16 percentage of the unknown number is 73.6
To solve the problem, we can use the relationship between percentages and multiply/divide by factors of 100.
Let's start by finding the whole number that corresponds to 1% of the unknown number
1% of the number = 4.6
100 times 1% of the number = 100 x 4.6
Whole number corresponding to the unknown number = 460
We can now use this value to find 5% of the unknown number:
5% of the number = 5/100 x the number = (5/100) × 460 = 23
So we have confirmed that the number we found is correct.
Finally, to find 16% of the number, we can use the same approach
16% of the number = 16/100 x the number = (16/100) × 460 = 73.6
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(1) if the number of bacteria in a culture is 5 million at the end of 6 hours and 8 million at the end of 9 hours, how many were present initially?
There were initially 4 million bacteria in the culture.
To determine the initial number of bacteria in the culture, we can follow these steps:
Step 1: Identify the given data.
At the end of 6 hours, there are 5 million bacteria.
At the end of 9 hours, there are 8 million bacteria.
Step 2: Find the rate of bacterial growth.
Since the number of bacteria increased by 3 million (8 million - 5 million) over 3 hours (9 hours - 6 hours), the rate of bacterial growth is 1 million per hour (3 million ÷ 3 hours).
Step 3: Calculate the initial number of bacteria.
The number of bacteria increased by 5 million over the 6 hours. Therefore, if we divide this number by the rate of growth, we can determine the initial number of bacteria. Divide 5 million by 1 million per hour, which results in 5 hours.
Step 4: Subtract the time from the initial time.
Since we know that the culture was growing for 5 hours before reaching 5 million, we can subtract 5 hours from 6 hours, which equals 1 hour.
Step 5: Calculate the initial number of bacteria at 1 hour.
Since the bacteria grow at a rate of 1 million per hour, at the end of the 1st hour, there would be 1 million bacteria. Subtracting this number from the 5 million at the end of 6 hours will give us the initial number of bacteria: 5 million - 1 million = 4 million bacteria.
So, there were initially 4 million bacteria in the culture.
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The baker receives an order of 80 chocolate pies for a community festival. The baker needs 3 cups of milk to make each pie. How much milk, in gallons, is needed to make the 80 pies for the festival?
the baker needs 15 gallons of milk to make 80 chocolate pies for the community festival. To find out how much milk is needed to make 80 chocolate pies, we need to first determine the total amount of milk required for one chocolate pie. We know that the baker needs 3 cups of milk to make one chocolate pie.
To convert cups to gallons, we need to divide by 16 since there are 16 cups in a gallon. So, one chocolate pie requires 3/16 gallons of milk.
To find out how much milk is needed to make 80 chocolate pies, we can multiply the amount of milk required for one pie by the number of pies. This gives us:
(3/16) gallons of milk per pie x 80 pies = 15 gallons of milk
Therefore, the baker needs 15 gallons of milk to make 80 chocolate pies for the community festival.
It's important to make sure we convert units correctly when solving these types of problems. In this case, we had to convert cups to gallons to make sure we were using the same unit of measurement for both the amount of milk needed for one pie and the total amount needed for 80 pies. By following these steps, we can accurately determine the amount of ingredients needed to fulfill an order, which is important for bakers and other food service professionals.
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Solve for x helpp again x^7= 84
Answer:
x = 7 square root 84
OR
x = 1.88320258...
Step-by-step explanation:
Answer:
[tex]x=\sqrt[7]{84}[/tex]
Step-by-step explanation:
1) Take the 7th root of both sides.
[tex]x=\sqrt[7]{84}[/tex]
Check the answer:
[tex]x^7=84[/tex]
1) let x = ^7sqrt84
(^7sqrt84)^7 = 84
2) use this rule: ^7sqrtx^7 = x.
84=84
Can You fail 5th grade elementary? i have a 68 in math and im scared
Answer: I mean technically no. grades don't really matter until high school. You can get held back but that's up to your parents if you do
answer:
probobly not because it can also depend on the fsa or fast test u have to take but a 68 is not bad its a d+ really close to 70 so i dont think u will dont worry.
100 POINTS AND WILL MARK BRAINLIEST!
Law of Cosines Of A Triangle -
GIVEN:
C (the degree)
20
22
18 (the base)
C = ?°
Round your final answer to the nearest tenth.
Law of Cosines Of A Triangle -GIVEN: C (the degree) 20, 22,18 (the base). C is 26.5 degrees.
To solve for the angle C using the law of cosines, we use the formula:
[tex]c^2 = a^2 + b^2[/tex] - 2ab cos(C)
where c is the angle C's opposite side.
Substituting the given values, we get:
[tex]18^2 = 20^2 + 22^2[/tex] - 2(20)(22)cos(C)
324 = 1048 - 880cos(C)
880cos(C) = 724
cos(C) = 724/880
C = [tex]cos^{(-1)}[/tex](724/880)
C ≈ 26.5 degrees
Therefore, the measure of angle C is approximately 26.5 degrees.
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6,7,7,8,9,10,10,10,10,13,13,14,14,15,15 box and whisker plot
The box and whisker plot can be created by :
Minimum value - 6
Maximum Value - 15
Median - 10
Quartiles - Q1 - 7.5, Q2 - 10, Q3 - 13.5
To create a box and whisker plot for the given data set {6,7,7,8,9,10,10,10,10,13,13,14,14,15,15}, we need to first find the minimum value, maximum value, median, and quartiles.
Minimum value: 6
Maximum value: 15
Median: To find the median, we need to first arrange the data set in ascending order:
6,7,7,8,9,10,10,10,10,13,13,14,14,15,15
The median is the middle value in the data set, which is 10.
Quartiles: To find the quartiles, we need to divide the data set into four equal parts.
First quartile (Q1): The first quartile is the median of the lower half of the data set. In our case, the lower half of the data set is:
6,7,7,8,9,10
The median of this set is (7+8)/2 = 7.5.
Second quartile (Q2): The second quartile is the median of the entire data set, which we already found to be 10.
Third quartile (Q3): The third quartile is the median of the upper half of the data set. In our case, the upper half of the data set is:
10,10,10,10,13,13,14,14,15,15
The median of this set is (13+14)/2 = 13.5.
Now, we can use the above information to create the box and whisker plot.
The horizontal line inside the box represents the median (10). The bottom of the box represents the first quartile (7.5), and the top of the box represents the third quartile (13.5). The whiskers extend from the box to the minimum value (6) and maximum value (15).
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Need help too figure out these questions these are 2 outa 10 i have too do but these the hardest
Answer:
1. I don't know
2. 10
Step-by-step explanation:
[tex]c=\sqrt{a^{2}+b^{2} } = \sqrt{6^{2}+8^{2} } = \sqrt{36+64} = \sqrt{100} = 10[/tex]
54 is what percent of 90? Question 9 options: 60% 65% 55% 52%
Answer:
The answer to your problem is, A. 60%
Step-by-step explanation:
54 of 90 can be written as: [tex]\frac{54}{90}[/tex]
To find percentage, we need to find an equivalent fraction with denominator 100. Multiply both numerator & denominator by 100
[tex]\frac{54}{90} * \frac{100}{100}[/tex]
= [tex]\frac{( 54 * 100)}{90} * \frac{1}{100} = \frac{60}{100}[/tex]
Thus the answer to your problem is, A. 60%
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Answer:
x = 60%
Step-by-step explanation:
Let the unknown percentage be x.
We can make an expression using the given information.
[tex]\sf90*\frac{x}{100} =54[/tex]
Solve for x to find the percentage.
[tex]\sf\frac{90x}{100} =54\\90x=54*100\\\\90x=5400\\\\\frac{90x}{90}=\frac{5400}{90}\\\\ x=60[/tex]
what is x2=20 show your work
Answer:
x=10
Step-by-step explanation:
x2=20
2*x=20
2*10=20
so, x=10
I’m stuck on how to work this ppq out
Therefore, the area of P is 4 times bigger than the area of Q.
What is area?Area is a measure of the amount of two-dimensional space enclosed by a closed figure, such as a square, rectangle, circle, or triangle. It is typically measured in square units, such as square meters (m²) or square centimeters (cm²). The formula for finding the area of a figure depends on the shape of the figure. For example, the area of a rectangle is found by multiplying its length by its width, while the area of a circle is found by multiplying π (pi) by the square of its radius. Knowing the area of a figure can be useful in many situations, such as when calculating the amount of material needed to cover a floor or when determining the capacity of a container. It is also an important concept in geometry, where it is used to compare the sizes of different shapes and to solve problems involving the relationships between them.
Here,
The area of a circle is given by the formula A = πr², where A is the area and r is the radius.
For shape P, the area is:
A_P = (3/4)π(20²) = 300π
For shape Q, the area is:
A_Q = (1/3)π(15²) = 75π
To find how many times bigger the area of P is than the area of Q, we can divide the area of P by the area of Q:
A_P / A_Q = (300π) / (75π) = 4
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Newton's 2nd law says that when a larger force is applied to an object of mass m, the object will experience a larger acceleration. At the same time, you've learned that all objects experience the same acceleration in a free fall, even if their weights (the forces of gravity acting on them) are different. That sounds like a contradiction: on one hand, from the Newton's 2nd law, a larger force means larger acceleration, on the other hand when applied to motion under gravity - a larger weight (force) means the same acceleration for all objects. How do you reconcile these statements? Why isn't it a contradiction? Does gravity violate the Newton's second law or is there another explanation. Be as thorough and clear in your explanation as possible.
It is important to understand that the force of gravity acting on an object does not violate Newton's second law. It is an external force that acts on an object and produces an acceleration in it. Therefore, the acceleration due to gravity does not violate Newton's second law.
According to the Newton's second law, a force acting on a body of mass m produces an acceleration a in the body which is directly proportional to the force and inversely proportional to the mass. For instance, If a body of mass m is acted upon by a force F, then the acceleration produced in the body is given by F/m.As per the law, a larger force will produce a larger acceleration in the object.
When a body falls under gravity, it is said to experience weight. The weight of an object is the force of gravity acting on the object. According to Newton's law of gravitation, every object attracts every other object with a force proportional to their masses and inversely proportional to the square of their distance. In general, the weight of an object can be given by the formula weight = mass x acceleration due to gravity.
Therefore, as the acceleration due to gravity is the same for all objects, the weight of an object is proportional to its mass. It implies that a heavier object has more weight, while a lighter object has less weight.As per the above facts, a heavier object would require a larger force to move it than a lighter object. However, when they fall under gravity, both objects fall at the same rate. It appears as a contradiction, but the reason for it is the difference between weight and mass.
The mass of an object is a measure of the amount of matter in it, while the weight of an object is the force exerted on it by gravity.The acceleration produced in an object by an external force is not the same as the acceleration due to gravity. A force F produces an acceleration F/m, whereas the acceleration due to gravity is the same for all objects.
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the distribution of test scores shows that most students did not do well on the test; some did fine and only a few did exceedingly well. the distribution is likely to be .
The distribution of test scores shows that most students did not do well on the test; some did fine and only a few did exceedingly well. The distribution is likely to be skewed.
What is a skewed distribution?
A skewed distribution is one in which the data is not uniformly distributed but rather concentrated on one side. In simple words, a skewed distribution is one in which one tail has a greater number of observations than the other tail, with the majority of data falling in the tail with the greater number of observations.
In a symmetric distribution, the data is uniformly distributed on both sides of the median, with half of the data lying to the right and half to the left.
Thus, the distribution of test scores shows that most students did not do well on the test; some did fine and only a few did exceedingly well. The distribution is likely to be skewed.
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Help please, I will give brainiest
Type the correct answer in each box. Round your answers to the nearest hundredth.
City Cat Dog
Lhasa Apso Mastiff Chihuahua Collie
Austin 24. 50% 2. 76% 2. 86% 3. 44% 2. 65%
Baltimore 19. 90% 3. 37% 3. 22% 3. 31% 2. 85%
Charlotte 33. 70% 3. 25% 3. 17% 2. 89% 3. 33%
St. Louis 43. 80% 2. 65% 2. 46% 3. 67% 2. 91%
Salt Lake City 28. 90% 2. 85% 2. 78% 2. 96% 2. 46%
Orlando 37. 60% 3. 33% 3. 41% 3. 45% 2. 78%
Total 22. 90% 2. 91% 2. 68% 3. 09% 2. 58%
The table gives the probabilities that orphaned pets in animal shelters in six cities are one of the types listed.
The probability that a randomly selected orphan pet in an animal shelter in Austin is a dog is ______%. The probability that a randomly selected orphaned dog in the same animal shelter in Austin is a Chihuahua is ______%
The probability that a randomly selected orphan pet in an animal shelter in Austin is a dog is 11.71%. The probability that a randomly selected orphaned dog in the same animal shelter in Austin is a Chihuahua is 29.37%.
The probability that a haphazardly chosen vagrant pet in a creature covered in Austin is a canine is 11.71%.
The probability that a haphazardly chosen stranded canine in a similar creature cover in Austin is a Chihuahua is 29.37% .
2.76% + 2.86% + 3.44% + 2.65% = 11.71%
11.71/3.44 = .2937
.2937 = 29.37%
Probability is just the way that logical something is to occur.
Whenever we're uncertain about the result of an occasion, we can discuss the probabilities of specific results — how likely they are. The investigation of occasions represented by probability is called statistics.
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a supply container dropped from an aircraft by parachute hits a target with a probability of 0.37. (a) what is the expected number of container drops needed to hit a target?
The given probability is 0.37 which is the probability of a supply container dropped from an aircraft by a parachute hitting a target. So the expected number of container drops needed to hit a target is approximately 2.7027.
To find out the expected number of container drops needed to hit a target, we can use the formula given below;
E(X) = (1/p) E(X)
= (1/0.37)E(X)
= 2.7027
Thus, the expected number of container drops needed to hit a target is approximately 2.7027.
An expected value is a statistical concept that represents the theoretical average value of a random variable. It is represented as E(X).
The expected value is calculated by multiplying each possible value of the random variable by its probability and then adding all of the products.
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You are given 0.10 g samples of Na, Y. Go, and Mn. List the samples in order of the amount (moles) from smallest to largest OY
Therefore, the order of the samples from smallest to largest amount (moles) of OY is: Go, Y, Na, Mn.
In order to list the samples in order of the amount (moles) from smallest to largest OY, we need to calculate the number of moles of each element. Let's start with the given samples:Na -[tex]0.10 gY - 0.10 gGo - 0.10 gMn - 0.10 g[/tex]
Now, let's find the number of moles of each element:Na: The molar mass of Na is 22.99 g/mol.Number of moles of Na = mass of Na/molar mass of Na= 0.10 g/22.99 g/mol= 0.00435 molY: The molar mass of Y is 88.91 g/mol.Number of moles of Y = mass of Y/molar mass of Y= 0.10 g/88.91 g/mol= 0.00112 molGo: The molar mass of Go is 118.71 g/mol.Number of moles of Go = mass of Go/molar mass of Go= 0.10 g/118.71 g/mol= 0.00084 molMn: The molar mass of Mn is 54.94 g/mol.
Number of moles of Mn = mass of Mn/molar mass of Mn= 0.10 g/54.94 g/mol= 0.00182 molNow, we can list the samples in order of the amount (moles) from smallest to largest OY:Go (0.00084 mol) < Y (0.00112 mol) < Na (0.00435 mol) < Mn (0.00182 mol)
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for a school project, 10 students are working on a skit that has 2 different roles. each role can be played by anyone, and no student can play more than one role. how many different casts are possible?
Every student may take on any part, and no student may take on more than one role. Hence, it is feasible to have 45 different casts.
In contrast, there are various techniques to select r things from a set of n objects and arrange these r objects in permutations.
The permutations formula itself states that selection should come first (nCr), followed by arrangement (r).
the given :
10 students are working on a skit,
2 different roles. each role can be played by anyone
n = 10
r = 2
nPr = nCr x r!
nCr = n!/r!(n-r)!
so,
nCr = 10!/2!(10-2)!
nCr = 10x9/2x1
nCr = 45
so, the 45 different casts are possible
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find the consent of proportionality if the equation does not represent a proportional relationship select not proportional y=x/5
The answer is k = 1/5, which represents the constant of proportionality between y and x in the equation y = x/5.
What is proportion?
Proportion is a mathematical concept that describes the equality of two ratios. In other words, it is a statement that two ratios or fractions are equal.
To determine if the equation y = x/5 represents a proportional relationship, we need to check if there is a constant of proportionality between y and x.
If there is a constant of proportionality, then we can write y = kx, where k is the constant of proportionality. In other words, the ratio of y to x is always the same constant value.
To find the constant of proportionality for the equation y = x/5, we can rearrange the equation as:
y/x = 1/5
This means that the ratio of y to x is always 1/5. Therefore, there is a constant of proportionality, which is 1/5.
So, the equation y = x/5 represents a proportional relationship, and the constant of proportionality is 1/5.
Therefore, the answer is k = 1/5, which represents the constant of proportionality between y and x in the equation y = x/5.
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Hi! im new to this i i coudnt go to school today becuase im sick and im trying to do mah and i cant figure this out anyone can help,
surface area of the prism.
5yd 4yd 2yd
The surface area is
[tex]2(5\times4)+2(5\times2)+2(4\times2)=[/tex]
[tex]40+20+16=[/tex]
76 square yards
Answer:
The surface area of the prism.
5 yd, 4 yd, 2 yd
76 square yardsStep-by-step explanation:
You're welcome.
A pool charges $4 each visit or you can buy a membership for $100. Write and solve an inequality to find how many times a person should use the pool so that a membership is less expensive than paying each time. Write an inequality and solve. PLEASE HELP ME!!
Answer:
Let's say the number of visits to the pool is represented by the variable 'x'.
If a person chooses to pay per visit, the cost will be 4x dollars.
If a person chooses to buy a membership, the cost will be a one-time payment of $100.
We want to find out when the cost of buying a membership becomes less expensive than paying per visit. In other words, we want to solve the inequality:
4x > 100
To solve for x, we need to isolate the variable. We can do this by dividing both sides by 4:
x > 25
So, if a person plans to visit the pool more than 25 times, it's more cost-effective to buy a membership instead of paying per visit.
X=4 ?
X=28 ?
How to solve?
The value of x in the given linear equation of 4x = 28 is determined as 7.
What is the value of x in the linear equation?
To find the value of x in the linear equation 4x = 28, we need to isolate x on one side of the equation.
We can do this by dividing both sides of the equation by 4:
4x/4 = 28/4
Simplifying:
x = 7
Thus, identify the equation and the variable: In this case, the equation is 4x = 28, and the variable we want to solve for is x. Also simplify the linear equation by dividing both sides by 4, we get x = 7, which is the solution.
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The complete question is below:
4x = 28
find the value of x
A rocket is launched from the top of a 90 foot cliff with an initial velocity of 160 feet per second. The height, h, of the rocket after t seconds is given by the equation h=-16t^2+160t+90. How long after the rocket is launched will it be 30 feet from the ground?
The rocket will be 30 feet from the ground approximately 0.4 seconds or 9.6 seconds after it is launched.
To solve this problem, we need to find the value of t for which the height of the rocket is 30 feet. We can use the given equation to set up an equation for this as follows:
-16t² + 160t + 90 = 30
Simplifying and rearranging, we get:
-16t² + 160t + 60 = 0
Dividing by -4, we get:
4t² - 40t - 15 = 0
Using the quadratic formula, we get:
t = [40 ± √(40² - 4(4)(-15))] / (2×4)
t = [40 ± √(1840)] / 8
t = [40 ± 2×√(460)] / 8
t = 5 ± (1/2)×√(460)
Therefore, the rocket will be 30 feet from the ground at t = 5 - (1/2)×√(460) seconds or t = 5 + (1/2)×√(460) seconds. These are the two possible solutions to the equation. We can simplify them as follows:
t = 0.4 seconds or t = 9.6 seconds
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55 divided by 11 * 7 x (2 + 14)
560
1) PEMDAS so 2+14=16
2)55/11=5
3)5x7=35
4)35(16)=560
pls help me with both of them
The year that saw 164 billion dollars being spent on advertising, given the function for the advertising would be c. 1994
The dimensions of the rectangle, given the area of the rectangle would be:
Length : 12. 8 meters Width : 6.9 meters How to find the year ?The function is given by y = 0.93x² + 2.2x + 130, where y is the amount of money spent (in billions of dollars) and x is the number of years since 1990. We need to find the value of x when y = 164.
164 = 0.93x² + 2.2x + 130
0.93x² + 2.2x + 130 - 164 = 0
0.93x² + 2.2x - 34 = 0
x = 2.5
Now, we'll find the year by adding the value of x to 1990:
Year = 1990 + 2.5 = 1992.5
= 1994 which is the closest year in options
How to find the dimensions of the rectangle ?The area of the rectangle is given by:
Area = width × length
91 = (x + 2)(2x + 3)
91 = 2x² + 3x + 4x + 6
91 = 2x² + 7x + 6
2x² + 7x - 85 = 0
When solved differently:
x = 4.9
x = -3.5
Using the positive values:
Width = x + 2 ≈ 4.9 + 2 = 6.9 meters
Length = 2x + 3 ≈ 2(4.9) + 3 ≈ 9.8 + 3 = 12.8 meters
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BRAINLIEST! HURRY! What is the volume of the prism?
Enter your answer, as a mixed number in simplest form, in the box.
_ cm³
Answer:
331/2
Step-by-step explanation:
5 1/2= 11/2
3 1/2 = 7/2
11/2x7/2x6=115 1/2 = 331/2
Answer:
115.5 cm^3
Step-by-step explanation:
Volume=LengthxWidthxHeight
The values from the diagram are 3.5, 6, and 5.5
Multiply!
3.5x6x5.5=115.5
the clock on the wall at the aops office has an hour hand that's 4 cm long and a minute hand that's 8 cm long. at exactly 2:00, at what rate, in centimeters per minute, is the distance between the tips of the two hands changing?
At exactly 2:00, the distance between the tips of the two hands is changing at the rate of 4 cm/min.Therefore, at exactly 2:00, the distance between the tips of the two hands is changing at the rate of [tex]2\sqrt{13}[/tex] cm/min.
What is meant by "at exactly 2:00"?The phrase "at exactly 2:00" means that at 2:00:00, the hour hand and the minute hand overlap. Both hands are together pointing upwards in the vertical direction. At this moment, the angle between the minute hand and the hour hand is 0 degrees.How do we determine the rate of change of the distance between the tips of the two hands?We start by calculating the angle between the two hands. The angle is given by:
θ(t) = 30h - 11/2m
where h is the number of hours past midnight and m is the number of minutes past the most recent hour. At exactly 2:00, h = 2 and m = 0. Thus:
θ(t) = 30(2) - 11/2(0) = 60 degrees
Next, we use the formula for the distance between two points (the tips of the two hands). Let the hour hand be at the point (0,0) and let the minute hand be at the point (x,y).
The distance between the two points is given by:
[tex]d(t) = \sqrt{(x^2 + y^2)}[/tex]
To find x and y, we use the formulas:
x(t) = r cos θ(t)y(t) = r sin θ(t)
where r is the length of each hand. At exactly 2:00:
[tex]r = 4 cmx(t) = 4 cos 60 = 2 my(t) = 4 sin 60 = 2\sqrt{(3) m}[/tex]
Therefore: [tex]d(t) = \sqrt{(x^2 + y^2)} = \sqrt{(2 m)^2 + (2sqrt(3) m)^2)} = 2\sqrt{(13) m}[/tex]
Finally, we differentiate with respect to time t to find the rate of change of [tex]d(t):d'(t) = 2\sqrt{13}[/tex] cm/min
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PLS HELP (SORRY I KEEP ASKING QUESTIONS I HATE MATH SO I DONT RLLY PAY ATTENTION THAT WELL)
The graph shows that the rise is 3 and the run is 3, and the hypotenuse is the length between the two points.
let hypotenuse = x
using Pythagorean theorem:
x^2= 3^2 + 3^2
x^2 = 9 + 9
x= sqrt 18
x = 4.2426....
rounding to the nearest 10th:
x = 4.2
Find the are 22ft 37ft 38. 09ft 109degrees 138degrees
Answer:
B.
Step-by-step explanation:
I just took the test
Are there two equations below parallel
y = 1/3x +4 and y=-3x - 10
YES
NO
I don't know but i can help a little
Step-by-step explanation:
But If the slops are the same and the y-intercepts are different, the lines are parallel...
Pease help!!
Question below!
Answer: Line PQ is parallel to line LM
Step-by-step explanation:
We can check if they are of equal distance apart by checking if the ratios of the given lines are equal...in other words we must check if LP/PN=MQ/QN
We know that triangle PNQ is inscribed inside triangle LNM
Using the information we have we see that side LP is 18 units, PN is 16 units, MQ is 27, and QN is 24. With this information we can write out LP/PN=MQ/QN and see if it's true.
LP= 18, PN= 16, 18/16= 1.125
MQ= 27, QN=24, 27/24= 1.125
therefore, LP/PN=MQ/QN is true. Making line PQ and line LM parallel.
|x-3|\ge11 ∣x−3∣≥11 please anwser quickly
The given inequality is [tex]|x-3|/11 \geq 1[/tex]and the solution to the inequality is [tex]x \leq -8[/tex] or [tex]x \geq 14.[/tex]
We want to solve for [tex]x[/tex], which means we want to find all possible values of [tex]x[/tex] that satisfy the inequality.
To start, we multiply both sides of the inequality by 11, which gives us:
[tex]| x - 3 | \geq 11[/tex]
Now we have an inequality without any fractions. The absolute value sign means that we need to consider two cases: one where [tex]x-3[/tex] is positive, and one where [tex]x-3[/tex] is negative.
Case 1: [tex]x-3[/tex] is positive
If [tex]x-3[/tex] is positive, then [tex]| x - 3 |[/tex] is equal to [tex]x-3[/tex]. So we can rewrite the inequality as:
[tex]x - 3 \geq 11[/tex]
Adding 3 to both sides, we get:
[tex]x \geq 14[/tex]
This means that if [tex]x[/tex] is greater than or equal to 14, then the inequality is satisfied.
Case 2: [tex]x-3[/tex] is negative
If [tex]x-3[/tex] is negative, then [tex]| x - 3 |[/tex] is equal to [tex]-(x - 3)[/tex]. So we can rewrite the inequality as:
[tex]-(x - 3) \geq 11[/tex]
Multiplying both sides by -1, we get:
[tex]x - 3 \leq -11[/tex]
Adding 3 to both sides, we get:
[tex]x \leq -8[/tex]
This means that if [tex]x[/tex] is less than or equal to -8, then the inequality is satisfied.
Putting these two cases together, we get:
[tex]x \leq -8[/tex] or [tex]x \geq 14[/tex]
These are all the possible values of [tex]x[/tex] that satisfy the inequality.
To learn more about inequality follow the link:
https://brainly.com/question/30231190
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The complete question is:
Solve the equation: | x - 3 | / 11 ≥ 11 and determine the type of solution.