a) [tex]\[ \theta = 67.9^\circ, 112.1^\circ \][/tex], b) [tex]\[ \theta = 133.7^\circ, 226.3^\circ \][/tex], c) [tex]\[ \theta = 122.7^\circ, 302.7^\circ \][/tex], d) [tex]\[ \theta = 35.8^\circ, 215.8^\circ \][/tex], e) [tex]\[ \theta = 45.5^\circ, 314.5^\circ \][/tex] and f) [tex]\[ \theta = 154.4^\circ, 334.4^\circ[/tex].
Let's solve each part:
(a) [tex]\(\sin \theta = 0.9263\)[/tex]
1. Find the reference angle using [tex]\(\theta = \sin^{-1}(0.9263)\)[/tex]:
[tex]\[ \theta \approx 67.9^\circ \][/tex]
2. Since [tex]\(\sin \theta\)[/tex] is positive, the angles are in the first and second quadrants:
[tex]\[ \theta_1 \approx 67.9^\circ \][/tex]
[tex]\[ \theta_2 \approx 180^\circ - 67.9^\circ = 112.1^\circ \][/tex]
So, the solutions are:
[tex]\[ \theta = 67.9^\circ, 112.1^\circ \][/tex]
(b) [tex]\(\cos \theta = -0.6909\)[/tex]
1. Find the reference angle using [tex]\(\theta = \cos^{-1}(-0.6909)\)[/tex]:
[tex]\[ \theta \approx 133.7^\circ \][/tex]
2. Since [tex]\(\cos \theta\)[/tex] is negative, the angles are in the second and third quadrants:
[tex]\[ \theta_1 \approx 133.7^\circ \][/tex]
[tex]\[ \theta_2 \approx 360^\circ - 133.7^\circ = 226.3^\circ \][/tex]
So, the solutions are:
[tex]\[ \theta = 133.7^\circ, 226.3^\circ \][/tex]
(c) [tex]\(\tan \theta = -1.5416\)[/tex]
1. Find the reference angle using [tex]\(\theta = \tan^{-1}(-1.5416)\)[/tex]:
[tex]\[ \theta \approx -57.3^\circ \][/tex]
2. Adjust the reference angle to fall within the interval [tex]\([0^\circ, 360^\circ)\)[/tex]:
[tex]\[ \theta_1 = 360^\circ - 57.3^\circ = 302.7^\circ \][/tex]
3. Since [tex]\(\tan \theta\)[/tex] is negative, the angles are in the second and fourth quadrants:
[tex]\[ \theta_2 = 180^\circ + (-57.3^\circ) = 122.7^\circ \][/tex]
So, the solutions are:
[tex]\[ \theta = 122.7^\circ, 302.7^\circ \][/tex]
(d) [tex]\(\cot \theta = 1.3952\)[/tex]
1. Find the reference angle using [tex]\(\theta = \cot^{-1}(1.3952)\)[/tex]:
[tex]\[ \theta \approx 35.8^\circ \][/tex]
2. Since [tex]\(\cot \theta\)[/tex] is positive, the angles are in the first and third quadrants:
[tex]\[ \theta_1 \approx 35.8^\circ \][/tex]
[tex]\[ \theta_2 \approx 180^\circ + 35.8^\circ = 215.8^\circ \][/tex]
So, the solutions are:
[tex]\[ \theta = 35.8^\circ, 215.8^\circ \][/tex]
(e) [tex]\(\sec \theta = 1.4293\)[/tex]
1. Convert to [tex]\(\cos \theta\)[/tex]:
[tex]\[ \cos \theta = \frac{1}{1.4293} \approx 0.6996 \][/tex]
2. Find the reference angle using [tex]\(\theta = \cos^{-1}(0.6996)\)[/tex]:
[tex]\[ \theta \approx 45.5^\circ \][/tex]
3. Since [tex]\(\cos \theta\)[/tex] is positive, the angles are in the first and fourth quadrants:
[tex]\[ \theta_1 \approx 45.5^\circ \][/tex]
[tex]\[ \theta_2 \approx 360^\circ - 45.5^\circ = 314.5^\circ \][/tex]
So, the solutions are:
[tex]\[ \theta = 45.5^\circ, 314.5^\circ \][/tex]
(f) [tex]\(\csc \theta = -2.3174\)[/tex]
1. Convert to [tex]\(\sin \theta\)[/tex]:
[tex]\[ \sin \theta = \frac{1}{-2.3174} \approx -0.4316 \][/tex]
2. Find the reference angle using [tex]\(\theta = \sin^{-1}(-0.4316)\)[/tex]:
[tex]\[ \theta \approx -25.6^\circ \][/tex]
3. Adjust the reference angle to fall within the interval [tex]\([0^\circ, 360^\circ)\)[/tex]:
[tex]\[ \theta_1 = 360^\circ - 25.6^\circ = 334.4^\circ \][/tex]
4. Since [tex]\(\sin \theta\)[/tex] is negative, the angles are in the third and fourth quadrants:
[tex]\[ \theta_2 = 180^\circ + (-25.6^\circ) = 154.4^\circ \][/tex]
So, the solutions are:
[tex]\[ \theta = 154.4^\circ, 334.4^\circ[/tex]
The complete question is:
Approximate, to the nearest 0.1°, all angles θ in the interval [0°, 360°) that satisfy the equation. (Enter your answers as a comma-separated list.)
(a) sin θ = 0.9263
θ = °
(b) cos θ = −0.6909
θ = °
(c) tan θ = −1.5416
θ = °
(d) cot θ = 1.3952
θ = °
(e) sec θ = 1.4293
θ = °
(f) csc θ = −2.3174
θ = °
A car is tracing at a rate of 72 kilometers per hour. What is the car rates in kilometers per min? How many kilometers will the car travel in 5 mins
In 5 minutes, the car will travel 6 kilometers.
To convert the car's speed from kilometers per hour to kilometers per minute, we need to divide the given rate by the number of minutes in an hour, which is 60. So, for a car traveling at 72 kilometers per hour, the rate in kilometers per minute is:
72 km/hr / 60 = 1.2 kilometers per minute.
Now, to calculate how many kilometers the car will travel in 5 minutes, we simply multiply the rate in kilometers per minute by the number of minutes:
1.2 km/min * 5 min = 6 kilometers.
Therefore, the car will travel 6 kilometers in 5 minutes at the rate of 72 kilometers per hour.
PLEASE ANSWER IVE BEEN WAITING FOR AN HOUR
Rachel earned 34 in 4 hours at her job today she wants to know how much she could earn (e) tommorow if she works 10 hours at the same hourly rate
A. E/34 = 4/10
B. 34/4 = E/10
Solve the proportion to determine how much Rachel will earn in 10 hours.
Write a linear equation that models the cost y of one person going on x rides at the fair. Graph the equation. Admission is $12 and rides are a $1 each. Please help
Write the contrapositive of the conditional statement. If a polygon is regular, then it has congruent angles and congruent sides.
Of the students at Milton Middle School, 99 are girls. If 45% of the students are girls, how many total students are there at Milton Middle school?
About 11/12 of a golf course is in the fairways, 1/18 in the greens, the rest in the trees. What part of the golf course is in the trees?
The scores of adults on an iq test are approximately normal with mean 100 and standard deviation 15. clara scores 118 on such a test. she scores higher than what percent of all adults
Isosceles triangles may be obtuse or acute but never right
The statement, "Isosceles triangle may be obtuse or acute but not right", is a false statement.
Isosceles triangles can be defined as triangles that have two sides (angles) having equal measures.
Obtuse triangles have at least one angle greater than 90°.
Acute triangles have all three angles less than 90°.
Right triangles have one of the angles 90°.
Consider a right triangle ABC.
So, one of the angles, let it be A, will be right.
So, m ∠A = 90°.
By the angle sum property of triangles,
90° + m∠B + m∠C = 180°
m∠B + m∠C = 90°
Let both angles are having equal measures, let it be x.
x + x = 90°
2x = 90°
x = 45°
So, each of the angles has a measure of 45°, and so is an isosceles triangle since the two angles are equal.
So, a right triangle can be isosceles.
Hence the statement is false.
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Please help me!! How do you solve 4x+8=2x+7+2x-20. Thank you
The Murphys are on vacation and want to go on a helicopter tour. The tour itself costs $125 per person and they also have to pay a fuel fee of $50. If there are four people in the family, how much will the tour cost them?
The answer is, indeed, $550.
how to write 412.638 using fractions
A company wants to decrease their energy use by 15%. If their electric bill is currently $1300 a month, what will their bill be if they are successful?
the fully shaded grid shows 1. EXPLAIN how these three models are related
How do I FULLY answer this question. I have 2/4 marks
What is the equation for the linear model in the scatter plot obtained by choosing the two points to the closest line?
y=-1.5 X +6
yEquals 1.5 X +6
The equation for the linear model in a scatter plot can be determined by selecting any two points closer to the line and utilizing them to find its slope and y-intercept. This information is then used to write the equation y = mx + b, where m is the slope and b is the y-intercept.
Explanation:The question pertains to the equation of the linear model in a scatter plot which basically describes the best fit line passing through the points on the plot. In simple terms, in a scatter plot if you choose any two points closer to the line, we can use these to determine the equation of that line.
Suppose you have two points (x1, y1) and (x2, y2), where x represents the independent variable and y is the dependent variable. To find the slope (m) of the line, we use the formula: m = (y2 - y1) / (x2 - x1). Once the slope is determined, we proceed to find the y-intercept (b), which is the y-value where the line crosses the y-axis.
The general form of a linear equation is y = mx + b. Hence, using the values of slope and y-intecept obtained earlier, we can write the equation of our line. For example, in the equations given in the question, -1.5 and 1.5 are the slopes and 6 is the y-intercept.
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Rewrite the following statement using a number in scientific notation.
The diameter of a certain bacterium is about
0.00000002
0.00000002 meters.
Line ET is a tangent to circle A at point T and the measure of ∠TNG is 25°
What is the measure of ∠NET?
A) 130°
B) 50°
C) 65°
D) 90°
Answer:
C) 65°
Step-by-step explanation:
G ∈ NE, so ∠TNG = ∠TNE. ∠ATE = 90° because a radius (AT) is always perpendicular to a tangent line (ET) at the tangent point (T). A ∈ TN, so ΔTNG is a right triangle, and angles NET and TNE are complementary. Then ...
... ∠NET = 90° - ∠TNG
... = 90° - 25°
... ∠NET = 65°
Simplify the expression
–5.6 + 8.2
Answers:
–2.6
–13.8
2.6
13.8
Using the following production tally, determine how many total mousetraps were produced during a shift:
Quantity per package: 60
Number of packages you sealed: 41
Starting quantity in first package (from previous shift): 52
Ending quantity in your last unsealed package (leave for next shift): 24
Rejected mousetraps: 34
Find the value of x (7x) (2x+27)
A. 7
B. 49
C. 61
D. 17
The value of x is 17.
To find the value of x when (7x) and (2x+27) are the two angles made on a straight line, we can use the fact that the sum of the angles on a straight line is 180 degrees.
Let's set up an equation:
(7x) + (2x+27) = 180
First, we simplify the equation by combining like terms:
9x + 27 = 180
Next, we isolate the variable x by subtracting 27 from both sides of the equation:
9x = 180 - 27
9x = 153
Finally, we solve for x by dividing both sides of the equation by 9:
x = 153/9
Simplifying the division gives us:
x = 17
Therefore, the value of x is 17.
Complete question :-
Find the value of x, if (7x) and (2x+27) are the two angles made on a straight line?
A. 7
B. 49
C. 61
D. 17
So, the value of x is not one of the given options A, B, C, or D.
To find the value of x in the expression (7x)(2x+27), we need to simplify the expression and solve for x.
Step 1: Distribute the 7x to both terms inside the parentheses:
(7x)(2x+27) = 14x^2 + 189x
Step 2: Set the expression equal to 0 and factor out common terms, if possible:
14x^2 + 189x = 0
Step 3: Factor out x:
x(14x + 189) = 0
Step 4: Set each factor equal to 0 and solve for x:
x = 0 (from the first factor)
14x + 189 = 0
14x = -189
x = -189/14
So, the value of x is not one of the given options A, B, C, or D.
Subtract using the number line. −4−(8)
Answer:
-12
Step-by-step explanation: I Took K12 TEST
Colin took out a loan with a principal of $32,800. After five years, the interest and principal totaled $48,872. If Colin made monthly payments of $816 for five years until the loan was paid off, how much did Colin pay in service charges? a. $16,072 b. $88 c. $16,160 d. $163
The service charges would be, $88
What is mean by Subtraction?Subtraction in mathematics means that is taking something away from a group or number of objects. When you subtract, what is left in the group becomes less.
Given that;
Colin took out a loan with a principal of $32,800.
And, After five years, the interest and principal totaled $48,872.
Now,
The value of principal amount is,
⇒ 816 × 5 × 12 = 48960
Now, We get;
Amount of Colin pay in service charges is,
48960 - 48872= 88
Hence, The service charges were $88
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How to do you simplify
1/5(40x^5+13x^3-3x-5)-(3x^5-5x^3+5x)
Surface area of a cylinder with a diameter of 14 and height is 9
a triangle is reflected across the line x=2. which of the following is true?
A. the image and pre-image have the same orientation.
B. the image and pre-image have different sizes.
C. the image and pre-image are congruent.
D. the image and pre-image are separated by a given angle.
Answer: C
Step-by-step explanation:
Answer:
C. the image and pre-image are congruent.
Step-by-step explanation:
a triangle is reflected across the line x=2
Check with each option
A. the image and pre-image have the same orientation.
The image will not be in same order
B. the image and pre-image have different sizes. the size will not change
C. the image and pre-image are congruent. the reflection will not change the size. so they are congruent
D. the image and pre-image are separated by a given angle.
The angles never change in reflection
Find the equation of the line perpendicular to x−5y=15 that passes through the point (−2,5).
1. Solve the given equation for y.
x - 5y = 15
-5y = -x + 15
y = (-x + 15)/-5
y = (x/5) - 3
y = (1/5)(x) - 3
The slope is 1/5. See it?
The equation we are looking for has a slope which is the negative inverse of the slope in the equation we just solved for y.
The slope for the equation we want is -5 which is the negative inverse of 1/5. Undetstand?
We have the slope of the new equation and one point is given.
Plot BOTH into the point-slope formula and solve for y. To solve for a variable means to isolate the variable ALONE on one side of the equation.
y - y_1 = m(x - x_1)...This is the point-slope formula. Our given point is (5,-2)
y - 5 = -5(x - (-2))
y - 5 = -5(x + 2)
We now solve for y and that's it.
y - 5 = -5x - 10
y = -5x - 10 + 5
The equation we want is y = -5x - 5.
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Which function represents a reflection of f(x) = 5(0.8)^x across the x-axis?
g(x) = 5(0.8)^–x
g(x) = –5(0.8)^x
g(x) = (0.8)^x
g(x) = 5(–0.8)^x
Answer: The correct option is second.
Explanation:
The given function is,
[tex]f(x)=5(0.8)^x[/tex]
If we graph a function is f(x), then its coordinates is defined as (x,f(x)).
When the graph of f(x) is reflect across the x-axis, then the the x-coordinate remains the same and the sign of y-coordinate is changed. It means after reflecting across the x-axis,
[tex](x,y)\rightarrow(x,-y)[/tex]
The given given equation can be written as,
[tex]y=5(0.8)^x[/tex]
To find the equation of the graph after reflection across the x-axis multiply both sides by -1.
[tex]-y=-5(0.8)^x[/tex]
Because f(x)=y and g(x)=-y.
[tex]g(x)=-5(0.8)^x[/tex]
Therefore the second option is correct and the graph of both function is given below.
Answer:
B. g(x) = –5(0.8)^x
Step-by-step explanation:
We have the function, [tex]f(x) = 5(0.8)^x[/tex].
It is required to reflect the function about x-axis.
Now, as we know,
Reflection across x-axis will flip the graph of the function and the function [tex]f(x)[/tex] becomes [tex]-f(x)[/tex].
So, the reflection of [tex]f(x) = 5(0.8)^x[/tex] across x-axis will give the function [tex]f(x) = -5(0.8)^x[/tex]
So, we see that,
Option B i.e. [tex]g(x) = -5(0.8)^x[/tex] is correct.
How do you rename 4 thousands 7 hundreds = 47?
What ratio correctly compares the measurements 10,000 cm to 1000 m? Drag and drop the appropriate numbers into the boxes to show the ratio in the simplest form.
Evaluate 11x-4 when x=_4