Right triangles 1, 2, and 3 are given with all their angle measures and approximate side lengths. Use one of the triangles to approximate the ratio (KL)/(JL).
- 0.64
- 0.77
- 0.83
- 1.2
Answers
Answer:
\(\frac{KL}{JL}\) = \(\frac{6.4}{7.7}\) = 0.83
Step-by-step explanation:
The key understanding here is that ΔJKL is similar to triangle 3 based on the AA criterion (they both have a right angle and a 40° angle).
We can find \(\frac{KL}{JL}\) by setting up a proportion statement that includes KL, JL, and the lengths of their corresponding sides in triangle 3.
We can use this proportion:
\(\frac{KL}{6.4}\) = \(\frac{JL}{7.7}\)
\(\frac{KL}{6.4}\) ⇒ opposite to 40° angle
KL, JL ⇒ ΔJKL
\(\frac{JL}{7.7}\) ⇒ adjacent to 40° angle
6.4, 7.7 ⇒ triangle 3
[Now see the attachment]
Now we can rewrite the equation to show the ratios of the side lengths within each triangle.
\(\frac{KL}{JL}\) = \(\frac{6.4}{7.7}\)
\(\frac{KL}{JL}\) ⇒ ΔJKL
KL, 6.4 ⇒ adjacent to 40° angle
\(\frac{6.4}{7.7}\) ⇒ triangle 3
JL, 7.7 ⇒ adjacent to 40° angle
Answer: it’s 0.82
Step-by-step explanation:
Related Questions
What is the factored form of x2 − 4x − 5?
(x + 5)(x − 1)
(x + 5)(x + 1)
(x − 5)(x − 1)
(x − 5)(x + 1)
Answers
Answer:
x2 - 4x - 5 factored form is (x - 5)(x + 1)
Answer:
(x − 5)(x + 1)
Step-by-step explanation:
The answer above is correct.
what’s slope in this graph?
Answers
Answer:
1/2 !
Step-by-step explanation:
Since it's going up, we know its positive, but if you use RISE/RUN, you would go up 1, then over two, from any point. That makes it 1/2! I went up from the y axis to the next point on the line. I hope that makes sense, but the answer is 1/2!
Have a nice day :D
Help me please the best answer will get a crown
Answers
Answer:
is super easy Step-by-step explanation Do you?
Construct a frequency distribution and a relative frequency histogram for the accompanying data set using five classes. Which class has the greatest relative frequency and which has the least relative frequency?Complete the table below. Use the minimum data entry as the lower limit of the first class.Class Frequency, f Relative frequencyx-x x xx-x x xx-x x xx-x x xx-x x x sumf= X?(Type integers or decimals. Round to the nearest thousandth as needed.)DATA:Triglyceride levels of 26 patients (in milligrams per deciliter of blood)138 199 240 143 294 175 240 216 223180 138 266 161 175 402 172 459 147391 152 199 294 188 320 421 161
Answers
Answer:
\(\begin{array}{cc}{Class}& {Frequency} & 138 - 202 & 14 & 203 - 267 & 5 & 268 - 332 & 3 & 333 - 397 & 1 & 398 - 462 & 3 \ \end{array}\)
The class with the greatest is 138- 202 and the class with the least relative frequency is 333 - 397
Step-by-step explanation:
Solving (a): The frequency distribution
Given that:
\(Lowest = 138\) --- i.e. the lowest class value
\(Class = 5\) --- Number of classes
From the given dataset is:
\(Highest = 459\)
So, the range is:
\(Range = Highest - Lowest\)
\(Range = 459 - 138\)
\(Range = 321\)
Divide by the number of class (5) to get the class width
\(Width = 321 \div 5\)
\(Width = 64.2\)
Approximate
\(Width = 64\)
So, we have a class width of 64 in each class;
The frequency table is as follows:
\(\begin{array}{cc}{Class}& {Frequency} & 138 - 202 & 14 & 203 - 267 & 5 & 268 - 332 & 3 & 333 - 397 & 1 & 398 - 462 & 3 \ \end{array}\)
Solving (b) The relative frequency histogram
First, we calculate the relative frequency by dividing the frequency of each class by the total frequency
So, we have:
\(\begin{array}{ccc}{Class}& {Frequency} & {Relative\ Frequency} & 138 - 202 & 14 & 0.53 & 203 - 267 & 5 & 0.19 & 268 - 332 & 3 & 0.12 & 333 - 397 & 1 & 0.04 & 398 - 462 & 3 & 0.12 \ \end{array}\)
See attachment for histogram
The class with the greatest is 138- 202 and the class with the least relative frequency is 333 - 397
Pls help with this question pictured below.
Answers
The implicit derivative is given as follows:
dx/dt(x = 4) = 1/12.
How to obtain the implicit derivative?The function in this problem is given as follows:
y = 3x² + 1.
The implicit derivative, relative to the variable t, is given as follows:
dy/dt = 6x dx/dt.
(the derivative of the constant 1 is of zero).
The parameters for this problem are given as follows:
x = 4, dy/dt = 2.
Hence the derivative is obtained as follows:
2 = 6(4) dx/dt
dx/dt = 2/24
dx/dt = 1/12.
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PLEASE HELP ME I WILL GIVE YOU 5 STAR RATING A THANKS AND BRAINLIEST RATINGGGGG
Answers
Answer:
It's the third choice.
Step-by-step explanation:
IF y varies inversely as x then y = k/x where k is a constant,
and k = xy
For the 3rd choice
-1 * -2/7 = 2/7
4 * 1/14 = 2/7 and
6 * 1/21 = 2/7
so, this is inverse variation.
The price of an item has been reduced by 85%. The original price was $73. What is the price of the item after the reduction?
Answers
Answer:
$10.95
Step-by-step explanation:
85% = 0.85
We take
73 - (73 x 0.85) = $10.95
So, the price of the item after the reduction is $10.95
A firm has the following account balances. What is the amount of their net working capital?
Inventory $430
Fixed Assets $50
Accounts Receivable $660
Accounts Payable $ 920 30-day
Notes Payable $ 400
Cash $ 245
Long-term Debt $ 15
Answers
The amount of their net working capital is,
= $2,720
What is Addition?The process or combination of combining two or more numbers is called the Addition.
Given that;
A firm has the following account balances.
Inventory $430
Fixed Assets $50
Accounts Receivable $660
Accounts Payable $ 920 30-day
Notes Payable $ 400
Cash $ 245
Long-term Debt $ 15
Hence, The amount of their net working capital is,
= $430 + $50 + $660 + $920 + $400 + $245 + $15
= $2,720
Thus, The amount of their net working capital is,
= $2,720
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A zip wire runs between two posts, 25m apart. The zip wire is at an angle of 10∘ to the horizontal. Calculate the length of the zip wire.
Answers
The length of the zip wire is approximately 25.42 meters.
To calculate the length of the zip wire, we can use trigonometry and the given information about the angle and the distance between the two posts.
Given:
Distance between the two posts: 25m
Angle of the zip wire to the horizontal: 10°
We can use the trigonometric function cosine (cos) to find the length of the zip wire. Cosine relates the adjacent side to the hypotenuse of a right triangle.
In this case, the adjacent side is the distance between the two posts (25m) and the hypotenuse is the length of the zip wire that we want to calculate.
Using the cosine function:
cos(angle) = adjacent/hypotenuse
cos(10°) = 25m/hypotenuse
To find the hypotenuse (length of the zip wire), we can rearrange the equation:
hypotenuse = 25m / cos(10°)
Using a calculator or trigonometric tables, we can find the value of cos(10°) to be approximately 0.9848.
Therefore, the length of the zip wire is:
hypotenuse = 25m / 0.9848 ≈ 25.42m
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fplzz ans my question
factorize p^4+4
Answers
Answer:
Step-by-step explanation:
(p²)²+2²
(p²+2)²-2p²2
(p²+2)²-4p²
(p²+2)²-(2p)²
(p²+2-2p)(p²+2+2p)
2x – 7y = -14
Write the equation in slope- intercept form
Answers
Answer:
y= 2/7x +2
Step-by-step explanation:
y = 2/7x + 2 is the slope intercept form of the equation.
Writing equation of a line in slope intercept formGiven the equation below;
2x – 7y = -14
The slope intercept form of a line is expressed as:
y = mx + b
m is the slope
b is the intercept
2x – 7y = -14
-7y = -2x - 14
7y = 2x + 14
y = 2/7x + 2
Hence the equation in slope- intercept form is y = 2/7x + 2.
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What’s the graph to t/3 - 1 > -3
Answers
Answer: The answer is C
Step-by-step explanation: This is because the equation has a greater than or equal to sign (≥). This mean that there will be a closed dot. Also, when it comes to inequalities, the sign points to where the line will be drawn, (greater than is to the right and less than is to the left), which indicates that the answer is C
8x - 3 for x = 2 help me on this problem please
Answers
Answer:
13
Step-by-step explanation:
8(2)-3
16-3
13
Answer:
13
Step-by-step explanation:
8 (2) - 3
Multiply 8 and 2 to get 16.
16−3
Subtract 3 from 16 to get 13.
13
hope it helps and have a great day! =D
~sunshine~
50 PONTS
Complete the following statements:
< A corresponds to <
< B corresponds to <
< C corresponds to <
Side CA corresponds to side?
Side BC corresponds to side?
Side AB corresponds to side?
Answers
Answer:
Step-by-step explanation:
1. j
2. k
3. L
4. Lj
5. kL
6. jk
3,998-(-7)= can you please help me with this problem
Answers
Answer:
4005
Step-by-step explanation:
3,998 - (-7) = ?
Two negative signs will make a positive sign.
3,998 - (-7) = 3998 + 7 = 4005
So, the answer is 4005
What is the area of the trapezoid?
: /
Enter your answer in the box.
___ in2
Answers
The area of trapezoid is 82 square inches.
In the given figure,
There are two triangle of same measure and a rectangle.
The height of triangle = 8 in
base of triangle = 8 in
width of rectangle = 10 in
length of rectangle = 8 in
Since we know that,
Area of triangle = (1/2)x base x height
= (1/2) x 8 x 8
= 32 square inches
Area of rectangle = length x width
= 10 x 8
= 18 square inches
Therefore,
Area of the given trapezoid = 2 x area of triangle + area of rectangle
= 2x 32 + 18
= 82 square inches
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Jason ran 2 3/4 miles in 2/5 of an hour. How far can jason run in one hour
Answers
Answer:
6 7/8 miles per hour
Step-by-step explanation:
2 3/4 ÷ 2/5
change mixed number into improper fraction; 2 3/4 = 11/4
when dividing fractions, multiply by the reciprocal of the second fraction
11/4 ÷ 2/5 = 11/4 · 5/2 = 55/8 or 6 7/8 mph
I need help with this practice problem This problem asks two things, (a) and (b), answer these as they go along with the problem
Answers
For the ratio test of a series the ratio is defined as:
\(r=\lim _{n\to\infty}\lvert\frac{a_{n+1}}{a_n}\rvert\)And we have three possible outcomes:
- r<1 and the series converges.
- r>1 and the series diverges.
- r=1 and the test is inconclusive.
Knowing this let's apply the test to the series given by the question. We have:
\(\begin{gathered} a_n=\frac{2n!}{2^{2n}} \\ a_{n+1}=\frac{2(n+1)!}{2^{2(n+1)}} \end{gathered}\)As you can see both expressions are always positive so when writing the ratio we don't need to add the absolute value symbols. Then the ratio is:
\(\begin{gathered} r=\frac{a_{n+1}}{a_n}=\frac{\frac{2(n+1)!}{2^{2(n+1)}}}{\frac{2n!}{2^{2n}}}=\frac{2(n+1)!}{2^{2(n+1)}}\cdot\frac{2^{2n}}{2n!} \\ r=\frac{2(n+1)!}{2n!}\cdot\frac{2^{2n}}{2^{2n+2}} \end{gathered}\)Here is important to remember a property of the factorial:
\(\begin{gathered} a!=1\cdot2\cdot3\cdot\ldots\cdot(a-1)\cdot a \\ (a+1)!=1\cdot2\cdot3\cdot\ldots\cdot(a-1)\cdot a\cdot(a+1) \\ (a+1)!=a!\cdot(a+1) \end{gathered}\)And a property of powers:
\(b^{a+c}=b^a\cdot b^c\)Using these properties we get:
\(\begin{gathered} r=\frac{2(n+1)!}{2n!}\cdot\frac{2^{2n}}{2^{2n+2}}=\frac{2n!\cdot(n+1)}{2n!}\cdot\frac{2^{2n}}{2^{2n}\cdot2^2} \\ r=\frac{2n!\cdot(n+1)}{2n!}\cdot\frac{2^{2n}}{2^{2n}\cdot2^2}=\frac{2n!}{2n!}\cdot(n+1)\cdot\frac{2^{2n}}{2^{2n}}\cdot\frac{1}{2^2} \\ r=\frac{n+1}{2^2}=\frac{n+1}{4} \\ r=\frac{n+1}{4} \end{gathered}\)So the answer to part (a) is:
\(r=\frac{n+1}{4}\)For part (b) we have:
The ratio depends on n. As n increases the ratio increases and gets greater than 1:
\(\begin{gathered} r>1 \\ \frac{n+1}{4}>1 \\ n+1>4 \\ n>3 \end{gathered}\)So for any n>3 the ratio is greater than 1 which means that this value of r tells us that the series diverges.
The mean height of the students in a class is 152 cm. The mean height of boys is 158 cmwith a standard deviation of 5 cm. And the mean height of girls is 148 cm with a standarddeviation of 4 cm. Find the percentage of boys in the class and also the S.D of heights of allthe students in the class?
Answers
The percentage of boys in the class and also the standard deviation of heights of all the students in the class are 78% and 9 cm respectively
How to find the percentage of boys in the class?Percentage of the boys in the class deals with a ratio of the boys to the number of students in the class
The given parameters that will help us to get the percentage are
Mean height of the class = 152 cm
Mean height of the boys = 158 cm
The standard deviation of the boys = 5 cm
Mean height of the girls = 148 cm
Standard deviation of the girls = 4 cm
(1) The percentage of boys in the class is
Total mean height = 158 +148 = 306
Percentage = 158/306 * 100 = 51.6%
Then the percentages 51.6/100 * 152 = 78%
(2) The total standard deviation of all the students
Boys + girls = 5+4 = 9 cm
Therefore, the percentage of boys in the class and also the standard deviation of heights of all the students in the class are 78 students and 9 cm respectively
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A box of six pencils cost £1.56. A box of eight rubbers cost £2.72. What is the difference in cost between one pencil and one rubber?
Answers
By answering the presented question, we may conclude that As a result, inequality the cost difference between one pencil and one rubber is £0.08.
What is inequality?In mathematics, an inequality is a non-equal connection between two expressions or values. As a result, imbalance leads to inequity. In mathematics, an inequality connects two values that are not equal. Inequality is not the same as equality. When two values are not equal, the not equal symbol is typically used (). Various disparities, no matter how little or huge, are utilised to contrast values. Many basic inequalities may be solved by altering the two sides until just the variables remain. Yet, a lot of factors contribute to inequality: Negative values are split or added on both sides. Exchange left and right.
To determine the cost difference between one pencil and one rubber, we must first determine the cost per item for each product.
The price of a pencil is 1.56 / 6 = £0.26.
The price of a rubber is 2.72 / 8 = £0.34.
Therefore the cost difference between one pencil and one rubber is:
£0.34 - £0.26 = £0.08
As a result, the cost difference between one pencil and one rubber is £0.08.
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The area of a triangle is 120-meter square, if the height is equal 10 meter, what is the value of the base?
Answers
Answer:
24 meters
Step-by-step explanation:
The equation for the area of a triangle is A=1/2BxH where B is the base and H is the height. You are given the area and the height so you need to plug those values into the equation and solve.
120=1/2Bx10
240=Bx10
24=B
What is a perfect square 6^1
Answers
A perfect square refers to a number that is the result of multiplying an integer by itself. In this case, 6^1 is equal to 6.
However, 6 is not a perfect square because it cannot be obtained by multiplying an integer by itself. The perfect squares up to 6^1 would be 1^2 = 1 and 2^2 = 4.
I need help with this!
Answers
The length AC in the kite is 8.7 cm.
How to find the side AC in the kite?A kite is a quadrilateral that has two pairs of consecutive equal sides and
perpendicular diagonals. Therefore, let's find the length AC in the kite.
Hence, using Pythagoras's theorem, let's find CE.
Therefore,
7² - 4² = CE²
CE = √49 - 16
CE = √33
CE = √33
Let's find AE as follows:
5²- 4² = AE²
AE = √25 - 16
AE = √9
AE = 3 units
Therefore,
AC = √33 + 3
AC = 5.74456264654 + 3
AC = 8.74456264654
AC = 8.7 units
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3 cm
4 cm
6 cm
Find the volume. Round to the nearest tenth if necessary.
Answers
Answer:
72 cm squared
Step-by-step explanation:
3 x 4 x 6 = 72 cm squared
Answer: 72 cm ^2
Step-by-step explanation:
Volume of rectangular prism = length x width x height
Volume = 6 x 4 x3 = 72 cm ^2
A jar contains 6 blue gumballs, 4 yellow gumballs, and 8 red gumballs. What is the probability of choosing a yellow gumball and then a red gumball if the first gumball is placed back into the jar before the second is chosen?
Answers
Answer:
2/9 or 22.22% and 4/9 or 44.44%
Step-by-step explanation:
6+4+8=18 4/18=2/9 8/18=4/9
Im strugling on these question
Answers
Answer and Step-by-step explanation:
How're you struggling with this? Simply look for a point that is inside of the triangle.
The answer is A. (-1, -2)
because this point is INSIDE the triangle.
#teamtrees #PAW (Plant And Water)
Which of the following describes how to calculate net pay?
A)Subtract the total deductions from the net pay.
B)Add the total deductions to the gross pay.
C)Subtract the total deductions from the gross pay.
D) Subtract the total deductions from the take-home pay.
Answers
Answer: C
Step-by-step explanation: The answer is C because it is.
Four times the difference of a number and nine is -30 ."
Answers
Answer:
3/2
Step-by-step explanation:
Solve 4 (x - 9) = -30.
4x - 36 = -30
4x = 6
x = 6/4 = 3/2
Student Enrollment
The enrollment at a local college has been decreasing linearly. In 2004, there where 975 students enrolled. By
2009, there were only 730 students enrolled. Determine the average rate of change of the school's enrollment
during this time period, and write a sentence explaining its meaning.
The average rate of change=
The enrollment at the college has been [Select an answer at a rate of
Select an answer v
Answers
The average rate of change of the school's enrollment during this time period is -49 students per year. This means that on average, the enrollment at the college has been decreasing by 49 students per year.
To determine the average rate of change of the school's enrollment during the given time period, we can use the formula:
Average rate of change = (Change in enrollment) / (Change in time)
The change in enrollment is calculated by subtracting the initial enrollment from the final enrollment, while the change in time is calculated by subtracting the initial year from the final year.
Given that in 2004 there were 975 students enrolled and in 2009 there were 730 students enrolled, we can calculate the change in enrollment:
Change in enrollment = 730 - 975 = -245 students
The change in time can be calculated as:
Change in time = 2009 - 2004 = 5 years
Now we can calculate the average rate of change:
Average rate of change = (-245 students) / (5 years) = -49 students per year
Therefore, the average rate of change of the school's enrollment during this time period is -49 students per year. This means that on average, the enrollment at the college has been decreasing by 49 students per year.
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A bank offers a CD that pays a simple interest rate of 7.0%. How much must you put in this CD now in order to have $4500 for a home-entertainment center in 5 years.
The present value that must be invested to get $4500 after 5 years at an interest rate of 7.0% is $__ (Round up to the nearest cent.)
Answers
Rounding up to the nearest cent, the present value that must be invested in the CD now is approximately $3333.34.
To calculate the present value required to have $4500 after 5 years with a simple interest rate of 7.0%, you can use the formula for simple interest:
Present Value = Future Value / (1 + (Interest Rate × Time))
In this case:
Future Value = $4500
Interest Rate = 7.0%
= 0.07
Time = 5 years
Substituting these values into the formula:
Present Value = $4500 / (1 + (0.07 × 5))
Present Value = $4500 / (1 + 0.35)
Present Value = $4500 / 1.35
Present Value ≈ $3333.33
You may use the simple interest calculation to get the present value necessary to have $4500 after five years with a simple interest rate of 7.0%:
Future Value / (1 + (Interest Rate Time)) = Present Value
In this instance
$4500 is the future value.
Rate of Interest = 7.0% = 0.07
t = 5 years
Substituting these values into the formula:
$4500 / (1 + (0.07 5)) = Present Value
$4500 / (1 + 0.35) equals the present value.
Present Value = $4500 / 1.35
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The present value that must be invested now in order to have $4500 for a home-entertainment center in 5 years at an interest rate of 7.0% is approximately $3333.33
How to find the present value that must be invested to get $4500 after 5 yearsUsing the formula for calculating the future value of a single sum:
Future Value (FV) = Present Value (PV) + (PV * Interest Rate * Time)
We rearrange the formula to solve for the present value (PV):
PV = FV / (1 + Interest Rate * Time)
Plugging in the given values:
FV = $4500
Interest Rate = 7.0% = 0.07
Time = 5 years
PV = $4500 / (1 + 0.07 * 5)
PV = $4500 / (1 + 0.35)
PV = $4500 / 1.35
PV ≈ $3333.33
Therefore, the present value that must be invested now in order to have $4500 for a home-entertainment center in 5 years at an interest rate of 7.0% is approximately $3333.33 (rounded up to the nearest cent).
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