Answers
[tex]sin(51)= \frac{y}{12} [/tex]
and 12 sin(51) = y and y = 9.325
The second one has the reference angle as the unknown. You could use any of the identities here because you have all the sides of the triangle, but I will use sin again:
[tex]sin \beta = \frac{12}{13} [/tex]
and [tex]sin \beta =.9230769[/tex]
and [tex]sin ^{-1}(.9230769)=67.38 [/tex]
The next one has a referece angle of 13 with 24 being the side adjacent to it and the unknown being the side across from it. You will use the tangent identity here:
[tex]tan(13)= \frac{x}{24} [/tex]
and 24 tan(13) = x so x = 5.540
The last one has a reference angle of 20 with the hypotenuse as the unknown x, and the side across from it as 10. Use the sin identity again:
[tex]sin(20)= \frac{10}{x} [/tex] and
[tex]x sin(20)=10 [/tex] and
[tex]x= \frac{10}{sin(20)} [/tex] with x = 29.238
Everything is in regards to the reference angle; you HAVE to be able to identify the reference angle and then how the given sides are related to it.
Related Questions
Name an angle adjacent to ∠DGE.
A. ∠FGI
B. ∠EGH
C. ∠HGJ
D. ∠JGI
Answers
------------------------------------------------
The given angle is DGE. Exactly two of the letters (D, G, and E) will be found in any adjacent angle to this given one. For example, angle FGD is adjacent to DGE because of the shared letters D and G. The two angles share the segment DG.
Similarly, angle DGE is adjacent to EGH for the same reason. Now segment EG is the overlapping shared segment. Note how "E" and "G" can be found in the given angle and the answer.
Edit: see the attached image for visual proof. The given angle is in red. The angle for the answer is in blue.
HELP PLEASE !!! Find the measure of <2
Answers
answer
40 - last choice
Answer:
40
Step-by-step explanation:
Jillian’s begins to solve a linear equation that results in a variable expression set equal to the same variable as expression. Which is the best interpretation of this solution
Answers
the equation has infinite solutions
Answer:
infinity solutions
Step-by-step explanation:
A mathematics journal has accepted 14 articles for publication. However, due to budgetary restraints only 9 articles can be published this month. How many ways can the journal editor assemble 9 of the 14 articles for publication? A. 726,485,760 B. 14 C. 2,002 D. 126
Answers
Answer:
A. 726,485,760
Step-by-step explanation:
A mathematics journal has accepted 14 articles for publication.
However, due to budgetary restraints only 9 articles can be published this month.
As the journals are published one by one (arranged combination), so the order matters in this case.
So permutation should be used in this case, rather than combination.
Hence, the number of ways the journal editor can assemble 9 of the 14 articles for publication is,
[tex]=\ ^{14}\text{P}_9=\dfrac{14!}{(14-9)!}=\dfrac{14!}{6!}=726,485,760[/tex]
Store employees are handing out coupons. Every 10th customer gets a $1 coupon. Every 12th customer gets a $2 coupon.
Which customer is the first to receive both coupons?
Answers
correct answer 60th costumer
Saving account has a principal of 1,800.00 it earns 6 percent interest compounded semiannually. How much is the compound interest after 1 year
Answers
A=p (1+r/k)^kt
A future value?
P principle 1800
R interest rate 0.06
K compounded semiannual 2
T time 1 year
A=1,800×(1+0.06÷2)^(2×1)
A=1,909.62
Now find the compound interest
I=A-p
I=1,909.62−1,800
I=109.62
PLEASE HELP!!! For the given quadratic equation convert into vertex form, find the vertex, and find the value for x = 6. Show your work.
y = -2x2 + 2x +2
Answers
y = -2x^2+2x+2
y-2 = -2x^2+2x
y-2 = -2(x^2-x) ... notice the x coefficient here -1
y-2 = -2(x^2-x+1/4 - 1/4) ... take half of -1 to get -1/2, then square it to get 1/4
y-2 = -2(x^2-x+1/4)-2(-1/4)
y-2 = -2(x^2-x+1/4)+1/2
y-2-1/2 = -2(x^2-x+1/4)
y-5/2 = -2(x-1/2)^2
y = -2(x-1/2)^2+5/2
y = -2(x-0.5)^2+2.5
Answer in fraction form: y = -2(x-1/2)^2+5/2
Answer in decimal form: y = -2(x-0.5)^2+2.5
-------------------------------------------------------------------------------
Part 2) Find the vertex
The answer from part 1) leads to the answer to part 2). The nice thing about vertex form that it's easy to read off the vertex without having to do any extra work.
Vertex form is y = a(x-h)^2 + k
Match that to y = -2(x-1/2)^2+5/2 and we see that a = -2, h = 1/2, k = 5/2
The vertex is (h,k) = (1/2, 5/2) in fraction form. That's equivalent to (h,k) = (0.5, 2.5) in decimal form
Answer in fraction form: (1/2, 5/2)
Answer in decimal form: (0.5, 2.5)
-------------------------------------------------------------------------------
Part 3) Find the y value when x = 6
Plug in x = 6, to get...
y = -2x^2+2x+2
y = -2(6)^2+2(6)+2
y = -2(36)+2(6)+2
y = -72+12+2
y = -60+2
y = -58
Answer: y = -58
Maximal use of bezels, gradients, and drop shadows make an interface highly user friendly True False
Answers
FALSE
Using too much image effects can make an interface not user-friendly.
Use the graph below to answer the question that follows:
graph of curve that passes through the following points, 0, 5; pi over 2, 2; pi, negative 1; 3 pi over 2, 2; 2 pi, 5.
What is the rate of change between the interval x = π and x = three pi over two?
Answers
The rate of change between x = π and x = three pi over two is 6/π.
Explanation:The rate of change between the interval x = π and x = three pi over two can be found by calculating the slope of the line connecting these two points on the graph. In this case, we can calculate the slope by finding the difference in y-values and dividing it by the difference in x-values:
Slope = (y₂ - y₁) / (x₂ - x₁) = (2 - (-1)) / (π - 3π/2) = (2 + 1) / (3π/2 - π) = 3 / (π/2) = 6 / π
Therefore, the rate of change between the interval x = π and x = three pi over two is 6/π.
The rate of change between x = π and x = three pi over two is 6/pi.
Explanation:The rate of change between the interval x = π and x = three pi over two can be found by determining the slope of the line connecting the two points on the graph corresponding to these x-values.
Using the coordinates (pi, -1) and (3 pi over 2, 2), we can calculate the slope as follows:
Slope = (change in y)/(change in x) = (2 - (-1))/(3 pi over 2 - pi) = 3/(pi/2) = 6/pi
So, the rate of change between x = π and x = three pi over two is 6/pi.
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You thought the balance in ur cheking account was $68. When your bank statement arrives, you realize that you forgot to record a chem. The bank statement lists your balance as $26. Write and solve an equation to find out the amount of the chem that you forgot to record.
Answers
Answer is $42
Final Answer:
The amount of the check that you forgot to record is $42.
Step-by-step explanation:
Let x represents the amount which is forgotten in recording.
Bank balance + Amount of money forgotten in recording = Balance while checking account
26 + x = 68
x = 68 - 26
x = 42
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Show all work to write the equations of the lines, representing the following conditions, in the form y = mx + b, where m is the slope and b is the y-intercept:
Part A: Passes through (−2, 1) and parallel to 4x − 3y − 7 = 0
Part B: Passes through (−2, 1) and perpendicular to 4x − 3y – 7 = 0
Answers
-3y = -4x + 7
y = 4/3x - 7/3....slope here is 4/3
A. a parallel line will have the same slope
y = mx + b
slope(m) = 4/3
(-2,1)...x = -2 and y = 1
sub and find b, the y int
1 = 4/3(-2) + b
1 = -8/3 + b
1 + 8/3 = b
3/3 + 8/3 = b
11/3 = b
so ur parallel line is : y = 4/3x + 11/3
B. A perpendicular line will have a negative reciprocal slope. To get the negative reciprocal of a number, u flip the number and change the sign. So our perpendicular line will need a slope of -3/4
y = mx + b
slope(m) = -3/4
(-2,1)...x = -2 and y = 1
sub and find b, the y int
1 = -3/4(-2) + b
1 = 3/2 + b
1 - 3/2 = b
2/2 - 3/2 = b
-1/2 = b
so ur perpendicular equation is : y = -3/4x - 1/2
Final answer:
The equation of the line for Part A is y = (4/3)x + 11/3, since it is parallel to the given line with a slope of 4/3. The equation for the line in Part B is y = (-3/4)x - 1/2, as it is perpendicular to the given line and the slope is the negative reciprocal of 4/3.
Explanation:
Writing Equations of Lines
To find the equation of a line in the form y = mx + b, we first need to determine the slope (m) and the y-intercept (b). For Part A, since the line needs to be parallel to 4x - 3y - 7 = 0, the slope of our line must be the same as the slope of this given line. To find the slope of the given line, we can rewrite it in slope-intercept form:
4x - 3y = 7
-3y = -4x + 7
y = (4/3)x - 7/3
The slope is 4/3. Since parallel lines have the same slope, our line's slope is also 4/3. Using the point (-2, 1) it passes through, we can substitute into the equation y = mx + b to find b:
1 = (4/3)(-2) + b
1 = -8/3 + b
b = 1 + 8/3
b = 11/3
Thus, the equation of the line for Part A is y = (4/3)x + 11/3.
For Part B, to find a line perpendicular to the given line, we need the negative reciprocal of its slope. The negative reciprocal of 4/3 is -3/4. We then use the given point (-2, 1) to find the y-intercept:
1 = (-3/4)(-2) + b
1 = 3/2 + b
b = 1 - 3/2
b = -1/2
So, the equation for the line in Part B is y = (-3/4)x - 1/2.
The points in a coordinate plane are reflected in the y-axis. In general, every point (x, y) is mapped onto what point? (___,___)
Answers
In a Cartesian coordinate system, a point (x, y) reflected over the y-axis is mapped to the point (-x, y), as the x-component changes direction in the reflection while the y-component remains the same.
Explanation:When a point is reflected across the y-axis in a Cartesian xy-coordinate system, which has orthogonal directions defined by the unit vectors i and j for the x and y axis respectively, the coordinates of the point change in a specific way. For every point whose coordinates are initially (x, y), after being reflected over the y-axis, the resultant point will have coordinates (-x, y).
This happens because the reflection over the y-axis effectively reverses the direction of the x-component of the point's position vector, changing its sign from positive to negative or vice-versa, while leaving the y-component unaffected. Therefore, after reflection, a point (x, y) is mapped onto the point (-x, y).
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If angle SUT is 39, what does that tell us about angle TUV? What arc measure describes arc VTS? How can we make any assertions about these angle and arc measures? b. Which line segments’ length can be calculated based on knowing the radius length? Explain. c. If angle MOP is 49, which other angle measures can we calculate? What arc measures can we calculate? Describe which lesson concepts allow us to make these calculations.
Answers
In a circle, corresponding arc measures are equal to the angle at the center, while any chord, secant, or tangent length can be determined with a known radius. Furthermore, other angles and arcs can be obtained via properties of circles such as vertical angles, linear pairs, or the properties of quadrilaterals inscribed in circles.
Explanation:You've asked about the properties of angles, lines, and arc measures within a circle. For the first part, if angle SUT is 39 degrees, then since angle TUV is a vertical angle to it, angle TUV is also 39 degrees because vertical angles are equal. For the arc measure of VTS, since we know the measure of angle SUT, arc VTS will be 2 times that, or 78 degrees, due to the concept of inscribed angles.
Next, the lengths of any chord, secant, or tangent line segments can be calculated knowing the radius length, as they all relate back to the radius in some way. This knowledge comes from our study of circles.
For the third part, if angle MOP is 49 degrees, we can find other angle and arc measures because of the properties of circles. Other angle measures can be found using concepts like vertical angles, linear pairs, or the properties of quadrilaterals inscribed in circles, while arc lengths can be determined by the concept of inscribed angles or central angles. Understanding these concepts allows us to make calculated assertions on angles and arcs within circles.
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How do I solve this (step-by-step preferred) using common denominators?
Answers
[tex]\bf \textit{and now, if you recall }\textit{difference of squares} \\ \quad \\ (a-b)(a+b) = a^2-b^2\qquad \qquad a^2-b^2 = (a-b)(a+b)\\\\ -------------------------------\\\\ \textit{then we can combine }(x+1)(x-1)\implies x^2-1 \\\\\\ \cfrac{x^4+2x^3-x^2-2}{x(x+1)(x-1)}\implies \cfrac{x^4+2x^3-x^2-2}{x(x^2-1)}\implies \cfrac{x^4+2x^3-x^2-2}{x^3-x}[/tex]
Help please on that one
Answers
the circle is divided into 8 sections
5 are shaded
so 5/8 are shaded
5 divided by 8 = 0.625
0.625 = 62.5%
Round to 63% if you need to.
PLEASE HURRY!!! 30 POINTS
DIMENSIONAL ANALYSIS
A water cooler can hold 50 pt of water.
About how many liters of water can it hold?
1 L≈1.06 qt
23.6 L
26.5 L
94.3 L
106.0 L
Answers
The answer is 23.6 if I pretty sure
Eliza Savage received a statement from her bank showing a checking account balance of $324.18 as of January 18. Her own checkbook shows a balance of $487.38 as of January 29. The bank returned all of the cancelled checks but three. The amounts of these three checks are $15.00, $77.49, and $124.28. How much did Eliza deposit in her account between January 18 and January 29?
Answers
3 checks total : 15.00 + 77.49 + 124.28 = 216.77
that amount will still need to be deducted from the bank
so 324.18- 216.77=107.41
her checkbook has a total of 487.38
487.38-107.41 = 379.97 is the amount she deposited into her account
Answer:
The amount she deposited in her account between January 18 and January 29 is $379.97
Step-by-step explanation:
Given :
Eliza showing a checking account balance of $324.18 as of January 18.
Her own checkbook shows a balance of $487.38 as of January 29.
The bank returned all of the cancelled checks but three. The amounts of these three checks are $15.00, $77.49, and $124.28.
To Find : Eliza deposit in her account between January 18 and January 29.
Solution :
Eliza showing a checking account balance of $324.18 as of January 18.
Total amount of three checks = $15.00 + $77.49+ $124.28 =$216.77
The account balance after the deduction of three checks amount
= $324.18 -$216.77 = $107.41
So, the new balance is $107.41.
Her own checkbook shows a balance of $487.38 as of January 29.
So, the amount she deposited between January 18 and January 29
= $487.38-$107.41 = $379.97
Hence , The amount she deposited in her account between January 18 and January 29 is $379.97
Which one of the following tin-lead soldiers has the lowest melting point? A. 60/40 B. 70/30 C. 40/60 D. 50/50
Answers
Based on this, the soldier with the lowest melting point is the one with the highest tin ratio.
Answer : (B) 70/30
The product of twenty one negative integers is negative? True of false
Answers
Find the circumference of a circle that has an area of 452.16 square meters. (Use 3.1416 as the value of π.)
Answers
Final answer:
The circumference of a circle with a given area is 75.40 meters
Explanation:
To find the circumference of a circle, we can use the formula C = 2πr, where C is the circumference and r is the radius. First, we need to find the radius from the given area.
The formula for the area of a circle is [tex]A = \pi r^2[/tex]
Rearranging the formula, we get [tex]r = \sqrt{(A/\pi \p).[/tex]
Now, substitute the given area (452.16 square meters) into the formula and solve for r:
[tex]r = \sqrt{(452.16/3.1416)[/tex]
= 12.00 meters
Finally, plug the value of r into the circumference formula:
[tex]C = 2\pi (12.00)[/tex]
= 75.40 meters
Which of the following is quantitative data?
eye colors of a group of people
hair colors of a group of people
heights of a group of people
genders of a group of people
Answers
A rope is 66 feet long. It is cut into two pieces such that one piece is half the length of the other. What is the length of the longer piece of rope?
Answers
Then the other piece is 0.5x feet long
In total: x + 0.5x = 66 -> x = 44
So the longer piece is 44 feet, shorter piece is 22 feet
Rope Length = 1st Piece + 2nd Piece
Where 1st Piece = 1/2 the 2nd Piece.
Therefore.
Rope Length = 1/2x + x
Now substitute and solve for x.
66 = 1/2x + x
66 = 3/2x
/1.5 /1.5
44 = x
Therefore the longer piece is 44.
Proof.
First Piece: 1/2 x = 44 / 2 = 22
Second Piece = x = 44
22 + 44 = 66
Find the area under the standard normal curve to the left of z = −2.8 and to the right of z = 2.06
Answers
z₂ = 2.06 correspond to an area of = 0.9750
z₁ ≤ Area ≤ z₂ ↔ z₂ - z₁ = 0.9750 - 0.0026 = 0.9724
Answer Area = 0.9724
The area under the standard normal curve to the left of z = −2.8 and to the right of z = 2.06 is 0.9776.
Given that, z₁ = -2.8 and z₂ = 2.06.
What is normal a distribution?It is also called the Gaussian Distribution. It is the most important continuous probability distribution. The curve looks like a bell, so it is also called a bell curve.
The z-score is a numerical measurement used in statistics of the value's relationship to the mean of a group of values, measured in terms of standards from the mean.
The area under the standard normal curve to the left of z = −2.8 and to the right of z = 2.06 will be calculated as follows:
The standard normal table represents the area under the curve.
P(z<-2.8) ∩ P(z>2.06)=P(z<-2.8) + P(z>2.06)------(1)
According to the standard normal table, we have
z = -2.8 correspond to an area of = 0.0026
z = 2.06 correspond to an area of = 0.9750
Substitute these values in equation 1, we have
P(z<-2.8) + P(z>2.06) = 0.9750 + 0.0026 = 0.9776
Therefore, the area under the standard normal curve to the left of z = −2.8 and to the right of z = 2.06 is 0.9776.
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What reduced fraction corresponds to 92%?
Answers
An interior angle of a regular polygon has a measure of 108°. What type of polygon is it? The polygon is .
Answers
The polygon is a penthagon.
In a regular polygon with n sides, the sum of the interior angles is
[tex] 180(n-2) [/tex]
But we also know that each interior angle has a measure of 108, and of course there is a total of n angles. So, we also know that the sum of the interior angles is
[tex] 108n [/tex]
Since we have two expressions for the same quantity, these expressions must equal each other:
[tex] 180(n-2) = 108n [/tex]
To solve for n, let's start by expanding the left hand side:
[tex] 180n-360 = 108n [/tex]
Now move all terms involving n to the left hand side, and all constants to the right hand side:
[tex] 180n-108n = 360 [/tex]
Simplify the right hand side:
[tex] 72n = 360 [/tex]
And finally, divide both sides by 72:
[tex] n = \frac{360}{72} = 5 [/tex]
The correct polygon is, Pentagon
What is mean by Angle?An angle is a combination of two rays (half-lines) with a common endpoint. The latter is known as the vertex of the angle and the rays as the sides, sometimes as the legs and sometimes the arms of the angle.
We have to given that;
An interior angle of a regular polygon has a measure of 108°.
Since, We know that;
In a regular polygon with n sides, the sum of the interior angles is
⇒ 180 (n - 2)
Here, The sum of the interior angles is,
⇒ 108n
Hence, We can formulate;
⇒ 108n = 180 (n - 2)
⇒ 108n = 180n - 360
⇒ 360 = 180n - 108n
⇒ 72n = 360
⇒ n = 5
Thus, It shows the Pentagon.
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Orlando bought a new couch for $2,904, using the furniture store's finance plan. He will pay $121 a month for 24 months. Which equation can Orlando use to find out how much money he still owes after each month of the plan?
Select one:
a. y=2,904+121x
b. y=2904−121x
c. y=121x−2,904
d. y=121x
Answers
You have three $1 bills, four $5 bills, and two $10 bills in your wallet. You select a bill at random. Without replacing the bill, you choose a second bill at random. Find P($5 then $10).
Answers
P(5,10)=8/72
P(5,10)=1/9
The sides of a rhombus with angle of 60° are 6 inches. find the area of the rhombus. 9√3 in2 18√3 in2 36 in2
Answers
Drop a perpendicular from an obtuse vertex.
That makes a 30 - 60º right triangle, with
hypotenuse 6 and short leg 3. So the long leg,
which is the height of the rhombus, is 3√3 .
Since a rhombus is a parallelogram, its area
is base x height = 6 x 3√3 = 18√3 .
Drop a perpendicular from an obtuse vertex.
That makes a 30 - 60º right triangle, with hypotenuse 6 and short leg 3. So the long leg, which is the height of the rhombus, is 3√3 .
Since a rhombus is a parallelogram, its area is base x height = 6 x 3√3 = 18√3
Three painters can paint three walls in three minutes. how many painters are needed to paint 27 walls in nine minutes?
Answers
To paint 27 walls in 9 minutes, you would need 9 painters working at the same speed. This is based on the proportional relationship that each painter can paint 1 wall in 3 minutes.
Explanation:This problem can be solved with a clear understanding of proportions. Given that 3 painters can paint 3 walls in 3 minutes, it implies that each painter can paint 1 wall in 3 minutes.
Thus, in 9 minutes, a single painter can paint 3 walls.
Therefore, to paint 27 walls in 9 minutes, we would need 27/3 equals 9 painters.
It is important to note that this implies all painters are working at the same speed. This is a simple and practical example of proportions in mathematics
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4x=(cd)/(yz) solve for z