At 5pm, Li rented bikes from Pearl's
Wheels. She returned the bike at 11pm, after
riding 38 miles: Li paid $26.00 for the
rentals
a. What was her average speed in miles per hour?
b. What was her cost per hour, to the nearest cent?
c. What was her cost per mile, to the nearest cent?

Answers

Answer 1

Answer:

(a) 6.33 miles per hour

(b) $4.33 per hour

(c) $0.68 per mile

Step-by-step explanation:

Li drove 6 hours (5pm - 11pm) for a total of 38 miles
[tex]\textrm{(a) Her average speed is determined by the formula}\\\\\dfrac{\textrm{Distance Travelled}}{\textrm{Time taken for travel}}[/tex]

[tex]\textrm{So average speed }=$\dfrac{38}{6} = 6.33$ \;\textrm{miles per hour}}\\\\[/tex]

(b) She paid $26 for 6 hours of usage
[tex]\textrm{So cost per hour } = \dfrac{26}{6} = \$4.33\;\textrm{per hour}\\\\[/tex]

(c) Cost per mile, c, can be computed as follows
[tex]c = \dfrac{\textrm{Total Cost}}{\textrm{Miles Traveled}}[/tex]

[tex]\longrightarrow \dfrac{26}{38} = \$0.68\; \textrm{per mile}[/tex]


Related Questions

find the zeros f(x) = x 3 - 3x 2 – 5x +15

Answers

Answer:

x = ± [tex]\sqrt{5}[/tex] x = 3

Step-by-step explanation:

to find the zeros set f(x) = 0 , that is

x³ - 3x² - 5x + 15 = 0 ( factor the first/second and third/fourth terms )

x²(x - 3) - 5(x - 3) = 0 ← factor out (x - 3) from each term

(x - 3)(x² - 5) = 0

equate each factor to zero and solve for x

x - 3 = 0 ⇒ x = 3

x² - 5 = 0 ( add 5 to both sides )

x² = 5 ( take square root of both sides )

x = ± [tex]\sqrt{5}[/tex]

the zeros of f(x) are then

x = - [tex]\sqrt{5}[/tex] , x = [tex]\sqrt{5}[/tex] , x = 3

Three sides of a triangle have lengths 4, 5, and 6. The angle between the two sides 5 and 6 is nearest: a. 83° b. 56°C. 41° d. 32°

Answers

In the given triangle, the angle between the two sides 5 and 6 is nearest 41°.

The term triangle means the polygon which has three sides and three angles and three vertices,

Here we have given that three  sides of a triangle have lengths 4, 5, and 6.

And here we need to find the angle between the two sides 5 and 6

According to the given values, let us consider a = 4, b = 5 and c = 6

So, the angle between 5 and 6 can be written as ∠b

And it can be calculated as the following is one way to perform the calculation and it may not be the best way.

∠B = arc cos(a² + c² - b²)/2ac

When we apply the values one the formula, then we get

=> 0.72273 rad

The approximate degree is written as

=> 41.41°

When we round off it then we get the resulting value,

=> 41°

Therefore, option (c) is correct.

To know more about Triangle here.

https://brainly.com/question/2773823

#SPJ4

The formula A=23.1 e^{0.0152t} models the population of a US state, A, in millions, t years after 2000.
a. What was the population of the state in 2000 ?
b. When will the population of the state reach 28.3 million?
a. In 2000 , the population of the state was ? million.

Answers

We want to study the population formula of a given US state according to exponential equation.

a) 23.1 millions.

b) in 2013 - 2014

What is exponential equation?

The exponential function may be a function denoted by f(x)=\exp or e^. Unless otherwise fixed, the term usually refers to the positive-valued operate of a true variable

Main body:

The population state is:

A = 23.1*e^(0.0153*t)

In millions.

Where t represents the number of years after 2000.

a) For the population at the year 2000, we need to evaluate the function at t = 0 (2000 is 0 years after 2000).

A(0) = 23.1*e^(0.0153*0) = 23.1

The population at year 2000 was 23.1 millions.

b) Now we want to solve:

A(t) = 28.3 = 23.1*e^(0.0153*t)

        28.3/23.1 = e^(0.0153*t)

       1.23 = e^(0.0153*t)

Now we can apply the natural logarithm to both sides:

ln(1.23) = ln( e^(0.0153*t) )

ln(1.23) = 0.0153*t

ln(1.23)/0.0153 = t = 13.5

Hence, 13.5 years after 2000 the population will be 28.3 million.

To know more about exponential equation, visit:

https://brainly.com/question/2456547

#SPJ4

Find AE on the rhombus below when AD=4 x+2, DC=7 x-13 and BD=34 .
Note: Write your answer in simplest radical form. In the first blank put the number in front of the v. And in the second blank. put the number that is inside the . ** If there is no number in front of the v, enter a 1 in the blank **

Answers

The length AE of the rhombus is √195 units

How to determine the length AE of the rhombus?

From the question, we have the following parameters that can be used in our computation:

AD = 4x + 2

DC = 7x - 13

BD = 34

All the four sides of a rhombus are congruent

This means that

DC = AD

Substitute the known values in the above equation, so, we have the following representation

7x - 13 = 4x + 2

Evaluate the like terms

3x = 15

Divide both sides by 3

x = 5

Substitute x = 5 in AD = 4x + 2

So, we have

AD = 4 x 5 + 2

AD = 22

The length AE of the rhombus is then calculated as

AE² = AD² - (BD/2)²

Substitute the known values in the above equation, so, we have the following representation

AE² = 22² - (34/2)²

Evaluate

AE² = 195

Take the square roots

AE = √195

Hence, the length is √195 units

Read more about rhombus at

https://brainly.com/question/12918359

#SPJ1

2. Use the Pythagorean Theorem to solve for c.
5 feet
18 feet

Answers

The value of C using Pythagorean Theorem when a equal 5feet and b equals 18feet then, C = 18.68

Pythagorean theorem

In mathematics, the Pythagorean theorem is a fundamental relation in Euclidean geometry between the three sides of a right triangle and is written as a^2 + b^2 = C^2

Using the Pythagorean theorem a^2 + b^2 = C^2

from the question we are given 5 feet and 18feet respectively

to find c we substitute the value into the equation

a^2 + b^2 = C^2

a= 5feet and b= 18 feet

5^2 + 18^2 =C^2

25 + 324 = C^2

349 =C^2

Square root both side

C= [tex]\sqrt{349}[/tex]

C = 18.68

Therefore, C in the equation is C = 18.68

Learn more about Pythagorean Theorem here: https://brainly.com/question/10589258

#SPJ1

Using Pythagoras theorem the value of c is 18.68 feet

Pythagoras Theorem

Pythagoras theorem or Pythagorean theorem is an important topic in Mathematics, which explains the relation between the sides of a right-angled triangle. The sides of the right triangle are also called Pythagorean triples.

The value of c can easily be calculated using Pythagoras theorem which is given as;

c² = 5² + 18²

where;

c =  hypothenuse

c² = 25 + 324

c² = 349

c = √349

c = 18.68 feet

Learn more on Pythagoras theorem here;

https://brainly.com/question/343682

#SPJ1

if 1+1+10 x 34 what is it

Answers

Answer:

408

Step-by-step explanation:

1+1+10 equals 12, then do 12 x 34, which equals 408


9. Bob Rowinski made a $4,000 deposit to a
savings account paying 1.6% annual interest
compounded semiannually. If he kept the money
on deposit for 6 months, what would his account
balance be after the interest payment is made?

Answers

The account balance of Bob Rowinski if he kept the money on deposit for 6 months is $4,032.00.

What is Bob Rowinski account balance the interest payment is made?

The compound interest formula can be expressed as;

A = P(1 + r/n)^(n*t)

Where A is accrued amount, P is principal, r is interest rate, t is time elapsed.

Given the data in the question;

Principal P = $4,000Interest rate r = 1.6% = 1.6/100 = 0.016Compounded semi-annually n = 2Time t = 6 months = 0.5 yearAccrued amount A = ?

Plug the given values into the above formula and solve for A.

A = P(1 + r/n)^(n*t)

A = $4000( 1 + 0.016/2 )^(2*0.5)

A = $4000( 1 + 0.008 )^(1)

A = $4000( 1.008 )

A = $4,032.00

Therefore, the accrued amount after half a year is $4,032.00

Learn more about compound interest here: brainly.com/question/27128740

#SPJ1

If Corey scored higher than the mean on his SAT, but Jerry scored lower than the mean on his SAT, how will both Z scores differ? Jerry's Z score will be positive, while Corey's Zscore will be negative Jerry's Z score will be negative, while Corey's Z score will be positive Both Jerry and Corey's Z scores will be positive Both Jerry and Corey's Z scores will be negative

Answers

Based on the provided information, Jerry's Z score will be negative, while Corey's Z score will be positive.

A Z-score refers to a numerical measurement that defines the raw value's relationship to the mean of a group of values. It is measured in terms of standard deviations from the mean. If a Z-score is 0, it means that the data point's score is identical to the mean score. A negative z-score indicates that the data point is below average or mean and a positive z-score indicates that the data point is above average or mean. Consider the formula for z score which is given by:

z = (x - µ)/σ where x is the given data value, µ is the mean, and σ is the standard deviation.

Hence, if the x < µ, the z score will be negative while if x > µ, the z score will be positive. As Corey scored higher than the mean on his SAT, his z score will be positive, and Jerry scored lower than the mean on his SAT, his z score will be negative.

Learn more about Z-score:

https://brainly.com/question/27701525

#SPJ4

( i only need number one and number 7 )
someone please i’m desperate i have so much work i need done by monday even if you only do one of them it is greatly appreciated

Answers

Answer:

1.  x-intercept = (1, 0),   y-intercept = (0, -2)

7.  y + 4 = -6( x - 7)

Step-by-step explanation:

Question 1

Given point-slope equation:

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

The x-intercept is when y = 0:

[tex]\begin{aligned}y=0\implies 0-2 &=2(x-2)\\-2&=2x-4\\2&=2x\\x&=1\end{aligned}[/tex]

The y-intercept is when x = 0:

[tex]\begin{aligned}x=0\implies y-2 &=2(0-2)\\y-2&=2(-2)\\y-2&=-4\\y&=-2\end{aligned}[/tex]

Therefore, the intercepts are:

x-intercept = (1, 0)y-intercept = (0, -2)

To graph the equation, plot the intercepts and draw a straight line through them.  (See attachment 1).

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

Question 7

[tex]\boxed{\begin{minipage}{5.8 cm}\underline{Point-slope form of a linear equation}\\\\$y-y_1=m(x-x_1)$\\\\where:\\ \phantom{ww}$\bullet$ $m$ is the slope. \\ \phantom{ww}$\bullet$ $(x_1,y_1)$ is a point on the line.\\\end{minipage}}[/tex]

Given:

m = -6(x₁, y₁) = (7, -4)

Substitute the given slope and point (7, -4) into the formula to write the equation of the line in point-slope form:

[tex]\implies y-(-4)=-6(x-7)[/tex]

[tex]\implies y+4=-6(x-7)[/tex]

To graph the line, find the value of y when x = 6 and when x = 8:

[tex]\begin{aligned}x=6\implies y+4 &=-6(6-7)\\y+4 &=-6(-1)\\y+4&=6\\y&=2\end{aligned}[/tex]

[tex]\begin{aligned}x=8\implies y+4 &=-6(8-7)\\y+4 &=-6(1)\\y+4&=-6\\y&=-10\end{aligned}[/tex]

To graph the equation, plot the points (6, 2) and (8, -10) and draw a straight line through them.  (See attachment 2).

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

Please note that I have drawn the graphs using the same size 7x7 grids as shown in your question paper.  If you wish to graph more of the line, please change the scale from those I have used.

Write the fractional values under each note. Verify that the sum of the fractions is 1 for each measure.

Answers

Answer:

1/8, 1/8, 1/4, 1/4, 1/16, 1/16, 1/16, 1/16 = 1

1/2, 1/2 = 1

Step-by-step explanation:

from left to right

is this music class or math class lol?

Construct a polynomial function with the following properties: fifth degree, 2 is a zero of multiplicity 4, −5 is the only other zero, leading coefficient is 4.

Answers

The required equation of the polynomial is p(x) = 4(x - 2 )⁵(x+5).

What is a polynomial?

A polynomial in mathematics is an expression made up of coefficients and indeterminates and involves only the operations of multiplication, addition, subtraction, and non-negative integer exponentiation of variables.

Given the following properties: fifth degree, 2 is a zero of multiplicity 4, −5 is the only other zero, and the leading coefficient is 4.

The general form of the polynomial will be written as,

p(x) =  4(x - 2 )⁵(x+5).

Therefore, the required equation of the polynomial is p(x) = 4(x - 2 )⁵(x+5).

To know more about polynomials follow

brainly.com/question/2833285

#SPJ1

An area near a forest was monitored by researchers. The first graph shows the change in the amount of ground shade during a five-year period. The second graph shows how the population of milkweed changed over the same period.
Which hypothesis is supported by the data?
A. The milkweed population is a biotic factor that decreased as the amount of sunlight, an abiotic factor, decreased.
B. The milkweed population is an abiotic factor that decreased as the amount of sunlight, a biotic factor, decreased.
C. The milkweed population is a biotic factor that decreased as the amount of sunlight, an abiotic factor, increased.
D. The milkweed population is an abiotic factor that decreased as the amount of sunlight, a biotic factor, increased.

Answers

Option A is correct.

What is increasing and decreasing graphs?

Generally speaking, we are aware that if something is growing, it is moving upward, and if it is shrinking, it is moving downward. As a result, if we talk about a function's graph, an increasing function is one that is moving upward, and a decreasing function is one that is moving downward. 

From the graph, we infer that the sunlight, that is the shaded area increased in the given time. Which means that the sunlight was less.

From the milkweed population graph, we see that the milkweed population decreased over time.

Hence the most supportive hypothesis would be option A.

The milkweed population is a biotic factor that decreased as the amount of sunlight, an abiotic factor, decreases.

To learn more about the increasing and decreasing graphs, visit the following link:

https://brainly.in/question/25399990

#SPJ4

Which fraction is equivalent to the given fraction model?
10/4
4/5
4/10
2/10

Answers

4/10 is the fraction that is equivalent to the given fraction model

What is an equivalent fraction ?

According to equivalent fractions, two or more fractions are considered to be equal if, following simplification, both provide the same fraction. Let's imagine that a/b and c/d are two fractions. If these fractions are simplified to produce comparable fractions, such as e/f, they are then equal to one another.

For instance, if we simplify 5/15, the resulting fraction is the same as 1/3, hence that is the equivalent fraction of 1/3.

The fractions with distinct numerators and denominators but the same value are said to be equivalent fractions. For instance, since 2/4 and 3/6 both equal the 12, they are identical fractions. An element of a whole is a fraction. The same amount of the whole is represented by equivalent fractions.

As in the given model 2 out of 5 blocks are in red color which means the equivalent fraction to the given model is 2/5 which is equal to 4/10

Learn more about equivalent fraction from the link below

https://brainly.com/question/29769027

#SPJ1

It keeps saying I’m wrong

Answers

Answer:

translation of 2 squares left and 1 square down

Step-by-step explanation:

consider the top vertex of both figures

S → T

then shape T is a translation of shape S

by moving 2 squares to the left and 1 square down

"Use the formula A=P(1+r/n)ⁿt to solve the compound interest problem
Find how long it takes for $ 900 to double if it is invested at 6 % interest compounded monthly.
The money will double in value in approximately years."

Answers

After 11.61 years the given principal amount of $ 900 will be double.

What is Compound interest?  

Compound interest is interest charged on a loan and is determined by both the principal amount and the rate of interest compounding per year.

The formula for the Amount when compound interest is calculated is given by

                  Amount, A = P(1+r/n)^nt  

P = Principal amount

r = Rate of interest

n = Number of compounds

t = Time period in years

Given:

Principal amount = $ 900

Rate of interest = 6% = 6/100 = 0.06

Number of compounds = 12    [ ∵ compounded monthly]

We need to find the time period

Assume that after 't' years the amount will be doubled

From the given data and formula,

Amount, A = 900(1+0.06/12)^12t        

                  = 900(1+0.06/12)^12t

                  = 900(1 + 0.005)^12t

                  = 900 (1.005)^12t  

As we assumed after 't' years the amount is double

=> 900 (1.005)^12t  = 2 × 900

=>         (1.005)^12t  = 2    

Applying log on both sides

=>  log (1.005)^12t  = log 2

=>    12t log(1.005) = log 2

=>                     12t = log 2/log(1.005)

=>                     12t = 0.30108/ 0.00216  

=>                     12t = 139.888

=>                         t =  11.61

Hence, after  11.61 years the given principal amount of $900 will be double.

To know more about compound interest, click on the link

https://brainly.com/question/28020457

#SPJ4

CAN SOMEONE HELP WITH THIS QUESTION?✨

Answers

The equation of the transformed graph will be y = -3(2ˣ) + 2.

What is the transformation of a graph?

Transformation is rearranging a graph by a given rule it could be either increment of coordinate or decrement or reflection.

If we reflect any graph about y = x then the coordinate will interchange it that (x,y) → (y,x).

Suppose the equation of the given graph is y = A 2ˣ + k.

Substitute,(0,-1)

-1 = A 2⁰ + k

A + k = -1                (1)

Substitute, (1,-4)

-4 = A 2¹ + k

2A + k = -4            

A + k/2 = -2            (2)

Subtract 1 - 2 as

k - k/2 = -1 + 2

k/2 = 1

k = 2

And, A = -2 - 2/2

A = -3

Thus y = -3(2ˣ) + 2

Hence "The equation of the transformed graph will be y = -3(2ˣ) + 2 ".

To learn more about the transformation of graphs,

brainly.com/question/3099136

#SPJ1

how much more would it cost a family of 5 to get the jets game ($105.66) than a Lions game ($79.19?

Answers

Answer:

The answer is 26.47.

Step-by-step explanation:

To get this answer, you simply need to subtract $105.66, by $79.19. You would get the answer of 26.47.

Step 1.       [tex]$105.66 x 5 = 528.3[/tex]

Step 2.      [tex]$79.19 x 5 = 395.95[/tex]

Step 3.     [tex]528.3 - 395.95 = 132.35[/tex]

Thus, with all these steps it would cost $132.35 more to go to the jets game than to go to the lions game.

Question 1 One solution. 2x - 1 =_________x - 1​

Answers

Answer:

2

Step-by-step explanation:

2x-1 = __x-1

Make both sides match to make the statement true.

2x-1 = 2x-1

2 M 1 0 2 B 4 5 6 Triangle ABC is dilated by a factor of 2 with the center of dilation at the origin to form triangle A'B'C'. What are the coordinates of triangle A'B'C'? OA) A'(0, 4), B'(4, 0), C´(8, 8) B) A'(4, 0), B'(0, 4), C'(8,8) C) A'(0, -4), B'(-4, 0), C'(-8, -8) OD) A'(0, 4), B'(4, 0), C'(16, 16) Mange a N not a fan o​

Answers

The coordinates of triangle A'B'C' is A'(0, 4), B'(4, 0), C´(8, 8).

What are coordinates?

A coordinate system in geometry is a method for determining the precise location of points or other geometrical objects on a manifold, such as Euclidean space, using one or more numbers, or coordinates.

Here, we have

Triangle ABC is dilated by a factor of 2 with the center of dilation at the origin to form triangle A'B'C'.

A = ( 0,2)

B = (2, 0)

C = (4,4)

After applying dilated by a factor of 2, we get

A' = (0,4)

B' = (4,0)

C' =(8,8)

Hence, the coordinates of triangle A'B'C' is A'(0, 4), B'(4, 0), C´(8, 8).

To learn more about the coordinates from the given link

https://brainly.com/question/18269861

#SPJ1

Suppose that $11,353 is invested at an interest rate of 5.7% per year, compounded continuously.
a) Find the exponential function that describes the amount in the account after time t, in years.
b) What is the balance after 1 year? 2 years? 5 years? 10 years?
c) What is the doubling time?

Answers

Answer:

Step-by-step explanation:

1)11357*(105.7/100)^t

2)1 year 12000.121  2 year 12684  5 year 14979.1  10 years 19763.3

3)11357*(105.7/100)^t=22714 so t+12.5

What is the vertex of the graph f(z)= 2z² +82 +37

Answers

Answer:

The vertex of the function is located at coordinates (119, 0).

Step-by-step explanation:

1. Write the function and simplify it.

[tex]f(z)= 2z^{2}+82+37\\ \\f(z)= 2z^{2}+119[/tex]

2. Find the derivative with respect to z.

Check the attached image.

[tex]\frac{d}{dz} (2z^{2}+119)\\ \\f'(z)=2*2z^{2-1}\\ \\f'(z)=4z[/tex]

3. Find the roots of the resulting function.

[tex]f'(z)=4z\\ \\4z=0\\ \\z=0[/tex]

4. Evaluate the calculated value in the original function.

[tex]f(0)= 2(0)^{2}+119\\ \\f(0)=119[/tex]

5. Conclude.

The vertex of the function is located at coordinates (0, 119).

Find the most general antiderivative of the function f(x) = 7 sin(x) - 4 sec(x) tan(x) on the interval
[tex]( - \frac{\pi}{2} \: \: \frac{\pi}{2} )[/tex]

Answers

The most general antiderivative of the function is -7cosx-4secx+C on the interval (-π/2,π/2) is not defined.

Given that,

We have a function f(x)=7sinx -4secx tanx.

We have to find the most general antiderivative of the function on the interval (-π/2, π/2).

We know that,

Take the function,

f(x)=7sinx -4secx tanx.

The antiderivative is

= [tex]\int {7sinx-4secxtanx} \, dx[/tex]

= [tex]7\int{sinx} \, dx -4\int {secxtanx} \, dx[/tex]

= 7(-cosx)-4[tex]\int {sinx/cos^{2}(x) } \, dx[/tex]

Take cosx =u

-sinxdx=du

= -7cosx-4[tex]\int {-1/u^{2} } \, du[/tex]

= -7cosx-4(1/u)+C

=-7cosx-4(1/cosx)+C      ( since we know u=cosx)

= -7cosx-4secx+C

Now for the interval (-π/2,π/2)

= -7(cosπ/2-cos(-π/2))-4(secπ/2-sec(-π/2))+C

= -7(0-0)-4(∞-∞)+C

=not defined

Therefore, The most general antiderivative of the function is -7cosx-4secx+C on the interval (-π/2,π/2) is not defined.

To learn more about antiderivative visit: https://brainly.com/question/17072971

#SPJ1

A data set lists the grade point averages of 10th grade students. Which of the following charts could be used to display the data, and why?

Circle graph; because the data is categorical

Circle graph; because the data is numerical

Box plot; because the data is categorical

Box plot; because the data is numerical

Answers

The chart that could be used to display the data is given as follows:

Box plot; because the data is numerical.

What are numerical and categorical data?

A data-set can be classified as either numerical or categorical, depending on the values assumed by the data, as follows:

If the values assumed by the data are numbers, then the data-set is numeric.If the values assumed by the data are labels, then the data-set is categorical.

The correct charts for each type of data are given as follows:

Numeric: box plot.Categorical: circle graph.

The grade point average assumes numeric values, hence it is a numeric data and should be shown on a box plot, meaning that the last option is correct.

The box plot will show the number of grades in each range of the grade point averages, for example, how many grades between 0 and 1, how many between 1 and 2, and so on.

More can be learned about numerical and categorical data at https://brainly.com/question/28916326

#SPJ1

If the functions are combined using addition, which statements describe the resulting graph h(x)? Check two options. domain: x ≥ –2 domain: x ≥ 2 The point (2, 2) is on h(x). The point (–2, 0) is on h(x). The point (0, –3) is on h(x).

Answers

Answer:

(25,-5)

Step-by-step explanation:

PLEASE HELP!!!!
Which graph is linear?

Answers

Answer:

the second

Step-by-step explanation:

the second is a linear graph

Answer:

The second Graph

Step-by-step explanation:

The question is asking what graph is linear.

The first graph is of an absolute value function which is not linear.

The second is of a line. This is linear.

The third looks to be either an exponential or a logarithmic function. Both of which are not linear.

I need help with my home work

Answers

Answer:

Below

Step-by-step explanation:

If congruent then

x = y+5       and

x+3 = 3y          <======sub in the first equation for 'x'

y+5  +3 = 3y

8 = 2y    then   y = 4        x = y+5 = 9

Solve the equation without using a calculator

[tex]\bf\\\\log^2x+log^2(x+10)=log^211\\\\log(x+10)\neq 0[/tex]

[tex]\bf\\(\ lgx=log_{10}x=logx\ )[/tex]

Answers

The solution to the logarithmic expression log²x + log²(x + 10) = log²11 is;

x = -11 and 1

How to solve logarithm expressions?

We are given the logarithmic expression as;

log²x + log²(x + 10) = log²11

By the power rule of logarithm, we know that; log²x = 2log x

Thus;

log²x + log²(x + 10) = log²11 can be expressed as;

2log x + 2log (x + 10) = 2log 11

Divide through by 2 to get;

log x + log (x + 10) = log 11

We know from product rule of logarithm that log (ab) = log a + log b. Thus; log x + log (x + 10) = log 11 is;

log x(x + 10) = log 11

Log cancels out to get;

x² + 10x - 11 = 0

Using quadratic equation calculator gives;

x = -11 and 1

Read more about Logarithm Expressions at; https://brainly.com/question/28041634

#SPJ1

what is 3/4 - 1/4ygkfmvkbkmbkvmmf

Answers

Answer:

1/2

Step-by-step explanation:

a) Work out the minimum number of hikers who could have walked between 6 miles and 17 miles.
b) Work out the maximum number of hikers who could have walked between 6 miles and 17 miles.

Answers

a)  minimum of nine hikers might have covered the distance between 6 and 17 miles because it falls within the standard interval of 10 ≤ x ≤ 15.

b) The maximum no. of hikers who might have covered the distance between 6 and 17 miles is 19.

What do minimum and maximum value mean?

Rearrange the function using fundamental algebraic concepts to get the value of x when the derivative equals 0. This response gives the x-coordinate of the function's vertex, which is where the maximum or minimum will occur. To find the minimum or maximum, rewrite the solution into the original function.

Learn more about minimum and maximum values from the link below

brainly.com/question/14993153

#SPJ4

Which operations involving complex numbers have solutions represented by (-6, 7)? 2(1 − 2i) − (4 + 3i), 2(1 + 2i) + (-4 − 3i), 2(-1 + 2i) − (4 − 3i), (-2 + 4i) + (-4 + 3i) , (-2 − 4i) + (4 − 3i)

Answers

Option 3 and 4 are the operations involving complex numbers have solutions represented by (-6, 7).

What is a complex number ?Every complex number can be expressed in the form displaystyle a+bia + bi, where a and b are real numbers. A complex number is an element of a number system that extends the real numbers with a specific element denoted I also known as the imaginary unit, and satisfying the equation displaystyle i2=-1. René Descartes referred to me as an imaginary number since no actual number can satisfy the aforementioned equation. The real component of the complex number displaystyle a+bia+bi is referred to as a, and the imaginary part is referred to as b. The symbols C or displaystyle "mathbb "C" are used to represent the set of complex numbers.Complex numbers are crucial to many parts of the scientific explanation of the natural world, despite the historical appellation "imaginary," and are recognized in the mathematical sciences as just as "real" as real numbers.

Find the attachment answer

Learn more about a complex number refer to :

https://brainly.com/question/10662770

#SPJ1

Other Questions
Can someone help, please Employers should ensure all earthmoving/compacting equipment with obstructed view does not operate in reverse gear unless the equipment has a reverse signal alarm or a worker has been designated to signal when it is safe. For which type of safety is this action taken? Find x and y -- if your answer is not a whole number, round to the tenths!X=______Y=_______ the nurse in the emergency department is listening to the breath sounds of a client with respiratory distress and hears this sound. (refer to audio.) the nurse determines that this finding is characteristic of which disorder? I will give brainiest if u answer____ - the measurement of forcenewtongravityfrictionwork8. Match the word with the description.____ - the force between any two objects that are touchingmagnetic fieldgravityindirect forcedirect force9. King Cotton diplomacy built on the hope that European nations starving for cotton would intervene in the war and recognize the Confederacy.a. Trueb. False the researcher has no obligation to test to determine that a significant correlation has been found before reporting it. true false Write the inequality shown by the graph. Did the Confederacy'die of states' rights'? PLS HELP!!!! The revenue for a local photographer for the month is $1200. His costs include a studio rental of $600, props costing $105, materials fees of $115, and a make-up artist who charges $130. What is his total profit for the month? if a simple pendulum oscillates with small amplitude and its length is doubled, what happens to the frequency of its motion? Let C represent the cost in dollars and R represent the revenue in dollars. What is the break-even point? Use a table to help if necessary.C=24x+80R=44x Slides: Are there striations across the width of the muscle cells? Number of Nuclei? What are the size, shape, and arrangement of fibers? What function occurs as a result of the contractions in the selected muscle? (see page 3 of the lesson) What is the relationship between structure and function in the selected muscle? (see page 3 of the lesson)Muscle - Human Cardiac Intestines - Outer Wall Detail (smooth muscle) Slide 1: Muscle- Skeletal Longitudinal SectionandSlide 2: Muscle-Skeletal Cross Section Compare the magnitude of the electromagnetic and gravitational force between two electrons separated by a distance of 2.00 m. Assume the electrons have a mass of 9.11 1031 kg and a charge of 1.61 1019 C. Round to two decimal places. Fe = 1029 N Fg = 1071 N F Subscript e baseline over F Subscript g baseline.= 1042 in a scientifically developed public poll, a number that states how far the poll results may be from the actual preferences of the total population of citizens is called th Mr. Chung drove 248 miles in 4 hours. If he continues driving at the same speed, how many miles will Mr.Chung drive in 6 hours? The height of a statue of a boy was 12 meters and the scale used was 4 meters: 1 foot. Find his actual height. the following structure is that of ribose. is this a furanose or pyranose form? is it an alpha or beta anomer? is it a d or l sugar? What is the percent composition by mass of oxygen in the compound mgso4? the formulas mass of mgso4 is 120 g/mol. In virtually every stable compound, each of the atoms has achieved an electron configuration analogous to that of the ______ elements.