What are the coordinates of the vertices of the image after a 90-degree counter-clockwise rotation about the origin?

-7 = extraneous solution

The equation is

[tex]\sqrt{-3x - 5}[/tex] = x + 3

To find the value of x we need to square both sides of the equation

[tex](\sqrt{-3x - 5})^{2}[/tex] = [tex](x + 3)^{2}[/tex]

- 3x -5 = [tex]x^{2}[/tex] + 6x + 9

[tex]x^{2}[/tex] + 9x + 14 = 0

[tex]x^{2}[/tex] + 7x + 2x + 14 =0

x( x + 7) + 2( x + 7) = 0

(x + 7) (x + 2 ) = 0

x = -2, -7

To find the extraneous solution we have to put both the value of x in the equation.

x=-2

[tex]\sqrt{(-3 * -2) - 5}[/tex] = -2 +3

[tex]\sqrt{1}[/tex] = 1

1 = 1

x = -7

[tex]\sqrt{(-3 * -7) - 5}[/tex] = -7 +3

[tex]\sqrt{16}[/tex] = -4

4 = -4

The extraneous solution of the equation is -7 and -2 is the solution of the equation

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Answer:

Step-by-step explanation:

Answer:

This is more than Juan

Step-by-step explanation:

Answer:

D Maxwell drove further. He drove 18 miles.

Step-by-step explanation:

Distance = Speed × Time

Maxwell:

Distance = 45 × 0.4

Distance = 18 miles

Bianca:

Distance = 65 ×0.25

Distance = 16.25 miles

18 > 16.25

Maxwell drove further. He drove 18 miles.

Answer:

D. Maxwell. He drove 18 miles,

Step-by-step explanation:

Distance = speed * time

Maxwell drives:

45 * 0.4 = 18 miles.

Bianca drove:

65 * 0.25 = 16.25 miles.

Answer:

[tex]\frac{1}{2}[/tex]

Step-by-step explanation:

[tex]\frac{d}{dx}\left(\frac{x}{2}-\frac{1}{3}\right)[/tex]

= [tex]\frac{d}{dx}\left(\frac{x}{2}\right)-\frac{d}{dx}\left(\frac{1}{3}\right)[/tex]

=[tex]\frac{1}{2}\frac{d}{dx}\left(x\right) - 0[/tex]

= [tex]\frac{1}{2} - 0[/tex]

= [tex]\frac{1}{2}[/tex]

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Answer: the answer is no solution

Step-by-step explanation:

Answer:

No Solution

Step-by-step explanation:

An absolute value will always have a positive value. If you isolate the absolute value it shows the abs val LESS THAN a negative number. Its not possible to have a positive less than a negative.

If you just go on and do the problem in auto-pilot, the answers don't check. ALSO since it it a LESS THAN inequality statement BOTH of the inequalities have to be true at the same time which is not possible.

See image.

We need to know about natural exponential function to solve the problem. The given function is a natural base exponential function.

An exponential function is a function in which x is an exponent. An exponential function has an exponential graph that keeps growing. A natural base exponential function is one where the base of the function is e which is a mathematical constant and is approximately equal to 2.71828. The inverse of a natural exponential function is a logarithmic function. An exponential function is of the form y=[tex]b^{x}[/tex] where b is the base, in a natural base exponential function, the b is replaced by e which means y=[tex]e^{x}[/tex]. In the given question y=[tex]e^{x+7}[/tex] is a natural base exponential function since the base is the natural base.

Therefore we found that the given function is a natural base exponential function.

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The polynomial function is [tex]x^{2}-x-2ix+\sqrt{7}x-\sqrt{7}-2\sqrt{7}i[/tex]

In mathematics, polynomial function can be defined as the equation which consist of coefficient, variables and exponents. A polynomial equation has positive numbers as their exponent which is also known as its degree. All the equations such as quadratic equation, cubic equation which has non  negative number as their powers are part of polynomial equation.

Types of polynomial equations :

Some examples of polynomial equation are :

According to question,

roots are -√7 , 1+2i

Thus the factors are :

(x - (-√7)) (x-(1+2i))

=> (x+√7)(x-1-2i)

=>x²-x-2ix+√7x-√7-√7.2i

Thus polynomial function for given roots is x²-x-2ix+√7x-√7-√7.2i.

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Answer:

-3x^{4}+2x^{3}+4x^{2}

Step-by-step explanation:

Re-order terms so constants are on the left

-x^{2}\left( 3x^{2}-2x-4\right)

-x^{2}\left( 3x^{2}-2x-4\right)

2

Distribute

-\textcolor{#C58AF9}{x^{2}\left( 3x^{2}-2x-4\right) }

-\left( \textcolor{#C58AF9}{3x^{4}-2x^{3}-4x^{2}}\right)

3

Distribute

-\left( 3x^{4}-2x^{3}-4x^{2}\right)

-3x^{4}+2x^{3}+4x^{2}

The nature of the roots in the given quadratic equation (x - 3)² + (x - 4)² = 0 is; A: two rational roots

We are given the quadratic equation;

(x - 3)² + (x - 4)² = 0

Now, some of the rules in naming the roots are;

If b² – 4ac > 0, then the roots are real and unequal

If b² – 4ac = 0, then the roots are real and equal

If b² – 4ac < 0 then the roots are unequal and Imaginary

If b² – 4ac > 0 (is a perfect square), then the roots are real, rational and unequal

If b² – 4ac > 0 (is not a perfect square), then the roots are real, irrational and unequal

From the above rules and comparing to our given equations, it is clear that we have two rational roots which are x = 3 and x = 4.

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You can let the sides be a and b. You can then use the Law of Sines to create an equation relating the two sides and the angles opposite them, and finally isolate a/b.

Answer:

m is always the number in front of x

y=mx+c

so m=-3

Step-by-step explanation:

The domain of the function is: [-1, 10]

And the range of the function is: [-1,0,1,2,3,4,5,6,7,8,,9,10]

According to the question, the intervals can be defined by a common difference of one value.

Therefore, the domain of the function is: [-1, 10]

And the range of the function is: [-1,0,1,2,3,4,5,6,7,8,,9,10]

What is domain and range in the function?

The domain of a function can be defined as the complete set of all the possible values for the dependent variables. Similarly, the range of the function can be expressed as the set of all the values which can be assumed by the expression of the function.

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Answer:

Step-by-step explanation:oooooooooooooooooooooooooooooooooooooo

o

Answer:

1)3√5

2)5√5

3)3√5

Answer:

23/30

Step-by-step explanation:

4/15= 8/30

1/2= 15/30

8/30+15/30= 23/30

No extraneous solution to the equation.

The equation is:

3[tex]\sqrt{2x}[/tex] - 3= 9

To know whether the equation has an extraneous solution, first we need to find the value of x.

[tex]3\sqrt{2x}[/tex] = 12

[tex]\sqrt{2x}[/tex] = 4

2x = 16

x = 8

Now put the value of x in the equation.

3[tex]\sqrt{2 * 8}[/tex] - 3 = 9

3× 4 - 3 = 9

12 - 3= 9

9 = 9

Therefore there is no extraneous solution to the equation, x = 8 is the solution of the equation.

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Answer:

Brainliest pls

Step-by-step explanation:

-20

Answer:

The answer is -20.

Step-by-step explanation:

REMEMBER THIS:

Please excuse my dear aunt sally…

PLEASE = PARENTHESIS

EXCUSE= EQUATION

MY = MULTIPLICATION

DEAR = DIVISION

AUNT = ADDITION

SALLY = SUBTRACTION

^In that order^

Remember to use this statement to remember how to simplify the expression. PEMDAS.

The cost of the Ginnie's dinner is a $40 and the cost of his cousin's dinner is $25.

According to the statement

We have to find that the cost of their dinners.

So, For this purpose, we all know that the

The cost function may be wont to find the common cost, which is that the average amount of cash it costs to provide a unit.

From the given information:

Ginnie dinner cost $15 over her cousin's. If their combined bill was under $65.

Then

Let Ginnie dinner is x and his cousin's be y.

Then

x+y = 65 And x = y+15

Then

Substitute the values then y+15+y = 652

y+15 = 652

y = 65-152

y = 50

[tex]y = \frac{50}{2}[/tex]

y = 25.

Then x = y+15

x = 25+15

x = 40.

So, The cost of the Ginnie's dinner is a $40 and the cost of his cousin's dinner is $25.

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After solving the equation ln 3x =6, the value of x is equal to [tex]\frac{e^6}{3}[/tex]

We have been asked to find x in ln 3 x=6

⇒ ln 3 x = 6

⇒ 3x = [tex]e^6[/tex]

⇒ x = [tex]\frac{e^6}{3}[/tex]

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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The divide and simplify of the equation √36 x⁴ / √9 x⁶ will result to  [tex]\frac{2}{x^{2} }[/tex]

Let's begin by simplifying the equation;

Simplify the equation by finding the square root of both 36 and 9

The square root of 36= 6

The square root of 9= 3

= [tex]\frac{6x^{4} }{3x^{6} }[/tex]

The above equation can also be written as;

=  [tex]6x^{4} * 3x^{-6}[/tex]

The next step is to solve the powers, that is,

=   [tex]\frac{6x^{4} }{3x^{6} }[/tex]

Cancel out 6 by 3 and get  2

The result is,  

=  [tex]\frac{2}{x^{6-4} }[/tex]

The final submission result is,

=  [tex]\frac{2}{x^{2} }[/tex]

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Answer:

B

Step-by-step explanation:

6x - 8x - 4 = - 2x - 2 , that is

- 2x - 4 = - 2x - 2 ( add 4 to both sides )

- 2x = - 2x + 2 ( add 2x to both sides )

0 = 2 ← not possible

this indicates the equation has no solution

Answer:

6x-8x-4=-2x-2 (group the like terms)

6x-8x+2x= 4-2 (-8x+2x= -6x and 6x-6x=0) (4-2=2)

answer= 0=2

,therefore: it has no solution

Step-by-step explanation:

the answer is 0=2 which mean there is nothing that 2 is equivalent to because when you group the like terms and work out the answer the x in the equation will be canceled.

Answer:

10.083333...ft

Step-by-step explanation:

length = 12ft

area = 121sqft

area = length * width

121sqft = 12ft * width

width = 121sqft / 12ft

[tex]width = 10\frac{1}{12}\mathrm{ft}[/tex]

width = 10.08(3)ft

Answer:

kevin ate 1/6 more than Kathy or un simplified, 2/12

Step-by-step explanation:

least common denominator

Answer: 59 eggs

Step-by-step explanation: Dividing 3 will get you 19 eggs with 2 left over.  Dividing 59 by 5 will get you 11 eggs and 4 left over

Answer: 10 answers correct and 10 answers incorrect

Step-by-step explanation:

60 is the highest total assuming every one was correct

20 is the lowest total assuming every one was incorrect

40 is the middle meaning he got half write half wrong

Half of 20 is (10) (10 x 3 = 30 ) + ( 10 x 1 = 10 ) 30 + 10 = 40

Answer: 13.3 repeating is what I got see if it make sense according to my work

Step-by-step explanation: 20x3=60, and one mark per wrong answer, so 60-40=20 wrong. So, 40 divided by 3=13.3 repeating