Find the equation of the line tangent to the function at the given point. Your answer should be in slope-intercept form. SHOW ALL WORK, LABEL APPROPRIATELY. F(x)= x - 4x² + 7 at x = 1 Find the instantaneous rate of change of the function at the given value. f(x) = 2x² + x +1; -2

The x-coordinates where the line y = 2x + 3 intersects the circle is equal to -2 and -4.

Mathematically, the standard form of the equation of a circle is represented by this mathematical expression;

(x - h)² + (y - k)² = r²  

Where:

From the information provided, we have the following system of equations:

(x - 3)² + (y + 6)² = 50      ......equation 1.

y = 2x + 3              .............equation 2.

In order to determine the x-coordinates at the point of intersection, we would substitute the equation 2 into equation 1:

(x - 3)² + (2x + 3 + 6)² = 50

(x - 3)² + (2x + 9)² = 50

x² - 6x + 9 + 4x² + 36x + 81 - 50 = 0

5x² + 30x + 40 = 0

x² + 6x + 8 = 0

x² + 6x + 9 = 1

(x + 3)² = 1

Taking the square of both sides of the equation, we have;

x + 3 = ±1

x = ±1 - 3

x = -2 and -4

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Answer:

x = -0.8.

Step-by-step explanation:

To solve for x in the equation g(x) = 10, we need to find the value of x that makes g(x) equal to 10. Since we are given that g(x) = 2/x+1, we can substitute this expression for g(x) in the equation g(x) = 10 to get:

2/x+1 = 10

Next, we can multiply both sides of the equation by x+1 to get rid of the fraction on the left side:

2 = 10 * (x+1)

This simplifies to 2 = 10x + 10, which we can rearrange to get 2 - 10 = 10x. Subtracting 10 from both sides gives us -8 = 10x. Finally, dividing both sides by 10 gives us the solution: x = -0.8.

Therefore, the value of x that makes g(x) equal to 10 is x = -0.8.

TU with endpoints T(1,2) and U(4,6) and its images after the composition are T' = (-1, -1) and U' = (2,3) and T'' = (-3, 7) and U'' = (0,11).

Tradition holds that the reflection of point P across the line, denoted by the word P', is the "image" of point P. (pronounced "P prime").

Given, line TU with endpoints T(1,2) and U(4,6).

To find the translation:

In 1:

Translate TU 2 units left and 3 units down.

That means,

T' = (-1, -1) and U' = (2,3)

In 2:

Translate TU 4 units left and 5 units up.

That means,

T'' = (-3, 7) and U'' = (0,11)

Therefore, the image points are T' = (-1, -1) and U' = (2,3) and T'' = (-3, 7) and U'' = (0,11)

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The fraction 1¹/₂ + ⁵/₇ = 2³/₁₄

Fractions are numbers written in the form a/b where a and b are integers and b ≠ 0.

Since we have the fractions 1¹/₂ and  ⁵/₇ and we want to compute the sum

1¹/₂ + ⁵/₇, we re-write the first fraction as an improper fraction.

So, 1¹/₂ = ³/₂

Now, re-writting the equation, we have

³/₂ + ⁵/₇

To find the sum, wetake the L.C.M of both numbers which 2 × 7 = 14.

So, we make both denominators equal to the L.C.M.

So,  

³/₂ × ⁷/₇ + ⁵/₇ × ²/₂ = ²¹/₁₄ + ¹⁰/₁₄

= (21 + 10)/14

= 31/14

= (28 + 3)/14

= 28/14 + 3/14

= 2 + 3/14

= 2³/₁₄

So, 1¹/₂ + ⁵/₇ = 2³/₁₄

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Answer:

37.237%

Step-by-step explanation:

Use the Formula I = P x R x T

P = Principal amount (the beginning balance).

R = Interest rate (usually per year, expressed as a decimal).

T = Number of time periods (generally one-year time periods).

Plug in the values

I = 5305 x R x 20

Solve for R by dividing 20 by 5305

I=5305 x R x 20

20 / 5305 = 0.0037

Answer: 10.56 or 10.6 %

Step-by-step explanation:

5305 x x^20 = 39534

39534/5305 = x^20

20√39534/5305 = x

x = 1.1056

1.1056 x 100 = 110.56

110.56 - 100 = 10.56 or 10.6

Answer:

  (c)  y = -1

Step-by-step explanation:

You want the equation of the horizontal line through (0, -1).

A horizontal line has the same y-value for every x-value. Its equation is ...

   y = constant

If you want the line to go through a point with a y-coordinate of -1, then the constant must be -1.

  y = -1 . . . . . . . horizontal line through (0, -1)

answer: yes.

since y = 6 and x = -1 are parallel to the y and x axis, respectively, they hit each other at a 90° angle when graphed, making a plus sign. they are perpendicular lines.

Answer:

  0.5 oz

Step-by-step explanation:

You want the greatest possible error associated with the measurement 19 oz.

The possible error is generally considered to be half the place value of least-significant digit. Here, the least significant digit has a place value of units, so the greatest error is 1/2 unit, or 0.5 ounces.

__

Additional comment

We know that values of 18.5 oz up to 19.4999... oz will round to 19 oz. That is why the greatest error is considered to be 0.5 oz.

In practice, there can be some difficulty associated with knowing that a value is 18.5 instead of 18.49. Hence real-world error may actually be slightly larger than 0.5 oz. In math, we ignore that case.

Answer:

0.63 kg

Step-by-step explanation:

KE = 1/2mv²

solve for m:

m = 2(KE)/v²

m = 2(140J) / (21m/s)²

m = 280J / 441 = 0.63 kg

The maximum speed of the linear function is y = -7x + 90

a. we have two points connecting (speed, degree) are (+5,55) and (-2,104) representing (x₁ , y₁) and (x₂, y₂)

Slope = (y₂ - y₁) / (x₂ - x₁)

slope = (104-55) / (-2-5) = 49/-7 = -7 mph/1°

speed = slope x (degree) + b

Solve 'b':

55 = -7 x (5) + b

55 = -35 + b

b = 55 + 35

b = 90

y₁ = -7x₁ + 90

b) What does the speed-intercept equal and what does it represent?  

The speed is 90 mph when there is no hill.

c ) What does the degree of steepness-intercept and what does it represent?

Up the hill, the steepness is roughly 12.9 degrees at its maximum. Whenever there is a slope, the car will not move.

d) Interpret the slope in words.

The speed drops by 7 mph for every 1 degree that the hill's steepness increases.

e) If your top speed is 83 mph, how steep is the hill?  Be sure to include whether the direction is up or down.

83 = -7 x + 90

83 -90 = -7x

-7 = -7x

x = 1° up the hill

f) How fast could you go down a 7º hill?

y = -7 (-7) + 90

y = 139 mph

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Answer:

C. The solution to the system is (-4,3) where the 2 lines MEET

Step-by-step explanation:

D. The system has no solution only if the lines are PARALLEL

A. The system has infinite solutions only if both equations give ONE and the same line

minute math

Answer:

0.27563735723563.

Step-by-step explanation:

74 is an acute angle since it is less than 90° cos (74) = 0.27563735723563. Write cos (74) in terms of sin Since 74° is less than 90, we can express this in terms of a cofunction.

Answer: 10 pieces

Step-by-step explanation:

Answer:

10 ropes

Step-by-step explanation:

5 divided by 1/2 is 10

The amount needed to be deposited in an account in order to have $5000 in 27 month is $4997.74.

Simple interest is based on the principal amount of a loan or the first deposit in a savings account.

To calculate the amount that needed to be deposited, we use the formula below.

Formula:

Where:

From the question,

Given:

Substitute these values into equation 1

Hence, the amount needed to be deposited is $4997.74.

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Yes, in a group of 2,000 people, at least 5 must have the same birthday.

This is due to the Pigeonhole Principle, which states that if there are more pigeons than pigeonholes, then at least one pigeonhole must contain more than one pigeon.

In this case, there are 2,000 people (the pigeons) and 365 possible birthdays (the pigeonholes). This means that, since 2,000 is greater than 365, at least 5 people must share the same birthday.

The Pigeonhole Principle states that if you have more items than boxes, then at least one box must contain more than one item. It can also be used to prove that certain problems have no solution.

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Complete Question:

In a group of 2,000 people, must at least 5 have the same birthday? Why?  Let X be the set of 2000 people (the pigeons) and Y the set of all possible birthdays (the pigeonholes). Define a function B: X - Y by specifying th B(x) = x's birthday. Now 2,000 > 4.366 = 1,464, and so by the generalized pigeonhole principle, there must be some birthday y such that B-1(y) has --Select- 4 + 1 = 5 elements. Hence at -Select- 5 people must share the same birthday.

To find the time it took the cruise ship to travel to Madagascar, we need to use the formula for distance, which is distance = speed x time. We are given the distance and the speed of the ship on the trip there, so we can solve for the time by dividing the distance by the speed:

time = distance / speed

We are told that the distance of the trip there was the same as the distance of the return trip, which took 6 hours. We are also told that the ship traveled 12 km/h on the trip there, so the distance of the trip there was 12 km/h x 6 h = 72 km.

Now we can plug this information into the formula to solve for the time:

time = 72 km / 12 km/h = <<72/12=6>>6 hours

Therefore, it took the cruise ship 6 hours to travel to Madagascar. The correct answer is therefore (A) 12 hours.

Answer:

x is equal to 87

Step-by-step explanation:

42 +51=93

93-180=x

x=87

The prevalence of asthma on January 1, 2019 is 0.055, the prevalence of asthma on September 1, 2019 is 0.080, the incidence of asthma between January 1 and September 1 is 0.025, there is not possible to calculate asthma incidence rate for the year 2018.

Prevalence is the formula to determine the rate of some case based on population. This can be calculated by divide the case by the population.

Incidence rate is same as prevalence in some factor except it only calculate time range and for this case it have same formula which is we can calculate incidence rate by divide the case by the population.

So, for January 1, 2019 is

Prevalence = 1,098 / 19,800

= 0.055

For September 1, 2019 is

Prevalence = (1,098 +  new 495) / 19,800

= 1,593 / 19,800

= 0.080

For incidence of asthma between January 1 and September 1 is

Incidence = 495 / 19,800

= 0.025

For 2018 because we are not provided with data for that year so it is impossible to calculate it.

Thus, the prevalence in January 1 is 0.055, September 1 is 0.080, and incidence between January 1 and September 1 is 0.025, and also there is not possible to calculate asthma incidence rat for the year 2018.

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Answer:

4/15

Step-by-step explanation:

1/3 x 5/5 = 5/15, 2/5 x3/3 = 6/15

5/15+6/15= 11/15

15/15- 11/15= 4/15

so 4/15 people don't have neither blue nor brown eyes.

The statement is true. Functions that are concave upward are always increasing.

What is Concave Upward Function?

Where the derivative f′ is growing, a function f is concave up (or upwards). This is equivalent to the derivative of f′, which is represented by the notation f′′f, start superscript, prime, end superscript, positive.

Explanation:

If a function is concave upward on an interval, it must be increasing on the interval. Given statement is true. Functions that are concave upward are always increasing.

A function is said to be concave upward on an interval if f″(x) > 0 at each point in the interval and concave downward on an interval if f″(x) < 0 at each point in the interval.

At interval if function is increasing then functions that are concave upward are always increasing.

Hence, The statement is true. Functions that are concave upward are always increasing.

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So, the maximum volume of the cone is approximately 1047.19 cubic inches.

The volume of a cone is given by the formula V = (1/3) * pi * r^2 * h, where r is the radius of the base and h is the height of the cone. In this case, the height of the cone is the radius of the circle, which is 10 inches, and the radius of the base is half the length of the circumference of the sector, which is (theta/360) * 2 * pi * 10 inches.

We want to find the value of theta that maximizes the volume of the cone. We can do this by taking the derivative of the volume formula with respect to theta, setting it equal to 0, and solving for theta.

V = (1/3) * pi * r^2 * h

= (1/3) * pi * ((theta/360) * 2 * pi * 10)^2 * 10

= (1/3) * pi * (theta/36)^2 * 100

dV/dtheta = (2/3) * pi * (theta/36) * (100/36)

= (2/3) * pi * theta/36

Setting dV/dtheta = 0 and solving for theta, we get theta = 0.

Since the magnitude of theta must be positive, the maximum volume occurs when theta = 0, which means that the entire circle is used to form the cone. The maximum volume of the cone is then

V = (1/3) * pi * r^2 * h

= (1/3) * pi * (10)^2 * 10

= (1/3) * pi * 100 * 10

= (1/3) * pi * 1000

= approximately 1047.19 cubic inches

So, the maximum volume of the cone is approximately 1047.19 cubic inches.

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We want to find the value of theta that maximizes the volume of the cone. We can do this by taking the derivative of the volume formula with respect to theta, setting it equal to 0, and solving for theta.

V = (1/3) * pi * r^2 * h

= (1/3) * pi * ((theta/360) * 2 * pi * 10)^2 * 10

= (1/3) * pi * (theta/36)^2 * 100

dV/dtheta = (2/3) * pi * (theta/36) * (100/36)

= (2/3) * pi * theta/36

Setting dV/dtheta = 0 and solving for theta, we get theta = 0.

Since the magnitude of theta must be positive, the maximum volume occurs when theta = 0, which means that the entire circle is used to form the cone. The maximum volume of the cone is then

V = (1/3) * pi * r^2 * h

= (1/3) * pi * (10)^2 * 10

= (1/3) * pi * 100 * 10

= (1/3) * pi * 1000

= approximately 1047.19 cubic inches

So, the maximum volume of the cone is approximately 1047.19 cubic inches.

Here, in the given equation it is true because two different sign, and the result is negative.

To multiply or divide signed integers, always multiply or divide the absolute values and use these rules to determine the sign of the answer.

When multiply two integers with the same signs, the result is always positive. Just multiply the absolute values and make the answer positive.

When multiply two integers with the different signs, the result is negative.

Here in this equation,

20 ÷ (-5)

= - 4

So, it is true.

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Based on the definition of the angles of a straight line, the measure of the smallest angle is: are: 40°.

The sum of all the angles on a straight line is equal to 180 degrees.

To find the size of the smallest angle, find the value of a by creating the equation below:

(2a + 62) + (54 - a) + (5a - 20) = 180

Open the parentheses:

2a + 62 + 54 - a + 5a - 20 = 180

Combine like terms

6a + 96 = 180

6a = 180 - 96

6a = 84

6a/6 = 84/6

a = 14

Find the measure of each angles:

2a + 62 = 2(14) + 62 = 90°

54 - a = 54 - 14 = 40°

5a - 20 = 5(14) - 20 = 50°

The size of the smallest angle is 40°.

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The rate of change (slope) of the distance in feet below sea level with respect to time that the submarine traveled is 11 feet .

Slope and rate of change are the same thing. The difference is just semantics of the situation.

Typically we use the word “slope” when we are referring to a graph, and we use the phrase “rate of change” when we are referring to a table or a situation in real life.

But that’s not absolute. We can count the slope on a graph, but there’s also a “slope formula” for use when you have two coordinate points or two data points — even though you are not creating a graph.

It is the derivative of of the slope, or the second derivative of the original function.

For example, if you plot position verses time, the slope between two points(change in position per change in time) is the velocity. This is the first derivative.

Take any two points ( 0 , 380 ) and ( 15 , 545 )

slope m = 545 - 380 / 15 - 0

= 165 / 15

= 33 / 3

= 11 / 1

= 11 feet

Hence the slope m is 11 feet .

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Answer:

  117.79 m

Step-by-step explanation:

You have an observer 337 m from a skyscraper who measures the angle of elevation from a point 1.75 m above the ground to be 19°. You want to know the height of the skyscraper.

The tangent relation tells you ...

  Tan = Opposite/Adjacent

Solving for the side opposite the angle, we get ...

  Opposite = Adjacent · Tan

In this scenario, the height of the building above the eye height is ...

  height above eyes = (337 m)(tan 19°) = 116.038 m

Then the height of the building is ...

  skyscraper height = eye height + height above eyes

  skyscraper height = 1.75 m + 116.038 m = 117.788 m

The height of the skyscraper is about 117.79 meters.

Answer:

91.4%

Step-by-step explanation:

First do: 32,000/35,000 = X/100

Then multiply 32,000 by 100 which is 3,200,000

Then divide 3,200,000 by 35,000

You will get 91.42857142857143