Answers
Answer:
√(4/5)
Step-by-step explanation:
First, let's use reflection property to find tan θ.
tan(-θ) = 1/2
-tan θ = 1/2
tan θ = -1/2
Since tan θ < 0 and sec θ > 0, θ must be in the fourth quadrant.
Now let's look at the problem we need to solve:
sin(5π/2 + θ)
Use angle sum formula:
sin(5π/2) cos θ + sin θ cos(5π/2)
Sine and cosine have periods of 2π, so:
sin(π/2) cos θ + sin θ cos(π/2)
Evaluate:
(1) cos θ + sin θ (0)
cos θ
We need to write this in terms of tan θ. We can use Pythagorean identity:
1 + tan² θ = sec² θ
1 + tan² θ = (1 / cos θ)²
±√(1 + tan² θ) = 1 / cos θ
cos θ = ±1 / √(1 + tan² θ)
Plugging in:
cos θ = ±1 / √(1 + (-1/2)²)
cos θ = ±1 / √(1 + 1/4)
cos θ = ±1 / √(5/4)
cos θ = ±√(4/5)
Since θ is in the fourth quadrant, cos θ > 0. So:
cos θ = √(4/5)
Or, written in proper form:
cos θ = (2√5) / 5
Related Questions
A copy machine makes 32 copies per minute. How long does it take to make 136 copies?
I minutes ] seconds
Answers
Note: Enter your answer and show all the steps that you use to solve this problem in the space provided.
Mrs. Miller sells a house for $179,000. If she earns a commission of 6%, how much money does she earn? Write a proportion and show your work.
Please check my work.
I think that my answer would still be the same because $179,000
- 6%
-----------------------
$179,000
Answers
Answer:
The amount of money which she earn as commission after selling the house is $ 10,740 .
Step-by-step explanation:
Given as :
The selling price of the Mrs. Miller house = $ 179, 000
The percentage of commission which she earn = 6 % of the selling price
Let the amount of money she earn = $ x
Now, According to question
The amount of money she earn = 6 % of the selling price of house
I.e the amount of money she earn = [tex]\frac{6}{100}[/tex]×$ 179,000
Or, the amount of money she earn = 6 × 1790
∴ The amount of money which she earn as commission = $ 10,740
Hence The amount of money which she earn as commission after selling the house is $ 10,740 . Answer
Mrs. Miller earns a commission of $10,740 on selling a house for $179,000.
Explanation:To solve this problem, we need to calculate 6% of $179,000. The commission amount can be found by multiplying $179,000 by 6% (or 0.06). So, the commission earned by Mrs. Miller would be $179,000 * 0.06 = $10,740. Therefore, Mrs. Miller earns $10,740 as her commission.
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IZ) Samantha wants to determine the height of a flagpole at school. Her eye level is 4.6 feet from the ground and
she stands 26 feet from the flagpole. If the angle of elevation is about 68°, what is the height of the flagpole to
the nearest tenth foot?
Answers
Answer:
69 feet.
Step-by-step explanation:
See the attached diagram.
AB is the height of the flagpole and DE is the height of Samantha.
Now, ∠ CEB = 68°
Now, AC = DE = 4.6 feet, and CE = AD = 26 feet {Given}
Then, [tex]\tan 68 = \frac{CB}{CE} = \frac{CB}{26}[/tex]
⇒ CB = 26 tan 68 = 64.35 feet.
Now, height of the flagpole is AB = AC + CB = 4.6 + 64.35 = 68.95 feet ≈ 69 feet. (Answer) (Approximate}
Data were collected and showed an increase in ice cream sales as the weather gets warmer. Which of the following best describes this situation?
a.)Based on the data, this is an example of correlation and causation.
b.)Based on the data, this is an example of correlation.
c.)Based on the data, this is an example of causation.
d.)Based on the data, this is not an example of causation or correlation.
Answers
Based on the data, this is an example of correlation and causation. Option A is correct
To give the conclusion to data collected showed an increase in ice cream sales.
What is correlation?Correlation is defined as the two things depends on each other.
Here,
People would like to buy ice cream in warm weather this statement is correlation and causation is people would like to by ice cream cause the increase in temperature.
Thus, Based on the data, this is an example of correlation and causation.
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Final answer:
The increase in ice cream sales as the weather gets warmer is an example of correlation.
Explanation:
The best description for this situation is b.) Based on the data, this is an example of correlation. Correlation refers to a relationship or pattern between two variables. In this case, as the weather gets warmer, there is an increase in ice cream sales. However, correlation does not imply causation, meaning one variable does not cause the other. It is more likely that the warmer weather influences both the increase in ice cream sales and other factors that may affect sales.
In a given rectangle, the shorter side is 3 units less than the longer side. If we let the longer side be represented by the variable x, create an expression that represents the perimeter of the rectangle. (P=2L+2W)
Answers
The expression representing the perimeter of the rectangle with the longer side x and the shorter side 3 units less than the longer side is P = 4x - 6.
If the longer side of a rectangle is represented by the variable x, and the shorter side is 3 units less than the longer side, then the shorter side can be expressed as x - 3. The perimeter (P) of a rectangle is given by the formula P = 2L + 2W, where L is the length (the longer side) and W is the width (the shorter side). Plugging in the expressions for L and W in terms of x, the perimeter of the rectangle can be represented as P = 2x + 2(x - 3).
Simplifying this expression, we get P = 2x + 2x - 6, which simplifies further to P = 4x - 6.
Therefore, the expression that represents the perimeter of this specific rectangle is P = 4x - 6.
hamburgers cost $2 per lbs and chicken costs $3 lbs and you only have $30 to spend and expect At least 3lbs of hamburger
Answers
If you want at least 3 pounds of hamburgers, then $6 is enough to buy those 3 pounds of hamburgers. If you ONLY buy 3 Pounds, then you also have enough for 4 pounds of chicken. $3 a pound x 4 = $12. You have 2 dollars left to spare, which means you can buy another pound of hamburgers. So 4 pounds each are able to be purchased.
Which algebraic expression is a polynomial with a degree of 5
Answers
Answer: For example, the polynomial which can also be expressed as has three terms. The first term has a degree of 5 (the sum of the powers 2 and 3), the second term has a degree of 1, and the last term has a degree of 0. Therefore, the polynomial has a degree of 5, which is the highest degree of any term.
Step-by-step explanation: (If this helps)
Answer:
Step-by-step explanation:
the answer is 2xy4 + 4x2y3 – 6x3y2 – 7x4
Elena agrees to finish a knitting project for a friend. The graph shows the number of rows Elena completes compared to the amount of time spent knitting.
Assuming she worked at a constant rate, how many rows had been completed before Elena started working?
12
14
15
19
Answers
The graph that accompanies this question is in the figure attached.
Answer:
12
Explanation:
The assumption that Elena worked at a constant rate permits you to build a linear model for the the number of rows Elena completes (dependent variable) in function of the time spent knitting (independent variable).
The coordinates of the points shown on the graph are (14,19), (20,22), and (30,27), and you need to find how many rows had been completed before Elena started working.
The number of rows that had been completed before she started working is the number of rows for time equal 0, which is the y-intercept of the function that models the situation.
Then, what you need to do is to find the equation of the line, using two of the three given points, and then tell the y-intercept.
a) Find the slope, m:
m = rise / run = Δy / Δx = (22 - 19) / (20 - 14) = 3 / 6 = 1/2 = 0.5b) Use one point (20, 22) to find the equation of the line:
y - y₁ = m (x - x₁) ← point-slope formy - 22 = 0.5 (x - 20)y = 0.5x - 10 + 22y = 0.5x + 12 ← slope intercept formThe constant term of the slope-intercept equation, ie. 12, represents the y-intercept. Thus, your answer is 12.
Answer:
12
Step-by-step explanation:
On the first day of June, there were about 17.86 h of daylight in a city. Five months later, there were about 8.40 h of daylight. What was the percent decrease?(Round to the nearest whole number as needed.)
Answers
The percent decrease is 53%
Step-by-step explanation:
The percent decrease is given by:
[tex]Percent-Decrease = \frac{Old\ value-New\ value}{Old\ value} * 100[/tex]
Here
Old Value = 17.86 hours
New Value = 8.40 hours
So,
[tex]Percent-Decrease = \frac{17.86-8.40}{17.86}*100\\=\frac{9.46}{17.86}*100\\=0.5296*100\\=52.96\%[/tex]
Rounding off to nearest whole number
53%
So,
The percent decrease is 53%
Keywords: Percent, percentage
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Becky just measured herself and found out she is 65 inches tall. The last time she measured, she was 52 inches tall. What percent taller is Becky now?
Answers
Answer:
25%
Step-by-step explanation:
52 - 65 = 13 in growth.
13 = 25 % of 52.
So, Becky is now 25% taller.
PLS HELP ASAP I WILL GIVE BRAINLIST
Answers
Answer:
D
Step-by-step explanation:
4(4)+3-5
16-2
14
The first three terms of a geometric sequence are as follows. -5, 20, -80 find the next two terms of a sequence give exact values
Answers
Answer:
320, -1280
Step-by-step explanation:
r = -4
-5 , 20 , -80 , 320 , -1280
Final answer:
The next two terms of the geometric sequence (-5, 20, -80) are 320 and -1280, determined by multiplying each term by the common ratio of -4.
Explanation:
To find the next two terms of the given geometric sequence (-5, 20, -80), we need to determine the common ratio. We can calculate the common ratio by dividing the second term by the first term or the third term by the second term.
The common ratio (r) is:
r = 20 / (-5) = -4
r = (-80) / 20 = -4
Now that we know the common ratio is -4, we use it to find the next two terms by multiplying the most recent term of the sequence by the common ratio.
Fourth term: -80 × -4 = 320
Fifth term: 320 × -4 = -1280
The next two terms of the sequence are 320 and -1280.
Given: △AKM, KD ⊥ AM , AK = 6, KM = 10, m∠AKM = 93º Find: KD
Answers
Final answer:
To find the length of KD in ΔAKM, where KD is perpendicular to AM, and given AK = 6, KM = 10, and m∠AKM = 93º, we use trigonometry. Using the sine function, we determine that KD ≈ 9.99.
Explanation:
The question is about finding the length of KD, where KD is perpendicular from K to AM in triangle AKM, given AK = 6, KM = 10, and the measure of angle AKM is 93º. To solve this, we can use trigonometry, specifically the functions related to a right-angled triangle.
Since KD is perpendicular to AM, ΔAKD is a right-angled triangle at D. We can use the sine function, which is defined as the ratio of the length of the opposite side to the hypotenuse. In this case, α = m∠AKM, opposite = KD, and hypotenuse = KM.
Therefore, sine(α) = opposite/hypotenuse = KD/KM. Since we know that sine(93º) ≈ 0.999, KM = 10, we can find KD by rearranging the equation: KD = KM × sine(93º). Substituting the values gives KD = 10 × 0.999 ≈ 9.99.
17) Tony is retiring after 40 years and will receive a monthly pension of $1400
and Social Security of $1100 a month. What will be Tony's total annual
income?
Answers
Add the two monthly incomes together:
1400 + 1100 = 2500 a month.
There are 12 months in a year, multiply the monthly income by 12:
2500 * 12 = $30,000 per year.
Answer:
$30,000 per year.
Step-by-step explanation:
Add the two monthly incomes together:
1400 + 1100 = 2500 a month.
There are 12 months in a year, multiply the monthly income by 12:
2500 * 12 = $30,000 per year.
Richard and Teo have a combined age of 37. Richard is 4 years older than twice Teo's age. How old are Richard and Teo?
Answers
Answer:
Teo is 11 years old and Richard is 26 years old.
Step-by-step explanation:
Let R be the age of Richard and T be the age of Teo.
First set up the equations:
The combined age of Teo and Richard is 37:
R+T=37
Richard is four years old than twice Teo's age:
R=2T+4
Then, solve the equations:
Substitute (2) to (1) and solve for T:
(2T+4)+T=37
3T=11
T=11
Solve for R using (2):
R=2(11)+4
R=22+4
R=26
If the vine continues to grow at this rate, it will be. Inches long at the end of 5 weeks
Help ASAPP!!!!
Answers
3/12 x 5/x
12 x 5 / 3 = 20
Answer:
The growth at week 5 is 20 inches
Step-by-step explanation:
Topic: Arithmetic Progression
Given
From the table,
At Week 1: Total length = 4
At Week 2: Total length = 8
At Week 3: Total length = 12
There are two ways of solving this;
Method 1
Between each interval, the vine grows by 4 inches. This is supported by the calculation below
From week 1 to week 2; 8 - 4 = 4 inches
From week 2 to week 3; 12 - 8 = 4 inches
This means that; the vine will grow by 4 inches to week 4;
Hence, at week 4;
Total length = Week 3 + 4
Total length = 12 + 4 = 16
Similarly, the vine will grow by 4 inches to week 5;
Hence, at week 5
Total length = Week 4 + 4
Total length = 20 + 4 = 24
But this method is not always advisable because it'll be tedious to use for large data; hence the need for method 2
Method 1
Between each interval, the vine grows by 4 inches. This is supported by the calculation below
Here, we make use of arithmetic progression formula
[tex]T_{n} = a + (n - 1)d[/tex]
Take note of the following
a = First term = The growth at first week
a = 4
d = common difference = rate of growth
From week 1 to week 2; the rate of growth is 8 - 4 = 4 inches
From week 2 to week 3; the rate of growth is 12 - 8 = 4 inches
So, d = 4
n = nth term = 5; i.e the 5th week
Tn = the rate of growth at nth week;
In this case, Tn = 5
By substitution
[tex]T_{n} = a + (n - 1)d[/tex] becomes
[tex]T_{5} = 4 + (5 - 1)4[/tex]
[tex]T_{5} = 4 + 4 * 4[/tex]
[tex]T_{5} = 4 + 4 * 4[/tex]
[tex]T_{5} = 20[/tex]
Hence, the growth at week 5 is 20 inches
Ken made &14,500 in five months at his new job how much can he expect to make in two years if his pay remains constant
Answers
Answer:
$69,600
Step-by-step explanation:
$14,500 in 5 months,
14,500/5=2,900
so he makes $2,900 each month,
1 year=12 months
2 years=24 months
-------------------------------------------------
2900*24=69600
so he expects to make $69,600 in two years.
Answer:
$69,600
Step-by-step explanation:
14,500/5=2,900
2,900x24=69,600
'Polonium-210 is a radioactive substance with a half-life of 138 days. If a nuclear
facility is handling 310 grams of polonium-210, then how many grams of polonium-
210 will be left in 330 days. Round your answer 4 decimal places and remember to
use labels.
Answers
Answer:
59.0891 g (rounded to 4 decimal places)Explanation:
Half-life time of a radioactive substance is the time for half of the substance to decay.
Thus, the amount of the radioactive substance that remains after a number n of half-lives is given by:
[tex]A=A_0\cdot (1/2)^n[/tex]Where:
A is the amount that remains of the substance after n half-lives have elapses, andA₀ is the starting amount of the substance.In this problem, you have that the half-live for your sample (polonium-210) is 138 days and the number of days elapsed is 330 days. Thus, the number of half-lives elapsed is:
330 days / 138 days = 2.3913Therefore, the amount of polonium-210 that will be left in 330 days is:
[tex]A=310{g}\cdot (1/2)^{2.3913}=59.0891g[/tex]please help with steps:
18 - 24 (divide) (-6)
Answers
Answer:
Solution is 1 (one).
Step-by-step explanation:
The equation [tex]\frac{18-24}{-6}[/tex] can be solved by solving first the expression in the numerator. This is done by solving [tex]18-24=-6[/tex].Then, you just have [tex]\frac{-6}{-6}[/tex]. The negative is canceled when it appears twice, so we just have to solve [tex]\frac{6}{6}=1[/tex] (any number divided by itself equals to one).please solve with working thankyou much appreciated
Answers
Answer:
5cm
Step-by-step explanation:
its an equilateral triangle because all 3 angles are 60°
equilateral triangle's sides are all equal so its 5cm
(2) 345
Maria drove 715 miles in 13 hours.
At the same rate, how many miles would she drive in 5 hours?
miles
x
s
?
Answers
Answer:
275 miles in 5 hours
55 miles in one hour
Check
to check if im right
275×2 would be how many miles she drove in 10 hours rght ? 275×2=550
550 miles in 10 hours
we know one hour is 55 miles & 5 hours is 275 & 10 hours is 550
10 hours plus 3 hours = 13 hours right ?
55 ×3 = 165
550 +165=715
715 miles in 13 hours
Step-by-step explanation:
715÷13 to get how many miles she drove in one hour .
=55 miles in 1 hour .
then multiply 55 ×5 to get how many miles she drove in 5 hours
55×5=275
275 miles in 5 hours
some large frames for $14 each and some small frames for $4 each at a closeout sale. If she bought 16 frames for $114, find how many of each type she bought
Answers
Answer:
11 small frames, 5 large frames
Step-by-step explanation:
small: x
large : y
x + y = 16
4x + 14y = 114
Multiply first equation by 4 and subtract.
4x + 4y = 64
-(4x + 14y = 114)
-10y = -50
y = 5
Substitute y into the first equation.
x + 5 = 16
x = 11
how do you factor - 8x² +28x + 60
Answers
Answer:
-4 • (x - 5) • (2x + 3)
Step-by-step explanation:
Answer:
I wasn't sure if it was a 8x^2 or a -8x^2. So I have done both.
The factor of -8x^2+28x+60 is -8(x^2-11).
The factor of 8x^2+28x+60 is 4(2x^2+7x+15)
there are 12 girls and 18 boys in a class what is th largest number of groups they can be split into and have the same number of boys and girls on each team?
Answers
15 groups
Step-by-step explanation:
boys can be split in 9 groups of 2 and the girls can be split in 6 groups of 2
adding this 9+6=15
y+4/12 – y–1/12 = y/2
Answers
The value of "y" is 3
Solution:Given that,
[tex]y+\frac{4}{12}-y-\frac{1}{12}=\frac{y}{2}[/tex]
We have to solve for "y"
Let us simplify the given expression and solve for"y"
[tex]y+\frac{4}{12}-y-\frac{1}{12}=\frac{y}{2}[/tex]
On cross multiplication in L.H.S we get,
[tex]\frac{12 y+4-12 y-1}{12}=\frac{y}{2}[/tex]
Cancelling denominator 12 from both sides, we get
12y + 4 -12y - 1 = y
Again cancelling +12y and -12y we get
4 - 1 = y
y = 3
Thus the value of "y" is 3
Can you help me please?
Answers
Answer:
D
Step-by-step explanation:
Range
A segment is on a number line with endpoints at −5.3 and 8.7.
What is the length of the segment?
Answers
Answer:
about 6.3✔
Step-by-step explanation:
Answer:
Step-by-step explanation:
-5+8 =3
-3-7=4
Answer 3.4
Thomas decided to take the plane to save some time. Unfortunately, the plane was delayed for 1 5/6 hours. How long did the trip finally take?
Answers
Answer:
Finally, the trip of Thomas will take an hour and fifty minutes more than the normal time it usually takes.
Step-by-step explanation:
1. Let's check all the information provided to answer the question:
Time of Thomas flight delay = 1 5/6 hours
Time of normal flight = x hours
2. How long did the trip finally take?
For calculating how long the trip finally took, we need to do the following sum:
Time of normal flight + Time of delay
Like we don't know the time of the normal flight, we will define it as x, then:
x + 1 5/6 hours
x + 1 hour and 50 minutes ⇒ 5/6 of an hour = 5/6 * 60 minutes = 50 minutes
Finally, the trip of Thomas will take an hour and fifty minutes more than the normal time it usually takes.
hurry fast plz jxkdjdvdhkdkfvdvdkdkd
Answers
Answer:
The first one considering you are starting at -7/11... no other number line starts at or goes beyond -7/11....
Answer:
The answer would be -3/10. Therefore, the only timeline that has -7/10, 4/10 and -3/10 is the first one.
Step-by-step explanation:
The answer to the problem is -3/10, as -7 + 4 is -3, and the 10 stays the same. The first timeline accommodates all of the numbers well, and you can see how you get the answer. Hope this helps!
Five math questions
Answers
Answer:
1. 6
2. 36
3. 12
4. 30
5. 20