Point-Slope Form
*See photo*

The output light frequency of the material used before doubling will be 0.056 Hz.

Frequency is defined as the number of repetitions of a wave occurring waves in 1 second.

Frequency is given by the formula as,

[tex]\rm v = \lambda \times f \\\\\ \rm f = \frac{v}{\lambda} \\\\ \rm f = \frac{3 \times 10^8}{532 \times 10^-9} \\\\ \rm f = 3 \times 10^{12} \\\\ f= 0.056 \ Hz[/tex]

Hence the output light frequency of the material used before doubling will be 0.056 Hz.

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Answer:

Step-by-step explanation:

Simplify the following expression:

Simplify the following expression:

7a + 5b - 2a + b =

5a + 6b

[tex] \sf{\qquad\qquad\huge\underline{{\sf Answer}}} [/tex]

Let's solve for y and z ~

[tex]\qquad \sf  \dashrightarrow \: z + 61 = 180[/tex]

[ Co- interior angle pair ]

[tex]\qquad \sf  \dashrightarrow \: z = 180 - 61[/tex]

[tex]\qquad \sf  \dashrightarrow \: z = 119 \degree[/tex]

now,

[tex]\qquad \sf  \dashrightarrow \: 5y + 14 = 119[/tex]

[ by Alternate interior angle pair ]

[tex]\qquad \sf  \dashrightarrow \: 5y = 119 - 14[/tex]

[tex]\qquad \sf  \dashrightarrow \: 5y = 105[/tex]

[tex]\qquad \sf  \dashrightarrow \: y = 21 °[/tex]

If you vertically stretch the exponential function f(x)=2^x by a factor of 3, the resulting function will be y = 3*2^x

The standard exponential function is expressed as:

y = ab^x

The value of x determines the nature of a graph whether vertical or horizontal stretch.

If x  > 1, it is a vertical stretch

Given the function f(x) = 2^x, if you vertically stretch the exponential function f(x)=2^x by a factor of 3, the resulting function will be y = 3*2^x

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Answer

D

Step-by-step explanation:

The probability of 5 successes given n = 12, x = 5, and p = 0.25 is approximately 0.082 by solving binomial probability.

The correct answer is A) 0.082.

The probability of x successes given the probability p of success on a single trial, with n trials, can be calculated using the binomial probability formula:

[tex]P(x) = (n_C_x) * p^x * (1-p)^{(n-x)[/tex]

In this case, n = 12, x = 5, and p = 0.25. Let's substitute these values into the formula:

[tex]P(5) = (12C5) * (0.25)^5 * (1-0.25)^{(12-5)[/tex]

Using the combination formula ([tex]n_C_r[/tex]) to calculate ([tex]{12}_C_5[/tex]):

[tex]P(5) = (12!)/(5!(12-5)!) * (0.25)^5 * (0.75)^7[/tex]

Simplifying the combination:

[tex]P(5) = (12!)/(5!7!) * (0.25)^5 * (0.75)^7[/tex]

Calculating the factorial terms:

[tex]P(5) = (12111098)/(54321) * (0.25)^5 * (0.75)^7[/tex]

[tex]P(5) = 792 * 0.0009765625 * 0.1334838867[/tex]

P(5) ≈ 0.082

Therefore, the probability of 5 successes given n = 12, x = 5, and p = 0.25 is approximately 0.082 by solving binomial probability.

The correct answer is A) 0.082.

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The value of a₄₁ mean the expression in 4th row and 1st column will be 2. Then the correct option is B.

The complete question is attached below.

A matrix is a specific arrangement of items, particularly numbers. A matrix is a row-and-column mathematical structure. The [tex]\rm a_{ij}[/tex] element in a matrix, such as M, refers to the i-th row and j-th column element.

The matrix is given below.

[tex]\begin{bmatrix} 1&3&8&5&\\ 5&4&6&2\\6&7&1&8\\2&9&3&7&\\\end{bmatrix}[/tex]

Then the value of a₄₁ mean the expression in 4th row and 1st column will be 2.

Then the correct option is B.

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The equivalent expression of square root of -64 is 8i

We have:

square root of -64

Rewrite as:

√-64

Expand

√64 * √-1

Take the square root of 64

8√-1

In complex numbers

√-1  = i

So, we have:

8i

Hence, the equivalent expression of square root of -64 is 8i

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Answer:

Step-by-step explanation:

Solve for x in the equation

x/5 - 2 = 11

x/5 = 11 + 2

x/5 = 13

x = 5 * 13

x = 65

-----------------

check

65/5 - 2 = 11

13 - 2 = 11

11 = 11

the answer is good

Answer:

2

Step-by-step explanation:

lucky guess from my boi tony

Answer:

Step-by-step explanation:

slope=(1-3)/(-2-(-5))

=-2/(-2+5)

=-2/3

Answer:

Round of 969.991

970

Rules of round off

1) If the digit is odd no. the no. will increase to 1

2) if it is even the no. will be same.

An equation is formed of two equal expressions. The value of r in the given equation is 6.

An equation is formed when two equal expressions are equated together with the help of an equal sign '='.

The solution for the value of r in the given equation will be,

5r - r - 9 = 15

5r - r - 9 + 9 = 15 + 9

4r = 24

r = 6

A.) The first step is to Use the addition property of equality. Thus, the correct option is B.

B.) The value of r in the given equation is 6.

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The answer choice which represents a polynomial which is factored completely is; (y³ - 4y² +5)

The polynomials as given in the task content are;

4(4x⁴ -1) + 2x

(y³ - 4y² +5)

3x (9x² -1)

5x² -17x +14

Hence it follows that the polynomial which cannot be further factorised is; (y³ - 4y² +5).

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Answer:3 x (9 x squared + 1)

it is c because i did the test and put b but got it wrong

Step-by-step explanation:

Answer:

16

Step-by-step explanation:

x^2+16x+16

(x+4)(x+4)

x^2+ 4x+4x+16

Answer:

The answer is C.) 64 on edge.

We need to understand circles and colinear points in order to use the building tool to create a circle.

It is a point locus drawn equidistant from the center. The radius of the circle is the distance from the center to the circumference.

Draw arcs such that they all bisect one another at a point, which will be the center of the circle, starting with three non-colinear points (points A, B, and C).

Additionally, the radius will match the distance between the arcs' centers and their correspondingly drawn arcs.

Hence we need to understand circles and colinear points in order to use the building tool to create a circle.

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Answer:

1≥2x and 6x≥3+8x-4 are correct representations of the inequality 6x ≥ 3 + 4(2x – 1).Option A,B and C are correct.

Inequality is a sort of equation in which the equal sign is missing. As we will see, inequality is defined as a statement regarding the relative magnitude of two claims.

The solution to the given inequality is;

6x≥3+4(2x-1)

6x≥3+8x-4

2x≤1

x≤(1/2)

The correct options are;

A)1 ≥ 2x

B)6x ≥ 3 + 8x – 4

C)A number line from negative 1.5 to 1.5 in increments of 0.5. A point is at 0.5 and a bold line starts at 0.5 and is pointing to the left.

1≥2x and 6x≥3+8x-4 are correct representations of the inequality 6x ≥ 3 + 4(2x – 1).

Hence, options A, B, and C are correct.

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Answer:

A, B, C

Step-by-step explanation:

Answer: I know two methods of solving both of the sums. One is the method of elimination, the other is method of substitution. You can do any of the given methods which is easier for you. Both methods will be shown below:

1) 5x + y = 9       - - - - (i)
  10x - 7y = - 18 - - - - (ii)

eq. (i) multiplied by 2
   10x + 2y = 18  - - - - (i)
   10x - 7y = - 18 - - - - (ii)       {subtraction of eq. (ii) from eq. (i)}
    0   + 9y = 36
              y = 36/9
              y = 4

From eq. (i),
   5x + y = 9
-> 5x + 4 = 9
-> 5x = 9 - 4
->  x = 5/5
-> x = 1

So, x = 1 and y = 4

2) - 4x + 9y = 9 - - - - (i)
      x - 3y = - 6 - - - - (ii)

eq. (ii) multiplied by 3
    - 4x + 9y = 9 - - - - (i)
     3x - 9y  = - 18 - - (ii)        {addition of eq. (ii) and eq. (i)}
      - x + 0 = - 9
              x  =  9

From eq. (ii),
    x - 3y = - 6
->  9 - 3y = - 6
->  - 3y = -6-9
->  y = -15/-3
->  y = 5

So, x = 9 and y = 5

1) 5x + y = 9       - - - - (i)
  10x - 7y = - 18 - - - - (ii)

eq. (i)

  5x + y = 9
-> y = 9 - 5x

Value of eq. (i) in eq. (ii)
   10x - 7y = - 18
-> 10x - 7(9 - 5x) = - 18
-> 10x - 63 + 35x = - 18
-> 45x = - 18 + 63
-> x = 45/45
-> x =  1

From eq. (i),
   5x + y = 9
-> 5 + y = 9
-> y = 9 - 5
-> y = 4

So, x = 1 and y = 4

2) - 4x + 9y = 9 - - - - (i)
      x - 3y = - 6 - - - - (ii)

eq. (i)
   - 4x + 9y = 9
-> - 4x = 9 - 9y
-> x = (9 - 9y) / -4

Value of eq. (i) in eq. (ii)
      x - 3y = - 6
-> (9 - 9y) / -4  -3y = - 6
-> (9 - 9y + 12y) = - 6 * - 4
-> 3y = 24 - 9
-> y = 15/3
-> y =  5

From eq. (ii)
   x - 3y = - 6
-> x - 3(5) = - 6
-> x - 15 = - 6
-> x = - 6 + 15
-> x = 9

So, x = 9 and y = 5

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┏━∪∪━━━━┓
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From the power rules, the matching of  each expression with its result is:

[tex](8.6*10^7)(9.1*10^{-8})=7.8[/tex]

[tex](6.9*10^5)(4.8*10^{-3})=3.3*10^3[/tex]

[tex]\frac{(3.7*10^2)*(4.6*10^{-3})}{(1.4*10^{-6})*(5.7*10^{8})} =2.1*10^{-3}[/tex]

[tex]\frac{(3.1*10^5)*(5.3*10^{-9})}{(7.3*10^{2})*(6.1*10^{-7})}=3.7[/tex]

There are different power rules, see some them:

1. Multiplication with the same base: you should repeat the base and  add the exponents.

2. Division with the same base: you should repeat the base and  subctract the exponents.

3.Power. For this rule, you should repeat the base and multiply the exponents.

4. Zero Exponent. When you have an exponent equals to zero, the result must be 1.

From this for your question, you have:

[tex]\frac{(3.7*10^2)*(4.6*10^{-3})}{(1.4*10^{-6})*(5.7*10^{8})} =\frac{(3.7*4.6)*(10^2*10^{-3})}{(1.4*5.7)*(10^{-6}*10^{8})} =\frac{17.02*10^{-1}}{7.98*10^2} =2.13*10^{-3}=2.1*10^{-3}[/tex]

[tex]\frac{(3.1*10^5)*(5.3*10^{-9})}{(7.3*10^{2})*(6.1*10^{-7})}=\frac{(3.1*5.3)*(10^{5}*10^{-9})}{(7.3*6.1)*(10^{2}*10^{-7})} =\frac{16.43*10^{-4}}{44.53*10^{-5}}=0.36896*10^1=3.7[/tex]

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Answer: These ARE congruent to each other.

Step-by-step explanation: Do you see the ''tick marks?'' They both have 1 set of 2, and 1 set of 1. If that makes sense. They also have a "angle" in one of their acute angles.

Answer:

[tex]x \approx 2.740646096[/tex]

Step-by-step explanation:

Given:

[tex]x\log_{10}x=1.2[/tex]

Rewrite so that it's equal to zero:

[tex]\implies x\log_{10}x-1.2=0[/tex]

Therefore:

[tex]\implies f(x)=x\log_{10}(x)-1.2[/tex]

Differentiate the function:

Use the product rule to differentiate [tex]x\log_{10}(x)[/tex]:

[tex]\textsf{Let }u=x \implies \dfrac{du}{dx}=1[/tex]

[tex]\textsf{Let }v=\log_{10}(x) \implies \dfrac{dv}{dx}=\dfrac{1}{x \ln 10}[/tex]

[tex]\begin{aligned}\implies \dfrac{dy}{dx} & = u\dfrac{dv}{dx}+v \dfrac{du}{dx}\\& = \dfrac{x}{x \ln 10}+\log_{10}(x)\\& = \dfrac{1}{\ln 10}+\log_{10}(x)\end{aligned}[/tex]

[tex]\implies f'(x)=\dfrac{1}{\ln 10}+\log_{10}(x)[/tex]

[tex]\implies f'(x)=\dfrac{1+\ln 10 \log_{10}(x)}{\ln 10}[/tex]

Newton-Rhapson iteration formula

[tex]x_{n+1}=x_n-\dfrac{f(x_n)}{f'(x_n)}[/tex]

Substitute the function and its derivative into the formula, replacing x with [tex]x_n[/tex]:

[tex]\implies x_{n+1}=x_n-\dfrac{x_n\log_{10}(x_n)-1.2}{\dfrac{1+\ln 10 \log_{10}(x)}{\ln 10}}[/tex]

[tex]\implies x_{n+1}=x_n-\dfrac{x_n\ln 10\log_{10}(x_n)-1.2\ln 10}{1+\ln 10 \log_{10}(x_n)}[/tex]

Therefore, the iteration formula is:

[tex]x_{n+1}=x_n-\dfrac{x_n\ln 10\log_{10}(x_n)-1.2\ln 10}{1+\ln 10 \log_{10}(x_n)}[/tex]

Let [tex]x_0=3[/tex]

Substitute this into the formula and carry out 3 iterations:

[tex]\implies x_{1}=3-\dfrac{3\ln 10\log_{10}(3)-1.2\ln 10}{1+\ln 10 \log_{10}(3)}=2.746149035[/tex]

[tex]\implies x_2=2.740648841[/tex]

[tex]\implies x_3= 2.740646096[/tex]

Answer:

3c + 4

Step-by-step explanation:

Forming an expression

Number of books with Jill = c

To find the number of books with Tonya, multiply 'c' by 2 and then add 4 to it.

Number of books with Tonya = 2*c + 4

                                                 = 2c + 4

Total books all together = c + 2c + 4   {Combine like terms}

                                        = 3c + 4

The approximate number of bacteria after 16 hours is 60 bacteria ,Option C is the right answer.

A function is a Mathematical statement which connects a dependent variable and an independent variable.

The graph shows the  the growth rate of a certain bacteria in a lab

the number of bacteria is on the y axis and

the number of hours is on the x axis

The function is continuous ,

From the graph the approximate number of bacteria after 16 hours is

60 bacteria

Therefore Option C is the right answer.

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Answer:

Step-by-step explanation:

4567890987654345678

Answer:

see explanation

Step-by-step explanation:

the sum of the lengths of any two sides of a triangle is greater than the length of the third side.

if the sides are a, b, c , then the following must be true

a + b > c

a + c < b

b + c > a

for the 3 sides to form a triangle

Answer:

A. [tex]\frac{5}{9}[/tex]

Step-by-step explanation:

To find f(-2) in f(x)=5*3^x, plug in -2 into all the x values.

f(-2)=5*3^-2, you can use calculator to calculate 3^-2 which equals 0.1, forever 1's.

f(-2)=5*0.1=0.5  Forever 5's.

f(-2)=0.5 or [tex]\frac{5}{9}[/tex]

Hope this helps!

If not, I am sorry.

The correct option for the given vector is the third one:

If the initial point is (0, 0), then the component form of the vector is just equal to the terminal point of the vector.

Then we have:

u = (5, -8)

For a vector w = (x, y) the magnitude is:

[tex]||w|| = \sqrt{x^2 + y^2}[/tex]

In this case, the magnitude will be:

[tex]||u|| = \sqrt{5^2 + (-8)^2} = \sqrt{89}[/tex]

Then the correct option is the third one.

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Answer:

2 ± i

Step-by-step explanation:

by 5, I assume you mean +5

x² - 4x + 5 = 0

x = (-b±(√(b²-4ac)) / 2a

x = (4 ± (√(16 - 20)) / 2

x = (4 ± (√(-4)) / 2

√-4 = √4√-1 which is 2i

x = (4 ± 2i) / 2

x = 2 ± i

Answer:

The median is 3.

Step-by-step explanation:

Since, most of the values presented are 0-8 and median is the middle of any data set. It has to be 3.