Answer: 6 and 8
Step-by-step explanation: A right triangle is a triangle with one angle that measures 90 degrees. The side opposite the right angle is called the hypotenuse, and the other two sides are called the legs. In this case, the hypotenuse is 10cm long.
If one angle of the triangle is 40 degrees, then the other angle must be 90-40 = 50 degrees. The remaining two angles of a triangle must add up to 180 degrees, so the third angle is 180-40-50 = 90 degrees. This means that the triangle is a right triangle, and we can use the Pythagorean theorem to find the lengths of the legs.
The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the legs. In this case, we have a2 + b2 = c2, where a and b are the lengths of the legs and c is the length of the hypotenuse.
Substituting the values from the problem, we have a2 + b2 = 102, which simplifies to a2 + b2 = 100. Since we don't know the values of a and b, we can't solve for them directly. However, we can use the fact that the angle opposite the longer leg is 50 degrees, and the angle opposite the shorter leg is 40 degrees. This means that the longer leg is the opposite side of the 50-degree angle, and the shorter leg is the opposite side of the 40-degree angle.
Since the longer leg is opposite the 50-degree angle, and the shorter leg is opposite the 40-degree angle, we can use the tangent function to find the ratio of the lengths of the legs. The tangent of an angle is defined as the ratio of the opposite side to the adjacent side, so we have tangent(50 degrees) = opposite side / adjacent side = a / b, and tangent(40 degrees) = opposite side / adjacent side = b / a.
Solving for a and b, we have a = b * tangent(50 degrees) and b = a * tangent(40 degrees). Since the legs are the opposite sides of the 40- and 50-degree angles, we can substitute the values from the problem to get a = b * tangent(50 degrees) = 100 * tangent(50 degrees) and b = a * tangent(40 degrees) = 100 * tangent(40 degrees).
To find the values of tangent(50 degrees) and tangent(40 degrees), we can use a calculator or look up the values in a table of trigonometric functions. We find that tangent(50 degrees) = 1.191753592594, and tangent(40 degrees) = 0.839099631177. Substituting these values into the equations for a and b, we have a = 100 * 1.191753592594 = 119.1753592594 and b = 100 * 0.839099631177 = 83.9099631177.
Rounding to the nearest whole number, we have a = 119 and b = 84. The lengths of the legs of the triangle are therefore 6 and 8.
The figure is a kite with sides and angles drawn to scale. Solve for x, y and z.
Xx=
y =
Z=
y+4
13
000
63° 3x - 1
3zº
2x
[tex]y+4=13 \implies \boxed{y=9}\\\\2x=3x-1 \implies \boxed{x=1}[/tex]
Additionally, [tex]63=3z \implies \boxed{z=21}[/tex]
In a class of students, the following data table summarizes how many students have a
cat or a dog. What is the probability that a student chosen randomly from the class
has a cat or a dog?
The probability that a student is chosen randomly from the class has a cat or a dog is 26/29.
What is the probability?It is based on the probabilities that something could happen. The theory of probability primarily relies on the justification for probability. A coin is tossed, for instance, and the theoretical likelihood of randomly receiving a head is 1 in 2.
explanation:
The formula of probability is defined as the ratio of a number of favorable outcomes to the total number of outcomes.
P(E) = Number of favorable outcomes / total number of outcomes
The total strength of the class is 29
The probability that a student is chosen randomly from the class has a cat or a dog = Number of favorable outcomes / total number of outcomes
P(E) = 26/29
Hence, The probability that a student is chosen randomly from the class has a cat or a dog is 26/29.
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What is 4.5 repeating as a fraction?
Answer:
4.5 as a fraction is 9/2.
Step-by-step explanation:
Please give the brainliest.
PLEASE HELP ILL GIVE BRAINLIEST AND STUFF!!!!!
Answer:
The distributions of the income of the 3 states are pretty similar. The highest income in Maine is 50s, in Indiana it is pretty evenly spread out and Connecticut is highest in 60/70 and has multiple stragglers in 170 - 200 and a few near 300. The main place where most of the plot points are is 10 - 150.
Not completely sure if this helps, but I hope it does.
Fabio and Carlos play on a basketball team together. In the last game, Fabio had 7 points less than 2 times as many points as Carlos. Fabio scored 31 points in the game. How many points did Carlos score?
Carlos points are 12
Let , Fabio points = x= 31
Carlos points = Y
Fabio had 7 points less than 2 times as many points as Carlos.
X = 2Y - 7
X = 2Y - 7
X + 7 = 2Y
Y = (x + 7)/2
X = (31 - 7)/2
x = 24/2
X = 12
Carlos points are 12
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i need help with this please!!
There is no horizontal asymptote since n > m.
What is the explanation?Find the place where the phrase x 2 x 2 x 15 x 2 x 12 is undefined.
x = 0
When n is the degree of the numerator and m is the degree of the denominator, the rational function R (x) = an x n b x m is used.
1. The x-axis, with y = 0, is the horizontal asymptote if n m.
2. If n = m, then the line y = a b is the horizontal asymptote.
3. There is no horizontal asymptote if n > m. (there is an oblique asymptote).
Identify n and m.
n= 4 m = 2
There is no horizontal asymptote since n > m.
Domain and Range
Domain: (−∞,0)∪(0,∞),{x|x≠0}
Range: (−∞,∞),{y|y∈R}
Oblique Asymptotes: y = x 2 x 3 x 12.
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Given x>0x>0 and y>0,y>0, select the expression that is equivalent to [tex]\sqrt[4]{256x^6y^10}[/tex]
By simplifying the expression we get [tex]4x^{\frac{3}{2} }y^{\frac{5}{2} }[/tex]
What is square root ?A number can be obtained by multiplying the square root of that integer by itself. The word "square root" is represented by the symbol [tex]\sqrt[2]{}[/tex] .The opposite of squaring an integer is finding its square root.
According to the given information
Given x > 0
y > 0
we need to simply the following expression
[tex]\sqrt[4]{256x^{6}y^{10} }[/tex]
By simplifying
we get
= [tex](4^{4}x^{6} Y^{10}) ^{\frac{1}{4} }[/tex]
= [tex]4x^{\frac{6}{4} } y^{\frac{10}{4} }[/tex]
= [tex]4x^{\frac{3}{2} }y^{\frac{5}{2} }[/tex]
Hence
By simplifying the expression we get [tex]4x^{\frac{3}{2} }y^{\frac{5}{2} }[/tex]
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40-(-16)=
Can someone help me with this please I really am confused
Answer:
56
Step-by-step explanation:
When you subtract a negative number. Just consider it addition.
So, 40+16
It's very simple from there.
Answer:
56!
Step-by-step explanation:
The question is 40 minus negative 16.
When you subtract a negative, it's the same as adding.
So 40 - (-16) is the same as 40 + 16, which equals 56.
Example:
If you have 3 apples, and you remove negative 3 apples from 3, now you have 6.
So, 3 - (-3) = 6.
The larger number i 18 more than twice the maller. If the un of the number i 93 find both number
Both a smaller and a bigger number are 25 and 68
What is sum of numbers?The outcome or conclusion we get at when we add two or more integers is known as the SUM. example the total of the addends, 6, and 4, is 10. In other words, we may argue that 8 plus 5 equals 13 or that 8 plus 5 equals 13.
Here, we've been given two numbers, one smaller and one bigger, where the smaller number is X and the larger number is 18 more than twice the smaller number.
2X + 18 is the greater number.
Because the total is now 93, X + (2X+18) = 93
3X = 93 - 18 .
X = 25
larger number will be 2(25) + 18 = 68
Thus the numbers are smaller number is 25 and larger number is 68.
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a restaurant offers a choice of 4 salads, 5 main courses, and 3 desserts. how many possible 3-course meals are there?
Using the Fundamental Counting Theorem, it is found that there are 60 possible 3-course meals.
Given,
In the question:
A restaurant offers a choice of 4 salads, 5 main courses, and 3 desserts.
To find the how many possible 3-course meals are there?
Now, According to the question:
Let's know:
What is the Fundamental Counting Theorem?
It is a theorem that states that if there are n things, each with ways to be done, each thing independent of the other, the number of ways they can be done is:
[tex]N=n_1[/tex] × [tex]n_2[/tex] × [tex]n_3[/tex]... ×[tex]n_n[/tex]
In this problem, considering the number of salads, main courses and desserts, we have that:
[tex]n_1=4 , n_2=5,n_3=3[/tex]
The total number of options is given by:
N = 4 × 5 × 3
N = 60
Hence, Using the Fundamental Counting Theorem, it is found that there are 60 possible 3-course meals.
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Gerald is conducting an experiment with 3 possible outcomes. Kasey is conducting an experiment with 20 possible outcomes. Which statement best relates the possible outcomes to the number of trials needed to produce results similar to their predicted outcomes?
Answer:
Step-by-step explanation:
The number of trials needed to produce results similar to their predicted outcomes is likely to be higher for Kasey's experiment with 20 possible outcomes than for Gerald's experiment with 3 possible outcomes.
2. A loan is amortized over five years with mnthly payments at a nominal interest rate of 9%
compounded monthly. The first payment is ₱10,000 and is to be paid one month from the
date of the loan. Each succeeding monthly payment will be 2% lower than the prior payment.
Calculate the outstanding loan balance immediately after the 40th payment is made.
Answer:
Step-by-step explanation:
hard
The second and third terms of the fibonancci sequence are x and y. what is the first, fourth and fifth term
Answer:
the first term = y-x
and the fourth term= y+x
and the fifth term = 2y+x
Step-by-step explanation:
Write the equation of the line in
fully simplified slope-intercept form.
the equation of the straight line is y = -x-7
What is equation straight line?
Y = mx + c is the general equation for a straight line, where m denotes the line's slope and c the y-intercept. It is the version of the equation for a straight line that is used most frequently in geometry. There are numerous ways to express the equation of a straight line, including point-slope form, slope-intercept form, general form, standard form, etc. A straight line is a geometric object with two dimensions and infinite lengths at both ends. The formulas for the equation of a straight line that are most frequently employed are y = mx + c and axe + by = c. Other versions include point-slope, slope-intercept, standard, general, and others.
In the graph the slope m = -1
the y-intercept will be -7
Hence the equation of the st. line is y = -x-7
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You ask your best friend to lend you 200 to buy your favourite toy. She says she can lend you the money
only if you give her an extra 2 for every month that passes before you return it.
What is the annual rate of interest she is charging you?
The annual rate of interest she is charging you is 12%.
Given that, you ask your best friend to lend you $200 to buy your favorite toy.
What is the rate of interest?An interest rate tells you how high the cost of borrowing is, or high the rewards are for saving. So, if you're a borrower, the interest rate is the amount you are charged for borrowing money, shown as a percentage of the total amount of the loan.
Here,
Extra money per month =$2
Extra money per year = $2×12
Extra money per two year = 2×2×12 = 4×12 = $48
Money lend = $200
Money given after two years = $(200+48) = $248
Now, the rate of interest can be find using SI=(P×R×T)/100
48= (200×R×2)/100
⇒ 48= 4R
⇒ R=12%
Hence, the annual rate of interest she is charging you is 12%.
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"Your question is incomplete, probably the complete question/missing part is:"
You ask your best friend to lend you $200 to buy your favorite toy. She says she can lend you the money only if you give her an extra $2 for every month that passes before you return it. What is the total amount you must pay her if you return it after two years? rupees What is the annual rate of interest she is charging you?
............ i need help past due
In right triangle ABC, m∠C=3y-10, m∠B=y+40, and m∠A=90 What is the measure of ∠C?
The unknown angle of the right angle triangle is as follows:
∠C = 35°How to find the angle of a right angle triangle?A right angle triangle is a triangle that has one of its angles as 90 degrees. The sides of a right angle triangle can be named base on the position of the angles. The sides includes hypotenuse side, opposite side and adjacent side.
The sum of angles in a right angle triangle is 180 degrees. Therefore, let's find the ∠C in the triangle ABC.
Therefore,
180 = ∠A + ∠B + ∠C
m ∠B = y + 40
m ∠C = 3y - 10
m ∠A = 90°
Hence,
180 = 3y - 10 + y + 40 + 90
180 = 4y + 120
180 - 120 = 4y
y = 60 / 4
y = 15
Hence,
m ∠C = 3(15) - 10
m ∠C = 45 - 10
m ∠C = 35 degrees
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Help me please with this math question find the equation that matches this table
The equation that matches this table is X=Y*k,k=12, Hence Given table is direct variation.
What is Direct variation?X=12,Y=1
X=Y*kk=12=1*12=12X=24,Y=2
X=Y*kk=12=2*12=24 and so on.The relationship between two variables in which one is a constant multiple of the other is referred to as direct variation. For instance, two variables are said to be in proportion when one affects the other. b = ka is the equation if b is directly proportional to a. (where k is a constant). When two variables are coupled in a way that ensures the ratio of their values never changes, this relationship is referred to as being in direct variation. Different mathematical structures are used to express direct variation. Since the ratio of y to x never changes, y and x fluctuate directly in equation form.As follows is the Direct Variation Formula:X=KYTo learn more about direct variation refer to:
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What is the value of x?
Enter your answer in the box.
Step-by-step explanation:
angle bisector theorem :
the ratio of the 2 baseline segments is the same as the ratio of the 2 legs of the main triangle.
in our case :
44.8/56 = (x + 4)/35
x + 4 = 44.8×35/56 = 44.8×5/8 = 28 mm
x = 24
FYI : one way of explaining the theorem is : we could see this as 2 projections originating from E at the same angle but onto a tilted projection screen.
the length on the projection screen (HD or GD) is directly related to the distance from the projection point to the end of the tilted projection : ED or EG. and so the ratios of both projections must be equal (due to the equal angle).
so, in our case
35/56 = (x + 4)/44.8
which leads, of course, to the same result
44.8×35/56 = x + 4
Answer and explain for 10 points!
Answer: 100
Step-by-step explanation:
To solve this expression, we can start by performing the operations inside the parentheses first:
560 divided by 7 + 140 divided by 7
= 80 + 20
= 100
So the result of the expression is 100.
I hope this helps! Let me know if you have any questions.
Solve each system by elimination: 4x+3y=19 3x-4y=8
Answer: x =4 , y =1
Step-by-step explanation:
Multiply the first equation by 4,and multiply the second equation by 3.
4(4x+3y=19)
3(3x−4y=8)
Becomes:
16x+12y=76
9x−12y=24
Add these equations to eliminate y:
25x=100
Then solve 25x=100 for x:
25x=100
(Divide both sides by 25)
x =4
Now that we've found x let's plug it back in to solve for y.
Write down an original equation:
4x+3y=19
Substitute4forxin4x+3y=19:
(4)(4)+3y=19
3y+16=19( Simplify both sides of the equation)
3y+16+−16 = 19+−16 (Add -16 to both sides)
3y=3
(Divide both sides by 3)
y=1
Hobi mows two lawns. The first lawn is 7 feet long and 3 feet wide.
The area of the second lawn is 4 times as big but has the same
width as the first.
What is the length of the second lawn?
Answer:
28 feet long
Step-by-step explanation:
we find the area of the first lawn using recent angle formula (l)(w)=a
(7)(3)
21
Now we multiply this by 4 since the second lawn is four times it
21x4
84
Now we rearrange the rectangle area formula to where length is what we are trying to find
a=(l)(w)
/w. /w
a/w=l
Now we fill in this formula
84/3=a
28
Hopes this helps
what is the equation of the line that passes through the point (5, 4) and is perpendicular to the line whose equation is 2x y
The equation of the line that passes through the point (5, 4) and is perpendicular to the line whose equation 2x + y = 3 is y = 1/2x + 3/2
The given equation of the line is
2x + y = 3
y = 3 - 2x
y = -2x + 3
The slope of the line is -2
The slope of the original line will be negative inverse of -2
= - 1/-2
= 1/2
The line is passing through the point (5, 4)
The slope intercept form is
y = mx + b
Substitute the values in the equation
4 = 1/2(5) + b
4 = 5/2 + b
b = 4 - (5/2)
b = 3/2
Therefore, the equation of the line is y = 1/2x + 3/2
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Wesley is going backpacking in a couple of days and is buying trail mix for the trip. The amount of trail mix he will bring depends on how long he plans to backpack. a = the amount of trail mix Wesley will bring /= the length of the backpacking trip Which of the variables is independent and which is dependent?
Answer: In this scenario, the length of the backpacking trip is the independent variable and the amount of trail mix Wesley will bring is the dependent variable.
The independent variable is the variable that is being changed or controlled in an experiment or study. In this case, the length of the backpacking trip is the independent variable because it is being determined by Wesley and is not influenced by any other factor.
The dependent variable is the variable that is being measured or observed in an experiment or study. In this case, the amount of trail mix Wesley will bring is the dependent variable because it depends on the length of the backpacking trip. Wesley's decision on how much trail mix to bring will be influenced by how long he plans to go backpacking.
what is the probability that when a pair of dice are rolled, either (at least) one dice shows a 5, or that the dice sum to 8?
Observing the cases provided with the formula of probability and implementing it with OR rule , The answer is 0.22.
What do you mean by probability?Simply put, probability is the likelihood that something will occur. When we don't know how an event will turn out, we can discuss the likelihood or likelihood of several outcomes. Statistics is the study of events that follow a probability distribution.
What is sample space?All potential results make up the sample space of a random experiment. A subset of the sample space is an event connected to a random experiment. Any outcome's probability is a value between 0 and 1. The sum of all the outcomes' probabilities is one.
Probability that dice rolled shows a 5 once = 1/36
Probability that dice rolled shows a 5 twice = 2/36
Probability that the sum is 8 = 5/36
Total probability = 1/36 + 2/36 + 5/36 = 0.22
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Write a story that can be represented using the equation y=x+1/5x
A story that can be represented using the equation y=x+1/5x is "John has an apple and he cut another apple into 5 equal parts and took on part. What's the rural fraction of apple that he has?
How to illustrate the equation?An equation is the statement that illustrates the variables given. In this case, two or more components are taken into consideration to describe the scenario. It is vital to note that an equation is a mathematical statement which is made up of two expressions that are connected by an equal sign.
In this case, if John has an apple and he cut another apple into 5 equal parts and took on part.
This can be illustrated as:
y = x + 1/5x
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question is attached
For the given equation y=x+1/5x, if the value of x is 40, y will be 48.
What is the equation?An equation is a statement that two expressions, which include variables and/or numbers, are equal. In essence, equations are questions, and efforts to systematically find solutions to these questions have been the driving forces behind the creation of mathematics.
It is given that, the equation is
y=x+1/5x
We have to find the value of y when the value of x is 40.
Substitute the value of x in order to obtain the value of y as
y=40+40/5
y=40+8
y=48
Thus, for the given equation y=x+1/5x, if the value of x is 40, y will be 48
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Answer:
48
Step-by-step explanation:
y = x + 1/5 x
y = 40 + 1/5 × 40
y = 40 + 8
y = 48
an english professor assigns letter grades on a test according to the following scheme. a: top 13 % of scores b: scores below the top 13 % and above the bottom 61 % c: scores below the top 39 % and above the bottom 22 % d: scores below the top 78 % and above the bottom 6 % f: bottom 6 % of scores scores on the test are normally distributed with a mean of 75.1 and a standard deviation of 9.1. find the numerical limits for a d grade. round your answers to the nearest whole number, if necessary.
The numerical top and bottom limits for a d grade is 68 and 61 respectively
What can we learn from mean and standard deviation?
In statistics, the measurement of variability known as the standard deviation (SD) is frequently utilised. It demonstrates how different things are from the norm (mean). While a high SD shows that the data are dispersed throughout a wide range of values, a low SD suggests that the data points tend to be close to the mean.
Given,
Mean = 75.1
Standard Deviation = 9.1
For a D grade at / 6th Percentile and 78th Percentile critical
Z- Scores are -0.77 and -1.55 respectively
The Corresponding Top grade for d
x + z * σ
75.1 + (-0.77) * 9.1 =68
The Corresponding Bottom grade for d
x + z * σ
75.1 + (-1.55) * 9.1 =61
A d grade has numerical top and bottom limitations of 68 and 61, respectively.
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The x-intercept is -4 and the y-intercept is 5. What is the slope of the line?
Answer:
y = 1.25x + 5
Step-by-step explanation:
I found the answer using linear regression.
Find in SIMPLEST FORM. thank you!
The probability that the card has a multiple of 3 is 5/16. We use the concept of probability and multiples to get the answer.
Define Probability.Probability of an event = (no of possible ways it can happen) / (total number of outcomes)
Define Multiples.For instance, 20 is a multiple of 4 and 5 if we declare that 4 + 5 = 20. The remaining multiples of four can be written as follows: 4, 8, 12, and so on. Four times one equals four. Numerous other mathematical ideas can be explored with the aid of multiples knowledge.
Given, total number of the cards in the bag is from 1 to 16.
So, total number of cards = 16.
Multiples of 3 below 16 = 3,6,9,12,15.
Number of cards below 16 which are multiples of 3 = 5
Therefore P(E) = No. of possible ways/Total no. of ways
=5/16
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