Answers
Answer:
Step-by-step explanation:
Given expression is,
[tex]\text{cot}A=\frac{1}{2}(\text{cot}\frac{A}{2}-\text{tan}\frac{A}{2})[/tex]
To prove this identity we will take the right side of the identity,
[tex]\frac{1}{2}(\text{cot}\frac{A}{2}-\text{tan}\frac{A}{2})=\frac{1}{2}(\frac{1}{\text{tan}\frac{A}{2}}-tan\frac{A}{2})[/tex]
[tex]=\frac{1}{2}(\frac{1-\text{tan}^2\frac{A}{2}}{tan\frac{A}{2}})[/tex]
[tex]=\frac{1}{2}[\frac{2(1-\text{tan}^2\frac{A}{2})}{2tan\frac{A}{2}}][/tex]
[tex]=\frac{1}{2}(\frac{2}{\text{tan}A} )[/tex] [Since [tex]\text{tan}A=\frac{2\text{tan}\frac{A}{2}}{1-\text{tan}^2\frac{A}{2}}[/tex]]
= cot A
Hence right side of the equation is equal to the left side of the equation.
Related Questions
Can some one help me on this 10pts
Answers
Answer:
x = 20
Step-by-step explanation:
Since the triangles are congruent then corresponding angles are congruent, that is
∠ A = ∠ D , thus
3x - 10 = 2x + 10 ( subtract 2x from both sides )
x - 10 = 10 ( add 10 to both sides )
x = 20
SOMEONE HELP ME PLEASE!!!!
Answers
Answer:
2 < X < 77 is the right answer.
solution,
5x - 10 < 25
5x < 25 + 10
5x < 35
X < 35/5
X < 7
Hope this helps...
Good luck on your assignment..
4. 5. 6. None of the choices are correct.
Answers
Answer:
A. 4
Step-by-step explanation:
Triangle ABD = Triangle BCD
Both hypotenuse are equal in length.
x + 2 = 3x - 6
x - 3x = -6-2
-2x = -8
x = 4
Hi !!
Find the value of x :
We have :
• x + 2
• 3x - 6
Match the values to find x :
x + 2 = 3x - 6
x - 3x = -6 - 2
-2x = -8
x = 8/2
x = 4
* 4 + 2 = 3(4) - 6
6 = 12 - 6
6 = 6
Equality is checked, it is an isosceles triangle
Both the correct value is 4.
1 Dentro de seis años tendré el doble de la edad que tenía hace cuatro años. ¿Qué edad tendré dentro de nueve años?
Answers
Answer:
23 años
Step-by-step explanation:
Para resolver la situación, consideremos que x es la edad de la persona. Sabemos que dentro de seis años esta tendrá el doble de la edad que tenía hace cuatro años. La edad dentro de 6 años se puede expresar como x+6 y esto será igual al doble de la edad que tenía hace cuatro años, lo que se puede expresar como 2(x-4). De acuerdo a esto:
x+6=2(x-4)
x+6=2x-8
6+8=2x-x
x=14
Ahora que sabemos que la edad de la persona es 14 años, le sumamos 9 y esto da como resultado 23 y esta es la edad que la persona tendrá en 9 años.
study the diagram of circle K where JL and LM are tangent to circle K at points J and M respectively. Also JL=3x+10 and ML =7x-6
Answers
Answer:
22
Step-by-step explanation:
The answer is 22. You solve the equation 3x+10=7x-6 like so
3x+10=7x-6
-3 = -3
10= 4x-6
+6 +6
16=4x
x=4
You then plug in the value of x to the equation for LM.
7x-6 becomes 7*4-6 which is 22.
1. A bag contains 12 mangoes, of which 4 are not ripe.
What is the chance of picking at random a ripe mango from the bag ?
2. There are 12 red and 8 blue balls in a bag. If a ball is selected at random from the bag, what is the probability that it is
red ?
3. What is the number of all possible outcomes of tossing a fair die ?
4. A boy throws a fair die once. What is the probability of getting the number 4 ?
5. There are 10 red and 15 green balls in a bag.
Find the probability of selecting at random a red ball from the bag.
Answers
Answer:
1. 2/3 or 66.7%
2. 3/5 or 60%
3. 6
4. 1/6 or 16.7%
5. 2/5 or 40%
Step-by-step explanation:
Which is the best reason that a geologist might carry a small dropper bottle filled with hydrochloric acid when doing fieldwork?Which is the best reason that a geologist might carry a small dropper bottle filled with hydrochloric acid when doing fieldwork?
Answers
Answer:
"To search whether carbonate mineral content in another material" is the right answer.
Step-by-step explanation:
We want it just because it lets them better examine the calcareous. Once before in interaction against carbonate minerals, any drop of hydrogen peroxide can splash. Those who add this one to the fluid or acidic solution to see how resources respond that makes them know through substances where certain rocks can indeed be contained. Commonly aspects like calcite assistance and guidance.So that the above is the right answer.
The following expression models the total number of pizzas sold in an hour, where x represents the number of discount coupons
offered. 41x/5x+2+12
What does the constant term in the above function represents?
Answers
Answer:
A. The constant term 12 represents the number of pizzas sold in an hour if 0 discount coupons are offered.
Step-by-step explanation:
Below is the complete question
What does the constant term in the above function represents?
A. The constant term 12 represents the number of pizzas sold in an hour if 0 discount coupons are offered.
B. The constant term 12 represents the maximum number of pizzas sold in an hour.
C. The constant term 12 represents the amount of additional pizzas sold for each additional discount coupon offered.
D. The constant term 12 represents the number of discount coupons offered in an hour.
I need to know the volume of this droplet in cubic meters!
Answers
Answer:
There are 100³ = 1000000 cubic cm in one cubic meter so the answer is 0.1 / 1000000 = 1 / 10000000 = 0.0000001 cubic meters.
Please help me simplify this equation
Answers
Answer:
A. x
Step-by-step explanation:
1. Simplify parentheses
[tex]\frac{13*(x-3)+39}{13}[/tex]
2. Divide by 13
[tex](x-3)+3[/tex]
3. Basic math ([tex]x-3+3[/tex])
[tex]x[/tex]
PLS HELP ME ANSWER, i Need it quick
Answers
Answer:
69
Step-by-step explanation:
The median is the middle number. Using the box and whisker box, the median is the middle line in the box. The line is at 69 for Genevieve
A grocer wants to make a 10-pound mixture of berries and chocolate that he can sell for $3.48 per pound. If chocolate cost $5.40 per pound and berries cost $2.20 per pound, how many pounds of berries must he include in the mix?
Answers
Answer:
9
Step-by-step explanation:
Since he only has to buy one pound of chocolate to make it a berry chocolate mix, he can just put 9 pounds of berries into it. Why would he want to break even? Make some profits grocer or you are not going to be in that house for very long.
The HCF of 59 and 62 is (a) 4 (b) 28 (c) 6 (d) None of the above
Answers
Answer:
An object balances itself when a perpendicular line drawn through its Centre of Gravity (CG), passes through its base.
See the picture of a popular toy given below. The horse, the rider and the ball are all joined together as one single unit. This entire unit is balanced on the thin black rod shown. At which of the indicated positions, could the Centre of Gravity (CG) of the horse, rider and ball unit be?
July 10 book Science up55 down8
AA BB
CC DD
Step-by-step explanation:
Answer:
The answer is d. none of the above
Step-by-step explanation:
59= 1,59
62= 1, 2, 31, 62
Common factors= 1
HCF = 1
I hope this helps.
Points A, B, C, and D lie on a line consecutively so that AB = BC = CD = 6 in. Find the distance between the midpoints of segments AB and CD . Answer: Distance between midpoints is in
Answers
Answer: 12 inches
Step-by-step explanation:
Given that :
Points A, B, C, and D lie on a line consecutively so that AB = BC = CD = 6 in
Therefore, A, B, C and D lie on a line which has a distance of 6 inches between each consecutive point.
A could be taken as the starting point with and D taken the end of the line with B and C in between them.
For instance:
A = 6; B = 12 ; C = 18 ; D = 24
Midpoint of AB = (12 + 6) / 2 = 18/2 = 9
Midpoint of CD = (18 + 24) / 2 = 42/2 = 21
Distance between the Midpoint AB and CD equals:
Midpoint CD - Midpoint AB
(21 - 9) inches = 12 inches
Answer:
Step-by-step explanation:
12in
Put the following numbers in ascending order.
A.540 g
B.180,000 mg
C.0.8 tonnes
D.2.3 kg
Answers
Answer:
B, A, D, C
Step-by-step explanation:
Covert all units into grams.
540 g = 540 g
180,000 mg = 180g
0.8 tonnes = 800000 g
2.3 kg = 2300 g
Arrange in ascending order.
180,000 mg, 540 g, 2.3 kg, 0.8 tonnes
I need help with this honestly
Answers
Answer:
D.(-4,-8) and(2,4)
Step-by-step explanation:
y=-2x
y=x²-8
this means that the two equations are equal because they both add up to y
thus; x²-8=-2x
formulae=Ax²+bx+c=0
x²+2x-8=0
find two numbers which multiplied will give you x² and when added will give you 2x that is x and x
x²+x+x-8=0
x(x+1)+1(x-8)=0
(x+1)(x-8)=0
1)x+1=0. x= -1
further explanation on answers1)y=-2x
y=-2(-1)=2
y=2
2)y=x²-8
y=1²-8= -8
y= -8
note*this means that the answer should have both 2 and -8 thus d is the answer
Plzzzzzzzz! A suitcase lock has a code 4 symbols long. The symbols on the lock are a star, a square, a circle, a triangle, a line, and a pentagon. What is the probability that a randomly chosen code starts with a star followed by triangle and doesn't contain the same symbol twice? Enter your answer as a fraction in simplest form.
Answers
Answer:
[tex]\dfrac{1}{30}[/tex]
Step-by-step explanation:
6 symbols and 4-symbol code so number of combinations wich doesn't contain the same symbol twice would be:
6•5•4•3 = 360
If code starts with a star followed by triangle that means only one posibility for first two symbols and code doesn't containing the same symbol twice means that left 4 symbols for next two.
So number of combinations of code starting with a star followed by triangle and doesn't containing the same symbol twice will be:
1•1•4•3 = 12
The probability that a randomly chosen code starts with a star followed by triangle and doesn't contain the same symbol twice:
[tex]\dfrac{1\cdot1\cdot4\cdot3}{6\cdot5\cdot4\cdot3}=\dfrac{1\cdot1}{6\cdot5}=\dfrac{1}{30}[/tex]
plz help!! tell me which ones you solve
Answers
Answer:
Step-by-step explanation:
17)-8(5-n)=-96
-8*(5-n)-(-96)=0
(0 - 8 • (5 - n)) - -96 = 0
8n + 56 = 8 • (n + 7)
8 • (n + 7) = 0
Solve : 8 = 0
This equation has no solution.
A a non-zero constant never equals zero.
Solve : n+7 = 0
Subtract 7 from both sides of the equation :
n = -7
n = -7 is your answer
Consider the expression. (StartFraction 2 m Superscript negative 1 baseline n Superscript 5 Baseline Over 3 m Superscript 0 Baseline n Superscript 4 Baseline EndFraction) squared What is the value of the expression if m = –5 and n = 3? Negative StartFraction 24 Over 25 EndFraction Negative StartFraction 4 Over 25 EndFraction StartFraction 4 Over 25 EndFraction StartFraction 24 Over 25 EndFraction
Answers
Answer:
The correct option is option (3) 4 ÷ 25.
Step-by-step explanation:
The expression in terms of m and n is:
[tex]F(m,n)=[\frac{2m^{-1}n^{5}}{3m^{0}n^{4}}]^{2}[/tex]
Exponent rule of division:
[tex]a^{x}\div a^{y}=a^{x-y}[/tex]
Compute the value of the expression for m = -5 and n = 3 as follows:
[tex]F(m,n)=[\frac{2m^{-1}n^{5}}{3m^{0}n^{4}}]^{2}[/tex]
[tex]F(-5,3)=[\frac{2\csdot (-5)^{-1}\cdot (3)^{5}}{3\cdot (-5)^{0}\cdot (3)^{4}}]^{2}[/tex]
[tex]=\{\frac{2}{3}\times [(-5)^{-1-0}\times (3)^{5-4}}]\}^{2}\\\\=\{\frac{2}{3}\times \frac{-1}{5}\times 3\}^{2}\\\\=\{-\frac{2}{5}\}^{2}\\\\=\frac{4}{25}[/tex]
Thus, the correct option is option (3) 4 ÷ 25.
Answer:
4/25
Step-by-step explanation:
I just did the test
Write the quadratic function in f(x)= a(x-h)^2+k form whose graph is shown.
f(x)=
Answers
Answer:
f(x) = - (x - 2)² + 2
Step-by-step explanation:
The equation of a parabola in vertex form is
y = a(x - h)² + k
where (h, k) are the coordinates of the vertex and a is a multiplier
Here (h, k) = (2, 2 ), thus
y = a(x - 2)² + 2
To find a substitute the point (0, - 2) into the equation
- 2 = a(- 2)² + 2 ( subtract 2 from both sides )
- 4 = 4a ( divide both sides by 4 )
a = - 1
Thus
f(x) = - (x - 2)² + 2
If 2^2.322 = 5 then what does 2^5.322 equal? Explain how you found your answer.
Answers
Answer:
40.002
Step-by-step explanation:
[tex]2^{5.322}[/tex] is 2 to the power of 5.322. Only way to find the exact decimal is to calculate in a calculator. When we do so we should get 40.002 as our answer.
The question says:
'If 2^2.322 = 5 then what does 2^5.322 equal? Explain how you found your answer. '
So we have to use the fact that 2^2.322 = 5, in order to work out what 2^5.322 equals
_______________________________________________
Remember the following indices rule:
a^m times a^n = a^(m+n)
So first we have to use the indice rule to split apart 2^2.322:
[tex]2^{2.322}=2^{2+0.322}=2^2\times2^{0.322}=4\times2^{0.322}[/tex]
Now we can substitute this into the original equation, and work out the approximate value for [tex]2^{0.322}[/tex]:
[tex]2^{2.322} = 5[/tex]
[tex]4\times2^{0.322}=5[/tex]
[tex]2^{0.322}=\frac{5}{4} =1.25[/tex]
Now lets use the indices rule again to split apart 2^5.322:
[tex]2^{5.322} = 2^{5+0.322}=2^5\times2^{0.322}= 32\times2^{0.322}[/tex]
From the previous equation, we worked out that [tex]2^{0.322} = 1.25[/tex]
Therefore:
[tex]2^{5.322} = 32 \times 1.25 = 40[/tex]
____________________
Answer:
40
The tip jar at a sandwich shop has been found to have a dollar value 0.65h + 1.25, where h is the number of
hours since the shop opened.
a. By how much is the value of the tip jar increasing per hour?
Answers
Answer:
H is showing how the amount of the tip jar is increasing over time
Step-by-step explanation:
Which normal distribution has the greatest standard deviation?
50 POINTS TO YOU
Answers
Answer:
Given : Few Distributions Mean & Standard Deviation.
To find : normal distribution which has the greatest standard deviation.
Solution:
=> Distribution 4 has the greatest standard deviation.
Graph at top has more spread hence more standard deviation.
Answer:
its A i just took the test
Step-by-step explanation:
i hope this helped ;)
Which expression has the same value as Negative 18 divided by (negative 9)? Negative 18 divided by 2 Negative 12 divided by (negative 3) Negative 10 divided by 5 Negative 8 divided by (negative 4) (for brainliest)
Answers
Answer: -8/-4
Step-by-step explanation:
When a negative integer gets divided my another negative integer, it results in a positive number. This means that we can eliminate all the negative symbols in this problem
18/9 = 2
Now all is left to determine which other expression is equivalent to 2
In the expression -10 / 5, since there is only one negative symbol, the postulate for negative number division states that two negative integers makes a positive number, and there is one negative integer and one positive whole number.
18/2 = 9 = incorrect
12/3 = 4 = incorrect
-10/5 = -2 = incorrect
8/4 = 2 = correct
So the expression -8/-4 is equivalent to the expression -18/-9
Answer:
Its D
Step-by-step explanation:
took the test its right, yw
29. one of the following has always two points of parallel sides
A. Quadrilateral
B. Triangle
C. Rhombus
D. Pentagon
Answers
Answer:
c
Step-by-step explanation:
only rhombus satisfied the question
Answer:
C, Rhombus.
Step-by-step explanation:
A rhombus has 2 pairs of parallel sides. Also a rhombus has 4 congruent sides.
Assume m<22=35. Find the measure of all of the other angles in the figure given line L and line P are parallel.
PLEASE HELP!!! ASAP!!!
(Picture included)
Answers
Answer:
m∠1 = 145°
m∠3 = 35°
m∠4 = 145°
m∠5 = 145°
m∠6 = 35°
m∠7 = 35°
m∠8 = 145°
Step-by-step explanation:
In the picture attached,
line 'm' and line 'l' are the parallel lines and another line intersects these lines is a transverse.
m∠2 = 35°
Since ∠1 and ∠2 are supplementary angles,
m∠1 + m∠2 = 180°
m∠1 + 35° = 180°
m∠1 = 180° - 35°
m∠1 = 145°
∠1 ≅ ∠4 [Vertical angles]
m∠1 = m∠4 = 145°
∠2 ≅ ∠3 [Vertical angles]
m∠2 = m∠3 = 35°
∠3 ≅ ∠6 [Interior alternate angles]
m∠3 = m∠6 = 35°
Similarly, ∠4 ≅ ∠5 [Interior alternate angles]
m∠4 = m∠5 = 145°
∠6 ≅ ∠7 [Vertical angles]
m∠6 = m∠7 = 35°
Consider this function. f(x) = x + 4 Which graph represents the inverse of function f?
A.) W
B.) X
C.) Y
D.) Z
Answers
Answer:
C
Step-by-step explanation:
just took the unit test
Graph Y represents the inverse of function f.
What is the inverse of a function?In mathematics, the inverse function of a feature f is a function that undoes the operation of f.
How do you find an inverse of a function?To find the inverse of a function, write the function y as a function of x i.e. y = f(x) after which solve for x as a function of y.
Learn more about the inverse of a function here brainly.com/question/24992590
#SPJ2
Estimate the circumference of a circle that has a diameter of 13 yards.
______yd
Answers
Answer:
The answer is 40.8 ydStep-by-step explanation:
Circumference of a circle is πd
where d is diameter
diameter is 13 yards
Circumference of the circle is
π × 13 yd
= 13π
= 40.8yd to one decimal place
Identify the range of the function shown in the graph.
A. y is all real numbers.
B. {-2,2}
C. -2 < y < 2
D. Y > 0
Answers
Answer:
A. y is all real numbers.
Step-by-step explanation:
The range is the possible values that y can take
In this graph y goes from negative infinity to infinity so y can be all real numbers
A certain circle can be represented by the following equation x^2+y^2+18x+14y+105=0 What is the center and radius of the circle?
Answers
Answer:
center: (-9, -7)radius: 5Step-by-step explanation:
A graphing calculator can be helpful for questions of this nature. The attached shows the center is (-9, -7) and the radius is 5.
_____
You can separate the x- and y- terms and complete the square for each.
(x^2 +18x) +(y^2 +14y) = -105
Do that by adding the square of half the linear term.
(x^2 +18x +9^2) +(y^2 +14x +7^2) = -105 +81 +49
(x +9)^2 +(y +7)^2 = 25
Compared to the standard form equation ...
(x -h)^2 +(y -k)^2 = r^2 . . . . . . . center (h, k), radius r
We see that the given circle has a center of (-9, -7) and a radius of 5.