Answers
9514 1404 393
Answer:
A) 1
Step-by-step explanation:
Let the distance from A to BC be represented by y, and the distance DE be represented by x. We can write some relations using the definition of the tangent of an angle, and the double-angle formula for tangent. The double-angles are complementary
Left angles
Call the smaller angle α. Then the larger angle is 2α.
tan(α) = x/2
tan(2α) = 2tan(α)/(1 -tan(α)²) = 2(x/2)/(1 -(x/2)²) = 4x/(4 -x²)
Right angles
tan(β) = x/3
tan(2β) = 2tan(β)/(1 -tan(β)²) = 2(x/3)/(1 -(x/3)²) = 6x/(9 -x²)
__
Angles 2α and 2β are complementary, so the product of their tangents is 1.
(4x/(4 -x²))(6x/(9 -x²)) = 1
24x² = (4 -x²)(9 -x²) . . . . multiply by the product of denominators
x⁴ -37x² +36 = 0 . . . . . put in standard form
(x² -36)(x² -1) = 0 . . . . . factor
Solutions to this equation are x = ±1 and x = ±6. Only positive values less than 1.25 can possibly satisfy the geometry. Hence x = DE = 1.
The length of DE is 1.
Related Questions
Estimate the cost of 3.2 pounds of apples.
The cost of 3.2 pounds of apples is about
Answers
Answer:
It is about 6 pounds!
Exactly is 6.4 pounds!
Step-by-step explanation:
round 3.2 to 3 and the other 3.2 to 3 as well and add to equal 6
EXACT: 3.2 + 3.2 = 6.4
What is this number written in word form? 4,139,000 no links
A. Four thousand, one hundred thirty-nine million
B. Four billion, one hundred thirty-nine million
C. Four million, one hundred thirty-nine thousand
D. Four thousand, one hundred thirty-nine thousand
Answers
Answer:
Four million, one hundred thirty-nine thousand
Find the values of p and q given that x⁴ + x³ - 7x² + px + q is divisible by (x - 1) and (x + 2)
Answers
Answer:
p = - 5, q = 10
Step-by-step explanation:
If f(x) is divisible by (x - h) then f(h) = 0
Here
f(x) = [tex]x^{4}[/tex] + x³ - 7x² + px + q
dividing by (x - 1) with h = 1 , then
[tex]1^{4}[/tex] + 1³ - 7(1)² + p + q = 0, that is
1 + 1 - 7 + p + q = 0
- 5 + p + q = 0 ( add 5 to both sides )
p + q = 5 → (1)
Dividing by (x + 2) with h = - 2 , then
[tex](-2)^{4}[/tex] + (- 2)³ - 7(- 2)² - 2p + q = 0 , that is
16 - 8 --- 28 - 2p + q = 0
- 20 - 2p + q = 0 ( add 20 to both sides )
- 2p + q = 20 → (2)
Subtract (1) from (2) term by term, thus eliminating q
- 3p = 15 ( divide both sides by - 3 )
p = - 5
Substitute p = - 5 into (1) and solve for q
- 5 + q = 5 ( add 5 to both sides )
q = 10
I really need help, i dont quite understand this but would be happy if some could give me the answer or an explanation.
Answers
Answer:
Translate up 5 units, instead of focusing on the whole picture focus on one point and move it to the correct spot and the whole figure will follow.
Step-by-step explanation:
Which one of these shapes is not like the others? Explain what makes it different by representing
each width and height pair with a ratio.
Answers
Answer:
tassler said she doesn't know what to do with the out of my mind blowing up with me and I have to go to sleep please dont be sorry I was
Answer:
C
Step-by-step explanation:
Because the ratio at the short axis to the long axis is 4/5 in A and B but that is 3/5 in C.
Last month, Ben rode his bike 24 miles a week for 4 weeks. This month, Ben ride his bike 28 miles a week for 3 weeks. How many miles did Ben ride his bike in all?
Answers
Answer:
180
Step-by-step explanation:
Multiply 24x4=96
Then, multiply 28X3=84
Finally add the 2 for a total of 180
Answer:
180 miles
Step-by-step explanation:
Basically, if he rode his bike 24 miles each week and he rode it for 4 weeks you would multiply 24 times 4, which gives you 96 miles. Then, you would do the same for the 28, 28 times 3 gives you 89 miles. Lastly, you add it all up. 96+89= 180 miles
:)
Kylie is buying a new pair of tennis shoes. The price tag says that the shoes are
regularly priced at $68.80. Kylie has a coupon for 20% off.
Part A: How much money will Kylie save if she uses the coupon? Show your
work.
Part B: How much will Kylie pay for the shoes after the discount? Show your
work.
Answers
Answer:
Part A: $13.76 saved. Part B: $55.04
Step-by-step explanation:
Part A: Set a proportion up d/68.8 = 20/100
100·d=100d 68.8·20=1376
100d/100 cancels out
1376/100=13.76 so $13.76 was saved
Part B: 68.80-13.76= 55.04 so $55.04 was what he paid.
Help me or your pet squirrel will mysteriously grow a 5th leg.
Answers
Answer:
36 yards
Step-by-step explanation:
causeimsmart
solve pls brainliest
Answers
Answer:
a. 68℉ higher
b. -15℉
Step-by-step explanation:
a. [tex]42-(-26)=68[/tex]
b. [tex]-26+11=-15[/tex]
Given f(x) contains the point (-5,6), find the point contained on
f-1(x).
Answers
Answer:
[tex]\displaystyle f^{-1}(6) = -5[/tex]
Step-by-step Explanation:
Recall that by the definition of inverse functions:
[tex]\displaystyle \text{If } f(a) = b\text{, then } f^{-1}(b) = a[/tex]
We are given the function f which contains the point (-5,6). In other words:
[tex]\displaystyle f(-5) = 6[/tex]
Then by the definition of inverse functions:
[tex]\displaystyle f^{-1}(6) = -5[/tex]
Help asap!!! I will give brainliest, see attached screenshots!
Answers
Answer:
sorry I only know the first page but i couldn't just comment it because of the squares
in order
[tex](3bc)^{2}[/tex]
[tex](10mn^{3})^{2}[/tex]
PLZ HELP ME ON THIS QUESTION THIS IS THE LAST ONE I NEED
Answers
Answer:
(-3 1/3)(a)+6
Step-by-step explanation:
Choose
The.........is writing the number in any way. (number or digit or numerical form)
Answers
Answer:
The...digit......is writing the number in any way.
Latex paint sells for $27 per gallon and will cost you $270 to paint your room. If each gallon will cover 350 square feet, how many square feet of wall space do you have in your room?
Answers
Answer:
3500
Step-by-step explanation:
(270/27)× 350= 10 x 350
Find the straight line f(x) which intersects the coordinates (8,0) and (1, -7).
Answers
Answer:
y = x - 8
Step-by-step explanation:
7/7X - 8
the y intercept was the only tricky part
Answer:
f(x)=1x-8
Step-by-step explanation:
slope: 0-(-7)/ 8-1 = 7/7= 1
eg. (1,-7)
-7= 1 -y int.
y int. = 8
therefore:
f(x) = 1x-8
What is 30+X=180,what is the measurement for
Answers
Answer:
X=150
Step-by-step explanation:
30+x=180
30+(-30)+x=180+(-30) Get x by itself by subtracting -30 to both sides.
x=180-30
x=150
Please help me on my homework
Answers
Answer:
tge answer is -8
Step-by-step explanation:
-14+8-5+8-2-3=-8
Each big square below represents one whole. What percent is represented by the shaded area?
Answers
Answer: 145%
Step-by-step explanation: It is 145% because all the squares represent 1% and each graph is 100%. One of the graphs are 100% shaded and the other is only 45% shaded. Adding these two percentages make 145%.
Which of the following points lies on the line perpendicular to
y = -x + 4, passing through (0,4)?
A (6,12)
B (6,0)
C (-6,-5)
D (12,-4)
E (0,1/4)
Answers
Answer:
Step-by-step explanation:
recall that perpendicular lines have slopes that are opposite reciprocals. if u don't know what opposite reciprocals are, according to study.com they are, "The term opposite reciprocals refers to two numbers that have opposite signs and are flipped fractions of each other." for example, 1/2 and -2 are opposite reciprocals.
also recall that the formula to find the slope of a line is m=y2-y1/x2-x1
to solve this problem, we need to go through all of the options and find the slope of that line using the given point and point (0,4). After that, we need to check if that slope is equal to 1. One is the opposite reciprocal of -1, and -1 is the slope of the equation y= -x+4. if the slope is equal to 1, the line will be perpendicular to the line y= -x+4.
lets do the math now:
option a)
m=y2-y1/x2-x1
m=12-4/6-0
m=8/6
m=4/3
this line isnt perpendicular to y= -x +4 cuz the slope is 4/3, which isnt equal to 1
option b)
m=y2-y1/x2-x1
m=0-4/6-0
m=-4/6
m= -2/3
this line isnt perpendicular to y= -x +4 cuz the slope is -2/3, which isnt equal to 1
--------------
ok girl i dont wanna do all the rest of the calculations. just keep doing the same thing with all the other options until you find something that has a slope of 1.
toodles! :)
How many DECIMAL PLACES are in this problem: 0.02 x 32.4
Answers
Answer:
0.648
Step-by-step explanation:
I added multiplyed
Hector wants to make sure he has 50 texts left for the day of his birthday party. After how
many days will Hector have 50 texts left?
Answers
how many texts did he start with? is there more to the problem?
I NEED A 100% ACCURATE ANSWER FOR THIS QUESTION ASAP NO LINKS !!!
Answers
Answer:
one solution
Step-by-step explanation:
4(x+1)=3x+10
4x+4=3x+1
4x-3x+10-4
x=6
Answer:
Since x = 6, the equation only has one solution.
Step-by-step explanation
You have to solve the equation first.
Let's solve your equation step-by-step.
4 ( x + 1 ) = 3x + 10
Step 1: Simplify both sides of the equation.
4 ( x + 1 ) = 3x + 10
( 4 ) ( x ) + ( 4 ) ( 1 ) = 3x + 10 (Distribute)
4x + 4 = 3x + 10
Step 2: Subtract 3x from both sides.
4x + 4 − 3x = 3x + 10 − 3x
x + 4 = 10
Step 3: Subtract 4 from both sides.
x + 4 − 4 = 10 − 4
x = 6
Answer:
x = 6
Can someone explain how you do this and not only give me a answer?
Answers
Got it! Here you go!
Step-by-step explanation:
It seems you already know that you need to do 17-2/3(not two thirds, just over 3.)
The horizontal line means divide, so you will be dividing by 3. First, though,, you do...
17-2(which is 15)
and then divide it by 3.
15/3=5
Your answer is 5.
I hope I helped! Have a great day.
Djrjdjejciejfiejcjejdjejxj
Answers
Answer:
Djrjdjejciejfiejcjejdjejxj
QUICKKK?!!
Find the slope of the line passing through the points (-7, - 7) and (4,-7).
Slope:
through the points (4,7) and (4, -6).
slope:
Answers
Step-by-step explanation:
the line passing through the points (-7, - 7) and (4,-7).
Slope: (-7+7) /(4+7) = 0/11 = 0
this is a horizontal line
through the points (4,7) and (4, -6).
slope: (-6-7) /(4-4) = -13/0 = oo
this is a vertical line
Did you know that an unopened 355 mL can of diet Dr. Pepper will float in a lake? That's a fact! However, it's also a fact that an unopened 355mL can of regular Dr. Pepper will sink in that same lake! Based on these two facts, which type of soda is the least dense? Explain your answer.
Answers
Answer: An unopened can of Diet Dr. Pepper is the least dense.
Step-by-step explanation:
For a solid object to float in a liquid, it must be less dense.
Let's associate the density of Diet Dr. Pepper with x, Dr. Pepper with y, and lake water with z.
Because of the above fact, x < z, and y > z. Thus, x < z < y, and x < y.
Hope it helps :) and let me know if you want me to elaborate.
Mark works at a clothing store and earns a salary of $1.500 per month. In addition, he earns 20% commission on his total sales. Last month, Mark's clothing sales was
$2.600 What was his total income for the month?
$300
$520
$1,800
$2.020
Answers
Answer:
$2.020
Step-by-step explanation:
If you take 20% of 2.600, that gives you the equation 2.600/5 = x (should get 520
Add that to the base salary of 1.500 and that gets 2.020
Hope that helped :)
Use the Distributive Property to expand the
expression y(9 -0.2x).
Answers
Answer:
9y - 0.2xy
Step-by-step explanation:
Answer
9y−0.2yx
Step-by-step explanation:
9 times y = 9y
y times -0.2x = -0.2xy
help please ..:/ don’t get it
Answers
Question 2-4
20
Solve the compound inequality
<-4 or 5x +11 <-4.
3
Use the drop-down menus to provide the correct solutions to the compound inequality.
Solution: 2 < vor 2
Answers
Step-by-step explanation:
-x/3 < -4
-x < -12
x > 12
5x +11 ≤ -4
5x ≤ -4-11
5x ≤ -15
x ≤ -3
therefore, the solution is
x ≤ -3 or x > 12