The six trigonometric functions' values for angle B in this right triangle are as follows: Tan(B) = 8/15 CSC(B) = 17/8 Sin(B) = 8/17 Cos(B) = 15/17 Tan(B) = 8/15 (rationalized denominator)
cot(B) = 15/8 sec(B) = 17/15.
The length of the unknown side, which in this case is the hypotenuse c, can be determined using the Pythagorean theorem:[tex]c2 equals a2 + b2; c2 equals 82 + 152; c2 equals 64 + 225^2 = 289 \sc = √289 \sc = 17[/tex]
Thus, the hypotenuse's length is 17.
We must first get the measure of angle B before we can determine the values of the six trigonometric functions for that angle. Since angle C is a right angle and the total of the angles in a triangle is 180 degrees, we can calculate angle B's measure as follows:
angle B is equal to 90 times angle A, or 90 times angle B.
For now, since we lack sufficient data to estimate the size of angle A, angle B will be specified in terms of an unknowable angle. We are still able to calculate the six trigonometric functions for angle B using the ratios of the triangle's side lengths.
B = opposite/hypotenuse = a/c = 8/17;
B = adjacent/hypotenuse = b/c = 15/17;
B = opposite/adjacent = a/b = 8/15;
B = hypotenuse/opposite = c/a = 17/8;
B = cos(B) = (rationalized denominator)
Hypotenuse/nearby = c/b = 17/15; adjacent/opposite = b/a = 15/8; sec(B) = c/b = 17/15; cot(B) = b/a = 15/8.
For angle B in this right triangle, the values of the six trigonometric functions are as follows:
sin(B) = 8/17
cos(B) = 15/17
tan(B) = 8/15
csc(B) = 17/8 (rationalized denominator)
sec(B) = 17/15
cot(B) = 15/8
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PLEASE HELPPPP
A soccer coach determines that there is a 50% chance that a star player, Ralph,
will play in a tournament.
• The probability that another star player, Dan, will play is 0.48.
• The probability that both Ralph and Dan will play in the tournament is 0.25.
Answer50.5
ffffffffffffffff
As part of a study of grade inflation, you want to estimate the mean grade point average of all current college students in
the U.S. All grade point averages are to be standardized for a scale between 0 and 4. How many grade point averages must be
obtained so that the sample mean is within 0.2 of the population mean? Assume that a 99% confidence level is desired. Also
assume that a pilot study showed that the population standard deviation is estimated to be 0.79.
10352 grade point averages must be obtained. The solution has been obtained by using the concept of sample size.
What is sample size?
The sample size is the number of observations utilised to derive estimates for a certain population. By taking a sample from the population, the sample size was established. Sampling is the practise of selecting a subset of the population to infer characteristics about the complete population.
We know that for 99% confidence, the z- score is 2.5758
So, using this we get
N = (z * σ/E)²
N = (2.5758 * 0.79/0.02)²
N = 10351.86
Hence, 10,352 grade point averages must be obtained so that the sample mean is within 0.2 of the population mean.
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Find the HCF and LCM for these numbers using prime factors 60 and 150
Answer:
Step-by-step explanation:
prime factorization of 60= 2*2*3*5 = [tex]2^{2} * 3^{1} * 5^{1}[/tex]
prime factorization of 150 = 2*3*5*5 = [tex]2^{1} * 3^{1} * 5^{2}[/tex]
greatest (highest) common factor (divisor), calculated
HCF = 2*3*5 = 30
For LCM, when you compare the prime factorization of these two numbers, you want to look for the highest power that each prime factor is raised to
LCM = [tex]2^{2} * 3^{1} * 5^{2}[/tex]=300
How do i answer this
Answer:
6.21
Step-by-step explanation:
tha ratio 2.97/2.2 has to be the same as x/4.6.
so the new lenght, x, is 4.6×(2.97/2.2)
[tex]\stackrel{ \textit{ratio of (L)ength to (w)idth of old phone} }{\stackrel{L}{2.2}~~ : ~~\stackrel{w}{4.6}\qquad \implies \qquad \cfrac{L}{w}~~ = ~~\cfrac{2.2}{4.6}} \\\\\\ \stackrel{\textit{Length of new phone}}{2.97}\qquad \stackrel{\textit{keeping the same ratio}}{\cfrac{2.97}{w}~~ = ~~\cfrac{2.2}{4.6}} \\\\\\ (2.97)(4.6)=2.2w\implies \cfrac{(2.97)(4.6)}{2.2}=w\implies \stackrel{ new~width }{6.21=w}[/tex]
Solve this system of equations by subsitution {y= 2x +3
3x + 2y = 12
Find Monthly Payment on a Loan
Mila's monthly mortgage payment would be approximately $4,658.99.
Describe Interest?In finance, interest refers to the cost of borrowing money or the return earned on an investment. It is usually expressed as a percentage of the amount borrowed or invested and is typically calculated on an annual basis.
For borrowing money, interest is the cost that the borrower has to pay to the lender for the privilege of using their funds. The lender earns interest on the loan as compensation for lending their money to the borrower. The interest rate on a loan is determined by a variety of factors, including the borrower's creditworthiness, the term of the loan, and prevailing market conditions.
For investments, interest is the return earned by an investor on their principal amount. For example, when someone deposits money in a savings account, they earn interest on that money. The interest rate on savings accounts and other investments is typically determined by the prevailing market conditions and the financial institution offering the investment.
Interest can be calculated in different ways, including simple interest and compound interest. Simple interest is calculated on the original principal amount, while compound interest is calculated on the principal amount plus any accumulated interest. The frequency at which interest is compounded, such as monthly or annually, can have a significant impact on the total amount of interest earned or paid.
Overall, interest plays a critical role in finance and can have a significant impact on the cost of borrowing money or the return earned on an investment.
To calculate Mila's monthly mortgage payment, we can use the formula for a fixed-rate mortgage:
M = P * (r * (1 + r)^n) / ((1 + r)^n - 1)
where:
M = monthly mortgage payment
P = loan amount
r = monthly interest rate
n = number of payments (total number of years * 12)
Plugging in the given values, we get:
M = 730000 * (0.00325 * (1 + 0.00325)^(2012)) / ((1 + 0.00325)^(2012) - 1)
Simplifying this expression using a calculator, we get:
M ≈ $4,658.99
Therefore, Mila's monthly mortgage payment would be approximately $4,658.99.
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Select the correct answer.
Aaron made a picture frame with the dimensions shown in the figure. What is the area of the picture frame?
A bigger outer rectangle has sides of 12 cm and 10 cm, and an inner rectangle has sides of 8 cm and 6 cm.
A.
120 square centimeters
B.
88 square centimeters
C.
72 square centimeters
D.
64 square centimeters
The area of the picture frame is 72 cm². Thus, option C is correct.
What is area?Area is a quantity that measures the size of a two-dimensional surface or shape. It is expressed in square units such as square centimetres (cm²), square metres (m²) or square kilometres (km²).
Area is used to describe the size of a garden, a house, a room, a city and much more. It can also be used to calculate the amount of material required for a project, such as paint, carpet or tiles. Knowing the area of a shape can help to calculate costs, and to make sure that enough materials are ordered.
The area of the picture frame will be given by:
Area = (area of picture and frame)-(area of pictures)
area of picture and frame is given by:
A1=Length × width
A1 = 10 × 12
= 120cm²
area of the picture will be:
A2=8 × 6 = 48 cm²
thus the area of the frame will be:
A = A1 - A2
A = 120 - 48
A = 72cm²
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Complete question:
Select the correct answer.
Aaron made a picture frame with the dimensions shown in the figure. What is the area of the picture frame?
A bigger outer rectangle has sides of 12 cm and 10 cm, and an inner rectangle has sides of 8 cm and 6 cm.
A. 120 square centimeters
B. 88 square centimeters
C. 72 square centimeters
D. 64 square centimeters
What is the hexadecimal expansion of (ABC)16 + (2F5)16
Questions 19 and 20 refer to the following information.
Every Saturday morning, three friends meet for breakfast at 9:00 AM. Andrea walks, Kellan bikes, and Joelle
drives.
19. Last Saturday, all three friends were exactly
on time. Andrea left her house at 8:30 AM and
walked at a rate of 3 miles per hour. Kellan
left his house at 8:15 AM and biked at a rate of
14 mph. Joelle left her house at 8:45 AM and
drove an average speed of 35 miles per hour.
How many miles from the restaurant does the
person who traveled the farthest live?
20. Kellan lives 12 miles away from Andrea. On
a different Saturday, Kellan biked at a rate of
15 miles per hour to Andrea's house. The two
then walked to the restaurant at a rate of
2.5 miles per hour, and they arrived five
minutes early. What time did Kellan leave his
house? Enter your answer as three digits and
ignore the colon. For example, if your answer
is 5:30 AM, enter 530.
0000000
Answer:
Question 19: The person who traveled the farthest lives 12 miles from the restaurant, which is the same distance as Kellan.
Question 20: Kellan would have left his house at 8:10 AM in order to arrive at Andrea's house at 8:30 AM and then walk to the restaurant with Andrea at a rate of 2.5 miles per hour, arriving at the restaurant at 8:50 AM, five minutes early. So the answer is 810.
Using the graph given below state the value of lim
The value for the [tex]\lim_{x \to 3^{+}}[/tex]f(x) = 3.
What is limit in graph?A limit in mathematics is the value that a function gets closer to when the input gets closer to a certain value.
A function may get close to two distinct limits. There are two scenarios: one in which the variable approaches its limit by values larger than the limit, and the other by values smaller than the limit.
Given:
We have given the graph, from the graph we can se a red dot.
So, the [tex]\lim_{x \to 3^{+}}[/tex]f(x) = 3
Also, limit is defined as a value that a function approaches the output for the given input values.
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Show that the path given by r(t)=(e" sint,e- cos t, e) intersects the sphere 2y224 once, traveling from outside the sphere to inside as t goes from -oo to oo. I
Answer:
Step-by-step explanation:
We need to show that the path given by r(t) = (e^t sin t, e^(-t) cos t, e) intersects the sphere 2y^2 + 2z^2 = 4 once, traveling from outside the sphere to inside as t goes from -∞ to +∞.
The equation of the sphere is 2y^2 + 2z^2 = 4. To find the intersection points of the path and the sphere, we need to substitute the components of r(t) into the equation of the sphere:
2y^2 + 2z^2 = 4
2(e^(-t) cos t)^2 + 2e^2 = 4
2e^(-2t) cos^2(t) + 2e^2 = 4
e^(-2t) cos^2(t) + e^2 = 2
Multiplying both sides by e^(2t), we get:
cos^2(t) + e^(4t) = 2e^(2t)
We can rewrite this equation as:
e^(4t) - 2e^(2t)cos^2(t) + cos^2(t) - 1 = 0
This is a quadratic equation in e^(2t) with solutions:
e^(2t) = cos^2(t) ± sqrt(cos^4(t) - 4(cos^2(t) - 1))
We want to show that there is only one intersection point, which means we want to show that the discriminant of the quadratic is negative, i.e.:
cos^4(t) - 4(cos^2(t) - 1) < 0
Expanding the left-hand side, we get:
cos^4(t) - 4cos^2(t) + 4 < 0
Simplifying, we get:
(cos^2(t) - 2)^2 < 0
Since the square of a real number is always non-negative, this inequality has no real solutions. Therefore, the discriminant of the quadratic is negative, and there is only one intersection point.
To show that the path travels from outside the sphere to inside as t goes from -∞ to +∞, we can observe that as t goes from -∞ to +∞, the first component of r(t) goes from -∞ to +∞, while the second and third components oscillate between 0 and +∞. This means that the path starts outside the sphere (at the point (0, +∞, +∞)) and ends inside the sphere (at the point (+∞, 1, 1)). Therefore, the path must intersect the sphere once, traveling from outside to inside.
The amount, a, in Chelsea's savings account after y years can be found using the equation a = 1000(1.03)".
After 5 years, Chelsea sells her car for its current value and adds the money to her savings account. The savings account continues to get the same interest rate as before.
Two years after that, 7 years after initially starting the savings account and buying the car, how much money is in Chelsea's savings account, to the nearest dollar?
Chelsea has $13,385 in her savings account after 7 years.
What is savings account ?A savings account is an effective way to store your money in a secure location where it can earn interest.
After 5 years, the amount in Chelsea's savings account will be:
a = 1000(1.03)^5 = 1000(1.159274) = 1159.27
Let's say that Chelsea sells her car for x dollars. She adds that to her savings account, so the new amount in her account is:
1159.27 + x
After two more years (i.e., 7 years after initially starting the savings account), the amount in her savings account will be:
a = (1159.27 + x)(1.03)^2 = (1159.27 + x)(1.0609) = 1232.56 + 1.0609x
To find the value of x, we need to know the current value of the car. Once we have that, we can substitute it into the equation above to find the final amount in Chelsea's savings account.
For example, let's say that Chelsea sold her car for $5000. Then, the final amount in her savings account would be:
a = 1232.56 + 1.0609(5000) = 13384.91
Therefore, to the nearest dollar, Chelsea has $13,385 in her savings account after 7 years.
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Identify the surface area of a sphere with a radius of 18 inches to the nearest tenth. Use 3.14 for π.
A. 4,147.9 in2
B. 8,134.2 in2
D. 4,069.4 in2
C. 16,201.4 in2
What is a characteristic of all cubic functions
The cubic function is one where the coefficient a, b, c, and d are correlational the variable are real numbers and are polynomial numbers. The function is either one or three real roots. The graph of the function is a cubic curve.
The example of a cubic function is that of the forms of y = ax3 + bx2 + cx + d, where the a, b, c, and d are constants. The cube root function is inverse to the cube function.
Hence they are increasing option A is correct.
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A stereo is sold at a 10% discount and then a 10% tax. If the final sale price is $589.05, what was the regular price of the stereo?
(Accurate Answers Please)
Answer:
Step-by-step explanation:
Let's call the regular price of the stereo "x".
The stereo is sold at a 10% discount, which means the selling price is 90% of the regular price:
Selling price after discount = 0.9x
Then, a 10% tax is added to the selling price, so the final sale price is:
Final sale price = (1 + 0.1)(0.9x) = 1.1(0.9x) = 0.99x + 0.1(0.9x) = 0.99x + 0.09x = 1.08x
We are given that the final sale price is $589.05, so we can set up the equation:
1.08x = 589.05
Solving for x, we get:
x = 589.05 ÷ 1.08
x = 545.83 (rounded to the nearest cent)
Therefore, the regular price of the stereo was $545.83.
NO LINKS!!! URGENT HELP PLEASE!!!! NOT MULTIPLE CHOICE!!!!
2. You go to the pool to hang out with your friends on a hot summer day. You jump off the diving board and your path through the air can be modeled by the equation m(d) = -4d^2 + 5.5d + 7 in meters per second. Use this scenario to answer questions a - c.
a. How far above the pool do you reach on your dive? (round to the nearest meter)
b. How long are you in the air? (Round to the nearest second)
c. How high is the diving board?
Answer:
a) You will reach 9 meters above the pool.
b) The length of time you are in the air is 2 seconds.
c) The height of the diving board is 7 meters.
Step-by-step explanation:
Given quadratic equation:
[tex]m(d)=-4d^2 + 5.5d + 7[/tex]
Part aTo determine how far above the pool you reach on your dive, find the y-value of the vertex of the given quadratic equation.
The formula for the x-value of the vertex is -b/2a for a quadratic equation in the form y=ax²+bx+c. Therefore, the x-value of the vertex for the given equation is:
[tex]\implies -\dfrac{5.5}{2(-4)}=0.6875[/tex]
To find the y-value of the vertex, substitute d = 0.6875 into the given equation:
[tex]\begin{aligned}m(0.6875)&=-4(0.6875)^2+5.5(0.6875)+7\\&=-1.890625+3.78125+7\\&=1.890625+7\\&=8.890625\\&=9\; \sf m\;(nearest\;meter)\end{aligned}[/tex]
Therefore, you will reach 9 meters above the pool (rounded to the nearest meter).
Part bYou will hit the water when your height is zero. Therefore, to find the length of time you are in the air, set the given quadratic equation to zero and solve for d using the quadratic formula.
[tex]\boxed{\begin{minipage}{3.6 cm}\underline{Quadratic Formula}\\\\$x=\dfrac{-b \pm \sqrt{b^2-4ac}}{2a}$\\\\when $ax^2+bx+c=0$ \\\end{minipage}}[/tex]
[tex]\implies d=\dfrac{-5.5 \pm \sqrt{5.5^2-4(-4)(7)}}{2(-4)}[/tex]
[tex]\implies d=\dfrac{-5.5 \pm \sqrt{142.25}}{-8}[/tex]
[tex]\implies d=\dfrac{-5.5 \pm \sqrt{142.25}}{-8}[/tex]
[tex]\implies d=-0.803357..., \;2.178357...[/tex]
As time is positive we can discount the negative solution. Therefore, the length of time you are in the air is 2 seconds (rounded to the nearest second).
Part cThe height of the diving board is the y-intercept of the graph of the equation. The y-intercept is the value of y when x = 0. Therefore, to find the height of the diving board, substitute d = 0 into the equation.
[tex]\begin{aligned}\implies d(0)&=-4(0)^2+5.5(0)+7\\&=0+0+7\\&=7\end{aligned}[/tex]
Therefore, the height of the diving board is 7 meters.
Find the value of n(A) if n(B) = 35, n(A nB) = 15, and n(A U B) = 55.
The value of n(A) is 35 if n(B) = 35, n(A nB) = 15, and n(A U B) = 55.
What is a Set?A set is a collection of well defined objects.
We can use the formula: n(A U B) = n(A) + n(B) - n(A nB)
Substituting the given values, we get:
55 = n(A) + 35 - 15
Simplifying, we get:
55 = n(A) + 20
Subtracting 20 from both sides, we get:
n(A) = 35
Therefore, the value of n(A) is 35.
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Nina made two investments:
Investment
A
Astart text, A, end text has a value of
$
50
$50dollar sign, 50 at the end of the first year and increases by
8
%
8%8, percent per year.
Investment
B
Bstart text, B, end text has a value of
$
60
$60dollar sign, 60 at the end of the first year and increases by
$
3
$3dollar sign, 3 per year.
Nina checks the value of her investments once a year, at the end of the year.
What is the first year in which Nina sees that investment
A
Astart text, A, end text's value exceeded investment
B
Bstart text, B, end text's value?
The requried first year in which Nina sees that investment exceeded investment B is 5th year.
What are equation models?The equation model is defined as the model of the given situation in the form of an equation using variables and constants.
Here,
According to the given data,
Equation models for the given condition are,
For investment A
y = 50(1.08)ˣ
For investment B
y = 60 + 3x
Where y is the total amount after x years of passing.
When plotting the graph of both equations we can see Investment A will surplus the graph of Investment B at x = 5.56
Thus, the requried first year in which Nina sees that investment exceeded investment B is 5th year.
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During the course of your examination of the financial statements of Trojan Corporation for the year ended December 31, 2021, you come across several items needing further consideration. Currently, net income is $100,000. An insurance policy covering 12 months was purchased on October 1, 2021, for $24,000. The entire amount was debited to Prepaid Insurance and no adjusting entry was made for this item in 2021. During 2021, the company received a $4,000 cash advance from a customer for services to be performed in 2022. The $4,000 was incorrectly credited to Service Revenue. There were no supplies listed in the balance sheet under assets. However, you discover that supplies costing $2,750 were on hand at December 31, 2021. Trojan borrowed $70,000 from a local bank on September 1, 2021. Principal and interest at 9% will be paid on August 31, 2022. No accrual was made for interest in 2021.
Answer: $3,700 or $90,650
Step-by-step explanation:
Answer:
3,700
Step-by-step explanation:
i thibk thisisthay answer
What is the left-hand limit of g(x)= |x-4|/x-4 as x approaches 4?
A. -1
B. 0
C. 1
D. 3
For given piecewise function, g(x)= |x-4|/x-4 when x approaches 4 the left-hand limit will be 0 i.e. B.
What exactly is a piecewise function?
A piecewise function is one that has multiple definitions in different x intervals. A piecewise function's graph is divided into parts that correspond to each of its definitions. A very excellent example of a piecewise function is the absolute value function. Let us investigate why it is thus named. We know that an absolute value function is defined as f(x) = |x|.
f(x)=(x if x≥0 ,
-x if x<0
This piecewise function should be interpreted as
When x is higher than or equal to 0, f(x) equals x.
When x is less than zero, f(x) equals -x.
Now,
when x will approach 0
given function will give value
g(x)=4-4/4-4
=0/0
=0
Hence,
for g(x)= |x-4|/x-4 when x approaches 4 the left-hand limit will be 0.
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For given piecewise function, g(x)= |x-4|/x-4 when x approaches 4 the left-hand limit will be 0 i.e. B.
What exactly is a piecewise function?
A piecewise function is one that has multiple definitions in different x intervals. A piecewise function's graph is divided into parts that correspond to each of its definitions. A very excellent example of a piecewise function is the absolute value function. Let us investigate why it is thus named. We know that an absolute value function is defined as f(x) = |x|.
f(x)=(x if x≥0 ,
-x if x<0
This piecewise function should be interpreted as
When x is higher than or equal to 0, f(x) equals x.
When x is less than zero, f(x) equals -x.
Now,
when x will approach 0
given function will give value
g(x)=4-4/4-4
=0/0
=0
Hence,
for g(x)= |x-4|/x-4 when x approaches 4 the left-hand limit will be 0.
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Which ordered pairs match the graph? Responses (0, 0), (2, 2), (2, 3), (2, 4), (3, 3.5) , begin ordered pair 0 comma 0 end ordered pair begin ordered pair 2 comma 2 end ordered pair begin ordered pair 2 comma 3 end ordered pair begin ordered pair 2 comma 4 end ordered pair begin ordered pair 3 comma 3.5 end ordered pair (0, 0), (0, 2.5), (2, 2), (2, 3), (2, 4) begin ordered pair 0 comma 0 end ordered pair begin ordered pair 0 comma 2.5 end ordered pair begin ordered pair 2 comma 2 end ordered pair begin ordered pair 2 comma 3 end ordered pair begin ordered pair 2 comma 4 end ordered pair (0, 0), (1, 1), (2, 2), (3.5, 4), (2, 0) , begin ordered pair 0 comma 0 end ordered pair begin ordered pair 1 comma 1 end ordered pair begin ordered pair 2 comma 2 end ordered pair begin ordered pair 3.5 comma 4 end ordered pair begin ordered pair 2 comma 0 end ordered pair (0, 0), (1, 3.5), (2, 3), (2, 2), (3, 2) begin ordered pair 0 comma 0 end ordered pair begin ordered pair 1 comma 3.5 end ordered pair begin ordered pair 2 comma 3 end ordered pair begin ordered pair 2 comma 2 end ordered pair begin ordered pair 3 comma 2 end ordered pair
Based on the choices, the ordered pairings that correspond to the graph are (2, 2), (2, 3), and (2, 4). (2, 4).
The x-coordinate of each point on the graph is always 2, since the vertical line passing through x=2 is a vertical asymptote, which implies the graph approaches but never reaches the line. Although the points where the graph crosses the y-axis are not shown, we may deduce from the curve's shape that the approximate y-coordinates of the first option, second choice, and third choice are 2, 3, and 4, respectively.
Hence, the suitable ordered pairings are (2, 2), (2, 3), and (2, 4).
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Can someone please explain these to me! Thanks!!
Answer:
9. 9x -4y = -36
10. geometric; terms have a common ratio of 1/2. Never 0 or negative; 1/2 times a positive number is a positive number.
Step-by-step explanation:
You want the equation of the line with x-intercept (-4, 0) and y-intercept (0, 9), and you want to know if the sequence 40, 20, 10, 5, ... is arithmetic.
9. LineIt is helpful to know a few different forms of the equation for a line. One of them is "intercept form," x/a +y/b = 1, where 'a' and 'b' are the x- and y-intercepts, respectively.
For intercepts (-4, 0) and (0, 9), the equation in this form is ...
x/(-4) +y/9 = 1
Multiplying by -36 puts it in standard form:
9x -4y = -36
10. Sequence(a) First differences of the sequence 40, 20, 10, 5 are ...
-20, -10, -5 . . . . . not constant
Since the first differences are not constant this is not an arithmetic sequence.
Ratios of successive terms are ...
20/40 = 10/20 = 5/10 = 1/2 . . . . . . constant
A sequence of terms with a common ratio is a geometric sequence. This sequence has a common ratio, so is geometric.
(b) The common ratio is 1/2, a positive number. The given terms of the sequence are positive numbers. Each successive term is 1/2 the previous term, so all terms will be positive—never 0 or negative. (The product of two positive numbers is always positive.)
graph the function plsss
Add a term to the expression so that it becomes a perfect square trinomial.
y² - 15y +
The expression representing a perfect square trinomial is given as follows:
y² - 15y + 56.25.
What are perfect square trionomial?There are two formats of perfect square trinomial, given as follows:
(x + a)² = x² + 2ax + a².(x - a)² = x² - 2ax + a².For this problem, we have a subtraction sign, meaning that the value of a is obtained as follows:
2ay = 15y
2a = 15
a = 15/2
a = 7.5.
Then the square of a is given as follows:
a² = 7.5²
a² = 56.25.
Meaning that the expression is given as follows:
y² - 15y + 56.25.
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( 20 points) \/ \/ \/ \/ \/ \\ \/ \/ \/ \ / simplify:
Answer:
D) -53.23
Step-by-step explanation:
Use PEMDAS to evaluate the expression
We do parentheses first.
[tex]|65.45-42.45|-76.23[/tex]
Evaluate what's inside of the absolute value bracket.
[tex]|23|-76.23[/tex]
Simplify
[tex]23+-76.23[/tex]
Evaluate
-53.23
What is the probability that a randomly selected person is male given the person is left handed?
Answer:
13/24
Step-by-step explanation:
13/11+13= 13/24
The probability that a randomly selected person is male given the person is left handed is 13/200.
What is the probability?Probability can be defined as the ratio of the number of favourable outcomes to the total number of outcomes of an event.
We know that, probability of an event = Number of favourable outcomes/Total number of outcomes.
Here, total number of outcomes = 200
Number of favorable outcomes = 13
Now probability of an event = 13/200
Therefore, the probability that a randomly selected person is male given the person is left handed is 13/200.
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find the TSA of a cube of side 8 cm
Answer: TSA( TOTAL SURFACE AREA) of the cube of side 8 cm is 384 square cm.
Step-by-step explanation: We know,
the total surface area of a cube is = 6 a^2 where a is the length of the side of the cube.
Here, a = 8cm
thus TSA = 6* 8*8= 384 square cm.
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Angles J and K are vertical angles. Angle J measures 85° and angle K measures
(2x + 5)°. What is the value of x?
Answer:
x= 45°
Step-by-step explanation:
They are angle on a straight line
85+2x+5 = 180
2x+ 90 = 180
2x = 180-90
2x = 90
dividing both sides of the equation by 2
x = 45
What is the length of CG??
The length of CG is approximately 5.4 units.
Describe Triangles?A triangle is a closed geometric figure that is formed by connecting three straight line segments called sides. These sides meet at three points called vertices. Triangles are one of the simplest and most fundamental shapes in geometry and can be found in many natural and man-made objects.
Triangles can be classified into different types based on their sides and angles.
By sides:
Equilateral triangle: all three sides are equal in length.
Isosceles triangle: two sides are equal in length.
Scalene triangle: all three sides are different in length.
By angles:
Acute triangle: all three angles are acute (less than 90 degrees).
Right triangle: one angle is a right angle (exactly 90 degrees).
Obtuse triangle: one angle is an obtuse angle (greater than 90 degrees).
Triangles have many properties and are used in various fields such as architecture, engineering, physics, and mathematics. They are also commonly used in trigonometry to solve problems involving angles and distances.
We can use the property of similar triangles to solve this problem.
First, let's label the intersection point of FG and BC as point H. Also, let's label the length of CG as x.
Since FG is parallel to AC, we can use the property of similar triangles to find that triangles ABF and HBG are similar.
Therefore, we can set up the proportion:
AB/FB = HG/GB
Plugging in the given values, we get:
10/63 = (x + 57)/57
Solving for x, we get:
x = 5.4
Therefore, the length of CG is approximately 5.4 units.
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A factory selling cell phones has a marginal cost function C(x)=0.01x2−3x+229, where x represents the number of cellphones, and a marginal revenue function given by R(x)=429−2x. Find the area between the graphs of these curves and x =0. What does this area represent?
The area between -
C{x} = 0.01x² - 3x + 229, R{x} = 429 - 2x and {x} = 0 is 492097.4 square
units.
What is function?A function is a relation between a dependent and a independent variable. Mathematically we can write the function as -
y = f(x)
Given is that a factory selling cell phones has a marginal cost function C(x) = 0.01x² - 3x + 229, where {x} represents the number of cellphones, and a marginal revenue function given by R(x) = 429 - 2x.
We can write the area between -
C{x} = 0.01x² - 3x + 229, R{x} = 429 - 2x and {x} = 0 as -
Area = ∫C(x) dx + ∫{C(x) - R(x)} dx
We can write the area with limits as -
Area =
∫(0.01x² - 3x + 229) dx {limits from 229 to 429}
+
∫(0.01x² - 3x + 229 - 429 + 2x) dx {limits from 429 to 629}
Area = 71548.7 + 420548.7
Area = 492097.4 square units
Therefore, the area between -
C{x} = 0.01x² - 3x + 229, R{x} = 429 - 2x and {x} = 0 is 492097.4 square
units.
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