Answer:
m < FGN = 88°
Step-by-step explanation:
The exterior angle theorem states that the measure of each exterior angle of a triangle is equal to the sum of the opposite and non-adjacent interior angles (also known as remote interior angles).
Given the exterior angle, m <FGN = (7x + 18)°, and the two remote interior angles, m < E = 38° and m < F = (6x - 10)°:
The following equality statement can be established according to the exterior angle theorem:
m < E + m < F = m <FGN
38 + 6x - 10 = 7x + 18
Combine like terms:
28 + 6x = 7x + 18
Subtract 6x from both sides:
28 + 6x - 6x = 7x - 6x + 18
28 = x + 18
Subtract 18 from both sides:
28 - 18 = x + 18 - 18
10 = x
Next, substitute the value of x = 10 into the equality statement to determine whether it is the correct value of x, and to find the measures of < FGE and < F.
m < E + m < F = m <FGN
38° + (6x - 10)° = (7x + 18)°
38 + 6(10) - 10 = 7(10) + 18
38 + 60 - 10 = 70 + 18
88 = 88 (True statement).
Therefore, m < FGN = 88°
Pls help me figure this out :D
Answer:
Well in this case the solution would be x = 19/9, I hope this helps! :)
Solve the simultaneous equation
2x-5y=9
3x+4y=2
Answer/Step-by-step explanation:
2x-5y=9
Add 5y to both sides of the equation.
2x=9+5y
Divide each term by 2 and simplify.
Divide each term in 2x=9+5y by 2
[tex]\frac{2x}{2} =\frac{9}{2} +\frac{5y}{2}[/tex]
Cancel the common factor of 2.
Divide x by 1.
[tex]x=\frac{9}{2} +\frac{5y}{2}[/tex]
[tex]y=\frac{-9}{5} +\frac{2x}{5}[/tex]
----------------------------------------------------------------------------------------------------------------
3x+4y=2
Add 4y to both sides of the equation
3x=2+4y
Divide each term by 3 and simplify.
Divide each term in 3x=2+4y by 3.
[tex]\frac{3x}{3} =\frac{2}{3} +\frac{4y}{3}[/tex]
Cancel the common factor of 3.
Divide x by 1.
[tex]x=\frac{2}{3} +\frac{4y}{3}[/tex]
[tex]y=\frac{-1}{2} +\frac{3x}{4}[/tex]
Show that:
[tex]\bigg(\frac{ \sqrt{7} + i \sqrt{3} }{\sqrt{7} - i \sqrt{3} } + {\frac{ \sqrt{7} - i \sqrt{3} }{ \sqrt{7} + i \sqrt{3} } } \bigg) \: is \: real \\ [/tex]
Please answer this question.
Step-by-step explanation:
[tex]\large\underline{\sf{Solution-}}[/tex]
Consider,
[tex]\rm \longmapsto\:\dfrac{ \sqrt{7} + i \sqrt{3} }{ \sqrt{7} - i \sqrt{3}} + \dfrac{ \sqrt{7} - i \sqrt{3} }{ \sqrt{7} + i \sqrt{3} } [/tex]
On taking LCM, we get
[tex]\rm \: = \: \dfrac{ {( \sqrt{7} + i \sqrt{3})}^{2} + {( \sqrt{7} - i \sqrt{3})}^{2} }{( \sqrt{7} + i \sqrt{3})( \sqrt{7} - i \sqrt{3})} [/tex]
We know,
[tex] \purple{\rm \longmapsto\:\boxed{\tt{ {(x + y)}^{2} + {(x - y)}^{2} = 2( {x}^{2} + {y}^{2})}}} \\ [/tex]
and
[tex] \purple{\rm \longmapsto\:\boxed{\tt{ (x + y)(x - y) = {x}^{2} - {y}^{2} \: }}} \\ [/tex]
So, using these Identities, we get
[tex]\rm \: = \: \dfrac{2\bigg[ {( \sqrt{7})}^{2} + {(i \sqrt{3}) }^{2} \bigg]}{ {( \sqrt{7}) }^{2} - {(i \sqrt{3})}^{2} } [/tex]
[tex]\rm \: = \: \dfrac{2(7 + 3 {i}^{2})}{7 - {3i}^{2} } [/tex]
We know,
[tex] \purple{\rm \longmapsto\:\boxed{\tt{ {i}^{2} = - 1}}} \\ [/tex]
So, using this, we get
[tex]\rm \: = \: \dfrac{2(7 - 3)}{7 + 3} [/tex]
[tex]\rm \: = \: \dfrac{2 \times 4}{10} [/tex]
[tex]\rm \: = \: \dfrac{4}{5} [/tex]
Hence,
[tex] \red{\rm\implies \:\boxed{\sf{ \dfrac{ \sqrt{7} + i \sqrt{3} }{ \sqrt{7} - i \sqrt{3}} + \dfrac{ \sqrt{7} - i \sqrt{3} }{ \sqrt{7} + i \sqrt{3} } \: is \: purely \: real}}}[/tex]
For every 10 tickets to a horror movie that a popular movie theater sells, they sell 9 tickets to a comedy movie. If they sold 5 more horror movie tickets in one night, how many tickets to both movies did they sell altogether?
May I please receive help?
Answer:
1 and 2 are parallel. 1 and 3 are perpendicular. 2 and 3 are perpendicular.
Answer: I'm gonna try my best. 1). neither 2). Parallel 3).perpendicular
Step-by-step explanation:
A family of 2 adults and 3 children goes to a play . admission costs $8per adults and $5 per child. what expression would show the total admission cost for the family
Answer:
8 + 8 + 16 5 * 3 is 15 16 + 15 is 31 that is the answer to the question
You have no more than $60 to spend. You want a drink that costs $1.50 including tax, and you
want to buy a pair of pants, which will have 4% sales tax. What is the inequality that represents
the pre-tax price of a pair of pants that you can afford if you buy the drink? *
X + 0.04x + 1.50 > 60
X + 0.04x + 1.50 2 60
X + 0.04x + 1.50 60
X + 0.04x + 1.50 60
Answer:
X + 0.04x + 1.50 > 60
Step-by-step explanation:
find the next two terms of the sequence 1.1 , 2.2 , 3.3, 4.4, ….. A) 4.5, 5.5 B ) 5.6 C) 5.6, 6.7 D) 5.5, 6.6
Answer:
D)
Step-by-step explanation:
Please Help, This is confusing. What is the equation of the line that passes through the point (2,-6) and has a slope of -1?
Answer:
ok ok it is y+6=-1(x-2)
Step-by-step explanation:
brainliest?
Answer:
Firstly, you can use the slope and the first point to find a second point:
2 + 1 = x2 and 6 + 5 = y2 because the slope is 5/1.
Next you can write the equation in point-slope form (remember point-slope form is y - y1 = m(x - x1):
y - 11 = 5(x - 3)
Another equation would be B because B is the correct equation if you choose 2 as x2 and 6 as y2.
Hope this helps!
Jasper and Muthu cycled from Town P to Town Q. Jasper cycled at a speed of 36 km/h
and reached Town Q in 5 h. Muthu's cycling speed was 40 km/h.
(a) What was the distance between Town P and Town Q?
(b) How many minutes did Muthu take to cycle from Town P to Town Q?
Answer:
a,khoảng cách từ thị trấn P đến thị trấn Q là
Step-by-step explanat io n:
36*5=180(km)
b,Muthu đi xe đạp từ thị trấn P đến thị trấn Q hết số phút là:
180/40=4,5(h)=270(phút)
Helpp! who ever gets it right gets brainliest!
1. K+9, When k = 5
Answer:
2. 4x - 3, when x = 2
Answer:
3. t/5 + t, when t = 15
Answer:
4. 5x2 + 3x, when x = 2
Answer:
5. 6y - 5, when y+7
Answer:
6. 4x2 + 3x, when x = 6
Answer:
7. 56/x + 3y, when x = 4 and y = 3
Answer:
8. 4d2 - 3d, when 4 = -2
Answer:
9. + 3p - 5t + 3, when p= 2 and t = 1
Answer:
10. 3(w-4) 2, when w + -5
Answer:
Answer:
1. 14
2. 5
3. 18
4. 16
5. 37
6. 26
7. 23
8. -10
9. 4
10. -54
Some questions are wrong so i answered what i understood. And giving me brainest will be helpful.
the difference between 4x and 2x is 70. Find the 2x
Answer:
2x = 70
Step-by-step explanation:
4x - 2x = 70
2x = 70
x = 70/2
x = 35
The U.S. population in 1910 was 92 million people. In 1990, the population was 280 million. This could either be a linear or exponential model. You will create both and then look at the true population increase and decide which model is closer the the true growth.
The actual U.S. population data (in millions) was:
Which model provides a better forecast for the U.S. population for the year 2030, linear or exponential or neither?
Question 5 options:
Linear model
Exponential model
Neither
Answer:
The linear model means that there is a uniform increase and in this case of US population from 92 million people in 1910 to 250 million people in 1990 .
This means an increase of 250 − 92 = 158 million in 1990 -1910 = 80 years or 158 80 = 1.975 million per year and in x years it will become 92 + 1.975 x million people. This can be graphed using the linear function 1.975 ( x − 1910 ) + 92 ,
graph{1.975(x-1910)+92 [1890, 2000, 85, 260]}
The exponential model means that there is a uniform proportional increase i.e. say p % every year and in this case of US population from 92 million people in 1910 to 250 million people in 1990 .
This means an increase of 250 − 92 = 158 million in 1990 − 1910 = 80 years or
p % given by 92 ( 1 + p ) 80 = 250 which gives us ( 1 +p ) 80 = 250 92 which simplifies to p = ( 250 92 ) 0.0125 − 1 = 0.0125743 or 1.25743 % .
This can be graphed as an exponential function 92 × 1.0125743 ( x − 1910 ) , which gives population in a year y and this appears as graph{92(1.0125743^(x-1910)) [1900, 2000, 85, 260]}
Step-by-step explanation:
Hope this helps
Hi guys.Hope you are all well…I need your help on this question and I will give you 34 points for it.It doesn’t matter who gets the answer first .It matters on that if you try your best.I will still give you points if you try and think what’s the answer for this question.Thanks…
Answer:
the size of the angel is 51
Step-by-step explanation:
The size of the angle is 52 p
plzzzzzzzzzzzzzzzzzzz helppppp
Answer:
15
Step-by-step explanation:
I'm not sure, but find out the coordinates of the two points, and then find the slope between them.
One fifth of the difference of a number and 1?
If you are asking for that to be in expression form, that would be:
1/5(x-1)
Let x be the number.
Answer: The expression that models this situation is given by:
x-1/5
---------------------------
The number is unknown, so it is called x.
The difference between 3 and 2 is 3 - 2 = 1, between 10 and 5 is 10 - 5 = 5, and so on. Thus, the difference between a number and 1 is x - 1.
One fifth of a number is the number divided by 5. Thus, in this context, the expression that represents one fifth of the difference of a number and 1 is given by:
x-1/5
There’s another problem that has the same question at this link:
https://brainly.com/question/20742606
Consider U = { 5,10, 15, 20, 25, 30, 35, 40} , A = { 20, 30, 40 } . Find A’
Answer:
A {5, 10, 15, 20}
Step-by-step explanation:
Solve for the value of x that makes likes r and s parallel.
F(-5)=7+|-5|=7+5=12
HOW DO I SOLVE THIS?? HELPASAP
can someone please help me
Answer:
x = 1 and it's undefined yaaaaaaaaaaa
can someone help me?
Step-by-step explanation:
a)
a whole circle represents always 360 degrees.
we see the angle J is 72 degrees. the angle K is 90 degrees.
that leaves us for M and L together :
360 - 72 - 90 = 198 degrees.
we now know that twice as many people voted for L as for M. that means the angle L is twice as big as the angle M
on other words : L = 2M
and when we now say
198 = L + M
this means
198 = 2M + M = 3M
M = 66 degrees
and L is then 2M = 2×66 = 132 degrees
b)
again, the whole circle is 360 degrees.
J covers 72 of these 360 degrees.
that is 72/360 of all voting people.
72/360 = 1/5
the total of all voting people was 15840.
so, 1/5 of 15840 is
15840/5 = 3168
that means 3168 people voted for J.
Calculate the surface area of the following objects.
Answer: 15150 [tex]cm^{2}[/tex]
Step-by-step explanation:
2(83 × 45) + 2(30 × 45) + 2(30 × 83)
2(3735) + 2(1350) + 2(2490)
7470 + 2700 + 4980
= 15150
please give me a brainliest answer
From the graph, write the linear equation in slope-intercept form
Answer:
y = -3x + 1
Step-by-step explanation:
slope intercept form -> y=mx+b
you can find your slope, m, by doing rise over run ( up 3, left one -> -3/1 )
you can find your y-intercept, b, by just looking at the y axis ( 0,1 -> 1 )
from there you just plug in the values
y = m ( slope ) x + b ( y-intercept )
y = -3x + 1
*HELP
What is the aspect ratio of a sheet of paper with the following dimensions:
20-inches x 8-inches
Round your answer to the nearest tenth.
Parallel to the graph of y = 7x - 6 with y-intercept (0,3)
Answer:
The graph of the lines is given in the picture below:
Which of these is NOT discrete data:
A. toppings on a pizza
B. boys in a family
C. temperature outside
D. planks in a deck
Answer:
C. temperature outside
Step-by-step explanation:
Discrete data is information that can only take certain values. ... This type of data is often represented using tally charts, bar charts or pie charts. Continuous data is data that can take any value. Height, weight, *TEMPERATURE* and length are all examples of CONTINUOUS data. = not discrete data
I believe, hope it is correct
What is an algebraic expression for this word phrase?
5 more than the product of 7 and n
5 + 7n
5(7+n)
7(5+n)
5 + 7 + n
A pack of $2.99 crayons is on sale 50% off what is the discount?
Answer:
$1.49
Step-by-step explanation:
Take your value: $.99 and since it is 50% off, divide it by 2.
You get $1.49.
what is the product of 1/2 × 2/3 × 3/4 × 4/5
Answer:
5/6
Step-by-step explanation:
brainly pls
Answer:
5/6
Step-by-step explanation:
make me brainliest please
Jaoquin buys 3 dozen lightbulbs. After changing the lightbulbs in his house, he has 15 lightbulbs left. How many lightbulbs did he use?
Answer:
21
Step-by-step explanation:
1 dozen=12
3 dozen= 36
15-36=21