Answers
Answer:
A
Step-by-step explanation:
Since cosine is positive and sine is negative that puts θ in Quad IV.
From right triangles we know:
Cos θ = adjacent/hypotenuse = 5/13
sin θ = opposite/hypotenuse = ?/13
To find the opposite side across from θ use the pythagorean theorem.
5² + y² = 13²
25 + y² = 169
y² = 144
y = 12
we are given that sin is < 0 so sinθ = -12/13
Answer:
A
Step-by-step explanation:
[tex]\cos(\theta)=\dfrac{\textsf{adjacent side}}{\textsf{hypotenuse}}=\dfrac{5}{13}[/tex]
[tex]\textsf{As }\cos(\theta) > 0 \textsf{ the angle is in quadrant I or IV}[/tex]
Using Pythagoras' Theorem a² + b² = c² to find the side opposite the angle:
⇒ 5² + b² = 13²
⇒ b² = 144
⇒ b = 12
⇒ opposite side = 12
[tex]\implies \sin(\theta)=\dfrac{\textsf{opposite side}}{\textsf{hypotenuse}}=\dfrac{12}{13}[/tex]
[tex]\textsf{As }\sin(\theta) < 0 \textsf{ then }\sin(\theta)=-\dfrac{12}{13} \textsf{ and the angle is in either quadrant III or quadrant IV}[/tex]
Therefore, the common quadrant is quadrant IV and
[tex]\sin(\theta)=-\dfrac{12}{13}[/tex]
Related Questions
seven subtracted from twice a number given 17, find this number.
Answers
Answer:
The number should be 12.
Step-by-step explanation:
We can form a simple equation and solve for the variable:
2x - 7 = 17
2x = 24
x = 12
Find the sum of the average monthly rainfalls 1/8 + 1/4 + 5/8 + 7/8 + 1 1/8 + 1 5/8 + 1 7/8 + 2
Answers
Answer:
37/4
Step-by-step explanation:
1/8 + 1/4 + 5/8 + 7/8 + 1 1/8 + 1 5/8 + 1 7/8 + 2 = 3/8 + 3/2 + 13/4 + 33/8 = 37/4
Please help. Systems of equations. Solve using elimination.
12X + 16y = 96
12X + 48y = 192
Answers
Answer:
x=4
y=3
Step-by-step explanation:
12X + 16y = 96--(1)
12X + 48y = 192---(2)
(2)-(1),
12x + 48y - (12x+ 16y)= 192- 96
12x + 48y - 12x - 16y = 96
32y = 96
y= 96÷32
y =3
substituting y=3 in (1),
12x +(16×3) = 96
12x + 48 = 96
12x = 96-48
12x = 48
x= 48÷12
x= 4
Hope this helps!
If the same number is subtracted from both the numerator and the denominator of 13/17 , the result is 3/5 . Find the number.
Answers
Answer:
10/12?
Step-by-step explanation:
Help!
What is the answer to this question?
Answers
Answer:
Its perimeter is 23 units
Step-by-step explanation:
The perimeter of any figure is the sum of the lengths of its outline sides
The rule of the distance between two points is:
[tex]d=\sqrt{(x_{2}-x_{1})^{2}+(y_{2}-y_{1})^{2}}[/tex]In the given figure ABCD:
Its perimeter = AB + BC + CD + DE + EA
→ Find the length of each side using the rule above
A = (-4, -2), B = (-1, 2), C = (2, 2), D = (5, -1), E = (2, -4)
→ Substitute them in the rule above to find the lengths of its sides
[tex]AB=\sqrt{(-1--4)^{2}+(2--2)^{2}}=\sqrt{(-1+4)^{2}+(2+2)^{2}}\\\\=\sqrt{(3)^{2}+(4)^{2}}=\sqrt{9+16}=\sqrt{25}[/tex]
∴ AB = 5
[tex]BC=\sqrt{(2--1)^{2}+(2-2)^{2}}=\sqrt{(2+1)^{2}+(0)^{2}}\\\\=\sqrt{(3)^{2}+0}=\sqrt{9+0}=\sqrt{9}[/tex]
∴ BC = 3
[tex]CD=\sqrt{(5-2)^{2}+(-1-2)^{2}}=\sqrt{(3)^{2}+(-3)^{2}}\\\\=\sqrt{9+9}=\sqrt{18}[/tex]
∴ CD = [tex]\sqrt{18}[/tex]
[tex]DE=\sqrt{(2-5)^{2}+(-4--1)^{2}}=\sqrt{(-3)^{2}+(-4+1)^{2}}\\\\=\sqrt{(-3)^{2}+(-3)^{2}}=\sqrt{9+9}=\sqrt{18}[/tex]
∴ DE = [tex]\sqrt{18}[/tex]
[tex]EA=\sqrt{(-4-2)^{2}+(-2--4)^{2}}=\sqrt{(-6)^{2}+(-2+4)^{2}}\\\\=\sqrt{(-6)^{2}+(2)^{2}}=\sqrt{36+4}=\sqrt{40}[/tex]
∴ EA = [tex]\sqrt{40}[/tex]
→ Add them to find the perimeter of the figure ABCDE
∴ Its perimeter = 5 + 3 + [tex]\sqrt{18}[/tex] + [tex]\sqrt{18}[/tex] +[tex]\sqrt{40}[/tex] ≅ 22.8098
→ Round it to the whole number
∴ Its perimeter = 23 units
3c. For each differential equation, find the Laplace transform of the solution y:
y'' + 3y' + 2y = 5 sin(πx), y(0) = y'(0) = 0.
Answers
Answer:
[tex]y(x)=\frac{5}{3\pi}-\frac{5\pi}{27+3\pi^2}e^{-3x}-\frac{15}{9\pi+\pi^3}cos(\pi x)-\frac{5}{9+\pi^2}sin(\pi x)[/tex]
Step-by-step explanation:
[tex]y''+3y'+2y=5sin(\pi x),\: y(0)=y'(0)=0\\\\\mathcal{L}\{y''\}+3\mathcal{L}\{y'\}+2\mathcal{L}\{y\}=\mathcal{L}\{5sin(\pi x)\}\\\\s^2Y(s)-sy(0)-y'(0)+3[sY(s)-y(0)]+2Y(s)=\frac{5\pi}{s^2+\pi^2}\\\\s^2Y(s)+3sY(s)=\frac{5\pi}{s^2+\pi^2}\\ \\(s^2+3s)Y(s)=\frac{5\pi}{s^2+\pi^2}\\ \\Y(s)=\frac{5\pi}{(s^2+\pi^2)(s^2+3s)}\\ \\Y(s)=\frac{5\pi}{s(s+3)(s^2+\pi^2)}[/tex]
Perform the partial fraction decomposition
[tex]\frac{5 \pi}{s \left(s + 3\right) \left(s^{2} + \pi^{2}\right)}=\frac{A}{s}+\frac{B}{s + 3}+\frac{C s + D}{s^{2} + \pi^{2}}\\5\pi=s \left(s + 3\right) \left(C s + D\right) + s \left(s^{2} + \pi^{2}\right) B + \left(s + 3\right) \left(s^{2} + \pi^{2}\right) A\\\\5 \pi=s^{3} A + s^{3} B + s^{3} C + 3 s^{2} A + 3 s^{2} C + s^{2} D + \pi^{2} s A + \pi^{2} s B + 3 s D + 3 \pi^{2} A\\\\5\pi=s^3(A+B+C)+s^2(3A+3C+D)+s(\pi^2A+\pi^2B+3D)+3\pi^2A[/tex]
Solve for each constant
[tex]\begin{cases} A + B + C = 0\\3 A + 3 C + D = 0\\\pi^{2} A + \pi^{2} B + 3 D = 0\\3 \pi^{2} A = 5 \pi \end{cases}[/tex]
[tex]3\pi^2A=5\pi\\A=\frac{5}{3\pi}[/tex]
[tex]A+B+C=0\\3A+3B+3C=0\\(3A+3B+3C=0)-(3A+3C+D=0)\\3B-D=0\\3B=D[/tex]
[tex]\pi^2A+\pi^2B+3D=0\\\pi^2(\frac{5}{3\pi})+\pi^2B+3(3B)=0\\\frac{5\pi}{3}+\pi^2B+9B=0\\ B(\pi^2+9)=-\frac{5\pi}{3}\\B=-\frac{5\pi}{3(\pi^2+9)}\\B=-\frac{5\pi}{3\pi^2+27}[/tex]
[tex]3B=D\\3(-\frac{5\pi}{3\pi^2+27})=D\\-\frac{5\pi}{\pi^2+9}=D[/tex]
[tex]A+B+C=0\\\frac{5}{3\pi}-\frac{5\pi}{3\pi^2+27}+C=0\\\frac{15\pi^2+135}{3\pi(3\pi^2+27)}-\frac{15\pi^2}{(3\pi)(3\pi^2+27)}+C=0\\\frac{135}{9\pi^3+81\pi}+C=0\\\frac{15}{\pi^3+9\pi}+C=0\\C=-\frac{15}{\pi^3+9\pi}[/tex]
Take the inverse transform and solve for the IVP
[tex]Y(s)=\frac{\frac{5}{3 \pi}}{s}+\frac{- \frac{5 \pi}{27 + 3 \pi^{2}}}{s + 3}+\frac{- \frac{15 s}{9 \pi + \pi^{3}} - \frac{5 \pi}{9 + \pi^{2}}}{s^{2} + \pi^{2}}\\\\Y(s)=\frac{\frac{5}{3 \pi}}{s}-\frac{\frac{5 \pi}{27 + 3 \pi^{2}}}{s + 3}-\frac{ \frac{15 s}{9 \pi + \pi^{3}}}{s^{2} + \pi^{2}}-\frac{\frac{5\pi}{9+\pi^2} }{s^2+\pi^2}\\ \\y(x)=\frac{5}{3\pi}-\frac{5\pi}{27+3\pi^2}e^{-3x}-\frac{15}{9\pi+\pi^3}cos(\pi x)-\frac{5}{9+\pi^2}sin(\pi x)[/tex]
joanna has 45 postcards in her postcard collection, which is 180% of the number of postcards Kyle has. How many postcards does Kyle have?
Answers
Answer:
Kyle has 25 postcards
Step-by-step explanation:
Joanna has 45 postcards in her collection, which is 180% of the number of postcards of Kyle.
If the number of postcards of Kyle is K, and the number of postcards of Joanna is J, then:
J=180% K
Recall a percentage can be expressed in decimal by dividing by 100:
J=180/100*K
To find the value of K, we solve the above equation:
K=100/180*J
Since J=45:
K=100/180*45=25
Kyle has 25 postcards
Which loan or loans listed below are awarded based on the financial need of the student?
I. Perkins loan
II. subsidized Stafford loan
III. unsubsidized Stafford loan
a.
I only
b.
I and II
c.
II and III
d.
I, II, and III
Answers
Answer:
B.
I and II
Step-by-step explanation:
The loan or loans listed below are awarded based on the financial need of the student are the Perkins loan and subsidized Stafford loan. Option B. This is further explained below.
What is loan?Generally, a loan is simply defined as a borrowed object, especially a quantity of money that is anticipated to be repaid with interest.
In conclusion, The Perkins loan and subsidized Stafford loan are two loans that are provided depending on the student's financial need.
Read more about Loan
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Help I Dont understand
Answers
Answer:
Q4 part d
Q5 part c
Step-by-step explanation:
Please answer if you know how to do this, thank you
Answers
9514 1404 393
Answer:
vertex: (-2, -1)dashed line, shaded inside, parabola is positive (opens up)Step-by-step explanation:
The given inequality is in vertex form:
y = a(x -h)^2 +k . . . . . . has vertex (h, k)
so the vertex can be read from the given expression.
y > (x +2)^2 -1 ⇒ (h, k) = (-2, -1) . . . the vertex
The leading coefficient (+1) is positive so the parabola opens upward.
__
The y > ( ) tells you the boundary line is dashed (is not part of the solution). It also tells you the shading is above the curve, hence inside the parabola.
The two offered points (0, 0), (2, -3) are NOT part of the solution set.
Solve the inequality 4(k − 5) + 12k ≥ −4
Answers
Answer:
k ≥ 1
Step-by-step explanation:
Step 1: Write inequality
4(k - 5) + 12k ≥ -4
Step 2: Solve for k
Distribute 4: 4k - 20 + 12k ≥ -4Combine like terms: 16k - 20 ≥ -4Add 20 to both sides: 16k ≥ 16Divide 16 on both sides: k ≥ 1Inequality Form:
k
≥
1
k
≥
1
Interval Notation:
[
1
,
∞
)
[
1
,
∞
)
Exercice 2:
Exprimer chacune des propositions suivantes par une égalité faisant intervenir des longueurs.
1) Le point A est l'image du point B par l'homothétie de centre i et de rapport 0,6.
2) Le point M a pour image de point P par l'homothétie de centre R et de rapport -3.
3) Le point A est l'image du point B par l'homothétie de centre i et de rapport -5.
4) Le point M a pour image de point P par l'homothétie de centre R et de rapport 0,2.
Answers
Answer:
this question is wrong
dounuts or snacks or chips
Answers
Answer:
snacks, the reason being that it can be anything
Step-by-step explanation:
Answer:
Donuts
Step-by-step explanation:
The donuts are specifically tastier than the options mentioned
Whats 1 + 1 please i need help, im taking a test
Answers
Answer:
I am sure it's 2
Step-by-step explanation:
Source: Trust me bro
Answer:
The answer is 2 because 1 plus 1 is like having 2 things
Caroline surveyed 380 of the students in her school about their favorite color. 209 students said their favorite color was blue. What percentage of the surveyed students said their favorite color was blue?
Answers
Answer:
55% of the students surveyed said their favorite color was blue
Step-by-step explanation:
[tex]\frac{209}{380}[/tex] as a percent = 55%, or 0.55 in decimal form.
whats a better way to solve a polygon and what are the steps to it.
Answers
Hey there!
Calculating the exterior angles of regular polygons
To find the sum of interior angles of a polygon, multiply the number of triangles in the polygon by 180°. The formula for calculating the sum of interior angles is ( n − 2 ) × 180 ∘ where is the number of sides. All the interior angles in a regular polygon are equal.
Compute using long division: 342 ÷ 23
Answers
Start by setting it up with the divisor 23 on the left side and the dividend 342 on the right side like this:
2 3 ⟌ 3 4 2
Step 2:
The divisor (23) goes into the first digit of the dividend (3), 0 time(s). Therefore, put 0 on top:
0
2 3 ⟌ 3 4 2
Step 3:
Multiply the divisor by the result in the previous step (23 x 0 = 0) and write that answer below the dividend.
0
2 3 ⟌ 3 4 2
0
Step 4:
Subtract the result in the previous step from the first digit of the dividend (3 - 0 = 3) and write the answer below.
0
2 3 ⟌ 3 4 2
- 0
3
Step 5:
Move down the 2nd digit of the dividend (4) like this:
0
2 3 ⟌ 3 4 2
- 0
3 4
Step 6:
The divisor (23) goes into the bottom number (34), 1 time(s). Therefore, put 1 on top:
0 1
2 3 ⟌ 3 4 2
- 0
3 4
Step 7:
Multiply the divisor by the result in the previous step (23 x 1 = 23) and write that answer at the bottom:
0 1
2 3 ⟌ 3 4 2
- 0
3 4
2 3
Step 8:
Subtract the result in the previous step from the number written above it. (34 - 23 = 11) and write the answer at the bottom.
0 1
2 3 ⟌ 3 4 2
- 0
3 4
- 2 3
1 1
Step 9:
Move down the last digit of the dividend (2) like this:
0 1
2 3 ⟌ 3 4 2
- 0
3 4
- 2 3
1 1 2
Step 10:
The divisor (23) goes into the bottom number (112), 4 time(s). Therefore put 4 on top:
0 1 4
2 3 ⟌ 3 4 2
- 0
3 4
- 2 3
1 1 2
Step 11:
Multiply the divisor by the result in the previous step (23 x 4 = 92) and write the answer at the bottom:
0 1 4
2 3 ⟌ 3 4 2
- 0
3 4
- 2 3
1 1 2
9 2
Step 12:
Subtract the result in the previous step from the number written above it. (112 - 92 = 20) and write the answer at the bottom.
0 1 4
2 3 ⟌ 3 4 2
- 0
3 4
- 2 3
1 1 2
- 9 2
2 0
You are done, because there are no more digits to move down from the dividend.
The answer is the top number and the remainder is the bottom number.
Therefore, the answer to 342 divided by 23 calculated using Long Division is:
14
The quotient after division is 322 and the remainder is 20.
What is long division?Long division is the mathematical method for dividing large numbers into smaller groups or parts.
Given that, 342 ÷ 23,
When we will divide 342 by 23, we will get,
The quotient 322 and the remainder is 20.
Hence, the quotient after division is 322 and the remainder is 20.
Learn more about long division, click;
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help model -5+(-6) on the number line
Answers
Answer:
-5 -6 = -11
You start at -5 and move to the left by 6 spaces until you get to -11 :)
Hope this helps!
Have a good day!
Please rate and mark brainliest!!
C, G, and D are collinear. E, G, and F are also collinear. The two lines
intersect at point G. Line EF bisects line CD. Find EG: if CG=5x-1, GD=7x-
13, EF=6x-4, and GF=13.
Answers
Answer:
EG is 19 units
Step-by-step explanation:
Let us solve the question
∵ Lines CD and EF intersected at point G
∴ CD = CG + GD
∴ EF = EG + GF
∵ Line EF bisects line CD
→ That means G is the midpoint of CD
∴ CG = GD
∵ CG = 5x -1
∵ GD = 7x - 13
→ Equate them to find x
∴ 7x - 13 = 5x -1
→ Add 13 to both sides
∴ 7x -13 + 13 = 5x - 1 + 13
∴ 7x = 5x + 12
→ Subtract 5x from both sides
∴ 7x - 5x = 5x - 5x + 12
∴ 2x = 12
→ Divide both sides by 2
∴ [tex]\frac{2x}{2}=\frac{12}{2}[/tex]
∴ x = 6
∵ EF = 6x - 4
→ Substitute x by 6 to find its length
∴ EF = 6(6) - 4 = 36 - 4
∴ EF = 32
∵ EF = EG + GF
∵ GF = 13
∴ 32 = EG + 13
→ Subtract 13 from both sides
∵ 32 - 13 = EG + 13 - 13
∴ 19 = EG
∴ EG = 19 units
30 points I need an answer asap please
Answers
Answer:
D. 0.05
Step-by-step explanation:
5 x 10 = 50
50 as a decimal
0.5
Hope it helps!!!Brainliest pls!!!Solve for x.
4x - 36
3x + 10
Answers
Answer:
x = 46
Step-by-step explanation:
Since the angles are equal to each other, make the equations equal to each other.
4x - 36 = 3x + 10 and simplify
x - 36 = 10
x = 46
Hope this helps!
The value of x is 46.
Since the angles are equal to each other, make the equations equal to each other.
4x - 36 = 3x + 10
First, let's move the term with 3x to the left side by subtracting 3x from both sides:
4x - 3x - 36 = 3x - 3x + 10
Simplifying further:
x - 36 = 10
Next, let's move the constant term -36 to the right side by adding 36 to both sides:
x - 36 + 36 = 10 + 36
Simplifying further:
x = 46
Therefore, the value of x is 46.
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PLEASE ANSWER ASAP!!!!
Rewrite each of the following expressions without using absolute value
-|-3|
Answers
Answer:
-3
Step-by-step explanation:
[tex]\downdownarrows\\ -\left|-3\right|[/tex]
Calculate the absolute value
[tex]-3[/tex]
I hope this helps you
:)
jenny's MP3 player has 97 songs on it. if each song cost $1.25, how much did it cost for all the songs on her MP3 player?
Answers
Answer:
$121.25
Step-by-step explanation:
97 X 1.25 = 121.25
PLS HELP ME. Been on the same question for a while now.
Answers
Answer:
1050
Step-by-step explanation:
So, we know 4/5 of a gallon can paint 280ft^2, but we don't know how much each gallon can paint, so to find x, do this
4/5x=280ft^2, next multiply both sides by 5/4 to get x by itself
x=350
Now multiply x by 3 to get your new answer.
350*3=1050
Hope this helps, feel free to leave any questions.
Can someone help answer this 6th grade question?
Answers
Answer:
Club A charges $4 per car and club B charges $4 also
Step-by-step explanation:
Answer:
Yes,
Step-by-step explanation:
Club A charges $4 per car and club B charges $4 also
Flying agaist the wind, an airplane travels 6300 kilometers in7 hours. Flying with the wind, the same plane travels 8400 in 6 hours. What is the rate of the plane is still air and what is the rate of the wind?
Answers
Answer:
plane: 1150 kphwind: 250 kphStep-by-step explanation:
The given relationships allow us to write a system of equations in the speeds of the wind and plane.
Let w and p represent the speeds of the wind and the plane, respectively. We know speed is the ratio of distance to time, so ...
p -w = 6300 km/(7 h) = 900 km/h
p +w = 8400 km/(6 h) = 1400 km/h
__
Adding these two equations gives ...
2p = 2300 km/h
p = 1150 km/h . . . . . . divide by 2
Subtracting the first equation from the second gives ...
2w = 500 km/h
w = 250 km/h
The speed of the plane in still air is 1150 km per hour; the speed of the wind is 250 km per hour.
Maura added 5/8 of a cup of walnuts to a batch of trail mix. Later, she added 3/4 of a cup of almonds. How many cups of nuts did Maura put in the trail mix in all? Write your answer as a fraction or as a whole or mixed number. cups
Answers
Answer:
1 3/8 cups
Step-by-step explanation:
the equation is 5/8 + 3/4
to figure it out we need the same denominator, we'll be choosing 8
3 (x2)/ 4 (x2) = 6/8
you would have to multiply 2 both on the top and bottem
then you would have to add
5/8 + 6/8 = 11/8
then make that into a whole fraction
11/8 = 1 3/8
A machine that drills holes for wells drilled to a depth of
–72 feet in one day (24 hours).
If the machine drilled at a constant rate, what was the
depth after 15 hours?
Answers
Answer:
depth of -117 feet
Step-by-step explanation:
24 hours 72 feet, so one hour 72/24 = 3 feet
after 15 hours, another 3*15 = 45 feet, so the depth become 72 + 45 = 117 feet
What is the cf of 32 and 24?
Answers
Answer:
8
24 divided by 8 =3
32 divided by 8 =4
Solve the proportion:
5/X=12.5/20
A X=8
B X=9
C X=10
Answers
Answer:
A. X =8
Step-by-step explanation:
5/X=12.5/20
cross multiply
12.5X = 20*5
12.5X=100
X=100/12.5
X=8