Find the measurement indicated. Round your answers to the nearest tenth. Use Law of Sines or Cosines
Answers
Answer:
5. 34°
6. 29.7
Step-by-step explanation:
5. Using sine law
25/sin(93) = 14/sin(C)
sin(C) = 0.5592325395
C = 34.00273934°
6. Using cosine law
AC² = 23.2² + 18.1² - 2(23.2)(18.1)cos(91)
AC² = 880.507229
AC = 29.67334206
Answer:
5. m∠C ≈ 34°
6. AC ≈ 29.7 metres
Step-by-step explanation:
5. We need to use the Law of Sines here, which says that for a triangle with sides a, b, and c and angles A, B, and C:
[tex]\frac{a}{sinA} =\frac{b}{sinB} =\frac{c}{sinC}[/tex]
Here, a = 25, ∠A = 93°, and c = 14, so we want to find ∠C:
[tex]\frac{a}{sinA} =\frac{b}{sinB} =\frac{c}{sinC}[/tex]
[tex]\frac{25}{sin93} =\frac{14}{sinC}[/tex]
sinC ≈ 0.56
∠C ≈ 34°
6. We need to use the Law of Cosines here, which says that for a triangle with sides a, b, and c and angles A, B, and C:
[tex]c^2=a^2+b^2-2abcosC[/tex]
[tex]b^2=a^2+c^2-2accosB[/tex]
[tex]a^2=b^2+c^2-2bccosA[/tex]
Here, a = 23.2, c = 18.1, ∠B = 91°, and b = x. We want to find b, so:
[tex]b^2=a^2+c^2-2accosB[/tex]
[tex]x^2=23.2^2+18.1^2-2*23.2*18.1*cos(91)[/tex] ≈ 880.5
x ≈ 29.7 metres
Related Questions
A family fair went to the fair and paid $24 for 2 adult tickets and 2 youth tickets. A youth ticket is half the price of an adult ticket. How much did a youth ticket cost?
Answers
Answer:
Youth tickets = $4
Step-by-step explanation:
Let x and y represent the price of adults and youth tickets respectively;
Given;
A youth ticket is half the price of an adult ticket
y = 0.5x ......1
They paid $24 for 2 adult tickets and 2 youth tickets.
2y + 2x = 24 ......2
Substituting equation 1 into 2;
2(0.5x) + 2x = 24
x + 2x = 24
3x = 25
x = 24/3 = 8
Since, y = 0.5x
y = 0.5(8) = 4
Adult tickets = $8
Youth tickets = $4
Elimination method using multiplication:3x+2y=0 and x-5y=17
Answers
Answer:
(2,-3)
Step-by-step explanation:
have to multiply (-3) to the second equation to get -3x + 15y = 51 then you add both equations .the 3 is remove (postive and negative cancels out )
2y+15y= 17y
0-51+-51
divide both sides by 17 y
-51/17= -3
then you plug -3 into the first equation and get
x= 2
y=-3
Answer:
x=2 y=- 3
Step-by-step explanation:
help please . will give brainliest
Answers
Answer:
A
Step-by-step explanation:
the last number is the y intercept so the intercept in the line is -3.5 so I just matched them up.
Please find the surface area of the sphere. Round your answer to the nearest hundredth.
Answers
Surface area = [tex]\frac{4}{3} \pi r^{3}[/tex] = [tex]\frac{4}{3}[/tex] x 3.14 x 3 x 3 x 3 = 3.14 x 4 x 3 x 3 = 113.04 yd^2 = approx. 113.1 yd^2
A chocolate factory made 708.6 pounds of dark chocolate in 6 days. How much dark chocolate, on average, did the factory make per day?
A) 116.76
B) 117.66
C) 118.10
D) 118.43
Answers
Answer: it’s answer C.
Step-by-step explanation: 708.6 ÷ 6 = 118.1(0)
Answer:
c
Step-by-step explanation:
What is the difference between a rectangular prism and a triangular prism?
The two bases of a rectangular prism are rectangles, while the two bases of a triangular prism are triangles.
A rectangular prism has two bases, while a triangular prism has one base,
A triangular prism has two bases, while a rectangular prism has one base.
A rectangular prism has two bases and three faces, while a triangular prism has two bases and four faces.
Dintro
Done
Answers
Answer:
The two bases of a rectangular prism are rectangles, while the two bases of a triangular prism are triangles.
Step-by-step explanation:
Any prism has two bases. Since we are talking about a rectangular prism and a triangular prism both must have two bases.
For example, a square prism has two bases and they are both square.
In this case a rectangular prism has two bases that are rectangles and a triangular prism also has two bases and both bases are triangles.
Note: For the figure to have only one base it must be called a pyramid.
Thus, the answer is:
The two bases of a rectangular prism are rectangles, while the two bases of a triangular prism are triangles
Answer:
a
Step-by-step explanation:
Selecting which seven players will be in the batting order on a 11 person team.
A) Permutation
B) Combination
C) Circular permutation
Answers
Answer:
a:) combination
b:) permutation
c:) combination
Step-by-step explanation:
There are 330 ways the coach can select a batting order of seven players from an 11 person team. Therefore, option B is the correct answer.
What is a combination?Combinations are selections made by taking some or all of a number of objects, irrespective of their arrangements. The number of combinations of n different things taken r at a time, denoted by nCr and it is given by, nCr=n!/r!(n−r)!,where 0 ≤ r ≤ n.
To determine the number of ways the coach can select a batting order of seven players from an 11 person team, we can use the combination formula, which is given by:
nCr = n! / r!(n-r)!
where n is the total number of players on the team, and r is the number of players in the batting order. In this case, n = 11 and r = 7.
So, the number of ways the coach can select a batting order of seven players from an 11 person team can be calculated as follows:
11C₇ = 11! / (7!(11-7)!)
= (11 x 10 x 9 x 8) / (4 x 3 x 2 x 1)
= 330
Therefore, option B is the correct answer.
To learn more about combination here:
brainly.com/question/17196495.
#SPJ2
The number of cameras produces since May at a plant can be modeled by the function N(m)=50m+600 and the cost per camera can be modeled by C(m)=4m^2-15m+45, where m is the number of months since May. According to this model, what is the total amount of revenue generated by the plant's camera production on September?
Answers
Answer:
39200
Step-by-step explanation:
Revenue = number of cameras * cost
R(m) = N(m) * C(m)
= (50m+600) * (4m^2-15m+45)
The months since may is June July August September = 4 months
R(4) = (50*4+600) * (4*4^2-15*4+45)
(200+600) * (64-60+45)
800*49
39200
Answer:
39,200
Step-by-step explanation:
September is 4 months after may, so m = 4
No. of cameras:
N(4)=50(4)+600 = 800
Cost per camera:
C(4)=4(4²)-15(4)+45 = 49
Total cost:
N × C
800 × 49
39200
Which equation is true for x= -6 and x=2
Answers
Answer:
What are you options
Step-by-step explanation:
A trapezoid was broken into a triangle and rectangle. The base of the triangle b is ______cm.
Answers
Find the area of the shaded regions:
Answers
Answer:
You are gonna need to gimme that shaded area
Step-by-step explanation:
I cant do it without them
Answer:
144
Step-by-step explanation:
72 the 72 it equals it and plus they are adjacent
Inequalities
Would this be correct?
Answers
Answer:yes
Step-by-step explanation: 20<_x-8 = 20 <_20 which is correct
Tennessee has a population of about 6,495,978. Its territory can be modeled as a trapezoid, as shown in the figure. Each unit on the coordinate grid represents one mile. Find the approximate population density of tennessee. Round to nearest whole number if necessary.
Answers
Answer:
The population density is 150 persons per square mile
Step-by-step explanation:
Firstly, we need to calculate the area of the trapezoid.
Mathematically, the area of a trapezoid is
(a+b)/2 * h
from the grid, we can obtain the lengths
on the x-axis , each line is 40(200/5 thin lines)
on the y-axis, each thin line also is 40(200/5 thin lines)
thus a = (8 * 40) = 320
b = (10* 40) = 400
h = (3 * 40) = 120
Inserting this into the area equation, we have the area of the trapezoid as (320 + 400)/2 * 120 = 43,200 units
since each unit = 1 mile, the area of Tennessee = 43,200 units
The population density is thus ; 6,495,978/43,200= which is approximately 150 persons per square mile
The population density is a number that gives the number of people located within the state.
[tex]\mathrm{The \ population \ density \ is \ approximately}\ \underline{150}\ \frac{persons}{mi.^2}[/tex]
Reasons:
The population of Tennessee = 6,495,978
The dimensions of the trapezoid model of the territory are;
Base length, a = 320
Base length, b = 400
Height of the trapezoid, h = 120
[tex]Area \ of \ the \ trapezoid = \mathbf{\dfrac{a + b}{2} \cdot h}[/tex]
Which gives;
[tex]Area \ of \ the \ trapezoidal \ territory = \mathbf{\dfrac{320 + 400}{2} \times 120 }= 43,200[/tex]
Area of the trapezoidal territory of the state = 43,200 mi²
[tex]The \ ratio \ of \ the \ population \ to \ the \ territory = \dfrac{6,495,978}{43,200} = 150.36986\overline 1[/tex]
Therefore;
[tex]The \ population \ density \approx \underline{150}\ \frac{persons}{mi.^2}[/tex]
Learn more here:
https://brainly.com/question/16098011
please help
If p(x) = 2x^3 - X, find p(a - 1)
Answers
I hope this helps you
The base of a triangle is 3cm and the height is 5cm. What mathematical operations described must be performed in order to find the area of this triangle
Answers
Plz answer this is trigonometry
Answers
Answer:
a = 47
b = 23.87
c = 90
d = 35.59
Step-by-step explanation:
I can only help this much. Not sure what the other two others below are asking
Zugo delivers muffins for the Pastry-and-Muffin company. Each muffin is packed in its own
little box. An individual muffin box has the shape of a cube, measuring three inches on
each side. Zugo packs the individual muffin boxes into a larger box. The larger box is also
in the shape of a cube, measuring two feet on each side. How many of the individual
muffin boxes can fit into the larger box?
Answers
Answer:
512
Step-by-step explanation:
You can figure this a couple of ways.
1) Figure the number of muffin boxes that goes into each dimension of the larger box:
(2 ft)/(3 in) = (24 in)/(3 in) = 8 . . . . muffin boxes in each direction.
Then the total number of muffin boxes that will fit in a larger box is ...
8×8×8 = 512
512 muffin boxes can fit into the larger box.
__
2) The volume of a muffin box in cubic feet is ...
((3 in)/(12 in/ft))^3 = (1/4 ft)^3 = 1/64 ft^3
The volume of a larger box in cubic feet is ...
(2 ft)^3 = 8 ft^3
Then the number of smaller boxes that will fit in the larger box is ...
(8 ft^3)/(1/64 ft^3) = 8×64 = 512
512 muffin boxes can fit into the larger box.
Question is in the photo above
Need the number of units.
Answers
Answer:
Step-by-step explanation:
rectangle and triangle is here
area of triangle = 1/2 * 5 * 12 = 30
area of rectangle = 1 * 12 = 12
total is 12 + 30 = 42
What is the quotient?
(-3)^0 / (-3)^2 = ?
A: -9
B: -1/9
C: 1/9
D: 9
Answers
Answer:
Step-by-step explanation:
Quotient means result of division
anything raised to 0 is 1
(-3)^0 = 1
(-3)^2 = -3 * -3 = 9
Quotient = 1/9
Answer:
1/9
Step-by-step explanation:
Calculate (full working out)
5.16 x 2.93 =
Answers
if the population is growing by 17% you will use 1.17 as your rate in the equation true or false
Answers
Answer:
False. 0.17
Step-by-step explanation:
A lodge rents snowboards for $40/day plus a $20 flat fee for safety gear. Write an equation to represent the relationship between the total cost, c, and number of days renting a snowboard, d.
Answers
Answer:
(40+20)^d=c
Step-by-step explanation:
Answer:= let me double check yall
Step-by-step explanation:40+20+c+d
What is the value of x in this equation 9 + 9 = 3(x - 6)?
Answers
Answer: [tex]x=12[/tex]
Step-by-step explanation:
[tex]9+9=3(x-6)[/tex]
simplify: add the 9's together and distribute the 3
[tex]18=3x-18[/tex]
add 18 to both sides
[tex]36=3x[/tex]
divide by 3
[tex]12=x[/tex]
[tex]x=12[/tex]
Laura has set out 60 m of a kite string which makes an angle of 68° with the ground what is the height of the kite
please help
Answers
odún and aderonke have 6:4 in 80 units of transcorp's share. how many units of this shares belong to odún
Answers
Answer:48
Step-by-step explanation:
Answer:
48 pecies
Step-by-step explanation:
Odun's share=80x 6/10
Odun's share=48
Hope you understand
What value of x makes the
equation frue?
113 - X = 98
Answers
Answer:
15
Step-by-step explanation:
you have to take 98 away from 113.
Answer:
X= 15
Step-by-step explanation:
Brenda and Jasmine are selling cookie dough for a school fundraiser. Customers can buy packages of chocolate chip cookie dough and packages of double chocolate cookie dough. Brenda sold 6 packages of chocolate chip cookie dough and 4 packages of double chocolate cookie dough for a total of $86. Jasmine sold 3 packages of chocolate chip cookie dough and 5 packages of double chocolate cookie dough for a total of $85. What is the cost each of one package of chocolate chip cookie dough and one package of double chocolate cookie dough?
Answers
Answer:
one package = $5. / double package= $14
Step-by-step explanation:
Lets say x is a package and y a double package
6x + 4y = $86
2(3x + 5y = $85)
6x + 10y = $170
-6x -4y. -86
6y = $ 84
÷6. ÷6
y= $14
6x +4y = $86
6x + 4($14) = $86
6x + $56 = $86
-56. -56
6x = $30
÷6. ÷6
x = $5
Answer:
chocolate chip = 5
double chocolate chip=14
Step-by-step explanation:
c = chocolate chip
d = double chocolate chip
Brenda
6c+4d = 86
Jasmine
3c+ 5d = 85
Multiply the second equation by -2
-6c -10d = -170
Add this to the first equation
-6c -10d = -170
6c+4d = 86
--------------------
- 6d = -84
Divide by -6
-6d /-6 = -84/-6
d =14
Now we can find c
3c+ 5d = 85
3c+5*14 = 85
3c +70 = 85
Subtract 70
3c = 85-70
3c = 15
Divide by 3
3c/3 = 15/3
c = 5
What is the range of the function y= e^4x
Answers
Answer:
The answer would be {y|y>0}
Step-by-step explanation:
hope this helps
What is the product of (-a + 3)(a + 4)?
Answers
Answer:
a² - a + 12
Step-by-step explanation:
(see attached)
using the Foil Method :
(-a + 3)(a + 4)
= (-a)(a) + (-a)(4) + (3)(a) + (3)(4)
= -a² - 4a + 3a + 12
= -a² - a + 12
Please help me now please I promise I will mark you brainliest
Answers
Answer:
On the circle
Step-by-step explanation:
I dont know the exact way to do this, but i graphed them, then drew a circle, and it was in the line. So i think its on the line
Answer:inside
Step-by-step explanation:
The distance from A to M is sq rt of 41
The distance from A to V is sq rt of 40
