Consider the slope field shown: (a) For the solution that satisfies y(0) 0,sketch the solution curve and estimate the following: y(I) ~ 0.75 and y(-1) 0.5 (b) For the solution that satisfies Y(O) = 4, sketch the solution curve and estimate the following: Y(0.5) -0.5 and Y(-1) 0.75 (c) For the solution that satisfies Y(O) = -1, sketch the solution curve and estimate the following: Y(I) ~ and y(-1) ~

The values of the variables namely x, y and z of the given triangle are;

x = 12, y = 9√13, z = 6√13

There are three sides of a right angle triangle namely; Opposite, Adjacent and Hypotenuse.

The formula for Pythagoras theorem is;

Hypotenuse² = Opposite² + Adjacent²

Thus;

y² = 27² + 18²

y = √(27² + 18²)

y = √1053

y = 9√13

Using concept of similar triangles, we can say that;

x/18 = 18/27

x = (18 * 18)/27

x = 12

Using Pythagoras theorem again;

z = √(12² + 18²)

z = √468

z = 6√13

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The polynomial X3-8 has a degree of 3 and 2 terms

Algebraic expressions are defined as mathematical expressions comprising of variables, coefficients, terms, constants and factors.

These algebraic expression are also comprised of arithmetic operations, such as;

Polynomials are also described as algebraic expressions composed of arithmetic operations and also non-negative integer exponentiation of variables.

Given the polynomial, the number of terms is 2

Hence, the number of terms is 2 and the degree is 3

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The function f(x) = 9 - x² is a one to one function and the value of f⁻¹(x) = √9 - x.

The graph of the function is attached below.

In math the term graph is defined as a pictorial representation or a diagram that represents data or values in an organized manner.

Here we have the function f(x) = 9 - x² and here we also know that on the interval 0≤x≤3 and a=8.

Now, we have to check the given function is one to one or not, for that we have to plot the function on the graph then we get the graph like the following.

While we looking into the graph we have identified that each input value has exactly only one output, therefore it is said to be one to one function.

And the inverse of the function is calculated by rewritten the function as,

=>  f⁻¹(x) = √9 - x.

And the graph of f⁻¹(x) is plotted as follows,

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Applying Pythagoras theorem, and drawing free body diagram we can measure the moments required.

First of all draw the free body diagram.

Now, in triangle AOC, apply Pythagoras theorem,

Now, write the coordinates of the points,

O (0, 0, 0) m

A (0, 15, 20) m

C (0, 0, 20) m

B (2.5, 0, 20) m

Now, write the position vector from A to B,

Now, write the unit vector rAB

Now, write the tensional force on the point A due to the cable AB,

Now, calculate the force ‘T’ about the origin,

Hence the moments about the coordinate axes are,

Mx = 78.9 kN.m

Mx = 13.15 kN.m

Mx = -9.86 kN.m

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The solution to the equations is x = 20/3 and y = -8

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

3x + 2y=4

3x + 6y=-28

The above equations is a system of linear equations

So, we can subtract them to eliminate x as follows

4y = -32

Divide both sides by 4

y = -8

Substitute y = -8 in the equation 3x + 2y=4

3x - 16 =4

Evaluate the like terms

3x = 20

So we have

x = 20/3

Hence, the soluton is x = 20/3 and y = -8

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Answer:

10 cm

Step-by-step explanation:

Original measures: 400 m and 200 m

Scale: 1 cm = 40 m

Use proportions.

Length:

1 cm / 40 m = x / 400 m

40 m × x = 400 m × 1 cm

40x = 400 cm

x = 10 cm

length = 10 cm

Answer: 10 cm

The set |x| < 7 using interval notation is given as follows:

0. < x < 7.

The absolute value of a number gives the distance of a number from the origin, hence it basically can be interpreted as the number without the signal.

The expression for this problem is defined as follows:

|x| < 7.

Then the bounds of the open interval are given as follows:

The lowest absolute value is given as follows:

0.

Hence the interval is given as follows:

0 < x < 7.

The problem asks for the interval notation of:

|x| < 7.

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The domain of the relationship for this problem is given as follows:

Real values of x and y, except y ≠ 0 and x ≠ y.

The domain of a relationship is composed by the set of all possible input values assumed by the relationship.

The relationship for this problem is given as follows:

(4x - 4y)/(2xy + 2y²).

It is a fraction, hence the restriction is that the denominator cannot be zero.

Then the domain is obtained as follows:

2xy + 2y² ≠ 0.

2y(x + y) ≠ 0.

Hence the restrictions are given as follows:

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Answer:

60

Step-by-step explanation:

54/90% =60

Answer:

Step-by-step explanation:

[tex]-48 - r = -39[/tex]

[tex]-48+-r=-39[/tex]

[tex]-r-48=-39[/tex]

[tex]-r-48+48=-39+48[/tex]

[tex]-r=9[/tex]

[tex]\cfrac{-r}{-1}=\cfrac{9}{-1}[/tex]

[tex]r=-9[/tex]

You have a 39.6% chance of winning according to the binomial distribution, it has been discovered.

Only two outcomes are conceivable for each trial. You either succeed or fail in hitting the target. The binomial distribution is used to answer this question because the likelihood that a target will be struck on any given trial is independent of all other trials.

It is determined by the number of unique combinations of x objects from a set of n elements and the likelihood of striking the objective, which is 63%, and is expressed as the probability of exactly x successes on n repeated trials with p probability.

hence, two throws

The likelihood is P(X = 2) since you must strike it twice to win.

0.396 = 39.6%

The complete question is,

Considering the circumstances, what is your likelihood of success: A plush animal is what you're attempting to win. To succeed, a target must be hit twice straight. It is 63% likely that you will succeed on your first attempt.

O 23.3% \sO 63%

O 106% \sO 39.6%.

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​

The indicated function values for f(x) = 8x + 4 if x is:

(a) f(-4) = -13,     (b) f(2) = 22

(c) f(0) = 8,        (d) f (-100) + f(100) = 215

What is meant by function ?

A function is an equation with just one solution for every value of y in the equation. A function pairs each input of a particular type with exactly one output. Instead of y, it is typical to name functions f(x) or g(x).

We must look at the value of x to determine which equation to take into account. In the first equation, we will substitute x if it is negative; in the second equation, we will substitute x if it is positive or null.

(a) x = -4 so x is negative.

We use the first equation f(x) = 5x + 7 and we have f(-4) = 5 × (-4) + 7 = -13

(b) x = 2 and is positive.

We use the second equation f(x) = 7x + 8.

The result is f(2) =7 × (2) + 8 = 22

(c) x = 0 In this case the function is defined by the second equation f(x) = 7x + 8. So f(0) =7 × (0) + 8 = 8

(d) We need to calculate the function values of each one and then make the sum.

With f(-100), x = -100 and is negative

We use the first equation f(x) = 5x + 7 and

we have f(-100) = 5 × (-100) + 7 = -493.

With f(00), x = 100 is positive so we use the second equation f(x) = 7x + 8 and get f(100) = 7 × 100 + 8 = 708

We add them to get the result: f(-100) + f(100) = -493 + 708 = 215

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The complete question is:

The function below is defined by two equations. The equation in the first row gives the output for negative numbers in the domain. The equation in the second row gives the output for​ non-negative numbers in the domain. Find the indicated function values.

f (x) = { 5x+7 if x < 0

{ 7x+8 if x ≥ 0

(a) f (- 4)

(b) f (2)

(c) f (0)

(d) f (-100) + f(100)

Probability of getting a marble is 0.3.

Probability is a branch of math which deals with finding out the likelihood of the occurrence of an event. measures the chance of an event happening and is equal to the number of favorable events divided by the total number of events. The value of probability ranges between 0 and 1, where 0 denotes uncertainty and 1 denotes certainty.

Two boxes Probability of selecting either of the box = 0.5

Box A contains: 3 blue and 2 red marbles. So, probability of selecting blue marbles,

let p(B1) = [3C1/5C1 ]= 0.6*0.5 = 0.3 (As Probability of selecting box 1 is 50:50 )

Box contains : 3 blue and 5 red marbles,

let p(B2) = [3C2/5C2] = 0.6*0.5 = 0.3 ( As the probability of selecting box 2 is also 50:50 )

So, the final probability of getting a blue ball is 0.3.

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Probability of getting a marble is 0.3.

Probability is a branch of math which deals with finding out the likelihood of the occurrence of an event. measures the chance of an event happening and is equal to the number of favorable events divided by the total number of events. The value of probability ranges between 0 and 1, where 0 denotes uncertainty and 1 denotes certainty.

Two boxes Probability of selecting either of the box = 0.5

Box A contains: 3 blue and 2 red marbles. So, probability of selecting blue marbles,

let p(B1) = [3C1/5C1 ]= 0.6*0.5 = 0.3 (As Probability of selecting box 1 is 50:50 )

Box contains : 3 blue and 5 red marbles,

let p(B2) = [3C2/5C2] = 0.6*0.5 = 0.3 ( As the probability of selecting box 2 is also 50:50 )

So, the final probability of getting a blue ball is 0.3.

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median set:130,140,149,150,159.Range set:10,20,149,159.

Step-by-step explanation:

Median:the value of a set that is arranged from lowest to highest and find the number that is right in between.If there are two numbers in the middle,add them and divide➗by two.Range:the difference between the highest and lowest number in a set.For example,the range for the set 10 20,38 and 50 , the highest and lowest numbers are 50 and 10 so we subtract 50-10 (the highest and lowest numbers) and get 40 as our range.

The shaded area is 169.56 inch² for the given set of semicircles with radius 6 inch and 12 inch.

The size of a region on a surface is measured in area. Surface area refers to the area of an open surface or the boundary of a three-dimensional object, whereas area of a plane region or plane area refers to the area of a shape or planar lamina. The total space occupied by a flat (2-D) surface or the shape of an object is defined as its area. Draw a square on a piece of paper with a pencil. It is a two-dimensional figure. The area of the shape on the paper is referred to as its Area. Consider your square to be made up of smaller unit squares.

Here,

area1=1/2*3.14*r²

=0.5*3.14*12²

area2=1/2*3.14*r²

=0.5*3.14*6²

area=area1-area2

=0.5*3.14*12²-0.5*3.14*6²

=169.56 inch²

The shaded area for the given set of semicircles with radius 6 inch and 12 inch is 169.56 inch².

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Answer:

[tex]\textsf{36)} \quad f(x)=\dfrac{7x}{x-12}[/tex]

[tex]\textsf{37)} \quad g(x)=\dfrac{1}{x+2}[/tex]

[tex]\textsf{38)} \quad h(x)=\dfrac{x-2}{(x-2)(x+3)}[/tex]

Step-by-step explanation:

Given that the function has a horizontal asymptote at y = 7, the degree of the numerator must be equal to the degree of the denominator.

Also, 7 will be the result of dividing the highest degree term of the numerator by the highest degree term of the denominator.

Given that the function has a vertical asymptote at x = 12, the denominator must equal zero when x = 12.

Therefore, a rational function that meets these conditions is:

[tex]f(x)=\dfrac{7x}{x-12}[/tex]

Given limits:

[tex]\displaystyle \lim_{x \to\infty} k(x)=0[/tex]

[tex]\displaystyle \lim_{x \to-2^+} k(x)=\infty[/tex]

The first limit means that as x approaches positive infinity, the function equals zero. Therefore, the rational function has a horizontal asymptote at y = 0. So the degree of the numerator should be less than the degree of the denominator.

The second limit means that as x approaches -2 from the positive side, the function equals positive infinity.  Therefore, the rational function has a vertical asymptote at x = -2.

Therefore, a rational function that meets these conditions is:

[tex]g(x)=\dfrac{1}{x+2}[/tex]

A removable discontinuity (hole) exists on the graph of a rational function at any input value that causes both the numerator and denominator of the function to be equal.

Therefore, a rational function that meets these conditions is:

[tex]h(x)=\dfrac{x-2}{(x-2)(x+3)}[/tex]

For this rational function the hole is at (2, ¹/₅), as when x = 2, the numerator and denominator are both zero.

The functions can be represented as y = 7x/(x - 7), y = 1/(x + 2) and y = (x - 3)/[(x - 3)(x + 1)]

Conditions #1

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

Vertical asymptote, x = 12

Horizontal asymptote, y = 7

A function with the following features

Vertical asymptote, x = a

Horizontal asymptote, y = b

Can be represented as

y = bx/x - a

So, we have

y = 7x/(x - 12)

Conditions #2

Here, we have the following limits

lim x⇒∝ k(x) = 0 and lim x⇒2⁺ k(x) = ∝

This means that:

Vertical asymptote, x = -2

Using the rule in (1), we have

y = 1/(x + 2)

Condition #3

Here, we have

Function with a hole

This implies that the denominator and the numerator have a common factor

An instance of this is

y = (x - 3)/[(x - 3)(x + 1)]

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The distance across the pond is 52 feet.

Two or more triangles are said to be congruent if and only if sides and angles of one triangle is equal to the corresponding sides and angles of another triangle.

In the given diagram, there are two triangles.

If we prove the two triangles are congruent, we will get the distance across the pond as 52 feet.

Already 2 sides of one triangle is given as equal to 2 sides of the other triangle, which are 41 ft and 29 ft.

Also since the lines are intersecting the included angles of the equal sides of both triangle are equal by vertical angle theorem.

So two sides and an included angle of a triangle is equal to corresponding two sides and an included angle of other triangle.

So the triangles are congruent by SAS theorem.

So all the sides of two triangles are equal.

Distance across the pond is 52 feet.

Hence we get the distance across the pond is 52 feet.

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The buoyant force is the upward force on an object submerged in a fluid that is caused by the fluid's pressure.

The magnitude of the buoyant force is equal to the weight of the displaced fluid. Therefore, the correct ranking of the three buoyant forces is fx > fy > fz.

The magnitude of the buoyant force can be calculated using the equation Fb = ρgV, where ρ is the density of the fluid, g is the acceleration due to gravity, and V is the volume of the displaced fluid. For orientation x, the buoyant force fx will be the greatest since the volume of the displaced fluid is the greatest. For orientation y, the buoyant force fy will be the second greatest since the volume of the displaced fluid is second greatest. Finally, for orientation z, the buoyant force fz will be the least since the volume of the displaced fluid is the least.

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Answer:

let the price in 2016= Y

Then the price since 2016 ( since the price decreased since 2016)= (1- 27/200)Y= 0.73Y

2016 since 2016

Y 0.73Y

Y now: 4803.40

0.73Y= 4803.40

Y= 4803.40/0.73

= 6580

the cost of the panel in 2016 is 6580

D) Win-win  is a situation in which both parties come away with a positive outcome.

Win-win is a situation in which both parties come away with a positive outcome. It is the ideal solution to a complex conflict, as it ensures that both parties benefit in some way. Win-win solutions involve a collaborative approach to problem solving, where each party works together to find a mutually beneficial solution. This can involve compromise, trade-offs, and creative negotiation.

For example, two companies may be in competition for the same contract. Rather than viewing each other as adversaries, they could work together to create a win-win solution that meets their respective needs. This could involve a collaborative approach to the project, or a mutually beneficial pricing arrangement.

Win-win solutions also require an understanding of each party's needs, interests, and values. It is important to identify the underlying interests that each party has, and use them to create a solution that meets everyone's needs. By taking the time to understand each other's perspectives, it is possible to create a solution that is beneficial to both parties. In this way, win-win solutions provide an opportunity to develop a constructive relationship that can be beneficial in the long term.

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The solution is g(ƒ(-2)) = 9.

What is meant by solution?

{g∘f}(2) = g(f(-2))

g(-2) = -6

ƒ(-6) = 2x - 1

ƒ(-6) = -2(-6) - 1

ƒ(-6) = 13

ƒ(g(2)) = 13

{f∘g(-2) = f(g(-2))

ƒ(2) = 3

g(3) = -3x

g(3) = -3(-3)

g(3) = -9

g(ƒ(-2)) = 9

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The new computer will take to loading a document with 2 graphics and 1 paragraph is 43.99 seconds.

Time taken can be calculated using percentages by determining the percentage of time that has already passed, then calculating the remaining time based on the percentage of time remaining.

For example, if you are asked to calculate the time taken for a project that is 50% complete, you would first need to determine the total length of the project. Let's say it is a project with a timeline of two months.

Next, you would need to calculate the percentage of time that has already passed. In this case, since the project is 50% complete, 50% of the two months has already passed. This means that one month has passed.

Finally, you can determine the time taken by subtracting the time that has already passed from the total length of the project. In this case, the time taken would be one month, since one month has already passed and there is one month remaining until the project is completed.

The old computer would load 2 graphs and one paragraph in:

22 × 2 seconds + 9 seconds = 53 seconds

The new computer is 17% faster so:

53 - (17% × 53) = 43.99 seconds

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The sum of his scores is -10

A summation, also called a sum, is the result of arithmetically adding numbers or quantities. A summation always contains a whole number of terms. There can be as few as two terms, or as many as a hundred, a thousand, or a million. Some summations contain infinitely many terms.

For example, If the value of ages of class is given as 5, 6,7,8,5,6. The sum of of their of ages will be 5+6+7+8+5+6 = 37

The score of jake are -12, 3 ,5 , 2 ,0 and -8. The sum of his scores = -12 + 3 + 5 + 2 + 0 + -8

collecting like terms

-12 + -8 + 3 + 5 + 2 + 0

= -10

Therefore the sum of Jake's score is -10

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The measure of the exterior angle x of the polygon is equal to 76°

The exterior angles of a polygon added together is equal to 360° so;

x + x + 60° + 64° + 36° + 48° = 360°

2x + 208° = 360°

2x = 360° - 208° {subtract 208° from both sides}

2x = 152°

x = 152°/2 {divide through by 2}

x = 76°

Therefore, the measure of the exterior angle x of the polygon is equal to 76°

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Answer:

14

Step-by-step explanation:

I don't know it right now

Answer:

111

Please mark brainliest

Step-by-step explanation:

The measure of the angle ABC and angle CBD are 48 and 42 degrees

As a general rule:

Complementary angles add up to 90 degrees

This means that

we get: ∡ABC + ∡CBD = 90

3x + 6 + 4x - 14 = 90 ------ Substituting 3x + 6 and 4x - 14 for ∡s ABC and CBD

Evaluate the like terms

7x = 98

Divide both sides by 7

x = 14

So, we have

Measure of ∡ABC: 3 * 14 + 6 = 48

Measure of ∡CBD:  4 * 14 - 14 = 42

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Complete question

Find the measure of each angle

angle ABC and angle CBD are complementary angles, m angle ABC=(3x+6)degrees, and m angle CBD=(4x-14)degrees

Answer:

the rate is 30:5

the unit rate is 6:1

Step-by-step explanation:

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