The length of the hypotenuse of the given right triangle is 117 millimeters because it is the longest side and it satisfies the conditions of the Pythagorean theorem.
The length of the hypotenuse of a right triangle with side lengths 45 millimeters, 108 millimeters, and 117 millimeters is 117 millimeters.
The hypotenuse of a right triangle is always the side opposite the right angle, and it is the longest side in a right triangle.
In this case, the side lengths are given as 45 millimeters, 108 millimeters, and 117 millimeters.
By comparing the lengths, we can see that 117 millimeters is the longest side, which makes it the hypotenuse.
To further understand why the hypotenuse is the longest side, we can refer to the Pythagorean theorem.
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 other two sides.
Mathematically, it can be written as c² = a² + b²,
where c represents the length of the hypotenuse, and a and b represent the lengths of the other two sides.
In this case, if we square the lengths of the sides, we get 45² = 2025, 108² = 11664, and 117² = 13689.
By comparing these values, we can see that 13689 is the largest, which corresponds to the length of the hypotenuse, 117 millimeters.
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Using the rule of 72, approximately how many years will it take a $1000.00
investment to double its value at an interest rate of 3.60%, compounded
annually?
Approximately 20 years will it take a $1000.00 investment to double its value at an interest rate of 3.60%, compounded annually.
What is rule of 72?The rules of 72, 70, and 69.3 are ways for calculating the doubling time of an investment in finance. To determine the roughly necessary number of periods for doubling, the rule number is divided by the interest percentage each period. For modest rates of return, the Rule of 72 is fairly accurate. The Rule of 72's estimates are compared to the actual number of years it takes for an investment to double in the graph below. Although it provides an estimate, the Rule of 72 becomes less accurate as rates of return rise.An investor or advisor can easily determine using the Rule of 72 how long it will take an investment to double based on its fixed annual rate of return. You may determine roughly how long it will take for your portfolio to double in size by dividing 72 by the fixed rate of return.Approximately 20 years will it take a $1000.00 investment to double its value at an interest rate of 3.60%, compounded annually.
The complete question is,
Approximately how many years will it take a $1000.00 investment to double its value at an
interest rate of 3.60%, compounded annually?
A. 5
B. 7.2
C. 20
D. 50
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Which statement best describes what software is?
the instructions written in human-readable form
the programming code that gives instructions to other parts of the computer
the code that manages all the hardware on a computer
O the electronic and mechanical parts of a computer device
The programming code that gives instructions to other parts of the computer.
What is computer programming code called?Computer programming code is typical referral source code. Source code is a set of instructions written using a computer programming language that tells a computer what to do.
It is written in a language that a computer can understand, and is usually written in a text file. Source code is the foundation of all computer programming and software development, and it is the basis for creating applications, programs, and websites. Source code is written in a language such as C++, Java, or Python and is compiled and then translated into machine language that the computer can understand and execute.
The source code is then tested and debugged to ensure that it works correctly. Source code is an essential part of software development and is the foundation for successful software projects.
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−5/6h−2/3h=−24 for h
Answer: h = 16
Step-by-step explanation:
We will isolate the variable, h, with inverse operations and simplifying to solve for h.
Given:
[tex]\displaystyle -\frac{5}{6}h-\frac{2}{3}h=-24[/tex]
Multiply both sides of the equation by 6:
➜ Why would we do this? This allows us to work without fractions.
-5h - 4h = -144
Combine like terms:
-9h = -144
Divide both sides of the equation by -9:
h = 16
Which equations represent circles that have a diameter of 12 units and a center that lies on the y-axis? Select two options. x2 + (y – 3)2 = 36 x2 + (y – 5)2 = 6 (x – 4)² + y² = 36 (x + 6)² + y² = 144 x2 + (y + 8)2 = 36
The equations that represent the circle are x² + (y - 3)² = 36 and x² + (y + 8)² = 36.
What is Circle?A circle is a two dimensional figure which consist of all the points which are at equal distance from a fixed point called center of the circle.
Standard equation of a circle is,
(x - h)² + (y - k)² = r², where (h, k) is the center and r is the radius.
Given that,
Diameter = 12
Radius = Half of diameter = 6
Center lies on the y axis.
So the coordinates of center (h, k) will be of the form (0, k).
So the equation will be of the form,
(x - 0)² + (y - k)² = 6² or x² + (y - k)² = 36
The equations of this form in options are,
x² + (y - 3)² = 36 and
x² + (y + 8)² = 36
Hence the equations are x² + (y - 3)² = 36 and x² + (y + 8)² = 36.
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The point-slope form of the equation of the line that passes through (–4, –3) and (12, 1) is y – 1 = y minus 1 equals StartFraction one-fourth EndFraction left-parenthesis x minus 12 right-parenthesis.(x – 12). What is the standard form of the equation for this line?
x – 4y = 8
x – 4y = 2
4x – y = 8
4x – y = 2
The standard form of the equation for the line which is as described is; x - 4y = 8.
Which equation represents the standard form equation of the line?It follows from the task content that the equation of the line in discuss in point-slope form as given in the question is;
( y - 1 ) = 1/4 ( x - 12 )
Therefore, the equation above can be written so that we have that;
4 ( y - 1 ) = ( x - 12 )
4y - 4 = x - 12
4y - x = -12 + 4
x - 4y = 12 - 4
x - 4y = 8
Therefore, the standard form equation of the line as required is; x - 4y = 8.
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Would it be unusual for a household to have three dogs? Explain your reasoning. The number of dogs per household in a small town
Dogs 0 1 2 3 4 5
Households 1488 421 173 49 33 16
Choose the correct answer below. O A. It would not be unusual because 49 people own three dogs in the town. O B. It would not be unusual because it does not have the smallest probability, O C. It would not be unusual because the probability of having three dogs is more than 0.05. O D. It would be unusual because the probability of having three dogs is less than 0.05.
It would not be unusual for a household to have three dogs, as the data you provided shows that there are households in the small town with three dogs.
The frequency of households with three dogs is 173, which is the third highest number after households with one or two dogs. Therefore, having three dogs in a household is not uncommon in this small town,
Frequency refers to the number of times an event or a value occurs within a specific data set. It can be represented as a count or a percentage. In statistics, frequency is used to describe the distribution of data, which can help to identify patterns and trends. For example, in the data you provided, the frequency of households with three dogs is 173, which means that there are 173 households in the small town that have three dogs. It's a way to understand how common or rare is something in the dataset. By counting the number of times each value appears on the dataset and organizing it, we can have a better understanding of how the variable is distributed.
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If 3/4 cup of chai tea latte concentrate is 60 calories, how many calories is 1/2 cup of chai tea latte concentrate?
If 3/4 cup of chai tea latte concentrate is 60 calories, we can use proportion to find out how many calories 1/2 cup of chai tea latte concentrate is.
What does a math ratio mean?
An ordered pair of numbers a and b, represented as a / b, is a ratio if b is not equal to 0. A proportion is an equation that sets two ratios at the same value. For instance, you could athe ratio as follows: 1: 3 if there is 1 boy and 3 girls (for every one boy there are 3 girls) There are 1 in 4 boys and 3 in 4 girls.
We know that:
(3/4 cup) = 60 calories
To find out the number of calories in 1/2 cup, we can set up a proportion using the information we have:
(1/2 cup) / x = (3/4 cup) / 60
we can cross-multiply to get:
x = (1/2 cup) * (60 / (3/4 cup))
then we can simplify
x= (1/2)*(4/3)*60
x= 80/3
Therefore, 1/2 cup of chai tea latte concentrate is 80/3 calories.
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what is the equation of the line that has a slope of 1/2 and goes though the point (4,-1)
The equation of line that has a slope of 1/2 and goes through (4,-1) is y=-3.
What is equation?An equation is a mathematical formula that connects two assertions using the equal sign (=) to denote equivalence. In algebra, an equation is a mathematical statement that establishes the equivalence of two mathematical expressions. For instance, an equal sign separates the components 3x + 5 and 14 in the equation 3x + 5 = 14. A mathematical formula is used to explain the connection between two sentences on either side of a letter. Frequently, there is just one variable, which is also the symbol. for example, 2x - 4 = 2.
y = mx + c
where m denotes the line's slope and c is the y-intercept.
In the question, we have been given the slope and the (x,y) through which it passes.
Substituting these in y = mx + c, we get
-1= 0.5(4)+c
-1= 2+c
-3=c
c=-3.
Hence, the equation of line is y=-3.
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The average person spends about 1/10 of their walking hours with their eyes closed. If Mrs. James was awake for 15 1/2 hours today, how much more time did she have her eyes open than closed.? PLEASE HELP
The time that Mrs James have her eyes open than closed will be 13 19/20 hours.
How to calculate the Fraction?A fraction simply means a piece of a whole. In this situation, the number is represented as a quotient such that the numerator and denominator are split.
From the information, the average person spends about 1/10 of their walking hours with their eyes closed. If Mrs. James was awake for 15 1/2 hours today.
The more time that she have her eyes open than closed will be:
= 15 1/2 - (1/10 × 15 1/2)
= 15 1/2 - 1 11/20
= 13 19/20
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Solve for x
I need 20 characters so I’m just typing this
Answer:
x = 4
Step-by-step explanation:
The sum of two interior angles in a triangle is equal to an exterior angle that is supplementary to the third interior angle.
We can write the following equation to find the value of x based on this information:
6x + 6 + 17x + 2 = 100
Add like terms.23x + 8 = 100
Subtract 8 from both sides23x = 92
Divide both sides by 23x = 4
QUICK HELP ME I'M STRUGGLING WITH THIS
The values of F, G and H are given as follows:
F = 5, G = 29, H = 1.
How to obtain the values of F, G and H?The expression at the right side of the equality represents the entire expression after the least common factor is applied at the left side.
The least common side of the denominators is given as follows:
(x - 3)(4x + 7).
Hence the simplified numerator is given as follows:
(2x + 1)(4x + 7) + (-3x + 2)(x - 3).
Expanding the operations, and combining the like terms, we have that:
(2x + 1)(4x + 7) + (-3x + 2)(x - 3) = 8x² + 18x + 7 - 3x² + 11x - 6.
(2x + 1)(4x + 7) + (-3x + 2)(x - 3) = 5x² + 29x + 1.
Then the equality of the two numerators is given as follows:
5x² + 29x + 1 = Fx² + Gx + H.
Hence the values of the letters are given as follows:
F = 5, G = 29, H = 1.
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please choose the correct answer and explain why it’s correct. i will mark you brainliest!
Answer: C
Step-by-step explanation:
This is simple algebra! First, try to find the slope which would be -3.
Let's say x is hours and y is degrees. We will find the slope by finding the change in x and y.
change in y 45 - 54 = -9
change in x 5 - 2 = 3
The slope is -3. Therefore the temperature decreases by 3 degrees every hour.
Hope that helps! :-)
Select the correct answer. A line t runs downward to the right through two parallel horizontal lines a and b, forming 8 angles numbered from 1 to 8. In the diagram, transversal t cuts parallel lines a and b. Which equation is necessarily true? A. m∠1 = m∠7 B. m∠3 = m∠6 C. m∠5 + m∠8 = 90° D. m∠6 + m∠7 = 180°
Since in the diagram, transversal t cuts parallel lines a and b, an equation which is necessarily true include the following: B. m∠3 = m∠6.
What is the Alternate Interior Angles Theorem?In Mathematics, the Alternate Interior Angles Theorem states that when two (2) parallel lines are cut through by a transversal, the alternate interior angles that are formed are congruent.
Based on the diagram representing (showing) the two parallel horizontal lines a and b, we can reasonably infer and logically conclude that angle 3 (m∠3) and angle 6 (m∠6) forms a pair of alternate interior angles because line a is parallel to line b and transversal (t) cuts parallel lines a and b.
Similarly, angle 4 (m∠4) and angle 7 (m∠4) forms a pair of alternate interior angles because line a is parallel to line b.
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brainly has it out for me
Answer:
answer is 341
pls mark me as brainlliest
Find the missing angle measure.
Answer:
35⁰
Step-by-step explanation:
because the sum of the interior angle of triangle is 180⁰ so 90+55+x=180
x=35
Two groups are hiking on a glacier. Group B starts 1 mile ahead of Group A and walks 2 miles per hour.
To catch up to Group B, Group A walks 3 miles per hour.
Q
* 2: hours since the start of the hike
v: miles from the start of the trail
) Which equation shows Group A's
distance from the start?
U = x + 1
3=2+3
Group A
3 miles
per hour
Group B
U = 3х
v=30+1
The equation that shows Group A's distance from the start, given their speed and the number of hours is C. y = 3 x.
How to find the equation for the distance ?When trying to find the distance that a person or object has travelled in a given time, the general formula is;
= Speed x Time
The speed is given as 3 miles per hour for Group A.
The time is given as x for either group
This means that the distance that Group A has gone since the hike up the glacier started is :
Distance from the start = Speed x Time
y = 3 miles per hour × x
y = 3x
In conclusion, given the speed that Group A is using, this means that their distance from the start can be modelled by the equation, y = 3 x.
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Answer:
Step-by-step explanation:
Olivia's class collected 3,591 bottle caps in 57 days. The same number of battle caps were collected each day. How many bottle caps did the class collect per day?
Answer: 63 bottle caps
Step-by-step explanation:
3591 caps collected
57 days
3591/57=63
Caps collected per day 63 caps
A bag contains 4 white, 5 red and 6 green balls. Three balls are drawn at random from
the bag. The probability that all of them are green, is:
The probability that all the balls are green when we randomly select them is:
P = 0.044
How to find the probability that all the balls are green?We know that a bag contains 4 white, 5 red and 6 green balls, then there are a total of:
4 + 5 + 6 = 15 balls.
The probability of getting a green one is given by the quotient between the number of green balls and the total number of balls, so for the first one we have:
p = 6/15
Now for the next ball, because we already took one, now there are 5 green balls and 14 in total, so the probability is:
q = 5/14
The probability for the last one is calculated in a similar way, we will get:
z = 4/13
The joint probability (the probability of getting the 3 green balls in a row) is given by the product of the probabilities above, here we will get:
P = *q*z = (6/15)*(5/14)*(4/13) = 0.044
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simplify 7.5s + 1.6t - 4.2s
The equation 7.5s + 1.6t - 4.2s is simplified to give a result of
3.3s + 1.6tHow to simplify the given equationThe given equation 7.5s + 1.6t - 4.2s is simplified by following the mathematical operator that is acting on the values after a consideration of like terms
The variables in the equation are t and s
terms in t: 1.6
terms in s: 7.5, -4.2
collecting like terms
this will lead to rearranging the equation to give
7.5s - 4.2s + 1.6t
using the mathematical operator (addition and subtraction)
= 3.3s + 1.6t
unlike terms cannot be operated on, because of this the answer is 3.3s + 1.6t
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Determine whether the statement is true or false.
(Bob) ≤ {Bob, Carol, Ted, Alice}
A.True
B.False
Help
The statement "(Bob) ≤ {Bob, Carol, Ted, Alice}" is False.
How to determine the truth value of the statementFrom the question, we have the following parameters that can be used in our computation:
Bob) ≤ {Bob, Carol, Ted, Alice}
Here, (Bob) is a singleton set which contains the element "Bob", while {Bob, Carol, Ted, Alice} is a set.
In general, the notation "A ≤ B" is used to indicate that set A is a subset of set B, which means that all elements of A are also elements of B.
Therefore, in this case (Bob) is not a subset of {Bob, Carol, Ted, Alice} because it is not a set of distinct elements, it is just a single element.
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Use the diagonals to determine whether a parallelogram with vertices P(−4,0), Q(0,4), R(4,0), and S(0,−4) is a rectangle, rhombus, or square. Give all the names that apply.
The shape of the parallelogram with vertices P(−4,0), Q(0,4), R(4,0), and S(0,−4) is a square
How to solve for the shapeIn order to get the shape using the vertices that we have, we would have to find the length of the diagonals
We have P(−4,0), Q(0,4), R(4,0), and S(0,−4)
The length of the diagonal PQ is given as:
PQ = [tex]\sqrt{(0-4)^2+(4-0)^2}[/tex]
= [tex]\sqrt{32}[/tex]
Next we have to solve for the length of the diagonal RS
RS = [tex]\sqrt{(4-(-4))^2+(0-(-4))^2[/tex]
RS = [tex]\sqrt{32}[/tex]
Since PQ = RS we would have to conclude that the shape is a square.
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show working
please A carton of strawberries weighs 2 pounds. A box of apples weighs 6 pounds more than that. How much does the box of apples weigh?
please some answer this please just answer and you'll know points 83
Answer: 8 pounds
Step-by-step explanation: Let’s first identify the main key details
Strawberry- 2 pounds
Apple- 6 more of strawberry
What is 6+2
8
The apple weighs 8 pounds.
Hope this helped
Can some one solve the inequality for me I have a d in class
-5x -1>9
Answer:
Step-by-step explanation:
-5x-1>9
add 1 to both sides
-5x>10
divide by negative 5
x<-2
the sign flips since you divided by a negative
and your answer is x<-2
help me to solve these questions
Answer: I can't solve all of them but I will give tips. i repeats in cycles so i^1 is sqrt-1, i^2 is -1, i^3 is -i and i^4 is 1. Look at the exponent and first divided out 4 then use the 1 2 3 answers. When you divided i and a number such as (1-i)/1+i) multiply by the conjugate of the denominator which is 1-i. To find conjugate replace the + with a -.
Step-by-step explanation:
The price of an item has been reduced by 20%. The original price was $55. What is the price of the item now?
The reduced price of the item will be $44.
What is the percentage?The percentage is defined as representing any number with respect to 100. It is denoted by the sign %. The percentage stands for "out of 100." Imagine any measurement or object being divided into 100 equal bits.
Given that the price of an item has been reduced by 20%. The original price was $55.
The reduced price of the item will be calculated as,
Price = 55 x ( 100% - 20 %)
Price = 55 x ( 1 - 0.2
Price = ( 55 x 0. 8 )
Price= $44
Hence, the price of the item will be $44.
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A metalworker has a metal alloy that is 30% copper and another alloy that is 65% copper. How many kilograms of each alloy should the metalworker combine to create 80 kg of a 51% copper alloy?
What is the sum of a °+c °?
Answer:
300 degrees.
Step-by-step explanation:
a = 180 degrees
c = 180 - 60 = 120 degrees
Select y = cos(x) + 2 sin(3x) in "The Limit of a Function" from the pull-down menu. Estimate to the nearest hundredth the value of the limit. L = lim x → 0.5 (cos(x) + 2 sin(3x)) L = 2.87256 Correct:
How large can δ be so that |x − 0.5| < δ guarantees that |cos(x) + 2 sin(3x) − L| < 0.5? What about for |cos(x) + 2 sin(3x) − L| < 0.02?
The equation as per the information that has been provided, the answer will be computed as:
The function's limit indicates its value as the independent variable gets closer to a certain point.
Finding the limit as the independent variable approaches both the positive and negative limits is necessary to determine whether a function's limit is present. If both limits are the same, the limit of the function is present.
L=limx→0.5(cos(x)+2sin(3x))
L=cos0.5+2sin3×0.5
L=0.87+2sin1.5
L=0.87+2(0.99)
L=0.87+1.99
L=2.86
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a. Calculate WTW: What do you get? Why should we expect this result? b. Enter the following vectors into MATLAB: 6 = ; Compute the norm of b and the norm of Wb. What do you notice? Also compute the dot products (a, b) and (Wa; Wb): One of the fundamental properties of orthogonal matrices is that they preserve norms of vectors and the standard inner product (You can define orthogonal matrices as the ones with this property; in fact:) c. The columns of W are linearly independent because the vectors are orthogonal, so W should clearly be invertible: Use inv(W) to compute the inverse of W, and then compare it to WT What do you observe?
We were informed that an is a matrix with numerous elements in this query. A is an order matrix, and we also have an order matrix.
3 by 3, resulting in a determinant of b that is -5. We were successful in locating a matrix c that is equal to minus three times of a b cube times a.
We must determine the determinant because an is equivalent to a transport and an is equal to an identity matrix. If I take into account the period of a transposition, what is the determinant of a so-called determinant of this identity, which is equal to 1 accurate and we are aware of this characteristic.
This will be the result of those who are in a situation where a transposition is crucial. This is the first result is that the cube's time has the same determinant as a matrix's time.
Because a 3 by 3 matrix and lambda are real numbers, we can leverage this property. Using this property, it will be -3 q in this case. Once more, I'll be able to obtain a transposition b times c times a determinant. Splitting it is a possibility. The times of the b cube determinant are determined by minus 3 c. We know that the determinants of a transpose and the determinant of a that is 1 are, so what we are obtaining is just minus 27.
We shall obtain the b cube's determinant from this location. This is only multiplied by 1 minus 27. There won't be an entire cube. The determinant of c is equal to 3125, which is the product of -27 and -125.
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2 variables x and y vary inversly and x=12 when y=4 what is the value of y when x=3
The value of y given the inverse proportional relationship between the variables is 16.
What is the inverse proportion?When two variables vary inversely, as one of the variable increases, the other variable decreases.
The equation that represents inverse proportion : x = k / y
where b = constant of proportionality
k = xy
k = 12 x 4 = 48
y = k / x
48 / 3 = 16
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