Shane biked 1 mile less than three times the number of miles Lissette biked. Shane biked a total of 7 miles. Write an equation to determine how many miles Lissette biked.
7 = 3x − 1
x − 1 = 3(7)
x over seven = 3(1)
7 + 3x = 1

Let f(x) = y

y = log3(x+1) - 1

Plug x in y and y in x

x = log3(y+1) - 1

x + 1 = log3(y+1)

3^(x+1) - 1 = y

[tex]y = 3^{x+1}[/tex] - 1

This is the inverse function.

Hope it helps! xxxx

Answer:

y = [tex]3^{(x+1)}[/tex] -1

Step-by-step explanation:

x = [tex]log_{3}[/tex](y + 1) - 1

x + 1 = log₃(y + 1)

[tex]3^{(x+1)}[/tex] = y + 1

[tex]3^{(x+1)}[/tex] -1 = y

Answer:

[tex]81+144i[/tex]

Step-by-step explanation:

We want to simplify:
[tex]\displaystyle (-3\sqrt{-81})(-5+\sqrt{-9}) + 9i[/tex]

Recall that:

[tex]\displaystyle \sqrt{-a} = i\sqrt{a}[/tex]

Therefore:
[tex]\displaystyle \begin{aligned} (-3\sqrt{-81})(-5+\sqrt{-9}) + 9i & = (-3i\sqrt{81})(-5+i\sqrt{9})+9i \\ \\ &= -(3i(9))(-5+i(3))+9i \\ \\ & = -27i(-5+3i)+9i \\ \\ & = 135i -81i^2 + 9i \\ \\ & = 144i - 81i^2 \\ \\ & = 81+144i\end{aligned}[/tex]

Note that i² = -1.

In conclusion:

[tex]\displaystyle (-3\sqrt{-81})(-5+\sqrt{-9})+9i = 81 + 144i[/tex]

Answer:

is infinite set... because dots meaning non stop

Answer:

ln(x) = 1/x... It's a basic rule of Calculus.

Answer:

Im pretty sure they stay the same. But that might just be me

Answer:

b=2

c=4

e=3

g=6

Step-by-step explanation:

Answer:

5/8

Step-by-step explanation:

(10 +/- √100-104)/4

(10 +/- 2i)/4

5/4 +/- 1/2i

5/4 * 1/2 = 5/8

Answer:

a = 53.13

b = 42.76

c= 0

Step-by-step explanation:

as the question said i was supposed to use a calculator which i did

Answer:

a. 6m

b. m-2

c. 5(m-2)

d. 6m +5m -10= 56

E. 11m=66

divide by 6: m=6

Maple Granola= 6$

Apple Granola= 4$

Answer:

[tex]\sqrt{2}[/tex] or 1.414

Step-by-step explanation:

1) Find the mean. 1+2+3+4+5 = 15. 15/5= 3

2) For each data point, find the square of its distance to the mean. (4, 1, 0, 1, 4)

3) Sum the values from Step 2. 10

4) Divide by the number of data points. 10/5= 2

5) Take the square root. [tex]\sqrt{2}[/tex]

Answer:

the answer square root of 2! just did the test and got it right :)

Step-by-step explanation:

Answer: 2 hours 15 minutes

Step-by-step explanation:

3/4 of an hour times 3 will be 9/4; each fourth is 15 minutes. 9 times 15 is 135 minutes, which is 2 hours and 15 minutes

Answer:

2.25 hours

Step-by-step explanation:

The man traveled 1/3 of the distance in 3/4 of an hour.

This means that he needs to travel for 3 times as long to travel the entire distance.

3 * 3/4 = 9/4 = 2.25

2.25 hours.

Or, 2 hours and 15 minutes (as 0.25 = 1/4).

Answer:

10

Step-by-step explanation:

m + 2p

2 + 2(4)

= 2 + 8

= 10

Answer:

10

Step-by-step explanation:

m +2p;

let m = 2, and p = 4​

2+2*4

2+8

10

You can use the distributive property to multiply:

( y )( y² - 2y + 4 ) + ( 2 )( y² - 2y + 4) =

y³ - 2y² + 4y + 2y² - 4y + 8 =

y³ + 8

The -2y² and the 2y² cancel each other, and the 4y and -4y cancel each other out!

Answer:

ljj

Step-by-step explanation:

llk

Yes , the series is an arithmetic sequence of common difference 2

What is Arithmetic Progression?

An arithmetic progression is a sequence of numbers in which each term is derived from the preceding term by adding or subtracting a fixed number called the common difference "d"

The general form of an Arithmetic Progression is a, a + d, a + 2d, a + 3d and so on. Thus nth term of an AP series is Tn = a + (n - 1) d, where Tₙ = nth term and a = first term. Here d = common difference = Tₙ - Tₙ₋₁

Sum of first n terms of an AP: Sₙ = ( n/2 ) [ 2a + ( n- 1 ) d ]

Given data ,

Let the number of terms n = 20

The number of tiles in the first row = 10 tiles

The number of tiles in the second row = 2 more than first row

The number of tiles in the second row = 12 tiles

The number of tiles in the third row = 14 tiles

So , the sequence will be , 10 , 12 , 14 , 16 ...

The number of terms n = 20

The first term a = 10

The common difference d = second term - first term

The common difference d = 12 - 10 = 2

The series is an arithmetic sequence and the 20th term of the sequence will be

a₂₀ = a + ( n - 1 )d

a₂₀ = 10 + ( 19 ) 2

a₂₀ = 10 + 38

a₂₀ = 48 tiles

Hence , the series is an arithmetic sequence

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Answer:

angle FEG = 66⁰

angle GFH = 90⁰

Answer:

The population of Namibia in the years 1940, 1997, and 2005 was 371.2 , 1671.64 and 2064.74 respectively.

Step-by-step explanation:

Refer the attached figure

We will use equation calculator to find the equation of given plot

[tex]y = 483.36 \times e^0.0264x[/tex]

We are supposed to find the population of Namibia in the years 1940, 1997, and 2005.

x values are years

y values are population

For 1940, [tex]x = -10, y = y = 483.36 \times e^{0.0264(-10)} = 371.2[/tex]

For 1997, [tex]x = 47, y = y = 483.36 \times e^{0.0264 \times 47} = 1671.64[/tex]

For 2005,[tex]x = 55, y = y = 483.36 \times e^{0.0264 \times 55} = 2064.74[/tex]

Hence The population of Namibia in the years 1940, 1997, and 2005 was 371.2 , 1671.64 and 2064.74 respectively.

Answer:

[tex]\boxed{ \sf Option \ 4}[/tex]

Step-by-step explanation:

The domain is all possible values for x.

There are no restrictions on x. The domain is all real numbers.

The range are all possible values of F(x) or y.

[tex]F(x)=5^{3(3)}= 1953125[/tex]

[tex]F(x)=5^{3(0)}= 1[/tex]

[tex]F(x)=5^{3(-2)}= 0.000064[/tex]

When the value of x increases, the value of F(x) increases until infinity. When the value of x decreases, the value of F(x) gets closer to 0 but does not equal to 0.

The range is [tex]y>0[/tex]

The coefficient of 3 does not affect the domain and range, as there are no real restrictions.

Answer:

Option B

Step-by-step explanation:

The slope of the line BC is,

[tex] \frac{ - 2 - 8}{7 - 3} [/tex]

[tex] = \frac{ - 10}{4} = - \frac{5}{2} [/tex]

Since AD is altitude to BC, we can say AD is perpendicular to BC, so the slope of the line AD which is perpendicular line to BC will be,

[tex] \frac{2}{5} [/tex]

Answer:

D

Step-by-step explanation:

-4xy

will be your answer after factoring

Answer:

d

Step-by-step explanation:

Given

(x - y)² - (x + y)² ← expand both factors using FOIL

= x² - 2xy + y² - (x² + 2xy + y²) ← distribute by - 1

= x² - 2xy + y² - x² - 2xy - y² ← collect like terms

= - 4xy → d

Answer:

Residual value

Answer:

1

Step-by-step explanation:

(-2)(1/4)=-1/2

(-2)(-1/2)

=1

the third term of the geometric sequence with first term = 1/4 and common ratio r = -2 is 1

We have a geometric sequence in which the first term is [tex]\frac{1}{4}[/tex] and the common ratio is -2.

We have to find the third term of this geometric sequence.

The formula to find the [tex]n^{th}[/tex] term of a geometric sequence with first term [tex]a_{1}[/tex] and common ratio r is -

[tex]a_{n} =a_{1} r^{n-1}[/tex]

In our question, [tex]a_{1}[/tex] = [tex]\frac{1}{4}[/tex]  and r = -2 and n =3.

Substituting the values, we get -

[tex]a_{3} =\frac{1}{4}(-2)^{3-1} = \frac{1}{4} (-2)^{2} =\frac{1}{4}\times4=1[/tex]

Hence, the third term of the geometric sequence with first term = 1/4 and common ratio r = -2 is 1.

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Answer:

See below.

Step-by-step explanation:

Central angles AOB and DOC are vertical angles, so they are congruent.

m<AOB = 50°

BD is a diameter, so the measure of central angle BOD is 180°.

The measure of an arc of a circle is equal to the measure of the central angle that subtends it.

m<AOB + m<AOE + m<EOD = 180°

50° + m<AOE + 60° = 180°

m<AOE + 110° = 180°

m<AOE = 70°

m(arc)AE = m<AOE = 70°

m(arc)AB = m<AOM = 50°

A full circle has 360 deg of central angle and of arc measure.

m(arc)ECB = 360° - m(arc)AE - m(arc)AB

m(arc)ECB = 360° - 70° - 50°

m(arc)ECB = 240°

Angle BOC is vertical with angle AOD.

m<BOC = m<AOD = m<AOE + m<EOD

m<BOC = 70° + 60°

m<BOC = 130°

Answer:

Formula for an opened end of a cylinder =

[tex]\pi r^2 +2\pi rh\\[/tex]

Closed at both end =

[tex]2\pi r^2 +2\pi r h[/tex]

Opened at both end =

[tex]2\pi rh[/tex]

Step-by-step explanation:

Answer:

h is the function name; t is the input, or independent variable; and h(t) is the output, or dependent variable.

Step-by-step explanation:

The explanation is in the answer.

h is the function name; h(t) is the input, or independent variable; and t is the output, or dependent variable is correct statement.

The given function is h(t) = 210 - 15t

The function is named h, and it takes an input value t (the independent variable) and produces an output value 15t (the dependent variable).

The function is often written as h(t) = 15t to make it clear that h is a function of t.

Hence, h is the function name; h(t) is the input, or independent variable; and t is the output, or dependent variable is correct statement.

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5.51181102 feet (5 feet 6 9⁄64 inches)

Answer:

D.

Step-by-step explanation:

Choices A., B., and C. are always true.

Choice D. is true only for rectangles with congruent sides, which are squares.

Answer: D.

Answer:

2,300,000pages  report.

Step-by-step explanation:

Given a USB drive with memory of 4.6*10⁶KB, in order to know the maximum number of pages a report can have so that it can be completely stored on the drive, the conversion factor must be used.

We must first understand that 1 page of a document uses up approximately 2kB of the storage.

Since 2kB = 1page

4.6*10⁶KB = x page

Cross multiply

2kB * x = 4.6*10⁶KB * 1

2x =  4.6*10⁶

x =  4.6*10⁶/2

x =  2.3*10⁶

x = 2,300,000

Hence the maximum number of pages that the report can have so that it can be completely stored on a USB drive that holds 4.6*10⁶KB is approximately 2,300,000pages  report.

Answer:

The lateral area of the figure = 480 m²

The surface area = 720 m²

Step-by-step explanation:

By definition, we have;

The lateral area is the area of the vertically facing sides of or the area of the triangular faces of a pyramid

The surface area is the area of the entire surface = Lateral area + The other surface areas of the object

For a pyramid, the surface area =   Lateral area  + Area of base

The figure in the question is a pentagon based pyramid with five triangles on the sides

The lateral area of the figure = 5 × area of the 5 triangles = 5 × Base × Height

The lateral area of the figure = 5 × 12 × 8 = 480 m²

The lateral area of the figure = 480 m²

The surface area = Area of the base + Lateral surface area

Area of the regular pentagon base = 1/2 × Perimeter of the pentagon × Apothem

Perimeter of the pentagon = 5 × 12 = 60 m

Apothem = Perpendicular distance from the pentagon's side to the center = 8.3 m

∴ Area of the regular pentagon base = 1/2 × 60 × 8 = 240 m²

∴ The surface area = 240 +480 =720 m²

The surface area = 720 m²