Answers
Answer:
Perimeter of ΔABC: [tex]\frac{27}{2}[/tex] + [tex]\frac{9}{2} * \sqrt6[/tex] units
Area of ΔABC: [tex]\frac{81}{8}*\sqrt3 + \frac{243}{8}[/tex] units
Skills required: HS Geo, Special Triangles
Step-by-step explanation:
1) The best option is to break down this triangle. Let's draw an altitude from Point B down to Segment AC. The point from the altitude that intersects AC is Point D. BD is the height of our triangle, AC is the base.
2) Angle A is 60 degrees, and since Angle BDA is 90 degrees, Angle ABD is 30 degrees. We can use the 30-60-90 degree right triangle property for the triangle BDA.
This states that if the side opposite the 30 degree angle is [tex]x[/tex], the side opposite the 60 degree angle is [tex]x*\sqrt3[/tex], and the side opposite the 90 degree angle is [tex]2x[/tex].AB is 9 units, and it is opposite the 90 degree angle. This means that [tex]2x=9, x = \frac{9}{2}[/tex] ==> This then means that AD, the segment opposite the 30 degree angle in this triangle is [tex]\frac{9}{2}[/tex] units. Segment BD (the height) is [tex]\frac{9}{2} * \sqrt3[/tex].
3) Angle C is 45 degrees, and Angle BDC is 90 degrees, which means that Angle CBD is 45 degrees. We can use the 45-45-90 degree right triangle property for the triangle BCD.
This states that if the side opposite the 45 degree angle is [tex]x[/tex], the other side opposite a 45 degree angle is also [tex]x[/tex], but the hypotenuse (side opposite the right (90 degree) angle) is [tex]\sqrt{2}*x[/tex].BD is [tex]\frac{9}{2} * \sqrt3[/tex], which means DC is the same. BC, which is the hypotenuse is BD multiplied by square-root-2, which is [tex]\frac{9}{2} * \sqrt6[/tex].
4) Area is [tex]\frac{1}{2}*b*h[/tex], the base (b) is AC (which is [tex]\frac{9}{2}+\frac{9}{2}*\sqrt3[/tex]), the height is BD ([tex]\frac{9}{2}*\sqrt3[/tex]). When multiple you will get [tex]\frac{81}{4}*\sqrt3 + \frac{243}{4}[/tex], then this multiplied by 1/2 is
[tex]\frac{81}{8}*\sqrt3 + \frac{243}{8}[/tex] <--> this is the area!
5) Perimeter is just the sum of all side: 9 + [tex]\frac{9}{2}[/tex] + [tex]\frac{9}{2} * \sqrt6[/tex] = [tex]\frac{27}{2}[/tex] + [tex]\frac{9}{2} * \sqrt6[/tex] unit
Related Questions
Find an ordered pair (x, y) that is a solution to the equation 3x-y=4
Answers
Answer:
(0,-4)
Step-by-step explanation:
3(0) - (-4) = 4
0 + 4 = 4
Plz help me with this question
Answers
Answer:
1422cm²
Step-by-step explanation:
Triangle:
First; 24 x 14 = 336
second: since there is 2 triangle u x 2
so its 672
-------------------------------------------------------------------------------------------------------
Rectangle:
third; 25 x 10 = 250
forth; since there is 3 rectangle u x3
so its 750
last u add all ur answer for triangle and rectangle and u get
-------------------------------------------------------------------------------------------------------------
672 + 750 =
1422cm²
If correct please give brainliest
Stay safe and healthy
Thank You
How many solutions does this equation have?
4h + 2 = 2 + 4h
Answers
should be 4
Step-by-step explanation:
y=2x squared +4x-1 . help me
Answers
Answer:
y = 9/8 for part one of solving y in this equation .
Step-by-step explanation:
Answer:
x= (√2y+6/2)-1
Step-by-step explanation:
Swap sides so that all variable terms are on the left hand side.
2x^2+4x−1=y
Subtract y from both sides.
2x^2 +4x−1−y=0
Using quadratics formula:
x=-4±√4²-4*2(y-1)/2*2
x= −4±2√ 2y+6/4
Next solve the equation by using either ± = subtraction or addition
I am using ± = addition. This means I add -4 to 2. From there I simplify equation.
x= (√2y+6/2)-1
Not sure if this means to find x, but I think this is what it would be.
Which form most quickly reveals the zeros (or "roots") of the function?
Choose 1 answer:
f(2)=3(x+6)2 - 75
B
f(x) = 3x2 + 36x +33
f(x) = 3(x + 1)(x +11)
Write one of the zeros.
T =
Answers
Answer:
c
Step-by-step explanation:
Write an equation for a line if m
3 and it passes through the point (1, -5).
Answers
y - -5 = 3 (x-1)
Pls help me with this
Answers
Step-by-step explanation:
a)
clearly, A and B are mirrored images of each other around the x-axis.
and the equation of the x-axis is simply
y = 0
b)
this is trickier.
first of all, the mirror line is now vertical and not horizontal.
and where is it ? of course, in the middle between A and B.
how many units are there between A and B ?
I am counting 5. so, the middle between them is 2.5 units.
so, let's go e.g. from A 2.5 units to the right (in the direction of B).
where do we end up ? at x = 0.5
and that is also the equation of the vertical line there.
again
x = 0.5
-2a
0b
-2
× -5b
4
× -b
Answers
Answer:
Step-by-step explanation:
Army DA administrative publications and forms by the Army Publishing Directorate APD. The latest technologies high quality electronic pubs and forms view ...
The yellow submarine was at sea level when the passengers boarded. The journey began with a descent of 40 meters. After examining the sea life, they rose 30 meters. Zach thought he saw an octopus, below. They dove again, a distance of 25 meters to watch the eight ‘legged’ sea creature.
a) Write an expression to describe the journey of the yellow submarine. _________________________________
b) At what depth did they stop to look at the octopus? ______________________
Answers
Answer:
20 meters
Step-by-step explanation:
..................
help please anybody hmm
Answers
Answer:
Step-by-step explanation:
The answer would be 6 because you would count the distance like it says!
photo to help u visualize using the “bunny hop” method
Which expression is equivalent to −78−(−34)
HELP PLEASE!
Answers
76-(-34) those two - turn into a plus
A plane travels 460 miles per hour. how many miles does the plane travel in feet per second?
Answers
Answer:
674.667 feet per second
it takes a swimmer 72.54 seconds to swim the 100 meter length of the pool going west what was his velocity.
(MUST show work and formula)
Answers
Step-by-step explanation:
Solution
(s) = 100m
(t) = 72.54s
(v) = ??
We have,
v = s÷t
v = 100 ÷ 72.54
v = 1.37 m/s
Hence, the velocity of the swimmer is 1.37 m/s
[this is how I personally have to do it but not sure about you]
I need help with this question
Answers
Answer:
2√14m
Step-by-step explanation:
Hypothenus = 9m
Second side = x
third side = 5m
Using Pythagoras theorem
9² = x² + 5²
81 = x² + 25
x² = 81 - 25
x² = 56
x = √56
= √4 × √ 14
= 2√14m
My mom gave me 5 dollar and I had 6 dollar and my dad gave me 8 dollar how much money I have?/
Answers
Answer:
19
Step-by-step explanation:
You had 6 dollars and your mom gave you 5. 6 + 5 = 11.
You dad gave you 8 dollars.
11 + 8 = 19
Answer:
19 dollars
Step-by-step explanation:
5+6+8=19
If you started off with 6 dollars and your mom gave you 5 you now have 11. If your dad gave you another 8 on top of the 11 you already had you now have 19.
10^5 =
easy question
Answers
[tex] \: \: \: [/tex]
[tex] \pink{100000}[/tex]
step-by-step explanation
[tex] {10}^{5} [/tex]
write the exponentiation as a multiplication[tex]10 \times 10 \times 10 \times 10 \times 10[/tex]
multiply the number[tex] = \pink{100000}[/tex]
hope it helps
Answer:
The solution is 100.000
Step-by-step explanation:
10⁵
= 10×10×10×10×10
= 100×10×10×10
= 1.000×10×10
= 10.000×10
= 100.000
What is 2+6 100 points the answer is 8 right?
Answers
Answer:
yes it is 8
Step-by-step explanation:
Answer:
Step-by-step explanation:
8
1 half times 2 / 6 times six plus four
Answers
[tex] \bold{answer \: \: \to} \\ 1\frac{1}{2} \times \frac{2}{6} \times \frac{6}{1} + 4 = \\ = \frac{3}{2} \times \frac{1}{3} \times \frac{6}{1} + 4 \\ = \frac{3}{6} \times \frac{6}{1} + 4 \\ \ = \frac{18}{6} + 4 \\ = 3 + 4 \\ = \boxed{ \bold{7}}[/tex]
WILL GIVE BRAINIEST IF CORRECT
Answers
1 pound of pork = 3.64
0.5 pounds of pork = 1.82 (divided 3.64 by 2 to find 0.5 pounds of pork)
3.64 + 1.82 = 5.46
Jeff also bought 2.5 pounds each of beer and chicken.
1 pound of beef = 5.99
2 pounds of beef = 11.98
0.5 pounds of beef = 2.995 (5.99 divided by 2)
11.98 + 2.995 = 14.975
1 pound of chicken = 4.79
2 pounds of chicken = 9.58
0.5 pounds of chicken = 2.395
9.58 + 2.395 = 11.975
Add up the total amount of the 1.5 pounds of pork and 2.5 pounds each of beef and chicken.
5.46 + 14.975 + 11.975 = $32.41
Answer:
$32.41
Step-by-step explanation:
Given that:
Amount of pork bought by Jeff = 1.5 pounds
Amount of beef bought by Jeff = 2.5 pounds
Amount of chicken bought by Jeff = 2.5 pounds
Cost of number of pounds of each type of meat bought by Jeff can be calculated by multiplying the number of pounds by the cost of each type per pound.
Cost of pork for 1.5 pounds = 1.5 3.64 = $5.46
Cost of beef for 2.5 pounds = 2.5 5.99 = $14.975
Cost of chicken for 2.5 pounds = 2.5 4.79 = $11.975
Total cost = Cost of pork + Cost of beef + Cost of chicken = 5.46 + 14.975 + 11.975 = $32.41
30 POINTS
A fabric paint manufacturing company fills the paint in containers using a machine. The amount of paint in a container follows a normal distribution with a mean of 99 ml and a standard deviation of 5 ml. What is the probability that the quantity of paint filled is less than 100 ml? A) 0.28 B) 0.42 C) 0.58 D) 0.92
Answers
Answer:
The correct answer is C) 0.58
Step-by-step explanation:
All this is from USATESTPREP:
The function normCdf(x0, x1, , ) gives the probability that a value drawn from a normal distribution with mean and standard deviation lies in the interval [x0, x1].As the normal distribution is symmetric, the probability that a value is less than the mean is exactly 0.5P(x ≤ 100) = P(x < 99) + P(99 ≤ x ≤ 100)= 0.5 + normCdf(99,100,99,5) = 0.5793Rounded to the nearest hundredth, the probability that a container is filed with less than 100 ml is 0.58.
Hire Refrigeration company floated Rs. 3 Billion bond on July 1, 2016. Each bond having face value of Rs. 1,000. Maturity of bond is 5 years, while interest coupon rate is 12%. What will be the value of bond if market interest rate is 8% and 15% respectively. Also what will be the new value of bond after 2 years if the market interest rate remains constant.
Answers
1. The value of the bond with a market interest rate of 8% is $1,159.71.
2. The value of the bond with a market interest rate of 15% is $899.44.
3. The new value of the bond after 2 years with market interest rate of 8% is $1,103.08.
4. The new value of the bond after 2 years with market interest rate of 15% is $931.50.
Data and Calculations:
N (# of periods) = 5 years
I/Y (Interest per year) = (A) 8% or (B) 15%
PMT (Periodic Payment) = $120
FV (Future Value) = $1,000
Results
PV = $1,159.71 and $899.44 for (B)
Schedule at 8% interest rate
Period PV PMT Interest FV
1 $1,159.71 $120.00 $92.78 $1,132.49
2 $1,132.49 $120.00 $90.60 $1,103.08
3 $1,103.08 $120.00 $88.25 $1,071.33
4 $1,071.33 $120.00 $85.71 $1,037.04
5 $1,037.04 $120.00 $82.96 $1,000.00
Schedule at 15% interest rate
Period PV PMT Interest FV
1 $899.44 $120.00 $134.92 $914.35
2 $914.35 $120.00 $137.15 $931.50
3 $931.50 $120.00 $139.73 $951.23
4 $951.23 $120.00 $142.68 $973.91
5 $973.91 $120.00 $146.09 $1,000.00
Learn more about the value of bonds based on effective interest rate here: https://brainly.com/question/25524725 and https://brainly.com/question/23265123
algebric expressions formula
Answers
Answer:
a2 – b2 = (a – b)(a + b)
(a + b)2 = a2 + 2ab + b
a2 + b2 = (a + b)2 – 2ab
(a – b)2 = a2 – 2ab + b
That's all i know- rip TvT
ABC is an isosceles right triangle in which has a slope of -1 and mABC = 90°. ABC is dilated by a scale factor of 1. 8 with the origin as the center of dilation, resulting in the image A'B'C'. What is the slope of ?.
Answers
The slope of B'C' is 1 and it can be determined by using formula of scale factor.
Given that,
ABC is an isosceles right triangle in which has a slope of -1 and m ∠ABC = 90°.
ABC is dilated by a scale factor of 1. 8 with the origin as the center of dilation, resulting in the image A'B'C'.
We have to determine,
What is the slope of B'C'?
According to the question,
ABC is an isosceles right triangle in which,
Slope of AB = -1
And AB is perpendicular to BC.
When the two lines are perpendicular to each other then,
[tex]\rm The \ slope\ of\ AB \times Slope\ of \ BC = -1\\\\-1 \times Slope\ of \ BC = -1\\\\ Slope\ of \ BC = 1\\[/tex]
ABC is dilated by a scale factor of 1. 8 with the origin as the center of dilation, resulting in the image A'B'C'.
Length of Line segment A'B'= 1.8 × AB
So, the slope of the two-line Segment that is AB and A'B' are the same.
Slope of A'B'= -1
Length of Line segment C'B'= 1.8 × CB
So, the slope of the two lines that is CB and C'B' are the same.
The slope of B'C' is 1.
Hence, The required slope of B'C' is 1.
For more details Slope refer to the link given below.
https://brainly.com/question/8102490
Answer:
Slope of 1
Step-by-step explanation:
C. 1
Rearrange the equation so w is the independent variable. u-5=-4(w-1)u−5=−4(w−1)
w =
Answers
Answer:
u=−4w+9
Step-by-step explanation:
u−5=−4(w−1)
u=−4(w−1)+5
u=−4w+4+5
u=−4w+9
The model below represents an equation. Which value of x makes the equation
true?
Answers
Answer:
1,1,1,1
Step-by-step explanation:
I believe this is right
Triangle P is rotated 180° about (0, 0) to give triangle Q. Triangle Q is translated by 5 2 to give triangle R. (a) Describe fully the single transformation that maps triangle P onto triangle R.
Answers
Answer:
(x, y) ⇒ (-x +5, -y +2)
Step-by-step explanation:
Rotation 180° is described by ...
(x, y) ⇒ (-x, -y)
Translation right 5 and up 2 is described by ...
(x, y) ⇒ (x +5, y +2)
The two transformations together that map P to R are described by ...
(x, y) ⇒ (-x +5, -y +2)
Logan spent $42 to buy 4 basketballs. What was the price per basketball
Answers
Answer:
$10.5
Step-by-step explanation:
$42 for 4 basketballs
price of 1 basketball = 42/4
42/4 = 10.5
-Chetan K
Answer:
10.5 dollars
Step-by-step explanation:
42÷4=10.5
Just gonna attach a picture of the problem so it’s easier
Answers
Answer:
Step-by-step explanation:
Part A
The first thing you have to do is develop a formula for the line.
It goes through (-2,3)
It has a y intercept of (0,-1)
So far what you know is
y = mx - 1
x = - 2
y = 3
3 = m(-2) - 1 Add 1 to both sides
3 + 1 = (-2)*m
4 = - 2*m Divide by - 2
4/-2 = m
m = - 2
The equation of the line is y = -2x - 1
Instead of y, we can use f(x)
f(x) = -2x - 1
Finally we can solve this part of the question.
f(1) = - 2(1) - 1
f(1) = -2 - 1
f(1) = - 3
Part B
f(x) = 5
y = 5
5 = -2x - 1 Add 1 to both sides
5+1 = - 2x Divide by - 2
6 / -2 = -2x/-2
-3 = x
.
A pie company made 57 apple pies and 38 cherry pies each day for 14 days. How many apples pies does the company make in all?
How many cherry pies does the company make in all show your work ?
Answers
Answer:
798 Apple Pies 57x14
532 Cherry Pies 38x14
Step-by-step explanation:
Ed is on a road trip. He has already traveled 226 miles and is driving at a rate of 66 miles per hour. Which equation could be used to find how many hours, x, Ed has left in his road trip if he is traveling 638 total miles?
Answers
Answer:
[tex]\purple{\rule{1000pt}{900000pt}} [/tex]
The equation is
[tex]\\ \sf{:}\Rrightarrow 66x+226=639[/tex]
[tex]\\ \sf{:}\Rrightarrow 66x=413[/tex]
[tex]\\ \sf{:}\Rrightarrow x\approx 6[/tex]