Answers
Answer:
1. ∠YZX = 37°
2. ∠YXZ = 53°
3. XZ = 30 meters
Step-by-step explanation:
1. To solve for an unknown angle, we need to utilize the inverse of a trigonometric function.
⭐What are the inverses of the trigonometric functions?
\(sin^-1 (opposite/hypotenuse)\)\(cos^-1 (adjacent/hypotenuse)\)\(tan^-1(opposite/adjacent)\)To know which inverse of the trigonometric functions we use, we have to see the type of side lengths we are given (opposite, adjacent, or hypotenuse)
We are given side length XY, which is opposite of ∠YZX, and we are given side length YZ, which is adjacent to ∠YZX. Therefore, we will use \(tan^-1 (opposite/adjacent) =\)
Substitute the values we are given into the function:
\(tan^-1 (18/24) =\)
Compute this equation using a scientific calculator. I recommend using the Desmos Scientific Calculator:
\(= 37\)
∴ ∠YZX = 37°
2. We already know 2 angles (∠YZX = 37°, and ∠ZYX = 90°) Therefore, to find ∠YXZ, we have to utilize the triangle sum theorem.
⭐ What is the triangle sum theorem?
\(angle_1 + angle_2 +angle_3 = 180\)The sum of all angles in a triangle is 180°Substitute the angles we know already (∠YZX and ∠ZYX), and solve for ∠YXZ.
\(< YZX + < ZYX + < YXZ = 180\)
\(37 + 90 + YXZ = 180\)
\(127 + YXZ = 180\)
\(< YXZ = 53\)
∴ ∠YXZ = 53°
3. We already know 2 side lengths (ZY = 24 meters, and XY = 18). Therefore, to find XZ, we have to utilize the Pythagoras' theorem.
⭐ What is the Pythagoras' theorem?
\((C)^2 = (A)^2 + (B)^2\)C is the hypotenuse of the triangle, A is a leg of the triangle, and B is another leg of the trianglePythagoras' theorem can only be used on right trianglesSubstitute the values of the side lengths into the formula:
\((XZ)^2 = (XY)^2 + (ZY)^2\)
\((XZ)^2 = 18^2 + 24^2\)
Solve for XZ:
\((XZ)^2 = 324 + 576\)
\((XZ)^2 = 900\)
\(\sqrt{(XZ)^2} = \sqrt{900}\)
\(XZ = 30\)
∴ XZ = 30 meters
Related Questions
Multiplying by which number is equivalent to finding 123.123%?
Answers
*☆*――*☆*――*☆*――*☆*――*☆*――*☆*――*☆*――*☆**☆*――*☆*――*☆*――*☆
Answer: Multiplying by 1.23123
Explanation: Slide the decimal points over by 2 points
I hope this helped!
<!> Brainliest is appreciated! <!>
- Zack Slocum
*☆*――*☆*――*☆*――*☆*――*☆*――*☆*――*☆*――*☆**☆*――*☆*――*☆*――*☆
Multiplying by 1.23123 number is equivalent to finding 123.123%.
What is multiplication?In mathematics, multiplication is a method of finding the product of two or more numbers. It is one of the basic arithmetic operations, that we use in everyday life.
here, we have,
123.123%
now, we have,
Multiplying by 1.23123 number is equivalent to finding 123.123%.
To learn more on multiplication click:
brainly.com/question/5992872
#SPJ2
80 cabins on a ship, 29 of them have windows.
What fraction of the cabins have windows
Answers
Answer:
29/80
Step-by-step explanation: It would be 29/80 because you cannot simplify that fraction. 29 is a prime number.
In parallelogram LMNOMP is equal to 21MLB is equal to Y plus 3MNP03Y minus 1MNOP is equal to 2X -1 and what are the values of X and Y
Answers
Answer: 3 and 2
Step-by-step explanation:
Answer:
3 & 2
Step-by-step explanation:
Evaluate each expression for x=-2,0,1 , and 4.
(1/2)x-8
Answers
The value for x = -2,0,1 , and 4 will be -9, -8, -15/2 and -6 respectively.
For x = -2
The value will be -
(1/2)x-8
(1/2)(-2) - 8
= -9
For x = 0
The value will be -
(1/2)x - 8
(1/2)(0) - 8
= -8
For x = 1
The value will be -
1/2(1) - 8
= -15/2
For x = 4
The value will be -
1/2(4) - 8
= -6
To learn more about solving for x from given link
https://brainly.com/question/28441305
#SPJ4
1 pts the number of violent crimes committed in a day possesses a distribution with a mean of 2.3 crimes per day and a standard deviation of 2 crimes per day. a random sample of 100 days was observed, and the mean number of crimes for the sample was calculated. describe the sampling distribution of the sample mean
Answers
The sampling distribution of the sample mean is a normal distribution with a mean of 2.3 crimes per day and a standard deviation of 0.2 crimes per day centered around population mean.
This distribution is centered around the population mean, and its standard deviation is much smaller than the population standard deviation, indicating that the sample mean is a more reliable measure of the population mean than individual observations.
1. The number of violent crimes committed in a day possesses a distribution with a mean of 2.3 crimes per day and a standard deviation of 2 crimes per day.
2. A random sample of 100 days was observed, and the mean number of crimes for the sample was calculated.
3. The sampling distribution of the sample mean is a normal distribution with a mean of 2.3 crimes per day and a standard deviation of 0.2 crimes per day.
4. This distribution is centered around the population mean, and its standard deviation is much smaller than the population standard deviation, indicating that the sample mean is a more reliable measure of the population mean than individual observations.
Learn more about population mean here
https://brainly.com/question/19538277
#SPJ4
what two numbers add up to be 116.5
Answers
Answer:
58.25
Step-by-step explanation:
116.5 / 2
= 58.25
Hope this helps!!
58.25+58.25
Those are the two numbers that add up to that number (116.5)
Btw there are also MULTIPLE numbers that add up to 116.5, I'm just putting the one that makes the most sense.
(｡ŏ﹏ŏ)
Miri
there are only two code categories assigned for reporting infectious arthropathies: m00 and m01.
Answers
In ICD-10-CM, only two code categories are used to report infectious arthropathies: M00 and M01.
The codes in these categories are used to describe the variety of arthropathies that can be caused by various bacterial, viral, fungal, and other infectious agents.
The M00 code group includes pyogenic arthritis, osteomyelitis, and other non-tuberculous infections of joints and bones. The M01 code category includes other types of arthritis and arthropathies caused by bacteria, viruses, fungi, and parasites, as well as other infectious agents.
Infectious arthropathies are diseases that cause joint inflammation and pain as a result of infection with a variety of infectious agents, such as bacteria, viruses, fungi, and parasites. Symptoms vary depending on the type of infection, but they usually include pain, swelling, redness, stiffness, and limited mobility.
The diagnosis of infectious arthropathies usually involves a combination of physical examination, laboratory testing, and imaging studies. Treatment usually involves antibiotics or antiviral medications, as well as pain management and physical therapy.
To know more about arthropathies visit:
https://brainly.com/question/32125546
#SPJ11
Consider the joint probability distribution below. Complete parts (a) through (c). X 1 2 Y 0 0.30 0.10 1 0.40 0.20 a. Compute the marginal probability distributions for X and Y. X 1 2 P(y) Y 0 0.30 0.10 1 0.40 0.20 P(x) (Type integers or decimals.) b. Compute the covariance and correlation for X and Y. Cov(X,Y)= (Round to four decimal places as needed.) Corr(X,Y)= (Round to three decimal places as needed.) c. Compute the mean and variance for the linear function W=X+Y. Hw= (Round to two decimal places as needed.) = (Round to four decimal places as needed.) ow
Answers
a) Marginal probability distributions for X and Y are: X 1 2 P(y) Y 0 0.30 0.10 1 0.40 0.20 P(x) 0.50 0.50 and b) Corr(X,Y) = -1.68 and c) Var(W) = -0.34
a) Marginal probability distributions for X and Y are: X 1 2 P(y) Y 0 0.30 0.10 1 0.40 0.20 P(x) 0.50 0.50
b) The covariance and correlation for X and Y are:
Cov(X,Y)= E(XY) - E(X)E(Y)
Cov(X,Y)= (1 * 0 + 2 * 0.3 + 1 * 0.1 + 2 * 0.2) - (1 * 0.5 + 2 * 0.5)(0 * 0.5 + 1 * 0.4 + 0 * 0.1 + 1 * 0.2)
Cov(X,Y)= (0 + 0.6 + 0.1 + 0.4) - (0.5 + 1) (0.4 + 0.2)
Cov(X,Y)= 0.12 - 0.9 * 0.6
Cov(X,Y)= 0.12 - 0.54
Cov(X,Y)= -0.42
Corr(X,Y)= Cov(X,Y)/σxσyσxσy
= √[∑(x-µx)²/n] × √[∑(y-µy)²/n]σxσy
= √[∑(x-µx)²/n] × √[∑(y-µy)²/n]σx
= √[∑(x-µx)²/n]
= √[(0.5 - 1.5)² + (0.5 - 0.5)² + (0.5 - 1.5)² + (0.5 - 1.5)²]/2σx
= 0.50σy
= √[∑(y-µy)²/n]
= √[(0 - 0.5)² + (1 - 0.5)²]/2σy
= 0.50
Corr(X,Y) = Cov(X,Y)/(0.50 * 0.50)
Corr(X,Y) = (-0.42)/0.25
Corr(X,Y) = -1.68
c) The mean and variance for the linear function W = X + Y are:
Hw = E(W)
Hw = E(X + Y)
Hw = E(X) + E(Y)
Hw = 1.5 + 0.5
Hw = 2
Var(W) = Var(X + Y)
Var(W) = Var(X) + Var(Y) + 2Cov(X,Y)
Var(W) = 0.25 + 0.25 - 2(0.42)
Var(W) = 0.50 - 0.84
Var(W) = -0.34
To know more about probability visit:
https://brainly.com/question/31828911
#SPJ11
I need help with this question
Answers
The length of the leg of the triangle (hypotenuse, opposite side, adjacent side) are 10, 17, and 5 respectively.
How to round the number to nearest whole number?To round a number to the nearest whole number, you have to look at the first digit after the decimal point. If this digit is less than 5 (1, 2, 3, 4) we don't have to do anything, but if the digit is 5 or greater (5, 6, 7, 8, 9) we must round up.
To find the length of each leg we need to consider the angle BAC.
\(sin60 = \frac{opposite side}{hypotenuse} =\frac{BC}{10}\)
\(\frac{\sqrt{3} }{2} = \frac{BC}{10}\\ BC = \frac{\sqrt{3} }{2} * 10\\ BC = \sqrt{3} * 10\\ BC = 17.32 = 17\)
\(cos60 = \frac{adjacent side}{hypotenuse} \\\frac{1}{2} = \frac{AB}{10} \\AB = \frac{1}{2} *10\\AB = 5\)
Therefore the length of the leg of triangle are 17 and 5.
Learn more about trigonometric ratio here:
https://brainly.com/question/25122825
#SPJ1
Assume multiplicity 1 unless otherwise stated
Answers
Answer:
f(x) = x^4 - 6x^3 + 18x^2 - 54x + 81
Step-by-step explanation:
We have a zero of 3 with multiplicity 2, and
since 3i is a root, -3i must also be a root.
f(x) = ((x - 3)^2)(x - 3i)(x + 3i)
f(x) = (x^2 - 6x + 9)((x^2 + 9)
f(x) = x^4 + 9x^2 - 6x^3 - 54x + 9x^2 + 81
f(x) = x^4 - 6x^3 + 18x^2 - 54x + 81
If a = -5, then 2a = -10
what is the property
Answers
Answer:
There would be no property because it doesn't form any conic sections.
Hope this helped :)
P.S. Are there answer choices?
a publisher reports that 29% of their readers own a particular make of car. a marketing executive wants to test the claim that the percentage is actually different from the reported percentage. a random sample of 250 found that 26% of the readers owned a particular make of car. determine the p-value of the test statistic. round your answer to four decimal places.
Answers
The test statistic's p-value is 0.0982.
According to one publisher, 29% of its readers are using a computer.
Claim: A marketing executive would like to put to the test the allegation that the percentage differs from the reported percentage.
\(H_{0}\): p = 0.29
\(H_{a}\): p ≠ 0.29
A random selection of 250 readers revealed that 26% had a computer.
The number of persons who own a personal computer,
26% × 250
= (26 ÷ 100) × 250
= 65
x = 65
n = 250
One sample proportion test should be used.
p-vector = x ÷ n
p-vector = 65 ÷ 250
p-vector = 0.26
The test statistic's formula,
((p-vector) - p) ÷ (√(p(1 - p)) ÷ n))
Substitute the above values,
((0.26) - 0.29) ÷ (√(0.29(1 - 0.29)) ÷ 250))
= -1.652
The p-value from the z table is 0.0982.
Read more about p-value at
https://brainly.com/question/13865364?referrer=searchResults
#SPJ4
Jasmine paid $380 for a playstation 5, originally priced at $500. What percent discount did Jasmine get?
Answers
She got it for 24% off
$500 - 24% = $380
If 500 = 100%
Then 380 = ?
Cross multiply 380 x 100 = 38000
Divide 38000 by 500 = 76
Subtract 76 from 100 = 24
Help me please no bots
Answers
Answer:
8/10 = 4/5
1/2 < 7/12
3/4 > 8/1
problem solving + 6 i can't see sadly
reg enters a triathlon race. He swims 1.25 kilometers, bikes 20.5 kilometers, and runs 1.59 kilometers.
How many kilometers is the race?
Enter your answer as a decimal in the box.
20 point 1 6
km
Answers
Total distance of the triathlon race is 23.34 kilometers.
Reg enters a triathlon race. He swims 1.25 kilometers, bikes 20.5 kilometers, and runs 1.59 kilometers.
The total distance of the race is 23.34 kilometers.
Reg enters a triathlon race.
He swims 1.25 kilometers, bikes 20.5 kilometers, and runs 1.59 kilometers.
In order to calculate the total distance of the race, we need to find the sum of the distance Reg swam, biked and ran. Therefore, Total distance = Distance swam + Distance biked + Distance ranTotal distance = 1.25 + 20.5 + 1.59 km
Total distance = 23.34 km.
The summary of this problem is that the total distance of the triathlon race is 23.34 kilometers.
Learn more about distance click here:
https://brainly.com/question/26550516
#SPJ11
using maria’s new budget, if she wanted to buy a new tv that costs $420 and wanted to do it in 6 months, how much additional money must she cut from her expenses each month?
Answers
Maria must cut an additional $70 from her expenses each month in order to save enough money to buy a new TV that costs $420 in 6 months. By allocating this additional amount towards her savings goal, she will be able to reach her target within the desired timeframe. It's important for Maria to review her budget and identify areas where she can reduce expenses in order to make room for the additional savings. This could involve cutting back on discretionary spending, finding ways to save on daily expenses, or exploring opportunities to increase her income.
Maria must cut an additional $70 from her expenses each month.
To determine how much additional money Maria must cut from her expenses each month to afford a new TV that costs $420 in 6 months, we divide the total cost by the number of months.
Additional money per month = Total cost / Number of months
Additional money per month = $420 / 6
Additional money per month = $70
With careful planning and commitment to her budget, Maria can achieve her goal of purchasing a new TV without compromising her financial stability.
To know more about expenses , visit
https://brainly.com/question/14697297
#SPJ11
\(log\frac{8}{3}\)
Answers
ANS
\( log \frac{(8)}{3} \)
\( = 0.30102999566\)
Thank You !!!!
Aaron is on his school's wrestling team. He and his teammates want to paint the school's mascot on the wrestling mats. The T-
shirts sold at Aaron's school show the mascot, a Bulldog, with a nose that is 1.2 cm long and a front paw that measures 4.5 cm
across. If Aaron and his teammates plan to paint an enlarged image of the Bulldog with a nose that is 6 cm long, how long
should they make the front paw?
Answers
Answer:
22.5 cm
I hope this answer helps!
ayudenme con esto por favor
Answers
Answer:
the answer is on the computer
Step-by-step explanation:
Finding the average values of the respective coordinates of the two endpoints of a line segment in a coordinate plane is also known as using the.
Answers
The average values of the respective coordinates of the two endpoints of a line segment in a coordinate plane is also known as midpoint.
A midpoint is a point lying between two points and is in the middle of the line joining the two points. If a line is drawn joining the two points, then the midpoint is a point at the middle of the line and is equidistant from the two points.
The midpoint formula is defined for the points in the coordinate axes. Let (x)1, (y)1 and (x)2, (y)2 be the endpoints of a line segment. The midpoint is equal to half of the sum of the x-coordinates of the two points, and half of the sum of the y-coordinates of the two points.
Hence, the average values of the respective coordinates of the two endpoints of a line segment in a coordinate plane is also known as midpoint.
Find out more information about midpoint here:
brainly.com/question/4728902
#SPJ4
Given a collection of 2023 closed squares of total area 4, prove that they can be arranged to cover a unit square (overlaps are allowed)
Answers
We can arrange the 2023 squares to cover the unit square, with overlaps allowed.
We can prove that a collection of 2023 closed squares of total area 4 can be arranged to cover a unit square by using the pigeonhole principle. Since the total area of the squares is 4, the average area of each square is 4/2023. Let's take a unit square and divide it into 2023 smaller squares of area (1/2023) each. By the pigeonhole principle, we can assign one of the 2023 squares to each of the smaller squares. Since the average area of each square is 4/2023, each of the assigned squares will overlap with at most 4 other squares. Therefore, we can arrange the 2023 squares to cover the unit square, with overlaps allowed.
Learn more about the pigeonhole principle here: brainly.com/question/30322724
#SPJ4
Find the distance between point A (2, -4) and point C (14,1)
Answers
Simplify the expression:
2(4 + 3v) =
Answers
Answer:
6v+8
Step-by-step explanation:
you multiply the equation in parantheses by 2
Answer:
=8+6v
all you had to do was simply the expression
There are two more quarters than dimes and as many nickels as dimes and quarters together. The total amount of money is 3. 75 dollars how many nickels dimes and quarters are there each
Answers
There are two more quarters than dimes and as many nickels as dimes and quarters together. The total amount of money is 3. 75 dollars, then nickels dimes and quarters are there each, D =7 dimes , Q = 9 quarters, and N = 16 nickels
tart by defining the variables for this problem :
Q : number of quarters
D : number of dimes
N : number of nickels
There are two more quarters than dimes so the equation :
Q = D+2
And as many nickels, as quarters and dimes together so the equation :
N = Q+ D
The total amount of money is $3.75 so the equation :
0.25Q + 0.10D + 0.05N =3.75
Solve the following system :
Q = D + 2 (I)
N = Q + D (II)
0.25Q + 0.10D + 0.05N =3.75(III)
In the equation (II) find Q in terms of N and D :
N = Q + D (II)
Q = N - D (IV)
If use (I) in (IV) :
Q = N - D
D + 2 = N - D
2D = N - 2
N = 2D + 2 (V)
If use (I) and (V) in (III)
0.25Q + 0.10D + 0.05N =3.75
(0.25) . (D + 2) + 0.10D + (0.05) . (2D + 2) = 3.75
0.25D +0.50 + 0.10D + 0.1D + 0.1 = 3.75
0.45D = 3.75
D = 3.75/ 0.45
D = 7
if D = 7 -----------replacing in (I)
Q = D + 2
Q = 7 + 2
Q = 9
If replace this values in (II)
N = Q + D
N = 9 + 7
N = 16
there are D =7 dimes,
Q = 9 quarters
N = 16 nickels
To learn more about Dollars visit:
brainly.com/question/28547396
#SPJ4
When graphed, all of the points in the table lie on the same line
What are the slope and y-intercept of the line?
Slope = 2, y-Intercept = -4
Slope = -1, y-Intercept = 2
Slope = 1, y-Intercept = 2
Slope = -2, y-Intercept = -4
Answers
Answer:
Slope: 1
y-intercept: 2
Step-by-step explanation:
(0,2) and (2,4)
Slope = (4-2)/(2-0) = 2/2 = 1
y-intercept: 2 - (1)(0) = 2
Which of the following graphs represent the dilation of
the given triangle XYZ with the center of dilation at the
origin with a scale factor 3?
Please I need it fast
Answers
Answer:
12y
Step-by-step explanation:
7y- (5y - 12) = 20 + 2y +4
Answers
Answer:
12
Step-by-step explanation:
7y-5y+12=20+2y+4(combine and subtract 7-5)
2y+12=20+2y+4
2y+12=24+2y(add)
2y+12=2y+24(flip 24+2y into: 2y+24)
2y+12-12=2y+24-12(subtract 12 from both sides)
2y=2y+12(simplify, subtract them)
2y-2y=2y+12-2y(subtract 2y from both sides)
0=12(simplify terms)
Hope this helps! If so, make me brainliest please! Thanks!
Pls help or I’m gonna fail
Answers
Answer:
SAMEEE
Step-by-step explanation:
Answer:
The equation for a cylinder is V = π r 2 h
Step-by-step explanation:
So this is what your equation would look like:
V = (π)(4)(2)(8)
Pi=3.14
log (x2 - 1) - log (2x + 2) = 0
Answers
Answer:
x=3
Step-by-step explanation:
log (x^2 - 1) - log (2x + 2) = 0
Add log (2x + 2) to each side
log (x^2 - 1) = log (2x + 2)
Since the logs with the same base are equal the x^2 -1 must equal 2x+2
x^2 -1 = 2x+2
Subtract 2x+2 from each side
x^2 -1 -2x-2 = 2x+2 -2x-2
x^2 -2x-3 = 0
Factor
What number multiplies to -3 and adds to -2
-3 *1 =-3
-3+1 =-2
(x-3) (x+1) =0
Using the zero product property
x-3 =0 x+1 =0
x=3 x=-1
Check to see if solutions are valid
x = -1
log ((-1)^2 - 1) - log (2*-1 + 2) = 0
log(0) - log 0 = 0
Log 0 is undefined x =-1 not a valid solution
x = 3
log ((3)^2 - 1) - log (2*3 + 2) = 0
log(8) - log 8 = 0
valid
Graph line with the equation y=x+6. (Can you explain how to do this overall)
Answers
Answer:
First using y = Mx + b with m = slope and b = y intercept so 1/3 = slope and (0,6) is y intercept next plot (0,6) the plot slope from that point with rise/run or from point (0,6) go up +1 point and over +3 and make a point then go up +1 and over +3 or from (0,6) use slope = -1/-3 since they equal the same thing. So from point (0,6) go down -1 and to the left -3. Then draw your line.
Step-by-step explanation: