Answers
x = 3.6 units
Step-by-step explanation:First, some definitions before working the problem:
The three standard trigonometric functions, cosine, tangent, and sine, are defined as follows for right triangles:
[tex]sin(\theta)=\dfrac{opposite}{hypotenuse}[/tex]
[tex]cos(\theta)=\dfrac{adjacent}{hypotenuse}[/tex]
[tex]tan(\theta)=\dfrac{opposite}{adjacent}[/tex]
One memorization tactic is "Soh Cah Toa" where the first capital letter represents one of those three trigonometric functions, and the "o" "a" and "h" represent the "opposite" "adjacent" and "hypotenuse" respectively.
The triangle must be a right triangle, or there wouldn't be a "hypotenuse", because the hypotenuse is always across from the right angle.
Working the problem
For the given triangle, the right angle is in the top right, so the side on the bottom left is the hypotenuse.
We know the angle in the lower right corner (angle S), so the side touching it (side ST) with unknown length is the adjacent side. (notice that the points that form the side include the vertex of the angle -- so, it's the adjacent side).
For this triangle, the "adjacent" leg is unknown, our "goal to find" side. Additionally, the "hypotenuse" is known.
Therefore, the two sides of the triangle that are known or are a "goal to find" are the "adjacent" & "hypotenuse".
Out of "Soh Cah Toa," the part that uses "a" & "h" is "Cah". So, the desired function to use for this triangle is the Cosine function.
[tex]cos(\theta)=\dfrac{adjacent}{hypotenuse}[/tex]
[tex]cos(69^o)=\dfrac{x}{10}[/tex]
To isolate "x", multiply both sides by 10...
[tex]10*cos(69^o)=x[/tex]
Make sure your calculator is set to degree mode, and calculate:
[tex]10*(0.3583679495453...)=x[/tex]
[tex]x=3.583679495453...[/tex] units
Rounded to the nearest tenth...
x = 3.6 units
Related Questions
I would be thankful if you help
Answers
To get a 1 in matrix row 1, column 1 all we have to do is divide the row by 7 which gives us:
[tex]\left[\begin{array}{ccc} 1\frac {-4}{7}&\frac{8}{7} \\-12&7&-13\end{array}\right][/tex]
Understanding MatrixThe solution provided above uses a method of matrix called Echelon.
Echelon matrix is a matrix that has been transformed using row operations into a specific form that makes it easier to solve systems of linear equations.
By applying these row operations, a matrix can be transformed into row echelon form, which is a weaker form of echelon form where the leading non-zero entry of each row is to the right of the leading non-zero entry of the row above it, but not necessarily strictly to the right.
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WILL GIVE BRAINLIEST IF CORRECT
Will report is answer is a guess. Include reasoning behind answer
Answers
The image of point R by rotation is equal to R'(x, y) = (- 4, 7).
How to find the image of a point by rotation
The statement of the problem asks us to find the image of point by a kind of rigid transformation known as rotation, whose formula is:
(x, y) → (x · cos θ - y · sin θ, x · sin θ + y · cos θ)
Where:
x, y - Coordinates of the original point.θ - Angle of rotation, in degrees.If we know that x = 4, y = 7 and θ = - 180°, then the coordinates of the image of point R are:
R'(x, y) = (4 · cos 180° - 7 · sin 180°, 4 · sin 180° + 7 · cos 180°)
R'(x, y) = (- 4, 7)
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Factor Completely
n^4 − 4n^3 − 17n^2 − 36n + 108
Answers
Answer:
It can't be factor
Step-by-step explanation:
n^4 − 4n^3 − 17n^2 − 36n + 108
The GCF of this is 1, so the equation can't be factor.
sum of 213341 & 444233 base 5
Answers
Answer:
1213124
To add 213341 and 444233 in base 5, we need to line up the digits of the two numbers according to their place values, and then add them digit by digit, carrying over to the next place value if the sum of the digits is 5 or greater.
Here's how to do it:
2 1 3 3 4 1
+ 4 4 4 2 3 3
-----------------------
1 2 1 3 1 2 4
Therefore, the sum of 213341 and 444233 in base 5 is 1213124.
What number of hours corresponds to making $41
Answers
13pi/6 terminal point
Answers
The terminal point of 13π/6 is (-√3/2, 1/2) by using unit circle.
What are the quadrants of a graph?The quadrants of a graph are the four sections that divide the coordinate plane. The quadrants are numbered in a counterclockwise direction starting from the positive x-axis.
1. Quadrant I is located in the upper-right section and contains points with positive x and y-coordinates.
2. Quadrant II is located in the upper-left section and contains points with negative x-coordinates and positive y-coordinates.
3. Quadrant III is located in the lower-left section and contains points with negative x and y-coordinates.
4. Quadrant IV is located in the lower-right section and contains points with positive x-coordinates and negative y-coordinates.
The quadrants are useful for determining the signs of coordinates, angles, and for plotting points on a graph.
To find the terminal point of 13π/6, we can start by recognizing that this angle is greater than 2π, which is one complete revolution around the unit circle.
To bring the angle back within one revolution, we can subtract 2π, which gives us 13π/6 - 2π/1 = 13π/6 - 12π/6 = 1π/6.
The angle 1π/6 is in the standard position between the positive x-axis and the first quadrant. The reference angle is π/6, which is the angle between the terminal side and the x-axis.
Since the angle is in the 2nd quadrant, the x-coordinate will be negative and the y-coordinate will be positive. Using the unit circle, we can find the values of sine and cosine at π/6 and then negate the value of cosine since the angle is in the second quadrant.
cos(π/6) = √3/2
sin(π/6) = 1/2
Therefore, the terminal point of 13π/6 is (-√3/2, 1/2).
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evaluate the expression
Answers
After substituting the values as x=3 and y=7, the value of the expression "2x²-y¹+3x⁰" is 14.
In mathematics, an expression is a combination of numbers, variables, and mathematical operations (such as addition, subtraction, multiplication, and division) that can be simplified or evaluated to a numerical value.
To evaluate the expression 2x²-y¹+3x⁰ for x=3 and y=7, we substitute the given values, which are x=3 and y=7 into the expression and simplify:
On substituting the values,
We get,
= 2x² - y¹ + 3x⁰
= 2(3)² - 7¹ + 3(1)
= 2(9) - 7 + 3
= 18 - 7 + 3
= 14
Therefore, when x=3 and y=7, the value of the expression 2x²-y¹+3x⁰ is 14.
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Suppose that the function f is defined as follows.
Answers
A graph of the piecewise function is shown on the coordinate plane in the image attached below.
What is a piecewise-defined function?In Mathematics, a piecewise-defined function can be defined as a type of function that is defined by two (2) or more mathematical expressions over a specific domain.
Generally speaking, the domain of any piecewise-defined function simply refers to the union of all of its sub-domains. By critically observing the graph of the given piecewise-defined function, we can reasonably infer and logically deduce that it is constant over several intervals such as -1 < x ≤ 0.
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If the prism on top of the figure was 4 inches tall instead of 3 inches tall, what would be
the difference between the volume of the original prism on top and the new prism on
top?
Show your work.
Answers
In the figure, TR−→− and TV−→− are secants to circle A.
mRV=99∘
mSU=45∘
What is the measure of ∠RTV?
Answers
The measure of <RTV = 1/2 * (99 - 45) = 27 degrees
What is a Secant of a Circle?Geometrically speaking, a secant is an intersecting line that marks two separate points on the circumference of a circle.
Primarily, it serves as a chord drawn across the diameter which transverses through each endpoint connecting them. The magnitude of the secant is determined by the distance between these intersectional points. This particular element of geometry has various applications in trigonometry, particularly in computing angles and lengths within circles.
According to the Exterior Angle of a Circle Theorem, the measure of an exterior angle of a circle formed by two secants is equal to half the difference of the measures of the intercepted arcs:
Using this theorem,
Thus, the measure of ∠RTV is given as 27
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What is the p value of a right tailed one-mean hypothesis test with a test statistic of z0-1.74
Answers
Answer:
The p-value is the probability of observing a test statistic as extreme or more extreme than the observed one, assuming the null hypothesis is true. In this case, since it is a right-tailed test, the p-value is the area to the right of the observed test statistic Z=1.74 under the standard normal distribution curve.
A metallurgist made two purchases. The first purchase, which cost $1224, included 48 kilograms of an iron alloy and 40 kilograms of a lead alloy. The second purchase, at the same price, cost $507 and included 24 kilograms of the iron alloy and 13 kilograms of the lead alloy. Find the cost per kilogram of the iron and lead alloys. What is the cost of the iron alloy and the lead alloy?
Answers
For the first purchase:
- 48 kilograms of iron alloy and 40 kilograms of lead alloy cost $1224.
- Let x be the cost per kilogram of the iron alloy and y be the cost per kilogram of the lead alloy.
- We can write a system of two equations to represent the cost of the alloys:
```
48x + 40y = 1224
x + y = ?
```
We don't know the total cost per kilogram of both alloys combined, so we'll use a variable to represent it: `x + y = z`.
For the second purchase:
- 24 kilograms of iron alloy and 13 kilograms of lead alloy cost $507.
- We can use the total cost per kilogram of both alloys combined to find the cost of each alloy. We know that the total cost per kilogram is the same for both purchases, so we can write:
```
24x + 13y = 507
```
Now we can solve the system of equations:
```
48x + 40y = 1224
24x + 13y = 507
```
Multiplying the second equation by 2 to get the same number of x's as the first equation:
```
48x + 26y = 1014
48x + 40y = 1224
```
Subtracting the first equation from the second:
```
14y = 210
y = 15
```
Substituting y into the first equation:
```
48x + 40(15) = 1224
48x = 624
x = 13
```
So the cost per kilogram of the iron alloy is $13 and the cost per kilogram of the lead alloy is $15.
To find the cost of each alloy:
- For the first purchase, the cost of the 48 kilograms of iron alloy is 48 x $13 = $624, and the cost of the 40 kilograms of lead alloy is 40 x $15 = $600.
- For the second purchase, the cost of the 24 kilograms of iron alloy is 24 x $13 = $312, and the cost of the 13 kilograms of lead alloy is 13 x $15 = $195.
So the total cost of the iron alloy is $624 + $312 = $936, and the total cost of the lead alloy is
!
The Regular polygon has the following measures.
a=7√3cm
s=14 cm
Segment a is drawn from the center of the polygon perpendicular to one of its sides.
What is the vocabulary term for segment a?
what is the area of the polygon?
Round to the nearest tenth and include correct units
Answers
The vocabulary for a is called the apothem
The area of the regular polygon is [tex]2419.68 cm^2.[/tex]
How to solve for areaa = 7√3 cm
s = 14 cm
The perimeter of the polygon is:
P = ns
where n is the number of sides of the polygon. We can find n using the formula:
[tex]n = 360 / (180 - (360 / 2n))[/tex]
where n is the number of sides. Substituting the given value for s, we get:
[tex]n = 360 / (180 - (360 / 2*7)) = 14[/tex]
Therefore, the polygon has 14 sides.
a = [tex]\sqrt{31.820 cm)^2 - (14 cm/2)^2}[/tex])
= 24.615 cm
A = (1/2) * apothem * perimeter
[tex](\frac{1}{2} ) * 24.615 cm * 196 cm \\=\\ 2419.68 cm^2[/tex]
Therefore, the area of the regular polygon is [tex]2419.68 cm^2.[/tex][tex]2419.68 cm^2.[/tex]
In summary,
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5. Which box-and-whisker plot represents this set of data? (1 point)
90, 98, 75, 84, 89, 91, 70, 81, 93, 84, 100
Answers
Lin has 9 plates she puts 1/4 of a sandwich on each plate which expression represents the sandwiches in the situation
A. 9x4
B. 9x1/4
C. 4x9
D. 4x1/9
Answers
Explanation:
It says there are 9 PLATES
she puts 1/4 of a sandwhich on EACH!
meaning that each plate of the 9 plates have 1/4.
can someone please helppp
Answers
Answer:
6 presents / minute
Step-by-step explanation:
We can represent the given information in a ratio:
amount of present wrapped : minutes it took to wrap
2/3 : 1/9
Then, we can multiply both sides by 9 (the reciprocal of 1/9) so that the right side of the ratio is 1 minute.
presents : minutes
2/3 : 1/9
× 9 × 9
6 : 1
So, Patricia can wrap 6 presents in 1 minute.
Please solve this for me!
Answers
Answer: 1; 520/9 number 2: 9/2 number 3: d number 4:d number 5: 151.7
Step-by-step explanation:
Suppose that the functions f and g are defined as follows.
Answers
Answer:
[tex]\dfrac{f}{g}(x) = \boxed{\dfrac{7}{x\left(x-3\right)}\\\\}[/tex]
Domain of [tex]\dfrac{f}{g}: \boxed{\:\left(-\infty \:,\:0\right)\cup \left(0,\:3\right)\cup \left(3,\:\infty \:\right)}[/tex]
Step-by-step explanation:
Given
[tex]f(x) = \dfrac{7}{x} , g(x) = x - 3[/tex]
[tex]\dfrac{f}{g} = \dfrac{f(x)}{g(x)} = \dfrac{7}{x} \div x - 3\\\\= \dfrac{7}{x} \times \dfrac{1}{x-3}\\\\ = \dfrac{7}{x\left(x-3\right)}[/tex]
To find the domain of
[tex]\dfrac{f}{g} = \dfrac{7}{x\left(x-3\right)}[/tex]
note that this function is defined everywhere in the range (- ∞, ∞) except for x = 0 and x = 3
At these two points, the function is undefined since the denominator becomes 0 and division by 0 is undefined
Therefore the domain consists of three parts expressed in inequality and interval forms
-∞ < x < 0 (-∞, 0)
0 < x < 3 (0, 3)
3 < x < ∞ (3, ∞)
Therefore the domain is obtained by combining these three intervals
- ∞ < x < 0 or 0 < x < 3 or x > 3
In interval notation with union:
[tex]\:\left(-\infty \:,\:0\right)\cup \left(0,\:3\right)\cup \left(3,\:\infty \:\right)[/tex] ANSWER
Tamika is seeking a loan with a simple
Answers
The interest that Tamika will be charged in interest after 24 months of borrowing $5,000 at 8% simple interest per year is $800.
What is simple interest?Simple interest is the interest system that computes interest only on the principal for each period.
Unlike the compound interest system, simple interest does not charge interest on accumulated interest and the principal.
The principal loan amount borrowed by Tamika = $5,000
The interest rate per year = 8%
The loan period = 24 months = 2 years (24/12)
Simple Interest = Principal x Rate x Period
= $800 ($5,000 x 8% x 2)
Thus, for borrowing $5,000 for 24 months of 2 years, Tamika would pay a simple interest of $800.
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Complete Question:Tamika is seeking a loan with a simple interest rate of 8% per year. If she wants to borrow $5,000, then how much will she be charged in interest after 24 months?
Help please
Expand the logarithm as much as possible
logy^10
Answers
Answer: 2.303
Explanation: In image
Directions - Answer the questions based on the following scenario and graph.
Jim and Cassie are both saving money each week in order to buy an awesome Bulls snapback hat (and leave the price stickers on it, of course). The hat costs $27.
Answers
Jim's rate of savings (slope): 3
Cassie's rate of savings (slope): 3
Jim's y intercept: 3
Cassie's y intercept: 12
Jim's Savings Equation: y = 3x + 3
Cassie's Savings Equation: y = 3x + 12
Number of weeks it will take to Cassie to save $27: 5
Number of weeks it will take to Jim to save $27: 8
Yes, Jim and Cassie's rates parallel.
Cassie will be able to buy the hat first.
We know that the slope intercept form of a straight line is,
y = mx + c, where m is the slope of the line and c is the y intercept.
For the straight line for Cassie:
The line passing through the points (0, 12) and (1, 15).
So the slope = (15 - 12)/(1 - 0) = 3
The y intercept is = 12.
Equation of the straight line is: y = 3x + 12 ....... (i), where y represents earning in dollars and x represents the time in weeks.
For the straight line for Jim:
The line passing through the points (0, 3) and (1, 6).
So the slope = (6 - 3)/(1 - 0) = 3
The y intercept is = 3
Equation of the straight line is: y = 3x + 3 .......... (ii), where y represents earning in dollars and x represents the time in weeks.
Since the slope of both are equal so the rates of both are parallel.
Substituting the value y = 27 in equation (i) and (ii) we get,
equation (i): 3x + 12 =27
3x = 27 - 12
3x = 15
x = 15/3
x = 5
So Cassie needs 5 weeks to save $27.
Equation (ii): 3x + 3 = 27
3x = 27 - 3
3x = 24
x = 24/3
x = 8
So Jim needs 8 weeks to save $27.
Hence Cassie will be able to buy the hat first.
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The question is incomplete. The complete question will be -
Suppose that the function is defined as follows.
Answers
Answer:
Step-by-step explanation:
what is the area of a circle with the diameter of 22 in
Answers
Answer:380.1 square inches
Step-by-step explanation:Area of a circle in terms of diameter: Area = π· (d2) 2 = 3.14· (222) 2 = 3.14· (11) 2 = 380.1 square inches (*)
blank g = blank kg =3/10kg
Answers
It should be noted that 3/10 kg to grams will be 300 grams.
How to convert the valueTo convert 3/10 kg to grams (g), we can use the following conversion factor:
1 kg = 1000 g
Therefore:
3/10 kg = (3/10) x 1000 g = 300 g
Hence, 3/10 kg is equal to 300 grams (g).
In conclusion, it should be noted that 3/10 kg to grams will be 300 grams.
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Based on the results, whaBased on the results,, what is the probability of needing fewer than 4 rolls to get doublest
Answers
The probability of needing fewer than 4 rolls to get doubles is 13/25.
What is Probability?Probability is a branch of mathematics that deals with the likelihood of something happening. It is used in many areas such as finance, engineering, and even gambling. Probability is the measure of how likely an event is to take place. This is usually expressed as a number between 0 and 1, where a 0 indicates an impossible event, and a 1 indicates an event that is certain to happen. Probability is an important component of decision making, as it allows us to calculate the chances of different outcomes.
This can be calculated by using the binomial probability formula. The binomial probability formula is used to calculate the probability of a certain number of successes in a certain number of trials. In this case, the number of successes is 2 (the number of doubles required to win the game) and the number of trials is 4 (the maximum number of rolls necessary to win the game).
Using the formula P(x) = nCx * pˣ* qⁿ⁻ˣ, where n is the number of trials, x is the number of successes, p is the probability of success and q is the probability of failure, we can calculate the probability of needing fewer than 4 rolls to get doubles as follows:
P(2) = 4C2 * (1/2)² * (1/2)⁴⁻² = 4 * ( 1/4 ) * (1/4) = 1/4
P(1) = 4C1 * (1/2)¹ * (1/2)⁴⁻¹= 4 * (1/2) * (1/2) = 1/4
The total probability of needing fewer than 4 rolls to get doubles is the sum of the probabilities of needing 1 or 2 rolls to get doubles, which is 1/4 + 1/4 = 1/2, or 13/25.
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Complete questions as follows-
Based on the results, what is the probability of needing fewer than 4 rolls to get doubles? 13/25.
Suppose that you are taking a course where the total class grade is the weighted average of your homework, worksheets, quizzes and tests.
The homework is worth 15% of the course grade, worksheets are worth 20% of the course grade, the quizzes are worth 25% of the course grade, and tests are worth 40% of the course grade. To get a B in the course, you must have an overall average of at least 80%.
Your current grades in each category are:
Homework =
74
%, Worksheets =
76
%, and Quizzes =
77
%.
What is the minimum test average you need to get a B in the course?.
Your answer is:
% (Round to at least 1 decimal place)
Answers
To calculate your overall average, we need to first find the weighted average of your homework, worksheets, and quizzes:
Weighted average = (0.15 x 74%) + (0.20 x 76%) + (0.25 x 77%)
= 11.1% + 15.2% + 19.25%
= 45.55%
Now we can set up an equation to solve for the minimum test average needed to get a B:
0.4555(100%) + 0.40(T) = 80%
45.55 + 0.40T = 80
0.40T = 34.45
T = 86.125
Therefore, you need to get at least a 86.125% average on your tests to get a B in the course. Rounded to one decimal place, the minimum test average you need is 86.1%.
pls help me on algebra here is screenshot
Answers
Answer:
The answer to the question provided is option 2.
Write 3.5 as a mixed number and as an improper fraction.
Write your answers in simplest form.
Answers
3.5= 35/10
35/10= 7/2
which is equal to 3 1/2
Therefore: 3 1/2 and 7/2
If the profit function for a product is
P(x) = 2400x + 105x^2 − x^3 − 167,000
dollars, selling how many items, x, will produce a maximum profit?
x = items
Answers
Selling 80 items will produce maximum profit if the profit function is [tex]P(x) = 2400x + 105x^2 - x^3 - 167,000[/tex].
What is the value of x that produces maximum profit?To find value of x that produces maximum profit, we must get critical points of the profit function and determine which one corresponds to a maximum.
The profit function is given as:
[tex]P(x) = 2400x + 105x^2 - x^3 - 167,000[/tex]
Taking the derivative of P(x) with respect to x, we get:
[tex]P'(x) = 2400 + 210x - 3x^2[/tex]
Setting P'(x) equal to zero and solving for x, we get:
[tex]0 = 2400 + 210x - 3x^2\\3x^2 - 210x - 2400 = 0\\x^2 - 70x - 800 = 0\\(x - 80)(x + 10) = 0[/tex]
Here, the critical points are x = 80 and x = -10.
To determine one that corresponds to a maximum, we can use the second derivative test. Taking the derivative of P'(x), we get:
[tex]P''(x) = 210 - 6x[/tex]
Evaluating P''(80), we get:
[tex]P''(80) = 210 - 6(80)\\P''(80) = 210 - 420\\P''(80) = -330[/tex]
Since P''(80) is negative, the critical point x = 80 corresponds to a maximum. So, selling 80 items will produce maximum profit.
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Can yall help me with this pls
Answers
Answer:
x=6.4
Step-by-step explanation:
2/3.2 = 4/x
2x=4(3.2)
2x=12.8
x=6.4