The population of a strain of bacteria doubles in a culture. At noon there were 80 bacteria present and by 4:00 PM there were 20 480 bacteria. Determine algebraically the doubling period. Hint: You DO NOT need to use systematic trials.

20. (2) 14

A perfect square trinomial will factor into two expressions that are the same, for example: x^2 + 6x + 9 = (x + 3)(x + 3). Since this problem has a C value of 49, it will factor into (x + 7)(x + 7). 7 doubled is 14, therefore one possible value of B is 7.

21. (4) 2, -12

x^2 + 10x + 25 = 24 + 25

(x + 5)^2 = 49

x + 5 = +/- 7

x = 2, -12

22. (3) 3 + sqrt(17)

x^2 - 6x = 8

Complete the Square

x^2 - 6x + 9 = 8 + 9

(x - 3)^2 = 17

x - 3 = +/- sqrt(17)

x = 3 + sqrt(17), 3 - sqrt(17)

23. (1) 1, -5

x^2 + 4x - 5 = 0

x^2 + 4x = 5

x^2 + 4x + 4 = 5 + 4

(x + 2)^2 = 9

x + 2 = +/- 3

x = 1, -5

Hope this helps!

here's the answer to your question

Answer:

y-intercept is (0, -21)

Step-by-step explanation:

For y-intercept, x = 0:

[tex]{ \sf{y + 11 = - 2(0 + 5)}} \\ { \sf{y + 11 = - 10}} \\ { \sf{y = - 21}}[/tex]

If f(x) = 7/(1 + x), then

f (2) = 7/3

f '(x) = -7/(x + 1)²   ==>   f ' (2) = -7/9

f ''(x) = 14/(x + 1)³   ==>   f '' (2) = 14/27

f '''(x) = -42/(x + 1)⁴   ==>   f ''' (2) = -14/27

Then the Taylor series of f(x) about a = 2 is

7/3 + 1/1! (-7/9) (x - 2) + 1/2! (14/27) (x - 2)² + 1/3! (-14/27) (x - 2)³

= 7/3 - 7/9 (x - 2) + 7/27 (x - 2)² - 7/81 (x - 2)³

9514 1404 393

Answer:

  B.  x^2/3^2 + y^2/4^2 = 1

Step-by-step explanation:

The graph looks like a circle, but is not. It is a unit circle scaled by a factor of 3 in the x-direction and a factor of 4 in the y-direction. Thus, its equation is ...

  (x/3)^2 +(y/4)^2 = 1

  x^2/3^2 +y^2/4^2 = 1

Answer:

I think 40 - 60 Million Americans would wear contact lenses.

Answer:

tk 30

Step-by-step explanation:

5 dozen = 5 * 12 = 60 oranges

12/4 = 3

total cost = 60 * 3 = tk.180

total sell = 50 * 3 = tk 150

total lose = 180 - 150 = tk 30

9514 1404 393

Answer:

Step-by-step explanation:

The perimeter ratio smaller : larger is the same as the side length ratio.

  18 : 24 = 3 : 4 . . . smaller : larger perimeter ratio

The area ratio is the square of this.

  3^2 : 4^2 = 9 : 16 . . . smaller : larger area ratio

Answer:

a

Step-by-step explanation:

work and answers below

Answer:

[tex]\text{Part A.}\\(-\frac{1}{8},0),\\(\frac{3}{2},0)\\\\\text{Part B.}\\(\frac{11}{16},\frac{169}{16})\\\\\text{Part C.}[/tex]

Draw a parabola concave down with vertex at [tex](\frac{11}{16},\frac{169}{16})[/tex]. Since the leading coefficient of the equation is -16, the parabola should appear thinner than its parent function [tex]y=x^2[/tex]. Ensure that the parabola passes through the points [tex](\(-\frac{1}{8},0)[/tex] and [tex](\frac{3}{2},0)[/tex].

Step-by-step explanation:

Part A:

The x-intercepts of a function occur at [tex]y=0[/tex]. Therefore, let [tex]y=0[/tex] and solve for all values of [tex]x[/tex]:

[tex]0=-16x^2+22x+3[/tex]

The quadratic formula states that the real and nonreal solutions to a quadratic in standard form [tex]ax^2+bx+c[/tex] is equal to [tex]x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}[/tex].

In [tex]-16x^2+22x+3[/tex], assign:

Therefore, the solutions to this quadratic are:

[tex]x=\frac{-22\pm\sqrt{22^2-4(-16)(3)}}{2(-16)},\\x=\frac{-22\pm 26}{-32},\\\begin{cases}x=\frac{-22+26}{-32}=\frac{4}{-32}=\boxed{-\frac{1}{8}},\\x=\frac{-22-26}{-32}=\frac{-48}{-32}=\boxed{\frac{3}{2}}\end{cases}[/tex]

The x-intercepts are then [tex]\boxed{(-\frac{1}{8},0)}[/tex] and [tex]\boxed{(\frac{3}{2},0)}[/tex].

Part B:

The a-term is negative and therefore the parabola is concave down. Thus, the vertex will be the maximum of the graph. The x-coordinate of the vertex of a quadratic in standard form [tex]ax^2+bx+c[/tex] is equal to [tex]x=\frac{-b}{2a}[/tex]. Using the same variables we assigned earlier, we get:

[tex]x=\frac{-22}{2(-16)}=\frac{-22}{-32}=\frac{11}{16}[/tex]

Substitute this into the equation of the parabola to get the y-value:

[tex]f(11/16)=-16(11/16)^2+22(11/16)+3,\\f(11/16)=\frac{169}{16}[/tex]

Therefore, the vertex of the parabola is located at [tex]\boxed{(\frac{11}{16},\frac{169}{16})}[/tex]

Answer:

x² - √3x / x² - 3

Step-by-step explanation:

To Do :-

Solution :-

We need to rationalize ,

Multiply numerator and denominator by x-√3 :-

Step-by-step explanation:

|a+b|=✓(a²+b²)

|a|+|b|=a+b

||a+b|| ≤ ||a||+|b||

Answer:

33

a2+b2 =c2

a2+ 33 squared = 55 squared

a + 1936 = 3025

3025-1936=1089

square root of 1089 is 33

pleeeaaasssseeee mark as brainliest

Answer: Number 1 is 150

Step-by-step explanation: If you put 72 / 48% in your calculator, you will get your answer.

He paid 0.40 x 50 = 20

He sold it for 0.44 x 50 = 22

His profit was 22-20 = 2

Percentage was 2/20 = 0.10 = 10 %

Answer 10 %

Answer:

X=1

f(x)=16^1

=16

X=2

f(x)=16^2

256

X=3

f(x)=16^3

=4096

X=4

f(x)=16^4

=65536

Here are four different ways to rewrite the function f(x) = 16^x, using a different base for each case:

Using base 2:

f(x) = (2^4)^x = 2^(4x)

Using base 3:

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

Using base 10:

f(x) = (10^(log10(16)))^x = 10^(log10(16) * x)

Using base e (natural logarithm):

f(x) = (e^(ln(16)))^x = e^(ln(16) * x)

In these rewritten forms, the exponentiation of the base is expressed as a simpler expression.

This involves the new base, which helps to illustrate the relationship between the original function and the different bases used.

Learn more about functions

https://brainly.com/question/11624077

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Answer:

3 =f

Step-by-step explanation:

Since this is a right triangle, we can use trig functions

tan theta = opp/ adj

tan 60 = f/ sqrt(3)

sqrt(3) tan 60 = f

sqrt(3) * sqrt(3) = f

3 =f

Answer:

n+3

Step-by-step explanation:

1/2 × 2(n+3)=n +3

I hope this helps

Answer:

yeah, teachers kinda suck

Work Shown:

[tex]7x^2*\sqrt{2x^4}*6\sqrt{2x^{12}}\\\\7*6x^2*\sqrt{2x^4*2x^{12}}\\\\42x^2*\sqrt{4x^{4+12}}\\\\42x^2*\sqrt{4x^{16}}\\\\42x^2*\sqrt{(2x^8)^2}\\\\42x^2*(2x^8)\\\\42*2x^{2+8}\\\\84x^{10}\\\\[/tex]

So that's why the answer is choice C

The requirement that x is nonzero isn't technically necessary. The original expression simplifies to choice C even when x = 0 is the case. Also, we don't have issues such as division by zero errors that could arise. It's a bit curious why your teacher put in that condition.

Answer:

C.

Step-by-step explanation:

7x²×sqrt(2x⁴)×6×sqrt(2x¹²)

we see right away that as constant multiplication factor we have 7×6 = 42.

and then we get from each sqrt expression a sqrt(2), which leads to sqrt²(2) = 2 and therefore 42×2=84.

the only answer option with 84 is C.

now, to be completely sure, and to get some practice, let's look at the other parts :

sqrt(2x⁴) = sqrt(2)×sqrt(x⁴) = sqrt(2)×x²

sqrt(2x¹²) = sqrt(2)×sqrt(x¹²) = sqrt(2)×x⁶

=>

7x²×sqrt(2)×x²×6×sqrt(2)×x⁶ =7×6×2×x²×x²×x⁶ = 84x¹⁰

perfect. C is confirmed.

Answer:

It is decreased by 9%

Step-by-step explanation:

First, find out how much money is decreased. To do this, subtract 13,000-11,830=1170. Finally, figure out how much percent 1170 is of the original price of $13,000.

The answer is 7%.

Hope this helps :)

9514 1404 393

Answer:

  3 ⇒ 12

Step-by-step explanation:

Apparently "a = b" in this case is used to mean f(a) = b. It appears as though the function is ...

  f(x) = x(x+1)

Then f(3) = 3(3+1) = 3·4 = 12

_____

Additional comment

IMO this is a poor use of the equal sign, which should be reserved for situations where the left side expression has the same value as the right side expression.

Answer:

0.0016 = 0.16% probability that the lot will pass inspection.

Step-by-step explanation:

For each bulb, there are only two possible outcomes. Either it is defective, or it is not. The probability of a bulb being defective is independent of any other bulb, which means that the binomial probability distribution is used to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

And p is the probability of X happening.

Sample of 18 light bulbs

This means that [tex]n = 18[/tex]

30% of the bulbs in the lot are defective.

This means that [tex]p = 0.3[/tex]

What is the probability that the lot will pass inspection?

It will pass inspection if there are no defective bulbs, that is, we have to find P(X = 0). So

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]P(X = 0) = C_{18,0}.(0.3)^{0}.(0.7)^{18} = 0.0016[/tex]

0.0016 = 0.16% probability that the lot will pass inspection.

Answer:

B

Step-by-step explanation:

i did the test and it was correct, ur welcome

Answer:

13.37 = BC

Step-by-step explanation:

Since this is a right triangle, we can use trig functions

cos theta = opp / hyp

cos 27 = BC / 15

15 cos 27 = BC

13.36509 = BC

Rounding to the nearest hundredth

13.37 = BC

Answer:

Step-by-step explanation:

First, I would find the point on the curve. By substituting t=1, I get (x, y). Next, I will try to eliminate the t and make a xy equation. In this case, the t's will cancel out in 'x=t-t-1" which wouldnt make this a curve. To find the equation of the tangent line, find the deretitave of the xy equation, and subsitute x in to find the slope at that point. Next, use point slope form to find the equation at the point.

9514 1404 393

Answer:

  8x +4h

Step-by-step explanation:

  [tex]\dfrac{f(x+h)-f(x)}{h}=\dfrac{(4(x+h)^2-8)-(4x^2-8)}{h}\\\\=\dfrac{(4x^2 +8xh+4h^2)-(4x^2-8)}{h}=\dfrac{8xh+4h^2}{h}\\\\=\boxed{8x+4h}[/tex]