Answer:
cos (α + β) = 0.9196Step-by-step explanation:
Given sin α = –4∕5 and sin β = 1∕2
To get α from sin α = –4∕5,
α = arcsin(-4/5)
α = arcsin (-0.8)
α = -53.13°
If angle α is in quadrant III, then α = 180+53.13 = 233.13° (sin is negative in the 3rd quadrant)
Similarly for sin β = 1∕2
β = arcsin(1/2)
β = arcsin(0.5)
β = 30°
Since β is in quadrant II, β = 180-30 = 150°
To find cos (α + β). where α = 233.13° and β = 30°
cos (α + β)= cos (233.13 + 150)
= cos 383.13°
cos (α + β) = 0.9196
Can someone help me with this.?
Answer:
Below.
Step-by-step explanation:
To find the answer, you have to compare the two equations:
[tex]y=\frac{1}{10}x+60[/tex] and [tex]y=\frac{1}{5}[/tex]
So first, the graph looks different because the two slopes are different. The first one will be more vertical than the second one.
The second difference is the y - intercepts. The first equation starts at (0, 60) and the second starts at the origin.
Sara is moving into a new apartment. The Resort complex charges a $600 security
deposit and costs $950 a month for rent. The Uptown Suites Duplex charges a $300
security deposit and costs $1100 a month for rent. After how many months would the
apartments cost the same amount? Which apartment would you recommend Sara move
to if she plans on staying for 6 months? Please show work.
Answer:
The rent is the same when 2 months have passed.
If she'd live in them for 6 months, I'd recommend the resort complex, since it'd be cheaper.
Step-by-step explanation:
Sara has two options, the resort complex and the uptown suites duplex, which can be represented by functions where "c" is the cost and "t" is the number of months Sara lives on each apartment.
The Resort complex:
[tex]c_{resort}(t) = 600 + 950*t[/tex]
The Uptown Suites Duplex:
[tex]c_{uptown}(t) = 300 + 1100*t[/tex]
To find the number of months she has to live in them in a way that they have the same cost, we need to find the value of t that makes both equations equal, this is done below:
[tex]600 + 950*t = 300 + 1100*t\\1100t - 950t = 600 - 300\\150t = 300\\t = \frac{300}{150} = 2\\[/tex]
The rent is the same when 2 months have passed.
If she intends to live in them for 6 months, the cost of each are:
[tex]c_{resort}(t) = 600 + 950*6 = 6300[/tex]
[tex]c_{uptown}(t) = 300 + 1100*6 = 6900[/tex]
If she'd live in them for 6 months, I'd recommend the resort complex, since it'd be cheaper.
PLEASE HELP THIS IS URGENT I AM BEING TIMED!!
Given the following list of data, is 9 the mean, the median, or the mode?
2, 7, 9, 8, 9, 4, 6
Answer:
The mode (number with the highest frequency or number with most appearance)
Answer:
Mode
Step-by-step explanation:
The number that occurs the most is 9.
What is the radius of a circle whose equation is (x + 5)2 + (y - 3)2 = 42?
2 units
4 units
8 units
16 units
Answer:
the answer is b, 4 units
Answer:
4
Step-by-step explanation:
quatro
The two lines graphed below are parallel. How many solutions are there to the
system of equations?
A. TWO
B. Zero
C. Infinitely many
D. One
Answer:
Zero
Step-by-step explanation:
Option C is correct, there are Infinitely many solutions are there to the system of equations.
What is slope intercept form of line?The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.
The two lines are parallel, they have the same slope, which means that m is the same for both equations.
Therefore, the system of equations can be simplified to:
y = mx + b₁
y = mx + b₂
Subtracting the two equations, we get:
0 = b₁ - b₂
This means that the y-intercepts of the two lines are equal.
The two lines coincide with each other, and there are infinitely many solutions to the system of equations.
Hence, Option C is correct, there are Infinitely many solutions are there to the system of equations.
To learn more on slope intercept form click:
https://brainly.com/question/9682526
#SPJ7
A sample of 100 was taken from a population, with the mean of the sample
being 25 and the standard deviation of the sample being 3. What is the 95%
confidence interval for the mean of the population?
O A. (24.3, 25.3)
O B. (24, 26)
O C. (23.8, 26.2)
O D. (24.4, 25.6)
Answer:
D
Step-by-step explanation:
I just took the test: 24.4, 25.6
Answer:
its D
Step-by-step explanation:
Can someone help me on these two questions?
Answer:
So to find ratio for questions like these we do x/y
So the ratio for the first one is 5/7
The ratio for the second is 12/7 or 1 5/7
Step-by-step explanation:
someone plz help i need it in like 3 minutes
Answer:
B
Step-by-step explanation:
A: -(3/-2)=-(-3/2)=3/2
B:3/-2=-3/2
C:-(-3/2)=3/2
D:-3/-2=3/2
What is the factored from of y2+6y-16
Answer:
(y + 8)(y - 2)
Step-by-step explanation:
Given
y² + 6y - 16
Consider the factors of the constant term (- 16) which sum to give the coefficient of the y- term (+ 6)
The factors are + 8 and - 2, since
8 × - 2 = - 16 and 8 - 2 = 6, thus
y² + 6y - 16 = (y + 8)(y - 2)
A line passes through the point (–7, 5) and has a slope of One-half. Which is another point that the line passes through?
(–13, 9)
(–9, 13)
(9, 13)
(13, 9)
Answer: the answer is C. (9,13)
Step-by-step explanation:
Sara went on a diet and reduced her daily calories from 2,000 to 1,400. By what percent did she reduce her daily calories?
Answer: 30%
Step-by-step explanation:
Difference is (2000 - 1400) = 600
%age reduction 600/2000 x 100 = 30%
Simplify the radical of that
Answer:
9 sqrt(d^6) thus d)
Step-by-step explanation:
2 Points
For what values of x is the rational expression below undefined?
Check all that apply.
x-7
2x2 - 32
DA. 7
B. 4
D C.-7
OD. -2
0 E. -4
F. 2
Answer:
B and E
Step-by-step explanation:
Given the rational expression
[tex]\frac{x-7}{2x^2-32}[/tex] ← factorise the denominator
2x² - 32 ← take out a common factor of 2 from each term
= 2(x² - 16) ← (x² - 16) is a difference of squares
= 2(x - 4)(x + 4)
The expression can now be written as
[tex]\frac{x-7}{2(x-4)(x+4)}[/tex]
The denominator of the expression cannot be zero as this would make the expression undefined. Equating the denominator to zero and solving gives the values that x cannot be.
2(x - 4)(x + 4) = 0
Equate each factor to zero and solve for x
x - 4 = 0 ⇒ x = 4
x + 4 = 0 ⇒ x = - 4
These are the values of x that make the expression undefined.
x = 4 → B
x = - 4 → E
a number t decreased by 2 is at least 7
(01.01 LC)
Evaluate the expression
5/7 - 4)2 + 3 + 11.
Answer:
Step-by-step explanation:
[tex](\frac{5}{7}-4)2+3+11=(\frac{5}{7}-\frac{4*7}{7})2+3+11\\\\=(\frac{5}{7}-\frac{28}{7})2+3+11\\\\=(\frac{-23}{7})2+3+11\\\\=\frac{-46}{7}+3+11\\\\=\frac{-46}{7}+14\\\\=\frac{-46}{7}+\frac{14*7}{1*7}\\\\=\frac{-46}{7}+\frac{98}{7}\\\\=\frac{-46+98}{7}\\\\=\frac{52}{7}\\\\=7\frac{3}{7}[/tex]
Solve the equation.4[x+1/3]=20
Answer:
[tex]x=\frac{14}{3}[/tex]
Step-by-step explanation:
Open the brackets.
[tex]4x +\frac{4}{3}=20[/tex]
[tex]4x=\frac{56}{3}[/tex]
[tex]x=\frac{14}{3}[/tex]
Answer:
So first we need to divide both sides by four. The four on the left side will cancel out and the right side will become 5. Next we have
x+1/3=5
Now we need to subtract both sides by 1/3. The 1/3 will cancel out and the 5 will become 4 2/3.
All we will be left with is x
x = 4 2/3
someone pls help mee
Answer:
-1/2
Step-by-step explanation:
The formula for slope is: y1-y2/x1-x2
The points given are: (x coordinate, y coordinate)
In the formula,
y1 is the y coordinate of the first point
y2 is the y coordinate of the second point
x1 is the x coordinate of the first point
x2 is the x coordinate of the second point
This said, we can plug our points in.
5-(-1)/-3-9
Simplify.
5+1/-12
6/-12
Divide both the numerator and denominator by -6.
-1/2
2 - (7/8 - 3/4) /'s are fractions
Answer:
[tex]1\frac{7}{8}[/tex] or [tex]\frac{15}{8}[/tex]
Step-by-step explanation:
[tex]2-(\frac{7}{8} -\frac{3}{4} )=\\\\2-(\frac{7}{8} -\frac{6}{8}) =\\\\2-\frac{1}{8} =\\\\1\frac{7}{8} =\\\\\frac{15}{8}[/tex]
Answer:
Brainliest here!
Step-by-step explanation:
2- (7/8 -6/8) = 2-1/8
simplify = 1 7/8 or 15/8
If it doesnt work please just tell me :)
Answer:
33units^2 is the answer
Step-by-step explanation:
I am giving you some data, I want you to make up 2 questions about probability using that data.
You have a bowl of Jelly Belly jelly beans. There are 5 flavors, 25 watermelons, 13 tutti fruitti, 45 cherry, 10 cinnamon, 32 buttered popcorn.
Answer:
What’s the probability of choosing a tutti fruitti and a cherry jelly bean?
What’s the probability of choosing a watermelon, replacing it, then choosing a buttered popcorn?
Step-by-step explanation:
what that answer to 21×-5
Answer: -105
Step-by-step explanation:
21 times -5 will be -105
Rewrite the expression with rational exponents as a radical expression by extending the properties of the integer exponents
Answer:
C
Step-by-step explanation:
[tex]\frac{y^{3/4} }{y^{1/2} }[/tex] Original expression
[tex]y^{\frac{3}{4}-\frac{1}{2} }[/tex] Division Property of Exponents
[tex]y^{\frac{3}{4}-\frac{2}{4} }[/tex] Find a common denominator (4)
[tex]y^{\frac{1}{4} }[/tex] Simplify
[tex]\sqrt[4]{y}[/tex] Rewrite as a radical expression (an exponent of 1/4 is equivalent to the 4th root of the expression)
One circle labeled internet 9 overlaps another circle labeled T V 12. The overlap is labeled 26. A 4-column table with 3 rows. The first column has no label with entries T V, not T V, total. The second column is labeled internet with entries 30, 11, 41. The third column is labeled not internet with entries 5, 4, 9. The fourth column is labeled total with entries 35, 15, 50. Students from School A and School B were asked whether they watch TV or use the Internet after finishing their homework. The Venn diagram and the two-way table show the results from the two surveys. Which statement is true? More students do both activities at A than at B. More students watch TV at B than at A. More students do neither activity at B than at A. More students were surveyed at A than at B.
Answer:
C
Step-by-step explanation:
edg2020
Answer:
C: More students do neither activity at B than at A.
Step-by-step explanation:
edg2021
A cake recipe calls for 40 milliliters of water for every 20 milliliters of cooking
oil. How many milliliters of water are needed if 50 milliliters of cooking oil
were used?
O A) 25 ml
OB) 100 ml
O C) 200 ml
OD 1,000 ml
Answer:
B
Step-by-step explanation:
20x2 is 40, so 50x2 is 100
Answer:
BBBBBBBBBBBBBBBB
Step-by-step explanation:
PLEASE HELP ME!....Check all that are possible units for measuring time in the metric system. A. Millisecond B. Hour C. Second D. Meter
Answer: A
Step-by-step explanation:
Took the test
question in attachment
Answer:
a₁ = 6
Step-by-step explanation:
The sum to n terms of a geometric sequence is
[tex]S_{n}[/tex] = [tex]\frac{a_{1}(r^{n}-1) }{r-1}[/tex]
where a₁ is the first term and r the common ratio
Here [tex]S_{8}[/tex] = 1530 and r = 2, thus
[tex]\frac{a_{1}(2^{8}-1) }{2-1}[/tex] = 1530 , that is
a₁ (256 - 1) = 1530
255a₁ = 1530 ( divide both sides by 255 )
a₁ = 6
If (5, 4) and (7, 2) are the endpoints of a diameter of a circle, what is the equation of the circle? A) (x − 6)2 + (y + 3)2 = 2 B) (x − 6)2 + (y − 3)2 = 2 C) (x + 6)2 + (y +3)2 = 8 D) (x + 6)2 + (y − 3)2 = 8
Answer:
B
Step-by-step explanation:
(5+7)/2 = 6
(4+2)/2 = 3
center = (6, 3)
diameter = √(5-7)²+(4-2)² = √8 = 2√2
radius is half diameter = √2
Equation for circle is (x-6)²+(y-3)²=2
The total cost for a bucket of popcorn and 4 movie tickets is $56. The total cost for the same size bucket of popcorn and 6
movie tickets is $80. The cost of a bucket of popcorn is $8. Which equation represents the relationship between y, the total
cost of the popcorn and movie tickets, and x, the number of movie tickets that are purchased?
y = 12x + 8
y = 12x - 8
y = 14x + 8
y = 14x - 8
Answer:
y = 12x + 8
Step-by-step explanation:
You can come to this conclusion by plugging in the amount of tickets bought as x in each equation, making sure the the answer y is $56 if x = 4 and $80 if x = 6
Answer:
a
Step-by-step explanation:
Mrs. Burgess, Mrs. Curry, Ms. Davis and Mrs.
Stowers went to lunch this weekend. The lunch
total was $81.20. How much does each person
owe if they split it evenly?
Answer:
$20.30
Step-by-step explanation:
There are 4 people so 81.20/4 = 20.30
Answer: $20.30
Step-by-step explanation:
There are 4 people and so you need to divide the cost by the amount of people to see what each person owes
Light travels [tex]9.45*10^{15}[/tex] meters in a year. There are about [tex]3.15*10^{7}[/tex] seconds in a year. How far does light travel per second? Write your answer in scientific notation.
Answer:
300000000
Step-by-step explanation:
Take speed of light and divide it by the number of years and you should have your answer.
