Answers
Answer:
[tex]\displaystyle d \approx 15.8768[/tex]
Step-by-step explanation:
We want to find the distance of d or AB.
From the right triangle with a 35° angle, we know that:
[tex]\displaystyle \tan 35^\circ = \frac{50}{PB}[/tex]
And from the right triangle with a 42° angle, we know that:
[tex]\displaystyle \tan 42^\circ = \frac{50}{PA}[/tex]
AB is PA subtracted from PB. Thus:
[tex]\displaystyle d = AB = PB - PA[/tex]
From the first two equations, solve for PB and PA:
[tex]\displaystyle \frac{1}{\tan 35^\circ } = \frac{PB}{50} \Rightarrow PB = \frac{50}{\tan 35^\circ}[/tex]
And:
[tex]\displaystyle \frac{1}{\tan 42^\circ } = \frac{PA}{50} \Rightarrow PA = \frac{50}{\tan 42^\circ}[/tex]
Therefore:
[tex]\displaystyle d = AB = \frac{50}{\tan 35^\circ} - \frac{50}{\tan 42^\circ}[/tex]
Using a calculator:
[tex]\displaystyle d= AB \approx 15.8768[/tex]
Related Questions
A triangle and a parallelogram have the same base and the same area.
If the sides of the triangle are 26 cm, 28 cm and 30 cm and the
parallelogram stands on the base 28 cm. Find the height of the
parallelogram.
Answers
Answer:
12 centimeters
Step-by-step explanation:
The side lengths of the triangle are: 26, 28, and 30 centimeters
a = 26 cm, b = 28 cm, c = 30 cm
To find the area, we first must find the semi-perimeter with the following equation:
s = (a+b+c)/2
= (28+26+30)/2
= 42 centimeters
Now, to find the area, we can use Heron's formula:
A = [tex]\sqrt{s (s-a)(s-b)(s-c)}[/tex]
[tex]\sqrt{42(42-28)(42-26)(42-30)[/tex]
[tex]\sqrt{42(14)(16)(12)}[/tex]
[tex]\sqrt{112896}[/tex]
336 squared centimeters
Since the area of the parallelogram is equal to the area of our triangle:
Area of Parallelogram = Area of Triangle
base ⋅ height = 336 squared centimeters
28 ⋅ height = 336 squared centimeters
height = 336/28
height = 12 centimeters
Which segment is the hypotenuse?
Answers
Answer:
SU
Step-by-step explanation:
The hypotenuse is opposite the right angle
The hypotenuse is US or SU
We have to pick,
The segment which is hypotenuse,
Hypotenuse will be the opposite segment of the right angle.
Now it will be,
→ SU (or) US
Hence, SU is the hypotenuse.
Line K has a slope of -3/4. If the slope of of lines that are perpendicular to each other are opposite reciprocals, what is the slope of a line perpendicular to line k?
Answers
Answer:
+4/3
Step-by-step explanation:
-3/4 * -1 = 3/4 then flip it to 4/3
Answer:
4/3
Step-by-step explanation:
the slope of a perpedicular line is the inverse times negative one.
1)the inverse of -3/4 is -4/3
2)-4/3*-1 is 4/3
PLEASE PLEASE PLEASE HELP. I WILL BE SO SO SO HAPPY!! WILL GOVE BRANLIEST! AND FOREVER BE SO HAPPY! POINTS!
Answers
Answer:
a
Step-by-step explanation:
follows geometric sequence. starting value is 1/3 and is multiplied by 1/3 every time
Find the surface area and volume for each of the following:
Answers
9.5cm is the answer
Answer:
mark brainlist..............
The graph shows a line and two similar triangles.
On a coordinate plane, a line goes through (0, 0) and (6, 4). A small triangle has a rise of 2 and run of 3. A larger triangle has a rise of 4 and run of 6.
Which expression finds the equation of the line?
StartFraction y Over x EndFraction = three-halves
StartFraction y Over x EndFraction = two-thirds
StartFraction y Over 2 EndFraction = StartFraction 3 Over x EndFraction
StartFraction y Over 3 EndFraction = StartFraction x Over 2 EndFraction
Answers
Answer: Choice B) [tex]\frac{y}{x} = \frac{2}{3}[/tex]
This is the same as saying y/x = 2/3
Or I suppose you could say "y over x = two-thirds".
===============================================
Explanation:
Recall that slope is rise over run
slope = rise/run
The rise being the change in y, while the run is the change in x.
So we could informally think of it as slope = y/x
-----------
Since we're told that it "has a rise of 2 and run of 3", this means slope = 2/3.
The slope is both y/x and also 2/3.
Equating the two expressions leads us to y/x = 2/3. This is why choice B is the final answer.
-----------
Side notes:
This trick only works when the line goes through the origin (0,0)To rephrase the last bullet point, the line must have y intercept 0.If you multiplied both sides by x, then you get y = (2/3)xAnswer:
B
Step-by-step explanation:
(-_-)
Tiana uses the equation c = 21h to figure out the total amount, c, she should
charge a customer for babysitting for h hours.
a. What is the constant of proportionality? What does it mean?
b. Tiana charges $94.50 for a job. How long did she babysit for?
Show your work.
Answers
Answer:
a. The constant of proportionality is, 21
b. Tiana charges $94.50 for a job, so, c=94.50
from the given equation,
c = 21h
or, 94.50 = 21h
or, h = 94.50/21
or, h = 4.5
She babysit for 4.5 hours.
Answered by GAUTHMATH
c = 21h
94.50 = 21h
h = 94.50 ÷ 21
h = 4.5hours.
Therefore, Tiana spent 4½ hours babysitting.
Learn more: https://brainly.com/question/20986361?referrer=searchResults
Help!!
I think I got these wrong, so please help!! Thank you!
Answers
Answer:
(x+3)(x+4)(x-4)
x+2 and x-3 are not factors but x-4 is
Step-by-step explanation:
let's factor it :)
x^3 + 3x^2 - 16x -48
first we will factor this:
x^3 + 3x^2
x^2(x + 3)
then factor the second part :
- 16x - 48
-16(x + 3)
so now,
x^2(x + 3) - 16(x + 3)
factor out x+3
(x+3)(x^2 - 16)
factor x^2 - 16
(x+3)(x+4)(x-4)
what is the reason for statement 8
a. third angle theorem
b. triangle proportionality theorem
c. congruent complements theorem
Answers
what is the value of 5 in the number 68.513?
Answers
Answer:
00000000.1
Step-by-step explanation:
1+1=2-1%000.1
Find the volume. Leave answer in exact form (in terms of π)
Answers
Answer:
704π
Step-by-step explanation:
V = π×r²×h
= π×8²×11
= 704π yd³
What is the product?
43 .4-3
0)
1)
4)
6)
Answers
Answer:
1
Step-by-step explanation:
So we can actually simplify the exponents here. The power rule for exponents is that when multiplying, you add the exponents. So,
3 + (-3) = 0
so the number is now 4^0.
Everything by the power of 0 is equal to 1, so the answer is 1.
Hope this helps !!
-Ketifa
By converting to an exponential expression, solve log3 (x + 9) = 5.
Answers
Answer:
[tex]{ \tt{ log_{3}(x + 9) = 5 }} \\ { \tt{x + 9 = {3}^{5} }} \\ { \tt{x + {3}^{2} = {3}^{5} }} \\ { \tt{x = {3}^{5} - {3}^{2} }} \\ { \tt{x = 234}}[/tex]
Given: F(x) = 2x^2+ 1, G(x) = 2x - 1, H(x) = x
F-2) =
Answers
Answer:
Step-by-step explanation:
5) where 2 coins are toased find the probability of getting:
1)both the coins with some place
2)both the coins with different place
3)at least one tail
5)at the most one head
Answers
Step-by-step explanation:
Let S be the sample space
S={HH, HT, TH, TT}
n(S)= 4
A: both the coins with some place
B: both the coins with different place
C:at least one tail
D:at the most one head
1) A={TT,HH}
n(A)=2
P(G)= n(A)/n(S)
= 2/4
= 1/2
2) B ={HT, TH}
n(B) = 2
P(B) = n(B)/n(S)
= 2/4
= 1/2
3) C= {HT, TH, TT}
n(C)=3
P(C) = n(C)/n(S)
= 3/4
4). D={HT, TH}
n(D) = 2
P(D) = n(D)/n(S)
= 2/4
=1/2
y is the element of the set {1.5, 7.2, 3.4, 4.1, 8.9, .75} and 5Y ÷ 6 is an integer. What is the value of Y
Answers
Answer:
7.2
Step-by-step explanation:
5y = 5 *7.2 = 36
36 ÷ 6 = 6
So, y = 7.2
Estimate the product of 32 and 19 ?
Answers
Answer:
608
Step-by-step explanation:
32 x 19
= 32 x ( 10 + 9 )
= 320 + 288
= 608
Which rule is a recursive rule for the sequence 1,-6,36, -216
Answers
Answer:
3rd option
Step-by-step explanation:
There is a common ratio between consecutive terms , that is
r = - 6 ÷ 1 = 36 ÷ - 6 = - 216 ÷ 36 = - 6
To obtain a term in the sequence multiply the previous term by - 6
Then the recursive rule is
[tex]a_{n}[/tex] = - 6 . [tex]a_{n-1}[/tex]
Answer: 1*6°=6
1*(-6)^1=-6
1*(-6)^2=36
1*(-6)^3=-216
The equation of line a is y=-x+ 3. If line b runs perpendicular to line a and
passes through (2, 6), what would be the equation of line b?
Answers
Answer:
y = 4x -2
Step-by-step explanation:
y = 4x + b
6 = 4(2) + b
6 = 8 + b
-2 = b
Graph: f(x) = 3/2 (2)x
Step 1: Calculate the initial value of the function.
f(0)=
Answers
Answer:
Step 1: 1.5
Step 2: Plot the points (0, 1.5)
Step 3: 3, then 0.75
Step 4: Plot the points (1, 3) and (-1, 0.75)
Step 5: y=0
Step-by-step explanation:
Ur welcome and have a nice day :>
The initial value of the function f(x) = 3/2 (2)^x is 3/2
How to calculate the initial value of the function?The function expression is given s:
f(x) = 3/2 (2)^x
Substitute 0 for x
f(0) = 3/2 (2)^0
Evaluate the exponent
f(0) = 3/2 * 1
Evaluate the product
f(0) = 3/2
Hence, the initial value of the function is 3/2
Read more about exponential functions at:
https://brainly.com/question/11464095
Please help me with this I really need help (ಥ_ಥ)
Answers
Answer:
i can help you i know this question
Which of the following is the solution to 9|x +4|>54 ?
O A. x2-10 or x 2 2
O B. xs-10 and x 2
C. x2
O D. X<-10 or x >2
Answers
Answer:
x>2 or x<-10
Step-by-step explanation:
9|x +4|>54
Divide each side by 9
9/9|x +4|>54/9
|x +4|>6
There are two solutions, one positive and one negative
x+4 >6 or x+4 < -6
Subtract 4 from each side
x+4-4 >6-4 or x+4-4 < -6-4
x>2 or x<-10
A standard deck of 52 cards has 13 ranks (Ace, 2, 3, 4, 5, 6, 7, 8, 9, 10, Jack, Queen, King) and 4 suits ($\spadesuit$, $\heartsuit$, $\diamondsuit$, and $\clubsuit$), such that there is exactly one card for any given rank and suit. Two of the suits ($\spadesuit$ and $\clubsuit$) are black and the other two suits ($\heartsuit$ and $\diamondsuit$) are red. The deck is randomly arranged. What is the probability that the top card is a 3 and the second card is an eight
Answers
Answer:
4 / 663
Step-by-step explanation:
Given that :
Number of cards in a standard deck = 52
Number of 3's in s standard deck = 4 (each suit has one card each)
Number of 8's in a standard deck = 4 (each suit has one card each)
Probability, P = required outcome / Total possible outcomes
Choosing without replacement :
P(top card is a 3) = 4 / 52
P(second draw is 8) = 4 / 51
P(top card is a 3 and second is 8) :.
4/52 * 4/51 = 16 / 2652 = 4 / 663
50 Points:
What are the coordinates of the point that is
2/3 of the way from A to B?
Point A: -4,-1
Point B: 5,5
A. 1,2
B. 0,5/3
C. 2,3
D. -1,1
Answers
Answer:
(-2,3)
Step-by-step explanation:
For the point to be 2/3 of the way; it means it divides AB into the ratio 2 to 1
Now, we can use the internal section formula to get the coordinates of this point
(x,y) = (nx1 + mx2)/(m + n), (ny1 + my2)/(m + n)
where (m,n) = (2,1)
(x1,y1) = (-4,-1)
(x2,y2) = (5,5)
(x,y) = (1(-4) + 2(-1)/(1+2), (1(-1)+2(5)/(1+2)
(x,y) = (-4-2)/3, (-1 + 10)/3
(x,y) = (-2,3)
If m ≠ 1 and mn - 3 = 3 - n , then what is the value of n?
A) 6/ m+1
B) 6/ m-1
C) 6/ m+n
D) 6/ m-n
Answers
[tex]n = \frac{6}{m + 1} [/tex]
Hope it helps you...
The value of n is n= 6/( m+1).
What is expression?An expression is a set of terms combined using the operations +, – , x or , /.
Given:
mn - 3 = 3 - n
mn + n = 6
n(m+ 1) =6
n= 6/( m+1)
Learn more about expression here:
https://brainly.com/question/14083225
#SPJ2
Can anyone help me please
Answers
Answer:
1
Step-by-step explanation:
Basically you just need to find the square root of all of them
36=6 -1=1 9=3 . -1=1
6-1-3-1=1
hello, help needed...again. 35 points !!! please show work for both. thank you:)) due today.
Answers
Answer:
16 direct
17 indirect
Step-by-step explanation:
16.
If it is a direct variation
y/x = constant
4/-2 -2
-8/4 = -2
-12/6 = -2
This is a direct variation
17.
y/x = -1/2 /-2 = 1/4
y/x = -1/-1 = 1
This is not a direct variation
If it is an indirect variation then
yx = constant
-1/2 * -2 = 1
-1*-1 =1
3 * 1/3 =1
This is an indirect variation
**HELP**
find the angle measures given the figure is a rhombus.
Answers
Answer:
m<1=74
m<2=37
Step-by-step explanation:
m<2 is the same as the other angle, 37 degrees. So now we need to find the other angle in the triangle.
37+37+x=180.
The total degree of a triangle is 180.
x=106
Subtract that from 180 to get m<1.
180-106=74
I hope this helps!
Good luck!
Caroline,Colin & Sarah share some money in the ratio 5:9:6.
In total, Caroline and Sarah receive £44. How much does Colin get?
Answers
Answer:
Caroline gets 4*5 = 20 pounds
Colin gets 9 * 4 = 36 pounds
Sarah gets 6*4 = 24 pounds.
Step-by-step explanation:
The ratios are 5x + 9x + 6x
5x + 6x = 11x
Caroline and Sarah get a total of 44 pounds. They don't get 44 pounds each.
11x = 44 Divide by 11
x = 44/11
x = 4
Colin gets 9x
x = 4
9*4 = 36
Colin gets 35 pounds.
Caroline gets 4*5 = 20 pounds
Colin gets 9 * 4 = 36 pounds
Sarah gets 6*4 = 24 pounds.
Caroline and Sarah get 20 + 24 = 44
can someone please help me with this?!?!!
Answers
Answer:
I can't help but I hope you succeed
