Answers
Answer: see proof below
Step-by-step explanation:
Use the Sum/Difference Identity: tan (A + B) = (tanA + tanB)/(*1 - tanA · tanB)
Scratchwork:
tan (50) = tan (40 + 10)
[tex]= \dfrac{\tan 40+\tan 10}{1-\tan 40\cdot \tan 10}[/tex]
tan 50 (1 - tan 40 · tan 10) = tan 40 + tan 10
tan 50 - tan 50 · tan 40 · tan 10 = tan 40 + tan 10
tan 50 = tan 40 + tan 10 + tan 50 · tan 40 · tan 10
Use the Reciprocal Identity: cot A = 1/ tan --> cot A · tan A = 1
Proof LHS → RHS
LHS: tan 50 - tan 40
Substitute tan 50: tan 40 + tan 10 + (tan 50 · tan 40) · tan 10 - tan 40
Simplify: tan 10 + (tan 50 · tan 40) · tan 10
Reciprocal Identity: tan 10 + tan 10
Simplify: 2 tan 10
LHS = RHS: 2 tan 10 = 2 tan 10 [tex]\checkmark[/tex]
Related Questions
7 Car A uses petrol at the rate of 4.8L/100 km, whereas car B uses it at a rate of
10L/100 km. What will the difference in petrol costs be in a year in which both
cars travel 30000 km, if the petrol costs on average $1.45/L?
Answers
Step-by-step explanation:
30,000 km × (4.8 L / 100 km) × ($1.45 / L) = $2088
30,000 km × (10 L / 100 km) × ($1.45 / L) = $4350
The difference is $4350 − $2088 = $2262.
1.25x12 divided by 0.6
Answers
(1.25 x 12)/ 0.6=
25
Hope this helps :)
Central subs made 27 sandwiches using 12 pounds of turkey, how much turkey was used per sandwich?
Answers
Answer: [tex]\frac{4}{9}[/tex] lbs of turkey
Step-by-step explanation:
hey there,
< Since we know 27 sandwiches = 12 lbs, then let's make a ratio table.
27 sandwiches = 12 lbs
1 sandwich = ? lbs
The way you solve a ratio table is multiply the two amounts that cross each other that do not include the thing we are trying to find. Here, it would be 12 lbs x 1 sandwich, as they are right across from each other and there is no "?" within either of those two. 12 x 1 = 12. Now, divide by the last amount left that we haven't touched yet (27 sandwiches).
12 ÷ 27 = [tex]\frac{12}{27}[/tex] = [tex]\frac{4}{9}[/tex] lbs of turkey or you can change it to a decimal so it would be 0.44 lbs (not precise so it's better to use a fraction). >
Hope this helped! Feel free to ask anything else if you still have questions.
Answer:
4/9 lbs per sandwich
Step-by-step explanation:
We want turkey per sandwich
12 lbs turkey/ 27 sandwiches
4/9 lbs per sandwich
For the constant function v(x) = 1, which statement describes the additive and multiplicative inverses? Both inverses are equal to v(x). Neither inverse is equal to v(x). The additive inverse is equal to v(x), but the multiplicative inverse is not. The multiplicative inverse is equal to v(x), but the additive inverse is not.
Answers
Answer:
The multiplicative inverse is equal to v(x), but the additive inverse is not.
Step-by-step explanation:
The multiplicative inverse is equals to v(x) but the additive inverse is not.
What is additive inverse?Additive inverse is a number which on getting added to the original number results in zero.
For example, 5 - 5 = 0
⇒ -5 is the additive inverse of 5.
What is multiplicative inverse?Multiplicative inverse of a number is a value which when multiplied by the original number results in 1.
For example
[tex]5 (\frac{1}{5} )= 1[/tex]
⇒ [tex]\frac{1}{5}[/tex] is the multiplicative inverse of 5.
According to the given question.
We have a function
v(x) = 1
Let the additive inverse of 1 is x.
⇒ 1 + x = 0
⇒ x = -1.
Hence, the additive inverse of 1 is -1.
Let the multiplicative inverse of 1 is y.
⇒ 1 × y = 1
⇒ y = 1/1
⇒ y = 1
Hence, the multiplicative inverse of 1 is 1.
From the above calculation we can see that, the multiplicative inverse is equals to v(x) but the additive inverse is not.
Thus last option is correct.
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Which statement is NOT true about Rational Numbers ? ( 2 answers ) a . Whole Numbers are Rational Numbers b . Integers, Whole Numbers, and Natural numbers are Rational Numbers. c. Only fractions are rational d. Repeating decimals and terminating decimals are Rational number.
Answers
Answer:
The answers are A and B.
Step-by-step explanation:
translating verbal expression: the quotient of twice a number t and 13
Answers
Answer:
My answer to the question is 2t÷13.
Answer:
[tex]\Huge \boxed{\frac{2t}{13} }[/tex]
[tex]\rule[225]{225}{2}[/tex]
Step-by-step explanation:
The number t is doubled.
[tex]\Rightarrow t *2[/tex]
[tex]\Rightarrow 2t[/tex]
Quotient is the result after dividing two or more values.
[tex]\Rightarrow \displaystyle \frac{2t}{13}[/tex]
[tex]\rule[225]{225}{2}[/tex]
how far will you travel in 4 seconds flying at a rate of 132 m/s?
Answers
Answer:
528 m
Step-by-step explanation:
Speed = Distance / Time
= Distance = Speed × Time
= 4 × 132
= 528 m
Answer:132×4=528
Step-by-step explanation:
For every second add another 132, as it's units are metres per second
The formula for the distance traveled over time ttt and at an average speed vvv is v\cdot tv⋅tv, dot, t. Amit ran for 404040 minutes at a speed of about 555 kilometers per hour. What calculation will give us the estimated distance Amit ran in kilometers?
Answers
Answer:
5 x 40/60
Step-by-step explanation:
The distance Amit ran will be 3.34 kilometers in 40 minutes.
What is speed?Speed is defined as the ratio of the time distance traveled by the body to the time taken by the body to cover the distance. Distance is defined as the length between the two points.
It is given that the distance traveled over time t and at an average speed is s. Amit ran for 40 minutes at a speed of about 5 kilometers per hour.
The distance will be calculated by using the speed formula:-
Speed = Distance / time
Convert the formula to calculate distance.
Distance = Speed x Time
Distance = 5 x ( 40/60 )
40/ 60 is the time in hours.
The distance will be calculated as:-
Distance = 10 / 3
Distance = 3.34 kilometers
Therefore, the distance Amit ran will be 3.34 kilometers in 40 minutes.
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A____ is a fixed position in space and has no dimensions or size. hins
Answers
Answer:
Point
Step-by-step explanation:
This is the definition of a point.
A "point" is a fixed position in space and has no dimensions or size.
Cheers.
Answer:
A point is a fixed position in space and has no dimensions or size.
Which of the following is an example of the Associative Property of Addition? A. c • (3 • f) = (c • 3) • f B. c • 3 = 3 • c C. c + 3 = c + 3 D. c + (3 + f) = (c + 3) + f
Answers
Answer:
D
Step-by-step explanation:
Associative property states that the sum of three or more numbers stays the same no matter how the numbers are grouped.
A is not correct because it is multiplication not addition and it asked for addition
If the length of a side of an
equilateral triangle is x, what is half of the perimeter?
Answers
Answer:
3/2 x
Step-by-step explanation:
length of a side of an equilateral triangle is x
The perimeter is
P = 3s where s is the side length
P = 3x
1/2 of the perimeter
1/2 (3x)
3/2 x
find all values of c such that the domain of the following function is the set of all real numbers
f(x) = (x + 7) / (x^2 + 2cx + 14)
Answers
Answer:
[tex]-\sqrt{14} < c < \sqrt{14}[/tex]
Step-by-step explanation:
For the function to have a domain of all reals, the denominator cannot have a value of zero. x^2 + 2cx + 14 will not have zero as a root if it has no real solutions. A quadratic equation has no solutions when the discriminant is negative.
b^2 - 4ac < 0
(2c)^2 - 4(1)(14) < 0
4c^2 - 56 < 0
4c^2 < 56
c^2 < 14
[tex]-\sqrt{14} < c < \sqrt{14}[/tex]
The domain of the function, f(x) = (x + 7) / (x^2 + 2cx + 14) is the set of all real numbers for the value of c as [tex]-\sqrt{14} < c < \sqrt{14}[/tex] .
Domain of a function are the values that a function can take that is the set of all possible inputs.
Given the following function:
[tex]f(x)=\dfrac{x+7}{x^2+2cx+14}[/tex]
For the real number domain of the given function, the denominator must be a non-zero term. Because, if the denominator is zero then the function will result in an undefined number which does not lie in the real number domain.
For denominator to be non zero, we have to find the value of x which is not the solution of the equation of denominator.
x²+2cx+14≠0
Such value of x can be determined using discriminant.
d<0, then no real solution exists.
d=b²-4ac
Here a=1, b=2c, c=14
d=4c²-4x14
d=4c²-56
d<0
4c²-56<0
4c²<56
c²<14
[tex]-\sqrt{14} < c < \sqrt{14}[/tex]
Thus, [tex]-\sqrt{14} < c < \sqrt{14}[/tex] is such that the domain of the function is the set of all real numbers.
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Prove theorems about triangles
Answers
a) impossible
b) the sum of the angles in a triangle is 180°
63° + 59° + 57° = 179°
17) 74x^2
What is the prime factorization of 74x^2?
Answers
This animation shows a situation in which two quantities are related. Enter the independent quantity in this situation: Enter the dependent quantity in this situation:
Answers
Answer:
[tex]\Large \boxed{\mathrm{independent: \ time}} \\\\\\ \Large \boxed{\mathrm{dependent: \ elevation }}[/tex]
Step-by-step explanation:
The independent variable is on the x-axis.
The independent quantity is time.
The dependent variable is on the y-axis.
The dependent quantity is elevation.
Answer:
The dependent variable is on the y-axis.
The dependent quantity is elevation.
The independent variable is on the x-axis.
The independent quantity is time.
Write –3/8 as a decimal number.
Answers
Answer:
-0.375
Step-by-step explanation:
you just divide the numbers.
solve the equation below
for the indicated variable
1/3ab^2=6 (solve for a)
Answers
Answer:
a=18/b2
Step-by-step explanation:
The required equation for the indicated variable is a = 18/b² which is solved for a.
What is an equation?The equation is defined as mathematical statements that have a minimum of two terms containing variables or numbers that are equal.
What are Arithmetic operations?Arithmetic operations can also be specified by subtracting, dividing, and multiplying built-in functions. The operator that performs the arithmetic operation is called the arithmetic operator.
We have been given the equation for the indicated variable as
⇒ 1/3ab² = 6
Multiply by 3 both sides of the above equation,
⇒ ab² = 6×3
⇒ ab² = 18
Divide by b² into both sides of the equation, and we get
⇒ a = 18/b²
Therefore, the required equation for the indicated variable is a = 18/b².
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What is the value of -2x+3yz if x=3, y=6, and z=
Answers
Answer:
Step-by-step explanation= 33
The length of a rectangle is represented by (6x - 2), and the width is represented by (x - 1). Which expression best
represents the perimeter of the rectangle?
Answers
Answer:
[tex] \boxed{ \bold{ \huge{\boxed{ \sf{14x - 6}}}}}[/tex]
Step-by-step explanation:
Given,
Length of a rectangle ( l ) = 6x - 2
Width of a rectangle ( w ) = x - 1
Perimeter of a rectangle ( P ) = ?
Finding the expressions that represents the perimeter of the rectangle
[tex] \boxed{ \sf{perimeter \: of \: rectangle = 2(l + w)}}[/tex]
⇒[tex] \sf{2(6x - 2 + x - 1)}[/tex]
Collect like terms
⇒[tex] \sf{2(7x - 2 - 1)}[/tex]
Calculate
⇒[tex] \sf{2(7x - 3)}[/tex]
Distribute 2 through the parentheses
⇒[tex] \sf{14x - 6}[/tex]
Hope I helped!
Best regards!!
2^(x-4) = 4a^(x-6) what is the value of x?
Answers
Answer:
First you have to make the values equal....
which is 2^(x-4)=2a^2(x-6).
then since 2 are equal and its x we are looking for.
x-4=2x-12.
x-2x=-12+4.
-x=-8.
x=8.
Which expression is equivalent to -36 - 8? Choose 1 answer:
Answers
Answer:
-44
Step-by-step explanation:
[tex] - 36 - 8 = - 44[/tex]
Please helppp I suckk at fractions!!!
Answers
Answer: a=2 b= 11/6 or 1 5/6
Step-by-step explanation:
Write 7.35 as a mixed number.
Answers
Answer:
7 7/20 is the answer.
Answer: 7 7/20
Step-by-step explanation:
Rewrite the decimal number as a fraction with 1 in the denominator
7.35=7.35 / 1
Multiply to remove 2 decimal places. Here, you multiply top and bottom by 100
7.35/ 1 × 100/ 100=735 / 100
Find the Greatest Common Factor (GCF) of 735 and 100, if it exists, and reduce the fraction by dividing both numerator and denominator by GCF = 5
735 ÷ 5 = 147
100 ÷ 5 = 20
Divide 147/ 20 = 7 7/20
28,000 times what is 1,251,000,000
Answers
Answer:
The number is 312750/7
Step-by-step explanation:
(312750/7)*28000=1251000000
Answer:16
Step-by-step explanation:
Glue
after being transformed the new point is called a(n):
Answers
It is called a image
Answer:
NEW Image
Step-by-step explanation:
Guys I’m scared to ask my dad for help cus he just helped me and the info went right out the window? Can someone help me? Ik the answer but I needa show work
Answers
Answer:
14. -5√30 +3√2
15. 18√5 -30√3
Step-by-step explanation:
You can multiply radicals using ...
(√a)(√b) = √(ab)
And you can simplify radicals using ...
√(a²b) = a√b
_____
14. Using the distributive property, then simplifying the radicals, we have ...
[tex]\sqrt{3}(-5\sqrt{10}+\sqrt{6})\\\\=-5\sqrt{3\cdot10}+\sqrt{3\cdot6}\\\\=-5\sqrt{30}+\sqrt{3^2\cdot2}\\\\=\boxed{-5\sqrt{30}+3\sqrt{2}}[/tex]
__
15. Similarly, ...
[tex]-2\sqrt{15}(-3\sqrt{3}+3\sqrt{5})\\\\=6\sqrt{15\cdot3}-6\sqrt{15\cdot5}\\\\=6\sqrt{3^2\cdot5}-6\sqrt{5^2\cdot3}\\\\=\boxed{18\sqrt{5}-30\sqrt{3}}[/tex]
To which subset(s) of real numbers does the number -4 belong? Choose all that apply Irrational numbers Integers Whole numbers Natural numbers Rational numbers
Answers
Answer:
The answer is: Integers, and Rational Numbers.
Step-by-step explanation:
the number -4 belongs to the subsets of real numbers: Integers and Rational numbers.
The number -4 belongs to the following subsets of real numbers:
1. Integers: Integers include all positive and negative whole numbers, as well as zero. Since -4 is a negative whole number, it is an integer.
2. Whole numbers: Whole numbers include all non-negative integers. Since -4 is negative, it is not a whole number.
3. Natural numbers: Natural numbers include all positive integers. Since -4 is negative, it is not a natural number.
4. Rational numbers: Rational numbers include all numbers that can be expressed as a ratio of two integers, where the denominator is not zero. -4 can be expressed as -4/1, where -4 is an integer and 1 is also an integer. Therefore, -4 is a rational number.
In conclusion, the number -4 belongs to the subsets of real numbers: Integers and Rational numbers.
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What is it can someone help me on question 11 plz
Answers
Answer:
D
Step-by-step explanation:
HOLY GOD
TSUKIIIIIIII.
I LOVE U TSUKIII
In Australia the speed limit is generally 80-110 km/h depending on the conditions of theroad. If someone in Australia is driving at a speed of 90 km/h, what would their speed be in miles per
hour? Show your work. Round to the nearest thousandth.
Answers
Answer:
55.923 MPH
Step-by-step explanation:
Divide by 1.609
Sheila Little has a gross monthly income of $3500. She has 15 remaining payments of $147 on a used car. The taxes and insurance on the house are $85 per month. What maximum monthly payment does the bank's loan officer feel that Sheila can afford?
Answers
Answer:
the maximum monthly payment is $958
Step-by-step explanation:
The computation of the maximum monthly payment for affording is shown below;
Let us assume that there is a 34% of the gross monthly income
So, it would be calculated below:
= Given percentage × gross monthly income - payments made - taxes & insurance per month
= 0.34 × $3,500 - $147 -$85
= $958
hence, the maximum monthly payment is $958