The sales price of the item is $48.
The sale price of an item that costs 60% of its original price which is $80 is $48. The original price of the item is $80, and it costs 60% of the original price. The amount of money we'll be spending is calculated as follows: 60 per cent of $80 (60/100) × $80= $48 Therefore, the sales price is $48. The percentage discount for the item is calculated as follows:$80 - $48 = $32
$32 is the amount of money saved due to the discount, which is then divided by the original price, $32/$80 = 0.4 or 40%. Thus, there was a 40% discount on the original price.
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Laura has a strip of ribbon 1 m long. How many one thirds strips can be cut from it
From the given information provided, Laura can cut 3 one-thirds strips from the 1 meter long ribbon.
If Laura has a strip of ribbon 1 meter long, we need to find out how many one-thirds strips can be cut from it.
To do this, we need to divide the length of the ribbon by the length of each one-third strip:
Number of one-thirds strips = Length of ribbon / Length of one-third strip
The length of each one-third strip is 1/3 meters, since one-third of a meter is required to make each strip.
So we can substitute these values into the formula:
Number of one-thirds strips = 1 meter / (1/3 meter)
Number of one-thirds strips = 1 meter x (3/1)
Number of one-thirds strips = 3
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HELPPPP
i need to have this doen by 9:17 am today pls help
im begging you
Answer:
[tex]26a - 10 = 2(13a - 5)[/tex]
When it comes to the sale of products such as pet food, the veterinary practice is at an advantage over feed stores and grocery stores because
When it comes to the sale of products such as pet food, the veterinary practice is at an advantage over feed stores and grocery stores because they have better knowledge and understanding about the pet food, and they have established trust with their customers.
What is pet food?
Pet food is a nutrient-rich food specially designed for domestic animals, like dogs, cats, and other pets. It is made from various animal and plant-based sources, such as beef, fish, and corn. Since pet food is designed to meet the nutritional needs of the pets, it must be balanced and complete to provide them with the necessary nutrients they need to be healthy and active.
Why veterinary practice is at an advantage over feed stores and grocery stores?Veterinarians are at an advantage over feed stores and grocery stores when it comes to the sale of pet food because they have the knowledge and expertise about the pet food. They are aware of the specific nutritional requirements of the pets and the various pet food brands available in the market. They can provide advice and recommendations to pet owners on what type of pet food is best suited for their pets based on their age, breed, and health conditions.
Moreover, veterinary practices have established trust with their customers. When customers know they can rely on a particular veterinary practice for quality products and trustworthy advice, they are more likely to shop there repeatedly.
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bill has a collection of 40 nickels and dimes. together, they add up to $3.50. how many does bill have of each coin?
The number of nickels Bill has is 10.
Therefore, Bill has 10 nickels and 30 dimes.
The given question is as follows.
Bill has a collection of 40 nickels and dimes.
Together, they add up to $3.50.
Bill have of each coin :
To solve the given problem, let's consider the following steps.
Step 1: Let x be the number of nickels and y be the number of dimes.
Based on the given data, we can form the following two equations:
x + y = 40 ... (1) (because Bill has 40 nickels and dimes)
0.05x + 0.10y = 3.50 ... (2) (because the sum of 40 nickels and dimes is $3.50)
Step 2: Solve the equations (1) and (2) by elimination method by multiplying equation (1) with 0.05 and subtracting it from equation (2).
0.05x + 0.05y = 2 ... (3)0.05x + 0.10y = 3.50 ... (4)
Subtracting equation (3) from equation (4),
we get0.05y = 1.50
Dividing both sides by 0.05, we get
y = 30
Therefore, the number of dimes Bill has is 30.
Step 3: Now, substitute the value of y in equation (1), we get
x + 30 = 40
Subtracting 30 from both sides, we get x = 10.
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every month, the number of friends max has on a social networking site increases by 21%. if he had 30 friends on 1 january, how many friends does he have on 1 january one year later? give your answer to the nearest integer. [answer format: integer, no units] g
Max has approximately 111 friends on January 1st of the next year.
Given that Max has 30 friends on January 1st, the number of friends increases by 21% every month.
We need to find out how many friends Max has on January 1st of the next year,
which is 12 months later.
First, we will calculate the number of friends Max has after one month: 30 + (21% of 30) = 30 + 0.21*30 = 36So, after the first month, Max has 36 friends.
Now, we will calculate the number of friends Max has after two months: 36 + (21% of 36) = 36 + 0.21*36 = 43.56 ≈ 44So, after the second month, Max has 44 friends.
Similarly, we can calculate the number of friends Max has after 12 months:30 + (21% of 30) + (21% of 30) + ... (12 times)≈ 30 + 6.3 + 7.65 + ... (12 terms)≈ 111.1
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example 5.12 the atoms of a radioactive element are randomly disintegrating. if every gram of this element, on average, emits 3.9 alpha particles per second, what is the probability that during next second the number of alpha particales omitted from 1 gram is (a) at most 6; (b) at least 2; (c) at least 3 and at most 6?
a) The probability that during next second the number of alpha particales omitted from 1 gram is at most 6 is 0.998.
b) The probability that during next second the number of alpha particales omitted from 1 gram is at least 2 is 0.985.
c) The probability that during next second the number of alpha particales omitted from 1 gram is at least 3 and at most 6 is 0.679.
This problem is an application of the Poisson distribution, which is commonly used to model the number of events occurring in a fixed interval of time. In this case, we are interested in the number of alpha particles emitted by 1 gram of the radioactive element in one second.
The average rate of emission is given as 3.9 alpha particles per second. This means that the mean or expected number of alpha particles emitted by 1 gram of the element in one second is also 3.9.
(a) To find the probability that at most 6 alpha particles are emitted from 1 gram of the element in one second, we can use the Poisson distribution with λ=3.9 and x=0, 1, 2, 3, 4, 5, or 6.
The probability is given by the cumulative distribution function (CDF) of the Poisson distribution, which can be calculated using software or a table. For example, using a Poisson table or calculator, the probability is approximately 0.998.
(b) To find the probability that at least 2 alpha particles are emitted, we can use the complementary probability: P(at least 2) = 1 - P(none or 1). Using the Poisson distribution with λ=3.9 and x=0 or 1, we find P(none or 1) = 0.015. Therefore, P(at least 2) = 1 - 0.015 = 0.985.
(c) To find the probability that at least 3 and at most 6 alpha particles are emitted, we need to add the probabilities for x=3, 4, 5, and 6. Using the Poisson distribution with λ=3.9, we can calculate P(x=3) = 0.089, P(x=4) = 0.172, P(x=5) = 0.212, and P(x=6) = 0.206. Therefore, the probability is approximately 0.679.
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Jordan is saving to buy a pair of shoes. He already has saved $30. If the shoes cost $75, write an inequality to determine how much more money he needs to save so he can buy the shoes
The inequality to determine how much more money he needs to save so he can buy the shoes is x ≥ $45
Let x be the amount of money Jordan still needs to save to buy the shoes.
The total cost of the shoes is $75, and Jordan has already saved $30. Therefore, the amount of money he still needs to save is:
x = $75 - $30
Simplifying the right side:
x = $45
So, the inequality that represents how much more money Jordan needs to save is:
x ≥ $45
This means that Jordan needs to save at least $45 more to be able to buy the shoes.
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Find the exact value of X.
In the given right angled triangle, using Pythagorean theorem, the value of x is 12.73 units.
What is Pythagorean theorem?The Pythagorean theorem, also known as Pythagoras' theorem, is a basic relationship between a right triangle's three sides in Euclidean geometry. According to this rule, the length of the squares on the other two sides add up to the length of the square whose side is the hypotenuse, or the side across from the right angle. This theory can be expressed as the Pythagorean equation, which is an equation relating the lengths of the sides a, b, and the hypotenuse c:
a² + b² =c²
What is Hypotenuse?The longest side of a right-angled triangle, or the side across from the right angle, is called the hypotenuse.
In the given right angled triangle, using Pythagorean theorem,
x² = (9[tex]\sqrt{2}[/tex] )²+ (9[tex]\sqrt{2}[/tex] )²
x² = 81×2
x = [tex]\sqrt{162}[/tex]
x = 12.73 units
Therefore, the value of x will be 12.73 units.
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how can you use a fuormula to find the sum of the measures of the interior angles of a regular polygon?
The formula to find the sum of the measures of the interior angles of a regular polygon is: S = (n - 2) * 180 where S is the sum of the interior angles, and n is the number of sides of the polygon.
This formula can be derived using the fact that the sum of the interior angles of any polygon is equal to (n - 2) * 180 degrees, where n is the number of sides.
For a regular polygon, all interior angles are equal, so we can divide the sum of the interior angles by the number of sides to find the measure of each angle. Let's call this measure x. Then we have:
S = nx
Solving for x, we get:
x = S/n
Substituting S = (n - 2) * 180, we get:
x = ((n - 2) * 180)/n
This formula gives us the measure of each interior angle of a regular polygon in terms of its number of sides. To find the sum of the measures of the interior angles, we can simply multiply the measure of each angle by the number of sides and then sum them up. Alternatively, we can use the formula S = (n - 2) * 180 directly to find the sum of the interior angles without finding the measure of each angle first.
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An automobile manufacturer of a certain model of car wants to estimate the mileage this model car gets in highway driving. The population standard deviation is known to be 5.7 mpg. How many cars does the manufacturer need to sample so that a 90% confidence interval for the mean mileage of all cars of this model will have a margin of error of 1.5
mpg?
Please show your work! I would really like to understand this :)
If an automobile manufacturer of a certain model of car wants to estimate the mileage this model car gets in highway driving. The manufacturer needs to sample at least 39 cars.
How to find the sample?We can use the formula for the margin of error in a confidence interval for a mean:
Margin of Error = z* (σ/√n)
Where:
z* is the critical value of the standard normal distribution for the desired level of confidence, which is 90% in this case.
σ is the known population standard deviation, which is 5.7 mpg.
n is the sample size we want to determine.
We want the margin of error to be 1.5 mpg, so we can set up the equation:
1.5 = 1.645 * (5.7 / √n)
where 1.645 is the z-score for 90% confidence level.
Simplifying this equation, we get:
√n = 1.645 * (5.7 / 1.5)
√n = 6.251
Squaring both sides, we get:
n = 39.07
Rounding up to the nearest integer, we get:
n = 39
Therefore, the manufacturer needs to sample at least 39 cars to estimate the highway mileage with a 90% confidence interval and a margin of error of 1.5 mpg.
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Which equation represents a line which is perpendicular to the x-axis
A line perpendicular to the x-axis is a vertical line, which means it has an undefined slope. Therefore, the equation of a line perpendicular to the x-axis is of the form x = a, where "a" is a constant.
what is 2 3/11 as an improper fraction?
Answer:
[tex]\frac{25}{11}[/tex]
Step-by-step explanation:
an improper fraction is one where the value on the numerator is larger than the value on the denominator.
2 [tex]\frac{3}{11}[/tex] is a mixed number, that is a whole number and a fraction
this can be converted to an improper fraction by summing the 2 parts , that is the whole number and the proper fraction as
2 + [tex]\frac{3}{11}[/tex]
= [tex]\frac{22}{11}[/tex] + [tex]\frac{3}{11}[/tex]
= [tex]\frac{22+3}{11}[/tex]
= [tex]\frac{25}{11}[/tex]
or
multiplying the whole number by 11 and adding 3 , over 11
[tex]\frac{2(11)+3}{11}[/tex]
= [tex]\frac{22+3}{11}[/tex]
= [tex]\frac{25}{11}[/tex]
In a class of students, the following data table summarizes the gender of the students
and whether they have an A in the class. What is the probability that a female student
does not have an A?
Has an A
Does not have an A
Female Male
4
8
5
11
A female student's probability of not receiving an A is 0.56, or 56%.
What makes probability so special?Probability and probability, as well as its cognates in various modern languages, come from the educated Latin of the Middle Ages called probabilis, which Cicero used to refer to a viewpoint as being plausible or generally accepted. Ancient French probabilite is where the word probability came from (14 c.)
We must utilise the data in the table to determine the likelihood that a female student will not receive an A.
There are 16 male students and 9 female students in the class, according to the table. Of the nine female students, four received As compared to five Bs.
Hence, the The likelihood that a female student won't receive an A is: P (Female student does not have an A) = Total number of female students / Number of female students without an A
P
Female student does not have an A (Female student does not have an A) = 5/9 P(Female student does not have an A) = 0.56 or 56%.
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There is an amoeba (a single-celled animal) on a dish.
After one hour, the amoeba divides to form two amoebas.
One hour later, each amoeba divides to form two more.
Every hour, each amoeba divides to form two more.
Write an expression for the number of amoebas after `24` hours.
An expression for the number of amoebas after 24 hours is 1 × 2²⁴ = 16,777,216
How do amoebas develop?Single-celled creatures knοwn as amοebas reprοduce asexually. An amοeba begins tο reprοduce when its genetic material dοubles, twο nuclei are fοrmed, and it begins tο alter shape by develοping a thin "waist" in the centre. Typically, this prοcedure gοes οn until the cells are finally divided intο twο.
Amοeba reprοduce typically asexually thrοugh a prοcess called binary fissiοn. The cell splits intο twο daughter cells οf equal size fοllοwing the replicatiοn οf its genetic material by mitοtic divisiοn.
a. It is given that an amοeba divides tο fοrm twο amοebas after οne hοur sο there are 2 amοebas after 1 hοur.
b. It is given that οne hοur later, each οf the twο amοebas divides tο fοrm twο mοre amοebas sο there are 2×2=4 amοebas after 2 hοurs.
c. The number οf amοebas is dοubling after each hοur since each amοeba divides intο twο amοebas every hοur. This means that the number οf amοebas after 6 hοurs can be fοund by multiplying the οriginal number οf amοebas, which was 1, by 2 six times. The number οf amοebas after 6 hοurs is then 1 × 2⁶ = 2⁶= 64 amοebas.
d. Using the same pattern frοm part (c), the number οf amοebas after 24 hοurs is 1 × 2²⁴ = 2²⁴ = 16,777,216 amοebas.
Expression = 1 × 2²⁴ = 16,777,216
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What is the weight of a 48 kg girl on Earth? Round the answer to the nearest whole number.
___N
Answer:
remember, in order to calculate the weight on earth, we need to multiply the mass of the object with the force of Gravity (9.8 m/s^2 on earth)
so, her weight would be:
48 x 9.8 = 470.4 >>>>>>> Will be 470 if we round it to the nearest whole number.
Step-by-step explanation: Hope this helps. Mark me brainliest!! :)))
Answer: 470
Step-by-step explanation:
This is for algebra 1 in grade 9. Can anyone help?
The repair costs $90 for parts, plus $70 per hour for labor describes the situation. The solution has been obtained by using the equation.
What is an equation?
An equation is an assertion that two expressions containing variables and/or numbers are equivalent. The basic driving factors behind the growth of mathematics have been the attempts to rationally answer equations, which are essentially questions.
We are given an equation of the function as C(x) = 90 + 70x.
This depicts that $90 is fixed cost whereas $70 is variable cost and is dependent on the value of x.
So, the statement that describes the given situation is that the he repair costs $90 for parts, plus $70 per hour for labor.
Hence, the fourth option is the correct option.
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Which function represents a vertical stretch of the function ƒ (x) = e^x
a)g(x)=e^x+7
b)g(x)=1/3e^x
c)g(x)=5e^x
d)g(x)=e^4x
Answer:
The function that represents a vertical stretch of the function ƒ (x) = e^x is option c) g(x) = 5e^x.
To see why, we can compare the graphs of the two functions. The graph of ƒ(x) = e^x is an exponential function that starts at the point (0,1) and increases rapidly as x increases. The graph of g(x) = 5e^x is also an exponential function, but it starts at the point (0,5), which is five times higher than the starting point of ƒ(x). This means that g(x) is a vertical stretch of ƒ(x) by a factor of 5.
Option a) g(x) = e^x + 7 is a vertical shift of ƒ(x) by 7 units, but it does not represent a vertical stretch.
Option b) g(x) = 1/3e^x is a vertical compression of ƒ(x) by a factor of 1/3, rather than a vertical stretch.
Option d) g(x) = e^4x represents a horizontal stretch of ƒ(x) by a factor of 1/4, but it does not represent a vertical stretch.
how many ways are there to put 23 identical objects into 7 distinct containers so that no container is empty?
This problem is a classic example of applying the stars and bars combinatorial method.
To solve this problem, we need to distribute 23 identical objects into 7 distinct containers so that none of the containers is empty. Let's start by assuming that each container has at least one object. This means we have distributed 7 objects, leaving 16 objects to be distributed.
We can now use the stars and bars method to distribute these 16 objects. Imagine placing all 16 objects in a line, and placing 6 dividers between them to separate them into 7 groups (one for each container). Each group will then receive the objects that are to the left of the divider.
For example, if we have the sequence OO|OOO|O|OOO|OO|OO|O, this corresponds to 2 objects in the first container, 3 objects in the second container, 1 object in the third container, and so on.
The number of ways to place the 6 dividers in the sequence of 16 objects is the same as the number of ways to choose 6 positions out of 16 to place the dividers. This can be computed using the formula for combinations:
$${16 \choose 6} = \frac{16!}{6!(16-6)!} = 8008$$
Therefore, there are 8008 ways to distribute 23 identical objects into 7 distinct containers so that no container is empty.
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The area of the patio is enter your response here , so the cost of concrete is $ enter your response here. The area of the garden is enter your response here , so the cost of soil is $ enter your response here. The total area of the deck is enter your response here , so the cost of wood is $ enter your response here. So, Yuri will spend $ enter your response here more on concrete than on soil and wood. (Type integers or decimals. )
Yuri will spend $ X more on concrete than on soil and wood.
When answering questions on Brainly, it is important to be factually accurate, concise, and professional.
It is also important to provide a step-by-step explanation of how you arrived at your answer.
The question is asking about the cost of materials for a patio, garden, and deck.
Let's break down the information we have.
Area of the patio = enter your response
Here
Cost of concrete = $ enter your response
Here
Area of the garden = enter your response
here
Cost of soil = $ enter your response
here
Total area of the deck = enter your response
here
Cost of wood = $ enter your response
here
Yuri will spend $ enter your response here more on concrete than on soil and wood.
To find the cost of each material, we need to multiply the area by the cost per unit area.
For example, the cost of concrete would be the area of the patio multiplied by the cost of concrete per unit area.
Let's call the cost per unit area for concrete C, the cost per unit area for soil S, and the cost per unit area for wood W.
Area of patio = P
Cost of concrete = C
Area of garden = G
Cost of soil = S
Total area of deck = D
Cost of wood = W
Yuri will spend X more on concrete than on soil and wood.
To find the values of P, C, G, S, D, and W, we need to use the information given in the question.
However, some values are missing.
We can use the given information to create equations that will help us find these values.
For example, we know that the total area of the deck is the sum of the area of the patio and the area of the garden, so we can write:
D = P + G
Similarly, we can write an equation for the cost of each material.
For example, the cost of concrete is the area of the patio multiplied by the cost per unit area for concrete, so we can write:
C = P * C
Similarly, we can write equations for the cost of soil and wood:
S = G * W, W = D * W
Now we have three equations and three unknowns: P, G, and D. We can solve this system of equations to find these values.
Let's solve for P and G first.
We'll use the equation
D = P + G
to eliminate G from the equations.
C = P * CS = G * WP = D - G
Substitute P = D - G into the first two equations.
C = (D - G) * CW = D * W - G * W
Now we have two equations and two unknowns: D and G.
We can solve for these values.
We'll use the equation
W = D * W - G * W
to eliminate W from the equations.
C = (D - G) * CS = G * SD = P + G = 2G - (W / C)
Substitute D = P + G into the first two equations.
C = P * C + G * CS = G * SW = P + G - DC = P * C + (D - P) * C + (W / C) * C = 2P * C + W
We can now solve for P, G, and D.
P = (C + S + W / C) / 2G = (S + W / C) / 2D = P + G = (C + S + W / C) / 2 + (S + W / C) / 2P = enter your response
here
C = enter your response
here
S = enter your response
here
W = enter your response
here
G = enter your response
here
D = enter your response
here
Now we can find the value of X, which is the difference between the cost of concrete and the combined cost of soil and wood.
X = C - (S + W)X = enter your response.
The area of the patio is enter your response here , so the cost of concrete is $ enter your response here. The area of the garden is enter your response here , so the cost of soil is $ enter your response here. The total area of the deck is enter your response here , so the cost of wood is $ enter your response here.
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Question:
Yuri bought a new house. The diagram shows the layout of his backyard. Yuri is designing improvements that he wants to make. Yuri plans to fill the patio with concrete, the garden with a special soil mixture, and the remaining areas that surround the hot tub with a wood deck. The table shows the costs associated with each project. How much more will Yuri spend on concrete than on soil and wood?
A 145 pound person burns 420 calories per hour riding an exercise bicycle at a rate of 15 miles per hour. Write a function rule to represent the total calories burned over time by that person. Explain how the information in the problem related to the function
Answer: 580
Step-by-step explanation: i learned that just like 1 hour ago in school
license plates are made using 2 letters followed by 2 digits. how many plates can be made if repetition of letters and digits is allowed?
The number of license plates that can be made if repetition of letters and digits is allowed is:
67,600
How to determine the number of plates when repeating the letters and numbers?Can be found by multiplying the number of possibilities for each position.
License plates are made using 2 letters followed by 2 digits. In this case, repetition is allowed, which means that each of the 2 letters can be any of the 26 letters of the English alphabet, and each of the 2 digits can be any of the 10 digits from 0 to 9. Thus, the total number of possible license plates can be found by multiplying the number of possibilities for each position.
There are 26 choices for each of the two letter positions, and 10 choices for each of the two digit positions, so the total number of possible license plates is:
26 x 26 x 10 x 10 = 67,600
Therefore, there are 67,600 plates that can be made if repetition of letters and digits is allowed.
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A publisher reports that 75% of their readers own a particular make of car. A marketing executive wants to test the claim that the percentage is actually different from the reported percentage. A random sample of 250 found that 69% of the readers owned a particular make of Car. Find the value of the test statistic. Round your answer to two decimal places
Rounded to two decimal places, the value of the test statistic is 0.41.
The value of the test statistic to compare the publisher's reported percentage of 75% and the marketing executive's claim that the actual percentage is different can be found by using the formula z = (p1 - p2)/(sqrt[p*(1-p)*((1/n1)+(1/n2))]), where p is the pooled proportion, p1 is the proportion of the publisher's readers owning the particular make of car, p2 is the proportion of the random sample owning the particular make of car, n1 is the total number of the publisher's readers, and n2 is the total number of the random sample.
In this case, p = [tex](75% + 69%)/2 = 72%, p1 = 75%, p2 = 69%, n1[/tex]is unknown, n2 = 250. Thus, the test statistic is z =[tex](75%-69%)/(sqrt[72%(1-72%)((1/n1)+(1/250))]) = 0.41.[/tex]
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Find the slope of the line that passes through (2,1) and (0,-2) with explanation please
Answer: 3/2
Step-by-step explanation:
To find the slope of the line that passes through the points (2, 1) and (0, -2), we can use the formula:
m = (y2 - y1) / (x2 - x1)
where:
m = slope of the line
(x1, y1) = coordinates of the first point
(x2, y2) = coordinates of the second point
Plugging in the values we have, we get:
m = (-2 - 1) / (0 - 2)
m = -3 / -2
m = 3/2
Therefore, the slope of the line that passes through the points (2, 1) and (0, -2) is 3/2.
Find an angle � θ coterminal to − 90 6 ∘ −906 ∘ , where 0 ∘ ≤ � < 36 0 ∘ 0 ∘ ≤θ<360 ∘
The angle that satisfies the necessary requirements is 1041° - 2(360°) = 321°. Coterminal angles are those with the same terminal point in the standard position.
To understand, follow the 2 basic steps:
Step 1: Find the specified angle.
Step 2: Finding a coterminal angle.
Tally up or tally down a multiple of 360.
θ = 1041°
Every multiple of 360 degrees added or subtracted results in an angle that is coterminal with the provided angle.
Hence, 1041° - 2(360°) = 321° is an angle that satisfies the necessary requirements.
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How to elimination 18x-6y=-20 -9x+3y=15
The elimination of the equations 18x-6y=-20 and -9x+3y=15 is 0 = 10, which is a contradiction. This means that there is no solution to the system of equations.
What is an elimination?
To eliminate one of the variables, we need to manipulate one or both of the equations so that when we add them together, one of the variables is eliminated.
Let's start with the given equations:
18x - 6y = -20
-9x + 3y = 15
We can see that the coefficients of y in both equations are opposite, which means we can eliminate y by adding the two equations together. However, we need to make sure the coefficients of y have the same absolute value, so we'll multiply the second equation by 2:
18x - 6y = -20
-18x + 6y = 30
Now we can add the two equations together:
0x + 0y = 10
This equation simplifies to 0 = 10, which is a contradiction. This means that there is no solution to the system of equations. In other words, the two equations represent two parallel lines that never intersect.
Alternatively, we can recognize that the two equations represent the same line when simplified, since the second equation is simply half of the first equation. In this case, there are infinitely many solutions, since any point on the line satisfies both equations.
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Complete question is: The elimination of the equations 18x-6y=-20 and -9x+3y=15 is 0 = 10.
Work out (1 + 9)² +5
Answer:
105
Step-by-step explanation:
10² is 100
100+5=105
how long will it take for $500 to amount to $850 at 10% simple interest? question 37 options: 7 years 5 years 3.5 years 10 years none of these
[tex]~~~~~~ \textit{Simple Interest Earned Amount} \\\\ A=P(1+rt)\qquad \begin{cases} A=\textit{accumulated amount}\dotfill & \$ 850\\ P=\textit{original amount deposited}\dotfill & \$500\\ r=rate\to 10\%\to \frac{10}{100}\dotfill &0.10\\ t=years \end{cases} \\\\\\ 850 = 500[1+(0.1)(t)] \implies \cfrac{850}{500}=1+0.10t\implies \cfrac{17}{10}=1+0.10t \\\\\\ \cfrac{17}{10}-1=0.10t\implies \cfrac{7}{10}=0.10t\implies \cfrac{7}{(10)(0.10)}=t\implies 7=t[/tex]
Sasha had 30 minutes to do a three-problem quiz. She spent 8 3/4
minutes on questions A and 5 1/2
minutes on question B. How much time did she have left for question C?
abc is a right triangle with points a 2,5 b 2,0 and c x,0. if the area of abc is 25 square units, what us the equation of ac?
As the given abc is a right triangle with points a(2, 5), b(2, 0), and c(x, 0). The area of 'abc' is 25 square units. and the equation of AC is x = 5√5.
The equation of ac has to be found. Since triangle ABC is right-angled, it can be shown that
AC² = AB² + BC²
Finding the lengths of AB and BC before using the Pythagorean theorem to find AC.
Using the distance formula,
AB =√(5²+0²)
= √25
= 5,
And BC = √(x²+0²)
= √x²
= x.
Area of a right triangle = ½(base × height)
Here base = AB and height = BC,
So, ½ × 5 × x = 25
⇒ 5x = 50
⇒ x = 10
Now, to find AC, use the Pythagorean Theorem.
AC² = AB² + BC²
= 5² + 10²
= 25 + 100
= 125AC
= √125
= 5√5
Thus, the equation of AC is x = 5√5. Answer: x = 5√5.
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The perimeter of a rectangular garden is 43. 8 feet. Its length is 12. 4 feet what is its width
The width of the rectangular garden is 9.5 feet.
Given that the perimeter of a rectangular garden is 43.8 feet and its length is 12.4 feet.
Let's assume the width of the rectangular garden be "w".
Now we need to find the width of the garden.
Solution: Perimeter of a rectangular garden is given by the formula: P = 2(l + w)
where l = length and w = width.
Substituting the given values in the above formula,
we get43.8 = 2(12.4 + w)
We can solve for "w" by simplifying the above equation.
43.8 = 24.8 + 2w43.8 - 24.8 = 2w19 = 2w
Dividing both sides by 2,we get
w = 9.5 feet.
Therefore, the width of the rectangular garden is 9.5 feet.
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