7.
Write the equation of the piecewise function ƒ that is represented by its graph.
A.) [tex]f(x)=\left \{{{x^{3}, if x\ \textless \ 1} \atop {x, if x \geq 1}} \right.[/tex]
B.) [tex]f(x)=\left \{{{x^{3}, if x\ \textless \ 0} \atop {x^{2}, if x\geq 0}} \right.[/tex]
C.) [tex]f(x)=\left \{{{x^{3}, if x\ \textless \ 0} \atop {x, if x\geq 0}} \right.[/tex]
D.) [tex]f(x)=\left \{{{x, if x\ \textless \ 0} \atop {x^{3}, if x\geq 0}} \right.[/tex]

Answer:

1, 2, 3, 5

Step-by-step explanation:

Answer: 54°

Step-by-step explanation: As the sum of all angles in a Pentagon is 540°

so value of X is 540° - 456 = 54°

An angle that is coterminal with -865° and has a measure between 0° and 360° is 75°. Since Angle b is coterminal with this angle, we can conclude that the measure of Angle b is 75°.

We must locate an angle that is coterminal with the -865° angle and has a measure between 0° and 360° in order to determine the size of angle b.

To do this, we can add or remove 360-degree multiples until we have an angle that is coterminal with -865° and is between 0° and 360°.

-865° + 360° = -505° (not between 0° and 360°)

-865° + 2(360°) = -145° (not between 0° and 360°)

-865° + 3(360°) = 75° (between 0° and 360°)

As a result, an angle with a measure between 0° and 360° that is coterminal with -865° is 75°. We can infer that Angle b's measure is 75° because it contaminates with this angle.

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Step-by-step explanation:

We can use the kinematic equations of motion to solve this problem. Let's assume the initial velocity of the snowball is 16 feet per second and its initial height is 32 feet. Also, we know that the acceleration due to gravity is -32.2 feet per second squared (assuming downward direction as negative).

To find out when the snowball hits the ground, we can use the equation:

h = 32 + 16t - 16t^2

where h is the height of the snowball at time t. We want to find the value of t when h = 0 (since the snowball hits the ground at that point). Therefore, we can rewrite the equation as:

16t^2 - 16t - 32 = 0

Dividing both sides by 16, we get:

t^2 - t - 2 = 0

Solving for t using the quadratic formula, we get:

t = (1 ± √(1 + 8))/2

t = 2 seconds or -1 second

Since time cannot be negative, the snowball hits the ground after 2 seconds.

To find the maximum height the snowball reaches, we can use the fact that the maximum height occurs at the vertex of the parabolic trajectory. The x-coordinate of the vertex is given by:

t = -b/2a

where a and b are the coefficients of the quadratic equation. In this case, a = 16 and b = -16, so:

t = -(-16)/(2*16) = 0.5 seconds

To find the corresponding height, we can substitute t = 0.5 seconds into the equation for h:

h = 32 + 16(0.5) - 16(0.5)^2

h = 36 feet

Therefore, the maximum height the snowball reaches is 36 feet.

Answer:

[tex]81 {d}^{4} {e}^{7} [/tex]

Step-by-step explanation:

Use properties of degrees:

1. When multiplying different degrees on one term, the degree indicators must be multiplied, for example:

[tex]( { {x}^{2}) }^{3} = {x}^{2 \times 3} = {x}^{6} [/tex]

2. When dividing like terms (with the same base) with different degrees, the degree indicators must be subtracted, for example:

[tex] \frac{ {x}^{5} }{ {x}^{2} } = {x}^{5 - 2} = {x}^{3} [/tex]

3. When squaring a negative term in parentheses, the minus is eliminated, for example:

[tex]( { - 3x})^{2} = 9 {x}^{2} [/tex]

.

[tex] \frac{ {(( { - 3d})^{2} \times {e}^{4} )}^{3} }{ {9d}^{2} \times {e}^{5} } = \frac{729 {d}^{6} \times {e}^{12} }{9 {d}^{2} \times {e}^{5} } = 81 {d}^{4} \times {e}^{7} [/tex]

Mr. Jackson will roll a 4 between 3 and 7 times, inclusive, out of his 30 rolls of a number cube is 0.332,

P(X=k) = [tex]C(n,k)[/tex][tex]* p^k * (1-p)^{n-k}[/tex]

Where:

P(X=k) is the probability of getting k successes

n is the total number of trials

k is the number of successful trials

p is the probability of success in one trial

(1-p) is the probability of failure in one trial

here, in the question given that

n = 30 (total number of rolls)

k = 3, 4, 5, 6, or 7 (number of times rolling a 4)

p = 1/6 (probability of rolling a 4 on one roll)

Now we can calculate the probability of rolling a 4 between 3 and 7 times:

P(3<=X<=7) = P(X=3) + P(X=4) + P(X=5) + P(X=6) + P(X=7)

now for  each value of k, we get:

[tex]P(X=3) = C(30,3) * (1/6)^3 * (5/6)^{27} = 0.182[/tex]

[tex]P(X=4) = C(30,4) * (1/6)^4 * x)5/6)^{26} = 0.106\\P(X=5) = C(30,5) * (1/6)^5 * (5/6)^{25} = 0.035\\P(X=6) = C(30,6) * (1/6)^6 * (5/6)^{24} = 0.008\\P(X=7) = C(30,7) * (1/6)^7 * (5/6)^{23} = 0.001[/tex]

Adding these probabilities , we get:

P(3<=X<=7) = 0.182 + 0.106 + 0.035 + 0.008 + 0.001 = 0.332

Therefore, the probability that Mr. Jackson will roll a 4 between 3 and 7 times, inclusive, out of his 30 rolls of a number cube is 0.332,

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Step-by-step explanation:

F(x) = 34    so    34 = -3x + 64

                         - 30 = -3x

                            x = 10

Answer:

22

Step-by-step explanation:

f(x) = 2x² + 4                         f(3)

f(3) = 2(3)² + 4

f(3) = 2(9) + 4

f(3) = 18 + 4

f(3) = 22

The power from the main engines, P = 0.

What is power?

Let P be the power from the main engines. Then, the total power of the space shuttle during launch is:

Total power = Power from solid rocket boosters + Power from main engines

Total power = 9,750,000,000 watts + P

We can isolate P by subtracting the power from the solid rocket boosters from both sides:

P = Total power - Power from solid rocket boosters

P = (9,750,000,000 watts + P) - 9,750,000,000 watts

P = P

Simplifying, we get:

P = 0

This means that the power from the main engines is zero. However, this result is not realistic since the space shuttle requires power from both the solid rocket boosters and the main engines to launch. Therefore, there may be an error in the given information or additional information is needed to accurately solve the problem.

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The range of the parabola is (-∞, -2). So correct option is A.

A parabola is a U-shaped curve that is defined by a quadratic equation of the form y = ax² + bx + c, where a, b, and c are constants. The graph of a parabola is symmetric around a vertical line called the axis of symmetry, which passes through the vertex of the parabola. The vertex is the point on the parabola where it changes direction.

The shape and position of a parabola depend on the values of the coefficients a, b, and c. If a is positive, the parabola opens upward, and if a is negative, the parabola opens downward. The value of b determines the horizontal position of the vertex, and the value of c determines the vertical position of the vertex.

Parabolas have many applications in mathematics, physics, engineering, and other fields. For example, the trajectory of a projectile launched into the air can be modeled by a parabolic curve, and the reflector dish of a satellite dish antenna is shaped like a parabolic curve to focus incoming signals at a single point.

The range of the parabola is (-∞, -2). So correct option is A.

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The capitalized costs for 2017 is $55,000.

Capitalizing means adding the cost of an asset to its book value or cost basis. Not all costs can be capitalized.

Generally, only costs that increase an asset's useful life or productive capacity should be capitalized.

In this case, the building and truck were purchased in 2015 and have been capitalized.

The following costs incurred in 2017 should be analyzed to determine whether they should be capitalized or expensed:

Painting the building for $5,000 - This cost does not increase the useful life or productive capacity of the building.

It is considered a repair and maintenance expense and should be expensed.

Installing new windows in the building for $10,000 - This cost improves the building's insulation and prevents leaking.

It is considered a capital improvement that extends the useful life of the building. Therefore, it should be capitalized.

Installing a new conveyor system for $40,000 - This cost increases the productive capacity of the company's operations. It is considered a capital expenditure and should be capitalized.

Repainting the delivery truck for $1,000 - This cost does not increase the useful life or productive capacity of the truck. It is considered a repair and maintenance expense and should be expensed.

Installing a hydraulic lift system on the truck for $5,000 - This cost allows better handling of large loads and increases the productive capacity of the truck. It is considered a capital expenditure and should be capitalized.

Overhauling the truck's engine for $4,000 - This cost is a repair and maintenance expense and should be expensed.

Therefore, the capitalized costs for 2017 are

$10,000 (new windows in the building) + $40,000 (new conveyor system) + $5,000 (hydraulic lift system on the truck) = $55,000.

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Question:  

On January 1, 2015, Jose Company purchased a building for $200,000 and a delivery truck for $20,000. The following expenditures have been incurred during 2017: • The building was painted at a cost of $5,000. To prevent leaking, new windows were installed in the building at a cost of $10,000. • To improve production, a new conveyor system was installed at a cost of $40,000. • The delivery truck was repainted with a new company logo at a cost of $1,000. • To allow better handling of large loads, a hydraulic lift system was installed on the truck at a cost of $5,000. • The truck's engine was overhauled at a cost of $4,000. Required: 1. Determine which of those costs should be capitalized. Assume that all costs were incurred on January 1, 2017.

The answer of the given question is the solution to the inequality h(t) > 9 is any value of t that makes h(t) greater than 9.

An inequality is a mathematical statement that shows a relationship between two values or expressions that are not equal. It uses symbols such as < (less than), > (greater than), ≤ (less than or equal to), or ≥ (greater than or equal to) to express the relationship between the two values. Inequalities are often used in algebra, geometry, calculus, and other areas of mathematics to represent constraints or limits on values or to compare two different sets of values. For example, an inequality might be used to determine if a certain number falls within a certain range, or to find the maximum or minimum value of a function given certain constraints.

The solution to the inequality h(t) > 9 is any value of t that makes h(t) greater than 9.

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If an acute angle increases, then its supplement decreases.

To give you a short quick answer, the supplement is going to have to decrease or get smaller.

Example

Suppose the acute angle is 10 (anything under 90 will do).

Then the supplement is going to be 180 - 10 = 170

Now suppose the acute angle increase to 50 degrees.

That means the supplement will go from 180 - 50 = 130

Conclusion

As the acute angle gets bigger, the supplement gets smaller. This is an important idea to get clear. Bigger and Smaller or More or Less can be ugly little words, so anytime you come across them, pay attention. It will make your life in science so much easier

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Using the Pythagorean theorem we know that the length of the given diagonal is 21.25 units respectively.

The Pythagorean theorem, sometimes known as Pythagoras' theorem, is a fundamental Euclidean geometry relationship between the three sides of a right triangle.

This statement states that the area of the square whose side is the hypotenuse is equal to the sum of the areas of the squares on the other two sides.

If a²+b²=c² and c is the triangle's longest side, the triangle is a right triangle.

If a triangle is not a right triangle, there are two additional types that can exist.

So, the formula is:

a² + b² = c²

Now, insert values as follows:

12.75² + 17² = c²

162.5625 + 289 = c²

451.5625 = c²

√451.5625 = c

21.25 = c

Therefore, using the Pythagorean theorem we know that the length of the given diagonal is 21.25 units respectively.

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The average speed of the bus is 600 meters / 900 seconds = 2/3 meters/second, or approximately 0.67 meters/second.

To find the average speed of the bus, we need to follow these steps:
1. Determine the total distance traveled:

Since each block is 100 meters long and the bus travels 6 blocks, the total distance is 6 blocks * 100 meters/block = 600 meters.
2. Determine the total time taken: .

The bus travels this distance in 15 minutes, so we need to convert this time to seconds.

Since there are 60 seconds in a minute, the total time taken is 15 minutes * 60 seconds/minute = 900 seconds.
3. Calculate the average speed:

The average speed is the total distance traveled divided by the total time taken.

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The new coordinates for point D after the rotation are (-4, 3).

To find the coordinates of each point after quadrilateral ABCD is rotated 270° counterclockwise about the origin, we can use the following formula:

(x', y') = (-y, x)

where (x, y) are the original coordinates of the point and (x', y') are the new coordinates after the rotation.

Starting with point A, which has coordinates (2, 1), we plug in the values into the formula:

(x', y') = (-y, x)
(-1, 2)

So the new coordinates for point A after the rotation are (-1, 2).

Moving on to point B, which has coordinates (4, 3), we apply the same formula:

(x', y') = (-y, x)
(-3, 4)

Therefore, the new coordinates for point B after the rotation are (-3, 4).

For point C, which has coordinates (5, 6), we get:

(x', y') = (-y, x)
(-6, 5)

Hence, the new coordinates for point C after the rotation are (-6, 5).

Finally, for point D, which has coordinates (3, 4), we have:

(x', y') = (-y, x)
(-4, 3)


So, the coordinates of each point after quadrilateral ABCD is rotated 270° counterclockwise about the origin are:

A' = (-1, 2)
B' = (-3, 4)
C' = (-6, 5)
D' = (-4, 3)

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By answering the presented question, we may conclude that Therefore, trigonometry the given identity is true.

The study of the connection between triangle side lengths and angles is known as trigonometry. The concept first originated in the Hellenistic era, during the third century BC, due to the application of geometry in astronomical investigations. The subject of mathematics known as exact techniques deals with certain trigonometric functions and their possible applications in calculations. There are six commonly used trigonometric functions in trigonometry. Sine, cosine, tangent, cotangent, secant, and cosecant are their separate names and acronyms (csc). The study of triangle characteristics, particularly those of right triangles, is known as trigonometry. As a result, geometry is the study of the properties of all geometric forms.  

= 1/sin x

= √(1/sin²x - 1) / (1/sin²x)

= √(1 - sin²x) / sin x

= √(cos²x) / sin x

= √(1 - sin²x) / cos x

= √(csc²x - 1) / cos x

cos x = √(csc²x - 1) / cos x

cos²x = csc²x - 1

cos²x + sin²x = csc²x

1 = csc²x

Therefore, the given identity is true.

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Answer:40

Step-by-step explanation:

90= 2x-10

Answer:

40°

Step-by-step explanation:

Measure of angle LOM(aka x) is equal to:

x+x+10 = 90

2x = 80

x = 40°

Step-by-step explanation:

There are SIX sides   3 pairs of equivalent sides

   2 * ( 1 1/3 x 3     + 3 * 2  2/3   +  2 2/3 * 1  1/3 )  = 31 1/9 square yards

The range in which x must lie in order for a triangle to exist is: 0 < x < 2.

The correct option is (D). 0 < x < 1.

A triangle has side lengths of 1 units, 1 units, and x units.

Determine the range in which x must lie in order for a triangle to exist.

Triangle is the type of polygon that is formed when three line segments join.

A triangle can be formed when and only when the sum of any two sides is greater than the third side.

Using the triangle inequality theorem we know that,1 + 1 > x1 + x > 11 + x > 1x > 0

Now combining both results:

x > 0

Therefore, the range in which x must lie in order for a triangle to exist is: 0 < x < 2.The correct option is (D). 0 < x < 1.

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Answer: y = 4x + 1, 25 inches at 6 years old

Step-by-step explanation:

   Our y-intercept will be 1 (5 inches at a year old - 4 inches per year = 1) with a slope of 4 (4 inches a year). Our equation will look like this:

            y = 4x + 1

   Next, to solve for the length of the tusk at 6 years old, we will input this value of 6 and solve.

            y = 4x + 1 = 4(6) + 1 = 25 inches

   See attached for a graph.

   We can also check our work using a different method.

6 years - 1 year = 5 years

5 years * 4 inches a year = 20 inches

20 inches + current 5 inches = 25 inches at 6 years

Answer:

x=5.8

Step-by-step explanation:

a^2+b^2=c^2

3^2+5^2=x^2

9+25 = 34

[tex]\sqrt{34)[/tex] = 5.8

Answer:

[tex]17\sqrt{2}[/tex]  or approximately 5.83

Step-by-step explanation:

The triangle is a right triangle so we use Pythagorean theorem to find the missing side.

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

x is the hypotenuse so that has to be the value of c but the other two sides are interchangeable.

[tex]3^{2} + 5^{2} = x^{2}\\\\9+25=x^{2} \\\\34=x^{2} \\[/tex]

Square both sides to isolate the x.

[tex]\sqrt{34} =x[/tex]

Simplify

[tex]17\sqrt{2} =x\\[/tex]

Answer: 1) C. 1.75

              2) C. 5.25

Step-by-step explanation:

For this first question, the answer is C. 1 3/4

First, you will need to calculate how many hours the 3/4-hour students studied versus the 1/4-hour students.

3/4 students: 3/4 · 3 = 9/4

1/4 students: 1/4 · 2 = 2/4

9/4 - 2/4 = 7/4 = 1 3/4

Therefore, your answer for the first question is C.

For the second question, the answer is C

We must calculate how many hours each group of students studied, then add them together. You can add or multiply in this situation.

1/4 students: 1/4 · 2 = 2/4 (No need for simplifying until the end.)

1/2 students: 1/2 · 5 = 5/2

3/4 students: 3/4 · 3 = 9/4

Now, let's change the 5/2 so we can add it to the other fractions.

5/2 ·2 = 10/4

Let's add.

2/4 + 10/4 + 9/4 = 21/4

Simplify.

21/4 = 5 1/4.

Therefore, answer choice C is correct.

Hope this helped!

Answer:

To find the cubic function with the given roots, we can use the factored form of a cubic function:

f(x) = a(x - r1)(x - r2)(x - r3)

where r1, r2, and r3 are the roots of the function.

Substituting the given roots, we get:

f(x) = a(x + 9)(x + 5)(x - 3)

To find the leading coefficient a, we need to use the y-intercept of the function, which is given as -27.

When x = 0, the function becomes:

f(0) = a(9)(5)(-3) = -27

Simplifying and solving for a, we get:

a = -27 / (9)(5)(-3) = 0.6

Rounding to two decimal places, the leading coefficient of the cubic function is a = 0.60.

When Gracie distributes her carrots equally among the 5 bunnies, each bunny gets 7,878 whole carrots, and 3,939 whole carrots remain without being given to a bunny. These figures are whole numbers.According to the statement, Gracie has 5 pet bunnies that love to eat whole carrots. Gracie has 3,939 carrots to feed the bunnies, and she will use as many carrots as she can and give each bunny the same number.

To calculate the number of carrots each bunny will get:Total number of whole carrots ÷ Total number of bunnies = Number of whole carrots each bunny gets Gracie distributes the 3,939 carrots equally among the 5 bunnies, with each bunny getting 7,878 carrots. This is illustrated in the calculation below:3,939 ÷ 5 = 7,878Hence, the number of whole carrots each bunny gets is 7,878.

When it comes to the number of carrots that remain without being given to a bunny, we need to calculate it using the following formula:Total number of whole carrots − (Number of whole carrots each bunny gets × Total number of bunnies) = Number of whole carrots that remain without being given to a bunnyUsing the figures from the above calculations, the computation will be as follows:3,939 − (7,878 × 5) = 3,939 − 39,390 = -35,451. Therefore, the number of whole carrots that remain without being given to a bunny is -35,451. However, since the answer must be a whole number, we can round this up to 0 carrots. This implies that all of the carrots were given to the bunnies.

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Answer:

158

Step-by-step explanation: