Answer:
Sum of interior angles of a triangle = 180°
Sine rule to find side lengths:
[tex]\dfrac{a}{\sin A}=\dfrac{b}{\sin B}=\dfrac{c}{\sin C}[/tex]
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Question 1a
Given: A = 40°, B = 20°, a = 2
40° + 20° + C = 180°
⇒ C = 120°
[tex]\dfrac{2}{\sin 40}=\dfrac{b}{\sin 20}=\dfrac{c}{\sin 120}[/tex]
[tex]\implies b=\sin20 \cdot\dfrac{2}{\sin 40}=1.064177772...[/tex]
[tex]\implies c=\sin 120 \cdot \dfrac{2}{\sin 40}=2.694592711...[/tex]
----------------------------------------------------------------------
Question 2b
Given: A = 50°, C = 20°, a = 3
50° + 20° + B = 180°
⇒ B = 110°
[tex]\dfrac{3}{\sin 50}=\dfrac{b}{\sin 110}=\dfrac{c}{\sin 20}[/tex]
[tex]\implies b=\sin 110 \cdot\dfrac{3}{\sin 50}=3.680044791...[/tex]
[tex]\implies c=\sin 20 \cdot\dfrac{3}{\sin 50}=1.339426765...[/tex]
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Question 3c
Given: B = 70°, C = 10°, b = 5
70° + 10° + A = 180°
⇒ A = 100°
[tex]\dfrac{a}{\sin 100}=\dfrac{5}{\sin 70}=\dfrac{c}{\sin 10}[/tex]
[tex]\implies a=\sin 100 \cdot \dfrac{5}{\sin 70}=5.240052605...[/tex]
[tex]\implies c=\sin 10 \cdot \dfrac{5}{\sin 70}=0.9239626545...[/tex]
----------------------------------------------------------------------
Question 4d
Given: A = 70°, B = 60°, c = 4
70° + 60° + C = 180°
⇒ C = 50°
[tex]\dfrac{a}{\sin 70}=\dfrac{b}{\sin 60}=\dfrac{4}{\sin 50}[/tex]
[tex]\implies a=\sin 70 \cdot \dfrac{4}{\sin 50}=4.906726388...[/tex]
[tex]\implies b=\sin 60 \cdot \dfrac{4}{\sin 50}=4.522063499...[/tex]
Angle θ forms a reference angle that is below the positive x axis (in quadrant IV). What will be the signs on the sine and cosine of angle θ?
Answer:
sin(θ) is negative, cos(θ) is positive
Step-by-step explanation:
Cosine corresponds to the x-coordinate within the unit circle, sine corresponds to the y-coordinate. In quadrant I, they are both positive, in quadrant II, x is negative whilst y is positive, and you would just continue by how they correspond as show in the unit circle, therefore, in quadrant IV, x is positive, y is negative.
The factor tree below provides the factors of 18.
18
N.
2
9
3
3
What is the prime factorization of 18?
2 x 3
2 x 9
2 x 3x3
02x3x9
Answer: it is (c)
i hope this helped :)
A cylinder has radius 9 inches and height 15 inches. A cone has the same radius and height
Find the volume of the cylinder
Find the volume of the cone
What fraction of the cylinder's volume is the cone's volume?
Answer:
See below
Step by step explanation:
Step-by-step explanation:
For cylinder:
r = 9 inches
h = 15 inches
[tex]V_{cylinder}=\pi r^2 h[/tex]
[tex]\implies V_{cylinder}=3.14 (9)^2 (15)[/tex]
[tex]\implies\huge\purple{ V_{cylinder}=3,815.1\:inch^3}[/tex]
[tex]V_{cone}=\frac{1}{3} V_{cylinder}[/tex]
[tex]\implies V_{cone}=\frac{1}{3}\times 3,815.1[/tex]
[tex]\implies \huge\orange{V_{cone}=1,271.7\: inch^3}[/tex]
Cone's volume is one third of the cylinder's volume.
Which of the equations or inequalities below are true?
A. 8-6<3
B. 8-6=2
C. 8-6>3
D. 6-8=2
Answer:
The answer is C because 8-6=2 and 2 is equal to 2
Step-by-step explanation:
solve the equation..
[tex]\\ \sf\longmapsto \dfrac{1}{4}y-7=\dfrac{1}{9}y[/tex]
[tex]\\ \sf\longmapsto \dfrac{1}{4}y-\dfrac{1}{9}y=7[/tex]
[tex]\\ \sf\longmapsto \dfrac{9-4}{36}y=7[/tex]
[tex]\\ \sf\longmapsto 5y=36(7)[/tex]
[tex]\\ \sf\longmapsto 5y=252[/tex]
[tex]\\ \sf\longmapsto y=50.4[/tex]
How can i use scatter plots to analyze two sets of data?
Step-by-step explanation:
A Scatter Analysis is used when you need to compare two data sets against each other to see if there is a relationship. Scatter plots are a way of visualizing the relationship; by plotting the data points you get a scattering of points on a graph.
3) g(x) = 3x - 5
f(x) = x² +3
Find g(x) + f(x)
A) x2 + 3x - 2
C) x² - 4x + 6
B) x² – 3x - 2
D) -x - x + 1
Answer:
C. X²-4X+6
MY ANSWER(not sure)
2. Change from dog/cat to tails/heads. DDC = TTH CDC = __________ DCD = __________ CCD = __________ DDD = __________ CCC = __________ DCC = __________ CDD = __________
Answer:
2. Change from dog/cat to tails/heads.DDC = TTH CDC = HTH DCD = THT CCD = HHT DDD = TTT CCC = HHH DCC = THH CDD = HTT
Twice the sum of a number and 9 is 30
Translate the statement into a mathematical equation & solve
Answer:
2x+9 is the equation
x = 10.5
Step-by-step explanation:
2x + 9 = 30
2x = 30 - 9 = 21
x = 21 ÷ 2 = 10.5
Hope this helps!
What does the • stand for n the problem. -4 • 6
Answer:
Multiplication
Step-by-step explanation:
simple form:
-4 x 6
-4 TIMES 6
therefore -4•6
Answer:
it stands for x or multiply
Step-by-step explanation:
How much more is required to make 780 g to 1 Kg ?
Answer:220g
Step-by-step explanation:
1 kg is equivalent to 1000g, therefore 1000g - 780g = 220g
The half-life of gold-195m is approximately 30.5 seconds.
Step 2 of 3: How much of a 12 gram sample of gold-195m would remain after 41 seconds? Round to three decimal places.
The amount of the 12 grams sample of gold-195m having a half-life of 30.5 s that would remain after 41 s is 4.726 g
How to determine the number of half-lives Half-life (t½) = 30.5 sTime (t) = 41 sNumber of half-lives (n) =?n = t / t½
n = 41 / 30.5
n = 82/61
How to determine the amount remaining Original amount (N₀) = 12 gNumber of half-lives (n) = 82/61Amount remaining (N) =?N = N₀ / 2ⁿ
N = 12 / 2^(82/61)
N = 4.726 g
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GIVING EXTRAS POINTS AND BRAINLIEST
Answer:
p<6
Step-by-step explanation:
this basically means she can buy 6 pounds or less
Answer:
p<7
Step-by-step explanation:
subtract 4 1/2 - 2 1/5?
Answer:
2.3 (decimal form)
Step-by-step explanation:
Convert 4 1/2 and 2 1/5 into improper fractions.
4 1/2 -> 9/2, 2 1/5 -> 11/5
Then you subtract, find the LCD (Least Common Denominator) and then you can combine.
Decimal form of answer: 2.3
Exact form of answer: 23/10
Mixed number form: 2 3/10
Any of those work! ⬆
Frank can mow lawns at a constant rate of 6/5 lawns per hour. How many lawns can Frank mow in 50 hours?
Answer:
60 lawns
Step-by-step explanation
6/5 lawns per hour times 50 hours = 60 lawns.
rate x time
We reached our goal by helping 2000 customers this month which is 14% more than last month. That means we must have helped how many customers last month?
Answer:
1754
Step-by-step explanation:
114% : 2000
100% : x
x =
[tex]2000 \times 100\% \div 114\% = 1754 \: customers \\ [/tex]
10 is 1/10 of
what is it?
What method would you choose to solve the
equation 2x- - 7 = 9? Explain why you chose this
method.
Answer:
2x2 - 7 = 9
Step-by-step explanation:
The factoring method can be chosen to solve the equation 2x2 - 7 = 9. It is one of the easiest methods as we can isolate the variable by factoring out the GCF and obtaining the values.
Hope it helps!!!brainliest pls!!!
Help me out I’m also at done!!!
Answer: 68
Step-by-step explanation:
(7-(-1))^2+(-2)^2
8^2+4
68
Answer:
im sry if i get it wrong i think it is 32
Step-by-step explanation:
What is the value of x (7x-1) (6x-1) now
Answer:
42
Step-by-step explanation:
Its impossible tto calculate x there.
But i can simply the expression for you...
42x²-13x+1
For what value of x is the given parallelogram a rhombus?
Answer:
[tex]\sf x = 6[/tex]
solving steps:
[tex]\sf in \ a \ rhombus \ the \ opposite \ angles \ are \ equal[/tex]
[tex]\hookrightarrow \sf 7x + 4 = 9x - 8[/tex]
[tex]\hookrightarrow \sf 7x -9x = - 8-4[/tex]
[tex]\hookrightarrow \sf -2x = - 12[/tex]
[tex]\hookrightarrow \sf x = 6[/tex]
What is the answer to 1+1
Answer:
5
Step-by-step explanation:
this is easy
Answer:
2
Step-by-step explanation:
What is the area of the region in the first quadrant bounded on the left by the graph of x=y^2/2 and on the right by the graph of x=3y−4 for 2≤y≤4 ?
The area of the region is -2/3 square units
The area bounded by the regionSince the region is bounded on the left by x = y²/2 and on the right by x = 3y - 4 for 2 ≤ y ≤ 4, the area of the region is given by
[tex]A = \int\limits^4_2 {\frac{y^{2}}{2} } \, dy - \int\limits^4_2 {(3y - 4)} \, dy \\[/tex]
Integrating, we have
A = [y³/6]₂⁴ - [3y²/2 - 4y]₂⁴
A = [4³/6 - 2³/6] - [3(4)²/2 - 4(4) - {3(2)²/2 - 4(2)]}]
A = [64/6 - 8/6] - [3(16)/2 - 16 - {3(4)/2 - 8]}]
A = [64/6 - 8/6] - [3(16)/2 - 16 - {3(4)/2 - 8]}]
A = [64/6 - 8/6] - [3(8) - 16 - {3(2) - 8]}]
A = [(64 - 8)/6] - [3(8) - 16 - {3(2) - 8]}]
A = [56/6] - [24 - 16 - {6 - 8}]
A = [56/6] - [8 - {-2}]
A = [56/6] - [8 + 2]
A = [56/6] - [10]
A = 56/6 - 10
Taking the L.C.M, we have
A = (56 - 10 × 6)/6
A = (56 - 60)/6
A = -4/6
A = -2/3 square units
So, the area of the region is -2/3 square units
Find the graph in the attachment
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(7-2i)(-2-4i)
show all work
Answer:
Step-by-step explanation:
-14 - 28i + 4i + 28i^2
-14 - 24i + 28(-1)
-14 - 24i - 28
-42 - 24i
HELP! 7-10 I need help with.
9514 1404 393
Answer:
7. odd angles, 143°; even angles, 37°
8. odd angles, 159°; even angles, 21°
9. even angles, 34°; odd angles, 146°
10. even angles, 29°, odd angles, 151°
Step-by-step explanation:
Angles 1 and 3 are vertical angles, so are congruent. The same can be said of angles 2 and 4. Each odd-numbered angle is supplementary to each even-numbered angle.
__
7. m∠1 = m∠3 = 143°, m∠2 = m∠4 = 180° -143° = 37°
8. m∠1 = m∠3 = 159°, m∠2 = m∠4 = 180° -159° = 21°
9. m∠2 = m∠4 = 34°, m∠1 = m∠3 = 180° -34° = 146°
10. m∠2 = m∠4 = 29°, m∠1 = m∠3 = 180° -29° = 151°
what is 44:20 = ?:5 ?
Answer:
11:5Step-by-step explanation:
[tex]44:20[/tex]
Cancel common factor : 4
[tex]44 \div 4 = 11 \\ 20 \div 4 = 5 \\ 11:5[/tex]
The ratios are 44:20=11:5
What is Ratio?A ratio is an ordered pair of numbers a and b, written a / b where b does not equal 0.
The given ratios are 44:20 = ?:5
we have to find the number in question mark place.
Let question mark be taken as x.
The ratios can be written in the form of fraction
44/20=x/5
Apply cross multiplication
44×5=20x
220=20x
Divide both sides by 20
x=220/20
x=11
Hence, the ratios are 44:20=11:5
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#SPJ2
WILL MARK BRAINLIEST Solve the following problems. Write the complete proof in your paper homework and for online (only) complete the probing statement (if any) that is a part of your proof or related to it. b Given: FD ⊥ AB ∠A ≅ ∠B Prove: ∠F ≅∠CEF
Answer:
AED congruent to FEC
Step-by-step explanation:
If you look closely, BOth of the angles are vertical.
what are the x- and y- intercepts for the graph of 3x + y = 15?
Answer:
X intercept=(5,0) and Y intercept=(0,15)
Step-by-step explanation:
3x + y = 15
to find the x int, sub in 0 for y and solve for x
3x + 0 = 15
3x = 15
x = 15/3
x = 5....so the x int is (5,0)
to find the y int, sub in 0 for x and solve for y
3(0) + y = 15
y = 15....so the y int is (0,15)
For the function defined here, find
Answer:
f(0) = 2f(1) = 3f(2) = -2Step-by-step explanation:
The function value is the y-coordinate of the point having the given x-value.
f(0) = 2f(1) = 3f(2) = -2A sports analyst determines that the number of points
scored in a basketball game is related to the number of
shots taken during the game. The least-squares
regression line is V = 5.0 + 1.2x, where y is the predicted
number of points scored and x is the number of shots
taken.
In one game, a team takes 50 shots and the residual is
10. How many points were scored by this team in this
game?
O 45
O 55
O 65
O 75
Answer:55
Step-by-step explanation:
i had that question in my test
Answer:
the person above me is correct!
Step-by-step explanation: