Answers
Answer:
[tex]A= \frac{400}{21} B=\frac{580}{21}[/tex]
Step-by-step explanation:
You just have to remember the rules of the triangles in order to be able to solve this:
The rule of trigonometry that you will have to use is a is similie to 20, B is simile to 29 and 20 is 20.
So you would have to put them like this:
[tex]\frac{21}{20}= \frac{20}{a}= \frac{29}{b}[/tex]
You just have to clear the equations for A and B:
[tex]a=\frac{20*20}{21}=\frac{400}{21}\\ b=\frac{29*20}{21} =\frac{580}{21}[/tex]
So that would be your answer.
The value of 'a' is 400/21 and the value of 'b' is 580/21 and this can be determined by using the properties of trigonometry.
According to the properties of trigonometry:
[tex]\dfrac{21}{20}=\dfrac{20}{a}=\dfrac{29}{b}[/tex] --- (1)
Now, in order to determine the value of 'a' use the above equation:
[tex]\dfrac{21}{20}=\dfrac{20}{a}[/tex]
Cross multiply in the above equation.
[tex]21a = 20\times 20[/tex]
21a = 400
Divide 400 by 21 in order to get the value of a.
[tex]a = \dfrac{400}{21}[/tex]
Now, to determine the value of 'b' again use the equation (1).
[tex]\dfrac{20}{\dfrac{400}{21}}=\dfrac{29}{b}[/tex]
Cross multiply in the above expression.
[tex]20b = 29\times \dfrac{400}{21}[/tex]
[tex]20b = \dfrac{11600}{21}[/tex]
Now, divide on both sides by 20 in the above expression.
[tex]\rm b = \dfrac{11600}{21\times 20}[/tex]
[tex]\rm b = \dfrac{580}{21}[/tex]
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Related Questions
△ABC is reflected to form △A′B′C′ . The vertices of △ABC are A(3, 1) , B(1, 5) , and C(6, 9) . The vertices of △A′B′C′ are A′(−1, −3) , B′(−5, −1) , and C′(−9, −6) . Which reflection results in the transformation of △ABC to △A′B′C′ ?
Answers
Answer:
that would be a reflection across the y axis resulting in a -x
Step-by-step explanation:
The scale on a map is 1 cm for every 400 km. If Maine and Japan are 22 cm apart on the map, what is the distance between Maine and Japan?
Answers
Which expression represents the sixth term in the binomial expansion of (5y+3)^10
Answers
[tex]\bf \stackrel{coefficient}{\left(\frac{n!}{k!(n-k)!}\right)} \qquad \stackrel{\stackrel{first~term}{factor}}{\left( a^{n-k} \right)} \qquad \stackrel{\stackrel{second~term}{factor}}{\left( b^k \right)}[/tex]
[tex]\bf \stackrel{coefficient}{\left(\frac{10!}{5!(10-5)!}\right)} \qquad \stackrel{\stackrel{first~term}{factor}}{\left( (5y)^{10-5} \right)} \qquad \stackrel{\stackrel{second~term}{factor}}{\left( (-3)^5 \right)} \\\\\\ 252(5y)^5(-3)^5\implies 252(5^5y^5)(-3)^5\implies -252(3125y^5)(243) \\\\\\ -191362500y^5[/tex]
Answer:
bb
Step-by-step explanation:
A rectangular prism has a length of 4 1/2 millimeters, a width of 4 1/2 millimeters, and a height of 6 millimeters.
Sally has a storage container for the prism that has a volume of 143 cubic millimeters.
What is the difference between the volume of the prism and the volume of the storage container?
Help Please?
Answers
V = (4 1/2)(4 1/2)(6)
Converting the fractions to mixed numbers we have
V = (9/2)(9/2)(6/1) = 486/4 = 121.5
The storage container has a volume of 143, so the difference is 143 - 121.5 = 21.5 cubic mm.
Answer:
21 1/2
Step-by-step explanation:
In an office, the number of chairs, c , is equal to five more than twice the number of desks, d. Which equation matches the information?
Answers
d (unknown)
chair is 5 more than twice the number of desks
So if I'm not wrong
The answer should be
c = 5+2d
Please correct me if I'm wrong :D
Final answer:
The algebraic equation that represents the relationship between the number of chairs, c, and the number of desks, d, in an office, where the number of chairs is five more than twice the number of desks, is c = 2d + 5.
Explanation:
The student's question pertains to creating an algebraic equation based on a given word problem describing the relationship between the number of chairs (c) and desks (d) in an office. The problem states that 'the number of chairs, c, is equal to five more than twice the number of desks, d'.
To formulate the equation that illustrates this relationship, we apply the information provided:
Identify the number of chairs as c.Determine that c is 'five more than' something, which suggests addition.Recognize that 'twice the number of desks' means 2 times d, or 2d.Combine the above to conclude that the 'five more than' is added to the 'twice the number of desks', which gives us the equation c = 2d + 5.If f(x)=7+4x and g(x)=1/2x What is the value of (f/g)(5)?
Answers
Answer:
[tex]\bigg(\displaystyle\frac{f}{g}\bigg)(5) = 270[/tex]
Step-by-step explanation:
We are given the following information in the question:
[tex]f(x) = 7 +4x\\\\g(x) = \displaystyle\frac{1}{2x}[/tex]
We have to find the values of [tex]\displaystyle\frac{f}{g}(x)[/tex]
[tex]\bigg(\displaystyle\frac{f}{g}\bigg)(x) = \frac{f(x)}{g(x)} = \frac{7 + 4x}{\frac{1}{2x}} = 2x(7+4x)[/tex]
Putting x = 5, we have:
[tex]\bigg(\displaystyle\frac{f}{g}\bigg)(x) = 2x(7+4x)\\\\\bigg(\displaystyle\frac{f}{g}\bigg)(5) = 2(5)(7+20)=270[/tex]
270 is the required value of [tex]\bigg(\displaystyle\frac{f}{g}\bigg)(5)[/tex].
What is the solution to 2log9(x)=log^9(8)+log9(x-2)
Answers
Log₉x² = log₉8 + log₉(x-2)
Log₉x² = log₉(8×(x-2))
Log₉x² = log₉8x-16
Log₉x² - log₉8x-16 = 0
Log₉(x²/(8x-16)) = 0
x²/(8x-16) = 9°
x² = 1 × 8x-16
x²-8x+16 = 0
x²-4x-4x+16 = 0
x(x-4)-4(x-4) = 0
(x-4)(x-4) =0
Therefore x = 4.....
Answer:
C. x=4
Step-by-step explanation:
1/6 of 3 yards=______feet
I know I just ask one but u get 17 points so plz help I'm stuck
Answers
In this question, first we have to see how many feets are in 1 yard .
And there are 3 feets in 1 yard.
So in 3 yards, there are 9 feets
Therefore we will get
[tex] \frac{1}{6}*3 yards= \frac{1}{6} * 9 feet = 1.5 feet [/tex]
Therefore the answer of the given question is 1.5 feet.
Final answer:
To find the equivalent feet for 1/6 of 3 yards, multiply 1/6 by 3 feet per yard to get 1.5 feet.
Explanation:
1/6 of 3 yards=_____feet
Step 1: 1 yard is equal to 3 feet.
Step 2: To find the equivalent feet for 1/6 of 3 yards, calculate 1/6 x 3 = 0.5 x 3 = 1.5 feet.
how to solve -2x+y=7, 3y=6x+4
Answers
To the additional, see the attached graph for this system.
Elijah is going to spin a spinner that goes to 4 180 times.He predicts that 60 of those spins will result in the spinner landing on the section labeled 3. Based on the theoretical probability, which best describes Elijah’s prediction?
Answers
Answer:
A. Elijah’s prediction is exact because 180 divided by 3 = 60.
Step-by-step explanation:
Patrick ate 2/3 of a fruit bar write an equivalent fraction for the amount of fruit bar Patrick ate
Answers
A radar gun used to determine the speed of passing cars must be within 7 mph of the actual speed of a selected car. If a highway patrol officer reads a speed of 59 mph for a car, does he have irrefutable evidence that the car was speeding in a 55 mph zone?
Answers
Point R is located at (11,5).point S is located at (-1,5). what is the distance between point R and point S
Answers
d=√(x2-x1)² + (y2-y1)²
d=√(-1-11)² + (5-5)²
d=√(-12)² + 0
d=12
how many radians are in a semicircle? a.2π, b.π, c.π/2, d.3π/2
Answers
A semicircle, which is half of a full circle, consists of half the total amount of radians in a full circle. Since a full circle has 2π radians, a semicircle contains π radians. Therefore, the correct answer is b.π.
Explanation:To answer your question, let's review the structure of a circle.It is divided by its radius into 360 degrees or by its diameter into a full rotation of 2π radians. Therefore, a semicircle, which is half of a circle, must consist of half the total amount of radians in a full circle.
In a full circle, there are 2π radians. Hence, in a semicircle, which is exactly half of the full circle, there would be 2π/2. This simplifies to π radians.
So, the correct answer to your question 'How many radians are in a semicircle?' is b.π.
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What is 1/4 as a whole number?
Answers
The measure of angle E, the angle of elevation from point A to point B, is 5(x-2). The measure of angle D, the angle of depression from point B to point A, is (x+14). Find the measure of each angle.
Answers
5(x -2) = x +14
5x -10 = x +14 . . . . . . . eliminate parentheses
4x = 24 . . . . . . . . . . . . add 10-x
x = 6
The angles of elevation and depression are both (6+14)° = 20°.
Answer:
measure of angle E equals 20 degrees, measure of angle D equals 20 degrees
HELP ME PLEASE! How is the graph of mc027-1.jpg related to its parent function, mc027-2.jpg?
Answers
The graph of [tex]y = \sqrt{-2x[/tex] relates to its parent function as a result of (d) horizontal compression by a factor of 2, and a reflection across the y-axis
What is a function transformation?A function transformation involves changing the form or equation of a function to another through reflection, dilation, translation or rotation
How to determine the function transformationThe parent function is given as:
[tex]y = \sqrt x[/tex]
Compress the function horizontally by a factor of 2, using the following rule
[tex](x,y) \to (2x,y)[/tex]
So, we have:
[tex]y = \sqrt {2x[/tex]
Next, reflect the function over the y-axis, using the following rule
[tex](x,y) \to (-x,y)[/tex]
So, we have:
[tex]y = \sqrt {-2x[/tex]
Hence, the function transformation is (d)
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What is the slope of a line that is parallel to to the one shown? (-3, 2) (0, -2)
Answers
slope = (2 + 2)/(-3 - 0) = -4/3
parallel lines have same slope
so answer is -4/3
Which is a disadvantage of withdrawing more money than is available in a checking account?
Answers
A disadvantage of withdrawing more than you have in your account is you will be charged an overdraft fee.
What is an Overdraft Fee?An overdraft fee can be described as the fee your bank charges you when you make a withdrawal from your account beyond what you have in it.
An overdraft fee is one of the disadvantages of withdrawing more money than you have in your account..
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amy is building a house. the basement floor is at -15 feet. the roof of the house is above the ground 25 feet. write an inequality to compare the heights. explain the meaning of the inequality.
BONUS: what is an inequality.
Answers
For example, this is a problem of heights.
There is a minimum height and a maximum height.
We can use the following inequation to describe the problem:
Let
x = height in feet.
The inequation is:
-15 <= x <= 25
answer:
-15 <= x <= 25
what is the square root of 4 multiplied by 16
Answers
the answer is 32.
Rearrange the formula A = P + Prt for t.
Answers
A=P+Prt
Solving for t.
Factor out P from the right side of the equation.
A=P(1+rt)
Divide both sides by P.
A/P= 1+rt
Subtract 1 from both sides
A/P-1=rt
Divide both sides by r.
(A/P) / r - 1/r= t
or
t= (A/P) / r - 1/r
t= A/Pr - 1/r
t= (A-P)/r
Answer: t= (A-P)/rP
Which statement best compares -1/2 and -2 1/2
Answers
The Comparison between -1/2 and -2 1/2 is -1/2 is -2 more than -5/2.
What are fraction?The fractional bar is a horizontal bar that divides the numerator and denominator of every fraction into these two halves.
The number of parts into which the whole has been divided is shown by the denominator. It is positioned in the fraction's lower portion, below the fractional bar.How many sections of the fraction are displayed or chosen is shown in the numerator. It is positioned above the fractional bar in the upper portion of the fraction.Given:
-1/2 and -2 1/2
So, -1/2 and -5/2.
So, the quantity -1/2 > -5/2
Also, -1/2 is -2 more than -5/2.
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A bucket is put under a leaking ceiling. the amount of water in the bucket doubles every minute. after 8 minutes, the bucket is full. after how many minutes is the bucket half full? show work
Answers
The water in the bucket doubles every minute. After 8 minutes the bucket is full. This means a minute earlier (i.e. at 7th minute) the water in bucket was half as compared to water in bucket after 8 minute.
So, if after 8 minutes bucket is full, after 7 minutes bucket will be half full. So the answer is 7 minutes.
Ruben has two congruent wooden dowels. He cuts one dowel in two in order to have three pieces to make a triangle. Explain why, despite having three sides, Ruben will not be able to make a triangle with his three pieces.
Answers
After cutting one of the dowels, the lengths will then be
x/2, x/2,x.
He cannot form a triangle using the three dowels because the triangle inequality requires that the sum of the two shorter sides of a triangle must be greater than the third side. Here x/2+x/2=x equals the third side, so a triangle cannot be formed.
By the way, if he cuts the long dowel a little shorter, he will then be able to make a triangle.
Answer:
The dowels are congruent, so they have the same length. If one is cut, the sum of the lengths of the two cut pieces will equal the length of the longer piece. If the pieces are to make a triangle, the sum of the lengths of the two cut pieces must be greater than the length of the third piece.
Step-by-step explanation:
A bond is a small, interest-bearing loan made by an individual to a corporate or government entity.
Please select the best answer from the choices provided
T
F
Answers
Answer: TRUE
Step-by-step explanation:
Please help me with questions 24
Answers
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After the translation, the triangle stays in quadrant IV. It then reflects over to quadrant I, only to rotate back to quadrant IV again. The size and shape does not change. These transformations are known as "rigid transformations" which preserve segment lengths (aka keep them the same). So the final triangle is congruent to the original triangle. All that has happened is that it has moved around.
Translated these questions to a equation:
6 more than 9 times a number x is -12
the quotient of a number t and 7, plus 2, is -4
Answers
6 + 9x = -12
the quotient of a number t and 7, plus 2, is -4 ...
(t/7)+ 2 = -4
Hope this helps :)
Find the sum of the geometric series with a1 = 7, r = 2, And n = 14
Answers
The sum of the geometric series with a1 = 7, r = 2, and n = 14 is -327661.
Explanation:The question is asking for the sum of a geometric series. In mathematics, the sum (S) of a geometric series is determined using the formula S = a1 * (1 - r^n) / (1 - r), where a1 is the first term, r is the common ratio, and n is the number of terms.
In the provided geometric series, a1 = 7, r = 2, and n = 14. Substituting these values into the formula gives us S = 7 * (1 - 2^14) / (1 - 2). After performing the calculations, the sum of the geometric series is -327661.
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The sum of the first 14 terms of the geometric series with the first term (a1) = 7, common ratio (r) = 2, is 114,691.
Explanation:Given the first term of the geometric series (a1) = 7, the common ratio (r) = 2, and the number of terms (n) = 14, we would like to find the sum of this series. Using the formula for the sum of a geometric series, S = a1 * (1 - r^n) / (1 - r), substituting the given values, we get:
S = 7 * (1 - 2^14) / (1 - 2)
This simplifies to S = 7 * ( -16383) / -1, which results in S = 114,691. So, the sum of the first 14 terms of this geometric series is 114,691.
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a kittens heartbeat can be as fast as 240 beats per minute . to find the number of times a kittens heart beats in 30 seconds , Aiden says divide 240 ny 30 . do you agree with him why or why not
Answers
In order to get the CORRECT answer, divide 240 by 60 seconds.
This would give you 4 heartbeats per second.
Then, multiply it by 30 seconds, which would give you 120 heartbeats.
CORRECT answer: 120