Simplify the following expression:

( 4 + 5i ) / 4i
Select one:

a.
( 5 + 4i ) / 4


b.
( 5 - 4i ) / 4


c.
( 5i + 4i ) / 4


d.
( 5i - 4 ) / 4

Answers

Answer 1

Answer: B

Step-by-step explanation:

[tex]\frac{4+5i}{4i}\\ \\ =\frac{1}{4} \left(\frac{4+5i}{i} \right)\\\\=\frac{1}{4}((-i)(4+5i))\\\\=\frac{1}{4}(-4i-5i^2)\\\\=\frac{5-4i}{4}[/tex]


Related Questions

Madison finished 4/5 of her homework before dinner. What percent of Maddison’s homework is left to finish?

Answers

Answer:

1/5 of it

Step-by-step explanation:

5/5 represents all of her homework

5/5-4/5= 1/5

4/5 represents the homework she did before dinner

1/5 represents the homework left to do

20% i think bc if you divided 4/5 and multiply by 100 is says 80 so there is 20 more until 100

how many significant figures are in this number 6.01x10^3

Answers

Answer:

3

Step-by-step explanation:

6.01 has 3 sig fig

I think that's how I do it

Help me with this equation, please. (Image Attached)

Answers

So, the equation is sin(x + y)/sin(x - y) = (1 + cotxstany)/(1 + cotxtany)

The question has to to with trigonometric identities?

What are trigonometric identities?

Trigonometric identities are equations that show the relationship between the trigonometric ratios.

How to solve the equation?

Given the equation sin(x + y)/sin(x - y)

Using the trigonometric identities.

sin(x + y) = sinxcosy + cosxsiny andsin(x - y) = sinxcosy - cosxsiny

So, sin(x + y)/sin(x - y) = (sinxcosy + cosxsiny)/(sinxcosy + cosxsiny)

Dividing the rnumerator and denominator of ight hand side by sinx, we have

sin(x + y)/sin(x - y) = (sinxcosy + cosxsiny)/sinx/(sinxcosy + cosxsiny)/sinx

sin(x + y)/sin(x - y) = (sinxcosy/sinx + cosxsiny/sinx)/(sinxcosy/sinx + cosxsiny/sinx)

= (cosy + cotxsiny)/(cosy + cotxsiny) (since cosx/sinx = cotx)

Dividing the numerator and denominator of the right hand side by cosy, we have

= (cosy + cotxsiny)/cosy/(cosy + cotxsiny)/cosy

= (cosy/cosy + cotxsiny/cosy)/(cosy/cosy + cotxsiny/cosy)

= (1 + cotxstany)/(1 + cotxtany)   [since siny/cosy = tany]

So,  sin(x + y)/sin(x - y) = (1 + cotxstany)/(1 + cotxtany)

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If an event has a 55% chance of happening in one trial, how do I determine the chances of it happening more than once in 4 trials?

Answers

The chances of it happening more than once in 4 trials is 13%

How to determine the number

From the information given, we have can deduce that;

Probability of 1 trial = 55%

= 55/ 100

Find the ratio

= 0. 55

We are to find the probability of it happening more than once in 4 different trials

If the probability of it happening in one trial is 555 which equals 0. 55

Then the probability of it happening in 1 in 4 trials is given as;

P(1/4 trials) = 1/ 4 × 55%

P(1/4 trials) = 1/ 4 × 0. 55

Put in decimal form

P(1/4 trials) = 0. 25 × 0. 55

P(1/4 trials) = 0. 138

But we have to know the percentage

= 0. 138 × 100

Multiply the values, we have

= 13. 8 %

Thus, the chances of it happening more than once in 4 trials is 13%

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What are the excluded values? –4 and –1 -1/2, 1, and 4 1 1 and 4

Answers

The excluded values are x = 4 and x - 1

How to determine the excluded values?

The complete question is added as an attachment

The function is given as:

(2x^2 - 7x - 4)/(x^2 - 5x + 4)

Set the denominator to 0

x^2 - 5x + 4 = 0

Expand

x^2 - x - 4x + 4 = 0

Factorize the equation

x(x -1) - 4(x - 1) = 0

This gives

(x - 4)(x - 1) = 0

Solve for x

x = 4 and x - 1

Hence, the excluded values are x = 4 and x - 1

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Answer: Its D 1 and 4

Step-by-step explanation:

I took the assignment

Using two six-sided number cubes, each labeled with the numbers 1 through 6, event A is rolling a sum less than 6. Which of the following shows the sample space of event A?

{(1, 1), (1, 3), (1, 4), (1, 5), (2, 2), (2, 3), (2, 4), (3, 1), (3, 2), (3, 3)}
{(1, 1), (1, 2), (1, 3), (1, 4), (2, 1), (2, 2), (2, 3), (3, 1), (3, 2), (4, 1)}
{(1, 1), (1, 2), (1, 3), (1, 5), (2, 1), (2, 2), (2, 3), (3, 1), (3, 3), (4, 1)}
{(1, 1), (1, 2), (1, 3), (1, 4), (1, 5), (2, 3), (2, 4), (3, 3), (4, 1), (4, 2)}

Answers

the sample space is:

{ (1, 1), (1, 2), (1, 3), (1, 4), (2, 1), (3, 1), (4, 1), (2, 2), (2, 3), (3, 2)}

Which of the following shows the sample space of event A?

Event A is rolling a sum less than 6.

Let's define the possible elements in this experiment as:

(outcome of dice 1, outcome of dice 2)

The outcomes where the sum is less than 6 are:

dice 1    dice 2     sum

  1               1           2

  1               2           3

  1               3          4

  1               4          5

  2               1          3

  3              1           4

  4               1          5

  2              2          4

  3              2          5

  2              3           5

 

So there are 10 outcomes, then the sample space is:

{ (1, 1), (1, 2), (1, 3), (1, 4), (2, 1), (3, 1), (4, 1), (2, 2), (2, 3), (3, 2)}

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Answer:

B) {(1, 1), (1, 2), (1, 3), (1, 4), (2, 1), (2, 2), (2, 3), (3, 1), (3, 2), (4, 1)}

Step-by-step explanation:

If the question said less than 6 meaning you have to find all possible solution that are 5 or lower.

However, if the problem said equal or less than 6 then you have to find all possible solution that are 6 or lower.

B option is only option that don't have sum of 6. Therefore, option B is correct.

Solve the inequality for x.
OA.
X S
5- 2/2 x ²
x 2
28
OB. x ≤ 7
OC.
28
9
OD. x ≥ 7

Answers

The solution to the inequality x-13<=7+4x is x >= -20/3

How to solve the inequality?

The inequality expression is given as:

x-13<=7+4x

Add 13 to both sides of the inequality

x <= 20 + 4x

Subtract 4x from both sides of the inequality

-3x <= 20

Divide both sides of the inequality by -3

x >= -20/3

Hence, the solution to the inequality x-13<=7+4x is x >= -20/3

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Complete question

Solve the inequality for x

x-13<=7+4x


Alok started a business investing Rs 90, 000. After three
months Prabir joined him with capital of Rs 1,20000
If at the end of 2 years, the total profit made
by them was
Rs 96,000 what will the difference
between Alok and Prabir's share in it?

Answers

The difference between Alok and Prabir share exists 8000.

What will the difference between Alok and Prabir share?

Given: Invested by Alok = Rs 90, 000

Invested by Prabir = Rs 1,20000

The time period of Alok = 3 months

The time period of Prabir = 2 years

They earn a profit = Rs 96,000.

Profit exists directly proportional to the product of the amount invested and the time period of investment.

8000 = 90000 [tex]*[/tex] 24/120000 [tex]*[/tex] 21

= 5/7

5x + 7x = 96000

x = 8000

first = 40000

second = 48000

so the difference exists at 8000.

The difference between Alok and Prabir share exists 8000.

Therefore, the correct answer is 8000.

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A yo-yo is moving up and down a string so that its velocity at time t is given by v(t) = 3cos(t) for time t ≥ 0. The initial position of the yo-yo at time t = 0 is x = 3.

Part A: Find the average value of v(t) on the interval open bracket 0 comma pi over 2 close bracket. (10 points)

Part B: What is the displacement of the yo-yo from time t = 0 to time t = π? (10 points)

Part C: Find the total distance the yo-yo travels from time t = 0 to time t = π. (10 points)

Answers

Part A - The average value of v(t) over the interval  (0, π/2) is 6/π

Part B -  The displacement of the yo-yo from time t = 0 to time t = π is 0 m

Part C - The total distance the yo-yo travels from time t = 0 to time t = π is 6 m.

Part A: Find the average value of v(t) on the interval (0, π/2)

The average value of a function f(t) over the interval (a,b) is

[tex]f(t)_{avg} = \frac{1}{b - a} \int\limits^b_a {f(t)} \, dx[/tex]

So, since  velocity at time t is given by v(t) = 3cos(t) for time t ≥ 0. Its average value over the interval  (0, π/2) is given by

[tex]v(t)_{avg} = \frac{1}{\frac{\pi }{2} - 0} \int\limits^{\frac{\pi }{2} }_0 {v(t)} \, dt[/tex]

Since v(t) = 3cost, we have

[tex]v(t)_{avg} = \frac{1}{\frac{\pi }{2} - 0} \int\limits^{\frac{\pi }{2} }_0 {3cos(t)} \, dt\\= \frac{3}{\frac{\pi }{2}} \int\limits^{\frac{\pi }{2} }_0 {cos(t)} \, dt\\= \frac{6}{{\pi}} [{sin(t)}]^{\frac{\pi }{2} }_{0} \\= \frac{6}{{\pi}} [{sin(\frac{\pi }{2})} - sin0]\\ = \frac{6}{{\pi}} [1 - 0]\\ = \frac{6}{{\pi}} [1]\\ = \frac{6}{{\pi}}[/tex]

So, the average value of v(t) over the interval  (0, π/2) is 6/π

Part B: What is the displacement of the yo-yo from time t = 0 to time t = π?

To find the displacement of the yo-yo, we need to find its position.

So, its position x = ∫v(t)dt

= ∫3cos(t)dt

= 3∫cos(t)dt

= 3sint + C

Given that at t = 0, x = 3. so

x = 3sint + C

3 = 3sin0 + C

3 = 0 + C

C = 3

So, x(t) = 3sint + 3

So, its displacement from time t = 0 to time t = π is

Δx = x(π) - x(0)

= 3sinπ + 3 - (3sin0 + 3)

= 3 × 0 + 3 - 0 - 3

= 0 + 3 - 3

= 0 + 0

= 0 m

So, the displacement of the yo-yo from time t = 0 to time t = π is 0 m

Part C: Find the total distance the yo-yo travels from time t = 0 to time t = π. (10 points)

The total distance the yo-yo travels from time t = 0 to time t = π is given by

[tex]x(t) = \int\limits^{\pi}_0 {v(t)} \, dt\\= \int\limits^{\pi }_0 {3cos(t)} \, dt\\= 3 \int\limits^{\pi }_0 {cos(t)} \, dt\\ = 3 \int\limits^{\frac{\pi }{2} }_0 {cos(t)} \, dt + 3\int\limits^{\pi }_{\frac{\pi }{2}} {cos(t)} \, dt\\= 3 \times 2\int\limits^{\frac{\pi }{2} }_0 {cos(t)} \, dt\\= 6 [{sin(t)}]^{\frac{\pi }{2} }_{0} \\= 6[{sin\frac{\pi }{2} - sin0]\\\\= 6[1 - 0]\\= 6(1)\\= 6[/tex]

So, the total distance the yo-yo travels from time t = 0 to time t = π is 6 m.

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Can someone please please help me

Answers

Answer:

  order: 2, 3, 1

Step-by-step explanation:

Reasonableness checks and your knowledge of integers and fractions will help you solve this. The offered questions are intended to help you think this through.

a.

For an output of -31, the machine (x -2)² cannot possibly be last. Its output can only be positive.

  machine 2, (x-2)², cannot be last

Also, machine 3 cannot be last. For the output to be -31, the input to machine 3 must be -1/31. Neither of the other machines can produce a fraction with the inputs they might receive.

b.

For an input of x=0, the machine 1/x cannot possibly be first. 1/0 is undefined.

The other two machines will give the following outputs for an input of 0:

  machine 1: 4(0) -32 = -32

  machine 2: (0 -2)² = 4

It is unlikely that machine 1 will be first, because the other two machines cannot do anything useful with -32 as an input.

  machine 3, 1/x, cannot be first

c.

The reasoning of part (a) tells you the last machine must be machine 1. The reasoning of part (b) tells you the first machine cannot be 3, so must be 2. The order of the machines must be ...

machine 2: (0 -2)² = 4 . . . . . . . using an input of 0machine 3: 1/4 = 1/4machine 1: 4(1/4) -32 = -31 . . . . desired output

How many three-digit positive integers have at least one prime digit?

Answers

Answer:

210

Step-by-step explanation:

[tex]512=2^9 \\[/tex] has 9 prime factors

Now, if you want to maximize the number of different prime factor, apply the following method: let [tex]p(n)[/tex]  be the nth prime number, in increasing order. Let [tex]v[/tex]  define as follow :  [tex]v(0)=1,v(n+1)=v(n)p(n+1)[/tex] , and find n  such that [tex]v(n) < 1000,v(n+1) > 1000[/tex]. n will be the number of factors and v(n) your integer.

[tex]v(1)=2v(0)=2v(2)=3v(1)=6v(3)=5v(2)=30v(4)=7v(3)=210v(5)=11v(4)=2310[/tex]

There you are,  210 , with only 4 different prime factors.

→Credits: Xavier Dectot←

In 2001 the total cost of manufacturing an article was sh.1250 and this was divided between the cost of materials was doubled,labour cost increased by 30% and transport costs increased by 20%.calculate the cost of manufacturing the article bin 2004

Answers

The cost of manufacturing the article bin 2004 will be 1875.

What is Percentage Increased ?

Percentage increase is the ratio of increase to the initial value in percentage.

Given that In 2001 the total cost of manufacturing an article was sh.1250 and this was divided between the cost of materials was doubled, labor cost increased by 30% and transport costs increased by 20%

Given that in 2001, the cost of manufacturing = 1250

If this cost was divided between the Material, labor, and transportation equally, then, cost for each sector will 1250/3 = 416.67

cost of materials was doubled, that is 416.67 x 2 = 833.33labor cost increased by 30% , that is 130/100 x 416.67 = 541.67transport costs increased by 20% that is, 120/100 x 416.67 = 500

The cost of manufacturing = 833.33 + 541.67 + 500

The cost of manufacturing = 1875

Therefore, the cost of manufacturing the article bin 2004 will be 1875.

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need heeeelp please

Answers

Answer:

  (x, y) = (-√3/2, 1/2)

Step-by-step explanation:

The terminal point for that angle can be read from a unit circle chart.

On the attached chart, the point of interest is the first one above the -x axis on the left side. The chart tells you the coordinates are ...

  (x, y) = (-√3/2, 1/2)

I need help solving this problem!

Answers

Answer: A

Step-by-step explanation:

The domain is the range of possible x that doesn't make y impossible to find, in this case, all real numbers work

The range is the range of possible y that doesn't make x impossible to find in the inverse function, in this case, all real numbers work

The answer is A.

As any number can be replaced in place of x for the function y, the domain of the function is All Real Numbers. Since any number can be inputted, the result will also vary accordingly. Hence, the range of the function is All Real  Numbers.

This is true for the listed function :

[tex]\boxed {y = \sqrt[3]{x-2} - 5}[/tex]

PLEASE HELP!

Let f be the function given by f (x) = (create an original sinusoidal function with an amplitude not equal to 1, a period not equal to 2π, and non-zero phase and vertical shifts).

ex: F of x equals negative one half times sine of quantity 3 times x plus pi over 2 end quantity minus 2


Part A: State the amplitude and vertical shift.


Part B: Determine the period of f (x), showing all necessary calculations.


Part C: Calculate the phase shift of the sinusoidal function with proper mathematical justification.


Part D: Graph the sinusoidal function by hand, using your answers from parts A–C.


Choose an angle θ, in radians, such that 2π < θ < 4π . Let θ = (create an original angle measure).


ex: Theta equals 13 pi over 6


Part E: Determine the exact value of cos θ using the sum formula. Show all necessary mathematical work.


Part F: Determine the exact value of sin θ using the difference formula. Show all necessary mathematical work.


Part G: Calculate the exact value of tan 2θ, using your answers from parts E – F.

Answers

The equation of the function f(x) is f(x) = 2 sin(π/2(x + 6)) - 3

How to create the sine function?

A sine function is represented as:

f(x) = A sin(B(x + C)) + D

Where

A = Amplitude

Period = 2π/B

C = Phase shift

D = Vertical shift

The requirements in the question are:

Amplitude not equal to 1Period not equal to 2πNon-zero phase and vertical shifts

So, we can use the following assumptions

A = 2

Period = 4

C = 6

D = -3

So, we have:

f(x) = 2 sin(B(x + 6)) - 3

The value of B is

4 = 2π/B

This gives

B = π/2

So, we have:

f(x) = 2 sin(π/2(x + 6)) - 3

The amplitude, vertical shift, period of f(x)and the phase shift

Using the representations in (a), we have:

Amplitude = 2Vertical shift = -3Period = 4Phase shift = 6

The graph of the function

See attachment for the graph of f(x)

The value of cos θ

Let θ = 3π

So, we have:

cos(3π)

This is calculated as:

cos(3π) = cos(2π + π)

Expand

cos(3π) = cos(2π) *cos(π) - sin(2π) *sin(π)

Evaluate

cos(3π) = -1

The value of sin θ

Let θ = 3π

So, we have:

sin(3π)

This is calculated as:

sin(3π) = sin(2π + π)

Expand

sin(3π) = sin(2π) *cos(π) + cos(2π) *sin(π)

Evaluate

sin(3π) = 0

The value of tan 2θ

Let θ = 3π

So, we have:

tan(2 * 3π)

tan(6π)

This is calculated as:

tan(6π) = tan(3π + 3π)

Evaluate

tan(3π) = 0

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Two factory plants are making tv panels yesterday plant A produced 3000 panels. Ten percent of the panels from plant A were defective and Three percent from plant B were defective. How many panels did plant be produce if the overall percentage of defective panels from the two plants was 6%. Thanks for the help

Answers

Answer: Plant B produced 4000 panels

Step-by-step explanation: Let the number of panels produced by plant A = a and the number of panels produced by plant B = x. In total, we have 3000 + x.  Now for the defective panels. 10% of plant a + 3% of plant b = 6% of both a and b. 300 + 3/100(x) = 6/100(3000 + x). 300 + 0.03x = 180 + 0.06x. Now, we simplify. 300 - 180 = 0.06x = 0.03x. So, 120 = 0.03x and 40 = 1% of x. This means x = 4000. So, therefore, Plant B produced 4000 panels. We can check our work by using the value of x we got. 4000 + 3000 = 7000. 6% of 7000 = 420. 120 = 3% of 4000. 120 + 300 = 420 so the answer we got is correct. Hope this helped

Write your answer as a fraction in simplest form.

-1 3/4 • 2 1/8

Answers

That is correct but you might have to write it as a mixed number (-3 23/32)

Write the ratio of 4 roses to 24 flowers

Answers

1:6

Initially we have 4:24 meaning 4 roses for 24 flowers. However, we can simplify this ration same as we do to fractions. If we divided both sides of the ration by 4, we get 1:6, or 1 rose for every 6 flowers.

Answer:

4:24 or also 1:6

Step-by-step explanation:

What are the potential zeros of f(x)=6x^4+ 2x^3 - 4x^2 +2?

Answers

The potential zeros of f(x)=6x^4+ 2x^3 - 4x^2 +2 are ±(1, 1/2, 1/3, 1/6, 2, 2/3)

How to determine the potential zeros of the function f(x)?

The function is given as:

f(x)=6x^4+ 2x^3 - 4x^2 +2

For a function P(x) such that

P(x) = ax^n +...... + b

The rational roots of the function p(x) are

Rational roots = ± Possible factors of b/Possible factors of a

In the function f(x), we have:

a = 6

b = 2

The factors of 6 and 2 are

a = 1, 2, 3 and 6

b = 1 and 2

So, we have:

Rational roots = ±(1, 2)/(1, 2, 3, 6)

Split the expression

Rational roots = ±1/(1, 2, 3, 6)/ and ±2/(1, 2, 3, 6)

Evaluate the quotient

Rational roots = ±(1, 1/2, 1/3, 1/6, 2, 1, 2/3, 1/3)

Remove the repetition

Rational roots = ±(1, 1/2, 1/3, 1/6, 2, 2/3)

Hence, the potential zeros of f(x)=6x^4+ 2x^3 - 4x^2 +2 are ±(1, 1/2, 1/3, 1/6, 2, 2/3)

The complete parameters are:

The function is given as:

f(x) = 3x^3 + 2x^2 + 3x + 6

The potential zeros of f(x)=6x^4+ 2x^3 - 4x^2 +2 are ±(1, 1/2, 1/3, 1/6, 2, 2/3)

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Fill in the P(X=x) values to give a legitimate probability distribution for the discrete random variable , whose possible values are 0, 1, 3, 4, and 5.

Answers

For a probability distribution to be represented, it is needed that P(X = 0) + P(X = 1) = 0.44. Hence one possible example is:

P(X = 0) = 0.40.P(X = 1) = 0.04.

What is needed for a discrete random variable to represent a probability distribution?

The sum of all the probabilities must be of 1, hence:

P(X = 0) + P(X = 1) + P(X = 3) + P(X = 4) + P(X = 5) = 1.

Then, considering the table:

P(X = 0) + P(X = 1) + 0.15 + 0.17 + 0.24 = 1

P(X = 0) + P(X = 1) + 0.56 = 1

P(X = 0) + P(X = 1) = 0.44.

Hence one possible example is:

P(X = 0) = 0.40.P(X = 1) = 0.04.

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Which expression represents seven less than the product of thirteen times a number, and two squared?

(13x + 22) · 7

7(13x · 22)

7 + 13x + 22

7 + 13x · 22

(13x · 22) − 7

Answers

Seven less than the product of thirteen times a number, and two squared is as follows;

(13x × 2²) - 7

How to represent an expression?

The expression says  seven less than the product of thirteen times a number, and two squared.

Let

the number  = x

Hence, the product of thirteen times a number, and two squared is as follows:

13(x)(2²)

Therefore,  seven less than the product of thirteen times a number, and two squared is as follows;

(13x × 2²) - 7

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What is the probability that the mean score for 10 randomly selected people who took the LSAT would be above 157? Round your answer to three decimal places. (Example: 0.398)

Answers

Using the normal distribution, there is a 0.007 = 0.7% probability that the mean score for 10 randomly selected people who took the LSAT would be above 157.

Normal Probability Distribution

The z-score of a measure X of a normally distributed variable with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The z-score measures how many standard deviations the measure is above or below the mean. Looking at the z-score table, the p-value associated with this z-score is found, which is the percentile of X.By the Central Limit Theorem, the sampling distribution of sample means of size n has standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].

Researching this problem on the internet, the parameters are given as follows:

[tex]\mu = 150, \sigma = 9, n = 10, s = \frac{9}{\sqrt{10}} = 2.85[/tex]

The probability is one subtracted by the p-value of Z when X = 157, hence:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

By the Central Limit Theorem

[tex]Z = \frac{X - \mu}{s}[/tex]

Z = (157 - 150)/2.85

Z = 2.46

Z = 2.46 has a p-value of 0.993.

1 - 0.993 = 0.007.

0.007 = 0.7% probability that the mean score for 10 randomly selected people who took the LSAT would be above 157.

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|3x-1|=4 help pleaseeeeeeeeee

Answers

Answer: x = -1 or x = 5/3

Step-by-step explanation:

|3x - 1| = 4

=> 3x - 1 = 4 or 3x - 1 = -4

=>x = 5/3 or x = -1

Each outcome or a collections of outcomes in a experiment is called as?​

Answers

Answer:

event

What is an event?

An event can be described as an individual or set of outcomes of an experiment.

Events are a subset of the experiment's sample space.

What is sample space?

The sample space of an experiment is the complete set of possible outcomes of that experiment.

x+2y=5 and 4x+12y=-20 elimination method

Answers

Answer:

x=25 and y=-10

Step-by-step explanation:

x+2y=5 ..........(1)

4x+12y=-20.........(2)

using elimination method.

multiply equ(1) by 4 and equ(2) by 1

so we have

x+2y=5..........*4

4x+12y=-20.........*1

4x+8y=20................(3)

4x+12y=-20.............(4)

subtract eq(4) from (3) we have

-4y=40

y=-10

substitute y=-10 in equation (1)

we have:

x+2(-10)=5

x-20=5

x=25

f(x) = 2x^2 - x -10

What are the x-intercepts of the graph of f(x)? Show your work

Answers

Answer:

[tex](-2,0) \textsf{ and }\left(\dfrac{5}{2},0\right)[/tex]

Step-by-step explanation:

Given quadratic function:

[tex]f(x)=2x^2-x-10[/tex]

The x-intercepts of the graph are the points at which the curve crosses the x-axis, so when f(x) = 0.

To find these points, factor the quadratic equation, set it to zero, then solve for x.

To factor a quadratic in the form [tex]ax^2+bx+c[/tex], find two numbers that multiply to ac and sum to b.

[tex]\implies ac=2 \cdot -10 = -20[/tex]

[tex]\implies b=-1[/tex]

Therefore, the two numbers are -5 and 4.

Rewrite the middle term as the sum of these two numbers:

[tex]\implies 2x^2-5x+4x-10[/tex]

Factor the first two terms and the last two terms separately:

[tex]\implies x(2x-5)+2(2x-5)[/tex]

Factor out the common term (2x - 5):

[tex]\implies (x+2)(2x-5)[/tex]

Set the factored function to zero:

[tex]\implies (x+2)(2x-5)=0[/tex]

Apply the zero-product property:

[tex]\implies (x+2)=0 \implies x=-2[/tex]

[tex]\implies (2x-5)=0 \implies x=\dfrac{5}{2}[/tex]

Therefore, the x-intercepts of the graph are:

[tex](-2,0) \textsf{ and }\left(\dfrac{5}{2},0\right)[/tex]

Learn more about quadratic equations here:

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pleaseee helpp
which of the following enequalities would produce the region indicated on the graph below

Answers

Answer: C

Step-by-step explanation:

The line [tex]y=x+2[/tex] is shaded below and is solid.

This eliminates all the options except for C.

give the answers to the remaining boxes left blank, you can give the answers all in one sentence starting from the first blank box all the way to the last

Answers

The domain of the functions are:

The domain of f(x) = √4x + 6 is [-3/2, ∞) or x >-3/2The domain of g(x) = -4√-20x - 6 is (-∞, -3/10] or x < -3/10The domain of f(x) = 15 + √5x - 16 is [16/5, ∞) or x >16/5The domain of p(x) = √20x + 6 is (-3/10, ∞] or x > -3/10

What are the domains of a function?

The domain of a function is the set of input values the function can take i.e. the set of values the independent variable can assume?

How to determine the domain of the functions?

Function 1

The function is given as:

f(x) = √4x + 6

Set the radicand greater than 0

4x + 6 > 0

Subtract 6 from both sides

4x > -6

Divide by 4

x > -3/2

Express as interval notation

[-3/2, ∞)

Hence, the domain of f(x) = √4x + 6 is [-3/2, ∞) or x >-3/2

Function 2

The function is given as:

g(x) = -4√-20x - 6

Set the radicand greater than 0

-20x - 6 > 0

Add 6 to both sides

-20x > 6

Divide by -20

x < -6/20

Simplify

x < -3/10

Express as interval notation

(-∞, -3/10]

Hence, the domain of g(x) = -4√-20x - 6 is (-∞, -3/10] or x < -3/10

Function 3

The function is given as:

f(x) = 15 + √5x - 16

Set the radicand greater than 0

5x - 16 > 0

Add 16 to both sides

5x > 16

Divide by 5

x > 16/5

Express as interval notation

[16/5, ∞)

Hence, the domain of f(x) = 15 + √5x - 16 is [16/5, ∞) or x >16/5

Function 4

The function is given as:

p(x) = √20x + 6

Set the radicand greater than 0

20x + 6 > 0

Subtract 6 from both sides

20x > -6

Divide by 20

x > -6/20

Simplify

x > -3/10

Express as interval notation

(-3/10, ∞]

Hence, the domain of p(x) = √20x + 6 is (-3/10, ∞] or x > -3/10

Read more about domain at:

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What's the Value of X in 1/2 + X = 5/6

Answers

Answer:

x = 1/3

Step-by-step explanation:

1/2 + X = 5/6

collecting the like terms

X = 5/6 - 1/2

making one fraction on the left side by taking the common denominator

X = (5 - 3)/6

X = 2/6

devide the numerator and denominator by 2, you get

X = 1/3

Sodas cost $1.75 each. Write a direct
proportional equation using (s) for sodas and
(t) for total cost.

Answers

Answer:

t = 1.75(s)

Step-by-step explanation:

I gotchu

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