right triangle ABC has area 32√3cm^2. The measure of <A = 30, m<B=90. What is the length of BC? AB? AC? Express all answers in simplest radical form.
Answers
"sqrt" stands for "square root"
=======================================================
Explanation:
Angle C is 60 degrees because adding the angles gets A+B+C = 180. Put another way, C = 180-A-B. Therefore, C = 180-30-90 = 60.
We have a 30-60-90 triangle with
BC as the short leg (since it is opposite the smallest angle A = 30)AB as the long leg (because it is opposite the medium angle C = 60)AC as the hypotenuse (it is opposite the largest angle, so AC is the longest side)Check out the diagram below.
----------
From here, we use the 30-60-90 triangle template. The short leg is x, the hypotenuse is 2x and the long leg is x*sqrt(3). The area of this template triangle is
area = 0.5*base*height
area = 0.5*(short leg)*(long leg)
area = 0.5*x*(x*sqrt(3))
area = 0.5*x^2*sqrt(3)
set this equal to 32*sqrt(3) and you should find that 0.5x^2*sqrt(3) = 32*sqrt(3) solves to x = 8
----------
Therefore we can say,
BC = short leg = x = 8AB = long leg = x*sqrt(3) = 8*sqrt(3)AC = hypotenuse = 2x = 16
Related Questions
Find the value of the determinant.
3
-3
-5
a. -39
b. -33
C.
75
d
33
Answers
Answer:33
Step-by-step explanation: i just did the problem
23 more than the product of 7 and a number
Answers
Answer:
7x + 23
Step-by-step explanation:
Remember BPEMDAS.
Product of 7 and a number means 7 times a variable: 7x
23 more than part means 23 + whatever we just did, so:
7x + 23
Answer:
23+7x
Step-by-step explanation:
23 + (7 * x)
23+7x
Hey guys please help find the area
Answers
Answer:
70.15 ft²
Step-by-step explanation:
The figure consists of two adjacent equilateral triangles (all angles are 60 degrees and all outer edges are 9 ft).
If we focus on one of these equilateral triangles, we can get the final area by multiplying the area of that one triangle by 2.
The formula for the area of a triangle is (1/2)(base)(height). Remembering to multiply this by 2, we get
area of figure = (base)(height)
√3
= (9 ft)(9 ft)(--------) = (81 ft²)(1.732) = 70.15 ft²
2
5 mL =____gtt
A. 75
B. 100
C. 50
D. 25
Answers
Answer:
Answer:
b. 100
Step-by-step explanation:
Which of the following is the correct scientific notation for 0.00566 meters?
A. 566 x 10-5 m
B. .566 x 10-3 m
C. 5.66 x 10-3 m
D. 5.66 x 103 m
Answers
HELP QUICK ILL GIVE A Brainliest to the first person Which of the answer choices is a coordinate point from the table below?
Answers
Answer:
2/$5.00
Step-by-step explanation:
It's the only one that makes sense
Answer:
4,10
It is the only option on the table
Step-by-step explanation:
Does it matter which dimensions you select for the length and the width when you find the area of a rectangle? Explain. I need this by 1 : 36
Answers
Answer:
The area of a rectangle is the product of the length and the width of the rectangle.
The dimensions chosen for length and width of a rectangle must be the lengths of two adjacent sides. The area is the product of the two dimensions. It does not make a difference which one you call length and which one you call width since length * width = width * length because of the commutative property of multiplication.,
Answer:
To find the area you need both the length and width
A= lw
Practically it doesn't matter which one you call length or width as long as both of them used in the calculation. The product of them doesn't change.
Help please....Thanks
Answers
Answer:
16 x 66 = 1056mm^2
Step-by-step explanation:
Point Q(-1,5) is reflected across the line x=-1. What are the coordinates of its image?
(15)
(1-5)
-1.5)
Answers
Answer:
(- 1, 5 )
Step-by-step explanation:
Since the x- coordinate of Q, x = - 1 lies on the line of reflection.
The point Q will remain unchanged, that is
coordinates of image are (- 1, 5 )
Jonathan has 2/3 of a pound of bird seed left to share equally among 6 bird cages in his pet shop. How many pounds can he put in each bird cage.
Answers
Answer: 4 scoops
Step-by-step explanation:
2/3 % 1/6 = 4 scoops
Answer:
1/9 pounds
Step-by-step explanation:
2/3 divide by 6
flip the 6 when dividing and then change division sign to multiplication
2/3 (1/6)
[tex] \frac{2}{3} \times \frac{1}{6} [/tex]
then multiply and simplify 2/18
You are miguel Cervantes de Navas y colon, captain in the royal spanish army in Sevilla in the year 1842. Outside your barracks window is a stack of cannonballs, as shown in the illusion. On an idle afternoon you dicide to calculate the number of cannonballs in the stack. What is the number of cannonballs? A. 650 B. 506 C. 623 D. 571
Answers
Answer:
650
Step-by-step explanation:
1st row has 1 ball
2nd row has 4 balls
3rd row has 9 balls
4th row has 16 balls
We can see that the number of balls is the square of the row number. There are a total of 12 rows. So, rest of the rows has:
5th row has 25 balls
6th row has 36 balls
7th row has 49 balls
8th row has 64 balls
9th row has 81 balls
10th row has 100 balls
11th row has 121 balls
12th row has 144 balls
If we add up all those, we get total number of balls
please mark me brainliest!
Using the graphing function on your calculator, find the solution to the system
of equations shown below.
y-2x = -2
y- x = 1
A. More than 1 solution
B. x = 4, y = 3
C. No solution
O D. x = 3, y = 4
Answers
Answer:a x=3 y=-4
Step-by-step explanation:
In a class of 35, students are numbered from 1 to 35. The ratio of boys to girls is 4:3.
The roll numbers of students begin with boys and end with girls. Find the probability
that a student selected is either a boy with prime roll number or a girl with composite roll number or an even roll number.
Answers
Answer:
The probability that a student selected is either a boy with prime roll number or a girl with composite roll number or an even roll number is [tex]\dfrac{4}{7}[/tex] .
Step-by-step explanation:
We are given that in a class of 35, students are numbered from 1 to 35. The ratio of boys to girls is 4:3.
The roll numbers of students begin with boys and end with girls.
Firstly, we will calculate the number of boys and girls in the class.
Number of boys in the class = [tex]\frac{4}{7}\times 35[/tex]
= [tex]4 \times 5[/tex] = 20
Number of girls in the class = [tex]\frac{3}{7}\times 35[/tex]
= [tex]3 \times 5[/tex] = 15
So, the roll numbers of boys are numbered as = {1, 2, 3,..........., 19, 20}
and the roll numbers of girls are numbered as = {21, 22, 23,..........., 34, 35}
Prime numbers are those numbers that come in their own tables and 1.
The roll number of boys having prime numbers are = {2, 3, 5, 7, 11, 13, 17, and 19}
There are total of 8 boys.
Composite numbers are those numbers that come in the tables of other numbers also.
The number of girls with composite roll number or an even roll number = {21, 22, 24, 25, 26, 27, 28, 30, 32, 33, 34, and 35}
There are a total of 12 girls.
So, the total number of favorable boys and girls = 8 + 12 = 20
Total number of students in class = 35
So, the probability that a student selected is either a boy with prime roll number or a girl with composite roll number or an even roll number is given by = [tex]\frac{20}{35}[/tex] = [tex]\frac{4}{7}[/tex] .
PLEASE HELP ASAP Eva is at a sushi restaurant. She ordered 2 pieces of squid for a total of $3.50, 1 piece of eel for $3.25, 3 pieces of tuna for a total of $6.75, and 4 pieces of crab for $8.00. Which list shows the unit cost of each pieces of sushi from least to greatest? A. squid, crab, tuna, eel B. eel, squid, tuna, crab C. squid, eel, crab, tuna D. eel, tuna, crab, squid
Answers
Answer:
I do not have enough time to put them in order if you don't mind but i can list the prices.
Step-by-step explanation:
each piece of squid is 1.25
each piece of tuna is 3.25
each piece of crab is 2.00
hope this helps <3
Answer:
A
Step-by-step explanation:
Find the distance d(A,B) between points A and B
A(2.-6), B(2.1)
d(A,B) =
Answers
Answer:
d = 7
Step-by-step explanation:
Distance Formula: [tex]d = \sqrt{(x2 - x1)^2+(y2-y1)^2}[/tex]
Plug in our 2 coordinates:
[tex]d = \sqrt{(2-2)^2+(1+6)^2}[/tex]
And you should get 7 as your final answer.
Answer:
7 units
Step-by-step explanation:
Since the x coordinates are the same, we only have to look at the difference between the y coordinates to determine the distance
1 - -6 = distance
1+6 = 7
The distance is 7 units
Estimate the difference of 10 2/3-6 9/11
6
3
06
4
Answers
Answer:
5
Step-by-step explanation:
If you calculate it it will be 4 28/33 which is closer to 5
In the circle below, suppose m FEH=272º and m EFG=116º. Find the following.
Answers
Answer:
m∠FEH = 44°
m∠EHG = 64°
Step-by-step explanation:
1) The given information are;
The angle of arc m∠FEH = 272°, the measured angle of ∠EFG = 116°
Given that m∠FEH = 272°, therefore, arc ∠HGF = 360 - 272 = 88°
Therefore, angle subtended by arc ∠HGF at the center = 88°
The angle subtended by arc ∠HGF at the circumference = m∠FEH
∴ m∠FEH = 88°/2 = 44° (Angle subtended at the center = 2×angle subtended at the circumference)
m∠FEH = 44°
2) Similarly, m∠HGF is subtended by arc m FEH, therefore, m∠HGF = (arc m FEH)/2 = 272°/2 = 136°
The sum of angles in a quadrilateral = 360°
Therefore;
m∠FEH + m∠HGF + m∠EFG + m∠EHG = 360° (The sum of angles in a quadrilateral EFGH)
m∠EHG = 360° - (m∠FEH + m∠HGF + m∠EFG) = 360 - (44 + 136 + 116) = 64°
m∠EHG = 64°.
Determine whether the function is linear or quadratic. Identify the quadratic, linear, and constant terms.
Answers
Answer:
B. Quadratic Function
Quadratic Term: 15x^2
Linear Term: 9x
Constant Term: -6
Step-by-step explanation:
1. F.O.I.L (firsts, outers, inners, lasts) the function
BREAK APART: 3x(5x - 2) and 3(5x - 2)
(fx) = 15x^2 - 6x + 15x - 6
f(x) = 15x^2 + 9x - 6
There is a square in the function, therefore it is quadratic. The quadratic term is the term being squared, and you go from there.
Find the perimeter of the right triangle. If necessary, round to the nearest tenth.
A right triangle with side 13 inches, side 14 inches, and blank hypotenuse.
a.
91 in.
b.
46.1 in.
c.
19.1 in.
d.
182 in
Answers
Answer:19.1
Step-by-step explanation:
Answer:
B. 46.1 in
Step-by-step explanation:
First, we must find the hypotenuse of the triangle.
Since this is a right triangle, we can use Pythagorean Theorem.
a^2+b^2=c^2
where a and b are the legs and c is the hypotenuse.
13 and 14 are the legs, because they form the right angle. x is the hypotenuse because it is opposite the right angle.
13^2+14^2=x^2
Evaluate each exponent.
13^2=13*13=169
14^2=14*14=196
169+196=x^2
Add 169 and 96
365=x^2
Take the square root of both sides.
√365=√x^2
√365=x
19.1049732=x
Round to the nearest tenth.
19.1=x
The hypotenuse is 19.1 inches
Now, find the perimeter. Add up all the sides of the triangle: the legs (13 in and 14 in) and the hypotenuse (19.1 in)
13 in +14 in +19.1 in
46.1 in
The perimeter is 46.1 inches and B is correct.
Simplify (*x* +2x? - 5x)+(-3x + x +1)+(3+* + 2x).
A. 3x + 2x* - 3x2 – 3x² +1
B 4x*- 3x + x2 + 4x +2
C. 4x4 - 3x + 3x² + 4x +2
D. 4x*- 3x + 3x? - 3x + 1
Answers
Answer:
D
Step-by-step explanation:
4x^4+3x^2-3x^3-3x+1
How many students all together?
Answers
Answer:
from the top of my head if I read the bars right I think its 98 but I could really see the bars
Answer:
102
Step-by-step explanation:
24+12+5+17+6+19+4+15= 102
Find the volume of a cylinder that has the following dimensions. Do not round your answer.
(Use 3.14 for pi.)
Radius = 5 cm
Height = 0.25 m
Volume = __ cm3
Answers
Answer:
19.625 cm^2
Step-by-step explanation:
The volume of a cylinder is given by
V = pi r^2 h
V = 3.14 * 5^2 * .25
V =19.625 cm^2
What is the form of the Sum of Cubes identity?
Answers
Answer:
D. a³+b³=(a+b)(a²-ab+b²)
Explanation:
That is the form of the Sum of Cubes identity
Olivia has $150 in her savings account. She will save and deposit $40 each week. What inequality show how many weeks it will take her to have at least $400 in her account?
Answers
Answer:
40x+150>=400 i think
Step-by-step explanation:
40x+150>=400
40x>=250
x=6.25
HELP ASAP Three generous friends, each with some cash, redistribute their money as follows: Ami gives enough money to Jan and Toy to double the amount that each has. Jan then gives enough to Ami and Toy to double their amounts. Finally, Toy gives Ami and Jan enough to double their amounts. If Toy has $36 when they begin and $36 when they end, what is the total amount that all three friends have?
Answers
Answer:
$252
Step-by-step explanation:
This is quite a neat question, with no fixed equation. Given that each person gives the other two enough money to double their cash, if Toy had 36 dollars beginning, and 36 at the end - presumably the cash of each person, ( their starting and original ) should be the same as well. Respectively each should be a multiple of 36 dollars.
Jan's " give away " = Ami + 36, Jan - 108, Toy + 72
Toy's " give away " = Ami + 72, Jan + 36, Toy - 108
Therefore, we can conclude that Ami = 144 at the start, presuming he gave away 108 dollars, with a remaining 36. Jan, having 144 dollars ( after having his 72 dollars doubled by Ami ) gives 36 to Ami to double his amount, and 72 to double Toy's doubled amount, remaining with 36 dollars. Now Ami has 72 dollars, Jan has 36, and Toy has 144. Then, Toy double's Ami and Jan's amount, giving away 72 and 36 dollars, remaining with 36 dollars himself. Therefore, Ami has 144 dollars, Jan has 72 dollars, and Toy has 36 dollars both at the beginning and end.
144 + 72 + 36 = 252 dollars ( in total )
Answer:
The answer is 252
Step-by-step explanation:
Name the similar triangles. ΔABC ~ ΔDEF ΔABC ~ ΔEDF ΔABC ~ ΔDFE ΔABC ~ ΔFED
Answers
Answer:
Since ∠E ≅ ∠A and ∠D ≅ ∠B, the answer is ΔABC ~ ΔEDF.
Answer:
option 2
Step-by-step explanation:
Let f be defined as shown. Which statement is
true?
Answers
The inverse of f exists
The inverse of f does not exists
Answers
Answer:
[tex]\boxed{\sf \ \ \ the \ inverse \ of \ f \ does \ not\ exist \ \ \ }[/tex]
Step-by-step explanation:
hello,
for one x you cannot get several values of f(x), otherwise this is not a function
as 6 and 7 gives 0 it means that
f(6)=f(7)=0 which is fine for f
but then for [tex]f^{-1}[/tex] it would mean that 0 has two different images
and this is not possible
so the inverse of f does not exist
hope this helps
Solve the equation 2(5x-4)=ax+b
Infinite solution
One solution
No solution?
Answers
Answer:
Infinite Solutions
Step-by-step explanation:
Since we don't have the values of a and b, a and b can be any number. If they can be any number, then our answer has to be infinite solutions, as our answer can vary between different values.
since you don’t know what a and b are there could be many solutions
I NEED HELP !!! If the probability of an event is StartFraction 2 over 7 EndFraction, what must be the probability of its complement?
StartFraction 1 over 7 EndFraction
StartFraction 2 over 7 EndFraction
StartFraction 4 over 7 EndFraction
StartFraction 5 over 7 EndFraction
Answers
Answer:
The answer is StartFraction 5 over 7 EndFraction
Answer:
The probability of the complement of the original event is 5/7.
Step-by-step explanation:
The probability of the complement of an event is 1 less the probability of the event, so
We get: 1 - 2/7, or 5/7
The probability of the complement of the original event is 5/7.
Note that 5/7 and 2/7 add up to 7/7, or 1.
Instructions
Search your home for a rectangular prism. Some examples are a cereal
box, a CD case, or a coffee table. Measure your prism using appropriate units, such as inches, centimeters, or feet.
Complete the following. Show all work for calculations.
Part 1).List the dimensions of your box. Be sure to include the units (in, cm, ft, etc.).
Length: 3 1/2in
Width: 1 1/2in
Height: 7in
Part 2) Describe the shape of the cross section when the box is cut parallel to the base.
• The cross section had a rectangular shape and goes through the box minimizing the width of the shape.
Part 3) What is the surface area of the box?
• 80.5 square inches
Part 4) What is the surface area of the box if it is scaled up by a factor of 10?
• 805 square inches
Part 5) What is the volume of the box?
• 36.75 square inches
Part 6) What is the volume of the box if it is scaled down by a factor of 1/10?