Answer:
[tex]a + b + c = \pi \\ = > c= \pi - a - b \\ < = > \tan(c) = \tan(\pi - a - b) = -\tan(a + b) [/tex]
Step-by-step explanation:
we have:
[tex] \tan(a) + \tan(b) + \tan(c) \\ = \tan(a) + \tan(b) - \tan(a + b) \\ = \tan( a) + \tan(b) - \frac{ \tan(a) + \tan(b) }{1 - \tan(a) \tan(b) } \\ = \frac{ ( \tan(a) + \tan(b) ) \tan(a) \tan(b) }{ \tan(a) \tan(b) - 1 } (1)[/tex]
we also have:
[tex] \tan(a) \tan(b) \tan(c) \\ = - \tan(a) \tan(b) \tan(a + b) \\ = \frac{ -(\tan( a ) + \tan(b) ) \tan(a) \tan(b) }{1 - \tan(a) \tan(b) } \\ = \frac{( \tan(a) + \tan(b)) \tan(a) \tan(b) }{ \tan(a) \tan(b) - 1 } (2)[/tex]
from (1)(2) => proven
Can you construct a triangle with side lengths of 1 meter, 7 meters, and 8 meters?
Yes or no and explain
Answer:
No.
Step-by-step explanation:
No.
Each side of a triangle must have a length between the difference and the sum of the lengths of the other two sides.
Let's look at the sum and difference of lengths of 2 sides.
Side with length 1 and side with length 7; third side with length 8
sum of lengths of first two sides = 1 + 7 = 8
difference = 7 - 1 = 6
The third side would have to have a length between 6 and 8. The third side has a length of 8. For a triangle, the third side must be between the sum and difference. Here, the third side is equal to the sum, so there is no triangle.
As soon as one side does not work, there is no triangle, and you don't need to check the sums and differences of the other two sets of two sides.
the slope of the line joining points (3 ;2) and (0;a) is-1 determine the value of a
Given:
The slope of the line joining points (3,2) and (0,a) is -1.
To find:
The value of a.
Solution:
If a line passes through two points [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex], the slope of a line is:
[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]
The slope of the line joining points (3,2) and (0,a) is -1. So,
[tex]\dfrac{a-2}{0-3}=-1[/tex]
[tex]\dfrac{a-2}{-3}=-1[/tex]
Multiply both sides by -3.
[tex]a-2=-1(-3)[/tex]
[tex]a-2=3[/tex]
[tex]a=3+2[/tex]
[tex]a=5[/tex]
Therefore, the value of a is 5.
7/11 as a decimal roundeded to 3 decimal places
Answer:
0.6364 is a decimal and 63.64/100 or 63.64% is the percentage for 7/11.
Someone please help me, this test determines if I pass or not.
Answer:
Your answer is C :)
May some one please answer this for me, if u are right i will give u brainliest
Answer:
b. 14x+4y
Step-by-step explanation:
The perimeter is determined by two times the length plus two times the width.
We will use the formula P = 2L+2W:
P = 2L+2W
P = 2(5x-y)+2(2x+3y)
P = (10x-2y)+(4x+6y)
P = 14x+4y
predict the next number in the table. cycle: 1,2,3,4,5. people told: 1,3,9,27,?
When Houa was born her parents started a college fund for her. They initially put $3500 in the account. They saved in additional $550 per year. How much we have in
the account after 10 years?
Answer: 9000
Step-by-step explanation:
3500+5500=9000
5500=10years x 550/year
Addition can be defined as the process of adding two numbers such that the result is the combined value of the two numbers. The balance that the account will have after 10 years is $9,000.
What is Addition?Addition can be defined as the process of adding two numbers such that the result is the combined value of the two numbers.
When Houa was born her parents started a college fund for her. They initially put $3500 in the account. They saved an additional $550 per year.
Therefore, the balance of the account after 10 years is,
Balance after 10 years = $3500 + $550(Number of years)
= $3500 + $550(10)
= $9,000
Hence, the balance that the account will have after 10 years is $9,000.
Learn more about Addition:
https://brainly.com/question/13167637
#SPJ2
The table displays the amount of money Stephen has in his piggy bank.
Stephen's Piggy Bank
Types of Coins Amount ($)
Quarters 7.50
Dimes 6.00
Nickels 5.50
Pennies 3.00
Which answer choice does NOT accurately approximate a comparison between the value of
the dimes in the piggy bank and the total value of Stephen’s coins?
A. 6%
B. 3/11
C.6/22
D. 27%
Answer:
A.6% Is the correct answer... #:Carry on Learning... ^_^Answer:
A. 6%
Step-by-step explanation:
The is no step by step explanation sadly
what is the first step to solving this equation?
-5+6=4
a. subtract 6 from both sides
b. multiply both sides by 5
c. divide both sides by -5
d. add 6 to both sides
Answer:
a. subtract 6 from both sides
Step-by-step explanation:
Given the algebraic expression;
-5c + 6 = 4
First of all, we would subtract 6 from both sides. This would eliminate the "6" on the left side.
-6 - 5c + 6 = 4 - 6
-5c = -2
5c = 2
Dividing both sides by 5, we have;
c = 2/5
A group of friends are ordering food. The total amount that they can spend on their food bill is $41, including the delivery charge of $6. The equation below represents the situation, where x is cost of each friends meal.
6+ax=41
The cost of each friends meal in terms of a is?
The cost of each friends meal when the number of friends is 5 is $?
Answer:
36
Step-by-step explanation:
Answer:
The first answer is 35.
the second answer is 7.
Step-by-step explanation:
hope this helps you!
The expected annual demand for the newly approved drug Prisdol is 50,000, but there is a lot of uncertainty. A plant to produce the drug will be built at a cost of $16 per unit of capacity, which is a one-time expense. In addition, there is an annual maintenance cost of $0.40 per unit of capacity. The production cost per unit is $0.20. The drug’s selling price will be $3.70/unit. Suppose that Z denotes the random demand for the drug in a year, and suppose that a plant is built with an annual capacity of 45,000. No inventory will be built up; the company will produce only what is needed for demand in a year, and no more than capacity. Select the least accurate statement regarding elements of a model for this setting.
1 The cost to build the plant is 45,000 * $16.
2 The annual maintenance cost is 45,000 * $0.40.
3 The sales revenue in a year is Z * $3.70
4 The unsatisfied demand in a year is max(Z – 45,000, 0).
Answer:
The least accurate statement regarding elements of a model for this setting is:
4 The unsatisfied demand in a year is max(Z – 45,000, 0).
Step-by-step explanation:
Expected annual demand for Prisdol = 50,000
Annual Plant Capacity = 45,000 units of drugs
Cost of building the plant = 45,000 * $16
Annual maintenance cost = 45,000 * $0.40
Production cost per unit = $0.20
Selling price per unit = $3.70
Sales revenue in a year = Z * $3.70,
where Z denotes the random demand in a year
b) Statements 1, 2, and 3 are accurate in this model setting. However, statement 4 sets up a model that does not concur with the setting. The unsatisfied demand in a year should be Z minus 45,000 if the plant produced full capacity. Otherwise, it is Z minus annual production units.
Solve the following system of equations using the elimination method.
5x + y = 9
Answer:
x= -1/5y+9/5
Step-by-step explanation:
5x+y=9
Step 1
First you need to add -y to both sides, basically subtracting y
5x+y-y= 9-y
Step 2
Divide both sides by 5, or multiply by 1/5. You want to do this because to cancel out 5, so you multiply the reciprocal, or divide the constant.
1/5*5x=-y+9/5
Then, you will get the answer
Hope this helps, sorry if it is wrong, I am just 4th grade :(
But I am sure this is correct :)
I need help like right now. Im brain dead
Answer:
y-intercept: [tex](0,-\frac{5}{2} )[/tex]
x-intercept: [tex](-2,0)[/tex]
Step-by-step explanation:
Hi there!
Important things to note:
the y-intercept occurs when x=0the x-intercept occurs when y=01) Find the y-intercept
[tex]-5x-4y=10[/tex]
Substitute x with 0
[tex]-5(0)-4y=10\\0-4y=10\\-4y=10[/tex]
Divide both sides by -4
[tex]\frac{-4y}{-4} =\frac{10}{-4} \\y=-\frac{5}{2}[/tex]
Therefore, the y-intercept is [tex]-\frac{5}{2}[/tex]. When written in (x,y) form, x will always be 0 while y is the y-intercept:
[tex](0,-\frac{5}{2} )[/tex]
2) Find the x-intercept
[tex]-5x-4y=10[/tex]
Substitute y with 0
[tex]-5x-4(0)=10\\-5x-0=10\\-5x=10[/tex]
Divide both sides by -5
[tex]-5x=10\\\frac{-5x}{-5}= \frac{10}{-5} \\x=-2[/tex]
Therefore, the x-intercept is -2. When written in (x,y) form, x will always be the x-intercept while y is always 0:
[tex](-2,0)[/tex]
I hope this helps!
Which number line correctly shows the location of -1 1/2?
9xy + 6ab + 2xb
The expression consists of ? terms, and each term contains ? factors
Answer:
They're 3 terms
Step-by-step explanation:
Im confused but the factor part because you can argue they're all factors of something. 81,18,4
negative x plus 1 is less than 5
Answer:
-x+1 < 5
Step-by-step explanation:
Not sure what the question is?
Answer:
-x + 1 < 5
Step-by-step explanation:
negative x plus 1 is less than 5
-x + 1 < 5
-TheUnknownScientist
what is the x in x/5 +1 = 7
PLEASE HELP FAST !!!
An artist creates a cone shape sculpture for an Art exhibit if the sculpture is 7 feet tall and has a base with a circumference of 21.980 feet what is the volume of the sculpture?
Answer:
The volume of the sculpture is 111.439
Step-by-step explanation:
HURRY!!!!!!!
Given the number of times I walk around the lake. Find the number of miles I walked around the lake. Note: it is 2.6 miles around the lake, and if I start walking a lap, I must finish the lap because I have to get back to my car. I had to walk ON THE PATH, and cannot go backwards, only forwards. I won't deviate off the path, so it will ALWAYS take 2.6 miles to go around!
Write the function rule, where x is the independent variable, and y is the dependent variable.
a
x=2.6y
b
y=2.6x
c
x=2.6+y
d
y=2.6+x
Answer:
A. x= 2.6y
Explanation
What does 5-10n equal ?
Maggie bought c CDs for $12 each, b books for $7 each, and a purse costing $24.
a. Write an expression to show the total amount of money Maggie spent.
b. If Maggie bought 4 CDs and 3 books, how much money did she spend?
Step-by-step explanation:
Given that,
Maggie bought c CDs for $12 each, b books for $7 each, and a purse costing $24.
(a) Cost of c CDs = 12c
Cost of b books = 7b
Cost of p purse = 24p
Total amount = 12c+7b+24p
(b) Cost of 4 CDs = 12(4) = $48
Cost of 3 books = 7(3) = $21
Hence, this is the required solution.
Start at the origin. Move 2 units right and 8 units up. What is the ordered pair for this point? pls help ASAP
Answer: (2,8)
Step-by-step explanation:
The origin is the point (0,0), so when you move two units right you land on the x-value of 2. From there you then add 8 units, putting you at the y-value of 8. Therefore, you end with the point (2,8) after this translation.
Who’s can help me with this, it is to hard
Answer:
x = 10
MB = 16
CM = 16
CB = 32
Step-by-step explanation:
Since it's the mispoint
2x - 4 = x + 6
Subtract x from both sides
x - 4 = 6
Add 4 to both sides
x = 10
MB = 2x - 4
MB = 20 - 4
MB = 16
CM = x + 6
CM = 16
CB = 16 + 16
CB = 32
If tan θ=1/4 and cos θ≤0, find the exact value of sin x
If you can answer this soon that would be great.
Answer:
Step-by-step explanation:
Tan(theta) = Sin(theta) / cos(theta)
1/4 = sin(theta) / sqrt(1 - sin^2(theta) ) Cross multiply
sqrt(1 - sin^2(theta)) = 4*sin^2(theta) Square both sides.
1 - sin^2(theta) = 16 * sin^4 (theta) Transfer the left side to the right side.
0 = 16 sin^4(theta) + sin^2(theta) - 1
Use the quadratic formula to find a value for sin^2(theta)
a = 16
b = 1
c = - 1
I'll leave solving the quadratic to you.
There are two answers
sin^2(theta)= .22069
The other root is - 0.28 which you cannot use.
Sin(theta) = +/- 0.4698
Cos(theta) is < 0 in quads 2 and 3
So sin(theta) is positive in quad 2
and sin(theta) is minus in quad 3
Is the relation a function? Why or why not?
please help me out please
Answer:
DCB = 44 degree
Step-by-step explanation:
DAB (given = 100
(180-100 ) / 2 = 40
ADB = ABD = 40 degree (each)
ADC (given = 108
BDC = DBA = 108-40 = 68 degree;
(subtracting angle inscribed within another triangle)
Triangle DBC = 180- 68+68 = 180 - 136 = 44 degree
Find DCB We have found BDC and DBA by deducting ADB from ADC
to get BDC
Then we deduct BDC from ADC to get DCB
(−10x^2+9)+(8x^2 −5x+7)
Answer:
-2x^2-5x+16
Step-by-step explanation:
Remove parenthesis:
-10x^2+9+8x^2-5x+7
Combine like terms:
-10x^2+8x^2-5x+9+7
= -2x^2-5x+9+7
=-2x^2-5x+16
Help me plz what is the theme
Making new friends is too difficult, so you shouldn’t try.
You have to take risks in order to get rewards.
Jared felt lonely and sad because he was too afraid to take a chance.
Honesty is always the best policy.
Answer:
There is no passage/short story etc. to base this question off of, but if you copy and paste it I'll come back and edit my answer :)
Which statements are true? Select all that apply.
Answer:
A,B, D
Step-by-step explanation: I just took that test and i got it right
f(x) = 2x3 - 3x2 + 5
g(x) = 3x3 + 2x2 - 4x - 9
Find (f - g)(x).
O – x3 – 5x2 + 4x + 14
O – x3 – x2 - 4x - 4
O 5x3 – x2 - 4x - 4
O x3 + 5x2 - 4x – 14
Answer:
(f - g)(x) = -x³ -5x² + 4x + 14
Step-by-step explanation:
f(x) = 2x³ - 3x² + 5
g(x) = 3x³ + 2x² - 4x - 9 subtract
(f - g)(x) = (2-3)x³ + (-3-2)x² + (0 - -4)x + (5 - -9)
(f - g)(x) = (-1)x³ + (-5)x² + (0 + 4)x + (5+ 9)
(f - g)(x) = (-1)x³ + (-5)x² + (4)x + (14)
(f - g)(x) = -x³ -5x² + 4x + 14