5 5/8= 45/8
1 1/2= 3/2
45/8 divided by 3/2
Or
45/8 times 2/3
15/4 or 3 3/4
Help me i will put your brainliest
Answer:
The first choice is the correct one
Step-by-step explanation:
That funny symbol is the Greek symbol for "the sum of". Sum means to add, so whatever numbers we have we are definitely adding them. The index goes from a starting point of 1 up to 4. That's those 2 numbers, one below and one above the sum symbol. The "n" in 7/n is what we are replacing with each number starting at 1 and ending at 4. 7/1, 7/2, 7/3, 7/4. Those are the numbers, now just put them together with plus signs between them and you're done.
During the player's career, the player attempted 1,507 free throws and made 1,213 of those free throws. What percentage of free throws has this player made?
The answer is 80%
Correct me if I’m wrong
Examine Kaitlyn's steps for solving the system of equations. –3x + 2y = 8 3x + 2y = –6 Step 1: 4y = 2 Step 2: y = 2 Step 3: –3x + 2(2) = 8 Step 4: –3x = 4 Step 5: x = –1.333 Kaitlyn found the solution to be (1.3, 2). Is her solution correct? Explain. Yes, she correctly solved the system of equations. No, she made an error in step 1. The y variable should have been eliminated when adding the system of equations. No, she made an error in step 2. She should have found y = 0.5. No, she substituted y into the wrong equation to solve for x in step 3.
The correct option will be No, she made an error in step 2, she should have found y=0.5
What is a system of equations?A system of equations is two or more equations that can be solved to get a unique solution. the power of the equation must be in one degree.
We have been Given the system of linear equations:
-3x + 2y = 8 --- eqn. 1
3x + 2y = -6 ---eqn. 1
First add both equations together
4y = 2
Now, divide both sides by 4:
y = 2/4
y = 0.5
Thus Kaitlyn got y = 2 instead of 0.5 in this second step. The solution she would get will be incorrect due to an error has occurred here.
Therefore, the error made by Kaitlyn while solving the equations is in step 2. Her solution will be incorrect.
The correct option will be: No
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Answer:
The correct answer is letter C
It took Fran 2.7 hours to drive to her mother's house on Monday morning. On her return trip on Tuesday night, traffic was heavier, so the trip took her 3 hours. Her average speed on Tuesday was 6 mph slower than on Monday. What was her average speed on Tuesday.
Answer:
Step-by-step explanation:
Set up a table for a distance = rate × time problem. We are considering the trips taken on Monday and Tuesday.
d = r × t
Monday
Tuesday
Now let's start filling in what we know. First off, Fran went to her Mother's both days. Unless her Mother moved overnight from Monday to Tuesday, the distance from Fran to her mom is the same both days, even though we don't know how far it is. So we will just call that "d".
d = r × t
Monday d =
Tuesday d =
Now we are told about the times it took to get there on both days. Monday took 2.7 hours and Tuesday took 3 hours. Filling in that:
d = r × t
Monday d = × 2.7
Tuesday d = × 3
We're getting there. Now let's look at rates. Again, we don't know her rate (that's what we are solving for!) but we do know that she drove faster on Monday than Tuesday. Tuesday she was 6 miles per hour slower than Monday. Since we don't know Monday's rate, we will call it r. Since we don't know Tuesday's rate, but only that it is 6 mph slower than Monday, we will call it r - 6
d = r × t
Monday d = r × 2.7
Tuesday d = r-6 × 3
Now we have our equations. We know that d = rt. Since the distances are the same, d = d, by the transitive property of equality, we can set the 2 expressions equal to each other:
2.7r = 3(r - 6) and solve for r:
2.7r = 3r - 18
-.3r = -18
r = 60
If r = 60, then that r value goes in for Monday. That means that Tuesday is 60 - 6 which is 54
What was her average speed on Tuesday is 54 mph
Monday
Time = 2.7 hours
Date = r mph
Distance = 4.5r miles
Tuesday
Time = 3 hours
rate = r-6 mph
Distance = 3(r-6) miles
Hence:
Distance = distance
2.7r=3(r-6)
2.7r = 3r - 18
0.3r = 18
r =18/0.3
r 60 mph ( Monday rate)
r-6=60-3 (Tuesday rate)
r-6 = 54 mph (Tuesday rate)
Inconclusion What was her average speed on Tuesday is 54 mph.
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Using Heron’s formula, calculate the area of the parallelogram to the nearest tenth of a square unit.
Area ≈
square units
Answer:
Step-by-step explanation:
36.7
Applying the Heron's formula, the area of the parallelogram = 36.7 square units.
What is the Heron's Formula?Heron's Formula = √[s(s - a)(s - b)(s - c)], where:
a, b, and c are the sides of a triangle.s = semi-perimeter = (a + b = c)/2.A diagonal of a parallelogram cuts a parallelogram into two equal triangles.
Thus, we have two equal triangles in the parallelogram given.
Area of the parallelogram = 2(area of triangle)
Find the area of one triangle using the Heron's formula:
a = 5
b = 8
c = 11
s = (5 + 8 + 11)/2 = 12
Area of one triangle = √[12(12 - 5)(12 - 8)(12 - 11)]
= √[12(7)(4)(1)]
= √336
= 18.33 sq. units.
Therefore, area of the parallelogram = 2(18.33) = 36.7 square units.
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Vanessa has two bags that contain slips of paper. One bag has 4 slips of paper that are numbered 2, 3, 4, and 5. The other bag has 4 slips of paper that are numbered 3, 4, 5, and 6.
Vanessa chooses one slip of paper from each bag without looking.
The random variable X is the product of the numbers on the slips of paper.
What is P(12 ≤ X ≤ 15)?
Enter your answer, in simplest fraction form, in the box.
Answer:
5/16
Step-by-step explanation:
If Vanessa pulls out a 2 from the first bag, then the possibilities based on the second bag are:
X = 2*3 = 6
X = 2*4 = 8
X = 2*5 = 10
X = 2*6 = 12
Repeat this for the other values from the first bag. If she pulls a 3, the possibilities are:
X = 3*3 = 9
X = 3*4 = 12
X = 3*5 = 15
X = 3*6 = 18
If she pulls a 4:
X = 4*3 = 12
X = 4*4 = 16
X = 4*5 = 20
X = 4*6 = 24
And finally, if she pulls a 5:
X = 5*3 = 15
X = 5*4 = 20
X = 5*5 = 25
X = 5*6 = 30
Of the 16 total combinations, 5 are greater than or equal to 12 and less than or equal to 15.
Therefore, P(12 ≤ X ≤ 15) = 5/16.
Write the sum using summation notation, assuming the suggested pattern continues. 4-24+144-864+...
Answer:
Sn = ∑ 4(-6)^n, from n = 0 to n = n
Step-by-step explanation:
* Lets study the geometric pattern
- There is a constant ratio between each two consecutive numbers
- Ex:
# 5 , 10 , 20 , 40 , 80 , ………………………. (×2)
# 5000 , 1000 , 200 , 40 , …………………………(÷5)
- The sum of n terms is Sn = [tex]\frac{a(1-r^{n})}{(1-r)}[/tex], where
a is the first term , r is the common ratio between each two
consecutive terms and n is the numbers of terms
- The summation notation is ∑ a r^n, from n = 0 to n = n
* Now lets solve the problem
∵ The terms if the sequence are:
4 , -24 , 144 , -864 , ........
∵ [tex]\frac{-24}{4}=-6[/tex]
∵ [tex]\frac{144}{-24}=-6[/tex]
∴ There is a constant ratio between each two consecutive terms
∴ The pattern is geometric
- The first term is a
∴ a = 4
- The constant ratio is r
∴ r = -6
∵ Sn = [tex]\frac{a(1-r^{n})}{(1-r)}[/tex]
∴ Sn = [tex]\frac{4(1-(-6)^{n})}{(1-(-6))}=\frac{4(1-(-6)^{n})}{(1+6)}=\frac{4}{7}[1-(-6)^{n}][/tex]
- By using summation notation
∵ Sn = ∑ a r^n , from n = 0 to n = n
∴ Sn = ∑ 4(-6)^n
Answer:
[tex] a_n = (4)(-6)^{n-1}, n =1,2,3,4,.... [/tex]
And we can verify:
[tex] n=1 , a_1 = 4 (-6)^{1-1}= 4[/tex]
[tex] n=2 , a_2 = 4 (-6)^{2-1}= -24[/tex]
[tex] n=3 , a_3 = 4 (-6)^{3-1}= 144[/tex]
[tex] n=4 , a_4 = 4 (-6)^{4-1}= -864[/tex]
And finally we can write the summation like this:
[tex] S_n = \sum_{i=1}^n 4 (-6)^{n-1} , n =1,2,3,... [/tex]
Step-by-step explanation:
For this case we have the following pattern of numbers :
4-24+144-864+...
And we want to express the sum in terms of a summation.
We can use the fact the the general term for the sum can be expressed as:
[tex] a_n = a_1 r^{n-1}[/tex]
And for this case we can identify the value of r dividing successive terms like this:
[tex] r = \frac{|24|}{|4|}= \frac{|144|}{|24|}=\frac{|864|}{|144|}= 6[/tex]
So for this case we know that the value of r =6 and the initial value 4 would represent [tex] a_1 = 4[/tex]
Since the sequence is alternating with + and - signs we can express the general term like this:
[tex] a_n = (4)(-6)^{n-1}, n =1,2,3,4,.... [/tex]
And we can verify:
[tex] n=1 , a_1 = 4 (-6)^{1-1}= 4[/tex]
[tex] n=2 , a_2 = 4 (-6)^{2-1}= -24[/tex]
[tex] n=3 , a_3 = 4 (-6)^{3-1}= 144[/tex]
[tex] n=4 , a_4 = 4 (-6)^{4-1}= -864[/tex]
And finally we can write the summation like this:
[tex] S_n = \sum_{i=1}^n 4 (-6)^{n-1} , n =1,2,3,... [/tex]
If T: (x, y) → (x - 7, y + 2), then T -1: (x,y) → _____.
A.( -x/7 , y/2)
B.(-7x, 2y)
C.(x - 7, y - 2)
D.(x + 7, y - 2)
Answer:
D. (x + 7, y - 2)
Step-by-step explanation:
To get back the original after translating left 7 and up 2, you must translate right 7 and down 2. The transformation of choice D does that.
Identify the corresponding word problem given the inequality: 1,200x < 50,000
A) An export company needs to purchase containers to ship cargo overseas, and the expense must be less than $50,000. If 41 containers are purchased, what is the cost of each container?
B) An export company needs to purchase containers to ship cargo overseas, and the expense must be $50,000 or less. If 41 containers are purchased, what is the cost of each container?
C) An export company needs to purchase containers to ship cargo overseas, and the expense must be less than $50,000. If a standard container costs $1,200, how many containers can be purchased?
D) An export company needs to purchase containers to ship cargo overseas, and the expense must be $50,000 or less. If a standard container costs $1,200, how many containers can be purchased?
Answer:
C) An export company needs to purchase containers to ship cargo overseas, and the expense must be less than $50,000. If a standard container costs $1,200, how many containers can be purchased?
Step-by-step explanation:
Note that in this question:
x = amount of containers to be purchased.
50,000 = the amount given
< means that the amount in total must be less than (& not equal to) 50000
1200 = the amount of the container cost.
C) is your best answer.
~
Answer:
It is C
Step-by-step explanation:
An export company needs to purchase containers to ship cargo overseas, and the expense must be less than $50,000. If a standard container costs $1,200, how many containers can be purchased?
1,200x < 50,000
x < 41.67
Thus, only 41 containers can be purchased, so that the purchase remains under $50,000.
The statement "the expense must be less than $50,000" means that the total cost must be less than $50,000.
BRAINLIEST AND 30 POINTS FOR WHOEVER CAN EXPLAIN HOW TO GET THESE ANSWERS...
Given: △ACM, m∠C=90°, CP⊥ AM. AP=9 cm, PM=16 cm.
Explain how to get these answers: AC = 15, CM = 20, CP = 12
Step-by-step explanation:
Since m∠ACM = 90°, then by angle addition, m∠ACP + m∠PCM = 90°.Since CP⊥ AM, then by definition of perpendicular, m∠APC = 90°. Since angles of a triangle add up to 180°, that means m∠PAC + m∠ACP = 90°.By substitution, m∠PCM = m∠PAC.Since m∠PCM + m∠CMP = 90°, then by substitution, m∠CMP = m∠PAC.Therefore, by AAA, △ACP and △CMP are similar.Having proven that the triangles are similar, we can write the proportion:
AP / CP = CP / MP
9 / CP = CP / 16
CP² = 144
CP = 12
Now, we can simply use Pythagorean theorem to find the other sides.
AC² = AP² + CP²
AC² = 9² + 12²
AC = 15
CM² = CP² + PM²
CM² = 12² + 16²
CM = 20
A collection of coins consists of dimes and nickels .The number of dimes is two more than the twice the number of nickels.The value of the collection is $2.70. How many dimes are in the collection ?
27 dimes for my answer
hope it works
4.375 rounded to nearest tenths
Answer:
4.4 is the answer hope it help you
Answer:
4.4 is the answer round it to the nearest ten
A real estate agent sold a home worth $475,000. She asks for 6% commission, but the people selling the home only want to pay her 5%. How much will the real estate agent lose?
Answer:
4750
Step-by-step explanation:
475000/100 = 4750
4750 * 6 = 28500
4750 * 5 = 23750
28500 - 23750 = 4750
Answer:
4750
explanation:
What’s the right answer
Answer:
x = 12.5
Step-by-step explanation:
The given triangle is a right angle triangle.
We cannot use the Pythagoras theorem as the lengths of all sides are not known. We will use triangular ratios here to solve the given problem.
As it is clear from the diagram that x is the hypotenuse of the triangle and 11 is the length of the base. We will use a ratio in which base and hypotenuse are used.
So,
cos θ= base/hypotenuse
cos 28=11/x
x=11/cos28
x=11/0.8829
x=12.45
Rounding off to nearest 10
x=12.5
Find the value of x, rounded to the nearest tenth
Answer:
x= 8.1
Step-by-step explanation:
The given triangle is a right angle triangle.
We cannot use the Pythagoras theorem as the lengths of all sides are not known. We will use triangular ratios here to solve the given problem.
As it is clear from the diagram that x is the hypotenuse of the triangle and 11 is the length of the base. We will use a ratio in which base and hypotenuse are used.
So,
cos θ= base/hypotenuse
cos 36=x/10
0.8090=x/10
8.090=x
x=8.090
Rounding off to nearest 10
x=8.1
PLEASE HELP ME!
5.
Find the number of two-letter permutations of the letters.
Q, I, E, R, T, Y, U
5,040
1,208
14
42
Answer:
42
Step-by-step explanation:
The permutation for that set of data looks like this:
[tex]_{7}P_{2}[/tex]
The formula looks like this:
[tex]_{7}P_{2}=\frac{7!}{(7-2)!}[/tex]
which of course simplifies to
[tex]_{7}P_{2}=\frac{7!}{5!}[/tex]
which further simplifies down to the most basic simplification:
[tex]_{7}P_{2}=7*6[/tex]
since the 5*4*3*2*1 that goes after the 6 in the numerator cancels with the 5*4*3*2*1 in the denominator.
You could also check this on your calculator. Hit "math", then arrow over to "Prob" and it's under nPr.
Please help me with this ratio.
Answer:
[tex]\frac{inches}{minute}[/tex]
Change the feet to minutes by multiplying by 12, and change the hour to minutes.
Speedy: [tex]\frac{240}{60}[/tex]
Slowpoke: [tex]\frac{80}{30}[/tex]
Cleo: [tex]\frac{96}{10}[/tex]
Speedy is the fastest.
[tex]\frac{feet}{hour}[/tex]
Speedy: [tex]\frac{20}{1}[/tex] Slowpoke: [tex]\frac{\frac{6.666666667}{.5}}{30}[/tex]Cleo: [tex]\frac{8}{\frac{1}{6}}[/tex]Change minutes to feet by dividing and change the minutes to hours by multiplying.
Hope this helps and have a great day!!!
[tex]Sofia[/tex]
A souvenir of the Eiffel Tower is scaled at 1/80 inch to 1 foot. If the total height of the tower is 1,069 feet, the approximate height of the souvenir of the Eiffel Tower to the nearest tenth is _____.
A.14
B.15
C.13
D.12
Answer: Option C
the approximate height of the souvenir of the Eiffel Tower to the nearest tenth is __13 in___.
Step-by-step explanation:
We know that each foot of height of the Eiffel Tower is equivalent to 1/80 inch of height of the souvenir.
The Eiffel Tower is 1,069 feet high.
Then the height of the souvenir the 1,069 times 1/80 in
[tex]h = 1,069 *\frac{1}{80}\\\\h=13.3\ in[/tex]
The answer is the option C
over five different weeks, Irina tracked the hours she spent exercising and the hours she spent playing video games. What is the strength of the correlation between the hours spent exercising and the hours spent playing video games?
Answer:
Moderate Negative Correlation
Step-by-step explanation:
I got 100% on Homework...
The strength of the correlation between the hours spent exercising and the hours spent playing video games moderate negative relationship.
What is the correlation coefficient?
The correlation coefficient helps us to know how strong is the relation between two variables. Its value is always between +1 to -1, where, the numerical value shows how strong is the relation between them and, the '+' or '-' sign shows whether the relationship is positive or negative.
1 indicates a strong positive relationship.-1 indicates a strong negative relationship.A result of zero indicates no relationship at all, therefore, independent variable.If Irina spends more time playing video games she will have less time to spend exercising, therefore, we can conclude that if she plays more video games the time spent on exercising will be less and vice versa. Thus, there exists a negative correlation coefficient between the two variables.
Since in a day there is limited time available, therefore, if time is spent on video games, there will be very less or no time left for exercising, hence, the relationship between the two is moderate and dependent.
Hence, the strength of the correlation between the hours spent exercising and the hours spent playing video games moderate negative relationship.
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A child launches a toy rocket from the top of a slide at the park. Suppose the equation -16t^2+28t+8=0 can be used to find how many seconds it will take for the rocket to hit the ground. A)Write the equation in factored form. B)Use the zero product property to solve the equation. Show all the steps needed to find both answers. C)Explain how the solution relates to this situation.
Answer:
A) The equation in factored form is (4t + 1)(t - 2) = 0
B) The solutions of the equation are t = -1/4 and t = 2
C) It will take 2 seconds for the rocket to hit the ground
Step-by-step explanation:
* Lets study the information in the problem
- A child launches a toy rocket from the top of a slide
- The equation of the motion is -16² + 28t + 8 = 0, where t is the time
of rocket to hit the ground
* Now lets solve the problem
- At first simplify the equation
∵ -16t² + 28t + 8 = 0
∵ Al the terms have a factor 4
- Divide all terms by 4
∴ -4t² + 7t + 2 = 0 ⇒ multiply all terms by -1
∴ 4t² - 7t - 2 = 0
- Lets factorize
∵ 4t² = 4t × 1t ⇒ 1st term in the 1st bracket × 1st term in the 2nd bracket
∵ -2 = 1 × -2 ⇒ 2nd term in the 1st bracket × 2nd term in the 2nd bracket
∵ 4t + -2 = -8t ⇒ product of the extremes
∵ 1t × 1 = 1t ⇒ product of means
∵ -8t + 1t = -7t ⇒ middle term
∴ The factorization of 4t² - 7t - 2 is (4t + 1)(t - 2)
∴ (4t + 1)(t - 2) = 0
A) The equation in factored form is (4t + 1)(t - 2) = 0
- Lets use the zero product property to solve the equation
∵ (4t + 1)(t - 2) = 0
- Equate each factor by 0
∵ 4t + 1 = 0 ⇒ subtract 1 from both sides
∴ 4t = -1 ⇒ divide both sides by 4
∴ t = -1/4
OR
∵ t - 2 = 0 ⇒ add 2 for both sides
∴ t = 2
B) The solutions of the equation are t = -1/4 and t = 2
C) We can not accept the answer t = -1/4 because there is no negative
value for the time
∴ The answer is t = 2 only
* It will take 2 seconds for the rocket to hit the ground
How do you think you could simplify f(x)+g(x) if f(x)=3x+2 and g(x)=4x?
f(x)+g(x)
f(x)=3x+2 and g(x)=4x
You have:
3x +2 + 4x
Combine like terms:
3x +4x = 7x
The answer becomes 7x +2
A regular polygon is defined to be a(n) _____ polygon with congruent sides and congruent angles
Answer:
Step-by-step explanation:
A regular polygon is defined to be a convex polygon with congruent sides and congruent angles.
Convex means that all interior angles are less than 180 degrees. However, if all interior angles are equal, the polygon has to be convex.
Final answer:
A regular polygon is a convex shape with sides and angles that are all congruent, exemplified by the faces of an icosahedron or an equilateral triangle.
Explanation:
A regular polygon is defined to be a convex polygon with congruent sides and congruent angles. This means that all sides are the same length and all interior angles are equal in measure, which contributes to the polygon's symmetry. As an example from three-dimensional geometry, an icosahedron is a symmetrical, solid shape with 20 faces, each of which is an equilateral triangle.
What’s the answer to this
Answer:
see below
Step-by-step explanation:
The graph extends to the left more or less horizontally, approaching the line y=3. The only choice that expresses that is the third one.
According to a survey, 15% of city workers take the bus to work. Donatella randomly surveys 10 workers. What is the probability that exactly 6 workers take the bus to work? Round the answer to the nearest thousandth.
0.001
0.002
0.128
0.900
Answer:0.001
x=the number of workers taking the bus to work
p= probability of success =(15/100) = 0.15
q= probability of failure =1- p = 0.85
P(X=6) = 10C6(0.15)^6(0.85)^4
= 0.001
Answer: 0.001
Step-by-step explanation:
Binomial probability formula :
[tex]P(x)=^nC_xp^x(1-p)^{n-x}[/tex], where P(x) is the probability of exactly x successes in n trials.
Given : The probability of city workers take the bus to work =15%=0.15
The sample size :n= 10
Now, the probability that exactly 6 put of 10 workers take the bus to work :-
[tex]P(6)=^{10}C_6(0.15)^{6}(1-0.15)^{10-6}\\\\=\dfrac{10!}{6!(10-6)!}(0.15)^6(0.85)^4\\\\=0.0012486552627\approx0.001[/tex]
Therefore , the probability that exactly 6 workers take the bus to work = 0.001
There are 24 members of a swim team. How many different combinations of 5 swimmers can be chosen to sit in the front row for a team photo?
Answer: 42,504
There Are 42,504 Different Combinations For The Swimmers
Answer:i dont
Step-by-step explanation:
At noon, a tree casts a shadow that is 40 feet long. The distance from the top of the tree to the furthest tip of the shadow is 60 feet. What is the height of the tree? Round to the nearest hundredth.
Answer:
44.72 feet
Step-by-step explanation:
Assuming that the bottom of the tree and the ground makes a right triangle-- use the Pythagorean theorem.
x^2 + 40^2 = 60^2
x^2 + 1,600 = 3,600
x^2 = 2,000
x = 44.72 ft
Answer:
C
Step-by-step explanation:
On edge
When Ahmed paid $81 he had received a 10% discount on the normal price.
Calculate the normal price.
Answer:
The normal price is $90
Step-by-step explanation:
Let
x-----> the normal price
we know that
100%-10%=90%=90/100=0.90
so
0.90x=$81
Solve for x
x=$81/0.90
x=$90
Which of the following are steps to use when formulating all that apply equation? Check an A. Write each fact as a variable expression. B. Write each fact as a sentence. C. Read the problem. D. Draw a picture. SUBMIT
Answer:
a
Step-by-step explanation:
Answer:
correct options are A, C and D
Step-by-step explanation:
While formulating an equation the first step is to read the problem carefully and then draw a picture if needed and the third step is write each fact as a variable.
so the steps which are used when formulating are as follows
Read the problem
Draw a picture if needed
Write each fact as a variable expression
Which statements are true about the fully simplified product of (b-2c)(-3b c) ?
Select two options.
( 1 )The simplified product has 2 terms.
( 2 )The simplified product has 4 terms.
( 3 )The simplified product has a degree of 2.
( 4 )The simplified product has a degree of 3.
( 5 )The simplified product has a degree of 4.
( 6 )The simplified product, in standard form, has exactly 2 negative terms.
The fully simplified product of (b-2c)(-3bc) has 2 terms and a degree of 3. The number of negative terms in the simplified product depends on the values of b and c, which are not provided.
Explanation:When simplifying the expression (b-2c)(-3bc), we use the distributive property to multiply each term in the first parenthesis by each term in the second parenthesis. However, since the two terms -2c and -3bc will multiply to produce a term with a higher degree than b times -3bc, the simplified expression does not have 4 terms, but rather only 2 terms. The correct simplified form is -3b^2c + 6c^2. There are two terms, and the highest degree of any term, which is the sum of the exponents of the variables in that term, is 3 (b^2c having degree 3, since 2+1=3).
Therefore, the correct statements about the fully simplified product of (b-2c)(-3bc) are:
The simplified product has 2 terms.The simplified product has a degree of 3.The simplified product, in standard form, does not have exactly 2 negative terms, as its terms will depend on the signs of b and c which are not specified.I got ALL of the answers but I can't explain it at all... please explain guys I have NO idea!
PROBLEM: In right △ABC, the altitude CH to the hypotenuse AB intersects angle bisector AL in point D. Find the sides of △ABC if AD = 8 cm and DH = 4 cm.
ANSWERS: AB = 16√3, AC = 8√3, BC =24
Explanation:
The altitude CH divides triangle ABC into similar triangles:
ΔABC ~ ΔACH ~ ΔCBH
Angle bisector AL divides the triangle(s) into proportional parts:
BL/BA = CL/CA
HD/HA = CD/CA
Of course, the Pythagorean theorem applies to the sides of each right triangle:
AH^2 +CH^2 = AC^2
DH^2 +AH^2 = AD^2
LC^2 + AC^2 = LA^2
AC^2 +BC^2 = AB^2
And segment lengths sum:
HD +DC = HC
AD +DL = AL
AH +HB = AB
CL +LB = CB
Solving the problem involves picking the relations that let you find something you don't know from the things you do know. You keep going this way until the whole geometry is solved (or, at least, the parts you care about).
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We can use the Pythagorean theorem to find AH right away, since we already know AD and DH.
DH^2 +AH^2 = AD^2
4^2 + AH^2 = 8^2 . . . . . . . substitute known values
AH^2 = 64 -16 = 48 . . . . . . subtract 16
AH = 4√3 . . . . . . . . . . . . . . take the square root
Now, we can use this with the angle bisector relation to tell us how CD and CA are related.
HD/HA = CD/CA
4/(4√3) = CD/CA . . . . . substitute known values
CA = CD·√3 . . . . . . . . . cross multiply and simplify
Using the sum of lengths equation, we have ...
CH = HD +CD
CH = 4 + CD
From the Pythagorean theorem ...
AH^2 +CH^2 = AC^2
(4√3)^2 + (4 +CD)^2 = (CD√3)^2 . . . . . substitute known values
48 + (16 +8·CD +CD^2) = 3·CD^2 . . . . . simplify a bit
2·CD^2 -8·CD -64 = 0 . . . . . . . . . . . . . . . put the quadratic into standard form
2(CD -8)(CD +4) = 0 . . . . . . . . . . . . . . . . factor
CD = 8 . . . . . only the positive solution is useful here
Now, we know ...
∆ADC is isosceles, so ∠ACH = ∠CAD = ∠DAH = ∠CBA
CH = 8+4 = 12
AC = 8√3 . . . . . = 2·AH
Then by similar triangles, ...
AB = 2·AC = 16√3
BC = AC·√3 = 24