6. Using any method(s), solve △KHP when h=16.1, p=24.9 and k=12.8
Answers
The angles of the triangle KHP are P ≈ 118.555°, H ≈ 34.614°, K ≈ 26.844°, respectively.
How to determine the measures of missing angles in a triangle
In this question we have the case of a triangle where the lengths of three sides are known and measures of angles must be determined. The missing angles can be found by means of law of cosine, whose equations related to the triangle are introduced below:
p² = h² + k² - 2 · h · k · cos P
h² = p² + k² - 2 · p · k · cos H
k² = h² + p² - 2 · h · p · cos K
Where:
h, k, p - SidesH, K, P - AnglesIf we know that h = 16.1, p = 24.9 and k = 12.8, then the measures of the angles are:
cos P = (p² - h² - k²) / (- 2 · h · k)
cos P = (24.9² - 16.1² - 12.8²) / (- 2 · 16.1 · 12.8)
cos P = - 0.478
P ≈ 118.555°
cos H = (h² - p² - k²) / (- 2 · p · k)
cos H = (16.1² - 24.9² - 12.8²) / (- 2 · 24.9 · 12.8)
cos H = 0.823
H ≈ 34.614°
cos K = (k² - h² - p²) / (- 2 · h · p)
cos K = (12.8² - 16.1² - 24.9²) / (- 2 · 16.1 · 24.9)
cos K = 0.892
K ≈ 26.844°
Triangle KHP has the following missing angles: P ≈ 118.555°, H ≈ 34.614°, K ≈ 26.844°.
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Related Questions
Which angle corresponds to <8?
Answers
Answer:
>4
Step-by-step explanation:
the answer of the question is >4
for each pair expalin why they are equivelent 5:6 15:18
Answers
The two ratios are equivalent because if we multiply both of the numbers by 3, we will get the other ratio.
Why are the two ratios equivalent?Here we want to explain why the two ratios:
5:6 and 15:18
Are equivalent, where equivalent means that these two ratios mean the same thing.
Now, if we take any ratio
a:b
and we multiply both numbers by the same real number k (except for zero) we will get the equivalent ratio.
k*a: k*b
Now, let's look to our ratios:
5:6
If we multiply these 2 numbers by 3, we will get.
3*5: 3:6
15: 18
So yes, these are equivalent.
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please help asap
• it would mean sm and make my day
Answers
The compound inequality for the graph given is -2 < x < 5.
How to find the compound inequality ?When a compound inequality is graphed such that there is an open circle instead of a filled - in circle over a number, then it means that x is either greater than this value, or less than this value. In other words, x is not equal to this value.
The circles over - 2 and 5 are not filled in which means that x is greater or less than - 2 and 5.
x is less than 5 because the arrow goes from 5 to infinity and x is greater than - 2 for the same reason.
The compound inequality is therefore:
-2 < x < 5
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how do you find the distance formula to find the distance between each of the specified points. (ie pythagorean theorem)?
Answers
Answer: The distance formula is a mathematical formula used to find the distance between two points in a plane. One way to find the distance formula is by using the Pythagorean theorem.
The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.
The distance formula can be derived from the Pythagorean theorem by considering the two points as the two endpoints of a line segment. The formula is as follows:
Distance = √(x2 - x1)^2 + (y2 - y1)^2
where (x1, y1) and (x2, y2) are the coordinates of the two points.
In this formula, the difference in the x-coordinates is squared and the difference in the y-coordinates is also squared. Then, these two values are added and the square root of the result gives the distance between the two points.
For example, if we have two points (x1, y1) = (2, 3) and (x2, y2) = (5, 8), we can use the distance formula to find the distance between these two points:
Distance = √((5 - 2)^2 + (8 - 3)^2)
Distance = √(3^2 + 5^2)
Distance = √(9 + 25)
Distance = √(34)
Distance = 5.83
Therefore, the distance between the two points is 5.83 units.
Step-by-step explanation:
Write and solve an inequality.
The speed limit of a highway is 65 miles per hour. A car is traveling at least 74 miles per hour. How many miles per hour, m, over the speed limit is the car traveling?
Answers
Answer:
The car is travelling at least 9 mph over the speed limit---------------------------
The speed limit is 65 mph, the speed of the car is at least 74 mph.
The difference m is the over the speed limit value.
Set an inequality:
65 + m ≥ 74m ≥ 74 - 65m ≥ 9A bank loaned out $14000, part of it at the rate of 7% per year and the rest at 17% per year. If the interest received in one year totaled $2000, how much was loaned at 7%
How much of the $14000 did the bank loan out at 7%
Answers
The required loan out of 14000 which is on 7% interest is given as $3800.
What are simultaneous linear equations?Simultaneous linear equations are two- or three-variable linear equations that can be solved together to arrive at a common solution.
Here,
Let part of the loaned amount at 7 % interest be x and another part with 17% interest be y,
A bank loaned out $14000, part of it at the rate of 7% per year and the rest at 17% per year, and the interest received in one year totaled $2000,
According to the question,
x + y = 14000
x = 14000 - y - - - - - (1)
and,
0.07x + 0.17y = 2000 - - - - (2)
Put x from equation 1 in equation 2
Gives,
y = 10200
Now,
x = 14000 - 10200
x = 3800
Thus, the required loan out of 14000 which is on 7% interest is given as $3800.
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The area of the regular octagon is 10.15 cm².
1.45 cm
What is the measure of the apothem, rounded to the
nearest hundredth of a centimeter
Answers
The measure of the apothem is 1.75cm.
What is a regular octagon?
Eight equal sides and eight equal angles make up a normal octagon. Each side is the same length, and each angle is the same size. The total interior and external angles are 1080° and 360°, respectively. The inner angle at each vertex of a regular octagon is 135°.
Here, we have
Given: The area of the regular octagon is 10.15 cm².
We have to find the measure of the apothem.
The octagon can be divided into 8 congruent (identical) isosceles triangles. One of them is AOB.
Area (triangle AOB) = 10.15/8 = 1.27cm².
Area(triangle AOB) is also 1/2*MO*AB
1.27 = 1/2*MO*1.45
MO = 1.75cm
Hence, the measure of the apothem is 1.75cm.
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M varies jointly as r² and as l. If M = 20 when I = 8 and r = 2, find: (a) the law connecting these variables, (b) r when M = 400 and l=10.
Answers
Answer:
(a) Law connecting the variables:
[tex]M = \frac{5}{8}Ir^{2}[/tex]
(b) r = 8 and r = -8
Step-by-step explanation:
(a) Equation for a joint variation is:
[tex]M = KIr^{2}[/tex] where K is the constant
Substituting the provided values of M, I and r:
= [tex]20 = K(8)(2^{2} )[/tex]
= [tex]20 = K(8)(4)[/tex]
= 20 = 32K
= [tex]K = \frac{20}{32}[/tex]
[Divide the numerator and the denominator by the highest common factor (i.e. 4)]
= [tex]K = \frac{5}{8}[/tex]
Therefore:
[tex]M = \frac{5}{8}Ir^{2}[/tex]
(b) [tex]M = \frac{5}{8} I r^{2}[/tex]
Substituting the values of M and I:
[tex]400 = \frac{5}{8} (10)r^{2}[/tex]
[tex]400 = \frac{5}{8} (10)r^{2}[/tex]
[tex]400 = \frac{50}{8} r^{2}[/tex]
[tex]\frac{(400)(8)}{500} =r^{2}[/tex]
[tex]\frac{3200}{50} = r^{2}[/tex]
[tex]64 =r^{2}[/tex]
Taking the square root on both sides of the equation:
[tex]r = \sqrt{64}[/tex]
[tex]r = 8[/tex] and [tex]r = -8[/tex]
Set up a ratio. If the ratio cannot be reduced to an equivalent ratio in terms of small integers, then express it as a ratio of decimal equivalents with the smallest term set at 1. Maintain three-figure accuracy.
Don, Bob, and Ron Maloney’s partnership interests in Maloney Bros. Contracting are in the ratio of their capital contributions of $78,000, $52,000, and $65,000, respectively.
What is the ratio of Bob's to Ron's to Don's partnership interest?
Answers
The ratio of Bob's to Ron's to Don's partnership interest is 26.6% : 33.3% : 40.0%.
What does partnership interest mean?A partnership interest is the percentage of a partnership that a specific member or individual owns. In this context, partnerships refer to a specific method of organizing business ownership in which each owner is a partner, with equal rights, privileges, and obligations to the company as a whole.
Data
Partnership interests in Maloney Bros:
Don - $78,000
Bob - $52,000
Ron Maloney’s - $65,000
The total capital contribution is:
= $78,000 + $52,000 + $65,000
= $195,000
Bob's partnership interest is:
= $52,000/$195,000
= 0.266 or 26.6%.
Ron's partnership interest is:
= $65,000/$195,000
= 0.333 or 33.3%.
Don's partnership interest is:
= $78,000/$195,000
= 0.400 or 40.0%.
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There are 135 people in a sport centre.
73 people use the gym.
73 people use the swimming pool.
67 people use the track.
36 people use the gym and the pool.
35 people use the pool and the track.
32 people use the gym and the track.
14 people use all three facilities.
How many people use exactly one of these facilities?
Answers
If there are 135 people in a sport centre. The number of people that use exactly one of these facilities is 49.
Number of people that uses gym= 73- ( 32-14+ 36-14 + 14)
Number of people that uses gym = 73 - 54
Number of people that uses gym = 19
Number of people that use pool only = 73-(36-14+35-14+14)
Number of people that use pool only= 73-57
Number of people that use pool only = 16
Number of people that use track only = 67-(32-14+35-14+14)
Number of people that use track only = 67-53
Number of people that use track only = 14
Number of people that use exactly one of these facilities =19+16+14
Number of people that use exactly one of these facilities = 49
Therefore we can conclude that the number of people that use exactly one of these facilities is 49.
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HELP MEEEEEE
10 Answer:
Evaluate the expression 7 + x + (-3) when x = 2:
11 Answer:
Evaluate the expression 4x2 + 2 when x = 2.
12 Answer:
Evaluate the expression |x + 10| when x = -12.
13 Answer:
Evaluate the expression |2x + 1| when x = 3/2.
14 Answer:
Evaluate the expression (x - 3)/4 when x = 4.
15 Answer:
Evaluate the expression (5 - x)/6 when x = 3.
Answers
The value of expression is ,
10) 6
11) 18
12) 2
13) 4
14) [tex]\frac{1}{4}[/tex]
15) [tex]\frac{1}{3}[/tex]
What is expression?
Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation. Unknown variables, integers, and arithmetic operators are the components of an algebraic expression. There are no symbols for equality or inequality in it.
Here the given expression
10) 7+x+(-3)
Put x=2 then
=> 7+2-3
=> 7-1 = 6
11) 4[tex]x^2[/tex]+2
put x=2 then
=> [tex]4*2^2+2[/tex]
=> 4*4+2
=> 16+2=18
12) Ix+10I
put x=-12 then
=> I-12+10I
=> I-2I = 2
13) |2x + 1|
put x= 3/2 then
=> I2*[tex]\frac{3}{2}[/tex]+1I
=> I3+1I
=> I4I = 4
14)(x - 3)/4
put x=4 then
=> [tex]\frac{4-3}{4}[/tex]
=> [tex]\frac{1}{4}[/tex]
15) (5 - x)/6
put x=3 then
=> [tex]\frac{5-3}{6}[/tex]
=> [tex]\frac{2}{6}[/tex] = [tex]\frac{1}{3}[/tex]
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4. The thickness of a textbook is b mm. Write the expression for each of the following:
The thickness of 5 stacked textbooks?
The thickness of each page, if the pages are numbered to 225?
Answers
When the thickness of a textbook is b mm the expressions for:
thickness of 5 stacked textbooks = 5b mm
thickness of each page, if the pages are numbered to 225 = b / 225
How to write the expressions for each conditionThe thickness for each of the condition is written as follows
For the thickness of 5 stacked textbooks
= b + b + b + b + b
= 5b
For thickness of each page, if the pages are numbered to 225
In this case division is used to ascertain the thickness of each page in the book. this is done by dividing the total thickness by the number of pages in the book
= b / 225
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(30 POINTS) A newly hired lawyer receives a $15,000 signing bonus from a law firm and invests the money in a savings account at 4.75% interest. After 42 months, the lawyer checks the account balance.
Part A: Calculate the interest earned, to the nearest dollar, if the interest is compounded quarterly. Show all work. (2 points)
Part B: Calculate the interest earned, to the nearest dollar, if the interest is compounded continuously. Show all work. (2 points)
Part C: Using the values from Part A and Part B, compare the interest earned for each account by finding the difference in the amount of interest earned. (1 point)
Answers
PLEASE HELP ASAP
what are the possible values for 1/4 + S = 18/20
Answers
Answer:
0.65 and 13/20
Step-by-step explanation:
What is the coefficient of the variable in the expression 2 − 5x − 4 + 8? (3 points) a −5 b −4 c 2 d 8
Answers
In the expression 2 − 5x − 4 + 8, the coefficient of x is -5. Thus, option a is correct.
What is a coefficient?A number or quantity combined with a variable is referred to as a coefficient. The variable is usually multiplied by an integer, which is then written next to it. It is assumed that the variables with no associated value have a coefficient of 1. For instance, in the expression 3x, the coefficient of x is 3, whereas in the expression x2 + 3, the coefficient of x2 is 1.
A variable's coefficient is the number or letter that the variable contains. As an illustration, the coefficient of variable x in the formula 2x + 3y is 2, and the coefficient of variable y is 3 in the same formula.
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answer for 10 points
Ann has collected 32 Beanie Babies. One half of all her Beanie Babies are puppies. One quarter of all her Beanie Babies are kittens, and one eighth of her Beanie Babies are mice. The rest of the Beanie Babies are a tiger, a crab and rabbits.
How many puppies does Ann have?
Answers
Answer:
16
Step-by-step explanation:
Basically one-half of 32
one-half = 1/2
Hence, 1/2 x 32 = 16
The rest of the information is not needed, it is a trick.
What is the value of y that makes T Parallel to U
Answers
Answer: y = 18
Sentence: The value of y that makes T Parallel to U is 18.
Step-by-step explanation:
We are given 3 expressions:
(7x)(6y + 9)(3x + 36)We know that since the angle (7x) is on the same line as the angle (3x + 36), we can therefore determine that they correspond to each other. I referred an image to help demonstrate this concept. So since they correspond to each other, that means they have the same value (meaning they are equal to each other).
We can set both expressions equal to each other.
7x = 3x + 36
And solve:
7x = 3x + 36
-3x -3x
4x = 36
/4 /4
x = 9
now we know the value of x, we can plug it into one of the equations. We can plug it in to 3x + 36 to help with the process in solving y.
3(9) + 36 = 63 degrees
Since 6y + 9 and 3x + 36 (63 degrees) are supplementary angles, we can subtract 180 from 63.
180 - 63 = 117
now we know that 117 degrees = 6y + 9 BUT!, we need to solve for y, because that's what the question is asking for.
So lets solve for y:
117 = 6y + 9
-9 -9
108 = 6y
/6 /6
y = 18
Aaron is remodeling his patio. He will decrease the length of his patio, L, by 7 feet. Aaron will also changed the patio's width to be 3 times the original width, W. Which expression shows the ratio of the length to the width of the remodeled patio?
Answers
Answer: top right
Step-by-step explanation:
It says decrease by 7 which mean subtract (-) and times 3 mean multiply by 3 (x3)
7) Yesterday, Cindy re-posted a meme on social media and tagged 3 of her friends. Today, each
of her 3 friends re-posts the meme and tags 3 of their friends. This pattern of re-posting and
tagging 3 friends continues for several days. How many people have re-posted the meme
after 8 days? (Hint: If this is geometric, you should write a formula to help answer the
question)
Answers
The people that have posted the meme after 8 days using the exponential equation y=t^3 will be 512.
What are Exponential Equations?
An exponential equation is an equation with exponents where the exponent (or) a part of the exponent is a variable. For example, 3^x = 81, 5^x - 3 = 625, 62^y - 7 = 121, etc are some examples of exponential equations. We may come across the use of exponential equations when we are solving the problems of algebra, compound interest, exponential growth, exponential decay, etc.
Now,
To find number of people who have re-posted
we need to make a exponential equation
Here, As cindy tags meme to 3 people in starting and they also tag 3 people in subsequent days, then equation will be y=t^3 where t=no of days.
No of people after 8 days,
y=8^3
y=512 (no of people after 8 days)
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This is an example of geometric growth, So after 8 days 6561 people will have re-posted the meme.
What is geometric growth and explanation of above answer? Geometric growth is a type of exponential growth where a quantity increases at a fixed rate multiplied by itself over time. It is represented by a geometric sequence, where each term is the previous term multiplied by a constant factor. It is commonly used to model population growth, compound interest, and viral spread of information.where each day the number of people who have re-posted the meme is multiplied by 3. The formula to calculate the total number of people who have re-posted the meme after 8 days is 3^8 = 6561 peopleTo learn more about geometric growth refer:
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Which expression represents the total area of the rectangle. (look at picture)
Answers
What is 7, 10, 13, 16, as a linear function
Answers
Answer:
This is a sequence of numbers that can be expressed as a linear function. The linear function would be of the form y = mx + b, where m is the slope of the line and b is the y-intercept. In this case, m = 3 and b = 7, so the linear equation for this sequence is y = 3x + 7.
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Lynne bought a bag of grapefruit, 1 5/8 pounds of
apples, and 2 3/16 pounds of bananas. The total
weight of her purchases was 7 1/2pounds. How
much did the bag of grapefruit weigh?
Answers
Using the mathematical operations of addition and subtraction, the weight of the bag of grapefruit is 3¹¹/₁₆.
What are the mathematical operations?The basic mathematical operations we have studied so far include addition, subtraction, division, and multiplication.
In addition operation, two or more addends are added to obtain a result known as the sum or total.
Using subtraction operation, the minuend, subtrahend, and difference are the major parts, including the subtraction operator (-).
There are two ways of solving this problem, we can add the fractional weights of apples and bananas and subtract the sum from the total weight of fruits Lynne bought.
We can also subtract each fractional weight from the total weight of fruits to arrive at the fractional weight of the bag of grapefruit.
The total weight of Lynne's purchases = 7¹/₂ pounds
The weight of apples = 1⁵/₈ pounds
The weight of bananas = 2³/₁₆ pounds
The weight of grapefruit = x
= 7¹/₂ - 1⁵/₈ - 2³/₁₆
= 3¹¹/₁₆
Add fractional weights:
1⁵/₈ + 2³/₁₆ = 3¹³/₁₆
Subtract the sum of the fractional weights from the total weight:
7¹/₂ - 3¹³/₁₆ = 3¹¹/₁₆
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factorise fully 6x^2y +15xy^2
Answers
Answer: 3 x y (2 x + 5 y)
Step-by-step explanation:
im not really sure but i gave it a try
In the following descriptions of a study, confounding in present. Describe the explanatory and confounding variable in the study and how the confounding may invalidate the conclusions of the study. Furthermore, suggest how you would change the study to eliminate the effect of the confounding variable.
(a)A hospital introduces a new blood clot medication that can be given to the patients suffering from a stroke during the crucial period of 12 hours after stroke begins. The new medication appears to be very successful because in the first year of its implementation there is a higher rate of total recovery by the patients in comparison to the rate in the previous year for patients admitted to the hospital.
(b) A high school mathematics teacher is convinced that a new software program will improve math scores for students take the SAT. As a method of evaluating her theory, she offers the students opportunity to use the soft-ware on the school’s computers during a 1-hour period after school. The teacher concludes the software is effective because the students using the software has significantly higher scores on the SAT than did the students who did not use the software.
Answers
a. The explanatory variable is the new blood clot medication, and the confounding variable is the time period of 12 hours after the stroke begins.
b. The explanatory variable is the new software program, and the confounding variable is the 1-hour period after school
What are the variables?The confounding variable may invalidate the conclusions of the study because it is possible that the higher rate of total recovery is not due to the new medication, but rather due to the fact that the patients are being treated within the crucial 12-hour period after the stroke begins. To eliminate the effect of the confounding variable, the study could be conducted as a randomized controlled trial, where patients are randomly assigned to receive either the new medication or a placebo, and both groups are treated within the 12-hour period after the stroke begins.
In (b) the explanatory variable is the new software program, and the confounding variable is the 1-hour period after school. The confounding variable may invalidate the conclusions of the study because it is possible that the higher scores are not due to the software, but rather due to the fact that the students using the software were given more time to study and practice. To eliminate the effect of the confounding variable, the study could be conducted as a randomized controlled trial, where students are randomly assigned to use the software or not, and both groups are given the same amount of time to study and practice.
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What can you say back to someone who asked: " How you been today?"
Answers
Answer:I think being honest with them just tell them how you really feel not because just they ask and you just say I am fine how are you just tell how you really feel about that day. Be honest ...
Step-by-step explanation:
How I've been today? Quite magnificent. Thank thou for your generosity.
work this out for points and brainliest !
Answers
Answer:
P = 5c + 11 , c = 3
Step-by-step explanation:
(a)
the perimeter P) is the sum of the sides.
Note that the 2 sides with a ' dash' through them are congruent
summing the 4 sides
P = c + 5 + 3c - 2 + 10 - 2c + 3c - 2 ( collect like terms )
= 5c + 11
(b)
equate the expression for P from (a) to 26
5c + 11 = 26 ( subtract 11 from both sides )
5c = 15 ( divide both sides by 5 )
c = 3
For what length of time did Kathy and Brian drive?
A) Kathy drove 3 hours and Brian drove 9 hours
B) Kathy drove 4 hours and Brian drove 8 hours
C) Kathy drove 6 hours and Brian drove 6 hours
D) Kathy drove 8 hours and Brian drove 4 hours
3) None of the above
Answers
Answer:
None of the above
Step-by-step explanation:
Beacuse,
3*65 +9*55 = 690miles
4*65 + 8*55 = 700 miles
6*65 + 6*55 = 720 miles
8*65 + 4*55 = 740 miles
The total length is 750miles which is not suitable in this above four answers
Change each algebraic fraction into an equivalent fraction with the denominator 24a^3b^2.
5b/8a^3
Answers
The algebraic fraction which is equivalent to the given expression in which case, the denominator is 24a³b² as required is; 15b³ / 24a³b².
Which algebraic fraction is equivalent to; 5b / 8a³?As evident in the task content; the given algebraic expression whose equivalent is to be determined is; 5b / 8a³.
However, to determine an equivalent expression whose denominator is; 24a³b²; one must determine the quotient of 24a³b² and 8a³.
= 24a³b² / 8a³.
= 3b²
On this note, it follows that the numerator and denominator of the given algebraic fraction can each be multiplied by 3b² in order to determine the equivalent expression.
= ( 5b • 3b² ) / ( 8a³ • 3b² )
= 15b³ / 24a³b².
Ultimately, thee required equivalent algebraic fraction is; 15b³ / 24a³b².
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How do I divide with rational expressions.
Answers
The value of the rational expression is q⁴ / 14p⁴
What are rational expressions?A rational expression is the ratio of two polynomials. If f is a rational expression, then f can be written in the form p/q where p and q are polynomials.
Given are rational expressions,
5pq / 16p³ ÷ 35p²q² / 8q⁵
Using identity, a/b ÷ c/d = a/b × d/c
5pq / 16p³ × 8q⁵ / 35p²q²
= 40q⁴ / 560p⁴
= q⁴ / 14p⁴
Hence, the value of the expression is q⁴ / 14p⁴
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The fourth grade is going on a field trip and taking two buses. One bus has 3 rows of seats with 9 seats in each row the other bus has four times as many seat as the first bus. How many seats are there in both buses?
Answers
The number of seats of each bus is given as follows:
First bus: 27. Second bus: 108.How to obtain the number of seats?The number of seats of each bus is obtained applying the proportions in the context of the problem.
One bus has 3 rows of seats with 9 seats in each row, hence the number of seats of the first bus is given as follows:
3 x 9 = 27.
The other bus has four times as many seat as the first bus, hence the number of seats of the second bus is given as follows:
4 x 27 = 108.
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