Given:
[tex]\tan A=\dfrac{1}{5}[/tex]
[tex]\tan B=\dfrac{1}{4}[/tex]
To find:
The value of [tex]\tan^2(A-B)[/tex].
Solution:
We know that,
[tex]\tan (A-B)=\dfrac{\tan A-\tan B}{1+\tan A\tan B}[/tex]
Putting the given values, we get
[tex]\tan (A-B)=\dfrac{\dfrac{1}{5}-\dfrac{1}{4}}{1+\dfrac{1}{5}\cdot \dfrac{1}{4}}[/tex]
[tex]\tan (A-B)=\dfrac{\dfrac{4-5}{20}}{1+\dfrac{1}{20}}[/tex]
[tex]\tan (A-B)=\dfrac{\dfrac{-1}{20}}{\dfrac{20+1}{20}}[/tex]
[tex]\tan (A-B)=\dfrac{-1}{21}[/tex]
Taking square on both sides, we get
[tex]\tan^2 (A-B)=\left( \dfrac{-1}{21}\right)^2[/tex]
[tex]\tan^2 (A-B)=\dfrac{1}{441}[/tex]
Therefore, the value of [tex]\tan^2(A-B)[/tex] is [tex]\dfrac{1}{441}[/tex].
A bag of M&Ms had 4 red, 5 orange, 3 yellow, 2 green, 7 blue, and 3 brown candies.
What is the probability of drawing and eating red candy and then drawing and eating an orange candy?
Answer:
4/20 red 5/20 orange
Step-by-step explanation:
see how many their are then add up all the candies then boom theres your answer
Can somebody help me on this problem please I will give you brainliest:)
Help me out from a through c (geometry/angle bisectors)
Answer:
A) supplementary
B) 148°
C) 50°
Step-by-step explanation:
A) supplementary
B) 180-32=148
C) 90-40=50
The sum of two numbers is 136 one number is 51 what is the other number? What are the common factors of these two numbers?
Find the value for the side marked below.
Answer:
10x25=250250÷2=125125 round to the nearest tenth is 130 answer: 130 that how I learn it qwqEvaluate function expressions 4 x f(6) - 6 x g(5) =
9514 1404 393
Answer:
24
Step-by-step explanation:
Find the parts of the expression from the graph, and evaluate the expression.
f(6) = -6
g(5) = -5
Then we have ...
f(6) -6·g(5) = (-6) -6(-5) = -6 +30 = 24
PLEASE HELP
Juan has $67 in $5 and $1 bills. If has 19 bills in all, how many $1 bills does he have?
Juan have 7 bill for $1 bills.
What is an expression?Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
Juan has $67 in $5 and $1 bills.
And, He has 19 bills in all.
Now, Let number of $1 bills = x
And, Number of $5 bills = y
Here, Juan has $67 in $5 and $1 bills.
So, We get;
⇒ x + 5y = 67 .. (i)
And, He has 19 bills in all.
So, We get;
⇒ x + y = 19
⇒ x = 19 - y .. (ii)
Substitute the value of x from (ii) in (i), we get;
⇒ x + 5y = 67
⇒ 19 - y + 5y = 67
⇒ 19 + 4y = 67
⇒ 4y = 67 - 19
⇒ 4y = 48
⇒ y = 12
And, from (ii),
⇒ x = 19 - y
⇒ x = 19 - 12
⇒ x = 7
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Explain how you can use multiplication to solve a division problem.
Answer:Inverse operation
Step-by-step explanation: an example is 5 x 5. That equals 25 so take 5 and divide that by 5. Inverse operation is important.
Which expression is equivalent to x+0.2x?
1.2x
0.2x2
0.2x
1.02x
Answer:
1.02x
Step-by-step explanation:
Which expression is equivalent to x+0.2x?
1.2x
0.2x2
0.2x
1.02x
the answer is
1x+0.2x = 1.02x
Probability Questions Help is needed plzzzzzzzzzz
Answer: 0.0049 hope this is right
If (a+b)= -5 and ab= -150 , find a-b
Answer:
(a-b) = -25
Step-by-step explanation:
(a+b) = -5
a*b=-150
So one of the letters have to be negative as you can only get a negative product from a positive and negative
There is probably a better way to do this, but I just plug in numbers that I think will work
So, (a*b) = -150, (-15*10) = -150
Okay that works so lets try the other one
(-15+10) = -5
This also works, so lets do the third one
(-15-10) = -25
HELPP ASAP!!!!
A. 2.5
B. 3.0
C. 4.5
D. 5.0
Answer:
C. 4.5
Step-by-step explanation
the sqr rt
A circle has a diameter of 10 cm. What is the circumference, and what is the area
Answer:
area=78.54cm squared
circumference =31.42cm
The prime factorizations of 54 and 72 are shown below. Prime factorization of 54: 2, 3, 3, 3 Prime factorization of 72: 2, 2, 2, 3, 3 Using the prime factorizations, what is the greatest common factor of 54 and 72
1.2'3
2. 2' 3'3
3.2'2' 3'3
4.2'2'2'3'3'3
Step-by-step explanation:
54 = 2 * 3³
72 = 2³ * 3²
To find the GCF of 54 and 72,
we find the highest common powers of their prime factors.
Highest common power for 2: 2
Highest common power for 3: 3²
Hence GCF of 54 and 72 = 2 * 3².
The answer is Option 2.
Answer:
b/2'3'3
Step-by-step explanation:
Select the correct answer. Which graph represents this inequality? 3x+y<1
Answer:
the answer is c the one above d
Step-by-step explanation:
the sum of 9 and the product of a number and -7 is -19
Answer:
9+x*-7=-19
9-7x=-19
-7x=-19-9
-7x=-28
x=-28/-7
x=4
The number 4 is the required expression.
What is PEMDAS?The abbreviation PEMDAS is used to indicate the sequence of steps to be taken when resolving expressions with multiple operations. P is for "parentheses," E is for "exponents," M is for "multiplication," D is for division, A is for addition, and S is for subtraction.
Let x be the required number.
And the given expression is the sum of 9 and the product of a number and -7 is -19
That means ,
9 + x × -7 = -19
Using PEMDAS,
9 - 7x = -19
-7x = -19 -9
-7x = -28
x = 4
Therefore, the required number is 4.
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Find the area of the shape shown below.
Answer:
Total Area = 26.75
Step-by-step explanation:
Remark
The hardest triangle to see is the top one. So we'll start with it.
It has a vertical leg of 3.5 and a horizontal one of 2 + 2 + 5 = 9
Top Triangle Area
Area = 1/2 base * height
Area = 1/2 * 9 * 3.5
Area = 15.75
Triangle on the lower left
Area = 1/2 * 2 * 2
Area = 2
Square on lower middle
Area = 2*2
Area = 4
Triangle on lower right area
Area = 1/2 * 2 * 5
Area = 5
Total Area
Total Area = 5 + 4 + 2 + 15.75
Total Area = 26.75
In what proportion should water and milk be mixed to reduce the price of milk from Rs 5 per liter to Rs 4 per liter?
Answer:
4:1
Step-by-step explanation:
Let us assume that the cost of water is free, that is Rs.0.
Let x represent the number of liters of milk, y represent the number of liters of water and z represent the volume of the mixture in liters, hence:
z = x + y (1)
Milk cost Rs.5 per liter, water cost Rs.0 per liter and the mixture cost Rs.4 per liter. Therefore:
5x + 0(y) = 4z (2)
Substituting z = x + y in equation 2 gives:
5x + 0(y) = 4(x + y)
5x = 4x + 4y
5x - 4x = 4y
x = 4y
x / y = 4 / 1
x : y = 4 : 1
The proportion in which the milk is to be mixed with water is 4 : 1, that is 4 liters of milk per 1 liter of water
Solve by linear elimination. 3x+y=-17. 5x-2y=13
Answer:
[tex]3x + y = - 17 - - - eqn(i) \\ 5x - 2y = 13 - - - eqn(ii) \\ by \: elimination \\ (2 \times eqn(i)) + eqn(ii) \\ (6 + 5)x + (2 - 2)y = ( - 34+ 13) \\ 11x = - 21\\ x = - \frac{21}{11} \\ substitute \: for \: x \: in \: eqn(i) \\ - \frac{ 63}{11} + y = - 7 \\ y = - 7 + \frac{63}{11} \\ y = - \frac{ 14}{11} [/tex]
Find the value of x help please.
Answer:
x= 6
Step-by-step explanation:
since the triangle is isosceles we know that opposite sides are equal
[tex]5x+5=35\\\\5x=35-5\\\\5x=30\\\\x=\frac{30}{5}\\\\x=6[/tex]
Answer:
[tex]\boxed {\boxed {\sf x=6}}[/tex]
Step-by-step explanation:
An isosceles triangle has 2 equal base angles and 2 equal legs.
In this triangle, 16 must be the base, because the base angles are adjacent. Therefore, the legs are 35 and 5x+5. They must be equal to each other.
[tex]35=5x+5[/tex]
Solve for the value of x by isolating the variable on one side of the equation.
5 is being added to 5x. The inverse of addition is subtraction. Subtract 5 from both sides of the equation.
[tex]35-5=5x+5-5 \\ 35-5=5x\\30=5x[/tex]
x is being multiplied by 5. The inverse of multiplication is division. Divide both sides by 5.
[tex]\frac{30}{5} =\frac{5x}{5} \\\frac{30}{5}=x\\6=x[/tex]
The value of x is 6.
HURRY PLEASE The top and bottom of a right rectangular prism are 4 inches long and 4 inches wide. What is true about the other faces
(front, back, left, and right)?
All four of the remaining faces will have a helght of 4 inches.
There is not enough information to tell what the other faces will look like.
Two of the remaining faces will be 4 inches wide.
All four of the remaining faces will be 4 inches wide.
Answer:
All four of the remaining faces will be 4 inches wide.Step-by-step explanation:
A right rectangular prism with square base and top with sides of 4 in.
It has four sides of 4 in wide each and of equal height of unknown measure.
Options:
All four of the remaining faces will have a height of 4 inches.
Incorrect, the height is unknown.There is not enough information to tell what the other faces will look like.
Incorrect, all the other faces are rectangular.Two of the remaining faces will be 4 inches wide.
Incorrect, all the faces are 4 in wide.All four of the remaining faces will be 4 inches wide.
Correct.Which equation has no solution?
A. 3x−9=5−3x
B. 3−3x=11+3x
C. −3x+7=7−3x
D. 3x+8=−2+3x
Answer:
C.
Step-by-step explanation:
C does not have a solution.
Enter the number 86.3865 rounded to the nearest hundredth (two decimal places)
Answer:
86.39
Step-by-step explanation:
Answer:
Your answer would be: 86.39
Step-by-step explanation:
What is the slope of the line that passes through the points (2,-6) and (-3,7)?
A. -5/13
B. -13/5
C. 13/5
D. -1/5
20/12, 35/21 do the ratios form a propprtion
is this linear or non linear y=-7x+8?
Is it
A.
B.
C.
D.
I really need help .
What is the difference between 3 more than 1/3 and 3
Answer:
Step-by-step explanation:
3 more than 1/3 represents 3 + 1/3 Which would equal 3 and 1/3 or 10/3. This is different than 3 since it equals 9/3. They don’t equal each other due to it being 3 added to 1/3
There are 24 seats in each row of the middle school auditorium.
The table shows the number of students from each grade who
attended a concert. If the students fill each row in the auditorium,
how many rows would be needed for all of the students?
Grade
Number of Students
Sixth
310
Seventh
256
Eighth
262
Answer:
34.5
Step-by-step explanation:
310 +256 +262= 810
810÷24=34.5
simplify the xepression 10(x + 2)
Answer: 10x + 20
Step-by-step explanation:
10 (x + 2)
Distribute
10x + 20
Answer:
10x + 20
Step-by-step explanation:
10(x + 2)
distribute
10 * x + 10 * 2
10x + 10 * 2
10x + 20