Answer: Choice D) 1 - sec^2(a) = tan^2(a) is not an identity.
================================================
Explanation:
a) is the pythagorean trig identity assuming you meant to write sin^2(a)+cos^2(a) = 1
b) is a rewritten version of tan = sin/cos. You multiply both sides by cos(a).
c) is an identity that you can find through dividing everything in equation (a) by sin^2. I'm assuming you meant to put exponent symbols before each "2".
d) is not an identity. I recommend looking at a table or graph that compares the two sides as separate functions. You should see they are not the same. The actual identity should be sec^2(a) - 1 = tan^2(a). You divide both sides of equation (a) by cos^2 and do a bit of algebra to get it into this form.
If a and b are acute angles such that tan (a+b)= 1.73 and tan(a-b) =1/1.73, find a and b
[tex] \LARGE{ \underline{ \boxed{ \orange{ \rm{Solution:)}}}}}[/tex]
Given,tan (a + b) = 1.73 [tex]\approx[/tex] √3tan (a - b) = 1 / 1.83 [tex]\approx[/tex] 1 / √3To find:Value of a and b in degrees....?Solution:☃️ Refer to the trigonometric table....
Then, proceeding
⇛ tan 60 ° = √3
⇛ tan 60° = tan (a + b)
⇛ 60° = a + b
Flipping it,
⇛ a + b = 60° --------(1)
And,
⇛ tan 30° = 1 / √3
⇛ tan 30° = tan (a - b)
⇛ 30° = a - b
Flipping it,
⇛ a - b = 30° ---------(2)
Now adding eq.(1) and eq.(2),
⇛ a + b + a - b = 60° + 30°
⇛ 2a = 90°
⇛ a = 90° / 2
⇛ a = 45°
Putting value of a in eq.(1),
⇛ 45° + b = 60°
⇛ b = 15°
☄ So, Our Required answers:
a = 45°b = 15°━━━━━━━━━━━━━━━━━━━━
PLZ HELP !!!!!! ASAP!!!
Part (a)
BC = opposite side (furthest leg from the reference angle)
AB = adjacent side (closest leg from the reference angle)
AC = hypotenuse (always opposite the 90 degree angle)
=============================================
Part (b)
i. False. Angle B is 90 degrees as shown by the square angle marker.
ii. False. Side AB is opposite angle C. Note how "C" is part of "BC", so that means we cannot have BC be opposite C.
iii. True. Leg AB is the closer leg to angle A. We have "A" in "AB" to see this without having to draw the diagram. Refer to part (a) above.
iv. False. The longest side of any right triangle is always the hypotenuse. The longest side of any triangle is always opposite the largest angle.
==============================================
Part (c)
cos(theta) = adjacent/hypotenuse = AB/AC
tan(theta) = opposite/adjacent = BC/AB
Refer back to part (a) to determine the opposite,adjacent and hypotenuse side lengths.
==============================================
Part (d)
The reference angle has changed, so the opposite and adjacent sides swap. The hypotenuse remains the same regardless of what reference angle you pick.
sin(C) = opposite/hypotenuse = AB/AC
cos(C) = adjacent/hypotenuse = BC/AC
tan(C) = opposite/adjacent = AB/BC
Note the tangent ratio is the reciprocal of what we found back in part (c).
Answer & Step-by-step explanation:
(a)
The hypotenuse is on line CA (the hypotenuse is always opposite the 90° angle (marked by a little square))
The adjacent is on the line BA (adjacent is next to the given angle, but NOT the hypotenuse)
The opposite is on the line CB (this is opposite the given angle)
(b)
i. false (b is a right angle)
ii. false (the side opposite C is BA)
iii. true
iv. false (the side opposite B is the hypotenuse, and the hypotenuse is always the longest side in a triangle)
(c)
cosine ratio: [tex]cos=\frac{adjacent}{hypotenuse}[/tex]
tangent ratio: [tex]tan=\frac{opposite}{adjacent}[/tex]
The cosine and tangent ratios of the given angle:
[tex]cos0=\frac{AB}{CA} \\\\tan0=\frac{CB}{AB}[/tex]
(d)
Remember SOH-CAH-TOA:
Sine=Opposite/Hypotenuse
Cosine=Adjacent/Hypotenuse
Tangent=Opposite/Adjacent
Using the angle C, plug in the appropriate sides:
[tex]sinC=\frac{BA}{CA}\\\\ cosC=\frac{CB}{CA}\\\\ tanC=\frac{BA}{CB}[/tex]
:Done
Alan travels eight and two thirds kilometers to get to school. He ran one and ten elevenths kilometers and walked the rest. How many kilometers were left to walk?
Answer:
4 and 34/63
Step-by-step explanation:
we know that he has to walk 8 and 2 thirds of an kilometer to school. so far he has ran 1 10/11 of a kilo.
To solve this you would have to divide 8 2/3 by 1 10/11.
you would have to make them into improper fractions so 26/3 divided by 21/11
your answer will be 4 34/63
Alan covers he distance by walking is 6+25/33 km.
what is distance?distance is a scaler quantity which means it only have magnitude and no direction if any person or any thing moves from place A to B then it will show the distance between A and B
Given that Alan's school a distance is 8+2/3 km which is 26/3 km,
and he ran one and ten elevenths kilometers
means 1+10/11 = 21/11 km
and walks rest
let distance covered by walking be x
total distance for Alan school = distance covered by running + distance covered by walking
26/3 = 21/11 +x
x = 26/3 - 21/11
x = 223/33 = 6+25/33
Hence rest walking distance for Alan is 6+25/33
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1 7/16 - 1 1/6
Any step by step explanations? I need help.
Answer:
13/48
Step-by-step explanation:
1 7/16 - 1 1/6
Make improper fraction
23/16 - 7/6
Common Denominator
69/48 - 56/48
Subtract
13/48
Hope that helped!!! k
Answer:
13/48
Step-by-step explanation:
1 7/16=1+7/16
1 1/6=1+1/6
So: 1 7/16 - 1 1/6=
1+7/16-(1+1/6)=
1+7/16-1-1/6=
7/16-1/6= (48 common denominator)
(7×3-8)/48=
(21-8)/48=
13/48
Arjun has two denominations of coins. Two of the smaller denomination coins and three of the larger denomination coins have a value of $2. Two of the smaller denomination coins and seven of the larger denomination coins have a value of $4. What denominations of coins does Arjun have?
Answer:
Smaller coin = s = $0.25 = 25cent.
larger coin = l = $0.5 = 50 cent
Step-by-step explanation:
Given the following :
Let the two coins be s and l
Where s = smaller denomination and l = larger denomination coins
Two of the smaller denomination coins and three of the larger denomination coins have a value of $2
2s + 3l = 2 - - - - (1)
Two of the smaller denomination coins and seven of the larger denomination coins have a value of $4
2s + 7l = 4 - - - (2)
2s + 3l = 2 - - - (1)
2s + 7l = 4 - - - (2)
Subtracting both equations
3l - 7l = 2 - 4
-4l = - 2
l = 2/4
l = 0.5
Put l = 0.5 into (1)
2s + 3l = 2
2s + 3(0.5) = 2
2s + 1.5 = 2
2s = 2 - 1.5
2s = 0.5
s = 0.5 / 2
s = 0.25
Smaller coin = s = $0.25 = 25cent.
larger coin = l = $0.5 = 50 cent
if a white birch tree and a pin oak tree each now have a diameter of 111 foot, which of the following will be closest to the difference, in inches, of their diameters 101010 years from now? (1(1(, 1 foot = 12=12equals, 12 inches))
Answer:
Can you solve #18 from practice test 5 calculator section? ... years old and a pin oak tree with a diameter of 12 inches is ... because on the test you would have figured these mechanics out on ... Now, note that the concept of a “growth factor” as provided in the table ... That's a difference of about 1.3 inches.
Step-by-step explanation:
What types of concurrent constructions are needed to find the orthocenter of a triangle? A. intersection of the lines drawn perpendicular to each side of the triangle through its midpoint B. intersection of the lines drawn to bisect each vertex of the triangle C. intersection of the lines drawn from each vertex of the triangle and perpendicular to its opposite side D. intersection of the lines drawn to the midpoint of each side of the triangle to its opposite vertex
Answer:
intersection of the lines drawn to bisect each vertex of the triangle
Step-by-step explanation:
trust
Help wanted ill do brainliest!!
Answer:
x=-1
Step-by-step explanation:
0.5 ( 5 - 7x ) = 8 - ( 4x + 6 )
- Distribute 0.5 by 5 and -7x
2.5 - 3.5x = 8 - ( 4x + 6 )
Second- Distribute the invisible one into 4x and 6
2.5 - 3.5x = 8 - 4x - 6
- Combine like terms: Subtract 6 from 8
2.5-3.5x= - 4x + 2
-Add 4x from both sides of the equation
2.5 + 0.5x = 2
-Subtract 2.5 from both sides of the equation
0.5x = 2- 2.5
0.5x = -0.5
-Then divide each side by 0.5x
0.5x = -0.5
0.5 0.5
-Cancel the common factor of 0.5
x = - 0.5
0.5
-Divide -0.5 by 0.5
X = -1
The average month end closing stock price for Company A over the past year is $34.57 with a standard deviation of $4.65. The average month end closing stock price for Company B over the same period is $26.15 with a standard deviation of $7.45. Based on this data, we can conclude that the stock price for Company A is more consistent when compared to the stock price for Company B.
a) true
b) false
Answer:
a) true
Step-by-step explanation:
$4.65. >$7.45.
what is the solution to the equation below log5(2x-3)=2
Answer:
14
Step-by-step explanation:
I just got it correct on a.p.e.x :)
The solution to the equation [tex]\log_5(2x - 3) = 2[/tex] is x = 14
How to determine the solution?The equation is given as:
[tex]\log_5(2x - 3) = 2[/tex]
Convert the equation to an exponential equation
2x - 3 = 5^2
Evaluate the exponent
2x - 3 = 25
Add 3 to both sides
2x = 28
Divide both sides by 2
x = 14
Hence, the solution to the equation [tex]\log_5(2x - 3) = 2[/tex] is x = 14
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What is the value of x in the equation 3x-4y=65, when y =4 will give brainliest
Hello!
Answer:
[tex]\huge\boxed{x = 27}[/tex]
Given:
3x - 4y = 65 where y = 4;
Substitute in 4 for "y":
3x - 4(4) = 65
Simplify:
3x - 16 = 65
Add 16 to both sides:
3x - 16 + 16 = 65 + 16
3x = 81
Divide both sides by 3:
3x/3 = 81/3
x = 27.
Hope this helped you! :)
Answer:
x=27
Step-by-step explanation:
3x-4y=65
Let y=4
3x - 4(4) = 54
3x -16 = 65
Add 16 to each side
3x -16+16 = 65+16
3x = 81
Divide each side by 3
3x/3 =81/3
x =27
find the number whose 13% is 65.
Answer:
500
Step-by-step explanation:
A = the unknown number that we need to find
A x 13/100 = 65
=> A x 13 = 6500
=> A = 6500 / 13
=> A = 500
13% of 500 is 65.
Let's check whether the answer is correct or not.
=> 500 x 13/100
=> 5 x 13
=> 65.
So, the number whose 13% is 65 is 500
Answer:
Step-by-step explanation:
Let the number be x,
Then,
13% of x =65
Or, 13/100 of x =65
Or,x=6500/13
:.x=500
[tex]2x {}^{2} + 10x - 72[/tex]
What is the factor
Answer:
2(x-4) (x+9)
Step-by-step explanation:
when a 200 g solution A and 400g of saline solution B are mixed a 6% salt solution is created also when a 400g of saline solution A and 200g of solution B are mixed 7% salt is created find what percent concentration of saline and saline b solution are
Answer:
A = 8%, B = 5%
Step-by-step explanation:
Let
a=concentration of solution A (in percent)
b=concentration of solution B (in percent)
Given
2a+4b = 0.06*(2+4) ...........(1)
4a+2b = 0.07*(4+2) ...........(2)
2(1) - (2)
4a-4a +8b-2b = 6 (2*0.06-0.07)
6b = 6(0.05)
b = 0.05 .............(3)
Substitute (3) into (1) and solve for a
2a+4(0.05) = 0.36
2a = 0.16
a = 0.08
Can you help me solve this problem & write my answer in simplest radical form.
Answer:
18
Step-by-step explanation:
30-60-90 triangles have a set of x values that you can plug your numbers into.
we know that the side length opposite to 30 is x
the side length opposite to 60 is xsqrt3
the side length opposite to 90 is 2x
from this we can gather that y=2x where x=9 therefore y=18
Help please Which is the equation of a trend line that passes through the points (3, 95) and (11, 12)? Round values to the nearest ten-thousandths. y = negative 10.375 x + 126.125 y = negative 0.096 x + 13.056 y = 0.096 x + 10.944 y = 10.375 x 63.875
Answer:
y = -10.375x + 126.125
Step-by-step explanation:
(12-95)/(11-3) = -83/8 = -10.375
y = mx + b
12 = -10.375(11) + b
12 = -114.125 + b
b = 126.125
y = -10.375x + 126.125
The solution is, y = -10.375x + 126.125, is the equation of a trend line that passes through the points (3, 95) and (11, 12).
What is a straight line?A straight line is an endless one-dimensional figure that has no width. It is a combination of endless points joined both sides of a point and has no curve.
here, we have,
given that,
a trend line that passes through the points (3, 95) and (11, 12).
so, the slope is,
(12-95)/(11-3) = -83/8 = -10.375
now, we have,
y = mx + b
12 = -10.375(11) + b
12 = -114.125 + b
b = 126.125
so, we get,
y = -10.375x + 126.125
Hence, The solution is, y = -10.375x + 126.125, is the equation of a trend line that passes through the points (3, 95) and (11, 12).
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Rewrite the radical expression as an expression with rational exponents. fifth root of x to the power of 9
Answer:
[tex]x^\frac{9}{5}[/tex]
Step-by-step explanation:
[tex]\sqrt[5]{x}[/tex] is the same thing as [tex]x^{\frac{1}{5}}[/tex].
Now if we have [tex]x^{\frac{1}{5}}[/tex] to the power of 9, the exponents are multiplied.
[tex]x^{\frac{1}{5} \cdot9} = x^{\frac{9}{5} }[/tex].
Hope this helped!
Ken has 86 feet of fencing , to make a vegetable garden . Which design below will give ken the largest garden ?
Answer:it’s the top right box
Step-by-step explanation: what I did was I added 24+24 and 19+19 which gives you 86ft
Answer:It is left side 21ft and top 22ft Step-by-step explanation:
Type the correct answer in each box. Use numerals instead of words. A race car is driven by a professional driver at 99 . What is this speed in and ? 1 mile = 1.61 kilometers 1 hour = 60 minutes Round your answers to the nearest tenth. The speed is equivalent to , or
Answer:
[tex]Speed = 159.4\ km/hr[/tex]
[tex]Speed = 2.6\ km/m[/tex]
Step-by-step explanation:
The question has missing details; However, the given parameters are
[tex]Speed = 99\ miles/hour[/tex]
Required
Determine the speed in
- kilometre per hour
- kilometre per minute
From the question; we have that
[tex]1\ mile = 1.61\ kilometers[/tex]
[tex]1\ hour = 60\ minutes[/tex]
[tex]Speed = 99\ miles/hour[/tex] can be rewritten as
[tex]Speed = \frac{99\ miles}{hour}[/tex]
It can be further expressed as
[tex]Speed = \frac{99\ *\ 1\ mile}{hour}[/tex]
Recall that [tex]1\ mile = 1.61\ kilometers[/tex]'
So;
[tex]Speed = \frac{99\ *\ 1.61\ kilometre}{hour}[/tex]
[tex]Speed = \frac{159.39\ kilometres}{hour}[/tex]
[tex]Speed = 159.39\ kilometres/hour[/tex]
[tex]Speed = 159.4\ km/hr[/tex] -- Approximated
Solving further to get kilometre per minute equivalent
[tex]Speed = \frac{159.39\ kilometres}{hour}[/tex]
This can be rewritten as
[tex]Speed = \frac{159.39\ kilometres}{1\ hour}[/tex]
Recall that [tex]1\ hour = 60\ minutes[/tex]; So,
[tex]Speed = \frac{159.39\ kilometres}{60\ minutes}[/tex]
[tex]Speed = \frac{2.5565\ kilometres}{minute}[/tex]
[tex]Speed = 2.5565\ kilometres/minute[/tex]
[tex]Speed = 2.6\ km/m[/tex] --- Approximated
Answer:
Speed of the car is equivalent to 159.39 KM/hour or 2.6565 Km/min.
-Step by Step-:
-The speed of the car is given as 99 mi/hour.
Now, WE know that 1 Mile = 1.61 KM
Hence, in order to calculate the speed of the car in KM/hour we will multiply the speed of the car in miles with 1.61.
⇒The speed of the car in KM/hour = 99 × 1.61 KM = 159.39 KM/hour
Also, 1 hour = 60 minutes
⇒ Speed of the car in KM/min = (159.39) ÷ 60 = 2.6565 K/min
Below are a list of costs and discounts for groceries. Round to the nearest dollar to estimate the total cost
+ $12.34
+ $5.07
- $0.73
+ $2.84
- $1.50
Answer:
$18
Step-by-step explanation:
$18.02 rounds to $18
Answer:
$17
Step-by-step explanation:
Rounded, the listed numbers are ...
12 + 5 -1 +3 -2 = 17
The estimate of total cost is $17.
3m-2-5n+p terms and coefficients
Answer: Answers are in the steps.
Step-by-step explanation:
The coefficients are 3, -5, and 1
The terms are, 3m, -2,-5n and p
Find the 6th term in this geometric sequence?
Answer:
91.125
Step-by-step explanation:
Each term is multiplied by 1.5 to get the next term.
12,18,27,40.5, 60.75, 91.125
Hope that helped!!! k
Answer:
91.125
Step-by-step explanation:
We know that this is a geometric sequence. By definition, this means that each subsequent term divided by the previous one is a common ratio r.
Here, divide 18 by 12 to get:
18/12 = 3/2 = 1.5
Divide 27 by 18 to check if it's also 1.5:
27/18 = 3/2 = 1.5
Indeed, the common ratio is 1.5. Now, we simply multiply 27 by 1.5 to get the 4th term:
27 * 1.5 = 40.5
Multiply 40.5 by 1.5 to get the 5th term:
40.5 * 1.5 = 60.75
Finally, multiply 60.75 by 1.5 to get the 6th term:
60.75 * 1.5 = 91.125
Our answer is thus 91.125.
~ an aesthetics lover
what is the area of a circle if the diameter is 16 millimeters?
━━━━━━━☆☆━━━━━━━
▹ Answer
A ≈ 201.06 mm²
▹ Step-by-Step Explanation
A = πr²
Radius = 1/2d
Radius = 1/2(16)
Radius = 8
Substitute:
A = π8²
A ≈ 201.06 mm²
Hope this helps!
CloutAnswers ❁
━━━━━━━☆☆━━━━━━━
Answer:
The answer is 201 mm²Step-by-step explanation:
Area of a circle is given by πr²
where r is the radius
To find the radius we use the formula
radius = diameter / 2
From the question
diameter = 16mm
radius = 16 / 2 = 8mm
So the area of the circle is
π(8)²
= 64π
= 201.061
= 201 mm² to the nearest whole number
Hope this helps you
how many are 6 raised to 4 ???
Answer:
[tex]\large \boxed{1296}[/tex]
Step-by-step explanation:
6 raised to 4 indicates that the base 6 has an exponent or power of 4.
[tex]6^4[/tex]
6 is multiplied by itself 4 times.
[tex]6 \times 6 \times 6 \times 6[/tex]
[tex]=1296[/tex]
calling all brainly users
Answer:
The triangles are not similar
Step-by-step explanation:
We can see that TU and EU are equal in length but SU and DU are not hence they are not similar
Write each fraction as a decimal and a percent. A) 7/8 B) 9/75 C/ 120/75
Answer:
A) 0.875, 87.5%
B) 0.12, 12%
C) 1.6, 160%
Step-by-step explanation:
Answer:
A) 0.875, 87.5%
B) 0.001, 0.1%
C) 1.6, 160%
Step-by-step explanation:
I honestly just used a calculator, but it could also be solved using the butterfly technique. For percentages just move the decimal to the left two places.
Find the missing factor D that makes the equality true -15y^4=(D)(3y^2)
Answer:
[tex]D=-5y^2[/tex]
Step-by-step explanation:
We have the equation:
[tex]\displaystyle -15y^4=D(3y^2)[/tex]
And we want to find D such that the equation is true.
So, we can divide both sides by 3y². This will yield:
[tex]\displaystyle D=\frac{-15y^4}{3y^2}[/tex]
We can split this into:
[tex]\displaystyle D=\frac{-15}{3}\cdot\frac{y^4}{y^2}[/tex]
Simplify. Hence:
[tex]D=-5y^2[/tex]
What is the inverse of the function h(x)=5/2x+4 h^{-1}(x)=
Answer:
Step-by-step explanation:
Hello, please consider the following.
[tex]h(x)=5/2x+4 \\\\x=(h^{-1}o})(x)=(hoh^{-1})(x)=h(h^{-1}(x))=\dfrac{5}{2h^{-1}(x)+4}\\\\<=> 2h^{-1}(x)+4=\dfrac{5}{x}\\\\<=> h^{-1}=\dfrac{\dfrac{5}{x}-4}{2}\\\\<=>h^{-1}=\dfrac{5-4x}{2x}[/tex]
Thank you.
There are three squares inside the triangle . Find the area of the third triangle with steps , please
Answer: 49 cm^2
Step-by-step explanation:
The length of the small pink square box will be:
L^2 = 9
L = sqrt( 9 )
L = 3
The length of the big pink square box will be:
L^2 = 16
L = sqrt( 16 )
L = 4
The length of the yellow square box will be:
4 + 3 = 7
The area of the third square box will be
A = 7^2
A = 49 cm^2
If x-a is a factor of polynomial x3-mn2-2nax+na2 prove that a=m+n and a is not = 0
Step-by-step explanation:
hope this helps
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