PLEASE HELP ME WITH THIS MATH! XC

The proof for  AB ≅ CD is:

Step                 Statement                                Reason

 1              ∠B ≅ ∠D, BC || AD                          Given

 2               ∠BCA ≅ ∠CAD                Alternate Interior angles

 3                      AC ≅ AC                             common side

 4                 ΔABC ≅ ΔADC         Angle-Angle-Side rule of congruency

 5                   AB ≅ CD            Corresponding sides of congruent triangle

Consider triangle ABC and triangle ADC.

Here, side BC is parallel to side AD.

From the attached figure we can observe that AC is a transversal.

so, ∠BCA and ∠CAD would be alternate angles formed by two parallel lines and transversal.

By property of  Alternate Interior angles,

∠BCA ≅ ∠CAD

Also, we can observe that side AC is common side to ΔABC and ΔADC.

We rewrite this proof as,

Step                 Statement                                Reason

 1              ∠B ≅ ∠D, BC || AD                          Given

 2               ∠BCA ≅ ∠CAD                Alternate Interior angles

 3                      AC ≅ AC                             common side

 4                 ΔABC ≅ ΔADC         Angle-Angle-Side rule of congruency

 5                   AB ≅ CD            Corresponding sides of congruent triangle

This is the required proof.

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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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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 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 volume of the pyramid is  9333 cubic centimetres

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

Base dimensions = 40 cm by 20 cm

Height = 35 cm

The volume of the pyramid is calculated as

Volume = Product of Base dimensions and Height/3

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

Volume = 40 * 20 * 35/3

Evaluate

Volume = 9333

Hence, the volume is 9333

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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:

  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.)

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 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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Answer: c

Step-by-step explanation: I’m smart

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 value of the expression is 2x³ + 3x² - 27x + 40

It is important we know that algebraic expressions are described as expressions that are composed of factors, constants, variables, coefficients and terms.

Algebraic expressions are also made up of arithmetic operations, such as;

From the information given, we have;

1. (x + 5)(2x² -7x + 8)

expand the bracket

2x³ - 7x² + 8x + 10x² -35x + 40

collect like terms

2x³ - 7x² + 10x² + 8x - 35x + 40

Add the like terms

2x³ + 3x² - 27x + 40

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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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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 ratio of apple oranges and bananas cannot be calculated with the given information

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

Fruits = Orange, Bananas and Apple

Total number of fruits = 48

The available parameters is not enough to determine the ratio

Assuming that we have

Banana = 10

Orange =  20

Apple = 18

Then the ratio would be:

Apple : oranges : bananas = 18 : 20 : 10

Simplify

Apple : oranges : bananas = 9 : 10 : 5

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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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Answer:

Step-by-step explanation:

True

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.

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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Answer:

90 children's tickets and 200 adult tickets were sold.

Step-by-step explanation:

Let's use the variables c and a to represent the number of children's and adult tickets sold, respectively.

From the problem, we know that:

The total number of tickets sold is 290: c + a = 290

The total revenue from ticket sales is $2250: 5c + 9a = 2250

We now have two equations with two unknowns. We can use substitution or elimination to solve for c and a. Here's one way to use elimination:

Multiply the first equation by 5 to get 5c + 5a = 1450

Subtract the above equation from the second equation to eliminate c: 5c + 9a - (5c + 5a) = 2250 - 1450

Simplify: 4a = 800

Solve for a: a = 200

Substitute a = 200 into the first equation to solve for c: c + 200 = 290

Simplify: c = 90

Therefore, 90 children's tickets and 200 adult tickets were sold.

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:

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 calculated surface area of the triangular prism is 976 square meters

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

The dimensions of the triangular prism

The surface area of the triangular prism is the sum of the individual shapes

So, we have the following formula

Surface area = Area of rectangle + Area of the 2 triangles + Area of the 2 rectangles

Using the dimensions, we have

Surface area = 10 * 14 + 2 * 1/2 * 24 * 14 + 2 * 25 * 10

Evaluate

Surface area = 976

Hence, the surface area is 976

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The value of c as per the law of cosines, to the nearest tenth, is 5.1 units.

Given information:

a = 8, b = 9 C = 34°.

To find the value of C:

According to the Law of Cosines, for any triangle ABC:

c² = a² + b² - 2ab cos(C)

Substituting the given values:

c² = 8² + 9² - 2(8)(9) cos(34°)

c² = 64 + 81 - 144 cos(34°)

c² = 145 - 144 cos(34°)

Taking the square root of both sides:

c = √(145 - 144 cos(34°))

Using a calculator:

c ≈ 5.1 units (rounded to the nearest tenth)

Therefore, the value of c is approximately 5.1 units.

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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.

Answer: (f+g)(x) = x² + 3x - 10

Step-by-step explanation:

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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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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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 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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