Is the function g(x)=8 linear or nonlinear?

Answer: The difference in temperatures was 19°F.

Step-by-step explanation:

Answer:

19F

Step-by-step explanation:

Answer:

Step-by-step explanation:

True

The insurance will pay toward Bob's expenses: $10,000.00.

The insurance will pay toward the wife and daughter's expenses: $11,000.00.

John will be responsible for paying the remaining amount, which is $3,000.00.

The insurance coverage of 10/20 means that the insurance company will pay up to $10,000.00 per person and up to a total of $20,000.00 for the entire accident.

The insurance will pay toward Bob's expenses: $10,000.00 (maximum coverage for one person).

The insurance will pay toward the wife and daughter's expenses: $11,000.00 ($8,000.00 for Mrs. Brownlee and $3,000.00 for the daughter).

John will be responsible for paying the remaining amount, which is $3,000.00 ($12,000.00 + $8,000.00 + $3,000.00 - $20,000.00 insurance coverage).

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Answer:

The insurance will pay toward Bob's expenses: $10,000.00.

The insurance will pay toward the wife and daughter's expenses: $11,000.00.

John will be responsible for paying the remaining amount, which is $3,000.00.

Step-by-step explanation:

The numbers arranged from greatest to least based on their absolute value is; |-34|, |-25|, |0.5|, |0.35|

The absolute value of a number is the expression or value of the distance of the number from 0 on the number line.

The numbers are; |-25|, |0.5|, |-34|, |0.35|

The absolute value of a number is positive, which indicates;

|-25| = 25

|0.5| = 0.5

|-34| = 34

|0.35| = 0.35

The above numbers arranged from greatest to least is therefore;

34 > 25 > 0.5 > 0.35

The numbers arranged from greatest to least based on their absolute value is therefore;

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Answer:

x+y-7=0

Step-by-step explanation:

y=-(x-3)+4

y=-x+3+4

y=-x+7

x+y-7=0

The set that could not represent the side of a right triangle are {27, 36, 46}.

A right angle triangle is a triangle that has one of its angles as 90 degrees. The sides of a right angle triangle can be found using Pythagoras's theorem.

Therefore, using Pythagoras's theorem,

c² = a² + b²

where

Therefore, the hypotenuse is the longest side of the right angle triangle.

27² + 36² ≠ 46²

729 + 1296 ≠ 2116

2025 ≠ 2116

Hence, the sides that can't form a right triangle is {27, 36, 46}

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Answer:

The top and middle shelves are parallel.

Step-by-step explanation:

<1 and <5 are corresponding angles.

When two lines are cut by a transversal such that corresponding angles are congruent, the lines are parallel.

If angles 1 and 5 are congruent, the shelves are parallel.

We are given m<5 = 60°.

Also, m<2 = 120°.

Angles 1 and 2 are a linear pair and are supplementary.

The measures of angles 1 and 2 add to 180°.

m<1 + m<2 = 180°

m<1 + 120° = 180°

Subtract 120° from both sides.

m<1 = 60°

m<1 = m<5 = 60°

Since angles 1 and 2 have the same measure, 60°, angles 1 and 2 are congruent.

Answer: The top and middle shelves are parallel.

Answer: c

Step-by-step explanation: I’m smart

Answer:

17/50

Step-by-step explanation:

When the bus is on time 4/5 of the time, it is late 1/5 of the time.

Mason arrives at 9 am when the bus is on time 3/4 of the time, so he doesn't arrive at 9 am 1/4 of the time.

Mason arrives at 9 am when the bus is late 3/10 of the time, so he doesn't arrive at 9 am 7/10 of the time.

The probability for Mason not to arrive at 9 am when the bus is on time is:

4/5 × 1/4 = 1/5

The probability for Mason not to arrive at 9 am when the bus is late is:

1/5 × 7/10 = 7/50

The probability for Mason not to arrive at work by 9 am is:

1/5 + 7/50 = 17/50.

If 75% of Brannan's class attended her twelfth birthday party, we can find the number of students who came to the party by multiplying the total number of students in the class by the percentage that attended.

First, we need to convert 75% to a decimal by dividing by 100:

75% = 75/100 = 0.75

Next, we can multiply the total number of students in the class by the decimal that represents the percentage who attended:

Number of students who came to the party = 0.75 * 24

Number of students who came to the party = 18

Therefore, 18 students came to Brannan's twelfth birthday party.

Answer:

  37.98°

Step-by-step explanation:

You want the value of θ in a right triangle with a hypotenuse of 13 cm and a side opposite the angle of 8 cm.

The sine relation is ...

  Sin = Opposite/Hypotenuse

In this figure, that means ...

  sin(θ°) = (8 cm)/(13 cm)

The value of θ is found using the arcsin function:

  θ° = arcsin(8/13) ≈ 37.98°

__

Additional comment

You will note the calculator mode is set to DEGrees.

The inverse function of the sine function is called the "arcsine" function. It is represented on most calculator keypads using a -1 exponent. (-1 is usually used with a function name to signify the inverse function. Here, the inverse sine function gives "the angle whose sine is ...".)

Typical units used for angles are degrees, radians, and gradians. The number that is the argument of the inverse sine function is a "pure number" with no units. If you find your calculation causes it to have units, then you need to check your work. (Here the units of cm in numerator and denominator cancel, leaving the unitless value 8/13.)

Answer: The correct answer is option A. a reference point.

Step-by-step explanation:

An reference point is required to determine whether or not an object moves.

The radius of circle M is equal to 3.99 cm.

In Mathematics and Geometry, the area of a sector can be calculated by using the following formula:

Area of sector = θπr²/360

Where:

By substituting the given parameters into the area of a sector formula, we have the following;

Area of sector = θπr²/360

12.36 = 89(3.142/360) × r²

12.36 = 0.7768r²

Radius, r = √15.9114

Radius, r = 3.99 cm.

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The measure of angles ∠1, ∠3, and ∠4 will be 131°, 131°, and 49°, respectively.

Given that:

∠2 = 49°

The measure of angle ∠1 is calculated as,

∠1 + ∠2 = 180°

∠1 + 49° = 180°

∠1 = 131°

The measure of the angles ∠3 and ∠4 is calculated as,

∠3 = ∠1

∠3 = 131°

∠4 = ∠2

∠4 = 49°

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The polynomial long division of (5x^4 − 2x^3 − 7x^2 − 39) ÷ (x^2 + 2x − 4) gives a quotient of 5x^2 - 12x + 37

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

(5x^4 − 2x^3 − 7x^2 − 39) ÷ (x^2 + 2x − 4)

Using the polynomial long division setup, we have

x^2 + 2x − 4   |  5x^4 − 2x^3 − 7x^2 − 39

Evaluating the division, we have

                         5x^2 - 12x + 37

x^2 + 2x − 4   |  5x^4 − 2x^3 − 7x^2 − 39

                         5x^4  + 10x^3 - 20x^2

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

                                      -12x^3 + 13x^2 - 39

                                      -12x^3 - 24x^2 - 48

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

                                                    37x^2 + 9

                                                    37x^2 + 74x - 148

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

                                                    -74x + 157

Hence, the quotient is 5x^2 - 12x + 37

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Answer:

19.8 units

Step-by-step explanation:

From the diagram attached, to find the length of side AB, we need to use Pythagoras theorem on the right triangles. We can see that AB is the base of the two right triangle.

For the first right triangle with hypotenuse of 13 and height of 12, let x be the base, therefore using hypotenuse:

13² = 12² + x²

169 = 144 + x²

x² = 169 - 144

x² = 25

x = √25 = 5

For the second right triangle with hypotenuse of 15 and height of 12, let y be the base, therefore using hypotenuse:

15² = 12² + y²

225 = 144 + y²

y² = 225 - 144

y² = 81

y = √81 = 9

The length of AB = x + y = 9 + 5 = 14 unit

Since for a square all the sides are equal, therefore the length of each side of the square ABCD is 14 units.

In triangle ADC, the hypotenuse = AC, AD = DC = 14 unit. Using Pythagoras:

AC² = AD² + DC²

AC² = 14² + 14²

AC² = 196 + 196 = 392

AC = √392 = 19.8

The length of its diagonal is about 19.8 units

Answer:

The slope is [tex]\frac{-1}{2}[/tex]

Step-by-step explanation:

the slope is the number before the x.

Helping in the name of Jesus.

The amount for one dose of IV vancomycin for this child is 350 mg.

The recommended dosage of IV vancomycin is 40 mg/kg/day divided q6h.

The child weighs 35 kg.

To calculate the amount for one dose, we need to first calculate the total daily dose and then divide it by the number of doses per day.

Total daily dose = 40 mg/kg/day x 35 kg = 1400 mg/day

Since the medication is divided q6h (every 6 hours), there are 4 doses per day.

Amount for one dose = Total daily dose / Number of doses per day

= 1400 mg/day / 4 doses per day

= 350 mg/dose

Therefore, the amount for one dose of IV vancomycin for this child is 350 mg.

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The 3 : 5 ratio of the number of cups of sparkling water to the number of cups of apple juice indicates;

7. a) 12 cups of sparkling water

b) 15 cups of apple juice

c) Please find attached the required graph of the pairs of measurements, which are plotted as points using MS Excel

A ratio expresses the quantitative relationship between two quantities, and it is obtained by dividing the quantity of one by the other.

7. The ratio of the number of cups of sparkling water to the number of cups of apple juice = 3 to 5

a) Where the number of cups of apple juice = 20, we get;

20 = 4 × 5

Therefore, the number of cups of apple juice in the current mixture is 4 times the amount that is mixed with 3 cups of sparkling water

b) 9 cups of sparkling water is 3 times the amount required per 5 cups of apple juice

c) The plot of the points can be presented as follows;

(3, 5), (9, 15), (12, 20)

Please find attached the graph showing the pairs of measurements, plotted as points, created with MS Excel

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The missing terms in the geometric progression given are:

x = 10      y = 20

The nth term of a Geometric progression is expressed by the formula:

an = ar^(n - 1)

Where we have:

an = nth term

a = first term of the geometric progression

n = number of terms

r = common ratio

We are given the geometric progression 5, x, y, and 40, where:

a1 = 5

a4 = 40

Therefore, we have:

40 = 5 * r^(4 - 1)

40 = 5 * r³

40/5 = r³

8 = r³

r = ∛8

r = 2

Since we know a and r, find the 2nd and 3rd which are represented by x and y respectively, by applying an = ar^(n - 1):

a2 = 5 * 2^(2 - 1)

a2 = 5 * 2^1

a2 = 10

x = 10

a3 = 5 * 2^(3 - 1)

a3 = 5 * 2²

a3 = 20

y = 20

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The smallest positive integer a that satisfies the conditions of the problem is a = 2.

The Intermediate Value Theorem states that if a function f(x) is continuous on the interval [a, b] and takes on values f(a) and f(b) at the endpoints a and b, respectively, then for any value c between f(a) and f(b), there exists at least one value x in the interval [a, b] such that f(x) = c.

In this problem, we are asked to find the smallest positive integer a such that the Intermediate Value Theorem guarantees a zero exists between 0 and a for the polynomial f(x) = 3x³ - 4x² - 3x - 1.

To find this value of a, we need to evaluate f(0) and f(a) and look for a value of a such that f(0) and f(a) have opposite signs. This will guarantee the existence of a root of f(x) between 0 and a.

Evaluating f(0), we get:

f(0) = 3(0)³ - 4(0)² - 3(0) - 1 = -1

To find f(a), we need to solve for a using the equation f(a) = 0. We can use a numerical method, such as the Newton-Raphson method or the bisection method, to find the root of f(x) = 0. Using a calculator or a computer program, we find that f(a) = 0 for a ≈ 1.353.

Since f(0) = -1 and f(a) = 0 have opposite signs, the Intermediate Value Theorem guarantees the existence of at least one zero of f(x) between 0 and a = 1.353. Therefore, the smallest positive integer a that satisfies the conditions of the problem is a = 2.

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The domain of a function can be determined​ by getting the set of input values of the function it can take

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

The definition of a function

As a general rule

The domain of a function is the set of input values of the function

Take for instance, the domain of y = x + 2 is all real number

This is so because it can accept all real numbers as its input

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Let's assume that the video game system and games cost a total of $x. Marshall has saved $68.50 so far. To represent the amount of money, a, that Marshall still needs to save, we can write the following inequality:

a ≥ x - 68.50

This inequality states that the amount Marshall still needs to save (a) must be greater than or equal to the cost of the video game system and games (x) minus the amount he has already saved ($68.50).

The volume of the given composite figure is: 1,283.33 ft³

The given composite figure is made up of a cone and a cylinder.

The formula for the volume of a cone is:

V = ¹/₃πr²h

Where:

r is radius

h is height

The formula for volume of a cylinder is:

V = πr²h

Where:

r is radius

h is height

Thus:

Total volume of composite figure is:

V =  (¹/₃* (22/7) * 7² * 7) + ((22/7) * 7² * 6)

V = 359.33 + 924

V = 1,283.33 ft³

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The measures of the angles are ∠1 = 35 and ∠2 = 30

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

The figure

Using the sum of opposite internal angles in a triangle, we have

∠1 + 80 = 115

Subtract 80 from both sides

So, we have

∠1 = 35

Using the same theorem of sum of opposite internal angles in a triangle, we have

∠2 + 85 = 115

Subtract 85 from both sides

So, we have

∠2 = 30

Hence, the angles are ∠1 = 35 and ∠2 = 30

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The amount of the sample remaining after 10 years is approximately 514 grams.

The amount of the sample remaining after 80 years is approximately 102 grams.

Using the exponential function given by in the problem as

A(t) = 647 (1/2) ^ (1/30 x t) the numbers remaining are calculated

For 10 years

substitute t = 10

A(10) = 647 * (1/2)^(1/30 * 10)

A(10) = 647 * (1/2)^(1/3)

A(10) ≈ 647 * 0.7937

A(10) ≈ 513.52 grams

A(10) ≈ 514 grams to the nearest gram

For 80 years

substitute t = 80

A(80) = 647 * (1/2)^(1/30 * 80)

A(80) = 647 * (1/2)^(8/3)

A(80) ≈ 647 * 0.1575

A(80) ≈ 101.9025 grams

A(80) ≈ 102 grams to the nearest gram

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The amounts needed to make 6 servings are given as follows:

Sauce: 12 servings.

Oregano: 3/4 teaspoons.

Here, we have,

The needed amounts to make 6 servings of the recipe are obtained applying the proportions in the context of the problem.

From the first line of the table, we get the amounts of sauce and oregano per serving are follows:

Sauce: 8/4 = 2 cups.

Oregano: 0.5/4 = 1/8 teaspoons per serving.

Hence the amounts for six servings are given as follows:

Sauce: 6 x 2 = 12 servings.

Oregano: 6 x 1/8 = 6/8 = 3/4 teaspoons.

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The perimeter of the parallelogram is 90 ft while it's area is calculated to be 900 square feet.

The sum of the boundary length of the parallelogram is it's perimeter so;

perimeter of the parallelogram = 15ft + 15ft + 30ft + 30ft

perimeter of the parallelogram = 90 ft

In calculating for the area of parallelogram, the base is multiplied by the height, as the same way for calculating the area of a rectangle.

height of the parallelogram = 30ft × tan 45°

height of the parallelogram = 30ft {recall tan 45° = 1}

area of the parallelogram = 30ft × 30ft

area of the parallelogram = 900 ft²

Therefore, the perimeter of the parallelogram is 90 ft while it's area is calculated to be 900 square feet.

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When the transformation is preformed on a coordinate plane, the coordinates of the new point would be located in a different quadrant.

The coordinates of the new point on this figure are (-6, -2).

In Geometry, the rotation of a point 180° about the origin in a clockwise or counterclockwise direction would produce a point that has these coordinates (-x, -y).

Furthermore, the mapping rule for the rotation of a geometric figure about the origin is given by this mathematical expression:

(x, y)                                            →            (-x, -y)

Coordinates of point A = (6, 2)  →  Coordinates of point A' = (-6, -2)

In conclusion, the transformation rule (x, y) → (-x, -y) is used for the rotation of a geometric figure about the origin in a clockwise or counterclockwise (anticlockwise) direction.

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Answer: (f+g)(x) = x² + 3x - 10

Step-by-step explanation: