In the right triangle ABC, CH (H is plotted on AB) is the altitude to the hypotenuse. Find the ratio of AH:HB, if the measure of BAC=30 degrees
Pls include full proof tysm!! <3
Answers
This can be expressed as 3:1
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-------------------------------------
Explanation:
Draw out the right triangle ABC where the right angle is at angle C. Draw a perpendicular line segment from point C to the hypotenuse AB. Mark the angle BAC to be 30 degrees. Let the opposite side of the 30 degree angle be x units long. Let AH = y and HB = z. The goal is to find y/z which is the ratio AH:HB.
See Figure 1 (attached) for what the drawing should look like.
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Now add in the other angles such as ABC = 60 degrees. If you focus on triangle AHC, we have a right angle at angle H. At angle A we have the initial 30 degree angle. At angle C we have 60 degrees. See Figure 2.
Similarly, we have another 30-60-90 triangle for triangle CHB as shown in Figure 2.
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We'll use the special 30-60-90 triangle template as shown in Figure 3. Compare Figure 2 and Figure 3. Do this for triangle ABC. We see that AH+HB = y+z matches up with AB = 2x. This must mean that 2x = y+z
Furthermore, we have two additional 30-60-90 triangles which are smaller. For triangle AHC we have what you see in Figure 4. It looks a bit ugly but basically AH is equal to (x*sqrt(3))/2 since we divide the original x*sqrt(3) over 2. This is due to the fact that the hypotenuse is twice as large as the short leg. Now multiply the length of CH by value sqrt(3) to get what you see shown as the work on Figure 4. We end up wih y = (3x)/2. We'll use this later.
So write y = (3x)/2 down and put a box around it to remember to use it later.
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Now turn to Figure 5. This figure is a lot nicer than figure 4. Start with focusing on triangle CHB. The hypotenuse is BC = x. Half of this is x/2 which is the length of the short leg HB.
So z = x/2
--------------------
We found earlier that
y = (3x)/2
z = x/2
Divide the values to get
y/z = [ (3x)/2 ] divided by (x/2)
y/z = [ (3x)/2 ] * (2/x)
y/z = (3x*2)/(2*x)
y/z = (6x)/(2x)
y/z = 3
So after all that complicated messy work, we end up with the simple final answer of 3.
This can be expressed as 3:1
This means that AH is three times longer compared to HB (eg: AH could be 12 units long while HB is 4 units long)
Related Questions
Use the LCD to rewrite 1/6 and 3/8 with the same denominator
Answers
u muliple 6 by 4 to get 24 so you also must multiple 1 by 4
u multiple 8 by 3 to get 24 so you also must multiple 3 by 3
to write it out
1/6=4/24
3/8=9/24
The two fractions expressed using lowest common denominator (LCD) is written as [tex]\frac{4}{24} \ and \ \frac{9}{24}[/tex]
The given fractions;
1/6 and 3/8
LCD is the lowest common denominator. To express the given fraction using LCD, we will consider the common multiples of the denominators.
The common multiples of 8 and 6 include the following;
first multiple = 24second multiple = 48With the first common multiple, we will rewrite the two fractions to have the same denominator as shown below;
[tex]\frac{1}{6} = \frac{4}{6\times 4} = \frac{4}{24} \\\\\frac{3}{8} = \frac{3\times 3}{8\times 3} = \frac{9}{24}[/tex]
Thus, the two fractions with the same denominator is written as [tex]\frac{4}{24} \ and \ \frac{9}{24}[/tex]
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Four friends paid a total of 32 dollars for movie tickets. What is the ratio 32 dollars for4 people written as a unit rate
Answers
The difference of the squares of twenty and thirteen
Answers
13 squared = 169
400
-139
(231)
How to add 3.4 plus 40
Answers
40 = 40.0
so line the decimals up...and once the decimals are lined up, any empty spaces, u can put a 0...if it is easier....let me show u
40.0
03.4
---------add
43.4
solve for p −160=22+8(3p−4)
Answers
Write an inequality that describes this graph.
Please explain HOW you got your answer, thanks a ton! :)
Answers
If the "dot" (initial point) is hollow, it is simply a "<" or ">" symbol. If the "dot" is filled in, it means that it includes that number and we should use a "≤" or "≥" symbol. In this case, our "dot" is filled, so we will be using a "≤" or "≥" symbol.
The second rule we must recall is that the "arrow" (symbol) points the direction that the line will go. In this case, our line is going left, so our "arrow" should point left (≤).
Using all of the logic above, we would be able to see that x≤1.
Answer:
z ≤ 1
Step-by-step explanation:
We know the following:
If the initial point is colored, then the only possible inequality signs are ≤ or ≥. However, if the initial point is not colored, then the possible inequality signs for the inequality is < or >. If the line goes to the left of the initial point, it means that the initial point is greater than the numbers on the left of the initial point. If the line goes to the right of the initial point, it means that the initial point is less than the numbers on the right of the initial point.The inequality sign "≤" defines "less than or equal to"The inequality sign "≥" defines "greater than or equal to"The inequality sign "<" defines "greater than"The inequality sign ">" defines "less than"We can observe that:
In the inequality, we can see that the initial point of the inequality is colored. Therefore, the possible inequality signs for the inequality shown on graph are ≤ or ≥. Let us start setting our inequality.
⇒ _ ≤ or ≥ _We can see that the inequality line shown on the graph, goes to the left. Therefore, the line shown on the graph defines that the initial point is greater than the numbers on the left of the number line.
⇒ _ ≥ _Since "1" is the initial point and is greater than or equal to the numbers on the inequality, we can put "1" on the L.H.S of the inequality. Now,
⇒ 1 ≥ _[Optional] Write the numbers, that are less than 1, on the R.H.S of the inequality. Then, we get the following inequality:
⇒ 1 ≥ 0, -2, -4, -6...[Optional] Include "1" in the series as ≤ means greater than or equal to.
⇒ 1 ≥ 1, 0, -2, -4, -6...Let us assume that the numbers less than and equal to 1, be known as z.
⇒ 1 ≥ 1, 0, -2, -4, -6...⇒ 1 ≥ zTherefore, the inequality that represents the graph is z ≤ 1.
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Brianna bought a new car for $15000. Each year the value of the car deprecaites by 30% of its value of the previous year. In how many years will the car be worth only $500?
Answers
A=p (1-r)^t
A future value 500
P current value 15000
R rate of depreciation 0.3
T time?
500=15000 (1-0.3)^t
Solve for t
Divide both sides by 15000
500/15000=(1-0.3)^t
Take the log for both sides
Log (500/15000)=t×log (1-0.3)
Divide both sides by log (1-0.3)
T=(log(500÷15,000)÷log(1−0.3))
T=9.5 years round your answer to get 10 years
Hope it helps!
r% is the growth or depreciation rate, depending on its sign:
If it's a depreciation, the formula becomes:
A = P(1 - r%)ⁿ
500 = 15000(1-0.3)ⁿ
500/15000 = (0.7)ⁿ
0.033333 = 0.7ⁿ
ln(0.03333) = n.ln(0.7)
n = ln(0.03333)/ln(0.7)
n = 9.5 years
Tom deposited $2410 in a bank that pays 12% interest, compounded monthly. Find the amount he will have at the end of 3 years
Answers
A=p (1+r/k)^kt
A future value?
P present value 2410
R interest rate 0.12
K compounded monthly 12
T time 3years
A=2,410×(1+0.12÷12)^(12×3)
A=3,448.15
Hope it helps!
At 7p.m last night the temperature was 10 °f at 7
a.m. the next morning the temperature was -2 by how much did the temperature change from 7 p.m. to 7
a.m.?
Answers
The answer is 12
What is the mode of this data set? {8, 11, 20, 10, 2, 17, 15, 5, 16, 15, 25, 6} 12.5 13 15 25 nextreset?
Answers
Mode = 15
Determine which value is a solution to the open sentence. 3 + 6x = 21
a. 3
b. 18
c. 12
d. 4
Answers
because
3+6x=21
6x=18
x=3.
The coordinates of the vertices of △ABC are A(−4, 6) , B(−2, 2) , and C(−6, 2) .
The coordinates of the vertices of △A′B′C′ are A′(2, 6) , B′(0, 2) , and C′(4, 2) .
Drag and drop the answers into the boxes to correctly complete the statement.
A sequence of transformations that maps △ABC to △A′B′C′ is a blank followed by a blank.
translation 2 units left
reflection across the x-axis
reflection across the y-axis
translation 2 units down
Answers
Answer-
The sequences of transformations that maps △ABC to △A′B′C′ are
Reflection across the y-axisTranslation 2 units leftSolution-
The coordinates of the vertices of ΔABC are
A = (−4, 6)
B = (−2, 2)
C = (−6, 2)
The coordinates of the vertices of ΔA′B′C′ are
A′ = (2, 6)
B′ = (0, 2)
C′ = (4, 2)
As all the y-coordinates of all the function are same, so the triangle is neither translated up or down (∵ (x, y) → (x, y±k)), nor reflected over x-axis(∵ (x, y) → (x, -y)).
As the signs of x-coordinate is changed, it might be reflected over y axis,
Rule for reflection over y axis is,
(x, y) → (-x, y)
so,
A" = (4, 6)
B" = (2, 2)
C" = (6, 2)
As the x-coordinates of vertices of ΔA′B′C′ are 2 units less than that of ΔA"B"C"
So it is then translated 2 units left.
Therefore, the sequences of transformations that maps △ABC to △A′B′C′ are
Reflection across the y-axisTranslation 2 units leftAnswer:
Here is my test answer
Step-by-step explanation:
A sweater was originally $55. It is now marked down to 65% of its original price. How much is the sweater now?
Answers
55 - 37.75 = 19.25
first you multiply the two numbers together, then you subtract the number you get with the original number, and then you get the marked down price
hope this helps
The measure of an obtuse angle is represented by the expression 2x + 5. What is a possible value for x?
90 < obtuse < 180
answer choices
87.6
42.3
75.4
35.2
Answers
A. 2(87.6)+5 = 180.2°
B. 2(42.3)+5 = 89.6°
C. 2(75.4)+5 = 155.8°
D. 2(35.2)+5 = 75.4°
Therefore, the answer is letter C.
A circle has its center at (-2, 5) and a radius of 4 units. What is the equation of the circle? (1 point)
(x + 2)2 + (y - 5)2 = 16
(x + 2)2 + (y + 5)2 = 16
(x + 2)2 + (y - 5)2 = 4
(x - 2)2 + (y + 5)2 = 4
Answers
Answer:
equation of circle (x +2)² + (x + 5)² = 16.
Step-by-step explanation:
Given : A circle has its center at (-2, 5) and a radius of 4 units.
To find : What is the equation of the circle.
Solution : We have given center at (-2, 5) and radius = 4 units .
Standard form of circle : (x -h)² + (x + k)² = r²
Where, ( h, k) is center , r = radius .
Plugging the values of h , k and r in standard equation
(x -(-2))² + (x + 5)² = (4)²
(x +2)² + (x + 5)² = 16.
Therefore, equation of circle (x +2)² + (x + 5)² = 16.
3rd grade math explain how you know if a number can be divided by 10 evenly
Answers
In order to know if a number can be divided by 10 evenly, then such a number must end with a zero.
In order to determine the number(s) that can be divided evenly;
The last digit of the number must be zero.For instance, given the numbers 450, 130, 100
Note that they all end in zeroThey can be divided by 10 without remainder.450/10 = 45, 130/10 = 13, 100/10 = 10Hence in order to know if a number can be divided by 10 evenly, then such a number must end with a zero.
Learn more here: https://brainly.com/question/2239179
Which property is illustrated by the following equation?
- 8 ( - 5 + 3 ) = - 8 ( - 5 ) + ( - 8 )(3)
Answers
(aka "distribution")
The distributive property has you multiply the outer number -8 by each number inside the parenthesis. The products are then added up. The term "product" in math means the result of multiplying two or more numbers.
Aaron deposits $8,000 into an account that earns 3% interest, compounded Annually. How much money will he have after 4 years
PLEASE HELP 60 POINTS FOR THE RIGHT ANSWER SHOW WORK
Answers
F = P(1+i)ⁿ
where
F is the future worth
P is the present worth
i is the effective interest rate
n is the number of years
Substituting the values,
F = $8,000(1 + 0.03)⁴
F = $9,004.07
Thus, after 4 years, Aaron will have $9,004.07.
Choose all the sets containing the number Pi:
natural numbers
whole numbers
integers
rational numbers
irrational numbers
real numbers
Answers
Answer:
The set containing Pi is:
Irrational numbers.Real numbers.Step-by-step explanation:
We have to classify the number "pi" or π.
We know that:
Pi is the ratio of a circumference of a circle to it's diameter.
Pi is an irrational number i.e. it could not be represented in the form of p/q where p is an integer and q is a natural number.
However we sometimes take pi to be 22/7 ; but it's not exactly the same it's just a close approximation.
Hence, we may classify Pi as:
Irrational number.
Also irrational number comes in the category of real numbers.
Hence, Pi is also a real number.
( As real numbers are divided into two category:
1. Rational number
2. Irrational number
Also Rational number contains whole numbers, integers and whole numbers)
Using the number sets, the correct options are:
irrational numbers real numbers-------------------------------------
Whole numbers: Set of numbers including all positive numbers and 0, so: {0,1,2,...} Integer numbers: Number without decimals, that can be positive of negative, so: {...,-2,-1,0,1,2,....} Rational numbers: Integer plus decimals that can be represented by fractions, that is, they either have a pattern, or have a finite number of decimal digits, for example, 0, 2, 0,45(finite number of decimal digits), 0.3333(3 repeating is the pattern), 0.32344594459(4459 repeating is the pattern). Irrational numbers: Decimal numbers that are not represented by patterns, that is, for example, 0.1033430290339. Real numbers: Rational plus irrational.-------------------------------------
The number [tex]\pi = 3.1415...[/tex] is a decimal number without repetition, that is, it has infinite decimal places, thus it is irrational.Irrational numbers are also real.Thus, the correct options are irrational and real.A similar problem is given at https://brainly.com/question/10814303
Cammie goes to the gym to exercise 4 times per week altogether how many times does she go t the gym in 10 weeks?
Answers
4*10 = 40 times
Hope this helps!
Suppose that there are eight corporations competing for nine different contracts. If the contracts are awarded randomly, what is the probability that each corporation will get at least one contract?
Answers
To find the probability that each corporation will get at least one contract out of eight corporations competing for nine different contracts, we can use the concept of permutations and the principle of inclusion-exclusion.
Explanation:To find the probability that each corporation will get at least one contract, we can use the concept of permutations. Since there are 8 corporations and 9 contracts, we can calculate the total number of ways to assign the contracts to the corporations without any restrictions, which is 9! (9 factorial).
Next, we need to find the number of ways that each corporation gets at least one contract. This can be calculated using the principle of inclusion-exclusion. We subtract the number of ways that at least one corporation doesn't get a contract from the total number of permutations.
The number of ways that at least one corporation doesn't get a contract can be calculated by assigning 9 contracts to 7 corporations, which is 7! (7 factorial).
Finally, we can calculate the probability by dividing the number of ways that each corporation gets at least one contract by the total number of permutations:
Probability = (9! - 7!) / 9!
After eating dinner at the local diner, your bill is $14.25. if you tip 10%, how much money will you leave the waiter?
Answers
Answer:
Money leave for the waiter is $ 1.43 .
Step-by-step explanation:
As given
After eating dinner at the local diner, your bill is $14.25.
if you tip 10% .
10% is written in the decimal form .
[tex]= \frac{10}{100}[/tex]
= 0.10
Money leave for the waiter = 0.10 × Dinner cost .
Put all the values in the above
Money leave for the waiter = 0.10 × $14.25
Money leave for the waiter = $ 1.43 (Approx)
Therefore money leave for the waiter is $ 1.43 .
What is the value of x
24
9
21
14
Answers
5x +15 + 3x - 3 = 180
8x - 12 = 180
+12 +12
8x = 192
x = 24
we know that
[tex](5x+15)\°+(3x-3)\°=180\°[/tex] -----> by consecutive interior angles
so
Solve for x
[tex](5x+15)+(3x-3)=180\\ 8x+12=180\\8x=180-12 \\x=168/8 \\x=21\°[/tex]
therefore
the answer is
[tex]x=21\°[/tex]
Complete the two-column proof.
Given: x/6 + 2 =15
Prove: x = 78
X/6 + 2 =15 a. __________
x/6= 13 b. __________
x = 78 c. ___________
Answers
[tex] \frac{x}{6}=13 [/tex] ⇒ Using the subtraction/addition property to subtract 2 from both sides
[tex]x = 78[/tex] ⇒ Using the multiplication property (multiply both sides by 6)
x = 78
Answer:
This is proved with two property of equality subtraction and multipication property.
Step-by-step explanation:
Given [tex]\frac{x}{6} + 2 = 15[/tex]
By subtraction property of equality
[tex]\frac{x}{6} +2 - 2 = 15 - 2[/tex]
⇒ [tex]\frac{x}{6} = 13[/tex]
Now by multiplication property
x = 13(6) = 78
Hence the result.
PLEASE HELP!
I will give you a 5 star rating and thanks
Answers
original coordinates are
A (0,3)
B(-1,1)
C(2,1)
so add 3 to the x's and subtract 3 from the y's
A becomes (3,0)
B becomes (2,-2)
C becomes (5, -2)
Answer:
i dont know either sorryyyyyyyy
Step-by-step explanation:
How many centigrams are there in 24 grams?
A. Restate the question: 24 grams=____centigrams
B. Use the place value chart to determine the multiplication factor,and solve.
Answers
If jay ran 1 mile in 5 minutes on monday, 2 miles in 10 minutes on tuesday, and 3 miles in 15 minutes on wednesday, how many miles do you think he might run in 20 minutes on thursday?
Answers
Answer:
Jay might run 4 miles in 20 minutes
Step-by-step explanation:
If Jay ran on Monday = 1 mile in 5 minutes
On Tuesday = 2 miles in 10 minutes
On Wednesday = 3 miles in 15 minutes
Jay is increasing his time by 5 minutes per day and distance 1 mile per day.
So the next day Jay might run 1 mile + previous day distance in 5 minutes + time of the previous day.
Therefore, Jay might run 4 miles in 20 minutes
Lin parachutes from a plane at a height of 22,000 ft above sea level. Several minutes later she notes from an instrument on her wrist that she had dropped 10,000 ft. How far above sea level is she now?
–12,000 ft
6000 ft
10,000 ft
12,000 ft
Answers
Lin is 12000 ft far above sea level.
What is subtraction?The process of subtracting one number from another is known as subtraction.
Given that, the initial height of Lin is 22000 ft.
Now, the height of Lin is dropped by 10000, therefore, the new height is:
22000 - 10000
= 12000
Hence, Lin is 12000 ft far above sea level.
To learn more about subtraction, click here:
https://brainly.com/question/2346316
#SPJ2
A company make concrete bricks shaped like rectangular prisms.
Answers
Which of the following demonstrates the commutative property across multiplication for 2 × 10 × 7
Answers
Answer:
2 × 10 × 7 = 7 × 10 × 2.
Step-by-step explanation:
Given : 2 × 10 × 7
To find : Which of the following demonstrates the commutative property across multiplication.
Solution : We have given 2 × 10 × 7
By the commutative multiplication property : a × b × c = c× b × a.
Example : 1 * 3 * 5 = 5 *3 *1
15 = 15.
So, 2 × 10 × 7 = 7 × 10 × 2.
140 = 140
Therefore, 2 × 10 × 7 = 7 × 10 × 2.