Given that f(x) = 10 - 3x and g(x) = x-3/2 find the value of fg(4)

Answer:

x = 3

Step-by-step explanation:

Given the linear function, f(x) = -4x + 2, for which we must determine the integer value of x that will provide an output of f(x) = -10:

The first step is to substitute the output value, f(x) = -10, into the given function, and solve for its corresponding input value, x:

f(x) = -4x + 2

-10 = -4x + 2

Subtract 2 from both sides:

-10 - 2 = -4x + 2 - 2

-12 = -4x

Divide both sides by -4 to solve for x:

[tex]\displaystyle\mathsf{\frac{-12}{-4}\:=\:\frac{-4x}{-4} }[/tex]

x = 3

Hence, when x = 3, f(x) = -10.  

Substitute the value of x = 3 into the original function:

f(x) = -4x + 2

f(3) = -4(3) + 2

f(3) = -12 + 2

f(3) = -10  ⇒  f(x) = -10.

Therefore, the input value of x = 3 gives an output value of f(x) = -10.

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Answer: 6

Step-by-step explanation:

13-7=6

Step-by-step explanation:

We have that

[tex](x + \frac{1}{x} ) {}^{2} = 3[/tex]

We are trying to find the number value so that we can apply in the later equation.

Qe first simplify.

Remeber that

[tex](a + b) {}^{2} = a {}^{2} + 2ab + {b}^{2} [/tex]

Also remeber that

[tex] \frac{1}{x} = {x}^{ - 1} [/tex]

so

[tex](x + x {}^{ - 1} ) {}^{2} = {x}^{2} + 2x {}^{0} + {x}^{ - 2} = 3[/tex]

We then simply remeber that x^0=1 so

[tex] {x}^{2} + 2 + \frac{1}{ {x}^{2} } = 3[/tex]

Multiply both sides by x^2.

[tex] {x}^{4} + 2 {x}^{2} + 1 = 3 {x}^{2} [/tex]

Subtract both sides by 3x^2

[tex] {x}^{4} - {x}^{2} + 1 = 0[/tex]

Notice that x^4= (x^2)^2.

So our reformed equation is

[tex]( {x}^{2} ) {}^{2} - {x}^{2} + 1 = 0[/tex]

Let a variable , w equal x^2. This means that we subsitute variable, w in for x^2.

[tex]w {}^{2} - w + 1 = 0[/tex]

Now we use the quadratic formula

[tex] w = \frac{ - b + \sqrt{b {}^{2} - 4ac } }{2a} [/tex]

and

[tex]w = - b - \frac { \sqrt{b {}^{2} - 4ac } }{2a} [/tex]

Let a=1 b=-1 and c=1.

[tex]w = \frac{1 + \sqrt{1 - 4(1)} }{2} [/tex]

[tex]w = \frac{1 - \sqrt{1 - 4} }{2} [/tex]

Now, we get

[tex]w = \frac{1}{2} + \frac{i \sqrt{3} }{2} [/tex]

and

[tex]w = \frac{1}{2} - \frac{ i\sqrt{3} }{2} [/tex]

Now since we set both of these to the x^2 we solve for x.

and

[tex] {x}^{2} = \frac{1}{2} + \frac{i \sqrt{3} }{2} [/tex]

and

[tex] {x}^{2} = \frac{1}{2} - \frac{i \sqrt{3} }{2} [/tex]

We can represent both of these as complex number in the form of a+bi. Next we can convert this into trig form which is

[tex] {x}^{2} = 1( \cos(60) + i \: \sin(60) [/tex]

and

[tex] {x}^{2} = 1( \cos(300) + i \: sin(300))[/tex]

Next we take the sqr root of 1 which is 1, and divide the degree by two.

[tex] {x} = 1( \cos(30) + i \: sin \: 30)[/tex]

and

[tex]x = 1( \cos(150) + i \: sin(150)[/tex]

We are asked for the 2nd root so just add 180 degrees to this and we have

[tex]x = 1 \cos(210) + i \: sin \: 210)[/tex]

and

[tex]x = 1( \cos(330) + i \: sin(330)[/tex]

which both simplified to

[tex]x = - \frac{ \sqrt{3} }{2} - \frac{1}{2} i[/tex]

and

[tex]x = \frac{ \sqrt{3} }{2} - \frac{1}{2} i[/tex]

Now we must find

x^18+x^12+x^6+1.

We just use demovire Theorem. Which is a complex number raised to the nth root is

[tex] {r}^{n} (cos(nx) + i \: sin(nx)[/tex]

So let plug in our first root.

[tex]1( \cos(330 \times 18)) + i \: sin \: (330 \times 18))) + 1( \cos(12 \times 330)) + i \: sin(12 \times 330) + 1( \cos(6 \times 330) + i \: sin(6 \times 330))) + 1[/tex]

To save time we multiply the angle and use rules of terminals angle and we get

[tex]1( \cos(180) + i \sin(180) ) + 1( \cos(0) + i \: sin \:( 0) + 1( \cos(180) + i \: sin(180) + 1[/tex]

And we get

[tex] - 1 + 1 + - 1 + 1 = 0[/tex]

So one of the answer is x=0

And the other, let see

[tex]1 \cos(210 \times 18) + i \: \sin(210 \times 18) + 1 \: cos(210 \times 12) + i \: sin(210 \times 12) + 1 \cos(210 \times 6) + \:i sin(210 \times 6) + 1[/tex]

[tex] \cos(180) + i \: sin(180) + 1 \cos(0) + i\sin(0) +1( \cos(0) + i \sin(0) + 1[/tex]

We get

[tex] - 1 + 1 + 1 + 1 = 2[/tex]

So our answer are 2.

So the answer to the second part is

0 and 2.

Answer:

-71

Step-by-step explanation:

Answer:

-71

Step-by-step explanation:

[-18+(-22)]-43+12

=(-18+22)-43+12

=-40-43+12

=-83+12

=-71

Answer:

0.9km(rounded to 1dp)

Step-by-step explanation:

2.7km on sat

1.8km on sun

2.7km-1.8km=0.9km

Answer:

-8x + 12

Step-by-step explanation:

-4(2x - 3)

then -4*2x and -4*-3(an even number of negative signs multiplied equals to a positive sign)

therefore= -8x + 12

Answer:

40

Step-by-step explanation:

Answer:

Marcus has 24 pens while Bryan has 12 pens.

Step-by-step explanation:

Let u rep 1 unit.

Marcus = 2u

Bryan = u

2u+u=36

   3u=36

     u=36÷3

       =12

No. of pens Marcus has

= 2u

= 2×12

= 24

No. of pens Bryan has

= u

= 12

Answer:

6 questions

Step-by-step explanation:

First, you divide the total score of 100 by the 64 questions to get 1.5625 points per question. Next, you divide the lowest score to qualify of 90 by the 1.5625 to get 57.6 questions correct to qualify. Then, you round 57.6 questions correct up to 58 questions correct because a fraction of a question correct doesn't make sense. Finally, you subtract the total number of questions (64) by the required correct answers (58) to get 6 questions you can miss to still qualify for the scholarship.

Using it's concept, it is found that the probabilities are given as follows:

A probability is given by the number of desired outcomes divided by the number of total outcomes.

In this problem, there is a total of 400 moviegoers.

From the table, 74 are adults who prefer comedies, hence:

P(C ∩ D) = 74/400 = 0.185.

2 + 48 + 19 + 74 = 143 are adults, while 24 + 64 = 88 are not adults but prefer comedies, hence the "or probability" is given by:

P(C ∪ D) = (143 + 88)/400 = 0.5775.

More can be learned about probabilities at https://brainly.com/question/14398287

Answer:

0.3575

0.405

Step-by-step explanation:

Answer:

The rate of change of function B is greater than the rate of change of function A

Answer:USE SUBSTITUTION METHOD. Algebra work right here

Step-by-step explanation:

[tex]\red{\bf{ {Answer = \: \: - 48}}} [/tex]

[tex]\qquad[/tex] [tex]\twoheadrightarrow\sf \underbrace {-22 \times 3} + \underbrace {12 \times 2} - \underbrace {6\times 2} + 4 + 2[/tex]

We carry out the three multiplications.

[tex]\qquad[/tex] [tex]\twoheadrightarrow\sf \underbrace {-66 \: + \: 24} \: - \: 12 \: + \: \underbrace {4 \: + \: 2}[/tex]

Now we make the ones that are marked.

[tex]\qquad[/tex] [tex]\twoheadrightarrow\sf \underbrace {-42} \: \: - 12 \: \: + \underbrace {6} \: \: [/tex]

[tex]\qquad[/tex] [tex]\twoheadrightarrow\sf \underbrace {-36 \: \: \: - \: \: \: 12}[/tex]

[tex]\qquad[/tex] [tex]\twoheadrightarrow\sf -48[/tex]

Answer:

30 31 33 are the three integer consective

Answer:

790 oz

Step-by-step explanation:

Ratio:

3oz syrup : 4oz water : 3oz apple juice: 1 serving: 10oz total mixture

We know there is 10oz total mixture because 3oz of syrup + 4oz of water + 3oz of apple juice = 10oz total mixture

We want to find

237oz apple juice: ?oz total mixture

To do this, we can multiply the ratio

3oz apple juice: 10oz total mixture by 237/3, because 237/3 * 3 = 237, getting us to 237oz apple juice on one side and maintaining the ratio so that we can find the total mixture amount, so we have

237oz apple juice: 10*237/3 oz total mixture = 10*79 = 790 oz

Note that

10² = 100

0.08² = 0.0064

and

101.6064 = 100 + 1.6 + 0.0064

It also happens that

1.6 = 2 • 10 • 0.08

which means

101.6064 = 100 + 1.6 + 0.0064

101.6064 = 10² + 2 • 10 • 0.08 + 0.08²

101.6064 = (10 + 0.08)²

101.6064 = 10.08²

which means

√101.6064 = 10.08

which, to one decimal place, is approximately 10.1.

Given that:

CI = ₹408

years = 2 years

Rate of interest = 4%

A = P{1+(R/100)}^

A-P = p{1+(R/100)}^n - P

I = P[1+(R/100)}^n - 1]

408 = P[{1+(4/100)²} - 1]

= P[{1+(1/25)²} - 1]

= P[(26/25)² - 1]

= P[(676/625) - 1]

= P[(676-625)/625]

408 = P(51/625)

P = 408*(625/51)

= 8*625 = 5000

Sum = 5000

Simple Interest (I) = (P*R)/100

= 5000*2*(4/100)

= 50*2*4 = 400

From the given above options, option (a) ₹400 is your correct answer.

The slope is 2The slope is 2The slope is 2The slope is 2The slope is 2The slope is 2

Answer:

(5,2)

Step-by-step explanation:

Answer:

30

Step-by-step explanation:

The man’s son. Since the man has no brothers and the father of the man in the photograph is the man’s father’s son, the father of the man in the photograph must be the man. That means that the man in the photograph is the man’s son.

Step-by-step explanation:

similar means that (with all angles being the same) the side lengths of one triangle all correlate to the corresponding side lengths of the second triangle by the same factor.

and so, because AD = 2 is 1/3 of AB = 4+2 = 6, we need to apply the same factor 1/3 to x compared to 12.

12 × 1/3 = 4.

so, A is correct.

Answer:

Step-by-step explanation:

The goal in scientific notation is to express a value in terms of a number that contains a single unit before the decimal point.  

Examples:

10000:  1.0 x 10^4

23456:  2.3456x10^4

In both cases, the x10^4 is telling us to multiply the first number by 10,000.  10^4 is the same as 10x10x10x10 = 10,000

The justification for scientific notation is that is makes expression large and small numbers much easier, as well as reduces errors due to an incorrectly placed decimal.

An example:  Divide 2500000000 by 5000.  That would normally require setting up a long-hand division problem that not only wastes paper and pencil, but is also prone to decimal point errors.

Do the same problem with scientific notation:

Count the places you want to move the decimal point backwards to just beyond the 5 in 2500000000.  It takes nine steps to move the decimal point to between the 2 and 5:  2.5 followed by 8 zeros.  That's a total of next steps to go in front of the 5.  This is written 2.5 x 10^9

5000 is represented by 5.0x10^4

Now when we divide the same numbers, but in scientific format, it is easier to see the answer:

(2.5x10^9)/(5.0x10^4)

2.5/5 = 0.5

10^9/10^4 = 10^5  [The exponents are subtracted when dividing with exponents:  9-4 = 5]

Put them together to find the final answer:  0.5x10^5

Then move the decimal point one spot to the right and reduce the exponent by 1:

5.0x10^4

------

Add exponents when multiplying:  10^3 x 10^5 = 10^8  (3+5=8)

Subtract when dividing:  10^7/10^2 = 10^5  (7-2=5)

Multiply when there is an exponent raised to another exponent:  (10^4)^3 = 10^12 (4x3 = 12)

Answer:

2

Step-by-step explanation:

[tex]16^{\frac{1}{4} }[/tex] can be rewritten as [tex]\sqrt[4]{16}[/tex].

Solve for the 4th root of 16.

16=4*4=(2*2)(2*2)=2

Answer:

-5/6

Step-by-step explanation:

to find the slope between to lines we can subtract the second y by the first y and subtract the second x by the first x and dividing them by each other

(18 - 3) / (-21 + 3)

minusing a negative is basically adding

after subtracting them you get this

15 / -18

then reduce

-5/6

the slope is -5/6

Answer:SORRY CANT HELP U THERE

Step-by-step explanation: