If a₁ = 4 and an = 5an-1 then find the value of a5.

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

Answer:

-1 and -11

Step-by-step explanation:

"sum" means we're adding.

-1 + -11 = - 12

"product" means we're multiplying.

-1 × -11 = 11

Answer:

y = -3x + 1

Step-by-step explanation:

the line crosses the y-axis at (0,1) then c = 1

The points (0,1) and (1,-2) lie on the line then

m = slope = [(-2)-1]÷(1-0) = [-3]÷(1) = -3÷1 = -3

Therefore,

The equation of the line is : y = -3x + 1

The odds in favor of the Cougars losing the toss in exactly two of three games is 3:8 option second is correct.

It is defined as the ratio of the number of favorable outcomes to the total number of outcomes, in other words, the probability is the number that shows the happening of the event.

We have:

A coin toss is used to determine which team will receive the ball at the beginning of a football game.

The Cougars always choose tails in the toss.

There will total of 8 cases and in 8 cases there will be three cases in which exactly two heads will come so,

3:8

The cases = {TTT, TTH, THT, HTT, HHT, HTH, HHT, HHH}

Thus, the odds in favor of the Cougars losing the toss in exactly two of three games is 3:8 option second is correct.

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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]

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:

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.

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.

See below for the vocabularies and their correct definition

Match the following vocabulary

The terms are given as:

To get the inverse of a conditional, the hypothesis and the conclusion are negated, without interchanging them.

So, we have:

Inverse of a conditional ⇒ A new statement formed by negating both the hypothesis and the conclusion.

To get the contrapositive of a conditional, the hypothesis and the conclusion are negated, after interchanging them.

So, we have:

Contrapositive of a conditional ⇒ Formed by exchanging the hypothesis and the conclusion and negating both of them.

To get the converse of a conditional, we simply interchange the hypothesis and the conclusion, without negating them

So, we have:

Converse of a conditional ⇒ A statement formed by interchanging the hypothesis and the conclusion in a conditional statement.

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Answer:

The answer is Convers because it literally takes the hypothesis and the conclusion and interchanges them.

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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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.

Answer:

The solution of the system of equations are x = -2 and y = 15, the factor is 2 and 4 for the 1st and 2nd equation respectively.

It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.

If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.

We have a system of equations:

1st Equation: 4x + y = 7

2nd Equation: 2x + y = 11

Subtract equation 2nd from 1st

(4x + y) - (2x + y) = 7 - 11

2x = -4

x = -2

Now in equation 1st multiply by 2 and in equation 2nd multiply by 4

8x + 2y = 14

8x + 4y = 44

Subtract:

-2y = -30

y = 15

The factor is 2 and 4 for the 1st and 2nd equation respectively.

Thus, the solution of the system of equations are x = -2 and y = 15, the factor is 2 and 4 for the 1st and 2nd equation respectively.

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Answer:

Using the concept of speed-distance-time, we find that the diameter of the circular path is 12 inches.

Step-by-step explanation:

Given that the object completes one revolution in 8 seconds. So, the circular speed of the object is 2πr/8 = πr/4 inches per seconds, where r is the radius of the circular path. The speed can be written as:

πr/4 inches per seconds = 60πr/4 inches per minute = 15πr inches per minute.

But, it is given that the circular speed of the object is 90π inches per minute. So,

90π = 15πr

r = 6 inches

Since, diameter is the double of radius, d = 2r = 12 inches.

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Answer:

They are the same angle.

Step-by-step explanation:

We have a diagonal line and two 180° parallel lines running through it. The x and y values should be identical because of the placement. The diagonal on the right and right above the 180° angle.

Option 2: Corresponding angles.

Hope this helps!

If not, I am sorry.

Answer:

Area=12x square units;  Perimeter=5x+14 units

Step-by-step explanation:

Recall the formulas for area and perimeter of a triangle:

Area of a triangle is half of the product of a base its corresponding height:

[tex]A=\frac{1}{2}bh[/tex]

Perimeter is the sum of all of the side lengths:

[tex]P=a+b+c[/tex]

In arbitrary triangles ABC, the sides are labeled across from a vertex with a matching lowercase letter.  So, in my diagram, side "b" is the bottom with length "8".  Side "b" is also the base, so the corresponding height is the perpendicular line segment that connects side "b" with vertex "B", which measures "3x"... 3 times some unknown value.

Side "a" is length "4x-3", and side "c" is length "x+9".

In this situation, where the sides have their specific relationship with "x" and the height is exactly triple "x", solving for x (and thus exact numerical values for the Perimeter and Area) involves trying to relate the two equations, possibly done with Heron's formula for area, or with trigonometry.  Ultimately, it involves solving a 4th degree polynomial to get an exact answer, which is not what the question intends, so we'll leave the Area and Perimeter in terms of x (meaning there will still be "x" in our expressions to represent the Area and Perimeter).

Area

[tex]A=\frac{1}{2}bh\\A=\frac{1}{2}(8)(3x)\\A=12x[/tex]

So the Area of the triangle equals 12x square units.

Perimeter

[tex]P=a+b+c\\P=(4x-3)+(8)+(x+9)\\P=5x+14[/tex]

So the Perimeter of the triangle equals 5x+14 units

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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The missing end of the line segment [tex]\overline {GH}[/tex] whose midpoint is M(x, y) = (5, 3) and known endpoint is G(x, y) = (1, -5) is the point H(x, y) = (9, 11).

In this question we know an end and a midpoint of a line segment. The missing end can be found from the following formula:

M(x, y) = G(x, y) + 0.5 · [H(x, y) - G(x, y)]

M(x, y) = 0.5 · G(x, y) + 0.5 · H(x, y)

0.5 · H(x, y) = M(x, y) - 0.5 · G(x, y)

H(x, y) = 2 · M(x, y) - G(x, y)     (1)

If we know that M(x, y) = (5, 3) and G(x, y) = (1, -5), then the coordinates of the point H are:

H(x, y) = 2 · (5, 3) - (1, -5)

H(x, y) = (10, 6) - (1, -5)

H(x, y) = (9, 11)

The missing end of the line segment [tex]\overline {GH}[/tex] whose midpoint is M(x, y) = (5, 3) and known endpoint is G(x, y) = (1, -5) is the point H(x, y) = (9, 11).

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Answer:

its A

Step-by-step explanation:

Answer:

2

Step-by-step explanation:

lucky guess from my boi tony

Answer:

the answer is 0

Step-by-step explanation:

because anything multiply by 0 is 0.

Can make me the brainliests answerer?Please

Answer:

Step-by-step explanation:

Simplify the following expression:

Simplify the following expression:

7a + 5b - 2a + b =

5a + 6b

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

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:

Step-by-step explanation:

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

=-2/(-2+5)

=-2/3

Answer:

r = 290°

Step-by-step explanation:

  In a triangle, exterior angles equals the sum of interior opposite angle.

In triangle A,

   x + 90 = 125   {Exterior angle property}

           x = 125 - 90

           x = 35°

In triangle B,

      y + 90 = 125

             y = 125 - 90

             y = 35°

    x + y + r = 360   {Complete angle}

35 + 35 + r = 360

         70 +r = 360

               r = 360 - 70

               r = 290°

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:

x= 4

y= -2

Step-by-step explanation:

[tex]-3y+5x=26\\-2y-5x=-16[/tex]

Solve by using the Elimination Method.

[tex]-5y=10\\\\\frac{-5y}{-5} =\frac{10}{-5} \\\\y=-2[/tex]

Now plug y into one of the original equation.

=======================================

[tex]-2y-5x=-16[/tex]

[tex](-2*-2)-5x=-16[/tex]

[tex]4-5x=-16[/tex]

[tex]4-5x+5x=-16+5x[/tex]

[tex]4+16=-16+5x+16[/tex]

[tex]20=5x\\\\\frac{20}{5} =\frac{5x}{5} \\\\x=4[/tex]

=======================================

[tex]\left \{ {{x=4} \atop {y=-2}} \right.[/tex]

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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