Answers
The solution to the question is:
c is 6 = [tex]\sqrt{a^{2} + b^{2} -2abcosC }[/tex]
b is 5 = [tex]\sqrt{a^{2} + c^{2} -2accosB }[/tex]
cosB is 2 = [tex]\frac{a^{2} + c^{2} - b^{2} }{2ac}[/tex]
a is 4 = [tex]\sqrt{b^{2} + c^{2} -2bccosA }[/tex]
cosA is 3 = [tex]\frac{b^{2} + c^{2} -a^{2} }{2bc}[/tex]
cosC is 1 = [tex]\frac{b^{2} + a^{2} - c^{2} }{2ab}[/tex]
What is cosine rule?it is used to relate the three sides of a triangle with the angle facing one of its sides.
The square of the side facing the included angle is equal to the some of the squares of the other sides and the product of twice the other two sides and the cosine of the included angle.
Analysis:
If c is the side facing the included angle C, then
[tex]c^{2}[/tex] = [tex]a^{2}[/tex] + [tex]b^{2}[/tex] -2ab cos C-----------------1
then c = [tex]\sqrt{a^{2} + b^{2} -2abcosC }[/tex]
if b is the side facing the included angle B, then
[tex]b^{2}[/tex] = [tex]a^{2}[/tex] + [tex]c^{2}[/tex] -2accosB-----------------2
b = [tex]\sqrt{a^{2} + c^{2} -2accosB }[/tex]
from equation 2, make cosB the subject of equation
2ac cosB = [tex]a^{2}[/tex] + [tex]c^{2}[/tex] - [tex]b^{2}[/tex]
cosB = [tex]\frac{a^{2} + c^{2} - b^{2} }{2ac}[/tex]
if a is the side facing the included angle A, then
[tex]a^{2}[/tex] = [tex]b^{2}[/tex] + [tex]c^{2}[/tex] -2bccosA--------------------3
a = [tex]\sqrt{b^{2} + c^{2} -2bccosA }[/tex]
from equation 3, making cosA subject of the equation
2bcosA = [tex]b^{2}[/tex] + [tex]c^{2}[/tex] - [tex]a^{2}[/tex]
cosA = [tex]\frac{b^{2} + c^{2} -a^{2} }{2bc}[/tex]
from equation 1, making cos C the subject
2abcosC = [tex]b^{2}[/tex] + [tex]a^{2}[/tex] - [tex]c^{2}[/tex]
cos C = [tex]\frac{b^{2} + a^{2} - c^{2} }{2ab}[/tex]
In conclusion,
c is 6 = [tex]\sqrt{a^{2} + b^{2} -2abcosC }[/tex]
b is 5 = [tex]\sqrt{a^{2} + c^{2} -2accosB }[/tex]
cosB is 2 = [tex]\frac{a^{2} + c^{2} - b^{2} }{2ac}[/tex]
a is 4 = [tex]\sqrt{b^{2} + c^{2} -2bccosA }[/tex]
cosA is 3 = [tex]\frac{b^{2} + c^{2} -a^{2} }{2bc}[/tex]
cosC is 1 = [tex]\frac{b^{2} + a^{2} - c^{2} }{2ab}[/tex]
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Related Questions
tìm số hữu tỉ
(x-5/6)^2=1/36
Answers
Answer:
x = [tex]\frac{2}{3}[/tex] , x = 1
Step-by-step explanation:
(x - [tex]\frac{5}{6}[/tex] )² = [tex]\frac{1}{36}[/tex] ( take square root of both sides )
x - [tex]\frac{5}{6}[/tex] = ± [tex]\sqrt{\frac{1}{36} }[/tex] = ± [tex]\frac{1}{6}[/tex] ( add [tex]\frac{5}{6}[/tex] to both sides )
x = [tex]\frac{5}{6}[/tex] ± [tex]\frac{1}{6}[/tex] , then
x = [tex]\frac{5}{6}[/tex] - [tex]\frac{1}{6}[/tex] = [tex]\frac{4}{6}[/tex] = [tex]\frac{2}{3}[/tex]
x = [tex]\frac{5}{6}[/tex] + [tex]\frac{1}{6}[/tex] = [tex]\frac{6}{6}[/tex] = 1
What is the area of the following circle? Either enter an exact answer in terms of π or use 3.14 for π and enter your answer as a decimal. d=10
Answers
Please help asap 25 points
Answers
Answer:
[tex]y = - 2 |x - 2| + 4[/tex]
Step-by-step explanation:
as the function moved to the right 2 steps, and up 4 steps
What does x= please help
Answers
The value of x is 8
This question is a proportion. To solve it, let's assemble it as follows:5 = 4
10 x
Now, just multiply in the form of a cross. Then, let's split the terms:5 . x = 10 . 4
5x = 40
x = 40 ÷ 5
x = 8
So, the result of x will be 8
5x-4y=10
slope intercept form
Answers
Answer:
5x-4y=10
solution
first find x intercept is the graph cross x-axis.to find the x intercept,we set y¹=0 and the Solve x.
5x-4y=10
5x-4(0)=0
x¹ =2 y¹=0
y intercept
5x-4y=10
5(0)-4y=10
y²=2.5 x²=0
Multiply the following
(a) 2.7x4
(b) 0.79x32.4
(c)1.07 x 0.02
(d) 2.3x4.35
(e) 2.5x100
(f) 0.0008x100
g) 0.25x 10000
h)3x0.55
i)0.08x5
j)351.06x4
k)0.3x0.03
l) 21.7x0.1
m) 200.02 x 2.2
Kindly look into this and try to answer all of them this contains 30 points
Answers
a) 10.8
b) 25.596
c) 0.0214
d) 10.005
e) 250
f) 0.08
g) 2500
h) 1.65
i) 0.4
j) 1404.24
k) 0.009
l) 2.17
m) 440.044
Note: I haven’t provided the steps since this is basic multiplication of decimal numbers. However, if you do need help please comment below this answer.
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y=4(3)^x complete a table showing y values for values of x from 0 to 5
Answers
To solve this problem, we just have to substitute the values into the exponential equations and solve.
Exponential EquationIn the given exponential equation, we simply need to plug in the values of x from 0 to 5
[tex]y = 4(3)^x[/tex]
when x = 0
[tex]y = 4(3)^x\\y = 4(3)^0\\y = 4[/tex]
when x = 1
[tex]y = 4(3)^x\\y = 4(3)^1\\y = 12\\[/tex]
when x = 2
[tex]y = 4(3)^2\\y = 36[/tex]
when x = 3
[tex]y = 4(3)^3\\y = 108[/tex]
when x = 4
[tex]y = 4(3)^4\\y = 324[/tex]
when x = 5
[tex]y = 4(3)^5\\y = 972[/tex]
From the calculations above, the value of y when x is from 0 to 5 are
x(0) = 4x(1) = 12x(2) = 36x(3) = 108x(4) = 324x(5) = 972Learn more on exponential equations here;
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The hour and minute hands of a clock form an angle that constantly changes. During each hour of the day, the clock hands will form right, acute, and obtuse angles. Assume the hour hand points directly at the hour.Write a time of day when the two clock hands form each type of angle
Answers
The each type of angle are discussed below
What is angle?An angle is formed when two straight lines or rays meet at a common endpoint. The common point of contact is called the vertex of an angle.
If the hours hand point to the hour 1 and minute hand at 12 then
angle will be acute.
If the hours hand point to the hour 2 and minute hand at 12 then
angle will be acute.
If the hours hand point to the hour 3 and minute hand at 12 then
angle will be right angle .
If the hours hand point to the hour 4 and minute hand at 12 then
angle will be obtuse.
If the hours hand point to the hour 5 and minute hand at 12 then
angle will be obtuse.
If the hours hand point to the hour 6 and minute hand at 12 then
angle will be straight angle .
If the hours hand point to the hour 7 and minute hand at 12 then
angle will be reflex.
If the hours hand point to the hour 8 and minute hand at 12 then
angle will be reflex.
If the hours hand point to the hour 9 and minute hand at 12 then
angle will be reflex.
If the hours hand point to the hour 10 and minute hand at 12 then
angle will be reflex.
If the hours hand point to the hour 11 and minute hand at 12 then
angle will be reflex.
If the hours hand point to the hour 12 and minute hand at 12 then
angle will be Complete angle.
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Given that XW bisects AXZ, what theorem or theorems could be used to justify that W is equidistant from the two outside rays?
Answers
Answer:
HA congruence postulate
Step-by-step explanation:
In order to show W is equidistant from A and Z, we must demonstrate that WA ≅ WZ. The HA congruence postulate can be used for that purpose.
__
proofWX bisects AXZ, so ∠WXA≅∠WXZ by the definition of an angle bisector. By the reflexive property of congruence, WX≅WX. The angles at A and Z are given as right angles.
So, we have triangles WAX and WZX that are right triangles with congruent hypotenuse and corresponding angle. These are the preconditions for the application of the HA congruence postulate. That postulate says the triangles WAX and WZX are congruent, so ...
WA ≅ WZ by CPCTC. Hence W is equidistant from the outside rays.
__
Additional comment
The definition of distance from a point to a line is the perpendicular distance from the point to the line. In this geometry, the perpendicular distances from W to the outside rays are the lengths of segments WA and WZ. That is why we need to show those lengths are the same.
The histogram shows the results of a survey that asked people how many hours of sleep they get each night. Which
statements are true?
Answers
The true statements are
The mean is near the median.
The mean is the best measure of center.
The five-number summary is the best measure of variation
What is a histogram?
A histogram is used to represent data graphically. The histogram is made up of rectangles whose area is equal to the frequency of the data and whose width is equal to the class interval.
If the mean is greater than the median, the histogram would be skewed to the right. If the mean is less than the median, the histogram would be skewed to the left.
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which of the following is the equation of a line in sloep intercept form for a line with slope = 1/3 and y intercept at 0,-4
Answers
Answer:
Step-by-step explanation:
y + 4 = 1/3(x - 0)
y + 4 = 1/3x - 0
y = 1/3x - 4
A pre-school has 12 four-year old children and 11 three-year old children. What is the ratio of four-year old
children to three-year old children?
Answers
Answer:
12:11
Step-by-step explanation
Answer:
I think it would be 12:11
Step-by-step explanation:
This is because you can't down size the 11
this is literally the easiest question, but for some reason I keep getting it wrong...
Answers
Answer:
Hi the correct answer will be C, E, and F.
Step-by-step explanation:
Why C? 23 is greater than 16
Why E? 23 is greater than or equal to 16. Remember here says "or"
Why F? 23 is not equal to 16.
Q
7/0
The mean weight of 8 girls in a group is 35 kg. The individual weights of seven of then
are 35kg, 28kg, 43kg, 25kg, 33kg, 51kg, and 22kg. Find the weight of the 8th girl.
Answers
The weight of the 8th girl in the class is 43 kg
How to determine the weight of the 8th girl?The given parameters are:
Mean weight = 35 kg
Weight of 7 girls = 35kg, 28kg, 43kg, 25kg, 33kg, 51kg, and 22kg
Let the weight of the 8th girl be x.
Mean is calculated using:
Mean = Sum/Count
So, we have:
(35+ 28+43+25+33+51+22 + x)/8 = 35
Evaluate the sum
(237 + x)/8 = 35
Multiply both sides by 8
237 + x = 280
Subtract 237 from both sides
x = 43
Hence, the weight of the 8th girl is 43 kg
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You have been given data about gas prices in 15 states. Comparing the two data sets below, what does the larger standard deviation, range, and variance say about gas prices in 2022 compared to gas prices in 2018?
Gas Prices in 2018 Gas Prices in 2022
Max: $2.42
Min: $2.03
Mean: $2.098
Median: $2.06
Mode: $2.04
Variance: 0.0121
Standard Deviation: $0.11
Max: $5.87
Min: $4.48
Mean: $4.83
Median: $4.72
Mode: $4.72
Variance: 0.0142
Standard Deviation: $0.38
Answers
Comparing the two data sets shown below
What is standard deviation and variance?Variance is the average squared deviations from the mean, while standard deviation is the square root of this number.
Both the mean and the median can be used to describe where the “center” of a dataset is located.
So, the mean of data in 2022 is more than mean of data in 2018.
It’s best to use the mean when the distribution of the data values is symmetrical and there are no clear outliers.
As the variance of 2022 more than in variance in 2018.
A high variance indicates that the data points are very spread out from the mean, and from one another.
As the standard deviation of 2022 more than in standard deviation in 2018.
The high standard deviation indicates data are more spread out.
The bigger the range, the more spread out the data.
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A cylinder has a radius of 12 m and a height of 9 m.
What is the exact volume of the cylinder?
108π m³
216π m³
972π m³
1296π m³
Answers
[tex]\textit{volume of a cylinder}\\\\ V=\pi r^2 h~~ \begin{cases} r=radius\\ h=height\\[-0.5em] \hrulefill\\ r=12\\ h=9 \end{cases}\implies V=\pi (12)^2(9)\implies V=1296\pi ~m^3[/tex]
Brainliest if you give correct answer + explanation
Answers
Answer:
x = 8
Step-by-step explanation:
Perimeter :
2(Length + Width) = 44 2x + 3 + x - 5 = 22 3x - 2 = 22 3x = 24 x = 8Perimeter is adding all 4 sides together
2x + 3 + 2x +3 + x - 5 + x - 5 = 44
Combine like terms
6x - 4 = 44
6x = 48
Divide both sides by 6 to isolate x
X = 8
Each pepperoni slice is 78 of an inch long and costs $0.03. Exactly enough pepperoni slices are laid end to end to have a total length of 56 inches. What is the total cost of these pepperoni slices?
Answers
The total cost of these pepperoni slices is $1.92
What is the total cost of these pepperoni slices?
Each slice measures 7/8 of an inch. Here we have N slices, such that the measure of the N slices is 56 inches, then we have:
N*(7/8 in) = 56 in
Now we can find the value of N, the number of slices used:
N = (8/7)*56 = 64
And each slice costs $0.03, then the cost of the 64 slices is:
C = $0.03*64 = $1.92
The total cost of these pepperoni slices is $1.92
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find the value of a 3a+2b=8 and b=-2
Answers
Answer:
The value of a in the given equation is '4'
Step-by-step explanation:
The given equation is: 3a + 2b = 8 and b = -2
Plug the value of b into the formula:
3a + 2(-2) = 8
3a - 4 = 8
We want 3a by itself so we will add +4 to both sides:
3a - 4 + (4) = 8 + (4)
3a = 12
Divide both sides by 3 so a is by itself:
3a/3 = 12/3
1a = 4
a = 4
Bella can rake the leaves in 3 hours and Jordan can complete the same task in 4 hours. If they work together, how long will it take Bella and Jordan to rake the leaves? Round your answer to the nearest hundredth of an hour.
Answers
Using the together rate, it is found that it will take 1.71 hours for Bella and Jordan to rake the leaves.
What is the together rate?It is the sum of each separate rate.
In this problem, the rates are given as follows:
Together: 1/x.Bella's: 1/3.Jordan's: 1/4.Hence:
[tex]\frac{1}{x} = \frac{1}{3} + \frac{1}{4}[/tex]
[tex]\frac{1}{x} = \frac{4 + 3}{12}[/tex]
[tex]x = \frac{12}{7}[/tex]
x = 1.71.
It will take 1.71 hours for Bella and Jordan to rake the leaves.
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Which lists all of the x-intercepts of the graphed
function?
O (0, 6)
O (1, 0) and (2, 0)
O (1, 0), (2, 0), and (-3, 0)
O (1, 0), (2, 0), (-3, 0), and (0, 6)
Answers
Answer:
(1, 0), (2, 0), and (-3, 0)
Step-by-step explanation:
The x intercepts are where it crosses the x axis. It crosses at (-3,0), (1,0) and (2,0)
Which polynomial function could be represented by the graph below?
A. [tex]f(x) = x^2 - 4x[/tex]
B. [tex]f(x) = x^2 + 4x[/tex]
C. [tex]f(x) = -x^2 - 4x[/tex]
D. [tex]f(x) = -x^2 + 4x[/tex]
Answers
Answer:
[tex]f(x) = {x}^{2} + 4x[/tex]
Step-by-step explanation:
The graph is concave up, this means that the leading term x^2 is positive.
[tex]f(x) = {x}^{2} + 4x[/tex]
[tex]y = {x}^{2} + 4x[/tex]
For the x intercept, let y = 0[tex] {x}^{2} + 4x = 0[/tex]
[tex]x(x + 4) = 0[/tex]
[tex]x = 0 \: \: \: or \: \: \: \: x = - 4[/tex]
The x intercepts are:
(0 , 0) and (-4 , 0)
For the y intercept, let x = 0
[tex]y = {0}^{2} + 4(0) = 0[/tex]
y intercept :(0, 0)
For the turning point:[tex]t.p = \frac{x1 + x2}{2} [/tex]
[tex]t.p = \frac{0 + ( - 4)}{2} = - 2[/tex]
[tex]f( - 2) = {( - 2)}^{2} + 4( - 2) = - 4[/tex]
Turning point:(-2 , -4)
If you connect all these coordinates you will get the parabola shown in the picture.
Find the value of y in 4y + 2x = 8 and 2x + 5y = 14.
Answers
Answer:
y = 6
Step-by-step explanation:
4y + 2x = 8 → (1)
5y + 2x = 14 → (2)
subtracting (1) from (2) term by term will eliminate x
y + 0 = 6
y = 6
Please Help I Don't Understand!
Answers
Answer:
a reduction
Step-by-step explanation:
this is because its growing smaller
Reduction
Explanation:
The heart reduced its size (went smaller).
what type of parent function is f(x) = |x|
Answers
Answer: Absolute value function
The type of parent function is f(x)= |x| is Absolute valued function
What is Absolute valued function?
An absolute value function is a function that contains an algebraic expression within absolute value symbols.
Given function:
f(x)= |x|
As, we know the modulus generally give the absolute value of any function and also the modulus always give the positive value.
The above property perfectly resemble the absolute valued function.
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Can anyone help me i really need it rn
Answers
Answer:
11. g
12. f
13. e (add all the frequencies)
14. d
15. c (eg. 17.5 -8.5 = 9)
16. b
17. a
Let me know if you have any questions.
Hope this helps!
The radius of a wheel on a toy truck is 4 inches. To the nearest foot, how far does the wheel
travel when it makes 7 revolutions?
Answers
Find the areas of the trapezoids.
Answers
Answer:
7.5 sq. un
Step-by-step explanation:
Hello!
The height is 3 units, the base is 4 units, and the other base is 1 unit.
Using the trapezoid area formula, [tex]A = \frac12(b_1+b_2)h[/tex], we can plug the values in and solve.
Solve:
[tex]A = \frac12(b_1+b_2)h[/tex][tex]A = \frac12(1 + 4)3[/tex][tex]A = \frac12(5)(3)[/tex][tex]A = 2.5(3)[/tex][tex]A = 7.5[/tex]The area is 7.5 sq. un
Select the correct answer.
One leg of a right triangle is 10 units, and its hypotenuse is 12 units. What is the length of the other leg?
A.
about 7 units
B.
about 15 units
C.
about 25 units
D.
about 122 units
E.
about 224 units
Answers
A box contains 50 batteries, of which 10 are dead and 5 are weak. Suppose you select batteries at random from the box and set them aside for recycling if they are dead or weak. If the first battery you select is dead and the second one is weak, what is the probability that the next battery you select will be weak?
Answers
Given: 50 total batteries, of which 10 are dead and 5 are weak. This is represented by: 10/50 (simplifies to 1/5) and 5/50 (simplifies to 1/10).
If the batteries are being set aside, it likely means no replacement. For every battery taken out of the box, the box holds one less battery.
Probability of selecting 1 dead, 1 weak, 1 weak is written as: (10/50)*(5/49)*(4/48) = 1/588.