solve the inequality 4x - 3 ≥ 22

Dilate the figure by a scale factor of 3 with the origin as the center of dilation.

The coordinates of the image are:

A'(9,9) B'(18,18) C'(27,9)

Transformation is the movement of a point from its original location to a new location. Transformation types: Rotate, Translate, Reflect, and Scale.

Expansion is an increase or decrease in the size of a picture. If point

A(x, y) expands from the center of extension located at point O(a, b), then the new point lies at point A'[k(x - a) + a, k(y - b). ) + b].

Triangle:

A triangle is a polygon with three edges and three vertices. It is one of the basic shapes in geometry. A triangle with vertices A, B, and C is called triangle ABC. In Euclidean geometry, three points that are not on the same straight line define a unique triangle and a unique plane at the same time.

Triangle ABC has vertices at A(3, 3), B(6, 6), C(9, 3).

For A(3,3)

A' = (3 ×3 , 3 × 3) = (9,9)

B' = (6 × 3 , 6× 3) = (18,18)

C' = (9× 3 , 3×3) = (27,9)

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The sum of the series (x-y)^2 + x^2 + y^2 is 2x^2 - 2xy + 2y^2.

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

(x-y)^2+x^2+y^2

The expression (x-y)^2 can be expanded as:

(x-y)^2 = x^2 - 2xy + y^2

Adding x^2 and y^2, we get:

(x-y)^2 + x^2 + y^2 = x^2 - 2xy + y^2 + x^2 + y^2

Combining like terms, we can simplify this expression to:

(x-y)^2 + x^2 + y^2 = 2x^2 - 2xy + 2y^2

Therefore, the sum of the series (x-y)^2 + x^2 + y^2 is 2x^2 - 2xy + 2y^2.

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Answer: 68 mph

Step-by-step explanation:

Answer:

distance ≈ 3.2

Step-by-step explanation:

calculate the distance d using the distance formula

d = \(\sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2 }\)

with (x₁, y₁ ) = (3, 1 ) and (x₂, y₂ ) = (6, 2 )

d = \(\sqrt{(6-3)^2+(2-1)^2}\)

   = \(\sqrt{3^2+1^2}\)

   = \(\sqrt{9+1}\)

   = \(\sqrt{10}\)

   ≈ 3.2 ( to the nearest tenth )

Answer:

yes 1.57 is a rational number you could write it as 1 & 57/100 or 157/1000

To find the equation of the normal line of the given curve \(y = 2x^2 + 4x - 3\) at the point \((0, -3)\), we need to determine the slope of the tangent line at that point and then find the negative reciprocal of the slope.

The equation of the normal line can then be determined using the point-slope form. The derivative of the curve \(y = 2x^2 + 4x - 3\) gives us the slope of the tangent line. Taking the derivative of the function, we get \(y' = 4x + 4\). Evaluating this derivative at \(x = 0\) (since the point of interest is \((0, -3)\)), we find that the slope of the tangent line is \(m = 4(0) + 4 = 4\).

The slope of the normal line is the negative reciprocal of the slope of the tangent line, which gives us \(m_{\text{normal}} = -\frac{1}{4}\). Using the point-slope form of a line, we can plug in the values of the point \((0, -3)\) and the slope \(-\frac{1}{4}\) to obtain the equation of the normal line.

Using the point-slope form \(y - y_1 = m(x - x_1)\) and substituting \(x_1 = 0\), \(y_1 = -3\), and \(m = -\frac{1}{4}\), we can simplify the equation to \(y - (-3) = -\frac{1}{4}(x - 0)\), which simplifies further to \(y + 3 = -\frac{1}{4}x\).

Rearranging the equation, we get \(4y = -x - 12\), which is equivalent to the equation \(x + 4y = -12\). Therefore, the correct answer is B. \(4y = -x - 12\).

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An employee who is looking for a job that offers variety and change would find contract work an incentive to work for an employer. So, correct option is A.

This is because a contract job offers a fixed duration of work with a specific project, and upon completion of the project, the employee is free to move on to another job or contract.

For employees who enjoy variety in their work or want to gain experience in different industries or projects, contract work can be a great option.

Contract work can also be beneficial for those who want flexibility in their work schedule or location, as many contracts can be performed remotely or have more flexible hours. Therefore, for an employee who values variety, change, and flexibility, contract work can be an incentive to work for an employer.

So, correct option is A.

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The z-score is greater in the case of Amber than in Roger so Amber had a better year relative to their peers.

First for Roger:

We have

Mean, μ = 4.371

Standard deviation, s = 0.787

so z-score for X = 3.14 will be

z = (X-μ)/s = (3.14 - 4.371)/0.787

or z = -1.564

Now In the case of Amber:

We have

μ = 4.363

s = 0.869

X = 3.38

so z = (X-μ)/s =  (3.38 - 4.363)/0.869

or z = -1.131

Therefore, The z-score is greater in the case of Amber than Roger so Amber had a better year relative to their peers.

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Answer:

3.3 or 10/3 or 3  1/3

Step-by-step explanation:

hope this helps

Answer:

\(x = \frac{10}{3}\)  

I hope this helps!

Ans6,2

Step-by-step explanation:

Answer:

its literally 2

Step-by-step explanation:

r = annual interest rate

F = final value (amount owed including interest)

P = principal (initial amount borrowed)

n = number of years the loan is taken out for

Plugging in the given values:

r = (1300 - 1200) / 1200 * 2

r = 0.15 or 15%

This formula also gives the same result, that the annual simple interest rate on Zhen's loan is 15%.

Answer:

Step-by-step explanation:

They are diffrent values

Answer:

Step-by-step explanation:

2

Answer:

4x+y=-4

Step-by-step explanation:

gradient(m)=y2-y1/x2-x1

the line also passes through points (x,y) and (-2,4)

-4=4-y/-2-x

cross multiplying

8+4x=4-y

option(A):4x+y=-4

is your answer.

Answer:

10.9 pounds

Step-by-step explanation:

50 ÷ (2.3*2) = 10.869

Since, 13 is not less than 13. Therefore, x = 5 is not a solution to the inequality 13 < 2x+3.

To determine whether a value of x is a solution to the inequality 13 < 2x+3, we need to substitute the value of x into the inequality and see if it is true or false.

Let's try x = 5. Then: 13 < 2x+3

13 < 2(5)+3

13 < 10+3

13 < 13

This is not true, since 13 is not less than 13. Therefore, x = 5 is not a solution to the inequality 13 < 2x+3.

Note that if we had found 13 < 13 instead, then we would have concluded that x = 5 is not a solution to the inequality. But since the inequality is strict (i.e., "less than"), we need to have a strict inequality when we substitute the value of x to determine whether it is a solution.

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A brute-force approach to evaluate a polynomial of degree n involves directly substituting x into each term. The time complexity is O(n), increasing linearly with the degree.

A brute-force approach to evaluating a polynomial p(x) of degree n involves substituting the value of x into each term of the polynomial and summing them to obtain the final result. This method calculates the polynomial value directly based on its definition, without using any optimization techniques.

The time complexity of this approach is O(n), where n is the degree of the polynomial. Since we need to evaluate each term individually, the number of operations increases linearly with the degree of the polynomial. As a result, the time complexity grows proportionally with the degree of the polynomial.

For example, if the polynomial is of degree 3, evaluating p(x) using the brute-force approach requires three multiplications and two additions. Similarly, for a polynomial of degree 5, it would require five multiplications and four additions. Thus, the time complexity increases linearly with the degree of the polynomial.

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Answer:

The 2nd one

Step-by-step explanation:

Answer: this is realy unclear but ill try my best man 1st,bot C . 2nd,bot A . 3rd,bot D, last or 4th, bot c

Step-by-step explanation:

the highest number is 38 clicks in 4.5 seconds so ill try to multiply or do more math to get the answer 0.5 x 9 adds up to 4.5 so ill do 4 x 9 is 36

2x2.25 gets you 4.5 seconds so 2.25 x 15 = 33.75 and bot b i dont even wanna do that math so 1st goes to bot c 2nd goes to bot A 3rd goes to bot d and last goes to bot b

Answer:

A. All men

Explanation

The probability of all men = 0.4219 while the probability of 2 women and 1 man = 0.14

The question says we have three times as much men as women

The probability it is a man that was chosen = 3/4

The probability of choosing a woman = 1/4

a. The probability that the chosen persons are all men = (3/4)³

= 0.4219

b. The probability of 2 women and 1 man

3 * 0.75 *0.25²

= 0.14

Hence the probabilities are  a. 0.4219 and b.  0.14

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Answer:

Step-by-step explanation:

a). Lines of symmetry of the circle given in the picture are,

   x = 0

   y = 0

   y = -x

   y = x

b). Since, a circle has infinite lines of symmetry (diameters) so the other lines of symmetry of the given circle will be all infinite numbers of the diameters.

c). Other symmetry this circle has a point symmetry.

  (Looks the same when rotated by 180°).

The required solution of the system of equations are x=-6 and y=-10.

An equation is a mathematical statement that is made up of two expressions connected by an equal sign. Equation, statement of equality between two expressions consisting of variables and/or numbers.

Given:

The system of equations are

-2x+2y=-8 and -3x+y=8

According to given question we have

Consider the first equation.

-2x+2y=-8

Taking  minus sign common  from both sides we get

-(2x-2y)=-8

2x-2y=8

Taking  2 common  from left sides,  we get

2(x-y)=8

Divide by 2 on both sides we get,

x-y= 4....(i)

-3x+y=8...(ii)

By adding 2 equation we get

-2x=12

x=-6

Put the value of x in Equation (i) we get

x-y= 4

-6-y=4

-y=4+6

y=-10

Therefore, the required solution of the system of equations are x=-6 and y=-10.

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Answer:

7.d

8.c

Step-by-step explanation:

I looked it up to make sure! Hope this helped!

The difference quotient of f(x) is \(\frac{-\frac{1}{h}+ 5}{5x+ h -12}\) .

According to the given question.

We have a function

f(x) = -1/(5x -12)

As we know that, the difference quotient is a measure of the average rate of change of the function over and interval.

The difference quotient formula of the function y = f(x) is

[f(x + h) - f(x)]/h

Where,

f(x + h) is obtained by replacing x by x + h in f(x)

f(x) is a actual function.

Therefore, the difference quotient formual for the given function f(x)

= [f(x + h) - f(x)]/h

= \(\frac{\frac{-1}{5(x+h)-12} -\frac{-1}{5x-12} }{h}\)

= \(\frac{\frac{-1}{5x + 5h -12}+\frac{1}{5x-12} }{h}\)

= \(\frac{\frac{-1+5h}{5x + 5h-12} }{h}\)

= \(\frac{-1+5h}{(5x +h-12)(h)}\)

= \(\frac{-1+5h}{5xh + h^{2} -12h}\)

= \(\frac{h(-\frac{1}{h}+5) }{h(5x+h-12)}\)

= \(\frac{-\frac{1}{h}+ 5}{5x+ h -12}\)

Hence, the difference quotient of f(x) is \(\frac{-\frac{1}{h}+ 5}{5x+ h -12}\) .

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When searching for the value 10 in the array [2, 3, 5, 6, 9, 13, 16, 19], a recursive binary search algorithm will return false since the element is not found in the array.

About Binary Search Algorithm

The binary search algorithm, applied on arrays are of recursive type. The broad strategy is to look at the middle item on the list. The procedure of the binary search algorithm is either terminated (key found), the left half of the list is searched recursively, or the right half of the list is searched recursively, depending on the value of the middle element.

The function carrying out the binary search algorithm in a code returns true if the desired element is found in the array, else returns false. Since the element 10 is not present in the given array: [2, 3, 5, 6, 9, 13, 16, 19], the binary search algorithm will return false.

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The formula or equation used to determine the slope of a straight line is as follows:

m = (Y₂-Y₁)/(X₂-X₁)

An equation is about two expressions, either arithmetic or algebraic, that are related with a "=" sign that indicates equality of expressions.

Equations can be graphed, they are used to model many problems and theories.

The straight lines are characterized by a finite succession of points, when they have an inclination they adopt a slope value different from 0, and to determine that slope it is necessary to know two points of the line and use the following equation:

m = (Y₂-Y₁)/(X₂-X₁)

Where the points are:

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Answer:

Step-by-step explanation:

y =  3x - 4

x = 0,  y = 3*0 - 4

          y = -4

(0 , -4)

x = 1 ,    y = 3*1 - 4

            y = 3 - 4

            y = -1

(1 , -1)

x = 2  , y = 3*2 - 4

           y = 6 - 4

           y = 2

(2 , 2)

Now mark these points (0 , -4) , (1 , -1) & (2 , 2) in the graph and join the points

Answer:

the x-coordinate and y-coordinate change places.

Step-by-step explanation: so you reflect a point across the line y = x, the x-coordinate and y-coordinate change places. If you reflect over the line y = -x, the x-coordinate and y-coordinate change places and are negated (the signs are changed). the line y = x is the point (y, x). the line y = -x is the point (-y, -x).

Answer:

after working for at least 10 1/4 years

Step-by-step explanation:

After working for at least  10 1/4 years  a project manager would be eligible for a $20,000 monthly salary.

A quadratic equation, \(ax^{2} +bx+c=0\) is solved by

\(x=\frac{-b \pm \sqrt{b^2-4ac} }{2}\)

Given function \(f(x)=x^4-10x^2+10000\)

Function that has monthly salary $20,000 will be \(x^4-10x^2+10000=20000\)

\(x^4-10x^2+10000-20000=0\)

\(x^4-10x^2-10000=0\)

Now using the formula \(x=\frac{-b \pm \sqrt{b^2-4ac} }{2}\)

\(x^2=\frac{10 \pm \sqrt{10^2+40000} }{2}\)

\(x^2=\frac{10 \pm \sqrt{40100} }{2}\)

\(x^2=\frac{10 \pm 200.2}{2}\)

\(x^2=5 \pm 100.1\)

\(x^2=105.1\)

\(x=\sqrt{105.1}\)

\(x=10.25\)

Hence, after working for at least  10 1/4 years  a project manager would be eligible for a $20,000 monthly salary.

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Answer:

Please double check what you've written

Step-by-step explanation:

Probability is, by definition, a number between 0 and 1, which can be expressed as a fraction or a percentage. For example, the odds of getting heads if you throw a fair coin are 50%, or ½. The odds of not getting heads are 1-½=½.

If the probability of something happening is 1, it means that that thing will happen for sure. Likewise, if the probability of an event is 0, it means that the event will never happen.

You can therefore easily understand that it doesn't make sense to have a probability greater than 1, I would thus advise you to read the question more carefully.

The answer is 3/10 , Option D

Probability is the branch of mathematics concerning numerical descriptions of how likely an event is to occur.

The probability of an event is a number between 0 and 1, where, roughly speaking, 0 indicates impossibility of the event and 1 indicates certainty.

Probability Formula = f/n

where,

f is the number of times an event occurs

n is the total number of trials

Odds are a/b ;

probability is a/(a+b)

The odds of event happening is 7/3

Probability is 7/(7+3)=0.7 of the event happening.

So the probability of it not happening is 1–0.7= 0.3.

probability of it not happening is 3/10

Therefore Option D is the correct answer.

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