given triangle ABC find the values of x and y. In your final answer, include all of your calculations.
Answers
Answer:
Step-by-step explanation:
X = ?
y = ?
The big triangle ABC is a right triangle, we can use Pythagoras theorem to find side y, then use SOH CAH TOA to find angles :)
also, there is a special rule for a triangle set up like this one
2CD = BD
for this triangle then,
2CD = 9
CD = 4.5
X = 13.5
now use Pythagoras to find y
\(13.5^{2}\) = \(6^{2}\) + \(y^{2}\)
182.25 -36 = \(y^{2}\)
\(\sqrt{146.25}\) = y
12.093386 = y
now that you have all 3 sides of the big triangle, use which ever trig function you are most comfy with to find angle B or C, i'll find C
CAH = Cos(C) = Adj / Hyp
Cos(C) = 6 / 13.5
arcCos(Cos(C)) = arcCos(6/13.5)
C = 63.6122°
now find B
180 = 90 + 63.6122 + B
26.3877° = B
got it?
Related Questions
You want to send a package . First class mail costs $.39 for the first ounce and $.24 for each additional ounce . You can spend at most $ 3.00 on postage . What is the maximum weight of your package ? Round down to the nearest ounce .
Answers
Answer: 10 ounces
Step-by-step explanation: Ounce is equal to O and price is y
y=mx+b : y=.24o+.39
y = 3.00
3.00-.39=2.61
2.61/.24 = 10.875
round it down and you get the maximum
Use Pythagorean Theorem to solve for x.
HELP ME PLZZZZ!!!! ASAP
Answers
Answer: \(2\sqrt{22}\)
Step-by-step explanation:
Pythagorean theorem: \(a^{2} +b^{2} = c^{2}\), where a and b are the legs and c is the hypotenuse.
We can solve for x by only using the left side of the triangle. Since we're only using the left side of the triangle, we can reduce 18 by 2 to get 9. Now we plug in our information to the equation.
\(9^{2} +b^{2} = 13^{2}\)
\(81 +b^{2} = 169\)
Since we don't know what \(b^{2}\) is, we're going to isolate it by subtracting 81 on both sides
\(b^{2} = 88\)
We have to square root both sides in order to find out b (or x in the problem).
\(\sqrt{b^{2}} = \sqrt{88}\)
When you put this on a calculator it would result in \(2\sqrt{22}\) which is the answer d in the problem.
yumiko solved |x|>5 by solving x>-5 and x<5. explain the error yumiko made
Answers
Answer:
switched signs around
Step-by-step explanation:
I believe that s/he switched the signs around so
|x|>5 is solved by x<-5 and x>5
but I'm not quite sure, sorry
State whether the data described below are discrete or continuous, and explain why.
The numbers of words in books
Choose the correct answer below.
A) The data are discrete because the data can only take on specific values.
B) The data are continuous because the data can only take on specific values.
C) The data are continuous because the data can take on any value in an interval.
D) The data are discrete because the data can take on any value in an interval Atenciar
Answers
The correct answer is A) The data are discrete because the data can only take on specific values.
The number of words in books is a discrete data type because it can only take on specific integer values. In a book, the number of words cannot be a fractional or continuous value. It is always a whole number. Each book has a finite number of words, and there are no intermediate values between the word counts of different books. Therefore, the data is discrete.
Discrete data refers to data that can only take on distinct, separate values. These values are often counted or categorized and cannot be subdivided further. Examples of discrete data include the number of students in a class, the number of cars in a parking lot, or the number of books on a shelf.
In contrast, continuous data can take on any value within a certain range. It is measured and can be subdivided infinitely. Examples of continuous data include the height of a person, the weight of an object, or the temperature of a room.
Learn more about data are discrete from
https://brainly.com/question/14812653
#SPJ11
in a certain company 120 of the employees are men. what is the total number of employees if 5 out of every 8 employees are men?
Answers
Answer:
There are 192 employees in the company.
Step-by-step explanation:
Let x be the total number of employees
Use ratio and proportion
\(\frac{120}{x} =\frac{5}{8} \\5x = 120(8)\\5x = 960\\\frac{5x}{5} = \frac{960}{5} \\x = 192\)
x = 192
Marissa found an isotope that has a half-life of 75 days. how many days will it take for a
20 mg sample of this isotope to decay to 2 mg? round your answer to the nearest day.
Answers
The isotope has a half-life of 75 days, Rounding to the nearest day, it will take approximately 249 days for the 20 mg sample of the isotope to decay to 2 mg.
The half-life of an isotope is the time it takes for half of the initial quantity to decay. In this case, we know that the half-life is 75 days.
To calculate the time it takes for a 20 mg sample to decay to 2 mg, we can use the formula for exponential decay: N = \(N_0 * (1/2)^{(t/t_{half})\), where N is the final amount, N0 is the initial amount, t is the time passed, and t_half is the half-life.
Let's plug in the values: 2 =\(20 * (1/2)^{(t/75).\)
To isolate the variable t, we can take the logarithm of both sides: \(log(2) = log(20) + (t/75) * log(1/2).\)
Simplifying further, we have \(log(2/20) = (t/75) * log(1/2).\)
Using logarithmic properties, we can calculate:\(t/75 = log(2/20) / log(1/2).\)
Evaluating this, we find t/75 ≈ 3.3219.
To find t, we multiply both sides by 75: t ≈ 3.3219 * 75.
Calculating this, we have t ≈ 249.14.
Rounding to the nearest day, it will take approximately 249 days for the 20 mg sample of the isotope to decay to 2 mg.
Learn more about rounding here:
https://brainly.com/question/29878750
#SPJ11
A ___ data table has input values that are listed either as column-oriented or row-oriented
Answers
The correct statement is: 'A one-variable data table has input values that are listed either down a column (column-oriented) or across a row (row-oriented). '
The correct answer is an option (a)
We know that a one-variable data table contain its input values either in a single column (column-oriented), or across a row (row-oriented).
And any formula in this data table must refer to only one input cell.
Whereas we se a two-variable data table to see how different values of two variables in one formula will change the formula results.
Custom data tables are used for: Building data-driven services that can easily be updated without modifying it and storing the results.
And the pre-formatted data tables stored as building blocks in galleries that can be accessed any time and be reused any number of times you want.
Therefore, the correct answer is an option (a)
Learn more about the data table here:
https://brainly.com/question/17023489
#SPJ4
The complete question is:
A ________ data table has input values that are listed either as column-oriented or roworiented.
A) one-variable
B) two-variable
C) custom
D) pre-formatted
What is the domain? I need help on this problem
Answers
The domain of the function \(f(x) = \sqrt{\frac{1}{3}x + 2\) is (d) x ≥ -6
How to determine the domain of the functionFrom the question, we have the following parameters that can be used in our computation:
\(f(x) = \sqrt{\frac{1}{3}x + 2\)
Set the radicand greater than or equal to 0
So, we have
1/3x + 2 ≥ 0
Next, we have
1/3x ≥ -2
So, we have
x ≥ -6
Hence, the domain of the function is (d) x ≥ -6
Read more about domain at
https://brainly.com/question/31900115
#SPJ1
what is the % for 40 is 50
Answers
Answer:
20 percent
Step-by-step explanation:
my dad told me
I need help with this please
Answers
Look at the pattern below.
3, 6, 9, 12, ...
Which number sentence can be used to determine n, the 9th number in the pattern?
A.
n = 3 + 9
B.
n = 3 ÷ 9
C.
n = 12 + 9
D.
n = 3 × 9
Answers
Because 9 is the 3rd number. You are trying to figure out the pattern. If you divide 9 by 3 you get three. The pattern is going up by 3
Frank can make 3 bird houses in 12 days. How many days will it take him to make 21 bird houses?
Answers
Answer:
5.25
Step-by-step explanation:
3 divided by 12 = 0.25 (this how many he can make per day)
Now that we have how many bird houses per day (0.25), we can multiply that for the amount it takes. (21 bird houses) to get 5.25
researchers found the demand for cheese in a particular country for a particular year can be estimated by the implicit equation -0.82 Inp where p represents the price of a unit of cheese and D represents a constant that can be calculated uniquely for a particular year. Here q represents the annual per capita cheese demand. Answer parts (a) and (b) below. P do 9 dp (a) Use implicit differentiation to calculate and interpret the elasticity of demand. Recall that elasticity of demand is E- Show the first step of implicit differentiation, the equation that results from differentiating each side of the equation da dp Find the elasticity of demand E =(Simplify your answer) Interpret the elasticity of demand you calculated O A. Demand is inelastic OB. Demand is elastic O C. Demand may be elastic or inelastic, depending on the value of D. OD. Demand has unit elasticity
(b) Solve the equation for then calculate the elasticity of demand q= E=
(Simplify your answer.)
Answers
(a) First step of implicit differentiation:
-0.82dP/dt = dq/dt
The equation that results from differentiating each side of the equation with respect to P is:
-0.82 - 0.82P(d^2q/dP^2) = (dQ/dP)(dP/dt)/(dq/dt)
To find the elasticity of demand, we need to use the formula:
E = (dQ/Q)/(dP/P)
We can rewrite this as:
E = (dQ/dP) * (P/Q)
We know that dQ/dP = -0.82P(d^2q/dP^2), so we substitute that into the formula:
E = (-0.82P(d^2q/dP^2)) * (P/q)
Simplifying this expression, we get:
E = -0.82P^2(d^2q/dP^2)/q
(b) We can solve the original equation for q by dividing both sides by -0.82:
q = (-1/0.82)P + D
Taking the derivative of q with respect to P, we get:
dq/dP = -1/0.82
We can use this result to calculate the elasticity of demand using the formula:
E = (dQ/dP) * (P/Q)
Substituting the values we found, we get:
E = (-1/0.82) * (P/((-1/0.82)P + D))
Simplifying this expression, we get:
E = -1/(P/((-1/0.82)P + D))
E = -1/((D/P) - 1.22)
(a) Interpretation: The elasticity of demand is a measure of how much the quantity demanded changes in response to a change in price. If E > 1, demand is considered elastic, meaning that a small change in price will result in a large change in quantity demanded. If E < 1, demand is considered inelastic, meaning that a change in price will result in a small change in quantity demanded. If E = 1, demand is unit elastic, meaning that a change in price will result in an equal proportional change in quantity demanded.
(b) Interpretation: The elasticity of demand in this case depends on the values of D and P. If D is relatively small compared to P, then the elasticity of demand will be close to -1.22, which is the upper limit of the elasticity. If D is relatively large compared to P, then the elasticity of demand will be close to zero, which means that demand is very inelastic.
Learn more about implicit differentiation here:
https://brainly.com/question/11887805
#SPJ11
With respect to the average cost curves, the marginal cost curve: Intersects average total cost, average fixed cost, and average variable cost at their minimum point b. Intersects both average total cost and average variable cost at their minimum points Intersects average total cost where it is increasing and average variable cost where it is decreasing d. Intersects only average total cost at its minimum point
Answers
With respect to the average cost curves, the marginal cost curve: intersects both average total cost and average variable cost at their minimum points that is option B.
The fixed cost per unit of production is the average fixed cost (AFC). AFC will reduce consistently as output grows since total fixed costs stay constant. The variable cost per unit of production is known as the average variable cost (AVC). AVC generally declines until it reaches a minimum and then increases due to the growing and then lowering marginal returns to the variable input. The average total cost curve's (ATC) behaviour is determined by the behaviour of the AFC and AVC.
The marginal cost is the cost added to the overall cost of producing one extra unit of output. MC initially falls until it hits a minimum and then increases. When both AVC and ATC are at their minimal points, MC equals both. Also, when AVC and ATC are dropping, MC is lower; when they are growing, it is higher.Initially, the marginal cost of manufacturing is lower than the average cost of preceding units. When MC falls below AVC, the average falls. The average cost will reduce as long as the marginal cost is smaller than the average cost.When MC surpasses ATC, the marginal cost of manufacturing one more extra unit exceeds the average cost.Learn more about Marginal cost curve:
https://brainly.com/question/15570401
#SPJ4
Complete question:
With respect to the average cost curves, the marginal cost curve:
A) Intersects average total cost, average fixed cost, and average variable cost at their minimum point
B) Intersects both average total cost and average variable cost at their minimum points
C) Intersects average total cost where it is increasing and average variable cost where it is decreasing
D) Intersects only average total cost at its minimum point
It costs $2.37 to paint one square foot of wall. You need to paint a wall that measures 864.5 square feet. It will cost to paint that wall. (Round your answer to the nearest hundredth)
a $204.88
b $2,048.87
c $2,048.86
d. $2,848.87
Answers
Answer:
B- hope this helps:)
Step-by-step explanation:
The total cost to paint 864.5 square feet of wall is $2,048.87.
It is given that the cost to paint one square foot of wall is $2.37.
We are asked to find the total cost to paint 864.5 square feet of wall.
What are the different place values in a given number with a decimal point?If we have a number that has a decimal point then we have two parts.
The whole number part and the fractional part.
After the decimal point, we will count the place value as tenths, hundredths, thousandths, and so on.
You can also see the given figure below.
We know that,
One square foot = $2.37.
Remember that Feet is the plural form of the foot.
We can write,
864.5 square feet = 864.5 x one square foot
Because in 864.5 square feet we have 864.5 one square foot.
And since one square foot cost $2.37.
864.5 square feet will cost 864.5 x 2.37 dollars.
Now,
864.5 x 2.37 = $2048.865.
Rounding to the nearest hundredth.
6 is in the hundredth place so we will round 86 to 87 since the number in the thousandth place is greater than 4.
Thus the total cost to paint a wall of 864.5 square feet is $2,048.87.
Learn more about rounding decimal numbers here:
https://brainly.com/question/15482780
#SPJ2
Uan zhang bought a 10-year bond that pays 8. 25 percent semiannually for $911. 10. what is the yield to maturity on this bond? (roundyour percentage answer to two decimal places. )
Answers
The yield to maturity on this bond according to the trial-and-error approach is 9.66 percent.
According to the statement
we have given that the Uan zhang bought a 10-year bond that pays 8. 25 percent interest per 6 months.
And we have to find that the yield to maturity on this bond.
So, For this purpose,
The amount given is $911. 10.
Years to maturity = n = 10
Coupon rate = C = 8.25%
Semiannual coupon = $1,000 × (0.0825/2) = $41.25
Yield to maturity = i
Present value of bond = PB = $911.10
Use the trial-and-error approach to solve for YTM. Since the bond is selling at a discount, we know that the yield to maturity is higher than the coupon rate.
Try YTM = 9.4%:
= $522.90 + 391.54 ≅ $914.43
The YTM is approximately 9.66 percent. Using a financial calculator provided an exact YTM of 9.656 percent (2 × 4.828%).
So, The yield to maturity on this bond according to the trial-and-error approach is 9.66 percent.
Learn more about percentage here
https://brainly.com/question/11360390
#SPJ4
Please help me please please
Answers
ok so at first if u have fractions like the first follow my instruction:
1st: u have 2/3---1/2, u will multiply 3 by 1 and 2 by 2 so u will get 6 and 4
but remember that 2/3 and 1/2 u cris cross it the left one comes first like 6 then 4 so it could balance and do the rest of the fractions like that.
2nd: if u have decimal u will check the number after the decimal but if the are the same u will compare the numbers before the decimal.
I hope it's usefull
Vanessa collected Barbie dolls. She began with 2 dolls and added the same amount of dolls to her collection each year. In the 24th year, Vanessa had 98 dolls. Which function, d(n), can be used to determine the number of dolls Vanessa had in any year? Show complete working format please
Answers
Answer:106
Step-by-step explanation:
106
balancing work and school: is there a correlation between how many hours per week a student works outside of school and how many units the student takes in a quarter? a cluster sample of 482 students is chosen.
Answers
Yes, there is a correlation between the number of hours per week a student works outside of school and how many units the student takes in a quarter.
The cluster sample of 482 students is chosen in order to examine the relationship between these two variables. The statistical relationship between two variables is known as correlation.
The correlation coefficient r is used to determine the degree and direction of the correlation between two variables. The correlation coefficient is a numerical value that ranges from -1 to +1.
A negative correlation exists when one variable decreases as the other variable increases. A positive correlation exists when both variables increase or decrease together.
In this case, if the number of hours per week a student works outside of school increases, the number of units the student takes in a quarter may decrease, indicating a negative correlation between the two variables. Similarly, if the number of hours per week a student works outside of school decreases, the number of units the student takes in a quarter may increase, indicating a positive correlation between the two variables.
Know more about correlation here:
https://brainly.com/question/13879362
#SPJ11
What is JL?
A 4.5
B 6.75
C 8.75
D 12.5
Answers
The length of the segment JL is 12.5, Option D is correct.
What is Trigonometry?Trigonometry is a branch of mathematics that studies relationships between side lengths and angles of triangles.
To find JL we have to find the JK.
By pythagoras theorem we find the Jk.
The sum of the squares on the legs of a right triangle is equal to the square on the hypotenuse.
JK²=KM²+JM²
JK²=36+64
JK=10
TanKJM=KM/JM
tanKJM=6/8
∠KJM=36.87 degrees
∠KJM=∠KJL represents same angles
So 36.87=∠KJL
∠KJL=36.87
Cos ∠KJL =JK/JL
JK=10, ∠KJL=36.87
Now cos(36.87)=10/JL
JL=12.5
Hence, the length of the segment JL is 12.5, Option D is correct.
To learn more on trigonometry click:
https://brainly.com/question/25122835
#SPJ2
find the value for the expression below if x = 2
Answers
Answer:
10 is the answer
Step-by-step explanation:
2(2) + 6
4 + 6
10
debbie is a cook in a restaurant that is open 6 days a week. she is responsible for recording and monitoring the amount of money she spends on food. in the summer she uses an average of 9 loaves and bread per day.
Answers
The quantity of bread that Debbie uses each week on the average is = 54 loaves of bread
Calculation of weekly quantity of breadThe number of days the restaurant opens per week = 6 days.
The number of bread she uses everyday is = 9 loaves.
Therefore, the quantity of bread that Debbie uses each week on the average is = 6×9 = 54 loaves of bread.
Learn more about multiplication here:
https://brainly.com/question/4721701
#SPJ1
It take 4 people 40 minutes to clean a garden. How long will it take 6 people to clean the same garden
Answers
Answer:
4/9 of an hour (26.666 minutes)
Step-by-step explanation:
4 * x * 40/60 = 1
x * 160/60 = 1
x=60/160 = 6/16 = 3/8 (this is the rate for one worker)
~~~~~~~~~~~~~~~~
6 * (3/8) * x = 1
x = 4/9
In a statistical test of hypotheses, we say the data are statistically significant at level α if.
Answers
If the P value in a statistical test of hypotheses is more than, we may claim that the data are statistically significant at level. Less than is the P-value. =0.05 .
What is hypotheses ?An assumption is said to as a hypothesis when it is supported by evidence. Any investigation that turns the research questions into predictions must start here. Variables, the population, and the relationships between the variables are among its constituent parts. A hypothesis used to examine the link between two or more variables is known as a research hypothesis.
One dependent variable and one independent variable are shown to be related. For instance, eating more vegetables will help you lose weight more quickly. In this scenario, increasing your vegetable intake is an independent variable, while weight loss is the dependent variable.
It makes a claim that conflicts with the premise. There is no connection between the independent and dependent variables, which is a negative assertion. The emblem stands for.
Hence, If the P value in a statistical test of hypotheses is more than, we may claim that the data are statistically significant at level. Less than is the P-value. =0.05 .
learn more about hypothesis click here:
https://brainly.com/question/606806
#SPJ4
Suppose that the coordinates of point G were (4, –3) instead of (4, 3). Would the area of the triangle be the same? Explain why or why not.
Answers
The coordinate of point G is its location on the coordinate plane
The area of the triangle would not remain the same
How to determine the area statement?From the question, we have the following points
G = (4,-3) and
G = (4,3)
The above coordinates are two different points, and so they would make the triangle have different areas.
Hence, the area of the triangle would not remain the same
Read more about areas at:
https://brainly.com/question/24487155
What is the positive root of the equation x^2− 5x = 14?
Answers
The positive root of the quadratic equation x² - 5x = 14 is 7.
What is the positive root of the given equation?A quadratic equation in its standard form is expressed as;
ax² + bx + c = 0
Where x is the unknown
To solve for x, we use the quadratic formula
x = (-b±√(b² - 4ac)) / (2a)
Given the equation in the question.
x² - 5x = 14
Rearrange in standard form
x² - 5x - 14 = 0
Plug the values of a, b and c into the quadratic formula and solve for x.
x = (-b±√(b² - 4ac)) / (2a)
x = ( -(-5) ±√( (-5)² - ( 4 × 1 × -14) )) / (2 × 1)
x = ( 5 ±√( 25 - ( -56 ) )) / 2
x = ( 5 ±√( 25 + 56 )) / 2
x = ( 5 ±√( 81 )) / 2
x = ( 5 ± 9 )/2
x = ( 5 - 9 )/2, x = ( 5 + 9 )/2
x = (-4)/2, x = (14)/2
x = -2, x = 7
Therefore, the solutions are x = -2 and x = 7.
Learn more about quadratic equations here: brainly.com/question/1863222
#SPJ1
Builders are replacing the congruent roofs on House A and House B. What is the measure of
Someone please help me ?!?!?
Answers
Answer:
c
Step-by-step explanation:
For the linear regression y = ẞ1 + ẞ2x + e, assuming that the sum of squared errors (SSE) takes the following form:
SSE = 382 +681 +382 + 18ẞ1ẞ2
Derive the partial derivatives of SSE with respect to B1 and B2 and solve the optimal values of these parameters.
a. B₁ = B1
b. B₂ =
Answers
The optimal values of these parameters are:
a. β₁ = 0
b. β₂ = 0
The linear regression y = β1 + β2x + e, assuming that the sum of squared errors (SSE) takes the following form:
SSE = 382 + 681 + 382 + 18β1β2
Derive the partial derivatives of SSE with respect to β1 and β2 and solve the optimal values of these parameters.
Given that SSE = 382 + 681 + 382 + 18β1β2 ∂SSE/∂β1 = 0 ∂SSE/∂β2 = 0
Now, we need to find the partial derivative of SSE with respect to β1.
∂SSE/∂β1 = 0 + 0 + 0 + 18β2 ⇒ 18β2 = 0 ⇒ β2 = 0
Therefore, we obtain the optimal value of β2 as 0.
Now, we need to find the partial derivative of SSE with respect to β2. ∂SSE/∂β2 = 0 + 0 + 0 + 18β1 ⇒ 18β1 = 0 ⇒ β1 = 0
Therefore, we obtain the optimal value of β1 as 0. Hence, the partial derivative of SSE with respect to β1 is 18β2 and the partial derivative of SSE with respect to β2 is 18β1.
Thus, the optimal values of β1 and β2 are 0 and 0, respectively.
Therefore, the answers are: a. β₁ = 0 b. β₂ = 0
Learn more about regression analysis at
https://brainly.com/question/31691955
#SPJ11
Find the value of a: 12 = a/4
Answers
Answer: 48
Step-by-step explanation:
In this question we multiply 12 and 4
Therefore the result is 48.
I hope it helps!
A triangular towelette has a base of 2 inches and a height of 3 inches. What is the area of a towelette with double the base and double the height?
Answers
The area of a towelette with double the base and double the height is 12 square inches.
A triangular towelette with a base of 2 inches and a height of 3 inches has an area of 3 square inches. If the base and height of the triangular towelette double, the area will quadruple (increase by a factor of 4) since the area of a triangle is proportional to the product of its base and height.Area of the original towelette is given by:(1/2)bh= (1/2)×2×3= 3 square inchesLet the new base and height be b and h respectively.
The new area of the towelette is given by:(1/2)bh= (1/2)×2(2)×3(2)= 12 square inchesTherefore, the area of a towelette with double the base and double the height is 12 square inches.
To know more about area visit:-
https://brainly.com/question/1631786
#SPJ11