Given:
Slope of line F = [tex]-\dfrac{6}{3}[/tex]
Slope of line G = [tex]-\dfrac{8}{4}[/tex]
To find:
The conclusion about distinct lines F and G.
Solution:
We have,
Slope of line F = [tex]-\dfrac{6}{3}[/tex]
= [tex]-2[/tex]
Slope of line G = [tex]-\dfrac{8}{4}[/tex]
= [tex]-2[/tex]
The slopes of lines F and G are equal and we know that the slopes of two parallel lines are always equal.
Therefore, the line F and line G are parallel to each other.
Find all possible values of α+
β+γ when tanα+tanβ+tanγ = tanαtanβtanγ (-π/2<α<π/2 , -π/2<β<π/2 , -π/2<γ<π/2)
Show your work too. Thank you!
Answer:
[tex]\rm\displaystyle 0,\pm\pi [/tex]
Step-by-step explanation:
please note that to find but α+β+γ in other words the sum of α,β and γ not α,β and γ individually so it's not an equation
===========================
we want to find all possible values of α+β+γ when tanα+tanβ+tanγ = tanαtanβtanγ to do so we can use algebra and trigonometric skills first
cancel tanγ from both sides which yields:
[tex] \rm\displaystyle \tan( \alpha ) + \tan( \beta ) = \tan( \alpha ) \tan( \beta ) \tan( \gamma ) - \tan( \gamma ) [/tex]
factor out tanγ:
[tex]\rm\displaystyle \tan( \alpha ) + \tan( \beta ) = \tan( \gamma ) (\tan( \alpha ) \tan( \beta ) - 1)[/tex]
divide both sides by tanαtanβ-1 and that yields:
[tex]\rm\displaystyle \tan( \gamma ) = \frac{ \tan( \alpha ) + \tan( \beta ) }{ \tan( \alpha ) \tan( \beta ) - 1}[/tex]
multiply both numerator and denominator by-1 which yields:
[tex]\rm\displaystyle \tan( \gamma ) = - \bigg(\frac{ \tan( \alpha ) + \tan( \beta ) }{ 1 - \tan( \alpha ) \tan( \beta ) } \bigg)[/tex]
recall angle sum indentity of tan:
[tex]\rm\displaystyle \tan( \gamma ) = - \tan( \alpha + \beta ) [/tex]
let α+β be t and transform:
[tex]\rm\displaystyle \tan( \gamma ) = - \tan( t) [/tex]
remember that tan(t)=tan(t±kπ) so
[tex]\rm\displaystyle \tan( \gamma ) = -\tan( \alpha +\beta\pm k\pi ) [/tex]
therefore when k is 1 we obtain:
[tex]\rm\displaystyle \tan( \gamma ) = -\tan( \alpha +\beta\pm \pi ) [/tex]
remember Opposite Angle identity of tan function i.e -tan(x)=tan(-x) thus
[tex]\rm\displaystyle \tan( \gamma ) = \tan( -\alpha -\beta\pm \pi ) [/tex]
recall that if we have common trigonometric function in both sides then the angle must equal which yields:
[tex]\rm\displaystyle \gamma = - \alpha - \beta \pm \pi [/tex]
isolate -α-β to left hand side and change its sign:
[tex]\rm\displaystyle \alpha + \beta + \gamma = \boxed{ \pm \pi }[/tex]
when is 0:
[tex]\rm\displaystyle \tan( \gamma ) = -\tan( \alpha +\beta \pm 0 ) [/tex]
likewise by Opposite Angle Identity we obtain:
[tex]\rm\displaystyle \tan( \gamma ) = \tan( -\alpha -\beta\pm 0 ) [/tex]
recall that if we have common trigonometric function in both sides then the angle must equal therefore:
[tex]\rm\displaystyle \gamma = - \alpha - \beta \pm 0 [/tex]
isolate -α-β to left hand side and change its sign:
[tex]\rm\displaystyle \alpha + \beta + \gamma = \boxed{ 0 }[/tex]
and we're done!
Answer:
-π, 0, and π
Step-by-step explanation:
You can solve for tan y :
tan y (tan a + tan B - 1) = tan a + tan y
Assuming tan a + tan B ≠ 1, we obtain
[tex]tan/y/=-\frac{tan/a/+tan/B/}{1-tan/a/tan/B/} =-tan(a+B)[/tex]
which implies that
y = -a - B + kπ
for some integer k. Thus
a + B + y = kπ
With the stated limitations, we can only have k = 0, k = 1 or k = -1. All cases are possible: we get k = 0 for a = B = y = 0; we get k = 1 when a, B, y are the angles of an acute triangle; and k = - 1 by taking the negatives of the previous cases.
It remains to analyze the case when "tan "a" tan B = 1, which is the same as saying that tan B = cot a = tan(π/2 - a), so
[tex]B=\frac{\pi }{2} - a + k\pi[/tex]
but with the given limitation we must have k = 0, because 0 < π/2 - a < π.
On the other hand we also need "tan "a" + tan B = 0, so B = - a + kπ, but again
k = 0, so we obtain
[tex]\frac{\pi }{2} - a=-a[/tex]
a contradiction.
(1 + sin x)(1 – sin x) = cos^2x
Answer:
(1 + sin x)(1 – sin x) = cos^2x
1 - sin^2x = cos^2x
cos^2x = cos^2x
Step-by-step explanation:
Simplify the left hand side:
(1 + sin x)(1 – sin x) = cos^2x
1 - sin^2x = cos^2x
Using the Pythagorean Identity, we can see that the two sides are equivalent if you subtract sin^2x from both sides:
sin^2x + cos^2x = 1
cos^2x = 1 - sin^2x
Lastly, write it out:
(1 + sin x)(1 – sin x) = cos^2x
1 - sin^2x = cos^2x
cos^2x = cos^2x
use the substitution method to find the value of y in the given system of equations y=2x+5 x+y=4
Answer:
y = 13/3
Step-by-step explanation:
substitute y=2x+5 in x+y = 4
x+2x+5 = 4
3x+5=4
3x= -1
x= -1/3
substitute x= 1-/3 in x+y = 4
-1/3 +y = 4
y = 13/3
A taxi firm charges a fixed cost of $10 together with a variable cost of $3 per mile. (a) Work out the average cost per mile for a journey of 4 miles. (b) Work out the minimum distance travelled if the average cost per mile is to be less than $3.25
Answer:
$5.5 per mile
40 miles
Step-by-step explanation:
Given :
Fixed cost = $10
Variable cost = $3
For a journey of 4 miles ;
Cost = fixed cost + Variable Cost
Cost = $10 + $3x
x = number of miles
Cost = $10 + $3(4)
Cost = $10 + $12 = $22
Average cost per mile for a journey of 4 miles
Cost / number of miles
$22 / 4 = $5.5 per mile
Minimum distance if average per mile is to be less Than 3.25
$3.25 = (10 + 3x) / x
3.25x = 10 + 3x
3.25x - 3x = 10
0.25x = 10
x = 10 / 0.25
x = 40 miles
Question 8: Find the equation of the straight line that:
(a) has a gradient of 4 and passes through the point (1, 10)
Answer:
[tex]y=4x+6[/tex]
Step-by-step explanation:
Hi there!
Linear equations are typically organized in slope-intercept form: [tex]y=mx+b[/tex] where m is the slope (also called the gradient) and b is the y-intercept (the value of y when x is 0)
1) Plug the gradient into the equation (b)
[tex]y=mx+b[/tex]
We're given that the gradient of the line is 4. Plug this into [tex]y=mx+b[/tex] as m:
[tex]y=4x+b[/tex]
2) Determine the y-intercept (b)
[tex]y=4x+b[/tex]
Plug in the given point (1,10) as (x,y) and solve for b
[tex]10=4(1)+b\\10=4+b[/tex]
Subtract 4 from both sides to isolate b
[tex]10-4=4+b-4\\6=b[/tex]
Therefore, the y-intercept of the line is 6. Plug this back into [tex]y=4x+b[/tex] as b:
[tex]y=4x+6[/tex]
I hope this helps!
answer = y = 4x + 6
y = mx + b
gradient = slope = m = 4
(1,10) = (x,y)
plug in the values
10 = 4 (1) + b
10 = 4 + b
b = 6
y = 4x + 6
translate the sentence into an equation
three more than the quotient of a number and 2 is 9
Answer:
Well the correct answer is 9=2+(x/3) or
(3/x)+2=9
help me pls beestar is not fun
Answer:
C. 3/9
Step-by-step explanation:
First, you need to understand what the tree diagram means.
You spin a three-color spinner once. You can get one of three results:
green, blue, or yellow. This is shown in the figure under "1st spin."
Now you spin the spinner a second time. This second spin can also have three outcomes, green, blue, or yellow. For each of the three outcomes of the first spin, you can have 3 different outcomes of the second spin. That is shown under the "2nd spin."
That means there are 9 possible outcomes (numbered from 1 to 9 below):
1. green, green
2. green, blue
3. green, yellow
4. blue, green
5. blue, blue
6. blue, yellow
7. yellow, green
8. yellow, blue
9. yellow, yellow
Each of the 9 outcomes above shows the outcome of the first spin followed by the outcome of the second spin. As you can see there are 9 different outcomes of the two spins.
Now count the number of outcomes that have the same color for the first and second spin. They are shown in bold below.
1. green, green
2. green, blue
3. green, yellow
4. blue, green
5. blue, blue
6. blue, yellow
7. yellow, green
8. yellow, blue
9. yellow, yellow
3 out of 9 outcomes are the same color twice.
Answer: C. 3/9
Find the values of x and y from the following equal ordered pairs. a) (x,-2) = (4,y) b) (3x, 4) = (6, 2y) c) (2x-1, y + 2) = (-1,2) d) (2x + 4, y + 5) = (3x + 3,6) e) (x + y,y + 3) = (6, 2y) f) (x + y, x - y) - (8,0)
Answer:
a)
x=4, y=-2
b)
x=2, y=2
c)
x=0, y=0
d)
x=1, y=1
e)
x=3, y=3
f)
x=4, y=4
Step-by-step explanation:
a) (x,-2) = (4,y)
x=4
y=-2
b) (3x, 4) = (6, 2y)
3x=6 => x=2
2y=4 => y=2
c) (2x-1, y + 2) = (-1,2)
2x-1 =-1 => x=0
y+2 = 2 => y=0
d) (2x + 4, y + 5) = (3x + 3,6)
2x+4 = 3x+3 => x=1
y+5 = 6 => y=1
e) (x + y,y + 3) = (6, 2y)
x+y = 6 => x+3 = 6 => x=3
y+3 = 2y => y=3
f) (x + y, x - y) - (8,0)
x+y = 8 => 2x=8 => x=4
x-y = 0 => x=y => y=4
please help asap
Find the volume of this cone.
Use 3 for TT.
5in
V =
Answer:
V=πr2h /3
V=πr2h /3=π·2.52·8 /3≈52.35988
so the volume is 52.36 inches
When Zero added to any integer, what is the result?
Answer:
answer will be the integer only which was added to zero
Which statistic is a measure of how data are dispersed in a population and can be used to give context to larger data sets
Answer:
standard deviation
Step-by-step explanation:
The standard deviation is defined as the measure of how spread out the numbers are in a given population. In other words, statistics refers to the amount of the dispersion or variation of a set of given values.
It is denoted by the Greek letter sigma, σ.
Thus the standard deviation is the measure of how dispersed the data are in the population which can be used to provide context to a larger data sets.
measured the volume of an object and recorded it as 46 cubic cm
which was 15% high from the actual volume. Find the actual volume.
Answer:
[tex]40\ cm^3[/tex]
Step-by-step explanation:
Let the actual volume is V.
The measured volume of an object is 46 cubic cm which was 15% high from the actual volume.
According to the given condition,
[tex]V+\dfrac{15V}{100}=46\\\\\dfrac{115V}{100}=46\\\\V=\dfrac{4600}{115}\\\\V=40\ cm^3[/tex]
So, the actual volume was [tex]40\ cm^3[/tex].
I need who help .. who can be my lifesaver
Answer:
Q = G
Step-by-step explanation:
We are already given that angle P = angle H
We are also given that side QP = side GH
Remember if two sides are congruent then so are their opposite angles meaning that the opposite angle of GH ( which would be angle F ) would be congruent to the opposite angle of QP ( which would be angle R )
The remaining angles would be angle q and angle g so the additional information needed would be G = Q
These dot plots show the weights (in kilograms) from a sample of leopards
and tigers.
Leopards
000
0000+
000000
00018
00
20
40
60
80
160
180
200
220
100 120 140
Weight (kg)
Tigers
000
2000
000000
2000
ooe
O
20
40
60
80
160
180
200
220
100 120 140
Weight (kg)
What are the differences between the centers and spreads of these
distributions?
Select two choices: one for the centers and one for the spreads.
No
Answer: A.Spreads: The weights of the tigers are more spread out.
B.Centers:The leopards have a lower median weight than the tigers
Step-by-step explanation:
On analyzing the dot plots, we find that the weight of Leopards are more spread out and the weight of Leopards has a lower median than Tiger.
What is median?Median is a statistical measure that determines the middle value of a dataset listed in ascending order. The measure divides the lower half from the higher half of the dataset.
Median of Weight of Leopard = 50 kg
Median of Weight of Tiger = 125 kg
This implies that the Leopards have a lower median weight than Tigers.
What is spread of data?
Spread describes the variation of the data. One of the measures of spread is range.
Range of weight of Leopards= 40 kg
Range of weight of Tigers = 90 kg
This implies that the weight of Tigers are more spread out.
Learn more about median here
brainly.com/question/21396105
#SPJ2
Find the prime factorization on 168
Answer:
The prime factors of 168 are 2, 3, and 7.
Step-by-step explanation:
Gabe went out to lunch with his best friend. The bill cost $16.40 before tax and tip. He paid a 9% tax and he left a 20% tip. How much did Gabe spend?
Hint: Tax and tip are both based on the original cost of the bill.
Don't forget to round to the nearest cent!
ayuda por favor es para mañana
Answer:
sorry??
Step-by-step explanation:
solve for
1) a
2) f
3) e
Answer:
Step-by-step explanation:
b + 70 = 180 {Supplementary angles}
b = 180 - 70
b = 110
a +b = 180 {Linear pair}
a + 110 = 180
a = 180 - 110
a = 70
d + 60 = 180 {linear pair}
d = 180 - 60
d = 120
c + d + 60 = 360 {one point angle}
c + 120 + 60 = 360
c + 180 = 360
c = 360 - 180
c = 180
f + 60 = 180 {Supplementary angles}
f = 180 - 60
f = 120
What are the coordinates of the point that 1/6 of the way from A to B
Answer:
D
Step-by-step explanation:
The distance from - 2 to 10 is 12. 12/6 is 2, so 2 spaces across
You are given the exponential function g(x)=3^x. Which ootion below gives the formula for the new function h created by stretching g by a factor of 3 along the y-axis?
Answer:
h(x) = 3^(x + 1)
Step-by-step explanation:
The exponential function is;
g(x) = 3^(x)
Now, in transformation of exponential functions of say f(x) = b^(x), when the new function g(x) is created by stretching by a factor of say c along the y-axis, we have;
g(x) = c•b^(x)
In this question, we are told it is stretched by a factor of 3 along the y-axis.
Thus, new function h is;
h(x) = 3 × 3^(x)
Using law of indices, we have;
h(x) = 3^(x + 1)
a person earns 17/5 dollars in 1/2 hours. What is the unit rate in dollars pure hour
Answer:
35 2/3 dollars per hour
Step-by-step explanation:
The unit rate in dollars per hour is 6.8 dollars per hour.
To find the unit rate in dollars per hour, we need to divide the amount earned by the time taken.
The person earns 17/5 dollars in 1/2 hours. To calculate the unit rate in dollars per hour, we divide the amount earned (17/5 dollars) by the time taken (1/2 hours):
Unit rate = (Amount earned) / (Time taken) = (17/5 dollars) / (1/2 hours)
To divide fractions, we multiply the numerator of the first fraction by the reciprocal of the second fraction:
Unit rate = (17/5 dollars) x (2/1 hours)
Simplifying the expression:
Unit rate = (17 x 2) / (5 x 1) = 34/5 = 6.8
Therefore, the unit rate in dollars per hour is 6.8 dollars per hour.
To know more about an expression follow
https://brainly.com/question/28699958
#SPJ2
Please help, im confused ;w;
Answer:
[tex]x=7\text{ and } m\angle KLM = 34^\circ[/tex]
Step-by-step explanation:
We are given ethat KM and JN are parallel.
And we want to find the value of x.
Notice that ∠JKM and ∠LKM form a linear pair. Linear pairs total 180°. Therefore:
[tex]m\angle JKM + m\angle LKM = 180[/tex]
We know that ∠JKM measures (14x + 8). Substitute:
[tex](14x+8)+m\angle LKM =180[/tex]
Solve for ∠LKM:
[tex]m\angle LKM = 172-14x[/tex]
Next, since KM and JN are parallel, by the Corresponding Angles Theorem:
[tex]\angle JNM \cong \angle KML[/tex]
Since we know that ∠JNM measure (10x + 2), we can conclude that:
[tex]m\angle KML = 10x+2[/tex]
Next, recall that the three interior angles of a triangle must total 180°. Therefore:
[tex]m\angle KLM + m\angle LKM + m\angle KML = 180[/tex]
Substitute:
[tex](5x-1)+(172-14x)+(10x+2)=180[/tex]
Solve for x. Rewrite:
[tex](5x-14x+10x)+(-1+172+2)=180[/tex]
Combine like terms:
[tex](1x)+(173)=180[/tex]
Therefore:
[tex]x=7[/tex]
To find ∠KLM, substitute in 7 for x and evaluate. So:
[tex]m\angle KLM = 5(7) - 1 =34^\circ[/tex]
You go out to lunch with some friends. Your lunch came to $9.76. If you want to leave a 15% tip, how much will you pay in total?
Answer:
1.47
Step-by-step explanation:
9.76/10=10% = 0.976 round to 0.98
5%=0.97/2 = 0.49
add them = 1.47 tip
A rectangular sheet of paper is 12 1/2 cm long and 10 2/3 cm wide.Find it's perimeter
Please help me with this one
Answer:
240
Step-by-step explanation:
well do *
so 8x6x5 = 240 there's your answer
Answer:
[tex]S.A=1/2(8+8)(9^{2})+8\times 6+8\times 5[/tex]
[tex]=26\times2+48+40[/tex]
[tex]=140 ~cm^{2}[/tex]
-------------------------
HOPE IT HELPS
HAVE A GREAT DAY!!
5 + 3bc =
9a + b =
cd + bc =
Answer:
You can't answer these questons
sorry
Hope This Helps!!!
The graph below shows the solution to which system of inequalities?
10-
TO
10
-10
If z varies jointly as x and y and inversely as w^2?, and
z = 72 when x = 80, y = 30 and
w=5, then find z when x = 20, y = 60 and w=9.
Answer:
Step-by-step explanation:
z = (k*x*y) / w²
Where,
k = constant of proportionality
z = 72 when x = 80, y = 30 and w = 5
z = (k*x*y) / w²
72 = (k * 80 * 30) / 5²
72 = 2400k / 25
Cross product
72 * 25 = 2400k
1800 = 2,400k
k = 2,400/1800
k = 24/18
= 4/3
k = 1 1/3
k = 1.33
find z when x = 20, y = 60 and w=9
z = (k*x*y) / w²
z = (1.33 * 20 * 60) / 9²
z = (1596) / 81
Cross product
81z = 1596
z = 1596/81
z = 19.703703703703
Approximately,
z = 19.7
Six liters of paint will cover 50 square meters. How many square meters will nine liters cover?
Answer:
75 m²Step-by-step explanation:
Six liters of paint will cover 50 square meters.
6L ⇒ 50m²
then,
1L ⇒ 50/6 m²
9L ⇒ 50 × [tex]\frac{9}{6}[/tex] m²
⇒ 75 m²
???????????????????????????
Answer: its 20 I think
Answer:
x = 50
I hope this help the side note also help me a lot as well
