Please help algebra question number one. Thx 1) If cos = -5/13 and tan <0 what is exact value of sin 0?5/12-12/1312/13-5/12
Answers
The quadrant for which cos Θ is negative is at Quadrant II and III.
The quadrant for which tan Θ is negative is at Quadrant II and IV.
The angle must be therefore found, in Quadrant II. Drawing a diagram of the angle, we have the following
Solve first for the missing side using the Pythagorean Theorem
\(\begin{gathered} a^2+b^2=c^2 \\ a^2+(-5)^2=(13)^2 \\ a^2+25=169 \\ a^2=169-25 \\ a^2=144 \\ \sqrt{a^2}=\sqrt{144} \\ a=12 \end{gathered}\)The missing side is 12, therefore,
\(\sin\theta=\frac{12}{13}\)
Related Questions
What is the common ratio and the general term equation, a, of the geometric sequence?
Answers
The common ratio and the general term equation, a, of the geometric sequence is A. r = 1/2 , an = 16(1/2)^(n - 1).
What is a geometric sequence?A geometric sequence simply means the sequence of non zero numbers whereby the term after the first is simony found by multiplying the previous number by a common ratio
Based on the information, the common ratio will be:
= Second term / First term
= -8 / -16
= 1/2
The nth term will then be 16(1/2)^(n - 1).
The correct option is A.
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Problems of the Week (P.O.W.)
Week of February 8-12
5. Hank went to the store and bought two erasers and three pencils. If each
eraser was half the price of each pencil, how much was each pencil if he
spent $2.04 in all (excluding tax)?
MY WORK
TEACHER REVIEW
Answers
Answer:
Each pencil cost $0.51
Step-by-step explanation:
Which two do i pick ? Evaporation changes gas / liquid water to ice (solid) / water vapor (gas).
Answers
Answer:
Evaporation changes liquid water and even soled water (ice) to water vapor, which is a gas. This all part of the water cycle
Step-by-step explanation:
thank you
Prime numbers have...
Less than two factors
More than two factors
Exactly two factors
Less than or equal to two factors
Answers
Answer:
(Exactly two factors)
Answer:(C) Exactly two factors
Step-by-step explanation:(C) Exactly two factors
...................................................................
Answers
Answer:
29 degrees
Step-by-step explanation:
Note how both triangles are isosceles triangles, which mean two angles will be equivalent. In the triangle with the marked angle measurement, since the total of angles in a triangle is 180, then the measurement of the unmarked angles have a sum of 180-64, which is 116. Then, as stated before, this triangle is isosceles, so the measurement of each unmarked angle is 116/2, which is 58.
Next, notice how the angle below angle x in that triangle shares a line with one of the 58 degree angles. This means that angle is 180-58, which is 122. Now, since the total of angles in a triangle is 180 and the triangle is isosceles, then angle x is (180-122)/2, which is 58/2, or 29 degrees
The scouts were constructing a scale model of their clubhouse. They were building the model out of toothpicks.
Below are some of the measurements they used.
One wall was made of 18 bricks and they used 3 toothpicks on the model.
A second wall they built used 6 toothpicks to represent 36 bricks on the actual clubhouse.
What was the scale factor (bricks : toothpicks) being used by the scouts?
A 6:1
B 8:1
12:1
D 16:1
Answers
The town of Euclid started a voluntary recycling program. The first year it was utilized by 1500 residents. Every year afterward, the number of new users was 120% of the new users the year before. After 6 years, how many people total were using the recycling program?
Answers
Answer:
170,070 residents
Step-by-step explanation:
Original population = 1500 residents
Total population after 6 years is calculated using the formula
A = P(1+r)^t
r is the rate = 120% = 1.2
t is the time = 6 years
P is the original population
A = 1500(1+1.2)^6
A = 1500(2.2)^6
A = 1500(113.379904)
A = 170,069.856
Hence the total people using the recycling program after 6 years is approximately 170,070 residents
Brooklyn is going to invest in an account paying an interest rate of 3.5% compounded continuously. How much would Brooklyn need to invest, to the nearest ten dollars, for the value of the account to reach $64o in 9 years?
Answers
Brooklyn needs to invest $432.43, rounded to the nearest ten dollars.
To determine how much Brooklyn needs to invest in an account that pays a continuously compounded interest rate, we can use the formula:
A = \(Pe^(^r^t^)\)
where A is the future value of the account, P is the principal investment, e is the mathematical constant approximately equal to 2.71828, r is the interest rate, and t is the time in years.
In this case, we want the future value of the account to be $640, the interest rate is 3.5% (or 0.035 as a decimal), and the time is 9 years. We can substitute these values into the formula and solve for P:
640 = \(Pe^(^0^.^0^3^5^*^9^)\)
640 = Pe^0.315
P =\(640/e^0^.^3^1^5\)
P = 432.43
Therefore, to have a future value of $640 in 9 years with a continuously compounded interest rate of 3.5%.
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HELP!!
Next, you will make a scatterplot. Name a point that will be on your scatter plot and describe what it represents.
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A point on the scatter plot is defined as (19, 3), which means that an input of 19 is mapped to an output of 3.
What is the scatter plot?The scatter plot is built inserting all the points of the table in a graph, which are in the following input-output format:
(Input, Output).
One point on the scatter plot for this problem has the coordinates given as follows:
(19, 3).
Hence the meaning is that an input of 19 is mapped to an output of 3.
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You visit the tallest building in a city and drop a penny off the edge of the observation deck. The distance the penny will fall is 16 feet the first second, 48 feet the next second, 80 feet the third second, and then it will continue falling at the same rate. How many feet will the penny fall during the 8th second?
384 feet
272 feet
256 feet
240 feet
Answers
The distance that an object falls due to gravity is given by the equation:
d = 1/2 * g * t^2
where d is the distance fallen, g is the acceleration due to gravity, and t is the time elapsed.
In this case, we are given that the penny falls 16 feet during the first second, 48 feet during the second second, and 80 feet during the third second. From this, we can see that the penny is falling with a constant acceleration of 32 feet per second per second (since the distance is increasing by 32 feet each second).
To find the distance that the penny falls during the eighth second, we can use the same equation as before, but with a value of t equal to 8 seconds:
d = 1/2 * g * t^2
d = 1/2 * 32 * 8^2
d = 1/2 * 32 * 64
d = 1024 feet
Therefore, the penny will fall 1024 feet during the eighth second.
5 2/3 divided by 3/2
Please help
Answers
Answer:
I think is 3 7/9
Step-by-step explanation:
hope it helps
Answer:
fraction form: 34/9
decimal form: 3.7 (repeating)
mixed number form: 3 7/9
hope it was helpful! ^^
Suppose that a study of elementary school students reports that the mean age at which children begin reading is 5.4 years with a standard deviation of 0.8 years.
Step 2 of 2: If a sampling distribution is created using samples of the ages at which 38 children begin reading, what would be the standard deviation of the sampling distribution of sample means? Round to two decimal places, if necessary.
Answers
Answer:
Step-by-step explanation:
The standard deviation of the sampling distribution of sample means is given by the formula:
standard deviation = population standard deviation / sqrt(sample size)
Here, the population standard deviation is 0.8 years, and the sample size is 38. Substituting these values into the formula, we get:
standard deviation = 0.8 / sqrt(38)
standard deviation ≈ 0.13
Rounding to two decimal places, the standard deviation of the sampling distribution of sample means is approximately 0.13 years.
A contractor is adding 243 CY backfill. If each truck can hold 162 CF, how many truck loads are needed
Answers
The number of trucks needed is an illustration of rates
The number of trucks needed is 42
How to determine the number of trucksThe size of the backfill is given as: 243 CY
A truck can load up to 162 CF
So, the number of trucks needed is calculated as:
\(n = \frac{243 CY}{162 CF}\)
Convert CY to CF
\(n = \frac{243 * 27CF}{162 CF}\)
Solve
\(n = 40.5\)
Approximate
\(n = 41\)
Hence, 41 trucks are needed
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The graph displays the distance a CO2 car traveled in a race. Which statement is a correct interpretation of the slope of the line in the graph?
Answers
Answer:
C sorry if im wrong
Step-by-step explanation:
Answer:
The CO2 car traveled 5 feet per second
Step-by-step explanation:
I took the test
Determine the surface area and volume. Note: The base is a square.
Answers
Answer:
volume=60cm3, surface area=96cm2
Step-by-step explanation:
volume=1/3×(6×6)×5
=60cm3
surface area= 4(1/2×6×5)+(6×6)
=96cm2
Triangle ABC is shown.Which fact is not used to prove that ABC is similar to DBE?
Answers
If triangle ABC is similar to DBE, then:
- Segments AC and DE must be parallel: Both lines are parallel because they do not intersect each other
-AB is a transversal line passing AC and DE: DE intersects AB and BC in the same ratio, So AC and DE are parallel.
Angle B is congruent to itself due to the reflexive property:
Looking at the triangles, the next angles ∠BAC and ∠BDE are corresponding.
Hence, the only option that is not valid for similar triangles is "The sum of angles A and B are supplementary to angle C".
The correct answer is the first option.
A suspect of a crime is traveling on 26th Street toward Cherry Street. The diagram shows the locations of the suspect and a police officer. Your friend says that the officer should wait at point C to intercept the suspect because the officer will have the same distance to travel no matter which route the suspect takes. Is your friend correct? Explain.
Answers
AC is not equal to CE based on the angle bisector theorem. The answer is: C. NO, you cannot use the angle bisector theorem to determine that AC = CE.
What is the Angle Bisector Theorem?According to the angle bisector theorem, when a line segment divides an angle of a triangle, the line segment also divides the opposite side but does so in such a way that the two segments are proportional to the other two sides of the triangle. However, the two segments are not congruent to each other.
In the diagram given below that shows the suspect, the police officer, and the 26th Street toward Cherry Street, the angle bisector divides the side opposite to the angle divided into AC and CE. Thus, their length cannot be ascertain to be congruent to each other, however, based on the angle bisector theorem, we can only prove that their length is proportional to the other two sides of the triangle.
Therefore, we can conclude as saying:
C. NO, you cannot use the angle bisector theorem to determine that AC = CE.
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7. Twenty students were asked whether they were freshmen, sophomores, juniors, or seniors. Their responses are as follows:SRFRFRSRSRSRJRSOSOSRFRFRSRSOFRSOSRSRSRSOConstruct a frequency table (including a relative frequency column) to describe this data.ValueFrequencyRelative FrequencyFRSOJRSR
Answers
Frequency is related to the number of times a value of the data occurs.
Relative frequency is the proportion this value occurs in the set of the total number of outcomes, it can be calculated as:
\(\begin{gathered} RF=\frac{Frequency}{Total\text{ number of values}} \\ \text{For example:} \\ RF=\frac{5}{20}=0.25 \\ RF=\frac{1}{20}=0.05 \\ RF=\frac{9}{20}=0.45 \end{gathered}\)The frequency table will be:
Select the irrational numbers.
Answers
Answer:1,4,7
Step-by-step explanation:
a charity run has prizes for the top finisher in each 10 age categories
Answers
The first step in solving the exercise is to identify which is the dependent variable and which is the independent variable.
The independent variable will go on the x-axis and the dependent variable will go on the y-axis.
The independent variable is age because the time of runners depends on their age, not the other way around.
Then, age is on the x-axis and time is on the y-axis, which rules out option A.
Now, you can discard option D. because, for example, the ordered pair (12, 23) is not graphed.
Finally, you can discard option C. because, for example, the ordered pair (71,33) is not graphed.
Therefore, the scatter plot that accurately reflects the data in the table is that of option B.
f(x)=2x+5
———
4
Find the inverse
Answers
Answer:
f^-1 (x) = 2x - 5/2
Step-by-step explanation:
First you swap the equation so it's 2x +5/4 = x then multiply both sides by 4 so it's 2y + 5 = 4x then move the constant to the right so it's 2y=4x-5 then you divide the equation by 2 so it's y=2x- 5/2 and substitute f^-1 (x) for y so it turns into f^-1 (x) = 2x - 5/2 Hope this helps I tried my best
The inverse of the given function is \(\rm f^{-1}(x) = \dfrac{4x - 5 }{2}\) and this can be determined by replacing x by f(x) and f(x) by x and then solving for f(x) and then replacing f(x) by \(\rm f^{-1}(x)\).
Given :
\(\rm f(x) = \dfrac{2x+5}{4}\)
The following steps can be used in order to determine the inverse of the given function:
Step 1 - Write the given function.
\(\rm f(x) = \dfrac{2x+5}{4}\)
Step 2 - Now, to determine the inverse of the given function, replace x by f(x) and f(x) by x and then solve for f(x) and then replace f(x) by \(\rm f^{-1}(x)\).
\(\rm x = \dfrac{2f(x)+5}{4}\)
Step 3 - SImplify the above expression in order to determine the value of f(x).
4x = 2f(x) + 5
\(\rm f(x) = \dfrac{4x - 5 }{2}\)
Step 4 - Replace f(x) by \(\rm f^{-1}(x)\) in the above expression.
\(\rm f^{-1}(x) = \dfrac{4x - 5 }{2}\)
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After hearing of the national result that 44% of student engage in binge drinking (5 drinks at a sitting for men, 4 for women), a professor surveyed a random sample of 244 students at his college and found that 96 of them admitted to binge drinking in the past week. Should he be surprised at this result
Answers
Answer:
Should he be surprised at this result
The found proportion is 1.56 standart deviations away from the expected. we should no be surprised .
Step-by-step explanation:
p=0,44
q=1-0.44=0.56
u=p=0,44
o=\(\sqrt{pq/n}\)=\(\sqrt{(0.44)(0.56)/244}\) = 0.032
proportion of students in binge drinking 96/244 = 0.39
The found proportion is 1.56 standart deviations away from the expected. we should no be surprised .
Graph the line with slope 1/3 and y-intercept −2.
Answers
The graph of the function y = 1/3x - 2 is added as an attachment
Sketching the graph of the functionFrom the question, we have the following parameters that can be used in our computation:
Slope = 1/3y-intercept = -2So, the equation is
y = 1/3x - 2
The above function is a linear function that has been transformed as follows
Vertically stretched by a factor of 1/3Shifted down by 2 unitsNext, we plot the graph using a graphing tool by taking note of the above transformations rules
The graph of the function is added as an attachment
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Hi, can you help me to solve this exercise please!!!
Answers
We are given the trigonometric ratio
\(\cos (\theta)=\frac{\sqrt[]{170}}{10}\)Thus
We can represent the ratio pictorially using a right-angle triangle
We will now have to find the value of x relationship
\(\begin{gathered} \text{where} \\ \text{hypotenuse}=\sqrt[]{170} \\ \text{opposite}=10 \end{gathered}\)\(\cos \sec x=\frac{1}{\sin x}=\frac{hypotenuse}{opposite}=\frac{\sqrt[]{170}}{10}\)Thus, re-writing, we will have
\(\sin x=\frac{10}{\sqrt[]{170}}\)Thus
\(\sin \theta=\frac{10}{\sqrt[]{170}}\)In rationalized form
\(\begin{gathered} \sin \theta=\frac{10}{\sqrt[]{170}}\times\frac{\sqrt[]{170}}{\sqrt[]{170}} \\ \\ \sin \theta=\frac{10\sqrt[]{170}}{170}=\frac{\sqrt[]{170}}{17} \end{gathered}\)Thus
\(\sin \theta=\frac{\sqrt[]{170}}{17}\)
Often the pay for a sales position is based on _______________________.
Group of answer choices
commission
salary
hourly rate
Answers
Answer:
Often the pay for a sales position is based on commission.
Step-by-step explanation:
Rewrite the two equations in the form (x−p)^2=q.
0=x^2-10x+10
x^2+26x+167.5=0
Answers
Answer:
(x - 5)^2 = 15 and (x + 13)^2 = 3
Step-by-step explanation:
Sure, I can help you with that.
Let's start with the first equation:
0 = x^2 - 10x + 10
To rewrite this equation in the form (x - p)^2 = q, we need to complete the square.
First, let's factor out the coefficient of x^2:
0 = 1(x^2 - 10x + 10)
Next, we want to add and subtract a value that will allow us to complete the square inside the parentheses. In this case, we will add and subtract (10/2)^2 = 25:
0 = 1(x^2 - 10x + 25 - 25 + 10)
Now we can rearrange the terms inside the parentheses and simplify:
0 = 1((x - 5)^2 - 15)
Finally, we can rewrite the equation in the desired form by adding 15 to both sides:
15 = (x - 5)^2
So the first equation in the form (x - p)^2 = q is:
(x - 5)^2 = 15
Now let's move on to the second equation:
x^2 + 26x + 167.5 = 0
Again, we need to complete the square to rewrite this equation in the form (x - p)^2 = q.
First, let's factor out the coefficient of x^2:
x^2 + 26x + 167.5 = 1(x^2 + 26x + 167.5)
Next, we want to add and subtract a value that will allow us to complete the square inside the parentheses. In this case, we will add and subtract (26/2)^2 = 169:
x^2 + 26x + 167.5 = 1(x^2 + 26x + 169 - 169 + 167.5)
Now we can rearrange the terms inside the parentheses and simplify:
x^2 + 26x + 167.5 = 1((x + 13)^2 - 1.5)
Finally, we can rewrite the equation in the desired form by adding 1.5 to both sides:
1.5 = (x + 13)^2 - 1.5
So the second equation in the form (x - p)^2 = q is:
(x + 13)^2 = 3
A study of women’s weights found that a randomly selected sample of 234 women had a mean weight of 157.3 lb. Assuming that the population standard deviation is 15.6 lb., construct a 95% confidence interval estimate of the mean weight of all women.
Answers
Answer:
(155.301 ; 159.299)
Step-by-step explanation:
Xbar = 157.3
Sample size, n = 234
Population standard deviation, σ = 15.6
The confidence interval :
Xbar ± standard Error
Standard Error = Zcritical * σ/√n
Zcritical at 95% = 1.96
Standard Error = 1.96 * (15.6/√234) = 1.999
Lower boundary : 157.3 - 1.999 = 155.301
Upper boundary : 157.3 + 1.999 = 159.299
(155.301 ; 159.299)
The $40 million lottery payment that you have just won actually pays $2
Answers
Answer:
wait what is the question?
Step-by-step explanation:
??
Given: sin (A) = 5/13, pi/2 < A < pi and tan (B) = - sqr root 13, pi/2 < B <. What is tan(A - B)? A. (5 + 12sqr root 13)/(12 - 5sqr root13) B. (12 - 5sqr root)/(5 + 12sqr root13) C. (12 + 5sqr root13)/(-5 + 12 sqr root13) D. (-5 + 12 sqr root13)/(12 + 5 sqr root13)
Answers
The value of tan (A - B) is (-5 + 12√13) / (12+ 5√13)
How to determine tan(A-B)?Trigonometry is a branch of mathematics dealing with the relationship between the ratios of the sides of a right-angled triangle with its angles.
tan (B) = - √13
Since sin(A) = 5/13 (opposite/hypotenuse)
adjacent = √(13² - 5²) = 12 units
Since π/2 < A < π, adjacent = -12
Thus, tan (A) = -5/12
Applying the angle difference formula,
tan (A - B) = (tan A - tan B) / (1 + tan A tan B)
tan (A - B) = (-5/12 - (- √13)) / (1 + (-5/12)×(-√13))
tan (A - B) = (-5/12 + √13) / (1 + (5√13)/12)
tan (A - B) = (-5 + 12√13) / (12+ 5√13)
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$1400 is invested at 4% per annum simple interest. How long will it take for the amount to reach $1624? Show you working.
Answers
Answer:
4 years
Step-by-step explanation:
I = prt
F = p + prt
F = 1400 + 1400 * 0.04 * t
1624 = 1400 + 1400 * 0.04 * t
224 = 56t
t = 4
Answer: 4 years