This graph of a function is a translation of y=4/x. What is an equation for the function?

a) The given function is

[tex]f(x)=\frac{x^2-4}{x^4+x^3-4x^2-4}[/tex]

The domain refers to all values of x for which the function is defined.

The function is defined for

[tex]x^4+x^3-4x^2-4\ne0[/tex]

This implies that;

[tex]x\ne -2.69,x\ne 1.83[/tex]

b) The vertical asymptotes are x-values that makes the function undefined.

To find the vertical asymptote, equate the denominator to zero and solve for x.

[tex]x^4+x^3-4x^2-4=0[/tex]

This implies that;

[tex]x= -2.69,x=1.83[/tex]

c) The roots are the x-intercepts of the graph.

To find the roots, we equate the function to zero and solve for x.

[tex]\frac{x^2-4}{x^4+x^3-4x^2-4}=0[/tex]

[tex]\Rightarrow x^2-4=0[/tex]

[tex]x^2=4[/tex]

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

[tex]x=\pm2[/tex]

The roots are [tex]x=-2,x=2[/tex]

d) The y-intercept is where the graph touches the y-axis.

To find the y-inter, we substitute;

[tex]x=0[/tex] into the function

[tex]f(0)=\frac{0^2-4}{0^4+0^3-4(0)^2-4}[/tex]

[tex]f(0)=\frac{-4}{-4}=1[/tex]

e) to find the horizontal asypmtote, we take limit to infinity

[tex]lim_{x\to \infty}\frac{x^2-4}{x^4+x^3-4x^2-4}=0[/tex]

The horizontal asymtote is [tex]y=0[/tex]

f) The greatest common divisor of both the numerator and the denominator is 1.

There is no common factor of the numerator and the denominator which is  at least a linear factor.

Therefore the function has no holes.

g) The given function is a proper rational function.

There is no oblique asymptote.

See attachment for graph.

Answer:

b- 4.6

Step-by-step explanation:

5y = 2.3√x

Let x = 100

5y = 2.3 sqrt(100)

5y = 2.3 (10)

5y = 23

Divide by 5

5y/5 = 23/5

y =4.6

Answer:

see explanation

Step-by-step explanation:

P - Q

= - 4b² + 6b - 9 - ( 7b² - 2b - 5) ← distribute by - 1

= - 4b² + 6b - 9 - 7b² + 2b + 5 ← collect like terms

= - 11b² + 8b - 4

Answer:

[tex]\large\boxed{P-Q=-11b^2+8b-4}[/tex]

Step-by-step explanation:

[tex]P=-4b^2+6b-9\\Q=7b^2-2b-5\\\\P-Q=(-4b^2+6b-9)-(7b^2-2b-5)\\P-Q=-4b^2+6b-9-7b^2-(-2b)-(-5)\\P-Q=-4b^2+6b-9-7b^2+2b+5\qquad\text{combine like terms}\\P-Q=(-4b^2-7b^2)+(6b+2b)+(-9+5)\\P-Q=-11b^2+8b-4[/tex]

Answer:

44 liters

Step-by-step explanation:

It is 44 liters !!!!!

PARALLEL slopes always have the same slope no matter what because they are parallel

Answer:

y = -3.3 then  -7.1

y = -7.1 then  -10.9

y = -2.6 then -6.4

y = 1 then -2.8

y = 4.2 then 0.4

Step-by-step explanation:

(-3.8)+0+y can be simplified to -3.8 + y. Evaluate each value for y by substituting it into the expression and solving.

y = -3.3 then -3.8 + -3.3 = -7.1

y = -7.1 then -3.8 + -7.1 = -10.9

y = -2.6 then -3.8 + -2.6 = -6.4

y = 1 then -3.8 + 1 = -2.8

y = 4.2 then -3.8 + 4.2 = 0.4

To evaluate the expression (-3.8) + 0 + y, substitute the given value of y and perform addition.

To evaluate the expression (-3.8) + 0 + y, you simply substitute the given value of y into the expression and perform the addition. Let's evaluate the expression for each given value of y:

Thus, the values of the expression for the given values of y are:

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3336_____________________________

Answer:

  The money Javier earned installing doors.

Step-by-step explanation:

The problem statement gives insufficient information to answer the question with certainty.

The $56 extra earnings from door installation seems to match the 56 added as a term in Javier's pay, so we assume they are related. There is nothing else in the problem statement suggesting that to be the case.

_____

Comment on this problem

The problem fails to teach anything about math or critical thinking. Rather, it requires a student to jump to conclusions without any basis in reasoning. If the rest of the curriculum materials are like this, they should be rejected.

See the attached picture:

Answer:

$34.5

Step-by-step explanation:

1. 268 - 130 = 138

2. 138 x .25 = 34.5

Answer:

Step-by-step explanation:false

Answer:

D) 4/5

Step-by-step explanation:

He drew and replaced cards 10 times.

8 out of the 10 times, he drew a red card.

8/10 = 4/5

Answer: D) 4/5

You are correct.

Final answer:

The experimental probability of drawing a red card, based on the information given, is 4/5, since Marco drew 8 red cards out of 10 total draws.

Explanation:

The student is asking for the experimental probability of drawing a red card based on Marco's actual draws from a standard deck of 52 cards. Experimental probability is calculated by dividing the number of times the event of interest (drawing a red card) occurred by the total number of trials. In this case, Marco drew a red card 8 times out of 10 total draws.

Therefore, the experimental probability is:

Experimental Probability = Number of red cards drawn / Total number of draws = 8/10

When simplified, 8/10 equals 4/5. Therefore, the correct answer is:

Experimental Probability of Drawing a Red Card = 4/5

Cost of chicken wings at Buffalo Bills = 8 wings for $7

Cost of 1 wing at Buffalo Bills = [tex]\frac{7}{8} =0.875[/tex]

Cost of chicken wings at Buffalo Mild Wings = 12 wings for $10

Cost of 1 wing at Buffalo Mild Wings = [tex]\frac{10}{12}= 0.833[/tex]

Cost of chicken wings at Wingers = 20 wings at $17

Cost of 1 wing at Wingers = [tex]\frac{17}{20}= 0.850[/tex]

Hence, comparing all the three costs per wing, we can see that Buffalo Mild Wings is serving chicken wings at lowest price of $0.833 per wing.

Answer:

It is B

Step-by-step explanation:

Answer:

[tex]f^{-1}(x)=\frac{ln(x)}{ln(3)}[/tex]

Step-by-step explanation:

Given: [tex]f(x)=3^x[/tex]

To find the inverse, let's first replace the [tex]f(x)[/tex] with [tex]y[/tex].

[tex]y=3^x[/tex]

Switch the [tex]x[/tex] and [tex]y[/tex].

[tex]x=3^y[/tex]

Solve for [tex]y[/tex].

[tex]y=\frac{ln(x)}{ln(3)}[/tex]

Write it in inverse notation.

[tex]f^{-1}(x)=\frac{ln(x)}{ln(3)}[/tex]

Answer: A) f^-1(x) = log₃x

Answer:

P = 0.3462

Step-by-step explanation:

See attached photo for work.

We have a sample mean of 35, a sample standard deviation of 8, and a sample size of 36.  

You need to see that the probability of the number of items you can deliver in a day is between 32.6 and 34.6.

The answer is 0.3462, so there's about a 34.62% chance that you will deliver an average of 32.6 to 34.6 packages per day.

The probability a random sample of 36 days would have a mean between 32.6 and 34.6 is 0.3462

Mean is actually the average of all the observations.

A standard deviation (or σ) is a measure of how dispersed the data is in relation to the mean

A z-score is a numerical measurement that describes a value's relationship to the mean of a group of values.

According to the problem,

Here we need to find  P(32.6 < x < 34.6)

[tex]z_{32.6}[/tex] = [tex]\frac{32.6-35}{\frac{8}{\sqrt{36} } }[/tex] = - 1.80

[tex]z_{34.6} = \frac{34.6-35}{\frac{8}{\sqrt{36} } }[/tex] = -0.30

∴ P(32.6 < x < 34.6) = P ( -1.80 < z < -0.30)

= P(z< -0.30) - P(z < -1.80)

= 0.3821 - 0.0359 = 0.3462

∴  The required probability is 0.3462

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Answer:

Equation I: C=2*3.14*r

Step-by-step explanation:

A linear equation is an equation whose highest exponent on the variable is 1.

C=2*3.14*r.................Exponent of 1

A = 3.14*r^2...............Exponent of 2

A = 3.14*r^2...............Exponent of 3

parts of 10% soln, x

parts of 25% soln, y

total soln, x+y =30

{x(0.1) + y(0.25)}/(x + y) = 0.12...eqn 1

x + y = 30...eqn 2

from eqn 2...=》 x = 30-y

subst for x in eqn 1...

=》 {(30-y)(0.1) + y(0.25)}/ 30-y+y = 0.12

=》 (3-.1y+.25y)/30 =0.12

=》 3+.15y = 3.6

=》 .15y = .6

=》 y =4

using x = 30 - y = 26

ans

26ml of 10% soln

4ml of 25% soln

Using a system of equations to represent the scenario, 26mL of 10% solution and 4mL of 25% solution would be required.

Let ;

From (1)

Substitute (3) into (2)

0.1(30 - b) + 0.25b = 3.6

3 - 0.1b + 0.25b = 3.6

0.15b = 0.6

b = 0.6/0.15

b = 4

From (3) :

a = 30 - 4

a = 26

Hence, 26mL of 10% solution and 4mL of 25% solution would be required.

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ANSWER:

~~~~~~~~~

Im pretty sure the answer is "Relation"

~~~~~~~~~

Relation definition:

A relation is a set of numbers that have a relationship through the use of a domain and a range.

~~~~~~~~~

HOPE THIS HELPS!!!

≠GoodLuck

It is a relation because even if they are negative they still can have a relation between them. Hope this is helpful for you!

Answer:   A) 3x + 5x - 4 = 1

Step-by-step explanation:

The second equation is y + 4 = 5x.  Solve this equation for y by subtracting 4 from both sides. --> y = 5x - 4

Now replace "y" in the first equation with "5x - 4".

     3x +      y     = 1

-->  3x + (5x - 4) = 1

Answer:

A = 204  

Step-by-step explanation:

The formula for the area of a parallelogram is

A = bh

Data:

   P = 60

   h = AX =12

MX = 5

Calculation:

MA² = MX² + h² = 5² + 12² = 25 + 144 = 169

MA  = √169 = 13

P = 2MA + 2MH =  2MA + 2(MX + HX) = 26 + 2(5 + HX) = 60

 26 + 10 + 2HX = 60

         36 + 2HX = 60

                 2HX = 24

                   HX = 12

b = MH = MX + HX  = 5 + 12 = 17

A = bh =17 × 12 = 204

The area of the parallelogram is 204.

there are 13 small dogs that compete

Here is your answer

[tex]\bold{-2}[/tex]

REASON :

Given equation -

[tex] \frac{-3}{4}{x}^{2}+2=0 [/tex]

when, written in general form equation is

[tex] \frac{3}{4}{x}^{2}-2=0 [/tex] (on multiplying both sides by -1)

Now this is quadratic equation in general form, where

[tex] a= \frac{3}{4} [/tex] [coefficient of x^2]

b= 0 [coefficient of x]

c= -2 [constant term]

Hence, c= -2

HOPE IT IS USEFUL

Answer:

-2

Step-by-step explanation:

a = 3/4

[coefficient of x^2]

b= 0 [coefficient of x]

c= -2 [constant term]

Answer:

This is correct PEMDAS

Step-by-step explanation:

Parentheses

Exponents

Multiplication/Division

Addition/Subtraction

Answer:

3 liters.

Step-by-step explanation:

If you go to the store and you buy a 2 liter of soda making a pitcher of lemonade with one more liter won't hurt.

A milliliter is not a lot. It won't even quench your own thirst. So 3 liters is the best option.

Answer:

9

Step-by-step explanation:

✯Hello✯

↪  There is a quadratic formula that needs to be used. 4ac and b^2 are a part of this formula

↪  First we need to work out the Values for A and B and C

A = 1

B = 5

C= 4

↪  now we can substitute this into what the equation is asking. (5)^2-4(1)(4)=9

↪  The answer is 9

↪   I hope this helps you :)

❤Gianna❤

Answer:

∠STP = 90°

Step-by-step explanation:

The diagonals of a square are perpendicular bisectors of each other, hence

∠STP = 90°

Answer:

x = 13

Step-by-step explanation:

The area of a rectangle is found by A = l*w. Since the length here is x and the width is 2x - 8, substitute these values and A = 234 to solve for x.

[tex]A = l*w\\234 = x(2x-8)\\234 = 2x^2 - 8x[/tex]

To solve for x, move 234 to the other side by subtraction. Then remove the common factor between all three terms of 2. Factor and solve.

[tex]2x^2 - 8x  - 234 = 0 \\2(x^2 - 4x - 117) = 0\\2(x - 13)(x+9) = 0\\[/tex]

Set each factor equal to 0 and solve.

x - 13 = 0 so x = 13

x + 9 = 0 so x = -9

Since x is a side length and length/distance cannot be negative, then x = 13 is the length of the rectangle.

1. would have to be team E because add up all the numbers 1058/8 (which is how many numbers that is there) 132.25.

2. (More of an explanation if you still don't understand)

52+52+53+54+55+55=321/6=53.5

52+53+54+55+57+57=328/6=54.66 repeated rounded to 54.7 so your answer is 1.2

Answer:

Answer is B

Step-by-step explanation:

To find the workers' compensation insurance premium, multiply the payroll for September ($179,805) by the base rate converted to decimal (0.1124), resulting in a premium of $20,210.08 (Option A).

The question involves calculating the premium for workers' compensation insurance based on the total payroll for the month of September. To determine the monthly premium, we need to apply the base rate to the total payroll amount. The base rate is given as $11.24 per $100 in wages paid. We can calculate the premium with the following steps:

Convert the base rate to a decimal by dividing by 100. This will give us 0.1124.

Multiply the total payroll amount ($179,805) by the decimal base rate (0.1124) to get the premium amount.

Let's perform the calculation:

$179,805 * 0.1124 = $20,210.08

Therefore, the correct option is:

A) $20,210.08

ANSWER

a. 2 real roots, 2 imaginary roots

EXPLANATION

The given equation is

[tex] {x}^{4} - 64 = 0[/tex]

We rewrite as difference of two squares,

[tex]( {x}^{2} )^{2} - {8}^{2} = 0[/tex]

We factor using difference of two squares to get;

[tex]( {x}^{2} - 8)( {x}^{2} + 8) = 0[/tex]

We now use the zero product property to get:

[tex]{x}^{2} = 8 \: or \: {x}^{2} = - 8[/tex]

Take the square root of both sides to get;

[tex]{x} = \pm \sqrt{8} \: or \: {x}^{2} = \pm \sqrt{ - 8} [/tex]

[tex]{x} = \pm 2\sqrt{2} \: or \: {x} = \pm 2\sqrt{ 2} i[/tex]

[tex]{x} = - 2\sqrt{2} \: or \: {x} = 2\sqrt{ 2}[/tex]

are two real roots.

[tex]{x} = - 2\sqrt{2}i \: or \: {x} = 2\sqrt{ 2} i[/tex]

are two imaginary roots.

The correct answer is A.

The correct answer is a. 2 real roots, 2 imaginary roots.

To determine the number and type of roots for the equation [tex]\(x^4 - 64 = 0\)[/tex]

1. Start with the equation:

[tex]\[ x^4 - 64 = 0 \][/tex]

2. Rewrite the equation as a difference of squares:

[tex]\[ x^4 - 64 = (x^2)^2 - 8^2 = (x^2 - 8)(x^2 + 8) = 0 \][/tex]

3. Set each factor equal to zero:

[tex]\[ x^2 - 8 = 0 \]\[ x^2 + 8 = 0 \][/tex]

4. Solve each equation separately:

For [tex]\(x^2 - 8 = 0\)[/tex]:

[tex]\[ x^2 = 8 \]\[ x = \pm \sqrt{8} = \pm 2\sqrt{2} \][/tex]

These are two real roots.

For [tex]\(x^2 + 8 = 0\)[/tex]:

[tex]\[ x^2 = -8 \]\[ x = \pm \sqrt{-8} = \pm \sqrt{8i^2} = \pm 2\sqrt{2}i \][/tex]

These are two imaginary roots.

Therefore, the equation [tex]\(x^4 - 64 = 0\)[/tex] has:

- 2 real roots: [tex]\(2\sqrt{2}\) and \(-2\sqrt{2}\)[/tex]

- 2 imaginary roots: [tex]\(2\sqrt{2}i\) and \(-2\sqrt{2}i\)[/tex]

The correct answer is:

a. 2 real roots, 2 imaginary roots

The complete question is- Which describes the number and type of roots of the equation [tex]x^4 - 64 = 0[/tex]

a. 2 real roots, 2 imaginary roots

b. 4 real roots

c. 3 real roots, 1 imaginary root

d. 4 imaginary roots