Answers
Step-by-step explanation:
1). Red
x² = 98² - 44² = 9604 - 1936 = 7668
x =√7668 = 6√213
2) orange
X² = 31²+30² = 1861
x = √1861
Related Questions
Stephen was thinking of a number. Stephen doubles it, then adds 11 to get an answer of 47.7. What was the original number?
Answers
The original number in the statement is 18.5
How to determine the original number?The statements in the question are given as:
A number. Doubles the numberAdds 11 to the numberResult = 47.7Let the number be x
So, we have the following equation
2x + 11 = 47.7
Subtract 11 from both sides
2x = 36.7
Divide by 2
x = 18.35
Hence, the number is 18.35
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cos \theta =-(5)/(13) ∅and sin θ > 0. Identify the quadrant of θ and find sin θ.
Answers
Answer: D. Qufdrant: II
sinΘ=12/13
Step-by-step explanation:
[tex]\displaystyle\\cos\theta=-\frac{5}{13} \ \ \ \ sin\theta > 0\\\\sin^2\theta+cos^2\theta=1\\\\sin^2\theta=1-cos^2\theta\\\\sin\theta=б\sqrt{1-cos^2\theta} \\\\sin\theta > 0, \ \ hence\\\\sin\theta=\sqrt{1-cos^2\theta} \\\\sin\theta=\sqrt{1-(-\frac{5}{13})^2 } \\\\sin\theta=\sqrt{1-\frac{25}{169} } \\\\sin\theta=\sqrt{\frac{169-25}{169} } \\\\sin\theta=\sqrt{\frac{144}{169} } \\\\sin\theta=\frac{12}{13}[/tex]
[tex]\displaystyle\\\left \{ {{cos\theta < 0} \atop {sin\theta > 0}} \right. \ \ \ \ \Rightarrow\ \ \ \ quadrant\ II[/tex]
A professor had students keep track of their social interactions
for a week. The number of social interactions over the week is
shown in the grouped frequency distribution. Identify the lower
limit of the fifth class.
The lower limit of the fifth class is
(Type a whole number.)
Answers
The lower limit of the fifth class for the track of social interactions
for a week is 50.
Explain the term lower limit of the class?The frequency distribution has an upper class limit and a lower class limit for each class.The smallest data point that really can correspond to a class is known as the lower class limit. The largest data object that can be a member of a class, or upper class limit.Allow the class intervals to be 30 - 34, 35 - 39, 40 - 44, 45 - 49, 50 - 54, etc. for some aggregated data.
In this case, the distribution is continuous, and all of the class intervals overlap.
Fifth class ; 50 - 54,
The class boundaries of the range from 50 - 54, 50 is the lower limit while 54 is the upper limit.
Thus, the lower limit of the fifth class for the track of social interactions
for a week is 50.
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Convert 8 weeks into days.
*Note: you must use these exact conversion factors to get this question right.
Answers
Answer:56 days
Step-by-step explanation:8 weeks*7 days= 56 days total
Help please asap!!
A- z=15
B- z= 20
C- z=23
D- z=41
Answers
Answer:
z = 15
Step-by-step explanation:
The sum S of the interior angles of a regular polygon is given by the formula
S = (n-2) x 180 where n is the number sides
Here n = 9
So S = (9-2) x 180 = 7 x 180 = 1,260
There are 9 interior angles and each angle is (5z + 65)
So the sum of all 9 interior angles = 9 (5z + 65)
= 45z + 585
Set these equal to each other and solve for z
45z + 585 = 1260
45z = 675
z = 675/45 = 15
Find the circumference of this circle.
Use 3.14 to approximate ™.
C = 2πr
14 ft
C = [?] ft
Entered
Answers
Answer:
43.9823
Step-by-step explanation:
14 / 2 = 7
7 = r
2π(7)
= 43.9823
On Saturday, the Milleman Family had dinner at a restaurant. They ordered 3 pizzas and 2 cheeseburgers for $41.50. The following weekend, the Anderson Family had dinner at the same restaurant where they ordered 2 pizzas and 5 cheeseburgers for $43.25. Which system of equations can be used to determine the cost of one pizza (p) and one cheeseburger (c)?
Answers
Answer: $8.64 and $7.79 respectively.
Step-by-step explanation: To determine the cost of one pizza and one cheeseburger, we can set up the following system of equations:
3p + 2c = 41.50
2p + 5c = 43.25
The first equation represents the total cost of the Milleman Family's meal, where 3p represents the cost of 3 pizzas, 2c represents the cost of 2 cheeseburgers, and 41.50 represents the total cost of the meal. The second equation represents the total cost of the Anderson Family's meal, where 2p represents the cost of 2 pizzas, 5c represents the cost of 5 cheeseburgers, and 43.25 represents the total cost of the meal.
By solving this system of equations, we can determine the cost of one pizza and one cheeseburger. For example, we can use the elimination method to solve the system of equations as follows:
First, we can multiply the first equation by 5 and the second equation by 3 to get the following equations:
15p + 10c = 207.50
6p + 15c = 129.75
Next, we can subtract the second equation from the first equation to eliminate the c terms and find the value of p as follows:
15p + 10c = 207.50
6p + 15c = 129.75
9p = 207.50 - 129.75
9p = 77.75
p = 77.75 / 9
p = 8.64
Finally, we can substitute the value of p that we found into one of the original equations to find the value of c as follows:
3p + 2c = 41.50
3(8.64) + 2c = 41.50
25.92 + 2c = 41.50
2c = 41.50 - 25.92
2c = 15.58
c = 15.58 / 2
c = 7.79
Therefore, the cost of one pizza is $8.64 and the cost of one cheeseburger is $7.79.
Suppose you go to work for a company that pays one penny on the first day, 2 cents on the second day, 4 cents on the third day and so on.
Hint: use an= a1 (r)^n-1 and Sn= a1 (1-r^n) / 1 - r
A. If the daily wage keeps doubling, what would your income be on day 31? Give your answer in dollars NOT pennies.
Income on day 31 = $ __________
B. If the daily wage keeps doubling, what will your total income be for working 31 days? Give your answer in dollars NOT pennies.
Total Income for working 31 days = $ _________
Answers
a. Your income on the 31st day is given as follows: $10,737,418.24
b. Your total income for working 31 days is of: $21,474,836.47
What is a geometric sequence?The definition of a geometric sequence is given as follows:
[tex]a_n = a_1(r)^{n - 1}[/tex]
In which the terms are given as follows:
[tex]a_1[/tex] is the first term.r is the common ratio of the sequence.In a geometric sequence, each term is the multiplication of the previous term by the common ratio.
The sequence in this problem is given as follows:
(0.01, 0.02, 0.04, ...).
Hence the first term and the common ratio of the sequence are given as follows:
[tex]a_1 = 0.01, q = 2[/tex]
Thus the definition is of:
[tex]a_n = 0.01(2)^{n - 1}[/tex]
The income on the 31st day is of:
[tex]a_{31} = 0.01(2)^{30} = 10,737,418.24[/tex]
The sum of the first n terms of a geometric sequence is given as follows:
[tex]S_n = a_1\frac{1 - r^n}{1 - r}[/tex]
Then the sum of the first 31 terms is of:
[tex]S_{31} = 0.01\frac{1 - (2)^{31}}{1 - 2} = 21,474,836.47[/tex]
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18=6h+2h pls help me with this answer im not understandin it
Answers
Answer:2.25 or 9/4
first we need to add 6h and 2h together, and we get 8h, and we divide 8 both side will get the fraction 18/8 and we can simplify will get 9/4 if you want more simple and will become 2.25
Which expression is equivalent to 27 + 63 ? 3(9 + 18) 9(3 + 7) 21(7 + 3) 7(21 + 9)
Answers
Which expression is equivalent to 27 + 63 ?
3(9 + 18)
9(3 + 7)
21(7 + 3)
7(21 + 9)
5. -4h + 3 + Th ≥ 9h - 21
Answers
(3.76x 10-8 )-(2.94 x 10-8)
Write your answer in scientific notation
Answers
You decide to buy a refurbished computer for $550.00 plus 6% sales tax. BB Electronics allow you to take out a no-interest loan for 12 months, and after that the interest rate is a 13.25% APR. You must make payments of $25/month, and if you miss one payment you are assessed a late fee of $29.00 plus 13.25% APR interest beginning from the date of purchase.
You missed the second payment. What is the amount of interest of the bill you will receive?
Answers
The interest on the bill will be calculated as follows:
Amount of Loan = $550
Sales Tax = 6% of $550 = $33
Total Loan = $550 + $33 = $583
Interest = 13.25% APR x $583 = $77.13
Late fee = $29
Total Interest = $77.13 + $29 = $106.13
What is the range of the function shown ???
Answers
Answer:
option number 2
Step-by-step explanation:
you can see inital and final co ordinate
Answer:
y > -2
Step-by-step explanation:
The range of a function is the set of all possible output values (y-values).
From inspection of the given graph:
The y-value of the lowest point of the curve is just above y = -2.The y-value of the highest point of the curve is more than y = 3.Therefore, the most appropriate range from the given answer options is:
y > -2Note: The graph appears to be the exponential function [tex]y=2^x-2[/tex] with a horizontal asymptote at y = -2. This means that the curve will get closer and closer to y = -2 as x approaches negative infinity, but it will never touch it. The function approaches infinity as x approaches infinity. Therefore, the range for this function is y > -2
Will give brainliest
Answers
Answer:
-5
Step-by-step explanation:
y (4) need to times 2.5 to be 10
so, x (-2) needs to times 2.5 to be the answer
-2 * 2.5 = -5
You withdraw $375 from your bank account. You receive a stack of 24 bills consisting of $5, $10, and $20 bills. The number of $5 bills is one-half the number of $10 bills. How many of each type of bill do you receive?
Answers
The number of $ 5 bills = 3
The number of $ 10 bills = 6
The number of $ 20 bills = 15
What is an Equation?
Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the total amount be = $ 375
Let the total number of bills = 24
Let the number of $ 5 bills be = x
Let the number of $ 10 bills be = y
Let the number of $ 20 bills be = z
The total number of $ 5 bills x = ( 1/2 ) x number of $ 10 bills
So , x = y/2
Now , the equation will be
The total number of bills = x + y + z
So , x + y + z = 24 be equation (1)
And ,
The total amount = 5x + 10y + 20z
So , 5x + 10y + 20z = 375
Divide by 5 on both sides , we get
x + 2y + 4z = 75 be equation (2)
On simplifying equation (1) and equation (2) , we get
x + y + z = 24
Substituting the value of y , we get
x + 2x + z = 24
3x + z = 24 be equation (3)
And ,
x + 2y + 4z = 75
x + 4x + 4z = 75
5x + 4z = 75 be equation (4)
Multiply equation (3) with 4 , we get
12x + 4z = 96 be equation (5)
Subtract equation (4) from equation (5) , we get
7x = 21
Divide by 7 on both sides , we get
x = 3
Therefore , the number of $ 5 bills is 3
Substitute the value of x , we get
y = 2x
y = 6
Therefore , the number of $ 10 bills is 6
Substitute the value for x and y in equation (1) , we get
x + y + z = 24
3 + 6 + z = 24
z + 9 = 24
Subtract 9 on both sides , we get
z = 15
Therefore , the number of $ 20 bills is 15
Hence ,
The number of $ 5 bills = 3
The number of $ 10 bills = 6
The number of $ 20 bills = 15
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Can someone help me with this?
Answers
$12,800 a year, about 15% is taken out for taxes. How much is taken out for taxes?
Answers
Answer: 1920
Step-by-step explanation:
2
10
It can be expressed as the percentage when the given expression is multiplied with 15%
=($12800×15%)
Simplify the above expression -
=(128×100×15100)
=
(
128
×
100
×
15
100
)
Common factors from the numerator and the denominator cancels each other. Therefore, remove from the numerator and the denominator.
=(128×15)
=
(
128
×
15
)
Simplify the above expression finding the product of the terms.
=1920$
=
1920
$
Hence, $1920
$
1920
was taken out for the taxes.
Write a linear function for the graph, and state and interpret the slope and y-intercept for the given scenario:
Water pressure can be measured in atmospheres (atm). Use the infomation in the graph to write an equation that models the pressure (y) at depth (x).
Answers
The linear function for the given graph is y = x + 0.1
What is a linear function?
The graph of a linear function is a straight line. The following is the form of a linear function. y = mx + b. One independent variable and one dependent variable make up a linear function. x and y are the independent and dependent variables, respectively.
The coordinates of the given graph are (0,1) and (10,2)
Then, slope (m) = (2-1)/(10-0) = 1/10 = 0.1
y-intercept (b) = 1
Then, y = 1x + 0.1
Hence, the linear function for the given graph is y = x + 0.1
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Square MNOP with vertices M(-7,-4),
N(-4,-3), O(-3, -6), and P(-6, -7): k = 2
Answers
The image of the scaled copy of the square is M'(-14,-8), N'(-8,-6), O'(-6, -12), and P'(-12, -14)
What is dilation?Dilation involves enlarging or reducing the side length of a shape to create another shape by a constant scale factor, where the scale factor does not equal one.
How to determine the image of the scaled copy of the square?From the question, we have the following parameters that can be used in our computation:
Square MNOP with vertices M(-7,-4), N(-4,-3), O(-3, -6), and P(-6, -7): Scale factor of dilation, k = 2This means that
Scaled copy = Scale factor * Vertices of MNOP
So, we have
M'N'O'P' =M(-7,-4), N(-4,-3), O(-3, -6), and P(-6, -7)* 2
Evaluate
M'N'O'P' =M'(-14,-8), N'(-8,-6), O'(-6, -12), and P'(-12, -14)
Hence, the image of the dilation is M'(-14,-8), N'(-8,-6), O'(-6, -12), and P'(-12, -14)
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Complete question
Given that Square MNOP with vertices M(-7,-4), N(-4,-3), O(-3, -6), and P(-6, -7): k = 2
Calculate the image of the scaled copy
Mia is traveling from her house to her sister’s home. She took the bus to the car rental lot and is now driving the rest of the way at a constant rate of speed. What does the -intercept represent in this problem?
the distance (mi) that Mia traveled on the bus to the car rental before she started driving the car
the distance (mi) that Mia traveled from the car rental lot to her sister's home
the amount of time (hr) elapsed for every mile the car travels from the car rental lot
the distance (mi) the car travels from the car rental lot for every 1 hour elapsed
Answers
Answer:
The distance (mi) the car travels from the car rental lot for every 1 hour elapsed.
Step-by-step explanation:
why did the chicken cross the rode
Answers
Answer: y did the chicken cross the road
Step-by-step explanation: ??????
Isaiah is trying to buy dry-erase markers for his teachers during teacher appreciation week. He
is able to collect 12 markers a day and started off with 15. How many days will it take him to get
to 135 markers? Make an equation to solve the problem using m for markers and d for days.
Answers
Answer:
It will take him 10 days to get to 135 markers.
[tex]d=12m+15[/tex]
Step-by-step explanation:
(attached)
Will give brainliest
Answers
Answer:
The first one is B
The second one is The y intercept is 8
Step-by-step explanation:
Change the Cartesian integral into an equivalent polar integral. Then evaluate the polar integral.
Answers
Find the slope of the line that passes through all of the points
on the table.
x
3
4
5
6
7
8
y
1
10
19
28
37
46
Answers
Answer:
this is what I got and hope this helps sorry if it's wrong
At as sale, suits were sold for $72 each. This price was 45% of a suits original price. How much did a suit originally cost?
Answers
Answer: 1680. The answer is 1680 because 56% of 3000 is 1680 people.
Answer:
The suit orginally costed $160 dollars.
Step-by-step explanation:
PLEASE SHOW ALL STEPS AND EXPLAIN
Answers
The greatest common factor will be 8.
What is common factor? What is a mathematical equation? What is Probability?A common factor is a whole number which is a factor of two or more numbers. The highest common factor (HCF) is the greatest factor that will divide into two or more numbers. The lowest common multiple (LCM) is the smallest multiple that is common to two or more numbers.A mathematical expression is made up of terms (constants and variables) separated by mathematical operators. A mathematical equation is used to equate two expressions. Equation modelling is the process of writing a mathematical verbal expression in the form of a mathematical expression for correct analysis, observations and results of the given problem.We have three numbers 24, 56 and 72.
The factors of 24 are : 1, 2, 3, 4, 6, 8, 12, 24
The factors of 56 are : 1, 2, 4, 7, 8, 14, 28, 56
The factors of 72 are : 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72
Therefore, the greatest common factor will be 8.
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can you help me with this
Answers
The result of the definite double integral over the interval is given as follows:
[tex]\int\int_D f(x,y)dxdy = -120[/tex]
How to solve the double integral?The double integral is solved in two steps, first the inner integral is solved, and then the result of the inner integral is used to calculate the outer integral.
Considering the function and the region, the complete integral in this problem is given as follows:
[tex]\int_{-4}^{2}\int_{-4}^{2} (3x + y)dxdy[/tex]
Then the inner integral in this problem is given as follows:
[tex]I = \int_{-4}^{2} (3x + y)dx[/tex]
We are integrating the variable x, then the variable y is a constant, as thus the result is given as follows:
I = 1.5x² + xy, from x = -4 to x = 2.
Then, applying the Fundamental Theorem of Calculus, the result is given as follows:
I = 1.5(2)² + 2y - 1.5(-4)² + 4y = 6y - 18.
Then the outer integral is calculated as follows:
[tex]O = \int_{-4}^{2} 6y - 18[/tex]
Then the result is given as follows:
O = y² - 18y, from y = -4 to y = 2.
O = (2)² - 18(2) - (-4)² + 18(-4)
O = -120.
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John brings $15 to the candy store. He buys a bag of jelly beans for $4 and plans to buy some chocolate that costs $5 per pound. Write an inequality to solve for all the possible values of x, the number of pounds of chocolate John could buy.
Use the on-screen keyboard to type the inequality that represents this situation in the box below.
Answers
Answer:
Step-by-step explanation:
he could buy 2 pounds of chocolates and save $1.