here is a cylinder with hight 4 units and diameter 10 units
what is the volume of the cylinder's base?
what is the volume of this cylinder's?
Step-by-step explanation:
Diameter = 10 units then radius, r = 5 inches
Cylinder's base AREA = pi r^2 = pi (5)^2 = 25 pi = 78.54 units^2
Base area * height = volume = 25 pi * 4 = 100 pi =314.2 units^3
Jason has a block of clay that is made up of two rectangular pieces of
different colors. Find the volume of the block of clay.
The measurements of the two clay blocks are:
6 cm
4 cm
3 cm
5 cm
Answer: 132 cubic centimeters
Step-by-step explanation:
To find the volume of the block of clay, we need to add the volumes of the two rectangular pieces.
The volume of a rectangular solid can be found by multiplying its length, width, and height. Let's call the first rectangular piece A and the second rectangular piece B. Then the dimensions of A are 6 cm (length), 4 cm (width), and 3 cm (height), and the dimensions of B are 5 cm (length), 4 cm (width), and 3 cm (height).
The volume of A is:
Volume of A = length x width x height = 6 cm x 4 cm x 3 cm = 72 cubic centimeters
The volume of B is:
Volume of B = length x width x height = 5 cm x 4 cm x 3 cm = 60 cubic centimeters
So the total volume of the block of clay is:
Volume of block = Volume of A + Volume of B = 72 cubic centimeters + 60 cubic centimeters = 132 cubic centimeters
Therefore, the volume of the block of clay is 132 cubic centimeters.
Determine whether segment lengths form a triangle. If so, classify the triangle as acute, right or obtuse.
1. 10, 7, sqrt(658)
Answer:
it is a triangle bc it has angles of points
Step-by-step explanation:
Out of 80 customers at an ice cream van, 48 had syrup, 28 had sprinkles and 16 had both
toppings on their ice cream. Use a Venn diagram to find the probability that a randomly
selected customer doesn't have either topping, given that they don't have sprinkles.
I know the answer is 20/52, I just can’t work out how to get to that answer…
Answer:
20/52 or simplified to 5/13
Step-by-step explanation:
The Venn Diagram is provided
Let
n(A) = number of customers who had syrup
n(B) = number of customers who had sprinkles
n(A and B) = number of customers who had both syrup and sprinkles = 16
This would be the number in the overlapping region
n(A or B) = number of customers who had either syrup or sprinkles or both
= n(A) + n(B) - n(A and B)
= 48 + 28 - 16
= 60
Therefore number of customers who had neither topping = 80 - 60 = 20
This number is indicated outside both circles but within the rectangle
The number of customers who had only syrup is given by set difference
= No. of customers who had syrup - No. of customers who had both
= n(A) - n(A and B)
= 48 - 16
= 32
This is the figure inside the left circle
Let's consider the statement: Customers who didn't have sprinkles
This would be customers who had only syrup(32) + customers who had neither topping(20)
= 32 + 20 = 52
Number of customers who did not have either topping = 20
P(selected customer doesn't have either topping, given that they don't have sprinkles)
= 20/52
= 5/13
Noah was at home. He got on his bike and rode to his friends
Answer:
what's your exact question
Answer:
can u pls type the full question
you roll a dice with 6 sides what is the probability of....... write your answer as a fraction....roll a 5,roll a 6,roll a c or 4,roll an odd number,roll an even nuber,roll a number greater than 3?,roll an even number less that 5?,roll a multiple of 2(2,4,6),roll a factor of 6(6,4,2,1).
Roll a 5: There is only one way to roll a 5 out of six possible outcomes, so the probability of rolling a 5 is 1/6.
Roll a 6: Similarly, there is only one way to roll a 6 out of six possible outcomes, so the probability of rolling a 6 is 1/6.
Roll a c or 4: There are two ways to roll a 4 (rolling a 4 or rolling a 3) and one way to roll a 3, so there are three ways to roll a 4 or c out of six possible outcomes. Therefore, the probability of rolling a 4 or c is 3/6, simplifying it to 1/2.
Roll an odd number: There are three odd numbers (1, 3, 5) out of six possible outcomes, so the probability of rolling an odd number is 3/6, simplifying to 1/2.
Roll an even number: There are three even numbers (2, 4, 6) out of six possible outcomes, so the probability of rolling an exact number is 3/6 or 1/2.
Roll a number greater than 3: There are three numbers greater than 3 (4, 5, 6) out of six possible outcomes, so the probability of rolling a number greater than 3 is 3/6, which simplifies to 1/2.
Roll an even number less than 5: There is only one number less than 5 (2) out of six possible outcomes, so the probability of rolling an actual number less than 5 is 1/6.
Roll a multiple of 2 (2, 4, 6): There are three multiples of 2 out of six possible outcomes, so the probability of rolling a multiple of 2 is 3/6, simplifying to 1/2.
Roll a factor of 6 (1, 2, 3, 6): There are four factors of 6 out of six possible outcomes, so the probability of rolling a factor of 6 is 4/6, which simplifies to 2/3.
So the probabilities for each event expressed as fractions are:
Roll a 5: 1/6
Roll a 6: 1/6
Roll a 4 or c: 1/2
Roll an odd number: 1/2
Roll an even number: 1/2
Roll a number greater than 3: 1/2
Roll an even number less than 5: 1/6
Roll a multiple of 2: 1/2
Roll a factor of 6: 2/3
How to turn 0. 1212121212 into a simplified fraction
Answer:
4/33
Step-by-step explanation:
You want to write 0.1212...(repeating) as a simplified fraction.
Repeating decimalA repeating decimal beginning at the decimal point can be made into a fraction by expressing the repeating digits over an equal number of 9s.
Here, there are 2 repeating digits, so the basic fraction is ...
12/99
This can be reduced by removing a factor of 3 from numerator and denominator:
[tex]0.\overline{12}=\dfrac{12}{99}=\boxed{\dfrac{4}{33}}[/tex]
__
Additional comment
Formally, you can multiply any repeating decimal by 10 to the power of the number of repeating digits, then subtract the original number. This gives the numerator of the fraction. The denominator is that power of 10 less 1.
0.1212... = (12.1212... - 0.1212...)/(10^2 -1) = 12/99
Doing this multiplication and subtraction also works for numbers where the repeating digits don't start at the decimal point. Finding a common factor with 99...9 may not be easy.
You can also approach this by writing the number as a continued fraction. The basic form is ...
[tex]x=a+\cfrac{1}{b+\cfrac{1}{c+\cdots}}[/tex]
where 'a' is the integer part of the original number, and b, c, and so on are the integer parts of the inverse of the remaining fractional part. The attachment shows how this works for the fraction in the problem statement.
A calculator cannot actually represent a repeating decimal exactly, so error creeps in and may eventually become significant.
Philippe knows there is a $20\%$ chance that it will rain tomorrow and an $80\%$ chance that it will not rain tomorrow. Part A Philippe considers making a spinner to simulate the probability of it raining tomorrow. Describe what the spinner could lPhilippe knows there is a $20\%$ chance that it will rain tomorrow and an $80\%$ chance that it will not rain tomorrow. Part A Philippe considers making a spinner to simulate the probability of it raining tomorrow. Describe what the spinner could look like and the steps he should take to perform the simulation. Ook like and the steps he should take to perform the simulation
Philippe can perform a simulation of rain or no rain for tomorrow by spinning a spinner with two sections labeled "Rain" and "No rain."
The spinner could be divided into two sections, one labeled "Rain" and the other labeled "No rain." To perform the simulation, Philippe would need to give the spinner a spin and observe which section it lands on. If it lands on the "Rain" section, he would consider that as an outcome of rain for tomorrow, and if it lands on the "No rain" section, he would consider that as an outcome of no rain for tomorrow. To make the simulation more accurate, he could repeat the process multiple times and record the number of times the spinner lands on each section.
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The supplement of an angle is 30 more than twice its complement. What is the measure of the
angle?
Answer: 30
180 - x = 180 - 2x + 30
x = 30
Answer:
The measure of the unknown angle is 30°.
Step-by-step explanation:
Let the measure of the unknown angle be x°.
Supplementary angles are two angles whose measures sum to 180°.
Complementary angles are two angles whose measures sum to 90°.
Therefore, the supplement of x° is (180 - x)°, and its complement is (90 - x)°.
Given that the supplement is 30° more than twice its complement:
(180 - x)° = 2(90 - x)° + 30°
To find the measure of the angle, solve the equation:
⇒ (180 - x)° = (180 - 2x)° + 30°
⇒ 180° - x° = 180° - 2x° + 30°
⇒ 180° - x° = 210° - 2x°
⇒ 180° - x° + 2x° = 210° - 2x° + 2x°
⇒ 180° + x° = 210°
⇒ 180° + x° - 180° = 210° - 180°
⇒ x° = 30°
Therefore, the measure of the unknown angle is 30°.
if the odds on a bet are 16:1 against, what is the probability of winning? express your answer as a fraction.
The probability of winning is 1/17, which can also be expressed as a decimal (approximately 0.059) or as a percentage (approximately 5.9%).
The odds on a bet represent the ratio of the probability of winning to the probability of losing. In this case, the odds are 16:1 against winning, which means that the probability of winning is 1 out of 16.
To express this probability as a fraction, we can use the formula:
Probability of winning = 1 / (odds + 1)
Plugging in the given odds, we get:
Probability of winning = 1 / (16 + 1)
Probability of winning = 1/17
In this case, the odds of 16:1 against winning correspond to a probability of 1/17, which represents the chance of winning the bet.
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the stopping distance s of a car varies directly as the square of its speed v. if a car traveling at 40 mph requires 80 ft to stop, find the stopping
If a car traveling at 40 mph requires 80 feet to stop, the stopping distance S of a car varies directly as the square of its speed v and is equal to 180 feet.
Given, the stopping distance S of a car varies directly as the square of its speed v. So the relation can be represented as,
S ∝ v2
Here, the constant of proportionality is k.
S = kv2 ——— (1)
Given, when the speed v = 40 mph, stopping distance s = 80 feet.
Therefore, from equation (1), we have
80 = k × 402
k = 80/1600
k = 0.05
Hence, the relation between the stopping distance S and the speed v of the car can be given as
S = 0.05v2
To find the stopping distance S of the car at speed v = 60 mph, substitute v = 60 in the above equation.
S = 0.05 × 602
S = 0.05 × 3600
S = 180 feet
Therefore, the stopping distance of a car traveling at 60 mph would be 180 feet.
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if the matrix product a1b is known, how could you calculate b1a without necessarily knowing what a and b are?
We can calculate its product by taking the dot product of each row of B1A and each column of A1B. In this way, we can calculate B1A without knowing the values of A and B.
The matrix product of two matrices, A and B, is defined as the matrix C, where C = AB. To calculate the product of two matrices, we must take the dot product of each row of A and each column of B. If we are given a matrix product A1B, then we can calculate B1A without necessarily knowing what A and B are.
To do so, we must first invert the matrix A1B. We can do this by solving a system of equations. We can set up this system of equations by treating the entries of A1B as the coefficients in a system of equations, and solving for the entries of B1A. Once we have found the inverse, we can calculate the matrix B1A.
Finally, once we have the matrix B1A, we can calculate its product by taking the dot product of each row of B1A and each column of A1B. In this way, we can calculate B1A without knowing the values of A and B.
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The number of shoes sold varies inversely with the price two thousand shoes can be sold at the price of $250
The phrase "the number of shoes sold changes inversely with price" suggests that as the price of the shoes rises, so does the number of shoes sold, and vice versa.
We know that 2000 shoes can be sold for $250 in this circumstance. Using the inverse variation formula, we can write: k/Price = number of shoes sold where k is a proportionality constant. We may use the following information to calculate the value of k: 2000 = k/250 When we multiply both sides by 250, we get: k = 500000 In this case, the equation for the inverse variation is: Price/number of shoes sold = 500000 We may use this equation to compute the number of shoes sold at various prices. For instance, if the price is If the price is $300, the number of shoes sold is: The number of shoes sold is 500000/300, which is 1666.67. As a result, at a price of $300, about 1666.67 pairs of shoes would be sold.
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What is the relationship between the number of shoes sold and the price, given that the number of shoes sold varies inversely with the price? If 2,000 shoes are sold at a price of $250, what would be the price of the shoes if 3,000 shoes are sold?
GIVING BRAINLIEST FOR THE CORRECT ANSWER (i need a proof that what you’re saying is right bc ppl are giving me the wrong answers)
Answer:
x [tex]\geq[/tex]2
Step-by-step explanation:
Since the arrow is pointing to the right, we know that it is greater than two. We also know that it could be equal to 2 because the dot is filled in on the number line. So, the answer is x is greater than or equal to 2.
two planes leave at 9 am from airports that are 2700 miles apart and fly towards each other at a speed of 200 mph and 250 mph. at what time will they pass each other?
The two planes will meet 6 hours after they start, i.e. at 3 pm.
Two planes leave at 9 am from airports that are 2700 miles apart and fly towards each other at a speed of 200 mph and 250 mph. At what time will they pass each other?
Let's assume the planes A and B leave the two airports that are 2700 miles apart at the same time. The speed of the first plane is 200 mph and the speed of the second plane is 250 mph. To find out the time at which they pass each other, we need to calculate the distance between them and divide it by the sum of their speeds.
Distance traveled by the first plane in time t1 is equal to 200t1.Distance traveled by the second plane in time t2 is equal to 250t2.The distance covered by the first plane and the second plane together will be 2700 miles.Time taken by both the planes to meet can be calculated as below:
t1 + t2 = 2700/(200+250) = 6 hoursAs both the planes start at 9 am, they will meet each other after 6 hours of their journey. Therefore, they will pass each other at 3 pm. This is the required answer. Explanation: So, the two planes will meet 6 hours after they start, i.e. at 3 pm.
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PLEASE HELP An elevator goes down 3 floors, up 5 floors, and finally down 7 floors. Which expression represents the total number of floors the elevator traveled?
*
A | -3 | + | 5 | + | -7 |
B | -3 | - | 5 | + | -7 |
C ( -3 ) + 5 + ( -7 )
D 3 - 5 + 7
Answer:
B is the answer
Step-by-step explanation:
what is the probability that the first question she gets right is question number 4? group of answer choices
The probability that the first question she gets right is question number 4, is 0.1054.
Number of options there are for a single query = 4
P(guessing correct answer for a single question) = 1/4
P(guessing correct answer for a single question) = 0.25
Probability of getting correct answer P(correct) = 0.25
Probability of getting wrong answer P(wrong) = 1 - Probability of getting correct answer
Probability of getting wrong answer P(wrong) = 1 - 0.25
Probability of getting wrong answer P(wrong) = 0.75
So, the probability that the first question she gets right is question number 4 = Probability of getting 1st question wrong × Probability of getting 2nd question wrong × Probability of getting 3rd question wrong × Probability of getting 4th question right
The probability that the first question she gets right is question number 4 = 0.75 × 0.75 × 0.75 × 0.25
The probability that the first question she gets right is question number 4 = 0.1055
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The complete question is:
In a multiple choice exam, there are 5 questions and 4 choices for each question (a, b, c, d). Nancy has not studied for the exam at all and decides to randomly guess the answers. (Round your answers to four decimal places.)
What is the probability that the first question she gets right is question number 4?
8x 2 + [ 3x3-8] = with explanation pls and its due in six minutes
Answer: 16x+3x^3−8
Please mark me brainliest :)
five girls and five boys randomly sit in ten seats that are equally spaced around a circle. the probability that there is at least one diameter of the circle with two girls sitting on opposite ends of the diameter is , where and are relatively prime positive integers. find .
The probability that there is at least one diameter of the circle with two girls sitting on opposite ends of the diameter is [tex]\frac{7}{12}[/tex] , where 7 and 12 are relatively prime positive integers. The answer is 7+12=19.
The probability that there is at least one diameter of the circle with two girls sitting on opposite ends of the diameter is 1 minus the probability that no diameter of the circle has two girls sitting on opposite ends of the diameter.
There are
[tex]{10\choose5}[/tex] =252
ways to seat the five girls and five boys.
There are 5 ways to choose a diameter of the circle.
Once this diameter is fixed, there are [tex]{5\choose2}[/tex] = 10 ways to choose a pair of seats on the diameter to place two girls (in the order in which they appear counterclockwise).
There are 5!=120 ways to seat the remaining 3 girls and 5 boys such that no two girls sit on the same diameter.
Hence, there are [tex]5\cdot10\cdot120[/tex] =6000 valid seatings that satisfy the condition in the question.
Thus, the desired probability is 1 - [tex]\frac{6000}{252}[/tex] = [tex]\frac{7}{12}[/tex], as stated above.
Thus, the answer is 7+12 = [tex]\boxed{19}[/tex]
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Six flags Great America sells adult tickets for $68 each and children tickets for $47 each. A middle school wants to take students and teachers on a field trip to Six Flags for spring break. The school has a budget of spending at most $12000. They can also only take no more than 225 teachers and students.
The school can purchase 91 adult tickets and 41 children tickets, allowing for a total of 132 teachers and students to go on the trip within the budget of $12000.
Let's start by defining some variables to represent the quantities we're interested in: Let A be the number of adult tickets purchased. Let C be the number of children tickets purchased. Let T be the total number of teachers and students who go on the trip. To maximize the number of teachers and students while staying within budget, we can use linear programming. The objective function is N = T - A - C, where N is the number of teachers and students. The inequalities are 68A + 47C ≤ 12000 and T ≤ 225. Solving this linear program, we find that the school can purchase 91 adult tickets and 41 children tickets, allowing for a total of 132 teachers and students to go on the trip within the budget of $12000.
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the complete question :
A middle school wants to take students and teachers on a field trip to Six Flags Great America for spring break. The school has a budget of spending at most $12,000. They can also only take no more than 225 teachers and students. The adult tickets cost $68 each, and children tickets cost $47 each. How many adults and children can the school take to Six Flags within the given budget and attendance limit?
Covert 1/4 to seconds
Answer:
a quarter of an hour, or 15 minutes is equal to 15 minutes × 60 = 90 seconds a quarter of an hour, or 15 minutes is equal to 15 minutes × 60 = 90 seconds
Answer:
90 seconds
Step-by-step explanation: We know that,
A quarter of an hour= 60×1/4 =15 mins
15 minutes is equal to 15 minutes × 60 = 90 seconds.
Proportions
Two plus x divided by twelve equals one dived by three. Solve for x.
Two plus x divided by twelve equals one divided by three
Case 1 :
Rewrite into numbers : 2 + x /12 = 1/3
-> x/12 = 1/3 - 2 = -5/3
-> x = -5/3 x 12 = -20
Case 2 :
Rewrite into numbers : (2 + x)/12 = 1/3
-> 2 + x = 1/3 x 12 = 4
-> x = 4 - 2 = 2
i dont know if you meant it the right way or the wrong way but ill just put them both
x=2
Step-by-step explanation:
(2+x)/12=1/3
3(2+x)=12
2+x=4
x=4-2
x=2
pizzas are sized by diameter. what percent increase in area results if chantel's pizza increases from a 10-inch pizza to a 12-inch pizza?
Step-by-step explanation:
Area of circle = pi r^2
10 inch = pi (5)^2 = 25 pi
12 inch = pi (6)^2 = 36 pi
12 inch is 11pi bigger
percentage: 11 pi is what percentage of 25 pi ?
11 pi / 25 pi x 100% = 44 % bigger
The area of a pizza increases with the square of the diameter. Therefore, a 10-inch pizza has an area of [tex]π*(10/2)^2= 78.54[/tex] square inches, and a 12-inch pizza has an area of [tex]π*(12/2)^2 = 113.10[/tex] square inches. This is an increase of 113.10 - 78.54 = 34.56 square inches, or an increase of 44.2%.
To explain further, the diameter of a pizza is measured from one side to the other through the center of the pizza. As the diameter of the pizza increases, the area of the pizza increases. This is because the area of a pizza is calculated as [tex]π*(d/2)^2[/tex], where d is the diameter. So, if the diameter increases, the area increases as well.
For example, if a 10-inch pizza has an area of 78.54 square inches, a 12-inch pizza would have an area of 113.10 square inches. This is an increase of 113.10 - 78.54 = 34.56 square inches, or an increase of 44.2%. This is because the diameter of the pizza has increased by 2 inches (10 inches to 12 inches), and the area has increased by 44.2%.
It is important to note that increasing the diameter of the pizza does not just increase the circumference of the pizza, but also the area. The increase in area is directly related to the increase in diameter, and can be calculated by taking the difference between the areas of the two pizzas.
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a children's liquid medicine contains 100 mg of the active ingredient in 5 ml . if a child should receive 300 mg of the active ingredient, how many milliliters of the medicine should the child be given? for the purposes of this question, assume that these numbers are exact.
The child should be given 15 ml of the medicine to receive 300 mg of the active ingredient.
The given problem requires us to determine the number of milliliters of a liquid medicine that a child should receive in order to obtain a specific dosage of the active ingredient. We are given that the medicine contains 100 mg of the active ingredient in 5 ml.
The child needs to receive 300 mg of the active ingredient, and there are 100 mg of the active ingredient in 5 ml of the medicine. Therefore, the child should be given:
[tex]\frac{300 mg}{100mg/5ml} = \frac{300\text{ mg} \times 5\text{ ml}}{100\text{ mg}} = 15\text{ ml}$$[/tex]
So the child should be given 15 ml of the medicine to receive 300 mg of the active ingredient.
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how many strings of 6 letters of the english alphabet contain one vowel? exactly two vowels? at least one vowel? at least two vowels? what is number of strings of length n with exactly k vowels?
Strings of 6 letters of the English alphabet containing one vowel: 2,832,240, exactly two vowels: 2,233,200, at least one vowel: 10,919,736, least two vowels: 8,087,496 and number of strings of length n with exactly k vowels: nCk * 5Ck * 21^(n-k)
There are 26 letters in the English alphabet, out of which 5 are vowels (A, E, I, O, U). To find the number of strings of 6 letters of the English alphabet that contain one vowel, we can choose the position of the vowel in 6C1 ways and fill the remaining positions with any of the 21 consonants in 21C5 ways.
Therefore, the total number of such strings is 6C1 * 21C5 = 2,832,240.
To find the number of strings with exactly two vowels, we can choose the positions of the vowels in 6C2 ways and fill them with any of the 5 vowels in 5C2 ways. We can fill the remaining positions with any of the 21 consonants in 21C4 ways.
Therefore, the total number of such strings is 6C2 * 5C2 * 21C4 = 2,233,200.
To find the number of strings with at least one vowel, we can subtract the number of strings with no vowels from the total number of strings. The number of strings with no vowels is 21^6 (since there are 21 consonants and we can choose any of them for each of the 6 positions).
Therefore, the number of strings with at least one vowel is 26^6 - 21^6 = 10,919,736.
To find the number of strings with at least two vowels, we can subtract the number of strings with one vowel or no vowel from the total number of strings. The number of strings with one vowel is 2,832,240 (as we found earlier) and the number of strings with no vowels is 21^6.
Therefore, the number of strings with at least two vowels is 26^6 - 2,832,240 - 21^6 = 8,087,496.
To find the number of strings of length n with exactly k vowels, we can choose the positions of the k vowels in nCk ways and fill them with any of the 5 vowels in 5Ck ways. We can fill the remaining positions with any of the 21 consonants in 21^(n-k) ways.
Therefore, the total number of such strings is nCk * 5Ck * 21^(n-k).
Hence, the number of strings of 6 letters of the English alphabet containing one vowel is 2,832,240, while the number of strings with exactly two vowels is 2,233,200. The number of strings with at least one vowel is 10,919,736, and the number of strings with at least two vowels is 8,087,496.
Finally, the number of strings of length n with exactly k vowels is nCk * 5Ck * 21^(n-k).
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The triangles are similar. Find the value of x.
Since the triangles are similar, the value of x is equal to: C. 18 units.
What are the properties of similar triangles?In Mathematics, two (2) triangles are said to be similar when the ratio of their corresponding side lengths are equal and their corresponding angles are congruent.
By applying the properties of similar triangles, we have the following ratio of corresponding side lengths;
AC/RS = AB/RT
By substituting the given side lengths into the above equation, we have the following:
x/24 = 24/32
By cross-multiplying, we have the following;
32x = 24(24)
32x = 576
x = 576/32
x = 18 units.
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Missing information:
The question is incomplete and the complete question is shown in the attached picture.
Angle PQR is isosocles with PQ=PR= 7. 5cm and QR = 9cm. The height PS from P to QR,is 6cm. Find the area of Angle PQR. What will be the height from R to PQ that is RT
The height RT from R to PQ is approximately 3.16 cm.
To find the area of triangle PQR, we can use the formula:
Area = 1/2 * base * height
Since PQR is isosceles with PQ = PR, the base is PQ or PR. We can choose PQ as the base. Then the height is PS.
Area of PQR = 1/2 * PQ * PS
Since PQ = PR = 7.5 cm and PS = 6 cm, we can substitute these values into the formula and simplify:
[tex]Area of PQR = 1/2 * 7.5 cm * 6 cm[/tex]
[tex]Area of PQR = 22.5 cm^2[/tex]
Therefore, the area of triangle PQR is [tex]22.5 cm^2[/tex].
To find the height RT from R to PQ, we can use the Pythagorean theorem.
Let's draw a perpendicular line from R to PQ, intersecting at T. Then we have a right triangle PRT with hypotenuse PR and legs PT and RT.
Since PQR is isosceles, we can also see that angle PQR is equal to angle PRQ. Therefore, angles PQR and PRQ are equal and each is approximately 69.3 degrees (using inverse cosine function).
Using the sine function, we can find the length of PT:
sin(69.3) = PT / 7.5
PT = 7.5 * sin(69.3)
PT ≈ 6.93 cm
Using the Pythagorean theorem, we can find the length of RT:
[tex]RT^2 + PT^2 = PR^2[/tex]
[tex]RT^2 = PR^2 - PT^2[/tex]
[tex]RT^2 = 7.5^2 - 6.93^2[/tex]
RT ≈ 3.16 cm
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Help me with these please!!
The angle ABD is 35 degrees, AC is 20 units long, and AB is 29 units long.
What in mathematics is an angle?An angle is created by combining two rays (half-lines) that have a common terminal. The angle's vertex is the latter, while the rays are alternately referred to as the angle's legs and its arms.
Triangle ABD's angle ABC is one of its outside angles, making it equal to the sum of the opposing interior angles.
Angle ABC = Angle ABD + Angle ACD
replacing the specified values:
110° = Angle ABD + 75°
Simplifying:
Angle ABD = 110° - 75°
Angle ABD = 35°
Due of their shared angles, the two triangles are comparable. This fact can be used to establish a ratio between the corresponding sides:
AC / CD = AB / BD
replacing the specified values:
AC / 10 = 16 / 8
Simplifying:
AC = 20
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Complete Question:
Find the angle ∠ABD jn the given figure
the number of hours needed to complete a trip, h, varies inversely with the driving speed, s. a trip can be completed in 5 hours at a speed of 60 miles per hour. find the equation that represents this relationship.
The equation that represents the relationship between the number of hours needed to complete a trip, h, and the driving speed, s, is h = 5/s. This means that the number of hours needed to complete the trip is inversely proportional to the driving speed.
When the driving speed is 60 miles per hour, the number of hours needed to complete the trip is 5 (h = 5/60). If the driving speed is increased to 90 miles per hour, the number of hours needed to complete the trip is 5/90 (h = 5/90).
In general, as the driving speed increases, the number of hours needed to complete the trip decreases.
To summarize, the equation that represents the inverse relationship between the number of hours needed to complete a trip and the driving speed is h = 5/s. This equation can be used to determine the number of hours needed to complete a trip at any given speed.
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Help please, Which value of x satisfies the equation 7/3(x+9/28)=20
Answer:
Step-by-step explanation:
[tex]\frac{7}{3} (x+\frac{9}{28} )=20[/tex]
[tex]7 (x+\frac{9}{28} )=60[/tex] (multiplied both sides by 3)
[tex]x+\frac{9}{28} =\frac{60}{7}[/tex] (divided both sides by 7)
[tex]x=\frac{60}{7}-\frac{9}{28}=\frac{240}{28}-\frac{9}{28}=\frac{231}{28} =8.25[/tex] (subtracted [tex]\frac{9}{28}[/tex] both sides and solved)