can someone please help me, as well as factoring the expression

Answer:

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The predicted population of bacteria when following a continuous exponential growth model, at a relative rate of 3% per hour, from an initial population of 428 bacteria grows to 512.4 bacteria in 6 hours.

A continuous exponential growth model is used to determine the final value of a quantity (V), from an initial value of the quantity (V₀), at a rate of continuous growth per unit time (r), after the time (t), as:

[tex]V = V_0e^{rt}[/tex].

In the question, we are given that the number of bacteria in a certain population is predicted to increase according to a continuous exponential growth model, at a relative rate of 3% per hour.

We are asked, to find the predicted population after six hours when the initial population was 428 bacteria.

Thus, we take V₀ = 428, r = 3% = 0.03, and t = 6, in the equation:

[tex]V = V_0e^{rt}[/tex] ,

to find the predicted population (V) of bacteria after 6 hours.

Thus,

[tex]V = 428e^{0.03*6}\\\Rightarrow V = 428e^{0.18}\\\Rightarrow V = 428*1.1972173631218\\\Rightarrow V = 512.40903141613\\\Rightarrow V = 512.4[/tex]

Rounding to the nearest tenth.

Thus, the predicted population of bacteria when following a continuous exponential growth model, at a relative rate of 3% per hour, from an initial population of 428 bacteria grows to 512.4 bacteria in 6 hours.

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Step-by-step explanation:

Question 46.

[tex](2\sqrt{5}-\sqrt{2} )^2=(2\sqrt{5})^2-2*2\sqrt{5}*\sqrt{2} +(\sqrt{2})^2 } =4*5-4*\sqrt{2*5} +2=\\=20-4\sqrt{10}+2=22-4\sqrt{10}.[/tex]

Answer: E. None of these.

Question 47.

[tex]\frac{4\sqrt{5} }{\sqrt{3} } =\frac{4*\sqrt{5}*\sqrt{3} }{\sqrt{3} *\sqrt{3} } =\frac{4*\sqrt{5*3} }{3}=\frac{4\sqrt{15} }{3} .[/tex]

Answer: E. None of these.

Answer:

45) E 47) E

Step-by-step explanation:

45)

Remember the formula [tex](a-b)^2=a^2-2ab+b^2[/tex]

[tex](2\sqrt5-\sqrt2)^2=(2\sqrt5)^2-2(2\sqrt5\times\sqrt2)+(\sqrt2)^2\\\\=20-2(2\sqrt{10})+4\\\\=24-4\sqrt{10}[/tex]

Hence E. None of these.

47)

[tex]\frac{4\sqrt{5}}{\sqrt3}=\frac{4\sqrt5\times\sqrt3}{\sqrt3\times\sqrt3}\\\\=\frac{4\sqrt15}{3}[/tex]

Hence E. None of these.

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Answer:

(1,0)

Step-by-step explanation:

I'm just gonna say that the point you want to be transformed is the origin. It will be moved to (1,0)

Answer:

Angle C = 68.7°

Step-by-step explanation:

The largest angle es angle C ([tex]\beta[/tex])

[tex]26^{2} =22^{2} +24^{2} -2(22)(24)cos\beta[/tex]

[tex]676=484+576-1056cos\beta[/tex]

[tex]676-1060=-1056cos\beta[/tex]

[tex]\frac{-384}{-1056} =cos\beta[/tex]

[tex]\beta =cos^{-1} (\frac{-384}{-1056} )=cos^{-1} (.36363)=68.676=68.7^{o}[/tex]

[tex] \frac{?}{20} = \frac{6}{10} [/tex]

[tex] \frac{?}{2} = 6 \\ ? = 6\times 2 = 12[/tex]

Answer:A.47.5 miles is 76

Step-by-step explanation:

in real life its like 76.44, but im rounding

The quadratic equation u² - u - 6 = 0 where u = (x -4) is equivalent to (x-4)² – (x − 4) − 6 = 0 option (D) is correct.

Any equation of the form [tex]\rm ax^2+bx+c=0[/tex] where x is variable and a, b, and c are any real numbers where a ≠ 0 is called a quadratic equation.

As we know, the formula for the roots of the quadratic equation is given by:

[tex]\rm x = \dfrac{-b \pm\sqrt{b^2-4ac}}{2a}[/tex]

We have a quadratic equation:

(x-4)² – (x − 4) − 6 = 0

Let (x - 4) = u

u² - u - 6 = 0

Thus, the quadratic equation u² - u - 6 = 0 where u = (x -4) is equivalent to (x-4)² – (x − 4) − 6 = 0 option (D) is correct.

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Answer:Option D on edge 2022

Step-by-step explanation:

Answer:

Step-by-step explanation:

2x squared, denoted (2x)2, is equal to 4x2. In general, we can raise a product to a power using the following product rule for exponents: (ab)n = an

The Big O notation of the composite function 5N^3 O(N^2) is c. O(N^3).

A composite function of two capabilities combines the given two functions inside the given order. i.e., for any given functions f(x) and g(x), there may be four composite functions: f(g(x)) that is substituting g(x) into f(x) g(f(x)) that's substituting f(x) into g(x).

A composite characteristic is a function that relies upon any other feature. A composite characteristic is created while one characteristic is substituted for another feature. For instance, f(g(x)) is the composite function that is fashioned whilst g(x) is substituted for x in f(x). f(g(x)) is studied as “f of g of x”.

In Maths, the composition of a character is an operation wherein two capabilities say f and g generate a brand new feature say h in one of these manners that h(x) = g(f(x)). It method right here feature g is implemented to the function of x. So, basically, a feature is carried out to the result of every other feature.

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Answer:

51.7661748226 degrees; 38.2338251774 degrees

Step-by-step explanation:

First, draw a diagram to illustrate this situation. Looking at angle A, Eric's height, 1.65 m, corresponds to OPPOSITE, and Eric's shadow, 1.30 m, corresponds to ADJACENT. Using SOH CAH TOA, the equation is:

tan(A) = 1.65/1.30

A = arctan(1.65/1.30)

A = 51.7661748226 deg

Looking at angle B, 1.65 m is ADJACENT and 1.30 m is OPPOSITE. Therefore, the equation is:

tan(B) = 1.30/1.65

B = arctan(1.30/1.65)

B = 38.2338251774 deg

Answer: 2   55   121

             22   5      11

Step-by-step explanation:

By looking at the diagram, we can see that:

As you can see, the ray DE starts at point D and then passes through E, and then continues.

Then the only endpoint of that ray is D.

The ray GA starts at point G and goes through A (so it goes to the left of G).

The ray DF starts at point F and goes through F (So it goes to the right of D).

Then these two rays don't intersect, because D is at the right of G.

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The inequality that correctly represents this scenario is given as follows:

[tex]2x + 5y \leq 25[/tex]

The graph is given at the end of the question.

A system of inequalities is when two or more variables are related, and inequalities are built to find the values of each variable.

In this problem, the variables are given as follows:

Chocolate chips are $2 per pound and pecans are $5 per pound. She wants to spend at most $25, hence:

[tex]2x + 5y \leq 25[/tex]

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The number of lighter boards and heavier boards in the truck is 216 and 192 boards respectively.

let

Light board = x

Heavy board = y

x = y + 24

x + y = 408

(y + 24) + y = 408

y + 24 + y = 408

2y = 408 - 24

2y = 384

y = 384 / 2

y = 192 boards

So,

x = y + 24

= 192 + 24

x = 216 boards

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Answer:

A

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

we know the thickness is x, so the sides are 3+2x and 4+2x

then we use foil:

(3+2x)(4+2x)=12+6x+8x+4x^2=4x^2+14x+12

we know the area is 15

4x^2+14x+12=15

4x^2+14x-3=0

So it is B

The value of k are -5 and -7 if the distance between points (2,k) and (0,−6) is √5

It is defined as the formula for finding the distance between two points. It has given the shortest path distance between two points.

The distance formula can be given as:

[tex]\rm d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

The question is:

Given the points (2,k) and (0,−6), for which values of k would the distance between the points be √5

[tex]\rm \sqrt{5}=\sqrt{(0-2)^2+(-6-k)^2}[/tex]

5 = 4 + (6 + k)²

After solving:

[tex]\rm 4+\left(6+k\right)^2-4=5-4[/tex]

(6 + k)² = 1

k = -5 or -7

Thus, the value of k are -5 and -7 if the distance between points (2,k) and (0,−6) is √5

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Answer:

26.4

Step-by-step explanation:

Law Of Cosines:

    [tex]cos(A)=\frac{b^2+c^2-a^2}{2bc}[/tex]

    This should work for any side. This can generally be thought as:

   [tex]cos(\text{angle}) = \frac{\text{sum of squares of two other sides-opposite side squared}}{\text{2 times the product of the other two sides}}[/tex]

    If this is too confusing here's the formula for the other sides (which is essentially the same, just different variables)

   [tex]cos(B)=\frac{a^2+c^2-b^2}{2ac}[/tex]

   [tex]cos(C) =\frac{a^2+b^2-c^2}{2ab}[/tex]

Anyways now just plug in the known values into the equation

[tex]cos(A)=\frac{4^2+6^2-3^2}{2(6)(4)}\\[/tex]

Square and multiply values

[tex]cos(A)=\frac{16+36-9}{48}[/tex]

Add the values in the numerator

[tex]cos(A)=\frac{43}{48}[/tex]

Take the inverse of cosine on both sides

[tex]A=cos^{-1}(\frac{43}{48})[/tex]

calculate arccosine (inverse cosine) using a calculator

[tex]A\approx 26.384[/tex]

Round to nearest tenth

[tex]A\approx26.4[/tex]

The choice which defines same arithmatic sequence using a Recursive Formula and an Explicit formula is (A) which is [tex]a_1= -23, a_n = a_{n-1}+ 12,a_n=-23 +12(n-1)[/tex]

If first term of a arithmatic sequence is a₁ and the common difference is d then,

By Explicit Formula, the n-th term of the sequence is given by,

[tex]a_n=a_1+(n-1)d[/tex]

By Recursive Formula,

[tex]a_n=a_{n - 1}+d[/tex]

In the first choice: a₁ = -23 and

[tex]a_n=a_{n-1}+12[/tex]

Then by recursive formula, it suggests arithmatic sequence with first term -23 and common difference 12.

and

[tex]a_n=-23+12(n-1)[/tex]

So by explicit formula it also suggests arithmatic sequence with first term -23 and common difference 12.

So it is one correct choice.

In second choice: a₁ = -100 and

[tex]a_n=a_{n-1}+1[/tex]

By recursive formula, it suggests arithmatic sequence with first term -100 and common difference 1.

[tex]a_n=100-1(n-1)[/tex]

By explicit formula, it suggests arithmatic sequence with first term 100 and common difference -1.

So it is not the correct choice.

In third choice: a₁ = -41 and

[tex]a_n=a_{n-1}+12[/tex]

By recursive formula, it suggests arithmatic sequence with first term -41 and common difference 12.

[tex]a_n=12-41(n-1)[/tex]

By explicit formula, it suggests arithmatic sequence with first term 12 and common difference -41.

So it is not the correct choice.

In fourth choice: a₁ = 50 and

[tex]a_n=a_{n-1}-4[/tex]

By recursive formula, it suggests arithmatic sequence with first term 50 and common difference -4.

[tex]a_n=50+4(n-1)[/tex]

By explicit formula, it suggests arithmatic sequence with first term 50 and common difference 4.

So it is not the correct choice.

Hence the option (A), the first choice is correct.

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Answer:

b. 120

Step-by-step explanation:

3t2s

3(2)2(10)

6(20)

120

Answer:

Hello! The answer is 120.

Step-by-step explanation:

s = 10 and t = 2

Substitute:

(3)(2)(2)(10)

3 × 2 = 6

2 × 10 = 20

6 × 20 = 120

Answer: B , c, E

Step-by-step explanation:

Given that ,

∡J=90° , ∡k=30° , ∡L=60°

In the triangle ΔJKL,

 tan ∠L = tan 60°

⇒ JK÷JL= √3

⇒JK = √3JL

Thus, A is incorrect and B is correct

Again,

cos ∠L = cos60° =0.5

⇒JL/KL = 1÷2

⇒ JL = (1÷2)KL

⇒JL×2= KL

⇒ KL=2JL

Hence, F & D are incorrect and C is correct

Earlier we got,

JK = √3.JL

⇒JL=JK÷√3

and JL= (1÷2).KL

So, JK÷√3=(1÷2)KL

⇒JK÷√3×2 = KL

⇒2.JK= √3KL

⇒JK = (√3÷2).KL

hence E is correct

Answer:

x-intercept of f(x)=x²+3x-4 is (1,0) &(-4,0)

x-intercept of g(x)=x-4 is (4,0)

y-intercept of f(x)=x²+3x-4 is (0,-4)

y-intercept of g(x)=x-4 is (0,-4)

Step-by-step explanation:

[tex]f(x) = x {}^{2} + 3x - 4 \\ to \: find \: x \: intercept \: subistitute \: f(x) = 0 \\ 0 = x {}^{2} - 3x - 10 \\ x { }^{2} - 3x - 1 = 0 \\ x {}^{2} + 2x - 5x - 10 = 0 \\ x(x + 2) - 5x - 10 = 0 \\ x(x + 2) - 5(x + 2) = 0 \\ (x + 2).(x - 5) = 0 \\ x + 2 = 0 \\ x - 5 = 0 \\ x = - 2 \\ x = 5 \\ the \:equation \: x \: intercept \: are \: - 2and \: 5 \\ f(0) = 0 {}^{2} + 3(0) - 4 \\ - 4 \: is \: y \: intercept \: of \: f(x) = x {}^{2} + 3x - 4 \\ where \: as \: for \: g(x) = x - 4 \\ to \: find \: x \: intercept \: f(x) = 0 \\ 0 = x - 4 \\ - x = - 4 \\ x = 4 \\ 4is \: the \: x \: intercept \: and \: for \: the \: y \: intercept \\ g(0) = 0 - 4 \\ y = - 4is \: the \: y \: intercept.[/tex]

The total weight of the two pieces together is 6 pounds.

A piece of raw silk that is 100 yards long by 1.25 yards wide weights 38lb.

Then, a piece that is 12.5 yards long (and still 1.25 yards wide) will weight:

M = (12.5/100)*38lb = 4.75 lb

And a piece of habotai silk that is 100 yards long by 1.25 yards wide weights 12lb.

Then, a piece that is 12.5 yards long will weigh:

M' = (12.5/100)*12lb = 1.5 lb

If we add these two, we get a total weight of:

M + M' = 4.5lb + 1.5lb = 6lb

The total weight of the two pieces together is 6 pounds.

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Answer:

75 / 192

Step-by-step explanation:

When it comes to multiplying fractions, you just multiply them straightforward. Multiply the numerator with the numerator, and the denominator with the denominator

Answer:

12

Step-by-step explanation:

just find the HCF, which will be

2² × 3 = 12

The true statements about the functions are:

The complete question is in the attached image

From the image, we have:

This means that the true statements about the functions are g(x) has the maximum greatest value and h(x) has a range of all negative numbers.

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Answer:

cant say you dont show

Step-by-step explanation:

id love to help but like send a picture next time

The probability that the randomly drawn card is an odd number (3, 5, 7, 9) or of spade suit is 25/52.

In the question, we are informed that a card is drawn at random from a standard 52-card deck.

We are asked the probability that the randomly drawn card is an odd number (3, 5, 7, 9) or of spade suit.

We assume the event of drawing an odd card from the random pick to be A, and the event of drawing a card of spade suit to be B.

The number of outcomes favorable to event A = 16 {4 odd cards of each of the 4 suits, that is, 4*4 = 16}.

The total number of possible outcomes = 52 {The number of cards in the deck}.

Therefore, the probability of event A, P(A) = 16/52.

The number of outcomes favorable to event B = 13 {The 13 cards of spade suit}.

The total number of possible outcomes = 52 {The number of cards in the deck}.

Therefore, the probability of event B, P(B) = 13/52.

The number of outcomes favorable to events A and B both = 4 {4 odd cards of the spade suit}.

The total number of possible outcomes = 52 {The number of cards in the deck}.

Therefore, the probability of events A and B both, P(A ∩ B) = 4/52.

The probability that the randomly drawn card is an odd number or of spade suit is represented by P(A ∪ B), which is calculated by the formula:

P(A ∪ B) = P(A) + P(B) - P(A ∩ B) = 16/52 + 13/52 - 4/52 = 25/52.

Hence, the probability that the randomly drawn card is an odd number (3, 5, 7, 9) or of spade suit is 25/52.

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Answer:

(5a+5b+3ab)/15

Step-by-step explanation:

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