1-
Find the area of the shaded region.
f(x)=x4-12x³ +48x², g(x)=44x+105
--
***
--
The area is 389.0 (Type an integer or a simplified fraction.)
340
(-1,61)
L
-
(5,325)
Foo
8
1

Answer:

x=18 or x=6

Step-by-step explanation:

2x=36

x=18

if it was x^2 then

x^2=36

x=6

The size of angle K (m∠K) as shown in the circle is 50°.

Tangent to a circle is the line that touches the circle at only one point.

To calculate the size of angle K (m∠K), we use the formula below

Formula:

From the diagram,

Given:

Substitute these values into equation 1

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Answer:

so you start with D-6>4

then you add 6 to both sides now you have D>10

the answer is D

f(x) = 4.1/(42.4x-10(x-2)), x-intercept = -4.878, y-intercept = (0,-2.05), asymptotes: vertical at x=2, horizontal at y=0, and slant at y=4.1/8x.

Given: f(x) = 4.1/(42.4x-10(x-2))

To find the x-intercept, we set f(x) to zero and solve for x:

0 = 4.1/(42.4x-10(x-2))

0 = 4.1/(32.4x+20)

0 = 4.1/4.08(x+4.878)

So, the x-intercept is x = -4.878.

To find the y-intercept, we set x to zero and solve for f(x):

f(0) = 4.1/(42.4(0)-10(0-2))

f(0) = -2.05

So, the y-intercept is (0,-2.05).

To write f(x) in the form f(x) = -1/(ax + b) + q, we can simplify the expression as follows:

f(x) = 4.1/(42.4x-10(x-2))

f(x) = 4.1/(32.4x+20)

f(x) = 4.1/4.08(8x+5)

So, a = 8, b = 5, and q = 4.1/4.08.

To draw the graph of f, we plot the x- and y-intercepts and the vertical asymptote x = 2.

We can find the horizontal asymptote by noting that as x becomes very large or very small, the term 10(x-2) dominates the expression, so f(x) approaches 4.1/-10x. Thus, the horizontal asymptote is y = 0.

To find the equations of the slant asymptotes, we divide the numerator by the denominator using long division:

4.1

8x + 5 | 4.1

- 4.1

0

So, the slant asymptote is y = 4.1/8x.

Therefore, the intercepts of f are x = -4.878 and (0,-2.05), and the equation of f(x) in the form f(x) = -1/(ax + b) + q is f(x) = -1/(8x + 5) + 1.0039.

The graph of f has intercepts with the x-axis at x = -4.878 and the y-axis at (0,-2.05), a vertical asymptote at x = 2, a horizontal asymptote at y = 0, and a slant asymptote at y = 4.1/8x.

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Using the concept of exponential decay, the predicted number of people is  233,176,000

To predict the number of gas-powered cars on the road in 10 years, we'll apply the given annual decrease rate of 1.9% to the initial count of 286 million.

First, let's calculate the decrease rate per year:

Decrease rate = 1.9% = 1.9/100 = 0.019

Next, we'll calculate the predicted count after 10 years using the formula for exponential decay:

Predicted count = Initial count * (1 - Decrease rate)^Number of years

Substituting the values:

Predicted count = 286 million * (1 - 0.019)^10

Calculating the value:

Predicted count ≈ 286 million * (0.981)^10

Rounding the answer to the nearest whole number:

Predicted count ≈ 286 million * 0.816

Predicted count ≈ 233,176,000

Therefore, the best prediction for the number of people driving gas-powered cars in 10 years, based on the given information, is approximately 233,176,000.

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After purchasing goods from China, the Italian trader has a number of non-Silk Road destinations to choose from, including:

Location in India

The Indian Ocean's Spot

the region rising from the Red Sea

the region above Italy

The network of commercial routes known as the "Silk Road" was used for more than 1,500 years, from the Han dynasty of China's opening of trade in 130 BCE to the Ottoman Empire's suspension of trade with the West in 1453 CE.

Over a distance of over 6,437 kilometers (4,000 miles), the Silk Road passed through some of the most challenging landscapes in the world, including the Pamir Mountains and the Gobi Desert. Because no single administration was in charge of maintenance, the roads were usually in poor condition.

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Answer: 314 mi

Step-by-step explanation:

Area of a circle = (pi) * (radius)^2

Radius is 1/2 the diameter

Radius = 10

10^2 = 100

100*3.14 = 314

The function r(x) - 3f(x+1) transforms the parent function f(x)=x^2 by shifting it left by 1 unit, vertically stretching it by a factor of 3, and translating it downward by 3 units. The resulting graph is a parabola with vertex at (-1,-3) and a steeper shape.

The function r(x) - 3f(x+1) is a transformation of the parent function f(x)=x^2. Let's consider each transformation step by step.

First, the function f(x+1) represents a horizontal shift of the parent function f(x)=x^2 to the left by 1 unit. This means that the vertex of the parabola is shifted to the point (-1,0).

Next, the function 3f(x+1) vertically stretches the parabola by a factor of 3. This means that the distance between the vertex and the x-intercepts of the parabola is tripled, while the shape of the parabola remains the same.

Finally, the function r(x) subtracts a constant value from the transformed function. This translates the entire graph downward by 3 units.

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To solve this inequality for x, we need to isolate x on one side of the inequality sign. Let's begin by distributing the -2 on the right-hand side:

7x + 5 < -2(4x - 3)

7x + 5 < -8x + 6

Adding 8x to both sides, we get:

15x + 5 < 6

Subtracting 5 from both sides, we get:

15x < 1

So the equivalent inequality to 7x + 5 < -2(4x-3) is 15x < 1.

Therefore, the answer is: 15x < 1.

Answer:

52° is approximately 0.907 radians

Step-by-step explanation:

To find the equivalent radian measure for an angle that measures 52°, we need to convert 52° to radians using the formula:

radians = degrees × π/180

Substituting the value of 52° into the formula, we get:

radians = 52 × π/180

radians ≈ 0.907

Therefore, the equivalent radian measure for an angle that measures 52° is approximately 0.907 radians.

The contrapositive of the statement "If x is a multiple of [tex]10[/tex], it is an even number" is "If [tex]x[/tex] is not a multiple of [tex]10[/tex], then it is not an even number."

To complete the contrapositive of the statement "If [tex]x[/tex] is a multiple of [tex]10[/tex], it is an even number," we need to negate and reverse the original statement.

The original statement can be represented as:

[tex]\[P: \text{If } x \text{ is a multiple of 10, then } x \text{ is an even number.}\][/tex]

The negation of this statement is:

[tex]\[\neg P: \text{If } x \text{ is not an even number, then } x \text{ is not a multiple of 10.}\][/tex]

To form the contrapositive, we reverse the implications:

[tex]\[\text{Contrapositive: If } x \text{ is not a multiple of 10, then } x \text{ is not an even number.}\][/tex]

In symbolic notation, the contrapositive would be:

[tex]\[\text{Contrapositive: } \neg P: \text{If } \neg(x \text{ is a multiple of 10}), \text{ then } \neg(x \text{ is an even number}).\][/tex]

Therefore, the contrapositive of the statement "If x is a multiple of [tex]10[/tex], it is an even number" is "If [tex]x[/tex] is not a multiple of [tex]10[/tex], then it is not an even number."

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The image of point P under a 90-degree counter Clockwise rotation about the origin is (-6, -4).

To find the image of point P = (-4, 6) after a 90-degree counterclockwise rotation about the origin, we can use the following formula:

(x', y') = (xcosθ - ysinθ, xsinθ + ycosθ)

where (x, y) are the coordinates of the original point, θ is the angle of rotation, and (x', y') are the coordinates of the rotated point.

In this case, θ = 90 degrees, so we have:

(x', y') = (-4cos90 - 6sin90, -4sin90 + 6cos90)

        = (-6, -4)

Therefore, the image of point P under a 90-degree counterclockwise rotation about the origin is (-6, -4).

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Answer:

The answer is down below

Step-by-step explanation:

1 -6 0 3 6

9 7 + 1 4 7

5 3 2 5 8

= 1+0 -6+3 0+6

9+1 7+4 0+7

5+2 3+5 0+8

= 1 -3 6

10 11 7

7 8 8

9x=28. x=28÷9

The experimental probability that in a group of 4 students, at least one of them has brown eyes, based on the given sample, is 0.898 or 89.8%.

We know that "2", "4", and "8" represent the 30% of students with brown eyes.

Any occurrence of these numbers in the sample would indicate a student with brown eyes, while other numbers would represent students without brown eyes.

Let's examine the sample of 20 random numbers:

3, 7, 1, 6, 4, 2, 0, 9, 8, 5, 2, 7, 6, 8, 4, 3, 1, 2, 0, 4

Out of these 20 numbers, the following represent students with brown eyes: 4, 2, 8, 2, 8, 4, 2, 4.

Total possible combinations of 4 students from the sample = C(20, 4) = 4845 (using the combination formula)

Number of combinations without any student having brown eyes = C(12, 4) = 495 (choosing 4 students from the remaining 12 who don't have brown eyes)

The number of combinations where at least one student has brown eyes = 4845 - 495 = 4350

Experimental probability of at least one student having brown eyes

= 4350 / 4845

= 0.898

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The terms that can be used to classify the triangle by angle measures and side lengths include the following: D. acute and isosceles.

In Mathematics and Geometry, an isosceles triangle simply refers to a type of triangle with two (2) sides that are equal in length (side lengths) and two (2) equal angles.

This ultimately implies that, an isosceles triangle comprises two (2) side lengths that are equal and two (2) angles with the same magnitude.

In conclusion, the angle measures of each of the angles represented by this triangle is equal to 90 degrees and as such, they are acute angles.

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Missing information:

The question is incomplete and the complete question is shown in the attached picture.

$6,500 is invested in 11% account.

$6,950 is invested in 14% account.

Let us use x to represent amount invested in the 11% account

Let us use y be represent amount invested in the 14% account.

We can set up system of two equations:

[tex]x + y =[/tex] Total amount invested

0.11x + 0.14y + 450 = Interest earned

Substituting y (Invested - x) into 2nd equation, we get:

0.11x + 0.14(Amount invested - x) + 450 = 255

We solve for x

0.03x + 450 = 255

0.03x = 195

x = 195 / 0.03

x = $6500

As $6,500 is invested in the 11% account. The amount invested in 14% interest account is:

= $6,500 + $450

= $6,950.

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Answer:

lj= 18 feet

mgm=52°

Step-by-step explanation:

lj=GJ/2=36/2=18feet

mGM=mHJ=52°

The graph of the derivative, F', shows that the slope is positive until x = 2 (the right end of the semicircle) and then becomes zero.

Since the graph of F' consists of two line segments and a semicircle, we can determine the values of F using the information provided.

Let's break down the problem into different intervals based on the graph:

Interval (-∞, -5):

Since we don't have specific information about this interval, we cannot determine the exact value of F(-5).

Interval (-5, 0):

In this interval, we have a line segment. Let's assume the equation of the line segment is y = mx + b. We can find the equation of this line segment by using the slope-intercept form of a line and the given point (2, 1).

The slope of the line can be calculated using the difference in y-coordinates divided by the difference in x-coordinates:

m = (1 - F(2)) / (2 - (-5)) = (1 - 1) / 7 = 0/7 = 0

Since the slope is 0, the equation of the line becomes y = b. Plugging in the point (2, 1) into the equation, we get:

1 = b

Therefore, the equation of the line segment for the interval (-5, 0) is y = 1.

Interval (0, ∞):

In this interval, we have a semicircle. The graph of the derivative, F', shows that the slope is positive until x = 2 (the right end of the semicircle) and then becomes zero. This indicates that the original function F is increasing until x = 2 and remains constant afterward.

Since F(2) = 1, we can conclude that F(x) = 1 for x ≥ 2. Therefore, F(-5) cannot be determined based on the given information.

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Answer:

These triangles are not similar because the ratios of corresponding sides are not equal.

Answer:

The blank is "Gross Domestic Product (GDP)."

"g" is the subject of the equation in terms of "a" and "h."

To make "g" the subject of the equation "a = (g + h)/2," we can rearrange the equation to isolate "g."

Let's follow the steps:

Multiply both sides of the equation by 2 to eliminate the fraction:

2a = g + h

Subtract "h" from both sides to isolate "g":

2a - h = g

By performing these operations, we have successfully isolated "g" on one side of the equation.

The resulting equation is "g = 2a - h."

This equation shows that "g" is equal to two times "a" minus "h."

By substituting the given values of "a" and "h" into the equation, you can calculate the corresponding value of "g."

If we have "a = 5" and "h = 3," we can substitute these values into the equation to find the value of "g":

g = 2(5) - 3

g = 10 - 3

g = 7

"a" is 5 and "h" is 3, the value of "g" is 7 according to the equation "g = 2a - h."

The equation "g = 2a - h" allows you to express "g" in terms of "a" and "h" by subtracting "h" from twice the value of "a."

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(26) The length FE in the intersecting chords is 6.

(27) The length of arc AE =  64⁰.

We know that,

The length FE is computed using the intersecting chord theorem, as shown below;

The power of a point theorem, commonly known as the intersecting chord theorem, says that:

If two chords of a circle cross inside the circle, the product of the lengths of one chord's segments equals the product of the lengths of the other chord's segments.

FE ≅ AB = 6

The length of the arc AE is computed as follows:

⇒ arc of AE + arc of AB + arc of ED = 180

Since sum of angles of a semi circle

⇒ arc of  AE + 58 + 58 = 180

⇒ arc of AE + 116 = 180

⇒ arc of AE = 64

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Answer:

Please provide more details!

To determine the specific type of roots for the given quartic equation, we need to solve it or analyze its discriminant. However, without further calculations, we cannot determine the exact types of roots for f(x) = 3x^4 + 7x^3 + 2x^2 + x + 9.

Answer:   ±1, ±3, ±9, ±[tex]\frac{1}{3}[/tex]  

Step-by-step explanation:

f(x)=3x⁴+7x³+2x²+9

To find all possible roots, you take the last number and all its factors and put it over the first number and all its factors.

Factors of last and first:

9:  1, 3, 9

3: 1, 3

Put all of the factors of 9 divided by all factors of 3 and also make them + and - versions.  Also eliminate any repeats like ± [tex]\frac{1}{1}[/tex]    and   ± [tex]\frac{3}{3}[/tex]

±1, ±3, ±9, ±[tex]\frac{1}{3}[/tex]    

A number line with a closed circle on -9 and shading to the left. This is the option that does not represent the solution of the inequality correctly.

1. Simplify the inequality: 8x - (5x + 4) ≥ -31
2. Distribute the negative sign: 8x - 5x - 4 ≥ -31
3. Combine like terms: 3x - 4 ≥ -31
4. Add 4 to both sides: 3x ≥ -27
5. Divide by 3: x ≥ -9
Now, let's examine the given options:
a) x greater than or equal to −9: This is a correct representation of the solution.
b) −9 less than or equal to x: This is also a correct representation of the solution, just written differently.
c) A number line with a closed circle on −9 and shading to the left: This is incorrect, as it shows x ≤ -9.
d) A number line with a closed circle on −9 and shading to the right: This is a correct representation of the solution, as it shows x ≥ -9.
Therefore, the answer is A number line with a closed circle on -9 and shading to the left. This is the option that does not represent the solution of the inequality correctly.

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Answer:

Step-by-step explanation:

You want the radius and area of a spherical ice cream scoop with a volume of 179.59 cubic inches.

The volume of a sphere is given by the formula ...

  V = (4/3)πr³

Then the radius will be ...

  r = ∛(3V/(4π))

  r = ∛(3·179.59/(4π)) ≈ 3.49997 . . . . in

The radius is about 3.50 inches.

The area of a sphere is given by ...

  A = 4πr^2

  A ≈ 4π·(3.49997 in)² ≈ 153.9355 . . . . in²

The area of that scoop is about 153.9 square inches.

__

Additional comment

A scoop 7 inches in diameter would likely be served in a bowl.

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The interest rate required to pay a simple interest of $53.96

from a principal of $500.00 is 18.50%.

Simple interest is expressed as:

[tex]\sf I = \dfrac{P\times r \times t}{100}[/tex]

Where I is interest, P is principal, r is interest rate and t is time.

Given that:

Plug the given values into the above formula and solve for interest rate.

[tex]\sf I = \dfrac{P\times r \times t}{100}[/tex]

[tex]\sf r = \dfrac{I}{P\times t}[/tex]

[tex]\sf r = \dfrac{\$53.96}{( \$500 \times \frac{7}{12} )}[/tex]

[tex]\sf r = 0.18501[/tex]

[tex]\sf r = 0.18501\times100\%[/tex]

[tex]\sf r = 18.50\%[/tex]

Therefore, the interest rate is 18.50%.

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Answer: Reflection on the x-axis and moved 5 units upwards.

Step-by-step explanation:

     First, we will transform the transformed function into an equation form we may be more familiar with.

g(x) = 5 - x⁴ ➜ g(x) = -x⁴ + 5

     We see that this function is reflected on the x-axis (as given by the "-") and is moved 5 units upwards (as given by the "+ 5").

     We can also graph this, see attached.

The calculated value of the distance covered is 2 km

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

Speeds = 24 km/h and 32 km/h

The time difference is given as

Time = 15 minutes

The distance covered is calculated as

Distance = (Change in speed) * Time

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

Distance = (32km/h - 24km/h) * 15 minutes

Evaluate

Distance = 2 km

This means that the distance covered is 2 km

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