The figure shows △ABC . BD is the angle bisector of ∠ABC .
What is AD ?
Enter your answer in the box as a fraction.
____ units
The length of AD is [tex]\dfrac{8}{3}[/tex].
Given:
BD is the angle bisector of the triangle ABC.
The figure of the triangle ABC.
To find:
The length of AD.
Explanation:
According to the Angle Bisector Theorem, the angle bisector of a triangle divides the opposite side in the same proportion of the other two sides.
Let [tex]x[/tex] be the length of AD. Then, the length of DC is [tex]6-x[/tex].
Using the Angle Bisector Theorem, we get
[tex]\dfrac{8}{10}=\dfrac{x}{6-x}[/tex]
[tex]\dfrac{4}{5}=\dfrac{x}{6-x}[/tex]
[tex]4(6-x)=5(x)[/tex]
[tex]24-4x=5x[/tex]
[tex]24=5x+4x[/tex]
[tex]24=9x[/tex]
[tex]\dfrac{24}{9}=x[/tex]
[tex]\dfrac{8}{3}=x[/tex]
Therefore, the length of AD is [tex]\dfrac{8}{3}[/tex].
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John Tucker is interested in purchasing stock. He wants to determine the costs.
Answer: a0 =$97.5 ; a1 =$87.96 ; a2=$282.48; a3=$1,722.5 ; a4=$1,553.96 ; a5=$4,990.48
Step-by-step explanation:
Hi, to solve this problem we have to multiply each total by the commission in decimal form (6 / 100= 0.06).
So:
$1625 x 0.06 = $97.5
$1,466 x 0.06 =$87.96
$4,708 x 0.06 =$282.48
And finally, to obtain the total costs we have to add to each total the commission of the total.
$1625 + $97.5 = $1,722.5
$1,466 +$87.96 = $1,553.96
$4,708 +$282.48 = $4,990.48
Feel free to ask for more if it´s necessary or if you did not understand something.
david kalb started a pet-walking business , he charges $20 to walk one dog, twice a day. He walks six dogs five days a week for four customers. He walks three dogs seven days a week for three other customers. How much money does David get from his customers each week? If his weekly expenses are $350, what is the profit?
Answer:
David earns $1,020 a week, and his weekly profit is $670.
Step-by-step explanation:
Since David walks six dogs per day, and each dog is $20, he earns a total of $120 per day from those six dogs. Also, knowing that he walks the six dogs five days a week, he earns $600 from walking the six dogs for five days per week alone. Using this same logic for the three dogs he walks seven days a week, we can conclude that he gets $60 from walking those three dogs. Knowing he walks those three dogs seven days a week, he gets $420 from walking those three dogs. Combining the totals gives us $1,020, the amount of money he earns per week. Since his weekly expenses are $350, we subtract that from $1,020 to get his weekly profit: $670.
How many six-letter passwords are there that use only lowercase letters with no letter repeated?
What number needs to be added to both sides of the equation in order to complete the square? x2+14x=−32
49 is the number to be added to both the sides of the equation to complete the square.
The equation given in the question is
[tex]x^{2} +14x=-32[/tex]Which can be written as [tex]x^{2} +2\times (7x)=-32[/tex]
We have to convert it into square form.
Since the standard form of the equation in square form is
(a + b)² = a² + 2ab + b²
By comparing this standard equation with the given equation,
a = x
&
b = 7
By substituting the values of 'a' and 'x' in the standard square form,
x² + 14x + 7² = -(32) + 7²
x² + 14x + 49 = -32 + 49
(x + 7)² = 17
Therefore, 49 should be added in both the sides of the equation in order to complete the square.
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If f(x) = 2/x and g(x) = x^2 what is f of g
Answer: The required value is [tex]f(g(x))=\dfrac{2}{x^2}.[/tex]
Step-by-step explanation: We are given two functions as follows :
[tex]f(x)=\dfrac{2}{x},~~~~~~~g(x)=x^2.[/tex]
We are to find f of g, i.e., f(g(x)).
To find the required value, first we have to find the f value of the function g(x).
We have
[tex]f(g(x))=f(x^2)=\dfrac{2}{x^2}.[/tex]
Thus, the required value is [tex]f(g(x))=\dfrac{2}{x^2}.[/tex]
How many feet are in 2000 meters?
There were 91 books on a shelf. Twenty-eight of the books were nonfiction, 13 of the books were poetry books, and the rest were fiction books. How many books were fiction?
Write an equation of the line passing through the point A(−6, 5)that is parallel to the line
y = 1/2 x−7.
Evaluate. 12+4⋅3−15 Enter your answer in the box.
Answer:
I think it is 9 because I know u multiply at the start plus I used a calculator and got 9 so if it is not my calculator it broke
At a high school with 1100 students, Jake is in the 70th percentile for height. How
many students at the school are either the same height or shorter than Jake?
Deniz had a full gallon of milk. She poured out 4 cups of milk. There are 16 cups in 1 gallon. About what percent of the original volume is left?
Answer:
75% of the original volume is left.
Step-by-step explanation:
Deniz had a full gallon of milk, or 16 cups of milk, and then she poured out 4 cups of milk. That is:
[tex]\\ A_{full-gallon} = \frac{16}{16}[/tex] cups of milk, since [tex]\\ \frac{16}{16} = 1[/tex] or [tex]\\ 1 * 100\% = 100\%[/tex] of the original volume.Deniz poured out 4 cups of milk from the 16 available (or [tex]\\ \frac{4}{16}[/tex]).Then,
The total left is:
[tex]\\ Total_{left} = \frac{16}{16} - \frac{4}{16} = \frac{12}{16} = \frac{3}{4}[/tex], since we are dealing here with fractions with the same denominator.
In other words, [tex]\\ \frac{3}{4} = 0.75[/tex] is the amount of milk left in the container.
In terms of percentage, [tex]\\ \frac{3}{4} = 0.75[/tex] is equivalent to [tex]\\ 0.75*100\% = 75\%[/tex] of the original volume, because Deniz poured out [tex]\\ \frac{4}{16} = \frac{1}{4} = 0.25[/tex] or [tex]\\ 0.25*100\% = 25\%[/tex] from the original volume.
So, Deniz left 75% of the original volume of milk after pouring out 25% of it.
This can be represented in the graph below.
Answer:
75%
Step-by-step explanation:
Find the area of a circle with a diameter of 10 units. Round answer to the nearest hundredth of a square unit.
Answer:
Step-by-step explanation:
The area of a circle is given by A = π*r²
If diameter is 10 units, the radius is 5, so:
A = π * 5² = 78,54units²
The Royal Fruit Company produces two types of fruit drinks. The first type is 65% pure fruit juice, and the second type is 90% pure fruit juice. The company is attempting to produce a fruit drink that contains 80% pure fruit juice. How many pints of each of the two existing types of drink must be used to make 120 pints of a mixture that is 80% pure fruit juice?
Jessica increases the temperature of a block of ice by 20º. Which integer represents the amount by which Jessica must change the temperature for the block of ice to return to its starting temperature? A. –40 B. –20 C. 20 D. 40
Answer:
B. -20
Step-by-step explanation:
Answer:
b
Step-by-step explanation:
For exercises 14-19, find an equation for the line that satisfies the conditions
Find the original price of a pair of shoes if the sale price is $44 after a 60% discount.
Final answer:
To find the original price of a pair of shoes after a 60% discount, divide the sale price by (1 minus the discount percentage). The original price of the pair of shoes is $110.
Explanation:
To find the original price of a pair of shoes after a 60% discount, we can use the formula:
Original price = Sale price / (1 - Discount percentage)
Substituting the given values:
Original price = $44 / (1 - 0.60)
Original price = $44 / 0.40
Original price = $110
Therefore, the original price of the pair of shoes was $110.
Final answer:
To determine the original price before a discount, subtract the discount percentage from 1, convert it to a decimal, and divide the sale price by this number. In this case, the original price for the shoes before a 60% discount, resulting in a $44 sale price, is $110.
Explanation:
To find the original price of an item before a discount, you can use the following steps:
First, understand that the sale price is the price after the discount has been applied to the original price.Express the discount as a decimal. A 60% discount is 0.60 when expressed as a decimal.Since the sale price reflects the remaining percentage after the discount, you subtract the discount decimal from 1 to find the multiplier for the original price. That is, 1 - 0.60 = 0.40.Divide the sale price by this multiplier to get the original price. So, $44 divided by 0.40 equals $110.Therefore, the original price of the shoes was $110 before the 60% discount was applied.
The polynomial equation x^3-4x^2+2x+10=x^2-5x-3 has complex roots 3+2i What is the other root? Use a graphing calculator and a system of equations.
a –3
b –1
c 3
d 10
Answer:
The correct option is b.
Step-by-step explanation:
The given expression is
[tex]x^3-4x^2+2x+10=x^2-5x-3[/tex]
Simplify the equation.
[tex]x^3-4x^2+2x+10-x^2+5x+3=0[/tex]
[tex]x^3-5x^2+7x+13=0[/tex]
It is given that 3+2i is a root of the equation and (x-3-2i) is a factor.
By complex conjugate root theorem if a+ib is a root of an equation then a-ib must be the root of the equation.
It means 3-2i is a root of the equation and (x-3+2i) is a factor.
[tex](x-3-2i)(x-3+2i)=(x-3)^2-(2i)^2=x^2-6x+9+4=x^2-6x+13[/tex]
Divide [tex]x^3-5x^2+7x+13=0[/tex] by [tex]x^2-6x+13[/tex], to find the remaining factor.
By the long division method, the quotient is (x+1) and remainder is 0. It means (x+1) is a remaining factor of the given equation. Equate each factor equal to 0, to find the remaining roots.
[tex]x+1=0[/tex]
[tex]x=-1[/tex]
Therefore the correct option is b.
Solve be graphing , elimination , or substitution
A wallet contains 23 bills. All the bills are $1 bills and $5 bills. There are 7 more $1 bills than 5 bills. How much money does the wallet contain
Final answer:
The wallet contains a total of $55, given that there are 8 $5 bills and 15 $1 bills.
Explanation:
The student's question involves determining the total amount of money in a wallet given a specific mix of $1 bills and $5 bills. According to the information provided, there are 23 bills in total, with 7 more $1 bills than $5 bills.
Let's denote the number of $5 bills as x. Therefore, there are x + 7 $1 bills. The total number of bills is the sum of the number of $1 bills and the number of $5 bills, which gives us the equation:
x + (x + 7) = 23
Solving the equation for x will give us the number of $5 bills:
2x + 7 = 23
2x = 23 - 7
2x = 16
x = 8
Now, since there are 8 $5 bills, and 7 more $1 bills than $5 bills, we have:
Number of $1 bills = 8 + 7 = 15
Thus, the total amount of money in the wallet is:
($5 × 8) + ($1 × 15) = $40 + $15 = $55
Therefore, the wallet contains $55.
2/3 is what percent of 1/4?
To determine what percent 2/3 is of 1/4, convert both fractions to percent form, where 1/4 is 25%. Converting 2/3 to a percent gives approximately 66.67%, and dividing this by 25% gives 266.68%. Thus, 2/3 is 266.68% of 1/4.
To find out what percent 2/3 is of 1/4, you first need to express the fractions in a way that allows comparison. A standard way of expressing a fraction as a percent involves having a denominator of 100. Since you know 1/4 equals 25 percent, you can use this as a basis for comparison with 2/3.
To convert 2/3 to a decimal, divide the numerator by the denominator: 2 divided by 3 equals approximately 0.6667. To then convert that decimal to a percent, multiply by 100, getting approximately 66.67 percent. To find what percent 2/3 is of 1/4, divide 66.67 by the percent value of 1/4, which is 25, and then multiply by 100 to get the percentage. This gives you (66.67 / 25) x 100 = 266.68 percent. So, 2/3 is 266.68 percent of 1/4.
A tour group with 22 people in it is getting rooms in a motel to stay in for the night. no more than 3 people can stay in each room. how many rooms will they need
8 rooms will be needed for a tour group of 22 people and the last room will have only one member of the group.
What is unitary method?The unitary method is a technique for solving a problem by first finding the value of a single unit, and then finding the necessary value by multiplying it with the value of a single unit.
Given is a tour group of 22 people. The group is looking for rooms in a motel to stay in for the night and no more than 3 people can stay in each room.
The number of people who can live in 1 room = 3
This means, we have 3 people for 1 room.
For 1 people, we will have - (1/3) room
For 22 people, we will need -
(22/3)
7.3 rooms
Approximately, 8 rooms will be needed and the last room will have only one member of the group.
Therefore, 8 rooms will be needed for a tour group of 22 people and the last room will have only one member of the group.
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What is f(6) ? Thanks
In Saudi Arabia it takes 20 kursh to equal 1 riyal.
a. Write the two unit multipliers implied by this relationship.
b. Use one of the unit multipliers to convert 16,000 kursh to riyals.
help
The problem is about converting between two units of currency from kursh to riyals. The two unit multipliers from this scenario are: 1 riyal equals 20 kursh and 1 kursh equals 1/20 riyal. The conversion from 16,000 kursh to riyals would be 800 riyals.
Explanation:The question is about converting between two units of currency, specifically from kursh to riyals based on the exchange rate provided. It's a classic problem in unit conversion.
a. The two unit multipliers implied by this relationship are:
1 riyal = 20 kursh 1/20 riyal = 1 kursh
b. To convert 16,000 kursh to riyals, you would use the first unit multiplier. Given that 1 riyal equals 20 kursh, you simply divide the amount in kursh by 20 to get the equivalent amount in riyals. So, 16000 kursh ÷ 20 = 800 riyals.
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The amount that results when $4,000 is compounded at 6% annually over seven years.
Use the numbers 8, 6, and 2 and one operation to write and expression that includes an exponent and has a value of 8. Use each number only once
The suitable way to use the numbers 8, 6, and 2 to create an expression with an exponent that results in the value of 8 is by utilizing the equation 2^3. This equation means 'two raised to the power of three', meaning 2 multiplied by itself thrice, giving us the desired result, 8.
Explanation:To solve this question, we need to consider the mathematical operation of exponentiation, which involves a base number and an exponent. The exponent represents the number of times the base number is to be multiplied by itself.
Given the numbers 8, 6, and 2, we aim to use each number only once to create an expression that includes an exponent and yields a value of 8. The suitable way to do this is by following the equation 2^3 (where 2 is the base number and 3 is the exponent).
To explain further, an exponent is the number of times a number, known as the base, is multiplied by itself. For instance, 2^3 should be read as 'two raised to the power of three', essentially depicting 2 * 2 * 2, resulting in 8. This follows the standard rules of Exponential Arithmetic.
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Scores on a test have a mean of 70 and q3 is 83. the scores have a distribution that is approximately normal. find p90. (you will need to first find the standard deviation.)
a. 94.84
b. 85.08
c. 85.31
d. 83.7
The value corresponding to the 90th percentile (p90) is 94.84. Option A is correct.
To find the value corresponding to the 90th percentile (p90), we first need to find the standard deviation of the scores.
We know that the third quartile (Q3) is 83, which corresponds to the 75th percentile (p75). Since the distribution is approximately normal, we can use the properties of the normal distribution to find the standard deviation.
In a standard normal distribution, the value corresponding to the p75 is approximately 0.6745 standard deviations above the mean. So, we can set up the following equation:
70 + 0.6745 * standard deviation = 83
Now, solve for the standard deviation:
standard deviation = (83 - 70) / 0.6745 ≈ 19.3047
Next, to find the value corresponding to the p90, we use the properties of the normal distribution again. The value corresponding to the p90 is approximately 1.2816 standard deviations above the mean.
Now, calculate p90:
p90 = 70 + 1.2816 * standard deviation
≈ 70 + 1.2816 * 19.3047
≈ 94.84
Rounding to two decimal places, we get p90 ≈ 94.84. So, the answer is (a) 94.84.
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To find p90 in a normally distributed set of scores, we need to find the standard deviation. Using the mean and q3, we can find the IQR and estimate the standard deviation. Finally, we can use the standard deviation to find the value corresponding to the 90th percentile.
Explanation:To find the value of p90 in a normally distributed set of scores, we need to first find the standard deviation of the scores. We know that the mean is 70 and q3 (the third quartile) is 83. Using the formula for the interquartile range (IQR = q3 - q1), we can calculate the value of q1. Subtracting q1 from q3 gives us the IQR. Since the distribution is approximately normal, we can assume that the IQR is approximately 1.35 times the standard deviation. Dividing the IQR by 1.35 gives us the standard deviation. Finally, we can use the standard deviation to find the z-score corresponding to the 90th percentile and then find the corresponding value in the original distribution using the mean and standard deviation. The correct answer is option (a) 94.84.
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The point-slope form of the equation of the line with slope 7 passing through the point (4, 6) is
62394 rounded to the nearest tenth
How to simplify rational expressions