What is the length of line segment KJ?
A. 2√3 units
B. 3√2 units
C. 3√5 units
D. 3√3 units
Answer:
the answer is the option C
[tex]KJ=3\sqrt{5}\ units[/tex]
Step-by-step explanation:
we know that
The triangle KMJ is a righ triangle
so
Applying the Pythagoras Theorem
[tex]KJ^{2}=KM^{2}+MJ^{2}[/tex]
in this problem we have
[tex]KM=6\ units[/tex]
[tex]MJ=3\ units[/tex]
substitute
[tex]KJ^{2}=6^{2}+3^{2}[/tex]
[tex]KJ^{2}=45[/tex]
[tex]KJ=\sqrt{45}=3\sqrt{5}\ units[/tex]
Rita and Tina each make $11 an hour working as cashiers at a supermarket. Last week, Rita worked r hours while Tina worked t hours. Rita also worked overtime hours during the week, for which she was paid an extra $32 flat wage. Which expressions represent the total weekly wages of both Rita and Tina? Rita and Tina's total weekly wages can be represented as 11(r)(t) + 32 (11r + 32) + 11t (11t + 32r) + 11r , 11(r + t) + 32 11(r + t) + 32r 11(rt) + 32 , or 11r + 11t + 32 11rt + 32 11r + 32t + 11
Alvin is 6 years older than Elga. The sum of their ages is 106 . What is Elga's age?
Write an equation of a vertical line passing through the point (5,-4). Show all work.
How long will it take to have R30 000 for a trip to Europe if I invest R20 000 now at 15% per year,
compounded quarterly?
Ron is five years older than twice his cousin Pats age. The sum of their ages is less than 35.
What is the greatest age that Pat can be.
A) 7
B)8
C)9
D)10
Answer:
C. 9
Step-by-step explanation:
Ron is five years older than twice his cousin's age. Lets assume that Pat's age is 'x' years.
So Ron's age is [tex]2\times x+5=2x+5[/tex]
The question says:
[tex]x+2x+5<35[/tex]
[tex]3x+5<35[/tex]
[tex]3x<35-5[/tex]
[tex]3x<30[/tex]
[tex]x<10[/tex]
Pat's age [tex](x)[/tex] should be less than 10. Therefore, the greatest age (in integer) that Pat can be is 9 years.
solve
5x+3y=-27
-9x+2y=19
The sum of a number and its square is 210. find the number(s).
The required number, whose sum with its square is 210, is -15 and 14.
Given that,
The sum of a number and its square is 210. To determine the number(s).
In mathematics, it deals with numbers of operations according to the statements. There are four major arithmetic operators, addition, subtraction, multiplication, and division,
Here,
Let the number be x,
according to the question,
x + x² = 210
x² + x -210 = 0
x² + 15x - 14x - 210 = 0
x(x + 15) -14 (x + 15) = 0
(x + 15)(x - 14) = 0
x = -15 and 14
Thus, the required number, whose sum with its square is 210, is -15 and 14.
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What is 60% off of 33.00
To find 60% off of $33.00, you multiply 33 by 60, then divide the product by 100. The result is $19.80, which is the discount amount. So after the discount, the cost is $13.20.
Explanation:To find out what 60% off of $33.00 is, you need to multiply 33.00 by 60 and then divide that product by 100, as percentages are always out of 100. Here's the process:
Multiply 33.00 by 60 to get 1980.00. Then divide 1980.00 by 100 to convert the result into a dollar amount. You get 19.80.
So, 60% off of $33.00 equals $19.80. Hence, after a 60% discount, you would pay $13.20 (33 - 19.80), as this is the remaining cost after the discount has been applied.
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Andrea is selling candles as a fundraiser. she spent $50 on supplies for making the candles. she plans to sell the candles for $10 each. her profit can be modeled by c(x)=10x-50. what is the domain and range of the function
The domain will consist of all non-negative real numbers (x ≥ 0).
And, the range will consist of all real numbers (-∞, +∞).
Given that;
The function is,
c (x) = 10x - 50
Now for the domain and range of the function c(x) = 10x - 50,
Since the domain refers to all the possible input values (x) for the function.
In this case, since c(x) represents the profit from selling candles, x would represent the number of candles sold.
The number of candles sold cannot be negative, as it wouldn't make sense to sell a negative number of candles.
So, the domain will consist of all non-negative real numbers (x ≥ 0).
And, The range refers to all the possible output values (c(x)) of the function.
In this case, c(x) represents the profit. The profit can be any real number because it can be positive, negative, or zero.
Therefore, the range will consist of all real numbers (-∞, +∞).
Thus, Domain: All non-negative real numbers (x ≥ 0).
Range: All real numbers (-∞, +∞).
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Which is a way to check the answer 120 divided by 4 = 30
What is the solution to the equation using the replacement set {2, 3, 4} 6+x/2=8
Petrolyn motor oil is a combination of natural oil and synthetic oil. It contains
4
liters of natural oil for every
5
liters of synthetic oil. If
296
liters of natural oil are used, how many liters of Petrolyn oil will be made?
how do you subract polynominals plz explain
The amounts of industrial waste generated in a region during two years were 31,900,000 tons and 53,400,000 tons. What was the total industrial waste generated over these two years in the region, expressed in scientific notation?
What is the length of hn¯¯¯¯¯¯ ? segment a n with point h between a and n. congruency markings on segment a h and segment h n. segment a n is labeled as being 38 units long enter your answer in the box?
Answer:
The length of HN is 19 unit.
Step-by-step explanation:
Consider the provided information:
It is given that the length of line segment AN is 38 units.
Now consider figure 1:
It is given that the point H is in between A and N. Also with the concurrency markings on segment AH and segment HN.
Therefore, the length of the segment AH = HN
AH + HN = AN
Consider the length of AH = HN = x
Therefore,
[tex]x+x=38[/tex]
[tex]2x=38[/tex]
[tex]x=\frac{38}{2}[/tex]
[tex]x=19[/tex]
Hence, the length of HN is 19 unit.
The sum of three consecutive even integers is 174 what are the integers?
The required three consecutive even integers are 56, 58, and 60.
Given that,
The sum of three consecutive even integers is 174 what are integers is to be determined?
Arithmetic progression is the series of numbers that have common differences between adjacent values
Here,
Let the three even integers be 2x, 2x+ 2 and 2x + 4
Now, accoding to the question,
2x + 2x + 2 + 2x + 4 = 174
6x + 6 = 174
x = 28
Now,
2x =28 * 2 = 56
2x + 2 = 56 + 2 = 58
2x + 4 = 56 + 4 = 60
Thus, the required three consecutive even integers are 56, 58, and 60.
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Please help don’t know how to do it iv tried and can’t figure it out. Please help thank you!
Suppose g is an odd function and let h = f ∘ g. is h always an odd function?
Final answer:
The composition h = f о g is only guaranteed to be an odd function if both g and f are odd functions. If f is an even function or neither odd nor even, h will not necessarily be an odd function. The property of the composition depends on the nature of both functions involved.
Explanation:
Whether the composition of functions h = f о g is always an odd function when g is an odd function depends on the nature of f. If g(x) is an odd function, it follows that g(-x) = -g(x). However, for h to also be odd, f must satisfy the condition h(-x) = -h(x). This can only be the case if f is also an odd function.
If f were an even function, then f(g(-x)) = f(-g(x)) would equal f(g(x)) due to the even property of f. In this scenario, h would not be an odd function since h(-x) = f(g(-x)) = f(g(x)) = h(x), which violates the definition of an odd function.
When an odd function and an even function are multiplied, the result is an odd function, as exemplified by g(x) = x³ - 3x and h(x) = x². But when composing functions, the outer function's properties dominate the result. Therefore, the composition h = f о g can only be assured to be odd if f itself is odd.
Suppose you write a sum of numbers as a product of their GCF and another sum. What is the GCF of the number in the other sum? Explain
How many times can 167 go into 1135.
Which of the following is not true regarding sets of numbers?
A-All rational numbers are integers.
B-All whole numbers are rational numbers.
C-All irrational numbers are real numbers.
D-All integers are rational numbers.
Answer:
A:All rational numbers are integers
Step-by-step explanation:
We are given that a set of numbers
We have to find not true statement about the regarding set of numbers
We know that all integers are rational number but all rational number .
are not integers.
All whole numbers are rational number but all rational number are not whole numbers.
All irrational numbers are real numbers but all real numbers are not irrational numbers.
Hence, option A is true.
Answer:All rational numbers are integers.
The amount of jen's monthly phone bill is normally distributed with a mean of $76 and a standard deviation of $9. what percent of her phone bills are between $49 and $103
Approximately 99.73% of Jen's phone bills are between $49 to $103. This is calculated by transforming the prices into z-scores regarding the normal distribution and then checking these z-scores in a standard normal distribution table.
Explanation:The problem is a question about the normal distribution. Using the properties of a normal distribution, we can solve it as follows:
First, transform the phone bill amounts into z-scores. The z-score is the number of standard deviations from the mean.For $49, the z-score is (49 - 76) / 9 = -3.For $103, the z-score is (103 - 76) / 9 = 3.Next, look up these z-scores in a standard normal distribution table or use a calculator that can calculate areas under the normal distribution.The table or the calculator will give you the percent of all observations falling below these two scores.The area to the left of z = 3 (or to the right of z = -3) is about 99.865%, and the area to the left of z = -3 is about 0.135%. Finally, subtract the percentages to get the percent of phone bills between $49 and $103.This is 99.865% - 0.135% = 99.73%.In conclusion, about 99.73% of Jen's phone bills are between $49 and $103.
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99.74% of Jen's monthly phone bills are between $49 and $103.
To answer this question, we need to understand the properties of the normal distribution. For a normally distributed variable with a mean (μ) of $76 and a standard deviation (σ) of $9, we can use the Z-score formula:
[tex]Z = \frac{(X - \mu)}{\sigma}[/tex]
We now convert $49 and $103 to Z-scores:
For $49:
[tex]Z = \frac{(49 - 76)}{9} = -3[/tex]
2. For $103:
[tex]Z = \frac{(103 - 76)}{9} = 3[/tex]
Next, we use the Z-table to find the probabilities corresponding to these Z-scores:
For Z = -3, the probability is 0.0013 (or 0.13%)
For Z = 3, the probability is 0.9987 (or 99.87%)
To find the percentage of phone bills between $49 and $103, we subtract these values:
[tex]P(49 < X < 103) = 0.9987 - 0.0013 = 0.9974[/tex]
Finally, converting this to a percentage, we get:
[tex]0.9974 \times 100\% = 99.74\%[/tex]
Therefore, 99.74% of Jen's monthly phone bills are between $49 and $103.
Factor the expression -24x+32
Which reason supports the true statement that angle1 and angle8 are supplementary?
m || n with
transversal t
What do you do to check whether a number is rational or irrational? In your explanation, use an example of an irrational and rational number.
Can someone check my answer, please? I would deeply appreciate it.
"Rational numbers are numbers that can be written in fraction form. The numbers are all integers. Irrational numbers are numbers that cannot be written as a fraction. They are non-repeating and nonterminating decimals. For example 6.12385546972578945213666479952145412639854845256987452874526874125874........ Is an irrational number. And 1/6, 2,9, and 3/4 are all rational numbers."
The selling price s, of an item is s=c+me, where c is the cost of the item and m is the percent markup based on the cost. What is the formula solved for m?
Study the Proof Given.
List the reasons for Items 2,3, & 4.
Right the number and then the answer.
A snowmobile traveled 32 miles in 2 1/3 hours. The distance is the product of the rate and the time. To the nearest tenth, what was the average speed of the snowmobile? Enter your answer in the box.
divide 32 miles by 2 1/3 hours
32/2.33333 = 13.7143
to nearest tenth = 13.7 miles per hour
Answer: [tex]13.7\text{ miles per hour}[/tex].
Step-by-step explanation:
Given : A snowmobile traveled 32 miles in [tex]2\dfrac{1}{3}[/tex] hours i.e.[tex]\dfrac{7}{3}[/tex] hours.
The distance is the product of the rate and the time.
i.e. The formula we use to find the average speed is given by :-
[tex]\text{Average Speed}=\dfrac{\text{Distance}}{\text{Time}}\\\\\Rightarrow\ \text{Average Speed}=\dfrac{32}{\dfrac{7}{3}}=\dfrac{32\times3}{7}=13.7142857143\approx13.7\text{ miles per hour}[/tex]
Hence, the average speed of the snowmobile was [tex]13.7\text{ miles per hour}[/tex].
paige deposited $490.28 in a savings account that earns 3.7% simple interest. what is paige’s account balance after eleven years