Mathematics College

I NEED THIS REALLY FAST!!!a brave knight traveled on his horse from one kingdom to another in 2 days the first day he rode at a speed of 10 mph and the second day he rode at a speed of 8 mph if he traveled exactly the same amount of time each day and went 180 miles find how many hors it took the knight to travel from one kingdom to another

Answers

Answer 1

Answer:

10 hours

Step-by-step explanation:

The rate x time of the first day + the rate x time of the second day equal the distance of 180 miles.

Let t = time

10t + 8t = 180

18t = 180

t = 10

Related Questions

Suppose y varies inversely with x, and y = 36 when x=112
What inverse variation equation relates x and y ?

Answers

The inverse variation equation that relates x and y is x = 4032 / y.

What is the equation that relates x and y?

if two variables vary inversely, there is a negative relationship between both variables. the increase in one variable leads to a decrease in the other variable

The equation that represents inverse proportion : x = b/y

where b = constant of proportionality

112 = b /36

b = 36 x 112 = 4032

The equation : x = 4032 / y

To learn more about inverse proportion, please check: https://brainly.com/question/27233899

#SPJ1

I need help with this geometry question asap!

Answers

No pair of lines can be proven to be parallel considering the information given, therefore, the answer is: D. None of the options are correct.

When are Two Lines Proven to be Parallel to each other?

Two lines that are cut across by a transversal can be proven to be parallel to each other if:

The alternate interior angles along the transversal and on the two lines are congruent [alternate interior angles theorem].The alternate exterior angles along the transversal and on the two lines are congruent [alternate exterior angles theorem].The same-side interior angles along the transversal and on the two lines are supplementary [same-side interior angles theorem].The corresponding angles along the transversal and on the two lines are congruent [corresponding angles theorem].

Thus, given the following information:

m∠2 = 115°

m∠15 = 115°

With only these two angles given, we can't use any of the theorems to prove that any of the two lines are parallel because angle 2 and angle 15 are located entirely on two different transversals that crosses two lines.

In summary, we can conclude that:

D. None of the options are correct.

Learn more about the Parallel lines on:

https://brainly.com/question/16742265

#SPJ1

Using the following accounts and balances, prepare the “Stockholders’ Equity” section of the balance sheet. 60,000 shares of common stock authorized, and 4,000 shares have been reacquired.

Common Stock, $50 par $2,400,000

Paid-In Capital from Sale of Treasury Stock 48,000

Paid-In Capital in Excess of Par—Common Stock 576,000

Retained Earnings 1,368,000

Treasury Stock 25,000

Answers

The total Stockholders’ Equity is $4,367,000

Total Stockholders’ Equity

Common Stock, $50 par $2,400,000

Paid-In Capital in Excess of Par—Common Stock $576,000

Paid-In Capital from Sale of Treasury Stock $48,000

Total paid in capital $3,024,000

Retained Earnings $1,368,000

Less Treasury stock $25,000

Total Stockholders’ Equity $4,367,000

Therefore the total Stockholders’ Equity is $4,367,000.

Learn more about total Stockholders’ Equity here:https://brainly.com/question/15709882

#SPJ1

a. P is equal to the set containing t,v,c and d
b. the set consisting of the elements 2 and 6 is a proper subset of [ 2,6,8,12}
c. the set consisting of the elements 0 and 3 is not a subset of {3,2,4,6}

a.P is equal to the set containing t,v,c and d

p=

Answers

The answers to the questions are:

a. p = { t, v, c, q}

b. {2, 6} ⊂ {2,6,8,12}

c. {0, 3} ⊄ {3,2,4,6}

How to write the mathematical expression s using mathematical symbols.

To represent sets we use

p = { }

Hence

a. p = { t, v, c, q}

b. If 2 and 6 is a proper subset of [ 2,6,8,12},

This can be represented as

{2, 6} ⊂ {2,6,8,12}

c. the set consisting of the elements 0 and 3 is not a subset of {3,2,4,6} is written as

{0, 3} ⊄ {3,2,4,6}

Answers

Option a. The equation that is used to show the graph of the limacon is given as r = 1 + 3 sin theta.

How to solve for the equation

We have these ppoints [-5,5] by [-5,5]

The limacoin is used to represent a shape that may appear like that of a snail.

This is written in the form of

r = a ± b sin θ

and

r = a ± b cos θ

Given that we have the ± sign, the curve that is at the top of the horizontal; line is the + sign and the one below is the -

If a/b < 1 then a circle is within the circle that was formed as a graph.

Hence from the description that we have given here, the graph has the forms of

r = a + b sin θ

This is the equation that can be used to suit the form r = 1 + 3 sin theta

Hence option a is right.

Answers

The events E and F are not independent

How to determine the probabilities?

The given parameters are:

P(E n F) = 0.036

P(E|F) = 0.09

P(F|E) = 0.1

To calculate P(E), we use:

P(F|E) = P(E n F)/P(E)

This gives

P(E) = P(E n F)/P(F|E)

So, we have:

P(E) = 0.036/0.1

Evaluate

P(E) = 0.36

To calculate P(F), we use:

P(E|F) = P(E n F)/P(F)

This gives

P(F) = P(E n F)/P(E|F)

So, we have:

P(F) = 0.036/0.09

Evaluate

P(F) = 0.4

To calculate P(E U F), we use

P(E U F) = P(E) + P(F) - P(E n F)

So, we have:

P(E U F) = 0.36 + 0.4 - 0.036

Evaluate

P(E U F) = 0.724

The events E and F are independent if

P(E n F) = P(E) * P(F)

This gives

0.036 = 0.36 * 0.4

Evaluate

0.036 = 0.144 --- false

Hence, the events E and F are not independent

Answers

The pieces of information that is provided by the box plots are the median and first quartile.

The piece of information that is not provided by the box plots is the mean.

The interquartile range is 22.50.

An outlier would distort the values of the median and the quartiles.

What is a box plot?

A box plot is used to study the distribution and level of a set of scores. The end of the first line represents the minimum number and the end of the second line represents the maximum number.

On the box, the first line to the left represents the lower (first) quartile. The next line on the box represents the median. The third line on the box represents the upper (third) quartile. The difference between the quartiles is the interquartile range.

Interquartile range = 60 - 37.50 = 22.50

To learn more about box plots, please check: https://brainly.com/question/27215146

#SPJ1

One week, Tanisha earned $255.00 at her job when she worked for 17 hours. If she is paid the same hourly wage, how much would she make the next week if she worked 11 hours?

Answers

Answer:

Step-by-step explanation:

Jeremiah is a salesperson who sells computers at an electronics store. He makes a base pay amount each day and then is paid a commission as a percentage of the total dollar amount the company makes from his sales that day. Let PP represent Jeremiah's total pay on a day on which he sells xx dollars worth of computers. The table below has select values showing the linear relationship between xx and P.P. Determine how many dollars worth of computers Jeremiah would have to sell in order to get paid $130 on a given day.

Answers

Jeremiah has to sell 5000 dollars worth of computers to get paid $130 on a given day. Using the linear equation, the required value is calculated.

What is a linear equation?

An equation in which if the highest degree of the variable is 1(one), then that equation is said to be a linear equation.

General form: ax + b = c; where the power of the variable x is 1.

Calculation:

It is given that,

Jeremiah makes a base pay amount each day and then is paid a commission as a percentage of the total dollar amount the company makes from his sales that day.

Consider,

P - as total pay on a day, x - as the number of dollars worth of computers, B - as basic pay, and C - as commission percentage.

So, the linear equation that relates x and P is,

P = Cx + B ...(i)

On substituting the values from the given table we get,

122.5 = C(4500) + B ...(ii)

160 = C(7000) + B ...(iii)

175 = C(8000) + B ...(iv)

By solving equations (iii) and (iv), we get

C = 15/1000 = 0.015

B = 55

Finding x value when P = $130:

We have P = Cx + B. Then for P = 130,

130 = Cx + B

We know C = 0.015 and B = 55

On substituting these values,

130 = (0.015) x + 55

⇒ 0.015x = 130 - 55 = 75

∴ x = 75/0.015 = 5000

Therefore, the required computers are 5000 dollars worth.

Learn more about linear equations here:

https://brainly.com/question/2030026

#SPJ1

Disclaimer: The given question on the portal was incomplete. Here is the complete question.

Question: Jeremiah is a salesperson who sells computers at an electronics store. He makes a base pay amount each day and then is paid a commission as a percentage of the total dollar amount the company makes from his sales that day. Let P represent Jeremiah's total payments on a day on which he sells x dollars worth of computers. The table below has select values showing the linear relationship between x and P. Determine how many dollars worth of computers Jeremiah would have to sell to get paid $130 on a given day.

Table:

x: 4500, 7000, 8000

P: 122.5, 160, 175

respectively.

By eating 1 egg, 1 cupcake, and 1 slice of pizza, a child consumes 303 mg of cholesterol. If the child eats 3 cupcakes and 4 slices of pizza, he or she takes in 90 mg of cholesterol. By eating 2 eggs and 1 cupcake, a child consumes 570 mg of cholesterol. How much cholesterol is in each item?

Answers

Using a system of equations, the amounts of cholesterol in each item are given as follows:

Egg: 278 mg.Cupcake: 14 mg.Slice of pizza: 11 mg.

What is a system of equations?

A system of equations is when two or more variables are related, and equations are built to find the values of each variable.

The variables for this problem are given as follows:

Variable x: Amount of cholesterol in an egg.Variable y: Amount of cholesterol in a cupcake.Variable z: Amount of cholesterol in a slice of pizza.

By eating 1 egg, 1 cupcake, and 1 slice of pizza, a child consumes 303 mg of cholesterol, hence:

x + y + z = 303.

3 cupcakes and 4 slices of pizza, he or she takes in 90 mg of cholesterol, hence:

3y + 4z = 90

y + 1.33z = 30.

By eating 2 eggs and 1 cupcake, a child consumes 570 mg of cholesterol, hence:

2x + y = 570.

Then, writing y and z as functions of x:

y = 570 - 2x.z = (30 - y)/1.33 = (30 - 570 + 2x)/1.33 = 1.5x - 406.

Then, replacing on the first equation:

x + y + z = 303.

x + 570 - 2x + 1.5x - 406 = 303.

0.5x + 164 = 303.

x = (303 - 164)/0.5

x = 278.

The amounts for the cupcake and the slice of pizza are given as follows:

y = 570 - 2(278) = 14 mg.z = 1.5x - 406 = 1.5(278) - 406 = 11 mg.

More can be learned about a system of equations at https://brainly.com/question/24342899

#SPJ1

Solve for v. -8=-2/v

Answers

Answer is 1/4
Step by step
-8 = -2/v
First we want to isolate “v”
-2 is divided by “v”, so we will multiply both sides by “v”
-8v = -2
Now we can solve for v
Divide both sides by -8
v = 2/8, simplified to 1/4
(Remember when you multiply or divide two negatives it becomes a positive)

If you want to check your work, substitute your answer of 1/4 into the original equation.

-8= (-2) divided by (1/4)
-8 = -8
Problem solved!!

someone please help me find the value of x

Answers

Hello,

5x² = 90/2

5x² = 45

x² = 45/5

x² = 9

x = √9 or x = -√9

x = 3 or x = -3

The value of X is = X= 3 or X= -3

Solve the inequality. -3x + 2x - 34 Enter the exact answer in interval notation.

Answers

Answer:

x = -34

Step-by-step explanation:

-3x + 2x -34 = 0

sum the x

-3x + 2x = -x

replace -x in the equation

-x -34 = 0

move -34 to other side

-x = 34

divide the two sides by -1 to get x value

x = -34

now replace x value in the equation:

-3(-34) + 2(-34) -34 =

102 -68 -34 =

102 -102 = 0

Which of the following equations represents F(x)= x4 reflected across the line
y = x?
OA. F(x)=√x
OB. F(x)=√x
OC. F(x)=-4x
OD. F(x) = ±**

Answers

The reflection of F(x) = x⁴, across the line y = x, results in the function [tex]y = F(x) = \pm \sqrt[4]x[/tex], making option A the right choice.

For any function f(x), the reflection across the line y = x, gives the inverse of the function f(x).

In the question, we are asked for the equation, representing the reflection of f(x) = x⁴, across the line y = x.

The function can be shown as:

y = f(x) = x⁴,

or, x⁴ = y,

or, [tex]x = \pm\sqrt[4]{y}[/tex]

Changing the variables to general form, that is, y as the dependent variable and x as the independent variable, we get the inverse function as, [tex]y = F(x) = \pm \sqrt[4]x[/tex].

Thus, the reflection of F(x) = x⁴, across the line y = x, results in the function [tex]y = F(x) = \pm \sqrt[4]x[/tex], making option A the right choice.

Learn more about inverse functions at

https://brainly.com/question/21927534

#SPJ1

The complete question is:

"Which of the following equations represents F(x) = x⁴ reflected across the line y = x?

A. [tex]F(x)= \pm\sqrt[4]{x}[/tex]

B. [tex]F(x)= \sqrt[4]{x}[/tex]

C. [tex]F(x)= \pm x^4[/tex]

D. [tex]F(x)=- \sqrt[4]{x}[/tex] "

Select the symbol = (equal to) or ≠ (not equal to) to make the expression true.
{0} ? { }

Answers

Answer:

Step-by-step explanation:

{0}={} because 0 means that there is nothing and in null set too, there is no elements.

An athlete has 75% of winning the race if he is not injured. If he is injured, his probability of winning the race is only 15%. If the total chances of winning is 51%, what is the probability that he gets injured?

Answers

Answer:

X = 'is the athlete injured' (X in {0,1})

Y = 'the athlete wins' (Y in {0,1})

P(Y=1|X=0) = 0.75

P(Y=1|X=1) = 0.15

P(Y=1) = 0.51

We are looking for P(X=1) - P(Y=1) = P(Y=1|X=0)*(1-P(X=1)) + P(Y=1|X=1)*P(X=1)

The above equation should provide you with the answer 0.4!

Step-by-step explanation:

Let a and b be real numbers where a b 0. Which of the following functions could represent the graph below?

Answers

A function which could represent the graph is: C. f(x) = x⁴(x - a)(x - b)².

How to interpret the graph?

The nature of the intercept on a polynomial graph highlights the nature of its multiplicity. Also, the polynomial graph has no single zero (factor) but bounced off the x-axis at three (3) different locations.

This ultimately implies that the polynomial graph has an even multiplicity at these three (3) points:

x⁴

x - a

(x - b)²

In conclusion, a function which could represent the graph is f(x) = x⁴(x - a)(x - b)².

Answers

The actual roots of f(x) are -4 and 3

How to determine the actual roots?

The function is given as:

f(x) = 2x^2 + 2x – 24.

Expand the function

f(x) = 2x^2 + 8x- 6x – 24.

Factorize the function

f(x) = 2x(x + 4) - 6(x + 4)

Factor out x + 4

f(x) = (x + 4)(2x - 6)

Set to 0

(x + 4)(2x - 6) = 0

Solve for x

x = -4 and 2x = 6

This gives

x = -4 and x = 3

Hence, the actual roots of f(x) are -4 and 3

Answers

Answer:

1/2

Step-by-step explanation:

This is an independent event. It does not matter what happened before the chances of getting a tail on one toss will always be what I want/all outcomes. There are only 2 outcomes: heads or tails. I am only looking for one of those outcomes, so 1/2.

This is the photo for the last question

Answers

All the angles required to complete each sentence are:

m ∠ 4 = 60, m ∠ 2 = 120m ∠ 3 = 110, m ∠ 4 = 70m ∠ 2 = x, m ∠ 1 = 180 - x

How to find measures of missing angles by Euclidean geometry

In this question we must take advantage of definitions and theorems of Euclidean geometry to complete the three sentences seen in the figure. Now we proceed to present each sentence completed in detail:

If m ∠ 5 = 60, then m ∠ 4 = 60 by alternal internal angles between parallel lines and m ∠ 2 = 120 by supplementary angles.If m ∠ 7 = 110, then m ∠ 3 = 110 by corresponding angles between parallel lines and m ∠ 4 = 70 by supplementary angles. If m ∠ 6 = x, then m ∠ 2 = x by corresponding angles and m ∠ 1 = 180 - x by supplementary angles.

To learn more on angles: https://brainly.com/question/7116550

#SPJ1

Cycles travel at an the average speed of 20km/h for 1.5 Hours
calculate the distance she travels in 1.5

Answers

Answer:

30 km

Step-by-step explanation:

Distance = rate x time

Distance = 20 x 1.5

Distance = 30

[tex]20*1.5=30[/tex] [tex]km[/tex]

Correct answer:-

Avg. speed = [tex]20km/h[/tex]

Time = [tex]1.5 hour[/tex]

Distance traveled in 1.5 hours is Distance = Speed x Time

So,

[tex]D = 20 * 1.5 = 30.[/tex]

reference link-

a cyclist travels at a speed of 20 km per hour how far will he ...https://brainly.in › Math ›

#f23

a infant grew 2/4 inches in the first month 7/4 inches in the third month . first find the total inches the infant grew over the three months . then find the difference in the infants from the second month to the third month

Answers

The fraction computed shows that the total inches the infant grew over the three months is 3 3/4 inches.

How to compute the fraction?

First month = 2/4 inches

Second month = 1 inch

Third month = 7/4 inches.

The total inches the infant grew over the three months will be;

= 2/4 + 1 + 7/4

= 3 1/4 inches.

The difference in the infants from the second month to the third month will be:

= 7/4 - 1

= 3/4 inches.

Learn more about fractions on:

brainly.com/question/78672

#SPJ1

(1)
Determine the equation of the line passing through the point (0; -1) and
parallel to the -axis. Do you remember what the gradient of this line is?

(2)
Determine the equation of the line passing through the point(-1;0) and
parallel to the -axis. Do you remember what the gradient of this line is?

Answers

We know that,

slope = [tex] \rm{\frac{(y2 - y1)}{(x2 - x1)} }[/tex]

Let (0,1)=(x 1 ,y 1 ) and (1,2)=(x 2,y 2 )

So,

Slope of line = [tex] \frac{(2 - 1)}{(1 - 0)} = 1[/tex]

Now,

The required line equaqtion is given by,

==> y−y 1 = m(x-x1)

==> y−1=1(x−0)

==> y−1=x

==> y=x+1

f(x)=2^x. What is g(x)?

Answers

The function g(x) is g(x)= (3x)^2

How to solve for g(x)?

The complete question is in the image

From the graph in the image, we have:

f(x) = x^2

The function f(x) is stretched by a factor of 3 to form g(x).

This means that:

g(x) = f(3x)

So, we have:

g(x)= (3x)^2

Hence, the function g(x) is g(x)= (3x)^2

Read more about function transformation at:

https://brainly.com/question/10222182

#SPJ1

questions 5 and 6 please!
will give brainliest to whoever answers
90 points

Answers

Answer:

rise over run so

5/5 = 1

-2/4 = -0.5

Part II: Use the formula from Part I to find the midpoint of the
segment with endpoints at (-2,-1) and (0, 9). Show your work.

PLS

Answers

Answer: (-1, 4)

Step-by-step explanation:

[tex]\left(\frac{-2+0}{2}, \frac{-1+9}{2} \right)=\boxed{(-1, 4)}[/tex]

(-1, 4) is the midpoint of the segment with endpoints at (-2,-1) and (0, 9). This can be obtained by using the formula for finding the midpoint of a line segment.

Find the midpoint of the line segment:

When the end points of a line segment are known, the mid point of the line segment is calculated using the midpoint formula,

Midpoint formula,

[tex](\frac{x_{1}+x_{2} }{2},\frac{y_{1}+y_{2} }{2})[/tex]

(x₁, y₁) and (x₂, y₂) are the endpoints of the line segment.

⇒ This means that, the midpoint of a line segment with endpoints (x₁, y₁) and (x₂, y₂) is [tex](\frac{x_{1}+x_{2} }{2},\frac{y_{1}+y_{2} }{2})[/tex].

From the question it is given that,

(x₁, y₁) = (-2,-1) (x₂, y₂) = (0, 9)

are the endpoints of the line segment.

By using the Midpoint formula we get,

[tex](\frac{x_{1}+x_{2} }{2},\frac{y_{1}+y_{2} }{2})[/tex] = [tex](\frac{-2+0 }{2},\frac{-1+9}{2})[/tex]

[tex](\frac{x_{1}+x_{2} }{2},\frac{y_{1}+y_{2} }{2})[/tex] = [tex](-1, 4)[/tex]

Hence (-1, 4) is the midpoint of the segment with endpoints at (-2,-1) and (0, 9).

Learn more about midpoint here:

brainly.com/question/14687140

#SPJ1

A compression wave is moving away from an explosion at 100 ft/sec. How fast is the volume within the spherical compression wave increasing in t = 4 seconds? You will need the formula for the volume of a sphere! *Leave π in your answer do not convert to a decimal!

Answers

The volume within the spherical compression wave increasing in t = 4 seconds is:64000000π cubic ft/sec.

Volume of a sphere

Given:

dr/dt=100 ft/sec

When: t=4 seconds, radius(r)=400ft

Hence:

Volume of a sphere (V)=4/3πr³

dv/dt=4/3π.3r² dr/dt

dv/dt=4πr²dt/dr

When t=4 seconds

dv/dt=4π×(100×4)²×100 cubic ft/sec

dv/dt=4π×(400)²×100 cubic ft/sec

dv/dt=64000000π cubic ft/sec

Therefore the volume within the spherical compression wave increasing in t = 4 seconds is:64000000π cubic ft/sec.

Learn more about Volume of a sphere here:https://brainly.com/question/22807400

#SPJ1

Graph the image of the polygon after a reflection in the line y = t.

Answers

Answer:

see the attached

Step-by-step explanation:

Reflection over a line moves each point so that the segment between it and its image has the reflection line as its perpendicular bisector.

Reflection over y=x

The line of reflection y=x has the effect of swapping the x- and y-coordinates:

(x, y) ⇒ (y, x) . . . . . reflection in y=x

For example, point C(2, 3) moves to point C'(3, 2).

The attachment shows the reflected figure.

A Ferris wheel with a diameter of 10 m and makes one complete revolution every 80
seconds. Assume that at time t = 0, the Ferris Wheel is at its lowest height above
the ground of 2 m. You will develop the equation of a cosine graph that models your
height, in metres, above the ground as you travel on the Ferris Wheel over time, t in
seconds. To do this, answer the following questions.

1. State the amplitude of the graph.
2. State the value of k in the general form y = a cos [k(x − d)] + c.
-
3. State the value of d.
4. State the value of c.
5. State the cosine equation of the graph.

Answers

A Ferris wheel with a diameter of 10 m and makes one complete revolution every 80 seconds. Assuming that at time t = 0, the Ferris Wheel is at its lowest height above the ground of 2 m, the cosine equation of the graph drawn is, y = 5 cos [( π/40)(x - (π/2))] + 3. Here, amplitude of the graph is 5, value of k is π/40, d is π/2 and c is 3.

Developing the Equation of a Cosine Graph

The given information constitutes the following,

Diameter = 10 m

⇒ Radius, r = 5 m

Time, t = 80 s

Height above the ground, h = 2 m

Thus, we can infer that,

Amplitude, A = 5 m

Period, T = 80 s

Minimum height = 2 m

The cosine function is given as,

a cos [k(x − d)] + c

Here, A is amplitude

B is cycles from 0 to 2π and thus period = 2π/k

d is horizontal shift

c is vertical shift (displacement)

Now, 2π/k = 80

⇒ k = 2π/80 = π/40

The value of c is given as,

c = Amplitude - Minimum height

c = 5 - 2

c = 3

For a shift to the left by π/2 gives, we have,

d = π/2

Thus, the desired equation of the drawn cosine graph is,

y = 5 cos [( π/40)(x - (π/2))] + 3

Learn more about amplitude here:

https://brainly.com/question/8662436

#SPJ1

Name the following polynomial: 4x^2 +8+16 cubic polynomial quartic trinomial quadratic trinomial cubic trinomial

Answers

The polynomial is quadratic trinomial

How to name the polynomial?

The polynomial function is given as:

4x^2+ 8x +16

The highest power in the above polynomial is 2.

This represents quadratic

The number of terms in the above polynomial is 3

This represents trinomial

Hence, the polynomial is quadratic trinomial