e Z+, Im E Z, m < n | m + n = 0, which states that if an integer m exists such that m + n = 0, then m is the additive inverse of n.

The formal statement can be expressed mathematically as:

Vn e Z+, Im E Z, m < n | m + n = 0

This statement translates to: Given an integer n, if there exists an integer m such that m + n = 0, then m is the additive inverse of n.

To understand this statement more clearly, we can use an example. Let's say n = 5. This means that we are looking for an integer m such that m + 5 = 0. In this case, m = -5, which is the additive inverse of 5. We can also calculate this mathematically. We know that m + n = 0, so we can rearrange and solve for m: m = -n. Therefore, the additive inverse of n is -n.

In summary, given an integer n, the additive inverse of n is -n. This can be expressed mathematically using the statement Vn e Z+, Im E Z, m < n | m + n = 0.

The additive inverse of an integer n can be expressed mathematically as Vn e Z+, Im E Z, m < n | m + n = 0, which states that if an integer m exists such that m + n = 0, then m is the additive inverse of n.

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The simple interest is given as SI = $ 9.90

Simple interest is a method of calculating interest that ignores the impact of compounding. While interest frequently compounds throughout the course of a loan's set periods, simple interest does not. Simple interest is calculated by multiplying the principal amount by the interest rate, times the number of periods.

Simple Interest = ( Principal Amount x Rate x Time Period ) / 100

Given data ,

Let the simple interest be represented as S

Now , the equation will be

The principal amount be P = $ 300

The rate of interest R = 6.6 %

The number of months T = 6 months = 1/2 year

So , the simple interest S = PRT / 100

Substituting the values in the equation , we get

S = ( 300 x 6.6 x 0.5 ) / 100

On simplifying the equation , we get

S = 3 x 6.6 x 0.5

S = $ 9.90

Hence , the simple interest is $ 9.90

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The value of x is 94/13 approximately equal to 7.23.

An equation is the statement of two expressions located on two sides connected with an equal to sign. The two sides of an equation is usually called as left hand side and right hand side.

Line segment described in the question is given below.

Given that,

Length of XY = 7x

Length of YZ = 6x - 11

Length of XZ = 83

We have the equation,

XY + YZ = XZ

7x + 6x - 11 = 83

13x = 83 + 11

13x = 94

x = 94/13 ≈ 7.23

Hence the value of x is 94/13.

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The smaller number is x and the larger number is 17

An algebraic expression in mathematics is an expression which is made up of variables and constants, along with algebraic operations (addition, subtraction, etc.). Expressions are made up of terms.

Given here: One number is 4 more than another. And 3 times the smaller number is equal to twice the larger increased by 5.

Let the smaller number be x then we have

3x=2(x+4)+5

3x-2x=8+5

x=13

Thus the smaller number is x and the larger number is 17

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To find the exact amount of raisins Charlotte will

From the problem, it can be deduced that Charlotte uses all of the almonds, cashews, and peanuts. hence we add the amounts of the nuts

= almonds + cashews + peanuts

= 7/8 + 1 1/2 + 2 3/8

= 19/4

= 4 3/4

hence Charlotte will need 4 3/4 pounds of nuts

The amount remaining for raisings

= 6 pounds of trail mix - total amount of nuts

= 6 pounds - 4 3/4 pounds

= 5/4

= 1 1/4

hence Charlotte will need 1 1/4 pounds of raisins

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complete question

Charlotte is making 6 pounds of trail mix using raisins and 3 different types of nuts. The table shows the amounts of different types of nuts that she has.

Type of Nut Amount (in pounds)

Almonds 7/8

Cashews 1 1/2

Peanuts 2 3/8

Pecans 1 1/4

Walnuts 1 3/4

Charlotte uses all of the almonds, cashews, and peanuts that she has Which of the following explains how she can find the exact amount of raisins she needs?

A Round 7/8 pound to 1 pound, 1 1/2 pounds to 2 pounds, and 2 3/8 pounds to 2 pounds. Then add the rounded almonds and subtract that total from 6 pounds.

B. Add 7/8 pound, 1 1/2 pounds, 2 3/8 pounds, 1 1/4 pounds, and 1 3/4 pounds. Then subtract 6 pounds from that total.

C. Subtract 7/8 pound from 6 pounds, subtract 1 1/2 pounds from 6 pounds, and subtract 2 3/8 pounds from 6 pounds. Then add all three differences.

D. Add 7/8 pound, 1 1/2 pounds, and 2 3/8 pounds. Then subtract that total from 6 pounds.​

The magnitude of the vector is shown by the length of the vector and the angle it makes with the positive x-axis is shown by the direction of the vector.

The magnitude of vector v is 2 and the angle it makes with the positive x-axis is given as θ = 3.

The component form of vector v can be found by using the following formula:

V = ||V|| (cosθi + sinθj)

Therefore, the component form of vector v is given by:

V = 2 (cos3i + sin3j)

We can calculate the components by substituting the values for ||v|| and θ in the above formula.

Therefore, the x component of vector v is given by:

Vx = 2 cos3

Vx = 1.86

The y component of vector v is given by:

Vy = 2 sin3

Vy = 3.42

Therefore, the component form of vector v is given by:

V = 1.86 i + 3.42 j

This can be represented graphically as shown in the figure.

The magnitude of the vector is shown by the length of the vector and the angle it makes with the positive x-axis is shown by the direction of the vector.

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Answer:

x=49

Step-by-step explanation: If we have the equation 2x-45=x+4 we would first subtract x from both sides of the equation giving us x-45=4. We then have to isolate x to do this we add 45 to both sides giving us the answer x=49.

The definite integral represents the area of the region ∫(x²-3x)dx.

The definite integral is the region beneath the curve of y1 = x2 - 3x between its first intersection with y2 = 0 and its subsequent intersection with y2 = 0. The curve looks like this:

In order to find their intersection, we equalize them:

x2 - 3x = 0

x(x - 3) = 0

x = 0 and x = 3.

Thus, the integral is:

∫(x²-3x)dx

The area lies below the x-axis, hence the result will be negative (see graph). I would argue that we should take this integral's absolute value in order to arrive at the correct answer for the region's area as we are asked to calculate it. Just place absolute value indications all around the integral.

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Answer:

348.6 kg

Step-by-step explanation:

(1220 kg / 7 days) x 2 days = 348.6 kg