Answer:
It is proved .
Step-by-step explanation:
[tex]\alpha +\beta +\gamma =\pi.....(1)\\\\sin\alpha + sin\beta +sin\gamma=4 cos\frac{\alpha}{2}cos\frac{\beta}{2}cos\frac{\gamma}{2}[/tex]
Take LHS
[tex]=sin\alpha + sin\beta +sin\gamma\\\\=2 sin \frac{\alpha +\beta }{2} cos\frac{\alpha -\beta }{2} + sin\gamma\\\\=2 sin\frac{180-\gamma}{2}cos \frac{\alpha - \beta}{2}+2 sin\frac{\gamma}{2}cos\frac{\gamma}{2}\\\\=2 cos\frac{\gamma}{2}cos \frac{\alpha - \beta}{2}+2 sin\frac{\gamma}{2}cos\frac{\gamma}{2}\\\\=2 cos\frac{\gamma}{2}\left [ cos \frac{\alpha - \beta}{2}+sin\frac{180-\alpha-\beta}{2}\\ \right ]\\\\=2 cos\frac{\gamma}{2}\times 2 cos\frac{\alpha}{2}cos\frac{\beta}{2}\\[/tex]
[tex]=4 cos\frac{\alpha}{2}cos\frac{\beta}{2}cos\frac{\gamma}{2}[/tex]
Hence proved.
Muffins are sold in packages of 18 and cost $27 per package. Each of 6 friends gets an equal share of muffins from p packages of muffins. Write an expression to represent how much each friend must pay.
Answer:
27/18= 1.5
18/6 = 3
3•1.5= 4.5
Step-by-step explanation:
$27 divided by 18 muffins equals $1.50, 18 muffins divided by 6 people equals 3, 3 muffins times $1.50 equals $4.50. So $4.50 is how much each person would have to pay.
Given F(x) = 2x - 1; G(x) = 3x + 2; and H(x) = x 2, find the function F(x) + G(x) + H(x).
Answer:
if H(x) is x²
Step-by-step explanation:
[tex]3x + 2 + 2x - 1 + {x}^{2} = \\ 3x + 2x = 5x \\ {x}^{2} + 5x - 1[/tex]
im not sure exactly hehe
The ratio of men to women working for a company is 4 to 7. If there are 165 employees total, how many women work for the company?
Answer: 105
Step-by-step explanation:
Given
The ratio of men to women working for a company is 4:7
There are total of 165 employees
Suppose, there is 4x men and 7x women such that the ratio remains constant
[tex]\therefore 4x+7x=165\\\Rightarrow 11x=165\\\Rightarrow x=15[/tex]
[tex]\text{Men= }4\times 15=60\\\text{Women= }7\times 15=105[/tex]
Tower A and B are 151 m apart.
From the top of tower A at 68 m above ground, the angle of elevation to the top of tower B is 23°.
How tall is tower B to the nearest metre?
Answer:
132m
Step-by-step explanation:
Height of tower B = Height of tower A + difference in height between tower B and A
The difference in height can be determined using tan
tan 23 = opposite / adjacent
tan 23 = opposite / 151
0.4245 x 151 = opposite
opposite = 64m
Height of tower B = 64m + 68m = 132m
help me solve for x.
What is 350-450:90+15x3
Let n be an odd integer with exactly 11 positive divisors. Find the number of positive divisors of 8n^3
Answer: 124
Step-by-step explanation:
As we know, the total number of positive divisors of n is the product of one more than each exponent in the prime factorization of n.
We know this product is equal to 11.
Since 11 is prime, so there can be only one number in this product, so the prime factorization of n must be [tex]$n=p^{10}$[/tex], where p is a prime number.
We take a cube of the prime factorization of n to give us a prime factorization for [tex]n^3[/tex]
[tex]$$n^{3}=\left(p^{10}\right)^{3}=p^{30} .$$[/tex]
We see that [tex]n^{3}\text{ has }$30+1=31$[/tex] positive divisors.
Now, [tex]8n^3=2^3\times p^{30}[/tex]
Totald divisiors = [tex](3+1)(30+1)=4\times31=124[/tex]
Hence, the number of positive divisors of [tex]8n^3=124[/tex]
which ordered pair is a solution to the system of inequalities graphed?
Answer:
(2,2)
Step-by-step explanation:
fits the requirements
What is the measure of the unknown angle?
WRITE an equation of the line that passes through the given point and is PARALLEL to the given line.
(10, -12), 3x + 4y = 1
Answer:
[tex]y=-\frac{3}{4}x-\frac{9}{2}[/tex]
Step-by-step explanation:
Hi there!
What we need to know:
Linear equations are typically organized in slope-intercept form: [tex]y=mx+b[/tex] where m is the slope and b is the y-intercept (the value of y when x is 0)Parallel lines always have the same slope1) Determine the slope (m)
[tex]3x + 4y = 1[/tex]
Rearrange the given equation into slope-intercept form (this will help us determine m)
Subtract 3x from both sides to isolate 4y
[tex]3x + 4y-3x = -3x+1\\4y= -3x+1[/tex]
Divide both sides by 4 to isolate y
[tex]y= -\frac{3}{4} x+\frac{1}{4}[/tex]
Now, we can identify that [tex]-\frac{3}{4}[/tex] is the slope of the line. Parallel lines have the same slope, so this would also be the slope of the line we're solving for. Plug this into [tex]y=mx+b[/tex]:
[tex]y=-\frac{3}{4}x+b[/tex]
2) Determine the y-intercept (b)
[tex]y=-\frac{3}{4}x+b[/tex]
Plug in the given point (10,-12) and solve for b
[tex]-12=-\frac{3}{4}(10)+b\\-12=-\frac{3}{2}(5)+b\\-12=-\frac{15}{2}+b[/tex]
Add [tex]\frac{15}{2}[/tex] to both sides to isolate b
[tex]-12+\frac{15}{2}=-\frac{15}{2}+b+\frac{15}{2}\\-12+\frac{15}{2}=b\\-\frac{9}{2} =b[/tex]
Therefore, the y-intercept is [tex]-\frac{9}{2}[/tex]. Plug this back into [tex]y=-\frac{3}{4}x+b[/tex]:
[tex]y=-\frac{3}{4}x-\frac{9}{2}[/tex]
I hope this helps!
How many solutions are there to the following equation?
2- 5x= 3(2 – 3x)
A. O
B. 1
C. Infinitely many
When completely factored, 2x3 - 200x
equals-
Answer:
Step-by-step explanation:
The only way this can be factored is by pulling out the GCF. 2 and x are common to both terms:
[tex]2x(x^2-100)[/tex]
BUT you should also recognize that what's inside the parenthesis is the difference of perfect squares. And that factors to
(x - 10)(x + 10). So the complete factorization is
2x(x - 10)(x + 10)
The scatter plot shows the relationship between tickets sales at a theme park and the number of cloudy days per month for the past year.
Theme Park Ticket Sales
(in thousands)
100
99
98
97
96
95
94
93
92
91
90
87
86
BS
0
9 10 11 12 13 14 15
Number of Cloudy Days per Month
Which statement best describes the relationship shown in the scatter plot?
A Ticket sales are high when there are few cloudy days.
O B. Ticket sales are low when there are many cloudy days.
C. Ticket sales go up if there are more cloudy days per month.
D. Ticket sales go down if there are more cloudy days per month
E Ticket sales are not affected by the number of cloudy days per month.
Answer:
E Ticket sales are not affected by the number of cloudy days per month.
Step-by-step explanation:
From the scatter plot Given, using visual observation, we can infer that the relationship between theme park ticket sales and the number of cloudy sales is randomly scattered with no defined linear pattern. That is, the plot does not ascertain of the number of ticket sales increases with increasing number of cloudy days, or vice versa. Hence, the relationship will best the described as concluding that ticket sales are not affected by the number of cloudy days per month.
Caio comprou uma lembrancinha para todos os seus amigos e gastou R$12,50. Qual fração pode representar esse valor? 125/2 25/5 125/5 25/2
Me ajuda
Answer:
25/2
Step-by-step explanation:
Caio comprou uma lembrança para todos os amigos e gastou R $ 12,50.
Comparando e resolvendo as opções dadas a nós,
a) 125/2 = 62,5
A opção a está errada
b) 25/5 = 5
Opção b está errada
c) 125/5 = 25
A opção c está errada
d) 25/2 = 12,50
A opção d está correta
Portanto, a fração que pode representar este valor é 25/2
the triangles are similar, what is the value of x?
Two triangles that intersect at a single vertex. The smaller triangle has an upper angle measuring 126 degrees and the angle where the vertices intersect measuring 16 degrees. The larger triangle has an upper angle measuring 126 degrees. The exterior angle made where the triangles intersect above the point of intersection measures 3 x degrees.
x = 16
x = 38
x = 42
x = 54
Answer:
I think it would be 42. If its wrong I'm sorry
Sabrina is tracking the growth rates of a colony of ants and of a bee hive. From her research, she has developed a function to represent the population growth of each type of insect, where y represents the population and x represents the number of weeks since Sabrina began her research.What is this function written in vertex form?
Answer:
A
Step-by-step explanation:
i think
The function that represent the growth rate of the population where y represents the population and x represents the numbers of weeks since Sabrina began her research is [tex]y=3.8^{x}[/tex] (for ant colony) [tex]y=3.8x[/tex] (for bee hive growth)
What is function?"A function is an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable)."
What is research?"Research is creative and systematic work undertaken to increase the stock of knowledge."
What is growth rate?"The growth rate of change of population size, for a given country, territory, or geographic area, during a specified period."
As we know that we have to check the growth of the population. According to the given data, the rate of growth for ant colony is [tex]y=3.8^{x}[/tex] and also the growth rate of bee hive is [tex]y=3.8x[/tex]
Hence, the growth rate of ant colony is [tex]y=3.8^{x}[/tex] and the growth rate of bee hive is [tex]y=3.8x[/tex]
To know more about growth rate of population here
https://brainly.com/question/15133607
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HELP
Find the distance from point P (-2, 8) to the line y = -1.
Step-by-step explanation:
Distance= ✓(-2-0)²+(8+1)²
=✓(4+81)
=✓85
A store offers a discount of 10% to customers who spend more than $20.00. If a customer’s bill is $80.00, how much will he actually pay?
Answer:
Step-by-step explanation:
Answer:
$72.00
Step-by-step explanation:
Amount of discounted money
= 10/100 x $80.00
= $8
Amount he will pay
= $80.00 - $8.00
= $72.00
Use pascal triangle to expand and simplify (5x+4y)³
Answer:
125x³+240xy²+64y³ +300yx²
Step-by-step explanation:
Row of pascals triangle to use is 1 3 3 1
For binomial expansion, use a³ +3a²b+3ab²+b³
the money used in south Africa is is called the rand . the estrange rate 7 rand for $1. Find how many dollars you would receive if you estrange 21 rand.
31 x 01111111111111111111111111
Answer:
3.444444444444444
Step-by-step explanation:
In a class of students, the following data table summarizes how many students have a cat or dog. What is the probability that a student chosen randomly from the class has a cat?
Answer:
from this we know there is 30 people in the class and 14 of them have a cat so the probability is 14/30
14/30
7/15
7/15 as a percent is 46.6667%
Find MN. See image below.
Answer:
Step-by-step explanation:
Tangents from the point outside the circle are equal
NL = JL
NM + ML =JK + KL
2x - 7 + 9 = 8 + 10
2x + 2 = 18 {Subtract 2 from both sides}
2x = 18 - 2
2x = 16 {Divide both sides by 2}
x = 16/2
x = 8
MN = 2*8 - 7 = 16 - 7 = 9
MN = 9
Sanjay uses the steps below to solve the equation 4 p + two-fifths (10 + 2 p) = 8. Step 1 Multiply both sides of the equation by Five-halves. 4 p + 10 + 2 p = 20 Step 2 Simplify like terms. 6 p + 10 = 20 Step 3 Subtract 10 on both sides of the equation. 6 p = 10 Step 4 Divide both sides of the equation by 6. p = StartFraction 10 over 6 EndFraction = Five-thirds = 1 and two-thirds Which is the first error that Sanjay made when finding the solution?
Answer:
Step 1 Multiply both sides of the equation by Five-halves
Step-by-step explanation:
First mistake:
Step 1 Multiply both sides of the equation by Five-halves
Correct First step:
Should have subtracted 4p from both sides
Answer:
In step 1, he did not multiply 4p by Five-halves when multiplying both sides by Five-halves.
Step-by-step explanation:
Just got it right on edge!! Hope this helps, have a great day!
what is the correct answer
Answer:
Step-by-step explanation:
B is correct answer
which point is a solution to the inequality shown in this graph
(0, 5)
(3, 2)
(-3, -6)
(5, 0)
Answer:
(0,5)
Step-by-step explanation:
if the point is graphed in the blue area then it is a solution to the inequality
Note: because the line is dashed points graphed on the line are not solutions
(0,5) is graphed in the blue region meaning that (0,5) is a solution to the inequality.
even though we may have found the answer let's check the rest just to be safe
(3,2) and (-3,-6) are graphed on the line
remember because the line is dashed points that fall on it are not solutions
therefore (3,2) and (-3,-6) are not Solutions
(5,0) when graphed is not in the shaded area and is therefore not a solution
we can conclude that a is the answer
Hi please help I have no idea how to even start my work, someone help!!!.
Answer:
x is greater than -3 and it is also less than or equal to 2
-3 < x ≤ 2
Step-by-step explanation:
Jenny rolled a pair of number cubes, each with the numbers 1 through 6.
What is the probability that Jenny rolled two 1s?
A. 1/36
B. 1/18
C. 1/12
D. 1/6
Jenny rolled 1/18
Answer:
D. 1/18
Please telll me answerPlease tell me answer
Answer:
x = 1 . Hopefully im reading this correct
Step-by-step explanation:
8x - 5 = 3
8x = 5 + 3
8x = 8
x = 8/8
x = 1
If my answer is incorrect, pls correct me!
If you like my answer and explanation, mark me as brainliest!
-Chetan K
Answer:
x is 1
Step-by-step explanation:
AC =PR
AB =PQ
8x - 5 =3
8x =3+5
8x =8
x=8/8
x=1
please give answer I will mark as brainliest if you give the right answer
a) 8.68 x 10^25
b) 1.439 x 10^12
Answer:
(8.6810±0.0013)×10^26 kg
1.439 time 10^12
Step-by-step explanation:
standard for is the whole numer with thousandth's place times 10^n or the number of zeroes