Answers
___________________________
Given: m∡3 = m∡4 = 123° ;
Since the sum of ALL ANGLES in ANY TRIANGLE equal 180°;
→ the m∡ KTL = 180 − ( m∡ KLT + m∡TKL)
We want to find
1) m∡ KLT ; AND:
2) m∡ TKL ,'
_____________
{Note: Alternatively, "m∡ KLT" can be written as: "m∡ TLK" ; and:
"m∡ TKL" can be written as: "m∡ LKT" . }.
________________________________________________
Since the sum of ALL ANGLES in ANY TRIANGLE equal 180;
→ m∡ KTL = 180 − ( m∡ KLT + m∡TKL) ;
___________________________________________
Or: → m∡ KTL = 180 − m∡ KLT − m∡TKL ;
Since, the distributive property of multiplication states:
________________________________
→ a* (b + c) = ab + ac ; AND
→ a *(b − c) = ab − ac
______________________________
Thus: m∡ KTL = 180 − ( m∡ KLT + m∡TKL) =
→ 180 − 1( m∡ KLT + m∡TKL ) ;
_____________________________________
→Note: The invisible "1" is implied, since anything multiplied by "1" equals that same value. We treat this as "-1" (negative one), due to the "minus sign).
_______________________________________
→ -1 * ( m∡ KLT + m∡ TKL ) =
→ -1 * (1 m∡ KLT + 1 m∡TKL ) =
→ (-1 * 1 m∡ KLT) + ( -1 * 1 m∡TKL ) =
→ (-1 m∡ KLT) + ( -1 m∡TKL) =
→ -1 m∡ KLT − 1 m∡TKL ;
_________________________________
Now, bring down the "180" and rewrite:
_____________________________________
→ 180 − 1 m∡ KLT − 1 m∡TKL ; → Delete the "ones" ; and Rewrite:
__________________________________________
→ 180 − m∡ KLT − m∡TKL ;
_______________________
→ m∡ KTL = 180 − m∡ KLT − m∡TKL = 180 − (m∡ KLT + m∡TKL) ;
__________________________________________________________
→Now, solve for: m∡ KLT ;
_____________________________
→Using the diagram; m∡ KLT = 180 − m∡4 ; Given m∡4 = 123; and
∡4 and ∡KLT are supplementary angles [the only two (2) angles on a particular straight line]; the sum of m∡4 and m∡KLT = 180.
→ m∡ KLT = 180 − m∡4 = 180 − 123 = 57 .
_____________________________________________
→Now, solve for: m∡TKL ;
______________________________
→Using the diagram; m∡ TKL = 180 − m∡3 ; Given m∡3 = 123; and
∡3 and ∡TKL are supplementary angles [the only two (2) angles on a particular straight line]; the sum of m∡3 and m∡KLT = 180.
→ m∡ KLT = 180 − m∡4 = 180 − 123 = 57
______________________________________________
→So, in our "triangle": ΔKTL; we want to find the m∡T; that is m∡KTL;
____________________________________________
We know that each of the other 2 (two) angles in this triangles measures 57° .
______________
So, we calculate as follows:
____________________________
Method 1:
___________
m∡ KTL = 180 − ( m∡ KLT + m∡TKL)
= 180 − ( 57 + 57) = 66° .
___________________________________________
Or: Method 2:
___________________________________________
m∡ KTL = 180 − ( m∡ KLT + m∡TKL)
= 180 − ( 57 + 57)
= 180 − (57 * 2) = 180 − 114 = 66° .
________________________________________
Or: Method 3:
_________________________
→ m∡ KTL = 180 − m∡ KLT − m∡TKL
= 180 − 57 − 57 = 66° .
______________________________________________________
Answer: m∡ KTL = 66° .
_______________________________________________________
→ Let us check our answer to see if it "makes sense":
____________________________________
66 + 57 + 57 =? 180?
66 + 57 = 123; 123 + 57 =? 180 ? Yes!
______________________________________________
Related Questions
some investments in the stock market have earned 10% annually. At this rate, earning can be found using the formula A=p(1.10)n, where A is the total value of the investment, P is the initial value of the investment, and n is the number of years the money is invested. If $1,5oo is invested in the stock market at this annual rate of return, what is the expected total value after 18 years?
A.) $29,700.00 B.) $28,050.00 C.) $8,339.88 D.) $7,581.71 I need some help on this one, I cant figure it out. I would say what I think it is, but I don't even have a good guess.
Answers
The answer to the above question is C which is $8,339.88. below is the solution:
just plug in 1500 for p, and 18 for n:
1500(1.10)^18 = 8339.88
free upvote + friend 4 free just ANSWER THE QUESTION
Erica filled 2/5 of a page of her notebook on Monday. She filled 5/6 of a page on Tuesday.
How many pages did Erica fill in her notebook?
Express your answer in simplest form.
Answers
2x6 = 12 5x6 = 30
5x5 = 25 6x5 = 30
12/30 + 25/30
= 37/30
What is the y-intercept of the line y=3x-7?
Answers
This is the slope intercept-formula.
Where:
m=slope
b=y-intercept
Compare that to the given equation:
y=3x-7
b=-7
b=y intercept
Final answer:
-7
short term goals are designed to be met in
A. less than 1 year
B. less than 6 months
C. between 6 and 9 months
D. between 1 and 5 Years
Answers
Answer:
A. less than 1 year is the answer.
Step-by-step explanation:
Short term goals are designed to be met in : A. less than 1 year
According to accounting concepts, a short term goal is less than one year and goals more than one year are considered long term goals.
Short term goals are like short term investments, that can be accomplished soon. Few other examples are - cutting costs, learning new skills, changing or having a good attitude etc.
Answer:
Correct answer would be: B less than 6 months
Step-by-step explanation:
Took test on edg 2020
What is the answer for 62 divided 5,821?
Answers
The simplified expression of 62/5821 is 62/5821
How to simplify the expressionFrom the question, we have the following parameters that can be used in our computation:
62 divided 5,821
This means that we divide 62 by 5821
So, we have the following representation
62/5821
In the above, we have
The numerator 62 is less than the denominator 5821
This means that the expression is already simplified
Hence, the simplified expression is 4/11
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What does a boy who likes to play with switches do
Answers
In a world filled with gadgets and gizmos, there exists a young enthusiast whose passion lies in the simple yet fascinating realm of switches.
This boy, with a twinkle in his eye, finds immense joy in the art of toggling buttons and flipping switches. His playtime is a symphony of clicks, a dance of circuits coming to life. Each switch, a gateway to a new adventure, ignites his imagination and curiosity.
Whether it's the satisfying snap of a light switch or the soft hum of an electronic button, he revels in the tactile magic of control. Through this seemingly mundane act, he discovers the power to illuminate, connect, and create, turning his play into a journey of endless possibilities.
Aimi is making Valentine’s Day cards for everyone in her class. She plans to use a whole sheet of paper for each of her 6 closest friends. She will use 1/8 of a sheet of paper for everyone else in the class. She has 34 sheets of paper. How many of the smaller cards can she make?
Answers
Aimi can make 224 of the smaller Valentine's Day cards after allocating a whole sheet of paper to each of her 6 closest friends, using the 34 sheets of paper she has available.
Explanation:The subject of the question is mathematics, specifically working with fractions and multiplication to solve a real-world application problem. Aimi is making Valentine's Day cards for her class and needs to calculate how many smaller cards she can make from the paper she has available. She is allocating a whole sheet of paper for each of her 6 closest friends and then needs to determine how many 1/8 sheet cards can be made with the remaining paper.
To solve this, we first calculate the amount of paper used for her close friends: 6 sheets (one for each friend). Then, we subtract this number from the total amount of paper she has, 34 sheets, leaving us with 34 - 6 = 28 sheets for the rest of the class.
The smaller cards use 1/8 of a sheet each, so we divide the remaining sheets by 1/8 to determine how many such cards she can make: 28 ÷ (1/8) = 28 × 8 = 224. Therefore, Aimi can make 224 of the smaller Valentine's Day cards.
Final answer:
After accounting for the 6 full sheets of paper used for her closest friends, Aimi can make 224 of the smaller Valentine's Day cards using the remaining 28 sheets.
Explanation:
Aimi is interested in creating Valentine's Day cards for her class and needs to determine how many of the smaller cards she can make after allocating a whole sheet of paper for each of her 6 closest friends. First, we need to calculate the total amount of paper Aimi will use for her 6 closest friends, which is 6 sheets since she is using one whole sheet per friend. Next, we'll subtract those 6 sheets from the total 34 sheets she has available, leaving us with 28 sheets for the rest of the class.
Since each of the smaller cards uses 1/8 of a sheet of paper, we'll divide the remaining sheets by 1/8 to find out how many of those cards she can make. We perform the following calculation: 28 sheets ÷ 1/8 which equals 224 cards. Therefore, Aimi can make 224 of the smaller Valentine's Day cards.
solve for d when 2x-2yd=y+xd ...?
Answers
Your new job guarantees you an eight percent raise for each year with the company. if your initial salary is $42,200, write an equation to model your salary after t years.
Answers
Answer:S=42200(1.08)^t
Step-by-step explanation:
Quincy found 120 shells during four days at the beach. if quincy found the same number of shells each day, how many shells did he find each day?
Answers
120/4 gives shells per day
30 shells per day.
Gilbert is graduating from college in twelve months, but he will need a loan in the amount of $5,125 for his last two semesters. He may either receive an unsubsidized Stafford Loan with an interest rate of 6.8%, compounded monthly, or his parents may get a PLUS Loan with an interest rate of 7.8%, compounded monthly. The Stafford Loan has a grace period of six months from the time of graduation. Which loan will have a higher balance at the time of repayment and by how much? (3 points)
The Stafford Loan has a higher balance by $134.35. The Stafford Loan has a higher balance by $274.36. The PLUS Loan has a higher balance by $54.79. The PLUS Loan has a higher balance by $85.22.
Answers
To determine which loan will have a higher balance at the time of repayment, we need to calculate the future value of both loans. The Stafford Loan will have a higher balance by approximately $234.36.
Explanation:To determine which loan will have a higher balance at the time of repayment, we need to calculate the future value of both loans. Let's start with the Stafford Loan:
Principal: $5,125
Interest Rate: 6.8%
Compounding Period: Monthly
Time: 12 months
Using the formula for future value of an ordinary annuity, we can calculate the balance of the Stafford Loan at the time of repayment:
FV = P * ((1 + r)^n - 1) / r
FV = 5125 * ((1 + 0.068/12)^(12*1) - 1) / (0.068/12)
Calculating this gives us an approximate loan balance of $5,259.35.
Now let's calculate the future value of the PLUS Loan:
Principal: $5,125
Interest Rate: 7.8%
Compounding Period: Monthly
Time: 12 months
Using the same formula, we can calculate the balance of the PLUS Loan at the time of repayment:
FV = P * ((1 + r)^n - 1) / r
FV = 5125 * ((1 + 0.078/12)^(12*1) - 1) / (0.078/12)
Calculating this gives us an approximate loan balance of $5,024.99.
Therefore, the Stafford Loan will have a higher balance at the time of repayment by approximately $234.36. The correct answer is: The Stafford Loan has a higher balance by $234.36.
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The price of a new Apple Ipod has increased by 1/4. If the original price of the Apple was $200, what is the new price today? ...?
Answers
That would be the original price of apple * incrased apple
200 * 1.25 = 250
Find the percent of increase from 320 to 380. Round to the nearest tenth of a percent if necessary.
Answers
Answer:
18.8% (gradpoint)
Step-by-step explanation:
The percent of increase from 320 to 380 is approximately 18.8%. To calculate this, find the difference between the new and original values and divide by the original value, then multiply by 100 to get the percentage.
To find the percent of increase from 320 to 380, use the formula:
Percentage increase =
[(new value - original value) / original value]
× 100%
Firstly, calculate the change in value: 380 - 320 = 60.
Then, plug this change into the formula:
Percentage increase = (60 / 320) × 100%
Now, compute the result:
Percentage increase = (0.1875) × 100%
Convert this to a percentage:
Percentage increase = 18.75%
Finally, round to the nearest tenth of a percent if necessary:
Percentage increase
= approximately 18.8%
What is the decimal equivalent of 11/8 ??
Answers
The solution is : 1.375 is the decimal equivalent of 11/8.
Here, we have,
given that,
equivalent of 11/8
Given the following mathematical expression;
11 / 8
We would apply the law of division for fractions.
11 / 8
= 11 ÷ 8
= 1.375
the decimal form.
Hence, The solution is : 1.375 is the decimal equivalent of 11/8.
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How do you construct a 112.5 degree angle? (step by step) Please help =)
Answers
next, you draw a horizontal line (red)
then find the value of the angle, and draw a line with the matched value (green)
please look at the image
PLEASE HELP!!!!!!!!!! Nobody will help me!! :(
Triangle ABC has the following vertices.
A( -6, 1) B(6, 1) C(6, 6)
List the sides of the triangle in order from largest length to smallest length.
CA, AB, and BC are the options that need to be placed in order.
Answers
Hope this helps!
A number decreased by 5 is less than 32
Answers
x-5<32
to solve add 5 to each side
x<37
According to charles law, the pressure P in pascals of a fixed volume of gas is linearly related to the temperature T in degrees celcius. In an experiment, it was found that when T =40, P=90 and when T=80, P=100.
a. What is the slope of the line containing these 2 points?
b. explain the meaning of slope in this context.
Answers
In this cotext, slope is the constant.
Which values are solutions to the inequality below?
Check all that apply.
Answers
√x > 8
This means that the square root of something is greater than 8.
So plug in everything for x and find the answer.
Anything 64 and below is NOT THE ANSWER.
√64 = 8, and 8 is not greater than 8, so anything 64 and below is wrong.
So the answer is...
D and F.
solve the inequality. graph the solution.
8a-15>73
Answers
Write the equation of a line in slope-intercept form that is perpendicular to the line y=3/5x-1 and passes through the point (-9, 4).
Answers
y = mx + b
slope(m) = -5/3
(-9,4)...x = -9 and y = 4
now we sub and find b, the y int
4 = -5/3(-9) + b
4 = 15 + b
4 - 15 = b
- 11 = b
so ur perpendicular line is : y = -5/3x - 11
Sam earned $450 during winter vacation. He needs to save $180 for a camping trip over spring break. He can spend the remainder of the money on music. Write an inequality to show how much he can spend on music.
Answers
Frogs have been breeding like flies at the Enormous State University (ESU) campus! Each year, the pledge class of the Epsilon Delta fraternity is instructed to tag all the frogs residing on the ESU campus. Two years ago (t = 0) they managed to tag all 42,000 of them (with little Epsilon Delta Fraternity tags). This year's pledge class discovered that all the tags had all fallen off, and they wound up tagging a total of 54,600 frogs.
Function: 42000 (1.3^t/2)
Assuming exponential population growth, and that all this year's tags have fallen off, how many tags should Epsilon Delta order for next year?
Answers
which means that the next year will be t = 3
So, Epsilon-delta should order :
42000 (1.3 ^ (3/2))
= 62,254 Tags
Hope this helps
Final answer:
Using the provided exponential growth function for frog population, 42000 (1.3^t/2), with t=3 for next year, the fraternity should order approximately 59621 tags.
Explanation:
To calculate the number of tags the Epsilon Delta fraternity should order for next year, we need to use the exponential population growth function provided: 42000 (1.3^{t/2}), where t is the number of years since the initial tagging. Since two years ago was t = 0, this year is t = 2. Next year will be t = 3.
Plugging t = 3 into the function, we get:
Tags needed = 42000 (1.3^{3/2})
This is an arithmetic problem involving an exponential function representing the population growth of frogs.
To solve the equation, first calculate 1.3^{3/2}, which is approximately 1.41907. Then multiply this by 42000 to get the number of tags needed for next year.
Tags needed ≈ 42000 * 1.41907
Tags needed ≈ 59621
So the fraternity should order approximately 59621 tags for next year.
Find two consecutive even integers whose sum is 126
Answers
is the soultion
What is 5.105 rounded to tge nearest hundredth?
Answers
Find the approximate value of the circumference of a circle with the given radius. Use = 3.14. Round your answer to the nearest hundredth.
5.1 cm
Answers
C = 2 r π
If r = 5.1 cm:
C = 2 · 5.1 · 3.14 = 32.028 cm ≈ 32.03 cm
Answer:
The approximate value of the circumference is 32.03 cm ( rounded to the nearest hundredth ).
ms. galan spent 55% of her savings on a television that cost $550. how much money did she have in her savings before she bought the television
Answers
However to properly solve the problem:
55% can be seen as 0.55 in decimal form. So... divide $550 by 0.55 and you'll get your answer.
550 / 0.55 = 1,000
Therefore she had 1,000 dollars before spending.
I hope that helps, have a great rest of your day! ^ ^
{-Ghostgate-}
Answer:$1000
Step-by-step explanation:my frend found this
How many 2.00-L bottles could be filled from a 24-can case of cola if in the United States a typical can holds 355 mL?
Answers
The number of bottles which could be filled are:
Approx 4 bottles ( since we got 4.260 )
Step-by-step explanation:One can case of cola holds- 355 mL
This means that:
24 can case of cola will hold= 24×355 mL
= 8520 mL
Also, 1 L=1000 mL
This means that:
1 mL= 0.001 L
Hence,
8520 mL= 8.520 L
Total amount of cola is: 8.520 L
Now, the number of bottles of 2 L which could be filled from this liquid is:
8.520/2=4.260 bottles.
A horseshoe weigs 8.2 ounces. The nails make up 0.2 of that weight. What is the weight of the horseshoe without the nails?
Answers
So, it's weight will be 8 ounce without the nails.
Hope this helps!
Graph the function y = 2x3 – x2 – 4x + 5. To the nearest tenth, over which interval is the function decreasing?
(1, ∞)
(–∞, –0.7)
(–0.7, 1)
(–1, 0.7)
Answers
Answer:
On (-2/3, 1) the given function is decreasing
Step-by-step explanation:
Do you know calculus? If so:
Differentiate y = 2x^3 – x^2 – 4x + 5 and set the derivative = to 0:
dy/dx = 6x^2 - 2x - 4 = 0, or 3x^2 - x - 2 = 0.
This factors as follows: (x - 1)(3x + 2) = 0.
The roots of this equation are {1, -2/3}.
Plot these two roots on a number line and then set up intervals as follows:
(-infinity, -2/3), (-2/3, 1), (1, infinity)
Choose a test number from each interval: { -1, 0, 2 }
By evaluating the derivative 6x^2 - 2x - 4 at each of these three test numbers, we get:
dy/dx = 6x^2 - 2x - 4 is positive on (-infinity, -2/3), and so we conclude that the given function is increasing on that interval.
dy/dx = 6x^2 - 2x - 4 is negative on (-2/3, 1), and so we conclude that the given function is decreasing on that interval. To the nearest tenth:
(-0.7, 1)
To find where the function y = 2x^3 - x^2 - 4x + 5 is decreasing, calculate the derivative, set it less than zero, solve for x, and use a sign chart to determine the intervals where the function is decreasing. The correct interval is (1, ∞).
Explanation:To determine where the function y = 2x3 − x2 − 4x + 5 is decreasing, we need to analyze its derivative. The first derivative of the function represents the slope of the tangent line to the curve at any given point, and when this slope is negative, the function is decreasing. Let's find the first derivative, f'(x) which is 6x2 − 2x − 4. To find where f'(x) is negative, we look for the x-values that make the derivative less than zero. This inequality can be solved by looking for the critical points where the derivative equals zero or is undefined, and then testing intervals around these points to see when the derivative is negative.
By factoring or using the quadratic formula, we find the critical points of f'(x) and then use a sign chart or test values to determine where the derivative is negative. For example, if we find that the derivative switches from positive to negative at x = 1, we can conclude that the function is decreasing for x values greater than 1. Therefore, the correct answer would be that the function is decreasing over the interval (1, ∞).