Answer:
Step-by-step explanation:
A linear pair are two given angles whose sum is equal to [tex]180^{o}[/tex].
Let the exterior angle be represented by [tex]x^{o}[/tex], and the three interior angles of the triangle be represented by [tex]a^{o}[/tex], [tex]b^{o}[/tex] and [tex]c^{o}[/tex].
Assume that the vertex angle [tex]c^{o}[/tex] is the linear pair to the exterior angle [tex]x^{o}[/tex].
i.e [tex]x^{o}[/tex] + [tex]c^{o}[/tex] = [tex]180^{o}[/tex] (sum of angles on a straight line)
Thus,
i. [tex]a^{o}[/tex] + [tex]b^{o}[/tex] = [tex]x^{o}[/tex] (sum of two opposite interior angles is equal to an exterior angle)
⇒ [tex]a^{o}[/tex] = [tex]x^{o}[/tex] - [tex]b^{o}[/tex]
Also,
[tex]b^{o}[/tex] = [tex]x^{o}[/tex] - [tex]a^{o}[/tex]
But,
[tex]a^{o}[/tex] + [tex]b^{o}[/tex] + [tex]c^{o}[/tex] = [tex]180^{o}[/tex] (sum of angles in a triangle)
⇒ [tex]c^{o}[/tex] = [tex]180^{o}[/tex] - ([tex]a^{o}[/tex] + [tex]b^{o}[/tex])
and
[tex]a^{o}[/tex] + [tex]b^{o}[/tex] = [tex]180^{o}[/tex] - [tex]c^{o}[/tex]
ii. [tex]a^{o}[/tex] + [tex]b^{o}[/tex] + [tex]c^{o}[/tex] = [tex]180^{o}[/tex] (sum of angles in a triangle)
[tex]a^{o}[/tex] = [tex]180^{o}[/tex] - ([tex]b^{o}[/tex] + [tex]c^{o}[/tex])
Also,
[tex]a^{o}[/tex] + [tex]b^{o}[/tex] = [tex]x^{o}[/tex]
⇒ [tex]b^{o}[/tex] = [tex]x^{o}[/tex] - [tex]a^{o}[/tex]
[tex]c^{o}[/tex] = [tex]180^{o}[/tex] - [tex]x^{o}[/tex]
if two equations are the same at two different points, what can be said about the two equations?
Answer:
They are parallel
Step-by-step explanation:
They will have the same slope but never intersect
Brantley tosses a ball out of a window that is 75 feet in the air. Its initial velocity is 12 feet per second. The path of the ball is represented by h=-16t^2+12t+75. How long does it take for the ball to hit the ground to the nearest hundredth?
Answer:
[tex]t = 2.57[/tex]
Step-by-step explanation:
Given
[tex]h=-16t^2+12t+75[/tex]
Required
Determine the time to hit the ground
The ground is at point 0.
So, to solve this; we simply set [tex]h =0[/tex], then calculate the value of t
[tex]0=-16t^2+12t+75[/tex]
Multiply through by -1
[tex]0=16t^2-12t-75[/tex]
Reorder
[tex]16t^2-12t-75 = 0[/tex]
Solve using quadratic formula:
[tex]t = \frac{-b\±\sqrt{b^2 - 4ac}}{2a}[/tex]
Where
[tex]a = 16; b = -12; c = -75[/tex]
[tex]t = \frac{-(-12)\±\sqrt{(-12)^2 - 4*16*(-75)}}{2*16}[/tex]
[tex]t = \frac{12\±\sqrt{144 +4800}}{32}[/tex]
[tex]t = \frac{12\±\sqrt{4944}}{32}[/tex]
[tex]t = \frac{12\±70.31}{32}[/tex]
Split:
[tex]t = \frac{12+70.31}{32}[/tex] or [tex]t = \frac{12-70.31}{32}[/tex]
[tex]t = \frac{82.31}{32}[/tex] or [tex]t = \frac{-58.31}{32}[/tex]
But time (t) can't be negative;
So, we make use of only
[tex]t = \frac{82.31}{32}[/tex]
[tex]t = 2.57[/tex]
Hence, the time to hit the ground is 2.57 seconds
Find the slope and y-intercept for the table.
slope:
y-intercept:
Answer:y is 60 slope is -10
Step-by-step explanation:
the tens digit is two less than the ones digit and sum of the digits is 8.
Answer:
35
Step-by-step explanation:
I need help big time
3 out of 4 students in one school named Apple
Pie as their favorite Thanksgiving food. If the
school has 100 students, how many chose Apple
Pie?
Answer
the answer is 75
Step-by-step explanation:
100 divided by 3 = 75 so there is 75 students
75 is the answer I have the same question as you
Tell whether the equation is linear. If so, enter the equation in standard form and give the values of A,B, and C.
1. y = 4x +9
2. 5x =6y - 2
Answer:
1. A=1, B=4, C=9
2.A=5 B=6, C=-2
1. You get paid $8.00 an hour to babysit. They will increase your pay 25% because
you are working during the lowa Game. (D)
A man invested 1000 rupees,split onto two schemes,at annual rates of interest 8% and 9%.After one year he got 875 rupees as interests from both. How much did he invest in each?
Given :
Total amount, T = 10000 . ( It should not 1000 )
Annual rates of interest in both scheme is 8% and 9% .
After one year he got 875 rupees as interests from both.
To Find :
How much did he invest in each.
Solution :
Let, amount invested in 8% annual interest scheme is x.
So, amount in other scheme is 10000-x .
Now, sum of interest is equal to 875.
[tex]\dfrac{x\times r_1 \times 1}{100}+\dfrac{(10000-x)\times r_2\times 1}{100}=875\\\\8x + 9(10000-x)=87500\\\\x = 90000-87500\\\\x = 2500[/tex]
Therefore, amount invested in 8% and 9% annual interest scheme is 2500 and 7500 rupees respectively.
Hence, this is the required solution.
Esteban stands on a dock 1.25 yd above the water. A fish swims below Esteban at -4.61 yd from the surface of the water. How many yards apart are Esteban and the fish?
Answer: 5.86yd
Step-by-step explanation:
From the question, we are informed that Esteban stands on a dock 1.25 yd above the water and that a fish swims below Esteban at -4.61 yd from the surface of the water.
The distance between Esteban and the fish can be calculated by subtracting -4.61 yd from 1.25 yd. This will be:
= 1.25 yd - (-4.61 yd)
= 1.25 yd + 4.61 yd
= 5.86 yd
Which pair of complex numbers has a real-number product?
(1 + 31 (6)
(1 + 3)(2-31)
(1 + 3)(1 – 31)
0 (1 + 3/)(31)
Answer: C. (1 + 3i)(1 - 3i)
Step-by-step explanation:
Took the test on edgnuity
Answer:
The person ontop is correct! It is C.
$1500 at 4% for 5 years find interst
Answer:
7,500
Step-by-step explanation:
Answer:
$5100.00
Step-by-step explanation:
Investors buy a studio apartment for $180,000. Of this amount, they have a down payment of $36,000. Their down payment is what percent of the purchase price? What percent of the purchase price would a $72,000 down payment be?
Their down payment is *blank*% of the purchase price.
Answer:
36,000 would be 20 percent. 72,000 would be 40 percent.
Step-by-step explanation:
You just divide 36,000 by 180,000
what about this one? can this be answered please? : )
Answer:
c. y=7x-2
Step-by-step explanation:
hope this can help
If you have 2\10 of an apple, how many fifths do you have
Answer:
4/5
Step-by-step explanation:
1 - 2/10 = 8/10 = 4/5
Answer:
[tex]\frac{1}{5}[/tex]
Step-by-step explanation:
You have [tex]\frac{2}{10}[/tex] ( divide numerator and denominator by 2 ), that is
[tex]\frac{2}{10}[/tex] = [tex]\frac{1}{5}[/tex]
HELP At the end of a snow storm, Eli saw there was a lot of snow on his front lawn. The
temperature increased and the snow began to melt at a steady rate. The depth of
snow on Eli's lawn, in inches, can be modeled by the equation S = 16 - t, where t
is the time, in hours, after the snow stopped falling. What is the y-intercept of the
equation and what is its interpretation in the context of the problem?
The y-intercept of the function is
which represents
Answer:
The y-intercept is 16, which represents the original depth of snow on the lawn
Step-by-step explanation:
t is the time in hours where the snow melted, so 16 was the original amount of snow on the ground before it melted over time.
The y-intercept is 16 inches. Then the y-intercept represents the height of the snow initially.
What is a linear equation?A connection between a number of variables results in a linear model when a graph is displayed. The variable will have a degree of one.
The linear equation is given as,
y = mx + c
Where m is the slope of the line and c is the y-intercept of the line.
Eli noticed a lot of snow on his front lawn towards the conclusion of a snowstorm. As the weather rose, the snow began to melt at a steady pace. The depth of snow on Eli's lawn in inches may be calculated using the equation S = 16 - t, where t is the time after the snow ceased falling in hours.
Compare the equation with the standard equation, then we have
c = 16
The y-intercept represents the height of the snow initially.
More about the linear equation link is given below.
https://brainly.com/question/11897796
#SPJ2
can someone please help me with this please and thank you
(-8/9) divided by (-2/3)x(-4 1/2)
Answer:
-0.29629629629 or -0.3
Step-by-step explanation:
first do (-2/3)*(-4 1/2) which is 3
then divide (-8/9) by 3 and you get -0.29629629629 which can be rounded to -0.3
The Answer will be -8 using fraction operation.
What is a fraction?If the numerator is bigger, it is referred to as an improper fraction and can also be expressed as a mixed number, which is a whole-number quotient with a proper-fraction remainder.
Any fraction can be expressed in decimal form by dividing it by its denominator. One or more digits may continue to repeat indefinitely or the result may come to a stop at some point.
First solve the 2nd part which is
[tex]\frac{-2}{3}*-4\frac{1}{2} \\=3[/tex]
Now -8/3 * 3 = -8
Hence the answer for the given question will be -8.
Learn more about Fraction, by the following link.
https://brainly.com/question/78672
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How would you graph the solution to 3x ≤ -15?
Answer:
I would put a shade over the region of x <= -5.
Step-by-step explanation:
The look of the graph would be a shaded rectangle over the line x = -5.
Hope this helped!
Answer:
Draw a closed circle on -5 and shade to the left
Step-by-step explanation:
At a real estate agency, an agent sold a house for $397,000. The commission rate is 4.5% for the real estate agency and the commission rate for the agent is 20% of the amount the real estate agency gets. How much did the agency make on the house? How much did the agent earn in commission?
Answer:
1. $97,265
2. $17,865
Step-by-step explanation:
Step one:
given data
cost of the house= $397,000.
we are told that the commission is 4.5% real estate agency
and also the agent commission is 20%
Step two:
1. How much did the agency make on the house?
this amount is 20% plus 4.5% together.
=20/100*397,000 +4.5/100*397,000
=0.2*397,000. +0.045*397,000.
=79400+17865
=97,265
The agent made a total of $97,265 on the house
2. How much did the agent earn in commission?
in commission, the rate is 4.5% which amounts to $17,865
Penelope is raising money for a school trip by selling bags of chips and fruit snacks. The price of each bag of chips is $1.75 and the price of each fruit snack is $1.50. Yesterday Penelope made $42.50 and sold 15 more bags of chips than fruit snacks. Determine the number of bags of chips sold and the number of fruit snacks sold.
Answer:
bag of chips - 20 ; number of fruit snacks - 5 .
Step-by-step explanation:
ratio// please help!!
Answer:
The loose sweets
Step-by-step explanation:
100 divided by 0.89 = 112
120 divided by 1.49 = 80
Answer:
Step-by-step explanation:
1.49 ÷ 120 = 0.0124 GBP per gram
0.89 ÷ 100 = 0.0089 GBP per gram < 0.01 (The price of loose sweets is better value)
please help its urgent
9514 1404 393
Answer:
they are in the same place on the number line
Step-by-step explanation:
-(-a/b) = a/b, so will be plotted on the number line in exactly the same place as a/b.
A one-minute advertisement on a local television station during prime time (8-10 p.m. on weeknights) costs the advertiser $12,800. To the nearest cent, how much does the advertisement cost per second? Show your work using dimensional analysis and Giant Ones
Sandra eats about 2000 calories per day with LaTeX: \frac{1}{4}1 4 of her calories from fat and LaTeX: \frac{1}{5}1 5 from carbohydrates. How many total calories does Sandra get from both fat and carbohydratesSandra eats about 2000 calories per day with LaTeX: \frac{1}{4}1 4 of her calories from fat and LaTeX: \frac{1}{5}1 5 from carbohydrates. How many total calories does Sandra get from both fat and carbohydrates
Answer:
Calories from both fat and carbohydrates = 900 calories/day
Step-by-step explanation:
Number of calories eaten by Sandra per day = 2000 calories/day
Calories from fat = [tex]\frac{1}{4}[/tex] of the total number of calories per day
OR
Calories from fat = [tex]\frac{1}{4}\times 2000 = 500\ calories/day[/tex]
Calories from carbohydrates = [tex]\frac{1}{5}[/tex] of the total number of calories per day
OR
Calories from carbohydrates = [tex]\frac{1}{5}\times 2000 = 400\ calories/day[/tex]
To find the total number of calories from both fat and carbohydrates, we need to add the calories from fat and calories from carbohydrates as calculated above.
Calories from both fat and carbohydrates = Calories from fat + Calories from carbohydrates = 500 + 400 = 900 calories/day
Which graph shows a function with a zero of –5?
Answer:
Look for the y-intercept where the graph crosses the y-axis. Look for the x-intercept where the graph crosses the x-axis. Look for the zeros of the linear function where the y-value is zero.
Step-by-step explanation:
Is a quadrilateral a square?
Answer:
No but a square is a quadrilateral
Step-by-step explanation:
hope this helps :)
Answer:
If I were to be honest no Edit: yes it is
Step-by-step explanation:
No because a square has straight parrallel corners. But a quadrilateral has slanted parallel corners.
Hope that helped. But maybe wait for sumone else to answer too. : )
Edit: nvm my bad I was wrong
Solve the equation 186+10x=25.5x to find how many diving lessons
__ lesson(s)
Answer: x=12
Steps shown in image below:
Let the number of games, `x`, and the number of rides, `y`
For `x+4y=28`, what is the slope of the graph?
-1/4 or -0.24 because you subtract x to get it away from the y ... y = mx + b (this is the forumla you try to get it at) .... then you divide by four and that will leave you with -1/4 ... complete formula answer y = -1/4x + 7
Entrance to a skatepark costs $6 per vehicle, plus $2 per person in the vehicle.
Is the relationship between the number of people and the total entrance cost a proportional relationship? EXPLAIN HOW YOU KNOW.
Hint: Create a table to organize the information.
Answer:
Yes, it is a proportional relation ship because 6 and 2 are equivalent to each other.
Step-by-step explanation