A traveler comes upon a fork in the road on the path to the travelers right a sign reads Mercer 24 km

Answer:

(1 , 1)

Step-by-step explanation:

Given in the question two equations

Equation 1

y = x² – x + 1

Equation 2

y = x

Equate both equations

x² – x + 1 = x

0 = x² – x + 1 - x

x² – 2x + 1 = 0

x² - x - x + 1 = 0

x(x - 1) -1(x - 1) = 0

(x - 1)(x - 1) = 0

(x-1)² = 0

x - 1 = 0

x = 1

Plug x = 1 in first equation

y = 1² – 1 + 1

y = 1

Answer:

The answer is option A, or (1,1)

Step-by-step explanation:

I just took the test

Answer:

See explanation

Step-by-step explanation:

Zeroe of the function is such velue of x at which f(x)=0.

1. Consider the function [tex]f(x)=-x(3x-2)^2 (x+9)^5.[/tex]  

Zeros are:

[tex]-x(3x-2)^2(x+9)^5=0\\ \\x=0\text{ or }x=\dfrac{2}{3}\text{ or }x=-9.[/tex]

Zero [tex]x=0[/tex] has multiplicity of 1, zero [tex]x=\dfrac{2}{3}[/tex] has multiplicity of 2, zero [tex]x=-9[/tex] has multiplicity of 5.

At [tex]x=0[/tex] or [tex]x=-9[/tex] the graph of the function crosses the x-axis, at [tex]x=\dfrac{2}{3}[/tex] the graph of the function touches the x-axis.

2. Consider the function [tex]f(x)=x^3+10x^2+25x=x(x^2+10x+25)=x(x+5)^2.[/tex]  

Zeros are:

[tex]x(x+5)^2=0\\ \\x=0\text{ or }x=-5.[/tex]

Zero [tex]x=0[/tex] has multiplicity of 1, zero [tex]x=-5[/tex] has multiplicity of 2.

At [tex]x=0[/tex] the graph of the function crosses the x-axis, at [tex]x=-5[/tex] the graph of the function touches the x-axis.

Answer: $72000

Answer:

9

Step-by-step explanation:

6 / 2 (1 + 2) = 9

PEMDAS

Parentheses first

1+2 =3

Substitute this in

6 / 2 (3) = 9

Multiplication and Division from left to right

Division first

6/2 =3

Substitute this in for 6/2

3 (3) =9

3*3 =9

Answer:

(n - 43)³

Step-by-step explanation:

Let the number be n.

Then the desired expression is (n - 43)³

Answer:

Algebraic expression = (x-43)^3

Step-by-step explanation:

Given , the verbal expression is the cube of the difference of a number and 43.

Let x be the number

Now, according to question

Difference means subtraction  in which a number is subtracted from the other number

Difference of a number and 43

It means 43 is subtracted from x

Now , the algebraic  expression =x-43

Cube of the difference of a number x and 43 =(x-43)(x-43)(x-43)

Cube of a number means multiply a number three times with self .

Therefore, Cube of the difference of a number x and 43=[tex](x-43)\times (x-43)\times(x-43)[/tex]

 Cube of the difference  of a number x and 43=(x-43)^3

Because in multiply  when base same then power of the number added.

I

[tex]\dfrac{\partial f}{\partial x}=7+8xy^2[/tex]

[tex]\dfrac{\partial f}{\partial y}=8x^2y[/tex]

The first equation gives

[tex]f(x,y)=7x+4x^2y^2+g(y)[/tex]

Differentiating with respect to [tex]y[/tex] gives

[tex]8x^2=8x^2y+\dfrac{\mathrm dg}{\mathrm dy}\implies\dfrac{\mathrm dg}{\mathrm dy}=0\implies g(y)=K[/tex]

for some constant [tex]K[/tex]. So

[tex]f(x,y)=7x+4x^2y^2+K[/tex]

and by the fundamental theorem of calculus,

[tex]\displaystyle\int_C\nabla f\cdot\mathrm d\vec r=f\left(3,\frac13\right)-f(1,1)=25-11=\boxed{14}[/tex]

To find a function f such that f = ∇f, we need to find a function whose gradient is equal to itself. The function f(x, y) = 0 is such that ∇f = f. To evaluate c·f · dr along the curve c, we need to find the dot product of the tangent vector to c and the function f.

To find a function f such that f = ∇f, we need to find a function whose gradient is equal to itself. Let's start by finding the partial derivative of f with respect to x and y. ∂f/∂x = (7 + 8y2)i + 16xyj and ∂f/∂y = 16xyi + 8x2j. Equating both partial derivatives to f gives us the following equations:

7 + 8y2 = (7 + 8y2)i + 16xyj

8x2 = 16xyi + 8x2j

Simplifying these equations, we find:

i = 0

j = 0

Therefore, the function f(x, y) = 0 is such that ∇f = f.

In order to evaluate c·f · dr along the curve c, we need to find the dot product of the tangent vector to c and the function f. The tangent vector to c is given by dr/dt = (-1/t2, 1/t3). Evaluating f at (x, y) = (1, 1/t) gives us f(1, 1/t) = (7 + 8/t2)i + 8/t2j. Taking the dot product of this with (-1/t2, 1/t3) yields:

c·f · dr = ((7 + 8/t2)(-1/t2) + 8/t2/t3)dt = (-7/t4 + 8/t2/t3)dt = (-7/t4 + 8/t5)dt.

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Answer:

The graph of the given equation is letter A.

Step-by-step explanation:

I used the geogebra application to plot the graph of the equation.

You input the formula and the app will show you its graph.

Answer:

Step-by-step explanation:

The volume of a rect. prism is V = (length)(width)(height).

Here the volume is V = (4 in)(6 in)(5 in) = 120 in³ or 120 in^3

Note:  Please use " ^ " to indicate exponentiation:  120 in^3

Answer:

120 in 3

Step-by-step explanation:

Answer:

(-8,5)

Step-by-step explanation:

The output corresponds to the y-value of an ordered pair while the input corresponds to the x-value of an order pair.

An ordered pair is written like this (x,y)

The 3rd one. The number of 8 ounce glasses of milk in 1 gallon. If you read all the options carefully you can see that there’s no way that the other options could be “normally” distributed. The only on that could be “normal” is the 3rd one. Hope I helped!

Answer:

Step-by-step explanation:

1)  x/5 = 10

multiply by 5 : x = 50

2)  x + 2 = 15

add -2 :  x = 13  

3)  5x = 40  

divid by 5  :  x =8

4)  2y = 44

divid by 2 : y = 22

5. r - 15 = 30

add 15 ;  5r =45

divid by 5 :  r = 9

Answer: Second Option

[tex]\sigma=0.760[/tex]

Step-by-step explanation:

We have the average January surface water temperatures (°C) of Lake Michigan from 2000 to 2009.

5.07, 3.57, 5.32, 3.19, 3.49, 4.25, 4.76, 5.19, 3.94, 4.34

We know that the average [tex]{\displaystyle {\overline {x}}}[/tex] of the data is:

[tex]{\displaystyle {\overline {x}}}=\frac{\sum_{i=1}^{10}x_i}{10}=4.312[/tex]

We also know that the variance [tex]\sigma^2[/tex] is equal to 0.577.

So by definition the standard deviation [tex]\sigma[/tex] is:

[tex]\sigma=\sqrt{\sigma^2}\\\\\sigma=\sqrt{0.577}\\\\\sigma=0.760[/tex]

Answer:0.760

just right by chance

Answer:

  124°

Step-by-step explanation:

Supplementary angles add to 180°.

  56° + second angle = 180°

Subtract 56° from both sides of the equation:

  second angle = 180° - 56° = 124°

Answer:

a = 5.

Step-by-step explanation:

The graph here is a probability density graph. What will represent [tex]P(X\le a)[/tex] on the graph?

[tex]P(X\le a)[/tex] is the area

The area under the graph between 0 and 9 is a trapezoid. Consider the trapezoid in three slices from left to right:

The area of the leftmost triangle plus that of the rectangle is exactly 0.6. In other words, the area to the left of [tex]a = 5[/tex] between the graph and the x-axis is [tex]0.6[/tex]. [tex]P(X \le 5) = 0.6[/tex]. [tex]a = 5[/tex].

As a side note [tex]a = 5[/tex] shall be the only answer to this question since the area under the graph to the left of [tex]a[/tex] can only increase or stay constant but not decrease as the value of [tex]a[/tex] increases.

Answer

m = 1

Explanation

Simple Method: Rise (go up) over Run (go left or right)

Start from a perfect point then rise and run.

Rise: 3, Run: 3 = 3/3 = 1

Alternatively, you could pick two points and use the formula y2 - y1/x2 - x1

Just as an example, I will choose (-2, -3) and (2, 1)

plug in:

1 + 3/2 + 2 = 4/4 = 1

ANSWER

1

EXPLANATION

The slope of the given line is obtained using the formula:

[tex]m = \frac{rise}{run} [/tex]

From the diagram the rise is 2 units and the run is 2 units.

This implies that,

[tex]m = \frac{2}{2} = 1[/tex]

Hence the slope of the given line is 1.

Answer:

x = 88.2

Step-by-step explanation:

The angle at the top of the triangle = 90° - 10° = 80°

and the left side of the triangle is x ( opposite sides of a rectangle )

Using the tangent ratio in the right triangle

tan80° = [tex]\frac{opposite}{adjacent}[/tex] = [tex]\frac{500}{x}[/tex]

Multiply both sides by x

x × tan80° = 500 ( divide both sides by tan80° )

x = [tex]\frac{500}{tan80}[/tex] ≈ 88.2

Answer:

1

Step-by-step explanation:

The amplitude is the maximum distance away from the middle of the wave. Here we can see that the middle of the wave is the x axis and the farthest point (largest difference between the y coordinate of the x-axis, or the line y = 0, and the wave) is 1 unit away.

Answer:

1

Step-by-step explanation:

Answer:the answer is 5

Answer:

answer is 5

Step-by-step explanation:

Given that the scatter plot shows the results of a survey in which 10 students were asked the number of hours they spent studying for a test and the score they earned.

The scatter plot shows

2 students got 100, 1 student between 90 and 100 and 2 students got 90.

Others got below 90

Hence no of students who scores 90 or above = 5

Answer: TRUE

Step-by-step explanation: This is true, because there is an infinite amount of real numbers in both, and they are both countably infinite (so these infinities are equal). Hope this helps!

Answer: 4/20

Step-by-step explanation:

Option b is correct. The probability that you and your friend are both chose is 4/20.

The probability provides a means of getting an idea of likelihood of occurrence of different events resulting from a random experiment in terms of quantitative measures ranging between zero and one.

P(E) = number of favorable outcomes/Total number of outcomes

Where,

P(E) is the probability of an event.

An arrangement of objects where the order in which the objects are selected does not matter is called combination.

[tex]C_{n,k} = \frac{n!}{(n-k)!k!}[/tex]

Where,

n is total number of objects in set

[tex]C_{n, k}[/tex] is number of combinations

k is number of choosing objects from the set

According to the given question

We have

Total six people.

And,

There are total [tex]6C_{3}[/tex]  ways to choose the 3 contestants.

⇒ [tex]6C_{3} = \frac{6!}{(6-3)!3!}[/tex] = [tex]\frac{(6)(5)(4)(3!)}{(3!)(3!)}[/tex] = 20

⇒ total number of outcomes = 60

⇒ There are 20 ways to select 3 contestant among 20 people.

Now, the number of ways that, you and your friend are chosen, along with 1 person from a set of 4 is given by

[tex]C_{4,1} = \frac{4!}{1!3!}= 4[/tex]

⇒ total number of favorable outcomes = 4

Therefore,

The probability that you and your friend are both chose = [tex]\frac{4}{20}[/tex]

Hence, option b is correct.

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From the equation, you can see that each value in the equation is multiplied (x - 2)

To get it into factored form, you can just factor out (x - 2) from the equation, and you would be left with:

x²(x - 2) - 3(x - 2)

(x - 2)(x² - 3)      Your answer is A

A and c —————- Bc 20 +8 is 28

Answer:

The answer is (8,20) on APEX. just did the test. good luck!

Answer:

[tex]h=2.04\ miles[/tex]

Step-by-step explanation:

Let

h-----> the high of the balloon

we know that

In the right triangle of the figure

[tex]tan(63\°)=\frac{4}{h}[/tex]

[tex]h=\frac{4}{tan(63\°)}[/tex]

[tex]h=2.04\ miles[/tex]

I’m not quite sure what the function is but if it’s sine the period is pi/8

ANSWER

The period is

[tex] \frac{\pi}{8} [/tex]

EXPLANATION

The given function completes four cycles on the interval

[tex]

[ - \frac{\pi}{4} , \frac{\pi}{4} ][/tex]

Therefore the period is

[tex] = \frac{ \frac{\pi}{4} - \frac{\pi}{4} }{4} [/tex]

Simplify the numerator:

[tex] = \frac{ \frac{\pi}{2}}{4} [/tex]

Simplify further to get:

[tex]= \frac{\pi}{8} [/tex]

Answer:

D) (4,5)

Step-by-step explanation:

Vertex E was dilated by 1/2 because 8/2 = 4. Thus, you will divide all the other coordinates by the same scale factor.

Answer:

The center is at [tex](2,4)[/tex]

3 units

Step-by-step explanation:

You can observe in the graph a circle.

The x-coordinate and the y-coordinate of the center of the circle shown in the figure are:

[tex]x=2[/tex] and [tex]y=4[/tex]

Therefore, the point of the center of the circle is:

[tex](2,4)[/tex]

 You can observe that the diameter goes from -1 to 5, then the diameter is:

[tex]diameter=1units+5units\\\\diameter=6units[/tex]

The radius is half the diameter. Therefore, you can say that the radius of this circle is:

[tex]radius=\frac{diameter}{2}\\\\radius=\frac{6units}{2}\\\\radius=3units[/tex]

ANSWER

The center is (2,4)

The radius is 2√2 units

EXPLANATION

Each of the ticks is 1 unit

Counting two ticks from the origin to the right and 4 units up will land us at the center of the circle.

Hence the center is (2,4)

The circle passes through (0,2).

The radius is

[tex]r = \sqrt{ {(2 - 0)}^{2} + {(4 - 2)}^{2} } [/tex]

[tex]r = \sqrt{8} = 2 \sqrt{2} [/tex]

Answer:

Part A) Option C. obtuse

Part B) Option B. acute

Step-by-step explanation:

we know that

Applying the Pythagoras Theorem

if [tex]c^{2}=a^{2}+b^{2}[/tex] ----> is a right triangle

if [tex]c^{2}>a^{2}+b^{2}[/tex] ----> is an obtuse triangle

if [tex]c^{2}<a^{2}+b^{2}[/tex] ----> is an acute triangle  

where

c is the greater side

Part A) A triangle has side lengths 32, 45 and 18. What type of triangle is it?

we have

[tex]c^{2}=45^{2}=2,025[/tex]

[tex]a^{2}+b^{2}=32^{2}+18^{2}=1,348[/tex]

therefore

[tex]c^{2}>a^{2}+b^{2}[/tex]

Is an obtuse triangle

Part B) A triangle has side lengths 44, 36 and 30. What type of triangle is it?

we have

[tex]c^{2}=44^{2}=1,936[/tex]

[tex]a^{2}+b^{2}=36^{2}+30^{2}=2,196[/tex]

therefore

[tex]c^{2}< a^{2}+b^{2}[/tex]

Is an acute triangle

Answer:

The final temperature of the solution was 5°C

Step-by-step explanation:

we know that

1) At the start of an experiment, the temperature of a solution was -12°C

In this moment the temperature is -12°C

2) During the experiment, the temperature of the solution rose 5°C each hour during 4 hours

so

5°C*4=20°C

In this moment the temperature is -12°C+20°C=8°C

3) The temperature changed by -3°C

In this moment the temperature is 8°C-3°C=5°C

Answer:

The final temperature of the solution was 5°C

Step-by-step explanation:

Answer:

d

Step-by-step explanation:

d is most likely

There are 3 trainers and 12 dogs. The correct answer would be an option (D).

The equation is defined as a mathematical statement that has a minimum of two terms containing variables or numbers that are equal.

Let's assume the number of trainers would be x and dogs would be y

As per the given information, we can write the system of equations as

x+y=15        .....(i)

2x+4y=54   .....(ii)

From equation (i),

x = 15 - y

From equation (ii), and solve for y

2(15-y)+4y=54

30-2y+4y=54

2y=24

y = 12

Substitute the value of y = 12 in equation (iii), and we get the value of x = 3

Hence, there are 3 trainers and 12 dogs.

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Answer:

LOLLLLLLLLLLLLLLLLLLLLLLLLLLLLLL

Step-by-step explanation: