Final answer:
To determine the lengths of the legs of a right triangle with a hypotenuse of 7 inches and an acute angle of 50°, we use the trigonometric functions cosine and sine. The adjacent leg (A) is approximately 4.5 inches and the opposite leg (B) is approximately 5.4 inches, both to the nearest tenth.
Explanation:
The student asked: "What are the lengths of the legs of a right triangle if one of the acute angles is 50° and the hypotenuse is 7 inches?"
To find the lengths of the legs of a right triangle, we can use trigonometry. The cosine of an angle in a right triangle is equal to the adjacent leg divided by the hypotenuse, and the sine of an angle is equal the opposite leg divided by the hypotenuse.
Since we know the hypotenuse (7 inches) and one acute angle (50°), we can find:
the length of the opposite leg (leg B) using sine (sin(50°) = leg B / 7 inches).
By solving these equations:
leg A = cos(50°) × 7 inches
leg B = sin(50°) × 7 inches
After calculating, we find:
leg A ≈ 4.5 inches (to the nearest tenth)
leg B ≈ 5.4 inches (to the nearest tenth)
The domain of a relation is
the output (y) values of the relation
the input (x) values of the relation
a set of points that pair input values with output values
x and y values written in the form (x, y)
Answer:
the input (x) values of the relation
Step-by-step explanation:
(a) No, The output (y) values of the relation are called Range. So it is the wrong option.
(b) Yes, the input (x) values of the relation are called Domain. Thus, it is the correct option.
(c) No, it is not a definition of Domain. Thus, this is an incorrect option.
(d) No, it is not a definition of Domain. It is called the cartesian point. Thus it is also an incorrect option.
Further,
The Domain is the all possible input values of a function that gives defined values.
The Range is the all defined output values that we get from a function (or y).
If one honey bee makes 1/2 teaspoon of honey during its lifetime, how many honey bees are needed to make 1/2 teaspoon of honey
Lourenço analyzed prices of laptop
computers based on the speed of the
processor. He calculated the trend line to
be y = 101x + 207.85, where x is the
speed of the processor in gigahertz and
y is the price. Which amount below is
closest to the price of a laptop with a
processor speed of 2.5 gigahertz?
A. $309
B. $455
C. $460
D. $620
(Please show your work because I'm beyond confused
What, roughly, is the percent uncertainty in the volume of a spherical beach ball whose radius is r = 2.86 plus or minus .09 m?
Final answer:
To calculate the percent uncertainty in the volume of a spherical beach ball when the radius is uncertain, you multiply the square of the radius by four (surface area), by the uncertainty in the radius, and then compare this value to the total volume. The percent uncertainty is found to be approximately 2.62%.
Explanation:
To determine the percent uncertainty in the volume of a spherical beach ball with a radius of 2.86 1 0.09 meters, one must first calculate the volume's uncertainty, then relate this to the total volume, and finally convert this relationship into a percentage.
The formula for the volume of a sphere is [tex]V = (4/3)\pi(r^3)[/tex]. Since volume is proportional to the cube of the radius, any uncertainty in the radius dramatically affects the volume uncertainty. Using a function for the volume V(r) and applying the approximation for small changes in r, we have:
[tex]V = (4/3)\pi(r^2))(r)[/tex]
For a radius of 2.86 meters and an uncertainty of 0.09 meters, the uncertainty V in volume is 170 [tex]cm^3[/tex]. The volume is approximately V = [tex](4/3)(3.14)(2.86^3)[/tex] = 6538 [tex]cm^3[/tex]. Therefore, the volume expressed with its uncertainty is [tex]6500 \pm170[/tex] [tex]cm^3,[/tex] rounded to avoid false precision.
To find the percent uncertainty:
Convert the uncertainty to the same units as the ball's volume if needed (here both are in cm^3).
Divide the uncertainty by the volume: (170/6500) x 100%.
The percent uncertainty is approximately 2.62%.
Graph the following piecewise function and then find the range.
Answer:
The correct option is 3.
Step-by-step explanation:
The given piecewise function is
[tex]f(x)=\begin{cases}3x^2+1 & \text{ if } -4<x<6 \\ 6 & \text{ if } 6\leq x<9 \end{cases}[/tex]
Range is the set of output or y values.
The given function for 6 ≤ x < 9 is
[tex]f(x)=6[/tex]
It is a constant function, the value of function is 6 for all values of x.
Range = 6
The given function for -4 < x < 6 is
[tex]f(x)=3x^2+1[/tex] .... (1)
It is a quadratic function.
The vertex form of a quadratic function is
[tex]f(x)=a(x-h)^2+k[/tex] ....(2)
Where (h,k) is vertex and a is constant.
From (1) and (2), we get a=3,h=0,k=1.
The vertex of this function is (0,1), it means the range of this function is greater than or equal to 1. But this function is only defined for -4 < x < 6.
[tex]f(-4)=3(-4)^2+1=49[/tex]
[tex]f(6)=3(6)^2+1=109[/tex]
The maximum value of the maximum value of the function is 109 at x=6. Since 6 is not included in the interval -4 < x < 6, therefore 109 is not included in the range.
Range = [1,109)
When we combined the range of both functions we get
Range = [1,109)
Therefore the correct option is 3.
If the base of a square pyramid is 9 centimeters, and it has a volume of 324 cubic centimeters, what is the height of the pyramid?
V=1/3bh
324=1/3(9)* h
324=3h
h=324/3
h=108
height is 108cm
Answer: 12 cm
The other guy that answered didn't do it correctly, he didn't find the height. You have to do:
1/3 (9 • 9) (x) = 324
1/3 • 81x = 324
27x = 324
x = 12
Trust me, I just finished my quiz and got ths answer right.
The sum of twice a number and 7
Sarah decides to take her six-year-old son to the circus the price for the child ticket is $4.75 dollars Less in the price for the adult ticket if you represent their price for the child ticket using the variable X how would you write the algebraic expression for an adult ticket price?
How can I do this with the function (x+2)/x-3
Create a rational function with a linear binomial in both the numerator and denominator.
Part 1. Graph your function using technology. Include the horizontal and vertical asymptotes and the x- and y-intercepts on your graph. Label the asymptotes and intercepts.
Part 2. Show all work to identify the vertical asymptote, the x-intercepts, and the y-intercept.
A state’s license plates consist of 3 letters followed by 3 numbers. What is the probability of randomly generating a license plate that reads AHW 304?
Answer: [tex]\frac{1}{17576000}[/tex]
Step-by-step explanation:
Given: A state’s license plates consist of 3 letters followed by 3 numbers.
Since, there are 26 letters in English alphabet and 10 digits in set of numbers(0,1,....,9).
Then , the total number of license plates can be generated (if repetition is allowed)=
[tex]26\times26\times26\times10\times10\times10=17576000[/tex]
In AHW304, each alphabet and number occurs only once, the number of license plate with this = 1
Now, the probability of randomly generating a license plate that reads AHW 304=[tex]\frac{1}{17576000}[/tex]
Answer:
1/17,576,000
Step-by-step explanation:
You need to have a password with 55 letters followed by 33 odd digits between 00 and 99, inclusive. if the characters and digits cannot be used more than once, how many choices do you have for your password?
Let f(x) = 2x − 6. Solve f−1(x) when x = 2. (1 point) explanation please! algebra 2 makes no sense to me!
Find the value of cos θ for the angle shown. A line is drawn from the origin through the point four comma negative square root of thirty-three. The angle theta is given as the measurement from the positive x axis counterclockwise to the line.
cos θ = seven-fourthsAnswer
Cos θ = 4/7
Explanation
The angle θ is in the 3rd quadrant. So, it is positive.
cos θ = adjacent / hypotenuse
hypotenuse = √(4² + (√33)²)
= √(16 + 33)
= √47
= 7
Cos θ = 4/7
Answer:
Step-by-step explanation:
cos 0= 4/7
reason: i took the test
Solve 3x2 + 2x + 7 = 0. Round solutions to the nearest hundredth. (5 points)
x ≈ −1.90 and x ≈ 1.23
x ≈ −1.23 and x ≈ 1.90
x ≈ −0.44 and x ≈ −3.56
No real solutions
Answer:
The answer is No Solutions Look Below
Step-by-step explanation:
A license plate comprised of 3 letters followed by 3 numbers is to be chosen (repetition is allowed). If the first letter cannot be a "Z", how many different ways can this occur? In your answer, include the set up and calculations for the license plate.
if a circle is inscribed in a triangle, the center of the circle is called the _____ of the triangle.
A. radius
B. incenter
C. circumcenter
Answer:
The correct answer to the following question will be Option B (Incenter).
Step-by-step explanation:
The middle of the circle which is carved in a triangle is the triangle incenter, the point where the triangle angle bisectors cross.
There are following steps to construct an inscribed circle in a triangle are as follows:
Step 1: Create the incenter.
Step 2: Construct a line that passes through incenter, perpendicular to one side of the triangle. The segment which connects the incenter with the triangle intersection point and the perpendicular line is the circle radius.
Step 3: Build a centered circle at the incenter with radius spotted in step 2.
Two parabolas are the graphs of the equations $y=2x^2-10x-10$ and $y=x^2-4x+6$. give all points where they intersect. list the points in order of increasing $x$-coordinate, separated by semicolons.
Answer:
(-2, 18) and (8, 38)
Step-by-step explanation:
First, set the two equations equal to each other to get $2x^2-10x-10=x^2-4x+6$. Combine like terms to get $x^2-6x=16$. To complete the square, we need to add $\left(\dfrac{6}{2}\right)^2=9$ to both sides, giving $(x-3)^2=16+9=25$.
So we have $x-3=\pm5$. Solving for $x$ gives us $x=-2$ or $8$. Using these in our original parabolas, we find the points of intersection to be $\boxed{(-2,18)}$ and $\boxed{(8,38)}$.
Credit: AoPs
May you help me please ? Thanks!
given that (6 3) is on the graph of f(x) find the corresponding point for the function f(-1/2x)
Answer:
this answer is wrong on plato, trust me
Step-by-step explanation:
We need to find the corresponding y-coordinate for x = -3. Unfortunately, since we don't have additional information about the function f(x), we cannot determine the value of f(-3) and provide the corresponding point.
To find the corresponding point for the function f(-1/2x) when (6, 3) is on the graph of f(x), we need to substitute the x-coordinate of (6, 3) into the function -1/2x and determine the resulting y-coordinate.
Given that (6, 3) is on the graph of f(x), it means that f(6) = 3.
Now let's substitute -1/2x into the function:
f(-1/2x) = f(-1/2 * 6) = f(-3)
Therefore, we need to find the corresponding y-coordinate for x = -3. Unfortunately, since we don't have additional information about the function f(x), we cannot determine the value of f(-3) and provide the corresponding point.
In summary, without more information about the function f(x), we cannot find the corresponding point for the function f(-1/2x) when (6, 3) is on the graph of f(x).
To know more about function:
https://brainly.com/question/4514680
#SPJ6
In a group of students 25% are enrolled in physics, 23% in sociology, 17% in chemistry, 14% in political science, 12% in anthropology, and 9% in math. you are going to select an individual from the group of students. the probability of event a is equivalent to the probability that you select someone who studies social science (sociology, political science and anthropology) or physics. what is the probability of the event a’s complement?
The probability of event A's complement, which signifies selecting a student not studying social science or physics, is 26%.
The probability of selecting someone who studies social science (sociology, political science, and anthropology) or physics is the sum of the individual probabilities for those subjects: 23% (sociology) + 14% (political science) + 12% (anthropology) + 25% (physics) = 74%. To find the probability of the event A's complement, which is selecting a student not studying any of these subjects, we subtract the probability of event A from 100%: 100% - 74% = 26%. Therefore, the probability of selecting a student not enrolled in any of the mentioned social science subjects or physics is 26%.
What is the discriminant of the polynomial below? 4x2 - 20x + 25
The discriminant of the given polynomial is 0, indicating one real root.
Explanation:The discriminant of a quadratic equation is a value that can be used to determine the nature of the solutions (roots) of the equation. It is calculated using the formula b^2 - 4ac, where a, b, and c are the coefficients of the equation.
In the given polynomial, the coefficients are a = 4, b = -20, and c = 25. Plugging these values into the formula, we get: (-20)^2 - 4(4)(25) = 400 - 400 = 0.
Since the discriminant is equal to zero, the polynomial has one real root.
if N is an acute angle and sin N=12over13, evaluate cos N and tan N.
A brick oven has an opening as shown. What is the area of the entire opening?
Answer:
[tex]13.93ft^{2}[/tex]
Step-by-step explanation:
The area of the opening will be the sum of the area of the two shapes shown which are rectangle and half ellipse:
[tex]Area =Area_{rectangle}+\frac{1}{2} Area_{Ellipse}[/tex]
The area of the rectangle is:
[tex]Area_{Rectangle}=a*b[/tex]
where:
[tex]a=4ft\\b=2\frac{1}{2}ft[/tex]
we replace values(we convert the mixed fraction to improper fraction by multiplying the whole number part by the fraction's denominator, then add that to the numerator then write the result on top of the denominator.):
[tex]Area_{Rectangle}=4*2\frac{1}{2} =4*\frac{5}{2}=10[/tex]
The area of the ellipse is:
[tex]Area_{Ellipse}=a*b*\pi[/tex]
where:
[tex]a=Radius1=1\frac{1}{4}ft\\b=Radius2=2ft\\[/tex]
Radius2 will be half the side of the rectangle
[tex]Radius2=\frac{4}{2}=2[/tex]
we replace the values:
[tex]Area_{Ellipse}=1\frac{1}{4} *2*\pi=\frac{5}{4}*2*\pi=\frac{5}{2}\pi =7.85[/tex]
we calculate now the total area:
[tex]Area =Area_{rectangle}+\frac{1}{2} Area_{Ellipse}\\Area=10+\frac{1}{2}(7.85)=10+3.93=13.93ft^{2}[/tex]
What is the fifth term in the expansion of (3x - 3y)7?
__ x3y4
Answer:
76545
Step-by-step explanation:
got it write on edge :)
Please help me round 34,699 to the nearest ten thousand
which situation involving raul's Bank account would be modeled by a positive number?
A.Raul deposited his paycheck.
B.Raul wrote a check to his grandmother
C.Raul withdrew cash from an ATM
D.Raul paid for groceries with his debit card.
positive means add
so it would be a deposit into the account
so A is the correct answer
Find a function in the form of y = f(x) for the parametric equation:
x = 2t
y = t² - 6t
The gold leaf on your necklace is 0.000045 of an inch thick. How do you write 0.000045 in scientific notation?
The diagonal of the rectangle is 13 inches, and the side lengths of the triangles are Pythagorean triples. To the nearest tenth, what is the area of the shaded part of the figure?
Select all of the coefficients in the expression.
12xy3 + 2x5y + 4x5y2 + 7x5y.
2
3
4
5
7
12
2,4,7,12 for edgynuity. the way you can tell is because you look at the front. 12xy3 + 2x5y + 4x5y2 + 7x5y. the 12 1 4 7 are the coefficients.
Final answer:
The coefficients in the algebraic expression are 12, 2, 4, and 7, which are the numerical multipliers of the variable terms.
Explanation:
The coefficients in the expression 12xy^3 + 2x^5y + 4x^5y^2 + 7x^5y are the numerical factors that multiply the variables x and y in each term of the polynomial expression. The coefficients in this expression are 12, 2, 4, and 7. These are the numbers in front of the variable terms and not the exponents or the variables themselves.