Answer:
Step-by-step explanation:
SecA - TanA
= 1/CosA - SinA/CosA
= 1 - SinA/CosA
We know that Sin2A = 2SinACosA and Cos2A = Cos²A - Sin²A
Thus SinA = Sin2(A/2) = 2Sin(A/2)CosA/2
CosA = Cos2(A/2) = Cos²A/2 - Sin²A/2
Now substituting the values back,
=> 1 - 2Sin(A/2)Cos(A/2) / Cos²(A/2) - Sin²(A/2)
// we know that Sin²θ + Cos²θ = 1
=> Sin²(A/2) + Cos²A/2 - 2Sin(A/2)Cos(A/2) / Cos²(A/2) - Sin²(A/2)
//We know that numerator is of form a² + b² - 2ab which is (a - b)².
//Similarly denominator is of form a² - b² which is (a - b)(a + b)
=> [Sin(A/2) - Cos(A/2)]² / [Cos(A/2) + Sin(A/2)][Cos(A/2) - Sin(A/2)]
=> [ - {Cos(A/2) - Sin(A/2)}]² / [Cos(A/2) + Sin(A/2)][Cos(A/2) - Sin(A/2)]
=> [Cos(A/2) - Sin(A/2)]² / [Cos(A/2) + Sin(A/2)][Cos(A/2) - Sin(A/2)]
=> [Cos(A/2) - Sin(A/2)] / [Cos(A/2) + Sin(A/2)]
= R.H.S
Hence proved.
What is the slope of a line that is perpendicular to the line whose equation is
y= 4x – 3?
Answer:
-1/ 4
Step-by-step explanation:
y = 4x-3 has a slope of 4 because the equation is in slope intercept form
y = mx+b where the slope is m
Perpendicular lines have slopes that are negative reciprocals
-1/ 4 is the slope of a line that is perpendicular to y = 4x-3
There are 4512 marbles which will be divided equally among 48 students how many marbles will each student get
Answer:
94 marbles
Step-by-step explanation:
4512/48 = 94
20. What is the transformation?:
a. rotation
b. reflection
c. translation
Please help me with this! It’s due in a few hours
Answer:
Reflection
Step-by-step explanation:
A rotation would be to rotate a figure around the origin
A reflection would be to reflect the figure around one of the axes.
A translation would be to move a figure a certain amount of units.
Since A and A' are 2 units away from the y-axis, and C, B, B', and C' are all one unit away from the y-axis, this could not be a translation because the position of A'B'C' is not the same position of ABC.
It could not be a rotation around the origin or any point because it would result the figure in either Quadrant 2 or 3, and in the one occasion it would be in Quadrant 1, the figure cannot be in that position.
This reveals only one option, that which is a reflection. A reflection about the x-axis would not make sense, since it would result in Quadrant 3, so a reflection around the y-axis would make the most sense.
The data we have above also accounts for a reflection, since all points are a certain distant away from the y-axis.
ITS TIMED HELP!!!
Assuming x and y are two odd numbers and x/y is an integer. Which of the following statements are true?
1: x + y is odd.
2: xy is odd.
3: x/y is odd.
4: x-y is odd.
A: 1 and 2 only.
B: 1 and 3 only.
C: 2 and 3 only.
D: 2, 3, and 4 only.
E: 2 and 4 only.
Answer:
C
Step-by-step explanation:
1: x + y is even. Try it. 3 + 5 = 8. 2x + 1 + 2y + 1 = 2x +2x + 2. That's even no matter what 2 odd numbers you use.
2: xy is again try it 3 * 5 = 15 which is odd. (2x + 1)(2y + 1) = 4xy + 2x + 2y + 1. The first 3 terms are even. The last one is odd. So xy is odd.
3. 9/3 = 3. Three should be true. The numerator is greater than the denominator. And x/y is given as an integer. So the statement should be true.
4. x - y is This can't be right. 2x + 1 - 2y - 1 = 2x + 2y. The result is even.
2 and 3 only
Help me
Pls its due soon and i have no clue how to do this
Question 10
Draw a 30-60-90 triangle template. Refer to the diagram below.
We have 1 as the short leg, 2 as the hypotenuse and sqrt(3) as the long leg.
Place the angle theta as the reference angle such that it's opposite the sqrt(3) side.
That allows tan(theta) = sqrt(3)/1 = opposite/adjacent
In other words, tan(60) = sqrt(3)/1
So theta = 60 is one solution. We add on 180 to get the other solution. So the other solution is 60+180 = 240
So tan(60) = tan(240) = sqrt(3)
Answers: 60 and 240======================================================
Question 11a
sin(theta) = -0.8
theta = arcsin(-0.8) or theta = 180-arcsin(-0.8)
theta = -53.1301 or theta = 180 - (-53.1301)
theta = -53.1301 or theta = 233.1301
Add 360 to the first angle to find a coterminal angle counterpart.
-53.1301 + 360 = 306.8699
So the two approximate solutions are
theta = 306.8699 or theta = 233.1301
and those round to 306.9 and 233.1 respectively.
Answers: 233.1 and 306.9======================================================
Question 11b
cot(theta) = 1.8
tan(theta) = 1/(1.8)
theta = arctan( 1/(1.8) ) or theta = 180+arctan( 1/(1.8) )
theta = 29.0546 or theta = 180+29.0546
theta = 29.0546 or theta = 209.0546
theta = 29.1 or theta = 209.1
Answers: 29.1 and 209.1Given 2 ||
m
|| n, find the value of x.
142°
m
(3x+8)°
n
PLSSSS HELP MEEEE
Answer:
x = 10Step-by-step explanation:
Given,
l || m
Therefore,
142° + (3x+8)° = 180° [Since Co-exterior angles]
=> 3x + 8 = 180 - 142
=> 3x + 8 = 38
=> 3x = 38 - 8
=> 3x = 30
[tex] = > x = \frac{30}{3} [/tex]
=> x = 10 (Ans)
1. You buy rice at $0.71 a pound. One batch of fried rice requires 6.5 pounds of rice. How much does the rice for one batch cost? Round to the nearest cent.
Select one:
a. $4.60
b. $4.65
c. $4.61
d. $4.62
The cost for one batch of fried rice will be $4.62.
Since the rice is bought at $0.71 a pound and one batch of fried rice requires 6.5 pounds of rice, then the cost of one batch of rice will be:
= $0.71 × 6.5
= $4.615
= $4.62 approximately.
In conclusion, the cost for one batch of fried rice will be $4.62.
Read related link on:
https://brainly.com/question/24017475
after how many years will Rs 21000 give Rs 5040 as interest at 6% pa simple interest
Answer:
within 4 years it will give the required interest
Which of the following describes an air mass with the symbol CT? a. it is a cold air mass over an ocean c. it is a warm air mass over an ocean b. it is a warm air mass over a continent d. it is a cold air mass over a continent Please select the best answer from the choices provided
Answer:
B is correct_
Please hurry I will mark you brainliest
Answer:
the answer is 120
Step-by-step explanation:
a trapezoid should measure 360 when all sides are added together
180-125=55
65+55=120
360-120=240
240÷2=120
Question 13 of 46
What is the remainder for the synthetic division problem below?
Answer:
Step-by-step explanation:
Let's do this out as best as we can here. Here's the problem:
2 | 3 1 2 -7
___________
The rule is to bring down the first term, whatever it is (ours is a 3), and multiply it by the number "outside" which is a 2. Put that product up under the number next to the 3:
2 | 3 1 2 -7
6
3
Then add straight down, and multiply that sum by the 2 outside and put that product under the next number (the 2 "inside" the box):
2 | 3 1 2 =7
6 14
3 7
And do the same thing. Add straight down, multiply the sum by 2 and put the product up under the next number, -7, and add again. The final is shown below:
2 | 3 1 2 -7
6 14 32
3 7 16 25
The last number in the very bottom row, the depressed polynomial row, is the remainder. Ours is a 25. This is the super easy way to divide polynomials, as long as our divisor is a linear (first degree) term.
HELPHELPHELPHELPHELP
Answer:
2¼ mph
Step-by-step explanation:
It takes ⅓hour to walk to the library.
⅓ •3 = 1 hour
¾ • 3 = 9/4 = 2¼ miles/hour
Find the missing length of the following with midsegment drawn
Answer:
18
Step-by-step explanation:
RQ = (22+14)/2 = 36/2 = 18
Answer:
QR = 18
Step-by-step explanation:
The midsegment QR is half the sum of the parallel bases, that is
QR = [tex]\frac{JM+KL}{2}[/tex] = [tex]\frac{22+14}{2}[/tex] = [tex]\frac{36}{2}[/tex] = 18
Multiply reciprocal of (-4/5) and 25/16 and add additive inverse of (-4/5) we get _____________
Find the surface area of each figure. Round your answers to the nearest tenth, if necessary
Answer: 109m^2
Step-by-step explanation:
(5)(8.4)/2 = 21 m^2
(4 ) (21) = 84 m^2
Base = 5^2 = 25 m^2
84 + 25 = 109 m^2
If x²+1/4x²=8 ,find the value of x+1/2x
Answer:
16/31
Step-by-step explanation:
x²+1/4x²=8
x²+1=32x²
1=32x²-x²
1=31x²
√1=√31x²
31x=1
x=1/31
Now x+1/2x
=31+1/2×31
=32/62
=16/31
I NEEEDDDD HELPPPP ASAPPPP ITS URGENTTTT!!!
Answer:
(x-13)^2+(y+16)^2=12.56
Step-by-step explanation:
tìm nghiệm của đa thức 2x² + 5x
Answer:
this is this because of PTI
Step-by-step explanation:
pto explain it to me on Monday and Friday Saturday morning
Answer:
[tex]2x^2+5x[/tex]
[tex]=2xx+5x[/tex]
[tex]=x\left(2x+5\right)[/tex]
Hope it helps u
What is the approximate radius of a sphere with a volume of 34 cm3?
A. 6 cm
O O
B. 2 cm
C. 8 cm
D. 4 cm
SUBMIT
Answer:
the answer is B.
Step-by-step explanation:
it is not A is because if the radius is 6 then the volume will be 904.32
the answer is B.
because is the radius is 2 cm then the area I calculate with this radius is 33.4933333333 and the question want the approximate radius and out of all the numbers this one is the closest so the answer is B
Find the area of the shaded regions:
Answer:
84.78
Step-by-step explanation:
Used calculator and formula
A rectangular garden has links twice as great as it's with a second rectangular garden has the same link as the first garden and with that is for meters greater than the width of the first garden the second Gordon has area of 120 m² what is the length of the two gardens
Solution :
For the bigger rectangle
Width of bigger rectangle = W
Length of bigger rectangle, L = 2W
For the smaller rectangle
Width , w = W+4
Length, l = L = 2W
Area, a =120 [tex]m^2[/tex]
Now we know,
Area = length x width
[tex]$a=l \times w$[/tex]
[tex]$120=(2W) \times (W+4)$[/tex]
[tex]$120=2W^2 + 8W$[/tex]
[tex]$2W^2+8W-120=0$[/tex]
[tex]$W^2+4W-60=0$[/tex]
[tex]$(W+10)(W-6) = 0$[/tex]
We get, either [tex]W=-10[/tex] (rejecting)
or [tex]W=6[/tex]
∴ length of the bigger rectangle, [tex]$L=2W $[/tex]
= 2(6)
= 12 m
Length of the smaller rectangle, [tex]$L=2W$[/tex]
= 2(6)
= 12 m
Hence, the length of the two gardens is 12 m.
Given that QR¯∥ST¯, identify the length of PT¯.
Answer:
PT = 16.3 units
Step-by-step explanation:
From the picture attached,
From ΔPQR and ΔPST,
QR ║ST [Given]
PQ is a transversal line.
Therefore, ∠PST ≅ ∠PQR [Corresponding angles]
∠P ≅ ∠P [Common angle]
ΔPQR ~ ΔPST [By AA property of similarity of two triangles]
Therefore, by the property of similarity, corresponding sides of the similar triangles will be proportional.
[tex]\frac{PQ}{PS}=\frac{PR}{PT}[/tex]
[tex]\frac{12+28}{28}= \frac{PT+7}{PT}[/tex]
[tex]\frac{40}{28}=1+\frac{7}{PT}[/tex]
[tex]\frac{10}{7}-1=\frac{7}{PT}[/tex]
[tex]\frac{10-7}{7}=\frac{7}{PT}[/tex]
PT = [tex]\frac{49}{3}[/tex]
PT = 16.3 units
x2 – 1x – 90 = 0 has solutions {a, b}. What is a + b?
Answer:
a + b =1
Step-by-step explanation:
Write the given quadratic as x^2 – 1x – 90 = 0. This factors into
(x - 10)(x + 9) = 0, and so the roots/solutions are {-9, 10}.
If we call -9 "a" and 10 "b," then the sum a + b is -9 + 10, or a + b =1.
Tess created a Pythagorean triple of (24, 32, 40) by multiplying the known Pythagorean triple 3, 4, and 5 by 8. Is Tess correct? Can a Pythagorean triple be created using multiples of a known Pythagorean triple.
Yes, as long as each number in the Pythagorean triple is multiplied by the same whole number.
Yes, as long as each number in the Pythagorean triple is multiplied by a different whole number.
No, Pythagorean triples only exist with small numbers.
No, multiplying a known Pythagorean triple by a whole number will not create a Pythagorean triple.
Answer:
Hello,
Answer A
Yes, as long as each number in the Pythagorean triple is multiplied by the same whole number.
Step-by-step explanation:
(a,b,c) is a Pythagorien triple : c²=a²+b²
and k is a naturel.
[tex](ka)^2+(kb)^2\\\\=k^2*a^2+k^2*b^2\\\\=k^2(a^2+b^2)\\\\=k^2c^2\\\\=(kc)^2\\[/tex]
Answer:
Yes, as long as each number in the Pythagorean Triple is multiplied by the same whole number.
General Formulas and Concepts:
Pre-Algebra
Equality PropertyTrigonometry
[Right Triangles Only] Pythagorean Theorem: a² + b² = c²
a is a leg b is another leg c is the hypotenuseStep-by-step explanation:
In order for it to remain a Pythagorean triple, we must follow the equality rules. To make it the exact same expression, all parts of an equation must be multiplied or divided by the same number. If this is done, then it would also remain a Pythagorean triple, and hence we arrive at our answer.
Please help !!!!!!!!!!!
Answer:
98°+62°+6x = 180
160+6x = 180
6x = 180 - 160
6x = 20
x= 20/6
x= 3.33
therefor your answer is 3.33
The segments shown below could form a triangle.
4. Determine all unknown sides and angles to 1 decimal place.
a.
b.
32°
12 cm
30°
38 cm
The unknown sides are 60.81cm and 51.57cm while the unknown angle is 58degrees
4a) Given the following
Opposite side = 38cm (side facing the given angle)
Required
Adjacent and hypotenuse side
According to SOH CAH TOA
[tex]tan \theta = \frac{opp}{hyp}\\tan 32=\frac{38}{hyp}\\hyp=\frac{38}{tan 32}\\hyp=\frac{38}{0.6249}\\hyp= 60.81cm[/tex]
Next is to get the adjacent
[tex]Cos 32=\frac{adj}{60.81}\\adj=60.81cos32\\adj=60.81(0.8480)\\adj= 51.57cm[/tex]
Next is to get the missing angle
Since sum of angle in the triangle is 180degrees
32 + 90 + x = 180
122 + x = 180
x = 180 - 122
x = 58degrees
The unknown sides are 60.81cm and 51.57cm while the unknown angle is 58degrees.
Learn more about the properties of triangles here: https://brainly.com/question/16908652
Solve inequality problem (urgent help please)
Answer:
B
Step-by-step explanation:
|3m-2|=>1
1 <= 3m-2 or 3m-2 <= -1
3 <= 3m or 3m <= 1
1 <= m or m <= (1/3)
in a data ,range is 17 and coefficient of range is 0.2 find the smallest term of the data.
I will make brainelist to the best answer
Answer:
Step-by-step explanation:
Let largest value of data be L
and smallest value of data be S.
We are given that the range and coefficient of range of the data are 17 and 0.2 respectively.
Range formula is given by = Largest value - Smallest value
17 = L - S
L = 17 + S ---------- [Equation 1]
Coefficient of range formula = (Largest - Smallest) ÷ (Largest + Smallest)
0.2 = l-s/l+s
0.2 = 17/l+s
L + S = 17/0.2 = 85
So, L + S = 85
17 + S + S = 85 {using equation 1}
2*S = 80
S = 80/2 = 40
Putting value of S in equation 1, we get L = 20 + 40 = 60
Therefore, Largest value, L = 60
smallest value, S = 40
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Step-by-step explanation:
rrgggggggjjhjjhgghghhh
What is the sum of the reciprocals of all the factors of 24. Both 1 and 24 are
considered to be factors of 24.
A: 59/24
B: 5/2
C: 65/24
D: 53/24
E: 41/24
Answer:
B
Step-by-step explanation:
1+2+3+4+6+8+12+24=60
60/24=5/2
so,B is the answer
The sum of all the reciprocals of the factors of 24 is 5/2.
What is fraction?An element of a whole is a fraction. The number is represented mathematically as a quotient, where the numerator and denominator are split. Both are integers in a simple fraction. A fraction appears in the numerator or denominator of a complex fraction. The numerator of a proper fraction is less than the denominator.
The factors of 24 are 1, 2, 3, 4, 6, 8, 12, 24.
The reciprocals of all the factors of 24 are;
1/1, 1/2, 1/3, 1/4, 1/6, 1/8, 1/12, 1/24
The sum of all the factors of 24:
1/1 + 1/2 + 1/3 + 1/4 + 1/6 + 1/8 + 1/12 + 1/24
Take LCM of the fractions:
1/1 + 1/2 + 1/3 + 1/4 + 1/6 + 1/8 + 1/12 + 1/24
= (24 + 12 + 8 + 6 + 4 + 3 + 2 + 1) / 24
1/1 + 1/2 + 1/3 + 1/4 + 1/6 + 1/8 + 1/12 + 1/24
= 60 / 24
Hence, the fraction:
1/1 + 1/2 + 1/3 + 1/4 + 1/6 + 1/8 + 1/12 + 1/24
= 5/2
Therefore, 5/2 is the sum of all the reciprocals of the factors of 24.
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