F(n+1)=f(n)-8. If f(2)=100, what is f(6)

Answer:

[tex]\large\huge\boxed{\left\{\begin{array}{ccc}a_1=9\\a_n=a_{n-1}\cdot\left(-\dfrac{1}{3}\right)\end{array}\right}[/tex]

Step-by-step explanation:

[tex]a_n=9\cdot\left(-\dfrac{1}{3}\right)^{n-1}\\\\\text{Calculate}\ a_1.\ \text{Put n = 1 to the explicit formula of the geometric sequence:}\\\\a_1=9\cdot\left(-\dfrac{1}{3}\right)^{1-1}=9\cdot\left(-\dfraC{1}{3}\right)^0=9\cdot1=9\\\\\text{Calculate the common ratio:}\\\\r=\dfrac{a_{n+1}}{a_n}\\\\a_{n+1}=9\cdot\left(-\dfrac{1}{3}\right)^{n+1-1}=9\cdot\left(-\dfrac{1}{3}\right)^n[/tex]

[tex]r=\dfrac{9\!\!\!\!\diagup^1\cdot\left(-\frac{1}{3}\right)^n}{9\!\!\!\!\diagup_1\cdot\left(-\frac{1}{3}\right)^{n-1}}\qquad\text{use}\ \dfrac{a^m}{a^n}=a^{m-n}\\\\r=\left(-\dfrac{1}{3}\right)^{n-(n-1)}=\left(-\dfrac{1}{3}\right)^{n-n-(-1)}=\left(-\dfrac{1}{3}\right)^1=-\dfrac{1}{3}\\\\a_n=a_{n-1}\cdot\left(-\dfrac{1}{3}\right)[/tex]

Answer:

[tex]\large\boxed{3\div\dfrac{1}{5}}[/tex]

Step-by-step explanation:

Each 1 was divided into five equal parts. Each of these parts is 1/5. We calculate how many times 1/5 is in 3.

[tex]\bf 125x^3+216~~ \begin{cases} 125=5^3\\ 216=6^3 \end{cases}\implies 5^3x^3+6^3\implies \stackrel{\textit{yes, it is}}{(5x)^3+6^3}[/tex]

Answer:

∠2 and ∠5

Step-by-step explanation:

we know that

Alternate Exterior Angles are a pair of angles on the outer side of each of those two lines but on opposite sides of the transversal

In this problem

∠12 and ∠2 are alternate exterior angles

∠12 and ∠5 are alternate exterior angles

therefore

∠2 and ∠5 are each separately alternate exterior angles with ∠12

Answer:

y=2x-10

Step-by-step explanation:

First step: Let's compute the slope. You can directly use the formula for slope given two points here but I just like to like them up and subtract vertically. Make sure you put 2nd difference on top of 1st difference (yes, like a fraction).

(7  ,  4)

-(4 ,  -2)

=======

3       6

So the slope is 6/3 =2.

So we know our line is in the form y=2x+b.

We have to find the y-intercept now.  To find b we will use a point that we know is on the line (you know two-just choose one of them) .  I will plug in (4,-2) giving me this equation -2=2(4)+b

       Solving:                              -2=8+b

                                      So            b=-10

The answer is y=2x-10

Answer:

y=6

Step-by-step explanation:

y = -x+7

We have the point (1,y)

That means x=1 and we want to find y

Let x=1

y = -1+7

y = 6

The point is (1,6)  where x=1 and y =6

Answer:

y = -1½x + 3; Parallel Equation: y = -1½x [Direct Variation (y = mx)]

Step-by-step explanation:

Set the equation equal to 6, move -3x to the right side of the equivalence symbol to get 2y = -3x + 6, then divide all terms by 2, to isolate the variable, resulting in y = -½x + 3. Now that we have our equation, we have to the PARALLEL equation [SIMILAR RATE OF CHANGES (SLOPES)] that passes through the origin [0, 0]. To do this, we simply plug these coordinates into the Slope-Intercept Formula, y = mx + b --> 0 = -½[0] + b. It is obvious that your y-intercept IS the origin [so as your x-intercept], so your parallel equation is y = -½x.

NOTE: The parent function of y = mx, is what is known as direct variation.

Answer:

y = -4x - 6

Step-by-step explanation:

The equation of a line in point-slope form.

[tex] y - y_1 = m(x - x_1) [/tex]

is the equation of the line containing point (x1, y1) and having slope, m.

The given point of the perpendicular bisector is (-1, -2), so in this case, x1 = -1, and y1 = -2.

We need the slope of the perpendicular bisector. First we find the slope of the segment. We start at point (-5, -3). We go up 1 unit and 4 units to the right, and we are at another point on the segment. Since slope = rise/run, the slope of the segment is 1/4. The slopes of perpendicular lines are negative reciprocals, so the slope of the perpendicular bisector is the negative reciprocal of 1/4, so for the perpendicular bisector, m = -4.

Now we use the equation above and our values.

[tex] y - y_1 = m(x - x_1) [/tex]

[tex] y - (-2) = -4(x - (-1)) [/tex]

[tex] y + 2 = -4(x + 1) [/tex]

[tex] y + 2 = -4x - 4 [/tex]

[tex] y = -4x - 6 [/tex]

Answer:

Step-by-step explanation:

y = -4x - 6

Answer:

$6,675

Step-by-step explanation:

Let

x -----> the number of tickets sold

y ----> the amount of money that the band earn

we know that

The linear equation that represent this problem is

y=4.50x+1,500

The greatest amount of money that the band can earn is when the number of tickets sold is equal to the maximum number of seats in the auditorium

so

For x=1,150

substitute

y=4.50(1,150)+1,500=$6,675

Equations are used to represent the relationships between variables. In [tex]y=x^2 -1[/tex], the variables are x & y and the following observations are true for the given equation:

Given that:

[tex]y=x^2 -1[/tex]

[tex]x^2 \to[/tex] the square of x

So, means that: the y is 1 less than the square of x

From the attached table, we have:

[tex]x = -2; y = a[/tex]

This means that:

[tex]a = (-2)^2 - 1[/tex]

[tex]a = 4 - 1[/tex]

[tex]a =3[/tex]

Also, we have:

[tex]x = b; y = -1[/tex]

This means that:

[tex]-1 = b^2 - 1[/tex]

Collect like terms

[tex]b^2 =1-1[/tex]

[tex]b^2 =0[/tex]

Take square roots

[tex]b = 0[/tex]

Hence, the values of a and b are 3 and 0, respectively.

The graph options are not made available. So, I will plot the graph of [tex]y=x^2 -1[/tex].

See attachment for graph of [tex]y=x^2 -1[/tex]

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Answer: In short for ed2020 :

1. 3rd answer

Graph: A

Table: A=3 B=0

Answer:

Yes, the right angle is angle B

Step-by-step explanation:

we have

[tex]A(-2, 3), B(-3,-6),C(2,-1)[/tex]

Plot the vertices

see the attached figure

we know that

If triangle ABC is a right triangle

then

Applying the Pythagoras Theorem

[tex]AB^{2} =AC^{2}+BC^{2}[/tex]

the formula to calculate the distance between two points is equal to

[tex]d=\sqrt{(y2-y1)^{2}+(x2-x1)^{2}}[/tex]

Find the distance AB

[tex]A(-2, 3), B(-3,-6)[/tex]

substitute in the formula

[tex]d=\sqrt{(-6-3)^{2}+(-3+2)^{2}}[/tex]

[tex]d=\sqrt{(-9)^{2}+(-1)^{2}}[/tex]

[tex]AB=\sqrt{82}\ units[/tex]

Find the distance BC

[tex]B(-3,-6),C(2,-1)[/tex]

substitute in the formula

[tex]d=\sqrt{(-1+6)^{2}+(2+3)^{2}}[/tex]

[tex]d=\sqrt{(5)^{2}+(5)^{2}}[/tex]

[tex]BC=\sqrt{50}\ units[/tex]

Find the distance AC

[tex]A(-2, 3),C(2,-1)[/tex]

substitute in the formula

[tex]d=\sqrt{(-1-3)^{2}+(2+2)^{2}}[/tex]

[tex]d=\sqrt{(-4)^{2}+(4)^{2}}[/tex]

[tex]AC=\sqrt{32}\ units[/tex]

Verify the Pythagoras theorem

[tex](\sqrt{82})^{2} =(\sqrt{32})^{2}+(\sqrt{50})^{2}[/tex]

[tex]82=82[/tex] ---> is true

therefore

Is a right triangle and the right angle is B

Answer:

x=1, y=-5

Step-by-step explanation:

Given equations are:

[tex]3x+10y=-47\ Eqn\ 1\\and\\5x-7y=40\ Eqn\ 2[/tex]

In order to solve the equation

Multiplying Eqn 1 by 5 and eqn 2 by 3 and subtracting them

So,

Eqn 1 becomes

15x+50y=-235

Eqn 2 becomes

15x-21y=120

Subtracting 2 from a

15x+50y - (15x-21y) = -235-120

15x+50y-15x + 21y = -355

71y = -355

y = -355/71

y =-5

Putting y= -5 in eqn 1

3x+10(-5) = -47

3x -50 = -47

3x = -47+50

3x = 3

x = 3/3

x = 1

Hence the solution is:

x=1, y=-5

Answer: x=1; y=-5

Step-by-step explanation: To solve this system we can use differente methods, in this case we are going to use substitution:

first equation: 3x+10y=-47

second equation: 5x-7y=40

we are going to isolate x from the first equation:

3x=-47-10y

[tex]x=\frac{-47-10y}{3}[/tex]

now we replace it in the second equation:

[tex]5*\frac{-47-10y}{3}-7y=40[/tex]

and now we solve for y:

[tex]\frac{-235-50y}{3} -7y=40[/tex]

[tex]\frac{-235-50y-21y}{3}=40[/tex]

[tex]-235-71y=40*3[/tex]

[tex]-235-71y=120[/tex]

[tex]-71y=120+235[/tex]

[tex]y=-355/71[/tex]

y=-5

now we replace the value of y in the first equation and solve for x:

[tex]x=\frac{-47-10y}{3}[/tex]

[tex]x=\frac{-47-10(-5)}{3}[/tex]

[tex]x=\frac{-47+50}{3}[/tex]

[tex]x=\frac{3}{3}[/tex]

x=1

Answer

[tex]\frac{m^{2}+mn }{3}[/tex]

Step-by-step explanation:

Reduce the numbers with the greatest commen divisor 6

Then calculate the product

ANSWER

Prime

EXPLANATION

The given quadratic expression is

[tex] {2t}^{2} - 19 - 6t[/tex]

We rewrite in standard form to obtain

[tex]{2t}^{2} - 6t - 19[/tex]

Comparing to the standard quadratic function in t,

[tex]a {t}^{2} + bt + c[/tex]

We have

[tex]a = 2[/tex]

[tex]b = - 6[/tex]

[tex]c = - 19[/tex]

We find that the product

[tex]ac = 2 \times - 19 = - 38[/tex]

There are no two factors of -38 that sums up to -6.

This means that, the given polynomial does not have rational factors.

Therefore the polynomial is prime.

Answer:

she owes nothing and the credit card company owes her nothing.

Answer:

It represents that the bank owes her nothing and she doesn't owe the bank anything. So it is neither postive or negative

Step-by-step explanation:

Answer:

One of the numbers is 5

The other number is 17

Step-by-step explanation:

You could do this just by guessing numbers. But I think you are intended to do it with algebra.

x + y = 22

y = 2*x + 7          Substitute the y value in this equation into the first equation

x + 2x + 7 = 22   Combine the xs on the left.

3x + 7 = 22          Subtract 7 from both sides.

3x+7-7=22- 7       Combine

3x = 15                 Divide by 3

3x/3 = 15/3           Combine

x = 5

x + y = 22             Substitute 5 for x

5 + y = 22            Subtract 5 from both sides.

5-5+y = 22-5

y = 17

Answer:

17 or 5

Step-by-step explanation:

I took the test

Answer:

Slope = 5

y-intercept = (0, 5)

x-intercept = (-2.5, 0)

Independent variable = x

Dependent variable = y

Domain = Any real #

Range = I believe it's any real #

Step-by-step explanation:

The slope of the equation is 2.

The y-intercept is 5.

The x-intercept is -5/2.

The independent variable is x.

The dependent variable is y.

The domain of the equation is any real number.

The range of the equation is any real number.

The graph of the linear equation y = mx + c is a line with m as slope, and m and c as the y-intercept.

The equation in slope-intercept form is;

y = 2x + 5

1. The slope of the equation is;

y = mx + c

y = 2x + 5

On comparing m = 2

The slope of the equation is 2.

2. The y-intercept is;

y = mx + c

y = 2x + 5

On comparing c = 5

The y-intercept is 5.

3. The x-intercept is;

y = 0

y = 2x + 5

0 = 2x +5

2x = -5

x = -5/2

The x-intercept is -5/2.

4. The independent variable is x.

5. The dependent variable is y.

6. The domain of the equation is any real number.

7. The range of the equation is any real number.

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Answer:

y + 12 = 3(x - 2)

Step-by-step explanation:

Insert the coordinates into the formula with their CORRECT signs. Remember, in the Point-Slope Formula, y - y₁ = m(x - x₁), all the negative symbols give the OPPOSITE term of what they really are. Since both lines contain have to have similar rate of changes [slopes], we do not go any further.

Answer:

B. 34.3 units

Step-by-step explanation:

We can see that the missing side is is the hypotenuse of the ΔDEF

So, Using the pythagoras theorem

H^2 = P^2 + B^2

= (8)^2 + (6)^2

= 64 + 36

= 100

√H^2 = √100

H = 10

Now we know all the three sides of triangle ΔDFG

We can use Hero's formula to find the area

[tex]s = \frac{(d+f+g)}{2}\\ = \frac{(7+11+10)}{2}\\ = \frac{28}{2}\\ = 14\\Area = \sqrt{s(s-d)(s-f)(s-g)} \\= \sqrt{14(14-7)(14-11)(14-10)} \\=\sqrt{(14)(7)(3)(4)}\\ =\sqrt{1176}\\ = 34.29\ units[/tex]

Rounding off will give us:

34.3 units

Hence Option B is correct ..

Answer: c

Step-by-step explanation:

Answer:

What triangle below?

Step-by-step explanation:

Im confused sorry

Answer:

0 because 0 is sea level, anything below is negative and anything above is positive.

Answer:

20 mg / hour

Step-by-step explanation:

The first step is to find the mg/mL of dopamine.

If there are 52 mg / 26 mL, then there are 2 mg / 1 mL (just reduce the fraction).

If we are losing 10 mL / 1 hour, and there are 2 mg / mL, then the flow rate of dopamine mg / hour is 20.

You can also do this using dimensional analysis.

[tex]\frac{52 mg}{26 mL} (\frac{10 mL}{1 hour})[/tex]

Just cross out the units that cancel in the numerator and denominator (mL in this case), and you're left with mg / hour. Then multiply the numerators and divide by the denominators. You get the same answer.

The first step is to find the mg/mL of dopamine.

If there are 52 mg / 26 mL, then there are 2 mg / 1 mL (just reduce the fraction).

If we are losing 10 mL / 1 hour, and there are 2 mg / mL, then the flow rate of dopamine mg / hour is 20.

You can also do this using dimensional analysis.

[tex]\frac{52 mg}{26 mL} (\frac{10 mL}{1 hour})[/tex]

Just cross out the units that cancel in the numerator and denominator (mL in this case), and you're left with mg / hour. Then multiply the numerators and divide by the denominators. You get the same answer.

[tex]x+100+3x=180\\4x=80\\x=20[/tex]

[tex]\text{Hey there!}[/tex]

[tex]\text{Note: This line/triangle have a degree of 180}[/tex]

[tex]\text{Firstly, you have to set up your equation, which is:}[/tex] [tex]\text{x + 100 + 3x =180}[/tex]

[tex]\text{Next, COMBINE your like terms: x + 3x}[/tex]

[tex]\text{x + 3x = 4x (Side note: the x by itself is equal to a(n) invisible 1)}[/tex]

[tex]\text{100 stays the same because it doesn't have a like term}[/tex]

[tex]\text{4x + 100 = 180}[/tex]

[tex]\text{Thirdly, we have to SUBTRACT by 100 on your sides:}[/tex] [tex]\text{4x + 100 - 100}\\\text{180 - 100}[/tex]

[tex]\text{Cancel out: 100 - 100 because it equals to 0}[/tex]

[tex]\text{Keep: 180 - 100 because it helps us solve for our answer}[/tex]

[tex]\text{Our new equation becomes: 4x = 80}[/tex]

[tex]\text{Fourthly, we have to DIVIDE by 4 on each of your sides:}[/tex] [tex]\dfrac{4x}{4}=\dfrac{80}{4}[/tex]

[tex]\text{Cancel out:}\dfrac{4x}{4}\text{ because it gives us the result of 1}[/tex]

[tex]\text{Keep:}\dfrac{80}{4}\text{ because it helps us solve for our answer}[/tex]

[tex]\uparrow\text{If you solved the kept answer correctly you would have your answer for x}[/tex]

[tex]\boxed{\boxed{\bf{Answer: x = 20}}}\checkmark[/tex]

[tex]\text{Good luck on your assignment and enjoy your day!}[/tex]

~ [tex]\frak{LoveYourselfFirst:)}[/tex]

Answer:

1. x=4 or x=10

2.  x=-10 or x=10

No equivalent

Step-by-step explanation:

1. |x-3|=7 and x-3=7

Absoulte rules.

x-3=-7 and x-3=7

Add 3 both sides.

x-3+3=-7+3

Simplify.

-7+3=-4

x=-4

x-3=7

Add by 3 both sides.

x-3+3=7+3=10

x=10

X=-4, and X=10 is the correct answer.

________________________________

2. |x|-3=7

Add by 3 both sides.

|x|-3+3=7+3

Simplify.

7+3=10

X=10

X=-10 and X=10 is the correct answer.

______________________________

The two equations |x-3|=7 and |x|-3=7, are solved differently. For |x-3|=7, the possible solutions are x=10 and x=-4. For |x|-3=7, the possible solutions are x=10 and x=-10.

The two equations you're looking at are: |x-3|=7 and |x|-3=7. They look very similar but they're solved differently because absolute value symbols affect all values inside them together.

For the first equation, |x-3|=7, we solve this by considering the two situations, x-3 = 7 and x-3 = -7. Solve each of these two equations separately, so you get x = 10 and x = -4.

For the second equation, |x|-3=7, firstly, we need to eliminate '-3' from the right-hand side by adding 3 to both sides, leading to |x| = 10. This is then broken down into the two possible situations as before: x = 10 and x = -10.

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Final answer:

The polynomial ₓ2y² has 1 term.

Explanation:

A polynomial is an algebraic expression consisting of terms that are variables raised to non-negative integer powers, multiplied by coefficients. The number of terms in a polynomial is determined by counting the number of distinct combinations of variables and exponents in the expression.

In the given polynomial, ₓ2y², there is only one term because there is only one combination of variables (x and y) raised to their respective exponents (2 and 2).

Therefore, the polynomial ₓ2y²has 1 term.

Answer:

-8

Step-by-step explanation:

Distribute.

-8x - 12 = 2x + 6 - 8x - 2

Combine like terms.

2x = -16

Divide by 2 on both sides

x = -8

Answer:

The solutions of given equations is x = -8

Step-by-step explanation:

It is given that,

-4(2x + 3) = 2x + 6 - (8x + 2)

To find the solution of given equation

-4(2x + 3) = 2x + 6 - (8x + 2)

-8x - 12 = 2x + 6 - 8x - 2

-8x - 12 = 4 - 6x

-8x + 6x = 4 + 12

-2x = 16

x = 16/(-2) = -8

Therefore the solutions of given equations is x = -8

Step-by-step explanation:

10.44 is correct as we have to add both dis and divide by both hrs

In this case, Taylor's average rate is 10 miles per hour.

To calculate Taylor's average rate during her trip, we can use the formula for average speed:

Calculate the total distance traveled: 62 miles - 32 miles = 30 miles.

Calculate the total time taken: 6 hours - 3 hours = 3 hours.

Divide the total distance by the total time to find the average speed: 30 miles / 3 hours = 10 miles per hour.

Answer:

20 miles per hour

Step-by-step explanation:

traveling against the wind was 160mph (400/2.5)

traveling with the wind was 200mph (400/2)

going against the wind is going in the negative direction of the wind speed, and going with the wind is going in a positive direction of the wind speed, therefore the wind speed is |direction1-direction2|/2, which would be |200-160|/2 = |40|/2 = 20mph

(180mph is neutral speed with no wind, with wind affecting this neutral speed ±20mph)

Final answer:

To determine the wind speed, we used the distances and times provided for the flights against and with the wind to set up equations for the airplane's effective speeds. Solving these equations, we found that the wind speed is 20 miles per hour.

Explanation:

To solve for the wind speed, we first need to establish the speed of the airplane without the influence of the wind. Let's denote the speed of the airplane in still air as A, and the speed of the wind as W. When the plane is flying into the wind, its effective speed is A - W, and while flying with the tailwind, its effective speed is A + W.

Speed against the wind = (A - W) = 400 / 2.5 = 160 mph

Speed with the wind = (A + W) = 400 / 2 = 200 mph

We now have two equations based on the effective speeds:

By adding these two equations, we eliminate W:

Thus, the speed of the airplane in still air (A) is 180 mph. We can now find the wind speed by subtracting this value from the effective speed with the wind:

Therefore, the speed of the wind is 20 miles per hour.

Answer:

N/A

Step-by-step explanation:

Which area of shaded segment?

Answer:

Area Of Shaded Segment =

In Pictures