Let f(x) = e = 1+x. a) Show that ƒ has at least one real root (i.e. a number c such that ƒ(c) = 0). b) Show that f cannot have more than one real root.

Answer:

44

Step-by-step explanation:

All angles on a triangle add up to 180 degrees so 180-(65+71) will give you 44

A motorist travels from a town P on a bearing of 150° to a town Q 40km away. From Q he travels to a town R on a bearing of 210° if R you s located directly south of P, how far is R from P? (a)40√3km(b)40√2km(c)40km(d)80km

​Let P be the starting point of the motorist .Let x be the distance of PR .Let PQR be the triangle formed by the towns P, Q, and R. Using the law of cosines, we have:(40)² = x² + (40 + x)² - 2(40)(40 + x)cos(150° + 30°)(40)² = x² + (40 + x)² - 2(40)(40 + x)cos(180° - 150° - 30°)1600 = x² + (40 + x)² + 2(40)(40 + x)cos(150° + 30°)1600 = x² + (40 + x)² + 2(40)(40 + x)cos(30°)1600 = x² + (40 + x)² + 2(40)(40 + x)(√3/2)1600 = x² + (40 + x)² + (40)(40 + x)(√3)800 = x² + (40 + x)² + (20)(40 + x)(√3)800 = x² + 1600 + 80x + x² + 1600 + 80x + 800(√3)1600 = 2x² + 160√3 x + 4000(√3) - 800x² + 240√3 x + 4000(√3)0 = -6x² + 400√3 x + 4000(√3)0 = -2x² + 133.33 x + 1333.33By the quadratic formula:  x = (–b ± √b² – 4ac)/2a x = [–133.33 ± √(133.33)² – 4(–2)(1333.33)]/2(–2)x = [–133.33 ± √(17777.1089)]/–4x ≈ 34.14, –19.61Since x must be positive, x ≈ 34.14km (nearest hundredth)Therefore, the distance between P and R is approximately 34.14 km. Answer: (a)40√3 km.

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Answer:

29.25 Interest

Step-by-step explanation:

Take the formula: I=PRT

The principal is 650.00, 4.5 is the rate, 1 year is the time, We do not know the interest.

Change the rate, 4.5 to 0.045 to help solve the problem.

Times 650.00, 0.045, and 1 together.

You will get 29.25, Which is the answer!

Booyah! You are done.

Hope this helps!

The original number from the given decimal number is  0.02.

For the given question;

Moving a decimal point 4 places towards the right corresponds to multiplying the given integer by 10,000 if it is x.

This results in:

10000x = 4.(1/x)

Simplifying.

x² = 4/10000

x > 0.

Taking square root of the number.

x = 2/100

x = 0.02

Thus, the original number from the given decimal number is  0.02.

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An isosceles triangle is one which has two equal sides and angles. Therefore, the measure of <NMO required in the given question is \(20^{o}\).

An isosceles triangle is a type of triangle which has two equal sides, thus angles.

So that comparing the triangles in the given question, we have:

i. ΔNMQ, ΔMPQ, ΔOPM, and ΔNMO are all isosceles triangles.

Thus;

<MQN = <MNQ = \(60^{o}\) (isosceles triangle base angle property)

So that;

<QMN = \(180^{o}\) - (<MQN + <MNQ)

           = \(180^{o}\) - \(120^{o}\)

<QMN = \(60^{o}\)

ii. In triangle MOP, we have;

<MPO = <MOP = \(80^{o}\) (base angle property of isosceles triangle)

Then,

<PMO = \(180^{o}\) - (\(80^{o}\) +

        = \(180^{o}\) - \(160^{o}\))

<PMO = \(20^{o}\)

But,

<QMP + <NMO = (\(60^{o}\) - \(20^{o}\))

                         = \(40^{o}\)

Since <QMP = <NMO, then;

m<NMO = \(\frac{40^{o} }{2}\)

              = \(20^{o}\)

Thus, the measure of <NMO is \(20^{o}\).

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Answer:

the fourth one

Step-by-step explanation:

Answer:

$3250

Step-by-step explanation:

interest=deposit×simple interest×time

interest=5000×6.5%×10

5000×65/1000×10=3250

ans;$3250

A $450 principal and a simple interest rate of 0.35% each quarter for 212 years would result in a savings account balance of $3768.

We can use the formula for simple interest to solve this problem:

Simple Interest = Principal x Rate x Time

where Rate is the interest rate as a decimal, and Time is the time in years.

The quarterly interest rate is 0.35% / 4 = 0.00875, and the time is 212 years, or 848 quarters.

Plugging in these values, we get:

Simple Interest = $450 x 0.00875 x 848 = $3318

Therefore, the balance of the savings account after 212 years would be:

Balance = Principal + Simple Interest = $450 + $3318 = $3768

Therefore, the balance of the savings account after 212 years with a simple interest rate of 0.35% each quarter and a principal of $450 would be $3768.

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Answer:

price of hotdog = $1
price of drink = $0.5

Step-by-step explanation:

let the price of hotdogs be x

let the price of drinks be y

10x + 5y = 12.50 ------- 1st eq

7x + 4y = 9 -------------- 2nd eq

10x + 5y = 12.50 ------------ ×4

7x + 4y = 9 -------------------- ×5

40x + 20y = 50

(-)35x + (-)20y = (-)45

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

5x = 5

x = 1

put the value of x in any of the prior eq.

(7)(1) + 4y = 9
4y = 9-7

y = 2/4

y = 1/2

answer:

price of hotdog = $1
price of drink = $0.5

Answer:

100°

Step-by-step explanation:

180-80=100

if it produced 500 units per day, its total cost would be $425. then average total cost is $0.61

The average total cost is calculated as the total cost divided by the number of outputs. The firm's ATC at these three levels of production will be:

1. 1,000 units per day at a total cost of $700.

ATC = Total cost/output

ATC = $700/1000

ATC = $0.58

2. If the firm produced 1,000 units per day, its total cost would be $450.

ATC = Total cost/output

ATC = $450/1000

ATC = $0.45

3. If it produced 700 units per day, its total cost would be $425.

ATC = Total cost/output

ATC = $425/700

ATC = $0.61

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Answer:

n = 7

Step-by-step explanation:

Your answers are correct.

For problem 3, we use error estimation:

| (-2)ⁿ⁺¹ / (n+1)! | < 0.01

(2)ⁿ⁺¹ / (n+1)! < 0.01

By trial and error:

If n = 3, (2)ⁿ⁺¹ / (n+1)! = 0.667

If n = 5, (2)ⁿ⁺¹ / (n+1)! = 0.089

If n = 7, (2)ⁿ⁺¹ / (n+1)! = 0.006

Answer:

Neither of the graphs show a proportional relationship.

Step-by-step explanation:

A proportional relationship is also known as a linear relationship, where when the points are plotted on the graph, the points increase or decrease at a constant rate. This will appear as a straight line with NO change.

Answer:

moderate since the lines are similar

Answer:

Rounding to the Nearest Integer

The most common type of rounding is to round to the nearest integer. The rule for rounding is simple: look at the digits in the tenth's place (the first digit to the right of the decimal point).

Answer:D

a=4

Step-by-step explanation:

Answer:

1. is D

2. is A

Step-by-step explanation:

The Titanic could stay afloat with four of its 16 watertight compartments flooded, more than anyone could imagine on a ship of its size. ... As the ice bumped along its starboard side, it punched holes in the ship's steel plates, flooding six compartments. In a little over two hours, the Titanic filled with water and sank.

Part A

q = 9 represents selling 9000 units, since q is thousands of units sold

Plug this into the D(q) function

D(q) = -q^2 - 2q + 597

D(9) = -(9)^2 - 2(9) + 597

D(9) = 498

The price per unit should be $498

You have the correct answer.

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

Part B

Plug in D(q) = 477. Then solve for x.

D(q) = -q^2 - 2q + 597

477 = -q^2 - 2q + 597

-q^2 - 2q + 597 = 477

-q^2 - 2q + 597-477 = 0

-q^2 - 2q + 120 = 0

q^2 + 2q - 120 = 0

(q+12)(q-10) = 0

q+12 = 0 or q-10 = 0

q = -12 or q = 10

Ignore negative q values. It is not possible to have negative demand.

So if the unit price is $477, then you can expect to sell 10,000 units.

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

Part C

Plug D(q) = 0 and solve for q

-q^2 - 2q + 597 = 0

q^2 + 2q - 597 = 0

1q^2 + 2q + (-597) = 0

1x^2 + 2x + (-597) = 0

We have an equation in the form ax^2+bx+c = 0 with a = 1, b = 2, c = -597

Use the quadratic formula to solve for x

\(x = \frac{-b\pm\sqrt{b^2-4ac}}{2a}\\\\x = \frac{-(2)\pm\sqrt{(2)^2-4(1)(-597)}}{2(1)}\\\\x = \frac{-2\pm\sqrt{2392}}{2}\\\\x \approx \frac{-2\pm48.90807704}{2}\\\\x \approx \frac{-2+48.90807704}{2} \text{ or } x \approx \frac{-2-48.90807704}{2}\\\\x \approx \frac{46.90807704}{2} \text{ or } x \approx \frac{-50.90807704}{2}\\\\x \approx 23.45403852 \text{ or } x \approx -25.45403852\\\\\)

We ignore any negative solution. The only practical solution is roughly x = 23.454, so q = 23.454 is when D(q) is equal to 0

The required answers are-

A) If 9000 units are to be sold, the price per unit is $498.

B) If the unit price is $477, then units sell is 10,000 units.

C) The value of q  = 23.454 when D(9) cross the q-axis.

A function from a set X to a set Y assigns to each element of X exactly one element of Y.

The given demand function is,

D(q) = - q^2 - 2q + 597

where q is thousands of units sold and D(q) is dollars per unit

A) If 9000 units are to be sold

Thus, q = 9

since q is thousands of units sold

Putting the value of q in D(q) function we get,

D(q) = -q^2 - 2q + 597

D(9) = -(9)^2 - 2(9) + 597

D(9) = 498

Thus, The price per unit is $498.

B) If a price of $477 is set for this item

Put D(q) = 477 in the given demand function.

Thus we get,

D(q) = -q^2 - 2q + 597

477 = -q^2 - 2q + 597

-q^2 - 2q + 597 = 477

-q^2 - 2q + 597-477 = 0

-q^2 - 2q + 120 = 0

q^2 + 2q - 120 = 0

(q + 12)(q - 10) = 0

q+12 = 0 or q-10 = 0

q = -12 or q = 10

Since q cannot be negative.

So if the unit price is $477, then units sell is 10,000 units.

C) Value of q when D(9) cross the q-axis

Put D(q) = 0 in the given demand function.

Thus we get,

-q^2 - 2q + 597 = 0

q^2 + 2q - 597 = 0

q^2 + 2q + (-597) = 0

We have an equation in the form ax^2+bx+c = 0 with a = 1, b = 2, c = -597

Using the quadratic formula to solve for q.

q = 23.454 ignoring the negative value of q

Thus, the value of q  = 23.454 when D(9) cross the q-axis.

Thus, The required answers are-

A) If 9000 units are to be sold, the price per unit is $498.

B) If the unit price is $477, then units sell is 10,000 units.

C) The value of q  = 23.454 when D(9) cross the q-axis.

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D

A B C E F G H I J K L M N O P Q R S T U V W X Y Z oh did i forget the d ;-)

Answer:

h = 440.94 feet

Step-by-step explanation:

It is given that,

An architect is standing 370 feet from the base of a building, x = 370 feet

The angle of elevation is 50°.

We need to find the approximate height of the building. let it is h. It can be calculated using trigonometry as follows :

\(\tan\theta=\dfrac{P}{B}\\\\\tan\theta=\dfrac{h}{x}\\\\h=x\tan\theta\\\\h=370\times \tan50\\\\h=440.94\ \text{feet}\)

So, the approximate height of the building is 440.94 feet

Of the following one that is not considered a guideline for developing visualizations is vary the scale to conserve space whenever possible. (Option B)

Data and information visualization refers to an interdisciplinary field that focuses on the graphic representation of data and information. It is an efficient way of communicating when the data or information is numerous. It aims to present the data in a clear manner and with a clear purpose. The aim of the texts and labels should be to clarify and not clutter. According to the guidelines for developing visualization, it is not recommended to vary the scale to conserve space whenever possible.

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The equation for the line in point-(1, 1) is y = -0.5x + 0.5.

Given that the slope of the line below is -0.5. We are to enter the equation for the line in point-(1, 1).The equation for the slope-intercept form of the line is y = mx + c where m is the slope and c is the y-intercept.

Now, the slope of the line is given as -0.5.Therefore, the equation for the slope-intercept form of the line is y = -0.5x + c. Now we need to find the value of c for the equation of the line.

To find the value of c, substitute the values of x and y in the equation of the slope-intercept form of the line.

Given that the point is (-1,1), x=-1 and y=1y = -0.5x + c⇒ 1 = (-0.5) (-1) + c⇒ 1 = 0.5 + c⇒ c = 1 - 0.5⇒ c = 0.5

Therefore, the equation for the line in point-(1, 1) is y = -0.5x + 0.5.The slope of a line refers to how steep the line is and is used to describe its direction. Slope is defined as the vertical change between two points divided by the horizontal change between them.A positive slope moves up and to the right, while a negative slope moves down and to the right. If a line has a slope of zero, it is said to be a horizontal line.

The slope-intercept form of a linear equation is y = mx + b, where m is the slope of the line and b is the y-intercept, or the point at which the line crosses the y-axis. To find the equation of a line with a given slope and a point, we can use the point-slope form of a linear equation.

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Answer:

D) 132

Step-by-step explanation:

y + 3x  =  180    {Co interior angles}

        y = 180 - 3x    ------------(I)

7x + 20 = y       {Vertically opposite angles}

7x + 20 = 180 - 3x   {From equation (I)}

7x + 3x +20 = 180

       10x + 20 = 180

            10x  = 180 -20

              10x = 160

                 x = 160/10

                x = 16

Plug in x = 16 in equation (I)

y = 180 - 3x

  = 180 - 3*16

  = 180 - 48

y = 132

The probability of getting stuck in traffic on any given day when leaving the city is 70%. When considering two separate days, we can use the multiplication rule of probability to find the probability of getting stuck in traffic on both days.

The multiplication rule of probability states that the probability of two independent events occurring together is the product of their individual probabilities. In this case, the events of getting stuck in traffic on two separate days are independent, meaning that the occurrence of one does not affect the probability of the other.

To find the probability of getting stuck in traffic on both days, we can multiply the probability of getting stuck on the first day (0.7) by the probability of getting stuck on the second day (also 0.7):

P(getting stuck on both days) = P(getting stuck on day 1) x P(getting stuck on day 2)
P(getting stuck on both days) = 0.7 x 0.7
P(getting stuck on both days) = 0.49 or 49%

Therefore, the probability of getting stuck in traffic on both days is 49%. This means that there is a less than 50% chance of getting stuck in traffic on both days, despite the 70% chance of getting stuck on each individual day.

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Answer:

Hi there! The answer is C

Step-by-step explanation:

I did it on edge 2020! have a nice day!

Answer:

yo

Step-by-step explanation:

C on edgenuinity

Answer:

Step-by-step explanation:

3 , -15 , 75 ......

Common ratio (r)= second term ÷ first term

                       = -15 ÷ 3

                        = -5

\(b) n^{th} \ term = a*r^{n-1} \\\\ t_{n}= 3*(-5)^{n-1}\)

\(c) t_{5}= 3*(-5)^{5-1}\\\\\\ = 3*(-5)^{4}\\\\= 3* 625\\\\= 1875\)

Answer:

2*(2)+3/2-1=7

Step-by-step explanation: