explain how ray ab an ac form both a line and an angle

The perimeter of triangle XYZ with vertices X(3,7), Y(-1,-5) & Z (6,-4) will be [4√10 + 5√2 + √130] units.

The polygonal shape of a triangle has a number of sides and three independent variables. Angles in the triangle add up to 180°.

The perimeter of the triangle is determined by adding together all of its sides.

The vertices are given below.

X(3,7), Y(-1,-5) & Z (6,-4)

The length of XY is given as,

(XY)² = (7 + 5)² + (3 + 1)²

(XY)² = 144 + 16

XY = 4√10 units

The length of YZ is given as,

(YZ)² = (- 4 + 5)² + (6 + 1)²

(YZ)² = 1 + 49

YZ= 5√2 units

The length of XZ is given as,

(XZ)² = (7 + 4)² + (3 - 6)²

(XZ)² = 121 + 9

XZ = √130 units

The perimeter of triangle XYZ is given as,

P = 4√10 + 5√2 + √130

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Answer:

C. 1.9090%

Step-by-step explanation:

We have been given that the APR of a savings account is 1.9% and interest is compounded semiannually. We are asked to find the APY of the account.

To solve our given problem, we will use APY formula.

[tex]APY=(1+\frac{r}{n})^n-1[/tex], where,

r = Annual interest rate in decimal form,

n = Number of times interest is compounded per year.

Let us convert our given rate in decimal form.

[tex]1.9\%=\frac{1.9}{100}=0.019[/tex]

Upon substituting [tex]r=0.019[/tex] and [tex]n=2[/tex] in APY formula we will get,

[tex]APY=(1+\frac{0.019}{2})^2-1[/tex]

[tex]APY=(1+0.0095)^2-1[/tex]

[tex]APY=(1.0095)^2-1[/tex]

[tex]APY=1.01909025-1[/tex]

[tex]APY=0.01909025[/tex]

Since APY is in decimal form, so we will multiply APY by 100 to get as percentage.

[tex]APY=0.01909025\times 100[/tex]

[tex]APY=1.909025\%\approx 1.9090\%[/tex]

Therefore, the the approximate APY of the account 1.9090% and option C is the correct choice.

The scenario describes calculating the multiple of growth in the US national debt from 1970 to 1990 using scientific notation, showing that the debt was nearly 9 times larger in 1990 than in 1970

Let's create a scenario involving the United States' national debt from two different decades using multiplication in scientific notation. Imagine the government wanted to compare the debt from 1970 to that of 1990 to analyze the growth. The debt in 1970 was approximately $370.9 billion, and in 1990, about $3,233.3 billion. To find out how many times larger the debt was in 1990 compared to 1970, we'd convert these numbers into scientific notation and divide the 1990 figure by the 1970 figure.

In scientific notation, the 1970 debt is 3.709 x 1011 dollars, and the 1990 debt is 3.2333 x 1012 dollars. To perform the division, we have (3.2333 x 1012) / (3.709 x 1011) which gives us approximately 8.71. This means the national debt in 1990 was nearly 9 times larger than it was in 1970

Answer:

The answers are :

1. parallel lines

2. midpoint of a line segment

Step-by-step explanation:

The mathematical terms that cannot be defined for all cases in a system of geometry are:

1. parallel lines and  

2. midpoint of a line segment.

A parallel line cannot be defined as lines do not occupy any space. It is a straight one dimensional figure with no thickness and it extends infinitely in both directions.

The points also do not have any dimension like length, area, volume etc.

Answer:

Option 3. 1/14

Step-by-step explanation:

The bag held some coins that are

pennies = 10

nickels = 6

dimes = 5

total coins = 10 + 6 + 5 = 21 coins

You drew 2 coins without replacement,

so the probability that first draw will be nickel = [tex]P_{1}[/tex] = 6/21 = 2/7

Second draw will be a dime  = [tex]P_{2}[/tex] = 5/20 = 1/4

P = [tex]\frac{2}{7}[/tex] × [tex]\frac{1}{4}[/tex] = 2/28 = 1/14

Option 3. 1/14 would be the answer.

Final answer:

The probability of withdrawing a nickel and then a dime from the bag without replacement is 1/14, calculated by multiplying the independent probabilities of drawing each coin in sequence (6/21 for the nickel and 5/20 for the dime).

Explanation:

The student has asked for the probability of withdrawing first a nickel and then a dime from a bag containing ten pennies, six nickels, and five dimes, without replacement. To solve this, we calculate the probability of each event independently and then multiply these probabilities, since the events are dependent.

First, the probability of drawing a nickel: There are six nickels and a total of 21 coins, so the probability is 6/21. After drawing a nickel, there are five dimes left out of 20 coins total, thus the second probability is 5/20. Multiplying these together gives us:

(6/21) * (5/20) = 30/420 = 1/14

So, the probability of drawing a nickel and then a dime without replacement from this bag of coins is 1/14.

Answer: 1773.54 mg

Step-by-step explanation:

Given: The daily dose of ampicillin for the treatment of an ear infection is 115 mg/kg of body weight.

The weight of a child = 34 lb

We know that 1 pound = 0.453592 kg

Then , the weight of child in kilograms = [tex]0.453592\times34=15.422128\text{ kg}[/tex]

Now, the daily dose of ampicillin for the treatment of an ear infection for the child is given by :-

[tex]115\times15.422128=1773.54472\approx1773.54\text{ mg}[/tex]

Hence, the  daily dose for a 34 lb child = 1773.54 mg

The conversion rate from Ib(pounds) to kg(kilograms)

1 Ib = 0.453592kg

Step 1

We convert the weight of the child to from lb to kg

1 Ib = 0.453592kg

34 lb = ?

Cross Multiply

34 x 0.453592kg

= 15.4221 kg

The weight of the child in kg = 15.4221 kg

Step 2

The daily dose of ampicillin for the treatment of an ear infection is 115 mg/kg of body weight.

Therefore the daily dose of ampicillin for the treatment of ear infection for the child = 15.4221 kg x 115 mg/kg

= 1,773.5415 mg

The daily dose for a 34 lb child is approximately to nearest whole number is 1,774 mg

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Answer: its b

Step-by-step explanation:

The employer would need to pay $19.13 in payroll taxes for this employee.

Payroll tax is a tax that employers are required to deduct from their employee's wages and pay to the government on their behalf.

It is a tax on the wages or salaries that employees earn and is used to fund various government programs, such as Social Security, Medicare, and unemployment insurance.

We have,

The amount an employer needs to pay for payroll taxes depends on several factors.

The employee's gross wages

The type of payroll taxes.

The tax rates are in effect.

Now,

The two primary types of payroll taxes that employers are responsible for are:

Social Security tax:

This tax funds the Social Security program and is calculated as a percentage of the employee's gross wages, up to a certain limit.

In 2023, the Social Security tax rate is 6.2% for both employers and employees, and the wage base limit is $147,000.

Medicare tax:

This tax funds the Medicare program and is calculated as a percentage of the employee's gross wages, with no limit.

In 2023, the Medicare tax rate is 1.45% for both employers and employees.

Assuming the employee owes $250 for Social Security and Medicare taxes combined, and the employer is responsible for paying the same percentage rate as the employee,

The employer would need to pay an additional $250 in payroll taxes.

i.e

Social Security tax.

= $250 x 6.2%

= 250 x 6.2/100

= $15.50

Medicare tax.

= $250 x 1.45%

= 250 x 1.45/100

= $3.63

Total payroll taxes owed by the employer.

= $15.50 + $3.63

= $19.13

Therefore,

The employer would need to pay $19.13 in payroll taxes for this employee.

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Final answer:

68% of the total combined amount of paint is used for the job, calculated by using 20% of the blue paint and 80% of the crimson paint from the initial amounts of 2 liters and 8 liters, respectively.

Explanation:

To calculate the percentage of the total combined amount of paint used during the job, we first identify the amount of blue and crimson paint used separately. From the question we know that there were initially 2 liters of blue paint and 8 liters of crimson paint.

Now, we compute the total paint used and the initial total paint:

To find the percentage of the total paint used, we divide the total paint used by the initial total paint and multiply by 100:

Percentage used = (Total paint used / Initial total paint) × 100

Percentage used = (6.8 liters / 10 liters) × 100 = 68%

Therefore, 68% of the total combined amount of paint is used for the job.

12 inches in a foot so 9 inches = 9/12 of a foot

9/12 reduces to 3/4

so 4 ft 9 inches = 4 3/4 feet

Answer: 0.003

Explanation: