9514 1404 393
Answer:
a) A = 73°, C = 59°, a = 16.7
b) A = 11°, C = 121°, a = 3.3
Step-by-step explanation:
The Law of Sines can be used to find angle C. Then the sum of angles in the triangle can be used to find angle A. The length of 'a' can be found either from the Law of Sines or the Law of Cosines at that point.
The given angle is opposite the shorter of the two given sides, so there are two possible solutions.
Acute triangle solution
The Law of Sines gives the relation ...
sin(C)/c = sin(B)/b
sin(C) = (c/b)sin(B)
C = arcsin(c/b·sin(B)) = arcsin(15/13·sin(48°)) ≈ 59°
Then angle A is 132° -59° = 73°, and side 'a' is ...
a = 13·sin(A)/sin(B) = 13·sin(73°)/sin(48°) ≈ 16.7
__
Obtuse triangle solution
The other value of arcsin(15/13·sin(48°)) is used:
C ≈ 121° ⇒ A = 11°
a = 13·sin(11°)/sin(48°) ≈ 3.3
__
The two solutions are ...
A = 73°, C = 59°, a = 16.7
A = 11°, C = 121°, a = 3.3
We note that the drawing is of an acute triangle, so that solution may be the one that is preferred.
_____
Additional comment
In the above presentation, we have rounded angle values to the precision required by the problem statement (nearest degree). However, in the actual calculations, we have used the full calculator precision. Only the final answers have been rounded.
Given f(x) =1 - 3/4x find the following.
a. f(-12) b. f(0) c. f(4)
Answer:
a. f(-12) = 10
b. f(0) = 1
c. f(4) = -2
Step-by-step explanation:
In order to find the function of each of these numbers, you just need to replace them in the function as x and then solve:
a. f(-12) = 1 - 3/4(-12)
- f(-12) = 1 - (-36/4)
- f(-12) = 1 + 9
- f(-12) = 10
b. f(0) = 1 - 3/4(0)
- f(0) = 1 - 0
- f(0) = 1
c. f(4) = 1 - 3/4(4)
- f(4) = 1 - 12/4
- f(4) = 1 - 3
- f4) = -2
Find the product. ( 5xy) ( 7xy)
Answer:
35x^2y^2
Step-by-step explanation:
just multiply and combine like terms
triangle PQR with side p across from angle P, side q across from angle Q, and side r across from angle R
HELP PLEASE I COULDN'T FIND THE ANSWER ANYWHERE
If ∠R measures 18°, q equals 9.5, and p equals 6.0, then which length can be found using the Law of Cosines?
1. p
2. q
3. RQ
4. PQ
Answer:
P
Step-by-step explanation:
Which of the following is the best approximation of the volume of the cylinder below?
A.22,507.5 m^3
B.5626.9 m^3
C.1406.7 m^3
Answer:
B.
Step-by-step explanation:
V = (pi)r^2h
V = 3.14 * (8 m)^2 * 28 m
V = 5626.9 m^3
Answer: B.
-5(y + 5) > 45
Answers y > -14
y > 4
Answer: your correct but the answer should be y<-14
Step-by-step explanation: i dont get the y>4 but if you solve -5(y + 5) > 45 you should get y<-14
hope this helped :)
Expanding a garden. The dimensions are 25 feet by 25 feet. I bought 10 cubic yards of soil. How many inches thick will the new dirt cover
Answer:
The thickness of the new dirt cover is 0.144 yards.
Step-by-step explanation:
Dimension of garden = 25 feet by 25 feet.
Volume of soil bought = 10 cubic yards
Volume = length x width x height
But,
1 foot = 0.333333 yard
So that,
25 feet = 25 x 0.333333
= 8.33333 yards
The new dimension of the garden = 8.33333 yards by 8.33333 yards.
Let the thickness of the new dirt cover be represented by h.
Thus,
Volume = 8.33333 x 8.33333 x h
10 = 69.44439 x h
h = [tex]\frac{10}{69.44439}[/tex]
= 0.144
h = 0.144 yards
The thickness of the new dirt cover is 0.144 yards.
Mr. Kelly was checking out his items at Dunkin Donuts, he bought three bags of coffee that cost $6.75 each. There is a sales tax of 8.75%, how much will Mr. Kelly pay in total?
Answer:
$22.02
Step-by-step explanation:
3(6.75)(1.0875) = 22.021875 ≈ $22.02 (Assuming the store rounds down.)
I NEEED HELP PLEASE ANYONE!! With step by step answer
Answer:
x = 2
Step-by-step explanation:
Let me know if you have questions
If sally invests $400 into the Bank of Reyonds that offers her a 6% interest, compounded monthly, how much money will she have in the bank in 5 years?
Given:
Principal = $400
Rate of interest = 6% compounded monthly
Time = 5 years.
To find:
The amount in the bank after 5 years.
Solution:
The formula for amount is:
[tex]A=P\left(1+\dfrac{r}{n}\right)^{nt}[/tex]
Where, P is principal, r is the rate of interest, n is the number of time interest compounded in an year and t is the number of year.
Interest compounded monthly. So, [tex]n=12[/tex].
Putting [tex]P=400, r=0.06, n=12[/tex] and [tex]t=5[/tex], we get
[tex]A=400\left(1+\dfrac{0.06}{12}\right)^{12(5)}[/tex]
[tex]A=400\left(1+0.005 \right)^{60}[/tex]
[tex]A=400\left(1.005 \right)^{60}[/tex]
[tex]A\approx 539.54[/tex]
Therefore, the amount of money in the bank after 5 years is $539.54.
Please Help me!!! The rectangle has a width of 6 in and a length of 8 in. What is the Perimeter? What is the Area? Remember: Area is length x width. P= A=
Point R is located at (8, 13). Where is R' after a translation 8 units left and 6 units down?
Answer:
R' = (0,7)
Step-by-step explanation:
pls answer it now!!
argatogozaimasu!!
Answer:
850 and 23
Step-by-step explanation:
pls help i only have a couple mins left to finish, i need help with both 1 and 2
I need help quick!
Q: The measure of
Answer:
x=34
Step-by-step explanation:
132-64=
68/2=
34
PLEASE MAKE ME BRAINLIEST
A sheet of origami paper is in the shape of a square with a side length of 7 inches, as shown. What is the area of the sheet of origami paper?
The answer is C!!
I took the unit test, your welcome tehe UwU
Answer:
what was c?
Step-by-step explanation:
A certain pipe can be used to fill a pool with water in 2 hours. A second pipe can be used to fill the pool in 4 hours. How long does it take to fill the pool when both pipes are used at the same time?
Answer:
1 1/3 hours
Step-by-step explanation:
Pipe 1 alone:
fills the pool in 2 hours
in 1 hour, it fills 1/2 of the pool
Pipe 2 alone:
fills the pool in 4 hours
in 1 hour, it fills 1/4 of the pool
Pipe 1 and Pipe 2 working together:
fill the pool in x hours
in 1 hour, they fill 1/x of the pool
Working together, in 1 hour the two pipes fill 1/2 + 1/4 of the pool.
Working together, in 1 hour the two pipes fill 1/x of the pool.
Therefore,
1/2 + 1/4 = 1/x
2/4 + 1/4 = 1/x
3/4 = 1/x
x = 4/3
x = 1 1/3
Answer: 1 1/3 hours
A shopper drives from the mall at point M to the post office located at point P. What distance does the shopper drive?
Part A: Explain the steps you would take to find the distance.
Part B: What distance does the shopper drive?
Answer:
Step-by-step explanation:
Part A: I would count the boxes from point M to point P.
Part B: The shopper drive 12 m.
The distance between the mall and the post office is 13 meters.
What is the distance between two points?It is the measure of distance between the two points and is known as length. The length is measured in meters generally.
Let one point be (x, y) and another point be (h, k). Then the distance between the points will be given as,
D² = (x - h)² + (y - k)²
From the diagram, the points are M(2, 5) and P(7, 17). Then the distance between the mall and the post office is calculated as,
MP² = (7 - 2)² + (17 - 5)²
MP² = 5² + 12²
MP² = 25 + 144
MP² = 169
MP = 13
Learn more about the distance between two points here:
https://brainly.com/question/18296211
#SPJ2
55 x 32 / 32
HELPPP GIVING BRAINLIEST
Answer:
55
Step-by-step explanation:
Just multiply then divide:
55 x 32 = 1760
1760 ÷ 32 = 55
Or just easier like:
55 x 32 ÷ 32 = 55
Hopefully this helps :3 Sorry if wrong :( Plz mark brainiest if correct :D Your bootiful/handsome! Have a great day luv <3
-Bee~
You travel 30 miles per hour for 4.2
hours. How far did you travel?
Answer:
126 miles
Step-by-step explanation:
If I remember right, you'll have to multiply 30 by 4.2 and get 126 miles since each hour is 30 miles.
Becky, an artist, plans to paint and sell some miniature paintings. She just bought some brushes for $1, and paint and canvas for each painting costs $21; she will sell each painting for $22. Once Becky sells a certain number of her paintings, she will be breaking even. How much will Becky have earned? How many paintings will that be?
Answer:
After one unit is sold, Becky will break-even.
Step-by-step explanation:
Giving the following information:
Fixed costs= $1
Unitary variable cost= $21
Selling price= $22
The break-even point is the number of units required to cover the fixed costs after deducting from the selling price the variable components. At this point, net income is zero.
Break-even point in units= fixed costs/ contribution margin per unit
Break-even point in units= 1 / (22 - 21)
Break-even point in units= 1
After one unit is sold, Becky will break-even.
Find the 60th term of the arithmetic sequence -27, -24, -21
PLEASE HELP I HAVE ANOTHER ONE NEEDED DONE if you answered last time lol.
A: Positive Correlation
B: Negative Correlation
C: No Correlation
What type of correlation is show in the scatter plot?
Answer:
B
Step-by-step explanation:
what fraction is equal to 3 1/4
Answer:
13/4
Step-by-step explanation:
Perform the operation.
(-8x² + 10x + 4) – (-4x + 10)
Answer:
-8x^2 + 14x -6
Step-by-step explanation:
Answer:
- 8x² + 14x - 6
Step-by-step explanation:
Given
(- 8x² + 10x + 4) - (- 4x + 10)
Distribute the parenthesis, noting to distribute the second one by - 1
= - 8x² + 10x + 4 + 4x - 10 ← collect like terms
= - 8x² + 14x - 6
LMN is a right triangle 39 36 15
PLZZ HELP find area of square KLMN?
Hello! The area of square KLMN is 25 cm²
Make sure to read an explanation for better understanding to the problem.
Any questions about my answer and explanation can be asked through comments.
Step-by-step explanation:
Since the square has same length for both sides. We can proceed side × side formula. Our side is 5 because if we count these small squares or grids, we'd get 5 for both sides.
Therefore 5 × 5 = 5² = 25 cm².
We can also use Calculus to solve the problem by using Integration.
Because both lines are horizontal, they are constant function. That means they are in the form of y = b where b is a constant.
A line that passes through (a,4) where a is all real numbers. The equation is y = 4
A line that passes through (c,-1) where c is all real numbers. The equation is y = -1
Therefore,
[tex] \large{ \int^{b}_a f(x) dx+ \int^{b}_a g(x)dx} \\ \large{ \int^{2}_{ - 3} (4)dx+ \int^{2}_{ - 3} ( - 1)dx}[/tex]
Because y = -1 is below x-axis. Therefore,
[tex] \large{ \int^{2}_{ - 3} 4 dx+ \int^{2}_{ - 3} 1dx} \\ \large{ (4x)^{2}_{ - 3} + (x)^{2}_{ - 3} } \\ \large{8 - ( - 12) + 2 - ( - 3)} \\ \large{8 + 12 + 2 + 3 = 25}[/tex]
can 4x+35 be factored? yes or no
Answer:
no it is not able to be factored
Christopher spent a total of 52.50 at a bookstore he purchased a calendar for 9 and three books that cost the same
Answer:
Cost of each book = 14.5
Step-by-step explanation:
Given:
Total amount spend = 52.50
Cost of calendar = 9
Number of books = 3
Assume;
Cost of each book = a
Find:
Cost of each book
Computation:
Total amount spend = Cost of calendar + Number of books(Cost of each book)
52.50 = 9 + 3(a)
Cost of each book = 14.5
Tasha needs to walk 7/10 miles to school. She has already walked 3/5 mile. How much farther does Tasha need to walk? Answer in simplified form, if needed.
Answer:
1/10
Step-by-step explanation:
We are to determine the difference between the miles walked Tasha already and the total number of miles to school
[tex]\frac{7}{10} - \frac{3}{5}[/tex]
[tex]\frac{7-6}{10}[/tex] = [tex]\frac{1}{10}[/tex]
find square root of 100
Answer:
10, -10
Step-by-step explanation:
Take the sqrt(100)
What number times itself = 100
10*10 = 100
-10*-10 = 100
sqrt(100) = +10 or -10