Find the value of tan W rounded to the nearest hundredth, if necessary.
W
V
41
40
U
Answers
\(\textit{using the pythagorean theorem} \\\\ c^2=a^2+b^2 \qquad \begin{cases} c=hypotenuse\\ a=adjacent\\ b=opposite\\ \end{cases} \\\\[-0.35em] ~\dotfill\\\\ WU^2=UV^2+WV^2\implies \sqrt{WU^2-UV^2}=WV \\\\\\ \sqrt{41^2-40^2}=WV\implies 9=WV\)
Check the picture below.
The value of tan W rounded to the nearest hundredth, in the right angle triangle UVW is 4.55.
What is Pythagoras theorem?Pythagoras theorem says that in a right angle triangle, the square of the hypotenuse side is equal to the sum of the square of the other two legs of the right angle triangle.
The opposite side is the 40 units, while the hypotenuse side is 41 units long in the right angle triangle. Thus, the value of base side W is,
\((VW)^2+(40)^2=(41)^2\\(VW)=\sqrt{(41)^2-(40)^2}\\VW=9\rm\; units\)
In the right angle triangle, the value of tan W is the ratio of side VW and UV. Thus,
\(\tan W=\dfrac{UV}{VW}\\\tan W=\dfrac{41}{9}\\\tan W=4.55\)
Thus, the value of tan W rounded to the nearest hundredth, in the right angle triangle UVW is 4.55.
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Related Questions
The images below show a picture of ricoffy tin container with no dimensions indicated.the container is 2,5 times smaller than what it is in reality. Measure the diameter of the tin in mm and write down the real diameter in mm
Answers
The diameter of the tin in the picture is \(3d/5\) where 'd' is the diameter of the tin in reality.
What is the measurement of the diameter?Determining the diameter of tin:
Since there is no indication of dimensions, represent the diameter with a variable 'd' and find the diameter of the tin according to the given condition in the problem.
Here we have assumed that the diameter of the tin is 'd' in reality and the diameter of the tin picture can be calculated as given below.
Here we have
A ricoffy tin container with no dimensions indicated
Let d and h be the diameter and height of the tin
Given that the container is 2/5 times smaller than d
then the diameter of the tin in the picture \(= d - 2/5(d)\)
\(= [5d - 2d]/5 = 3d/5\)
Therefore, The diameter of the tin in the picture is \(3d/5\) where 'd' is the diameter of the tin in reality.
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Triangle JKL has vertices at the points J(2.5,3), K(3.2,-4.7), and L(-6.9,3). Find the slope of side JL.
A. undefined
B. -11
C. -0.76
D. 0
Answers
slope = (y2 - y1) / (x2 - x1)
Let's calculate the slope of side JK first, using the coordinates of points J(2.5, 3) and K(3.2, -4.7):
slope_JK = (-4.7 - 3) / (3.2 - 2.5)
slope_JK = (-7.7) / (0.7)
slope_JK ≈ -11
Now, let's calculate the slope of side KL, using the coordinates of points K(3.2, -4.7) and L(-6.9, 3):
slope_KL = (3 - (-4.7)) / (-6.9 - 3.2)
slope_KL = (7.7) / (-10.1)
slope_KL ≈ -0.76
Therefore, the slope of side JK is approximately -11, and the slope of side KL is approximately -0.76.
The options provided are:
A. undefined
B. -11
C. -0.76
D. 0
Based on the calculations, the correct answer would be:
B. -11
For which of these does correlation most likely imply causation?A. As dishwasher use increases, the size of a DVD collectionincreases.B. As the hours spent studying increases, the number of pointsscored by a basketball team increases.OC. As the number of cups of coffee consumed increases, the price ofa dress increases.OD. As grade point average increases, the number of scholarshipoffers increases.SUBMIT
Answers
Causation means that one event is the result of the occurrence of the other event.
Let's evaluate the options:
A. As dishwasher use increases, the size of a DVD collection
increases.
One event does not seem to be the result of another.
B. As dishwasher use increases, the size of a DVD collection
increases.
One event does not seem to be the result of another.
C. As the number of cups of coffee consumed increases, the price of
a dress increases.
One event does not seem to be the result of another.
D. As grade point average increases, the number of scholarship
offers increases.
The increase in scholarships may be due to the increase in average grade points.
Answer:
D. As grade point average increases, the number of scholarship
offers increases.
(question 15) Find the derivative of the function
using logarithmic differentiation.
Answers
Answer:
\(\textsf{A.} \quad (2+x)^x\left[\dfrac{x}{2+x}+\ln(2+x)\right]\)
Step-by-step explanation:
Replace f(x) with y in the given function:
\(y=(x+2)^x\)
Take natural logs of both sides of the equation:
\(\ln y=\ln (x+2)^x\)
\(\textsf{Apply the log power law to the right side of the equation:} \quad \ln a^n=n \ln a\)
\(\ln y=x\ln (x+2)\)
Differentiate using implicit differentiation.
Place d/dx in front of each term of the equation:
\(\dfrac{\text{d}}{\text{d}x}\ln y=\dfrac{\text{d}}{\text{d}x}x\ln (x+2)\)
First, use the chain rule to differentiate terms in y only.
In practice, this means differentiate with respect to y, and place dy/dx at the end:
\(\dfrac{1}{y}\dfrac{\text{d}y}{\text{d}x}=\dfrac{\text{d}}{\text{d}x}x\ln (x+2)\)
Now use the product rule to differentiate the terms in x (the right side of the equation).
\(\boxed{\begin{minipage}{5.5 cm}\underline{Product Rule for Differentiation}\\\\If $y=uv$ then:\\\\$\dfrac{\text{d}y}{\text{d}x}=u\dfrac{\text{d}v}{\text{d}x}+v\dfrac{\text{d}u}{\text{d}x}$\\\end{minipage}}\)
\(\textsf{Let}\; u=x \implies \dfrac{\text{d}u}{\text{d}x}=1\)
\(\textsf{Let}\; v=\ln(x+2) \implies \dfrac{\text{d}v}{\text{d}x}=\dfrac{1}{x+2}\)
Therefore:
\(\begin{aligned}\dfrac{1}{y}\dfrac{\text{d}y}{\text{d}x}&=x\cdot \dfrac{1}{x+2}+\ln(x+2) \cdot 1\\\\\dfrac{1}{y}\dfrac{\text{d}y}{\text{d}x}&= \dfrac{x}{x+2}+\ln(x+2)\end{aligned}\)
Multiply both sides of the equation by y:
\(\dfrac{\text{d}y}{\text{d}x}&=y\left( \dfrac{x}{x+2}+\ln(x+2)\right)\)
Substitute back in the expression for y:
\(\dfrac{\text{d}y}{\text{d}x}&=(x+2)^x\left( \dfrac{x}{x+2}+\ln(x+2)\right)\)
Therefore, the differentiated function is:
\(f'(x)=(x+2)^x\left[\dfrac{x}{x+2}+\ln(x+2)\right]\)
\(f'(x)=(2+x)^x\left[\dfrac{x}{2+x}+\ln(2+x)\right]\)
I really need help with this I would be really happy happy If you could help me
Answers
as the picture say, we need to do constant/variable
the input variable i
Which of the following best describes the lines y-3x=4x and 6-2y=8x
○perpendicular
○parallel
○skew
○intersecting
Answers
Answer:
Intersecting (fourth answer choice)
Step-by-step explanation:
If the lines are perpendicular, parallel, or intersecting, they are not skew. Thus, we need to check if the lines can be classified as either perpendicular, parallel, or intersecting first. If the lines are classified as neither, then they are skew.First, let's convert both lines to slope-intercept form, whose general equation is y = mx + b, where
m is the slope,and b is the y-intercept.Converting y - 3x = 4x to slope-intercept form:
(y - 3x = 4x) + 3x
y = 7x
Thus, the slope of this line is 7 and the y-intercept is 0.
Converting 6 - 2y = 8x to slope-intercept form:
(6 - 2y = 8x) - 6
(-2y = 8x - 6) / -2
y = -4x + 3
Thus, the slope of this line is -4 and the y-intercept is 3.
Checking if y = 7x and y = -4x + 3 are perpendicular lines:
The slopes of perpendicular lines are negative reciprocals of each other.We can show this in the following formula:
m2 = -1 / m1, where
m1 is the slope of one line,and m2 is the slope of the other line.Thus, we only have to plug in one of the slopes for m1. Let's do -4.
m2 = -1 / -4
m2 = 1/4
Thus, the slopes 7 and -4 are not negative reciprocals of each other so the two lines are not perpendicular.
Checking if y = 7x and y = -4x + 3 are parallel lines:
The slopes of parallel lines are equal to each other.
Because 7 and -4 are not equal, the two lines are not parallel.
Checking if the lines intersect:
The intersection point of two lines have the same x and y coordinate. To determine if the two lines intersect, we treat them like a system of equations.Method to solve the system: Elimination:
We can multiply the first equation by -1 and keep the second equation the same, which will allow us to:
add the two equations, eliminate the ys, and solve for x:-1 (y = 7x)
-y = -7x
----------------------------------------------------------------------------------------------------------
-y = -7x
+
y = -4x + 3
----------------------------------------------------------------------------------------------------------
(0 = -11x + 3) - 3
(-3 = -11x) / 11
3/11 = x
Now we can plug in 3/11 for x in y = 7x to find y:
y = 7(3/11)
y = 21/11
Thus, x = 3/11 and y = 21/11
We can check our answers by plugging in 3/11 for x 21/11 for y in both y = 7x and y = -4x + 3. If we get the same answer on both sides of the equation for both equations, the lines intersect:
Checking solutions (x = 3/11 and y = 21/11) for y = 7x:
21/11 = 7(3/11)
21/11 = 21/11
Checking solutions (x = 3/11 and y = 21/11) for y = -4x + 3:
21/11 = -4(3/11) + 3
21/11 = -12/11 + (3 * 11/11)
21/11 = -12/11 + 33/11
21/11 = 21/11
Thus, the lines y = 3x = 4x and 6 - 2y = 8x are intersecting lines (the first answer choice).
This also means that lines are not skew since lines had to be neither perpendicular nor parallel nor intersecting to be skew.
(-0.4)^3 - (-0.4)^2.(-3)
Answers
Answer:
.416
Step-by-step explanation:
(-.04)^3=-.064
(-.064)-(-.04^2)(-3)
(-.064)-(.16)(-3)
(-.064)-(-.48)
.416
Answer:
0.416
Step-by-step explanation:
A band has 14 male members and 18 female members. What is the ratio of female members of the band to male members of the band? *
EVERYONE IS SAYING 14:18 BUT MY OPTIONS ARE
9:8
2:1
9:16
9:7
Answers
Answer:
9:7
Step-by-step explanation:
You divide both sides by a common denominator in this case 2 is the number that both can be divided by equally.
So
Girls (18) / 2 = 9Boys (14) / 2 =7Your answer is 9:7
Please help don’t understand
Answers
Answer:
y = 4/3(x +3)
Step-by-step explanation:
This sort of question is easily answered by making use of the point-slope form of the equation of a line:
y -k = m(x -h) . . . . . line with slope m through point (h, k)
You are given (h, k) = (-3, 0) and m = 4/3. Putting those into the above form gives ...
y -0 = 4/3(x -(-3))
y = 4/3(x +3) . . . . . . point-slope form equation
__
Additional comment
You can use the distributive property to eliminate the parentheses. That puts the equation into slope-intercept form.
y = 4/3x +(4/3)(3)
y = 4/3x +4 . . . . . . slope-intercept equation
__
You may find it useful to remember some different forms of the equation for a line:
y = mx +b . . . . . line with slope m and y-intercept b
y -k = m(x -h) . . . . . line with slope m through point (h, k)
ax +by = c . . . . standard form equation of a line, where a > 0, and a, b, c are mutually prime integers
Higher Order Thinking Mrs. Dryson
divided her collection of 52 glass
bears
into equal groups. She had 1 bear
left over. How many groups did
Mrs. Dryson
make? How many bears
are in
each group?
Answers
To ensure that there is an equal number of glass bears in each group, Mrs. Dryson constructed a total of 17 groups, which can be calculated using arithmetic operations.
What is arithmetic operations?
The study and application of numbers in all other fields of mathematics are covered in the area of mathematics known as arithmetic operations. Addition, subtraction, multiplication, and division are included in the basic operations.
As given in the question,
Mrs. Dryson divided her collection of 52 glass bears into equal groups and She had one bear left over
The steps listed below can be used to calculate the total amount of Mrs. Dryson's products:
Step 1: Arithmetic operations can be utilized to calculate Mrs. Dryson's overall output.
Step 2: Keep in mind that there are 52 glass bears in all, and after separating them into equal groups, she was left with just one bear.
Step 3 - The total bear population to divide into groups of an equal number is calculated as follows:
= 52 - 1 = 51
Step 4: The number that is divided by 51 such that the result is an integer is 3.
Step 5 - As a result, Mrs. Dryson created a total of the following groups:
= 51/3 = 17.
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Josh wants to add a model of a tree house to his model railroad layout how big should the tree be if the actual tree is 315 inches and the scale is 1:90
Answers
Answer:
3.5 inches on the scaled model
Step-by-step explanation:
So using the ratio, 1:90 I thought of two ways to solve this
1) Proportion
2) Equation
Using the proportion method
1:90=x:315
Now cross multiply
315=90x
Now solve and you’ll get 3.5
Equation is just
315/90=X?
Just solve and you’ll also get 3.5
In the year that this exercise was written, there were 611 challenges made to referee calls in professional tennis single ppay. Among these challenges, 172 were upheld with the cell overturned. Assume that 30% of the challenges were successfully upheld with the cell overturned. Find the probability amonng the 611 challenges the number of overturned calls is exactly 172.
Answers
Answer:
i use this formula at school but when i simply calculate at my calculator, it says "math error" . i am sorry but i hope this formula helped
Colton is building a new shed for his backyard. The shed has a right rectangular prism for the base and triangular prism for the roof component. Colton included the dimensions of the shed in his diagram.
1.) How much can Colton store inside the new shed? Explain your reasoning.
2.) Colton wants to paint the outside of the shed including the door to match his house. Explain how much paint Colton will need to paint the shed.
3.) A gallon of paint covers 200 square feet and cost $16.99.
-How many cans of pain are needed?
-How much will it cost Colton to paint the shed?
Answers
The volume Colton store inside the new shed is 640 cubic feet.
We are given that;
length=10, width=8, height=6
Now, we can calculate the volumes of each part:
Volume of base prism = lwh Volume of base prism = (10)(8)(6) Volume of base prism = 480 cubic feet
Volume of roof prism = Bh Volume of roof prism = (0.5)(8)(4)(10) Volume of roof prism = 160 cubic feet
Volume of shed = Volume of base prism + Volume of roof prism Volume of shed = 480 + 160 Volume of shed = 640 cubic feet
Therefore, by the given prism the answer will be 640 cubic feet.
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Simplify 20 + 52 × 2.
Answers
Answer:
124
Step-by-step explanation:
Following PEMDAS,
multiplication comes first, 52x2 equals 104
Then add 20 to 104
124
Answer:
124
Step-by-step explanation:
20+50x2
20+104
124
Revisa el mapa anterior y subraya la opción adecuada.
Está más cerca del restaurante
la gasolinera
el teatro
el parque
la biblioteca
Está más lejos del parque
Estándar curricular: Utilizo sistemas de referencia convencionales para ubicar puntos o de
su ubicación en planos, mapas y en el primer cuadrante del plano cortesiano
Answers
Answer:
no se ve el mapa así que no se puede responder
Step-by-step explanation:
Discuss the various factors which lead to the formation of droughts
Answers
Step-by-step explanation:
Below average rainfall in a region for several months
Not enough rain to be absorbed into the ground before evaporating
Cutting down trees and overuse of land
Hot dry air masses blown into a region by westerly winds
Human activities that deplete the water table faster than it can be replaced
a triangle has a base of 16 inches and a height of 1/8 inches what is the area
Answers
Answer:
the area is 2
Step-by-step explanation:
The area of the triangle will be 1 inch².
What is a triangle?
A triangle is a three-edged polygon with three vertices. It is a fundamental form in geometry. The sum of all the angle of a triangle is always equal to 180°.
Given that the height of the triangle is 1/8 inches and the base of the triangle is 16 inches. Therefore, the area of the triangle will be,
Area of the triangle = 0.5 × Height × Base
= 0.5 × (1/8) inches × 16 inches
= 1 inch²
Hence, the area of the triangle will be 1 inch².
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Write 18 hundreds 11 tens in standard form.
Answers
The standard form of "18 hundreds 11 tens" is 1910.
To write "18 hundreds 11 tens" in standard form, we need to convert the given number into its numerical representation.
We know that 1 hundred is equal to 100, and 1 ten is equal to 10.
So, to find the numerical value of "18 hundreds 11 tens," we multiply the respective values by their place values and then add them together.
18 hundreds = 18 x 100 = 1800
11 tens = 11 x 10 = 110
To find the standard form, we add the two values:
1800 + 110 = 1910
Therefore, "18 hundreds 11 tens" in standard form is 1910.
In standard form, numbers are written using digits, without any reference to place value units like hundreds or tens.
The standard form of a number represents its numerical value directly. So, the numerical value of "18 hundreds 11 tens" is 1910, which is its standard form.
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in the diagram,QOS and ROU are straight lines.OT is the bisector of angle UOS. Angle POQ and angle QOR are complementary angles. Find the values of x and y.pleaseeee answer sooonnn
Answers
Answer:
x=50° and y=45°
Step-by-step explanation:
x=QU(90°)-QP(40°)
x=50°
y=SU(90°)/2
y=45°
I need help please I don’t understand this
Answers
Answer:
f(1)= 1
Step-by-step explanation:
So assuming you're doing basic functions, f(x) just means "function of x".
This means that x is your input. So once you plug in the x value, you will see that when the x value of your function is 1, the y value is 1 as well.
This will be marked brainliest if correct ok?
2 in a half from f 2 and a half (2 1/2) units down from line. I'm not sure though but you just have to listen to your teacher help yall learn and you'll know! PLSSS MARK ME BRAINLIEST OR COMMENT ME OR STAR ME OR THANK ME OR SOMETHING PLSSS
Petra jogs 6 miles in 42 minutes. At this rate, how long would it take her to jog 8 miles?
Answers
Distance 1 / Time 1 = Distance 2 / Time 2
Using the information given:
6 miles / 42 minutes = 8 miles / Time 2
To solve for Time 2, we can cross-multiply and then divide:
6 miles * Time 2 = 8 miles * 42 minutes
6 * Time 2 = 8 * 42
6 * Time 2 = 336
Now, we divide both sides by 6 to isolate Time 2:
Time 2 = 336 / 6
Time 2 = 56 minutes
Therefore, it would take Petra 56 minutes to jog 8 miles at the same rate.
Answer:
56 minutes
Step-by-step explanation:
We can use proportions to solve.
6 miles 8 miles
------------ = ------------------
42 minutes x minutes
Using cross products.
6x = 42 *8
Divide each side by 6
x = 42/6 * 8
x = 7*8
x = 56
whats the equation of a line that passes through point (-1,3) with slope of 1
Answers
The equation of the line that passes through the point (-1, 3) with a slope of 1 is y = x + 4.
To find the equation of a line that passes through the point (-1, 3) with a slope of 1, we can use the point-slope form of a linear equation.
The point-slope form of a linear equation is given by:
y - y1 = m(x - x1)
where (x1, y1) represents the coordinates of a point on the line, and m represents the slope of the line.
Using the given point (-1, 3) and slope 1, we substitute these values into the point-slope form equation:
y - 3 = 1(x - (-1))
Simplifying:
y - 3 = x + 1
Now, we can rewrite the equation in the standard form:
y = x + 4
Therefore, the equation of the line that passes through the point (-1, 3) with a slope of 1 is y = x + 4.
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Find y.
Round to the nearest tenth:
у
270
350 ft
y = [? ]ft
![Find y.Round to the nearest tenth:270350 fty = [? ]ft](https://i5t5.c14.e2-1.dev/h-images-qa/contents/attachments/7Aaoo4bJIdszMK3prmQIY5AEddexQewJ.png)
Answers
Answer:
178.3
Step-by-step explanation:
Hello There!
We can find the value of y using trigonometry
These are the trigonometric ratios
Remember SOHCAHTOA
Sine = Opposite over Hypotenuse
Cosine = Adjacent over Hypotenuse
Tangent = Opposite over Adjacent
For the angle that has a measure of 27 degrees
we are given its adjacent angle and we need to find its opposite angle (y)
Adjacent and Opposite sides corresponds with the trigonometric ratio Tangent so we are going to use the trigonometric ratio tan to solve for y
Now we set up an equation (remember tangent = opposite over adjacent)
\(tan(27)=\frac{y}{350}\)
Now that we have created an equation we want to solve for y
What we want to do is isolate the variable using inverse operations
So basically we want to get rid of the 350
The opposite of division is multiplication so we multiply each side by 350 to get rid of it
\(tan(27)*350=350tan(27)\\\frac{y}{350} *350=y\\y=350tan(27)\\350tan(27)=178.3339073\\\)
so we can conclude that y = 178.3339073
finally we want to round to the nearest tenth and we get that the answer is 178.3
Emma is going to invest $5,300 and leave it in an account for 19 years. Assuming the interest is compounded continuously, what interest rate, to the nearest tenth of a percent, would be required in order for Emma to end up with $7,700?
Answers
Answer: r=2.0%
Step-by-step explanation:
a certain patcch of land sustains a population of heffalump. If the heffalump is presently 42 and expected to double every six years, how many heffalumps will be living on this patch of land fifty years from now?
Answers
The population of the patch land in 50 years is given as follows:
13,547.
How to define an exponential function?An exponential function has the definition presented as follows:
\(y = ab^\frac{x}{n}\)
In which the parameters are given as follows:
a is the value of y when x = 0.b is the rate of change.n is the time needed for the rate of change.The parameter values in this problem are given as follows:
a = 42, b = 2, n = 6.
Hence the function for the population after x years is given as follows:
\(y = 42(2)^\frac{x}{6}\)
The population in 50 years is given as follows:
\(y = 42(2)^\frac{50}{6}\)
y = 13,547.
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What is the product?
7•(-3)
Answers
the correct answer.
Which inequality represents the values of that ensure triangle ABC exists?
A
2x+4
B
O D.
18
OA.
<< 1
OB. -< < ¹
O c. 1 < x < 5
6x
2 < < 6
Answers
The Inequality which ensure triangle exists is A. 7/4 < x < 11/2
What is the inequalityInequality is defined as the relation between two quantities with the sign of inequality that is >, <, ≤ , ≥ ."
Inequalities are simply created through the connection of two expressions. In this case, it should be noted that the expressions in an inequality are not always equal.
Theorem used In ΔABC,
AB + BC >AC
AC+ BC >AB
AC + AB > BC
According to the question,
In triangle ABC.
AC = 18units
BC = 6x units,
AB = 2x + 4 units
Substitute the value in the inequality to ensure triangle exists we get 7/4 < x < 11/2. The correct option is A.
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solve this with an explantion i will say thanks
Answers
Answer: x=5
Step-by-step explanation:
divide both sides by the numeric factor on the left side, then that will give the answer for x
15x-8=52
Add 8 to both sides of the equation
12x-8=52
12x-8+8=52+8
Simply
Add the numbers
12x=60
Divide both sides of the equation by the same term
12x=60
Divide both side by 12
X=5
Identify the holes, vertical asymptotes, and horizontal asymptotes of the following.
\(f (x) = \frac{2}{x-3}\)
Answers
Answer:
Horizontal asymptote: y = 0
Vertical asymptote: x = 3
Step-by-step explanation:
The vertical asymptote in this graph would be when x = 3 because it would make the denominator 0, which would make the equation undefined.
There will not be any holes in the graph, because there won't be any point undefined in the function except for when x = 3, but that's a vertical asymptote.
Now, for the horizontal asymptote, we see what value y approaches as x approaches plus and minus infinity. Since x is in the denominator, y will approach 0 when it's plus or minus infinity.
Horizontal asymptote: y = 0
Vertical asymptote: x = 3
what are the solutions of the compound inequality 2d + 3 < -11 or 3d - 9 > 15
Answers
Answer:
d ≤ –7 or d > 8.
Step-by-step explanation:
Given : 2d + 3 ≤ –11 or 3d – 9 > 15.
To find : What are the solutions of the compound inequality .
Solution : We have given 2d + 3 ≤ –11 or 3d – 9 > 15.
For 2d + 3 ≤ –11
On subtracting both sides by 3
2d ≤ –11 - 3 .
2d ≤ –14.
On dividing both sides by 2 .
d ≤ –7.
For 3d – 9 > 15.
On adding both sides by 9.
3d > 15 + 9 .
3d > 24 .
On dividing both sides by 3 .
d > 8 .
So, A. d ≤ –7 or d > 8.
Therefore, A. d ≤ –7 or d > 8.