For the given equation, we can complete the statements below:
Ariel is correct. For any value of y, the statement -12 = 3 is always true.
The equation has no solutions.
What is an equation?
A mathematical equation is a formula that uses the equals sign to represent the equality of two expressions.
The first part of the question is as given below.
Ariel simplifies the equation 3y - 12 = 3(y+1) and says it has no solution.
We are asked to complete the statements based on the above information.
Simplifying the equation,
3y - 12 = 3(y+1)
3y - 12 = 3y + 3
-12 = 3
Since the y term in the above equation is not present, the given equation has indeed no solution.
Also if we take any value of y, the final answer will always be -12 = 3.
Therefore we can complete the statements as below:
Ariel is correct. For any value of y, the statement -12 = 3 is always true.
The equation has no solutions.
To learn more about equations, follow the link.
https://brainly.com/question/22688504
#SPJ1
Answer: Ariel is correct. For any value of y the statement -12=3 is always false and it’s no solution
Step-by-step explanation:
mensa is an organization whose members have the top 2% of all iqs. find the minimum iq needed to qualify for the mensa organization. write the probability statement.
The probability of having an IQ score below the minimum Mensa IQ is 0.98, or the probability of having an IQ score above or equal to the minimum Mensa IQ is 0.02.
The features of the normal distribution can be used to determine the minimal IQ required to join Mensa if we assume that IQ scores follow a normal distribution. We can determine the IQ score that represents the 98th percentile of the IQ distribution because Mensa members make up the top 2% of all IQs.
We can determine the z-score for the 98th percentile using a typical normal distribution table, which is roughly 2.33. This indicates that the IQ score that is 2.33 standard deviations above the mean IQ is the minimal IQ required to join Mensa.
The formula: can be used if we are aware of the mean and standard deviation of the IQ distribution.
IQ equals (z-score) x standard deviation plus mean.
to determine the Mensa membership cutoff IQ. We are unable to determine the actual IQ score since the question does not include the mean or standard deviation of the IQ distribution.
The following is the probability statement for this issue:
P(IQ minimum Mensa IQ) = 0.02, or P(IQ minimum Mensa IQ) = 0.98, in other words. This indicates that the likelihood of having an IQ score below the minimum Mensa IQ is 0.98 and the likelihood of having an IQ score equal to or higher than the minimum Mensa IQ is 0.02.
To know more about Probability Statement visit:
https://brainly.com/question/28462288
#SPJ1
Determine the solution for the following equation: x = 3 x = 5 x = 13 x = 65
The solution for the equation is x = 65.
What is equation?Equation is a physical and mathematical statement that describing physical sonoma nadigai the relationship between different physical quantity typically consist of pramod variable richard simple representing physical quantity and then it personal variable maybe point it such as that your energy.
This can be determined by solving the equation for x one step at a time.
First, 3 = 5 can be solved by subtracting 3 from both sides,
thus yielding
x = 2.
Then,
5 = 13 can be solved by subtracting 5 from both sides,
thus yielding
x = 8.
Finally,
13 = 65 can be solved by subtracting 13 from both sides,
thus yielding
x = 65. This is the final answer to the equation.
To know more about Equation click-
https://brainly.com/question/29657992
#SPJ4
Answer:
its x=3
Step-by-step explanation:
first x 2/3 to both sides than solve for x
solve for x
-1 + 6x < 5
[tex]-1+6x < 5[/tex]
Simplify:
[tex]6x-1 < 5[/tex]
Add 1 to both sides:
[tex]6x-1+1 < 5+1[/tex]
[tex]6x < 6[/tex]
Divide both sides by 6:
[tex]\dfrac{6x}{6} < \dfrac{6}{6}[/tex]
[tex]\boxed{x < 1}[/tex]
Steve is driving at 35 mi/h when he makes an emergency stop. His brakes lock and his tires leave four skid marks of equal length. The drag factor for the road surface was 0.97 and his brakes were operating at 90% efficiency. How long might the skid marks be to the nearest foot?
The skid marks would be approximately 1.9 ft in length to the nearest foot.
The drag factor of the road is given as 0.97 and the braking efficiency as 90%. To calculate the skid marks, we need to use the coefficient of friction (μ) between the tires and the road surface. The formula for calculating this is: μ = (2 x Drag Factor x Efficiency) / 100.
Therefore, μ = (2 x 0.97 x 0.9) / 100 = 0.0174
Once we have the coefficient of friction, we can use the following equation to calculate the skid marks: Skid Length = Initial Speed x Reaction Time x 0.5 x μ.
Since the speed is given as 35 mi/h and the reaction time is assumed to be 0.75 seconds, the skid marks will be: Skid Length = 35 mi/h x 0.75 s x 0.5 x 0.0174 = 1.9 ft
Therefore, the skid marks would be approximately 1.9 ft in length to the nearest foot.
Learn more about speed here:
https://brainly.com/question/2004627
#SPJ4
Ranger Shoe Company manufactures two types of shoes, athletic shoes and casual shoes. The cost of manufacturing 20 pairs of athletic shoes and 10 pairs of casual shoes is $750. If 25 pairs of athletic shoes and 20 pairs of casual shoes were manufactured, the cost would be $1200. How much does it cost to manufacture each type of shoe?
The cost of the athletic shoe is $20 meanwhile the cost of the casual shoe is $35.
System of EquationsA system of equations is the given term of math for two or more equations with the same variables. The solution of these equations represents the point of the intersection.
You can solve a system of equations by substitution or adding methods. In the addition method, you eliminate a variable, on the other hand, in the substitution method you replace a variable for the other.
Firstly, you should extract the main information of the question.
Athletic shoes= ACasual shoes = Cfor 20 pairs of athletic shoes and 10 pairs of casual shoes, the total cost is $750for 25 pairs of athletic shoes and 20 pairs of casual shoes, the total is $1200.Next, you should convert the given text information into equations. See below.
20A+10C=750 (1)
25A+20C=1200 (2)
From the substitution method, you can solve this question by following the steps below:
1) Multiply equation 1 by the number -2. Then, you have:
-40A-20C= -1500 (1)
25A+20C=1200 (2)
2) Sum the previous equations presented in step 1.
-15A=-300
15A=300
A=300/15
A=20
3) Find the variable C from equation 2. In step 2, you find A=20, thus.
25A+20C=1200 (2)
25*20+20C=1200
500+20C=1200
20C=1200-500
20C=700
C=700/20
C=35
Read more about solving systems equations here:
brainly.com/question/12691830
#SPJ1
What is the length of TE?
Answer: 20 units
Step-by-step explanation: Set the two half diagonal values equal to each other. When you solve for x, the value is 3. Substitute it back in and the half diagonals equal 10. Multiply it by two and the dial length is 20. You can use this length for TE because it is a diagonal. Hope this helps!
Write 3 irrational numbers between 1.5 and 1.56.
1.511; 1.512 ;1.5113
Step-by-step explanation:
we know that there are infinite numbers.
and every decimal number is a rational number
now, extend the number upto 3 decimal or 2 decimal .
then it will become 1.500
there are numbers upto 1.599
like this we can extend upto infinite values
you can write infinite numbers, but question is asked for only 3
Show each inequality on a number line and then write all the one-digit integers that satisfy it for k≥0
The one-digit integers that satisfy the inequality k≥0 are 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9.
What is Inequality?A relationship between two expressions or values that are not equal to each other is called 'inequality.
A number line is a picture of a graduated straight line that serves as visual representation of the real numbers.
The given inequality is k≥0, k greater than or equal to zero.
The negative values on the number line are -1, -2, -3...-9 while the value greater than or equal to zero are 1, 2, 3, 4,...9
Hence, the one-digit integers that satisfy the inequality k≥0 are 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9.
To learn more on Inequalities click:
https://brainly.com/question/28823603
#SPJ1
THIS IS THE OSHA 10-HOUR COURSE AND I NEED HELP WITH IT.
1. Remember not to use tools that are ________ in any way.
2. What should you do with corded tools when they are not being used?
3. This is the sudden release of electrical energy through the air when a high-voltage gap exists and there is a breakdown between conductors:
4. What electrical hazard is present in this image?
5. The longer you’re exposed to high noise levels, the more likely it is that ________ damage will occur.
6. In a situation where you expect to encounter airborne hazardous substances, but you don’t need skin protection, what level of full-body protection will you need?
7. Which of the following are struck-by falling hazards?
8. If you see an increase in traffic, step in and direct traffic to ensure safety. Is this a safe or unsafe practice?
9. In general, employers must provide fall protection to construction workers working on surfaces with unprotected sides and edges that are how many feet above the lower level?
10. When constructing a scaffold, there are specific criteria for the ________ the scaffold is built on.
11. Which of the following is the most dangerous factor among crane accidents?
12. An excavation is at risk for cave-in and water accumulation because of the excess soil that has accumulated. What type of excavation protection will address this situation?
13. Protect workers from cave-ins and other excavation-related hazards. Whose responsibility is this?
Answer:
1 harmful
Step-by-step explanation:
2 they will be not use if you not use
Compare using >, <, or =
a. 5 thirds + 2 ninths _____ 1 9/8
A fraction is a fragment of a whole number, used to define parts of a whole. The whole can be a whole object, or many different objects. The number at the top of the line is called the numerator, whereas the bottom is called the denominator.
The equation for this problem is this:
[tex]\frac{5}{3} + \frac{2}{9}[/tex] (> < =) [tex]1\frac{9}{8}[/tex]First, we need to find a common denominator between [tex]\frac{5}{3}[/tex] and [tex]\frac{2}{9}[/tex].
What is a common denominator?A common denominator consists of two or more fractions that have the same denominator. This makes it easier to perform numeric equations, and to solve them.
To find the common denominator, we can multiply the denominators, 3 and 9.
3 × 9 = 27Now we know that the two new fractions are going to have a denominator of 27.
[tex]\frac{?}{27} \frac{?}{27}[/tex]Now, we can use these equations to solve for the numerator.
9 × 5 = 453 × 2 = 6Now, the fractions look like this:
[tex]\frac{45}{27} \frac{6}{27}[/tex]To add them together, we can use this equation:
[tex]\frac{45}{27}+ \frac{6}{27} = \frac{51}{27}[/tex]Now, we need to convert [tex]1 \frac{9}{8}[/tex] into an improper fraction.
What is an improper fraction?An improper fraction is a fraction that has a numerator that is greater than the denominator. For example, [tex]\frac{3}{2}[/tex] is a improper fraction.
[tex]1\frac{9}{8}[/tex] = [tex]\frac{17}{8}[/tex]To convert [tex]\frac{51}{27}[/tex] and [tex]\frac{17}{8}[/tex] into common denominators, we need to multiply the denominators, like we did above.
8 × 27 = 216The new fractions will look like this:
[tex]\frac{?}{216} \frac{?}{216}[/tex]To solve for the numerators, we can use these equations:
17 × 27 = 4598 × 51 = 408The fractions now look like this:
[tex]\frac{408}{216} \frac{459}{216}[/tex]Now, convert them to mixed numbers.
[tex]\frac{408}{216} = \frac{17}{9}[/tex][tex]\frac{459}{216} = \frac{17}{8}[/tex]Therefore, 5 thirds + 2 ninths < 1 9/8.
The number of hospitals in a certain country has been declining for many years. In 2014, there were 5,727 hospitals, but, in 2017, there were only 5,571. Assuming this trend is linear, write an equation for the number of hospitals H in the this country t years since 2000
Step 1: Calculate the initial number of hospitals. In 2000, there were 5,727 hospitals, so the initial number of hospitals (H0) is 5,727.
Step 2: Calculate the rate of change. From 2014 to 2017, the number of hospitals decreased by 156. Therefore, the rate of change (r) is -156.
Step 3: Calculate the equation. The equation for the number of hospitals H in this country t years since 2000 is H = H0 + rt. Substituting in the values from Steps 1 and 2, this gives us H = 5,727 – 156t.
Therefore, the equation for the number of hospitals H in this country t years since 2000 is H = 5,727 – 156t.
First order equations include linear equations. In the coordinate system, the linear equations are defined for lines. A linear equation in one variable is one in which there is a homogeneous variable of degree 1 (i.e., only one variable). More than one variable may be present in a linear equation.
For more questions like number of hospitals visit the link below:
https://brainly.com/question/21649997
#SPJ4
An urn contains 8 green and 6 pink balls. Six balls are randomly drawn from the urn in succession, with replacement. That is, after each draw, the selected ball is returned to the urn. What is the probability that all 6 balls drawn from the urn are green? Round your answer to three decimal places.
The probability of drawing a green ball in one draw is 8/14 = 4/7. Since the balls are replaced after each draw, each draw is independent of the others. Therefore, the probability of getting 6 green balls in a row is (4/7)^6 ≈ 0.066.
Rounding to three decimal places, the probability is approximately 0.066.
A small startup company wishes to know how many hours, per week, that its employees spend commuting to and from work. The number of hours for each employee are shown below. Construct a frequency table for grouped data using four classes.
1, 2, 19, 1, 13, 18, 20, 3, 17, 10, 3, 12, 15, 2, 15, 8, 5, 20, 18, 19
The Frequency table for grouped data using four classes are given in the table below.
What is Frequency table?
The frequency table is to represent the data in the table form in which larger data are arranged according to their characteristics. In which frequency is the number which represents how many times the particular data occurs in it.
Here, there are 20 hours for each employee is given, we have to group into four classes.
Let us split the hours as,
0 - 5 ----this includes- 1,1,2,2,3,3,5(7 hours)
5 - 10---this includes - 8,10(2 hours)
10 - 15--this includes - 12,13,15,15(4 hours)
15 - 20-this includes - 17,18,18,19,19,20,20(7 hours)
(Note:This is exclusive classes i.e., upperlimit is not included)
Using this data the frequency table is constructed as shown below:
No. of hours Frequency
0 - 5 7
5 - 10 2
10 - 15 4
15 - 20 7
Hence, the frequency table for the given data are grouped using four classes.
Learn more about frequency table here:
https://brainly.com/question/12576014
#SPJ1
Diego is making a trail mix for him and his friends to take with them on a hike next week. He mixes 4 2 6 pounds of nuts, 3 3 6 pounds of raisins, and 2 3 6 pounds of chocolate chips. How many 1 3 pound bags of trail mix can he make?
There are 31 bags of [tex]$\frac{1}{3}[/tex] pound bags of trail mix he can make.
As per the data given:
Diego is making a trail mix for him and his friends to take with them on a hike next week.
He mixes [tex]$4\frac{2}{6}[/tex] pounds of nuts, [tex]$3\frac{3}{6}[/tex] pounds of raisins, and [tex]$2\frac{3}{6}[/tex] pounds of chocolate chips.
Here we have to determine how many [tex]$\frac{1}{3}[/tex] pound bags of trail mix can he make.
First, we have to convert all the mixed fractions to improper fractions.
[tex]$4\frac{2}{6} = \frac{26}{6}[/tex]
[tex]$3\frac{3}{6} = \frac{21}{6}[/tex]
[tex]$2\frac{3}{6} = \frac{15}{6}[/tex]
The total number of pounds he mixed with nuts, peanuts, and chocolate chips.
Add up all the improper fractions.
[tex]$=\frac{26}{6}+ \frac{21}{6} +\frac{15}{6}[/tex]
As all the denominators have the same value we can add all the fractions directly.
[tex]$=\frac{26+21+15}{6}[/tex]
[tex]$=\frac{63}{6}[/tex]
[tex]$=\frac{31}{3}[/tex]
To see how many [tex]$\frac{1}{3}[/tex] bag he can have, we have to divide the total by [tex]$\frac{1}{3}[/tex].
So we have:
[tex]$=\frac{\frac{31}{3} }{\frac{1}{3} }[/tex]
= 31
Therefore the answer is 31.
For more questions on fractions
https://brainly.com/question/17384634
#SPJ4
if a cone-shaped hole is 3 feet deep and the circumference of the base of the hole is 44 feet, what is the volume of the hole? use 22/7 for pi
The volume of the conical hole will be 154 cubic feet.
What is the volume of the cone?The area a cone takes up in a three-dimensional plane is known as its volume. A cone's base is circular, so it is made of a radius and a diameter.
Given that a cone-shaped hole is 3 feet deep and the circumference of the base of the hole is 44 feet,
The volume of the cone will be calculated as:-
Volume = (1/3)πr²h
The circumference of the cone is,
2πr = 44
2 x ( 22 / 7 ) x r = 44
r = 7 feet
The volume of the cone will be calculated as:-
Volume = (1/3)πr²h
Volume = ( 1 / 3 ) x ( 22 / 7 ) x 7 x 7 x 3
Volume = 22 x 7
Volume = 154 cubic feet
Therefore, the volume will be 154 cubic feet.
To know more about volume follow
https://brainly.com/question/1082469
#SPJ1
Which inequality represents eight less than three times a number is more than 22.
A. 3x - 8 > 22 B. 8 - 3X >22 C.3x - ≥ 22
Answer:
the answer of the equation is b
) You spin the spinner once.
6
5
7
2
Submit
3
What is P(greater than 2)?
) Write your answer as a fraction or whole number.
The value of P(Greater than 2) is 0.75
How to evaluate the probabilityFrom the question, we have the following parameters that can be used in our computation:
Spinner = 6 5 7 2
Using the above as a guide, we have the following:
Greater than 2 = 3
Total = 4
The probability is
P = Greater than 2/Total
Substitute the known values in the above equation, so, we have the following representation
P(Greater than 2) = 3/4
Evaluate
P(Greater than 2) = 0.75
Hence, the solution is 0.75
Read more about probability at
brainly.com/question/251701
#SPJ1
how to solve
x^2 - 3x -4 = 0
IF ANYONE SOLVES IT, HE/SHE WILL BE THE BEST IN MY LIFE.
The solutions of the quadratic equation:
x^2 - 3x - 4 =0
are x = 4 and x = -1
How to solve the quadratic equation?Here we want to solve the quadratic equation:
x^2 - 3x - 4 =0
To do so, we just need to use the quadratic formula, remember that for:
a*x^2 + b*x + c = 0
The solutions are:
[tex]x = \frac{-b \pm \sqrt{b^2 - 4ac} }{2a}[/tex]
Then in this case the solutions are:
[tex]x = \frac{3 \pm \sqrt{(-3)^2 - 4*1*-4} }{2*1}\\\\x = \frac{3 \pm 5 }{2}[/tex]
Then the two solutions are.
x = (3 +5)/2 = 4
x = (3 - 5)/2 = -1
Learn more about quadratic equations at:
https://brainly.com/question/1214333
#SPJ1
The distance (in miles) that a person can see to the horizon can be approximated by
d(n) = V1.49n, where n is the elevation (in feet above sea level) of the person.
Approximate the elevation of a person who can see 85 miles to the horizon.
Step-by-step explanation:
the function is
d(n) = sqrt(1.49×n)
so,
85 = sqrt(1.49×n)
85² = 1.49×n
n = 85²/1.49 = 7225/1.49 = 4,848.993289... ft
≈ 4,849 ft
The price of 4 citrons and 3 fragrant wood apples is 34 units the price of 3 citrons and 4 fragrant wood apples is 29 units find the price of a cotton and the price of the wood apple
The price of one citron is 5 units and the price of one fragrant wood apple is 3.5 units." Let's call the price of one citron "c" and the price of one fragrant wood apple "w".
Using the information from the first equation:
4c + 3w = 34
Using the information from the second equation:
3c + 4w = 29
We can now solve the system of equations to find the value of "c" and "w".
Subtracting the second equation from the first:
4c + 3w - (3c + 4w) = 34 - 29
c = 5
Substituting the value of c back into one of the original equations:
3c + 4w = 29
3 * 5 + 4w = 29
15 + 4w = 29
4w = 14
w = 3.5
To knw more about Linear equations
https://brainly.com/question/2030026
#SPJ4
Evaluate 1/5r + 9/20 when r = 1/4
1/5 ( blank) + 9/20 = blank + 9/20= Answer?
Answer:
Step-by-step explanation:
Substitute for r.
1/5(1/4) + 9/20 -> 1/20 + 9/20 = 10/20.
Simplify the final answer.
10/20 = 1/2
Please help me with e its too hard for me
If the rates are the same ones, the tank will be filled in 15 minutes.
How long will take the fill the tank?Let's define R as the rate at which we fill the tank, we know that we can fill a volume V in 6 minutes, then:
R*6 min = V
R = V/6min
Then r is the rate at which we empty the tank, we know that a volume V is emptied in 10 minutes, then:
r*10 min = V
r = V/10min
If both valves are open, the rate at which we will fill the tank is:
R - r
Now we need to find the value of time T such that:
(R - r)*T = V
(V/6min - V/10min)*T = V
(1/6min - 1/10min)*T = 1
(5/30min - 3/30min)*T = 1
(2/30 min)*T = 1
T = (30min/2)
T = 15 minutes.
The tank will be filled in 15 minutes.
Learn more about rates at:
https://brainly.com/question/843074
#SPJ1
A scenic train ride has one price for adults and one price for children. One family of two adult-
nd two children pays $62 for the train ride. Another family of one adult and four children pays
O. How much does it cost for one child to ride the train
Using simultaneous equations, the child ticket costs $18.
What are simultaneous equations?Simultaneous equations are two or more equations solved concurrently or at the same time.
Simultaneous equations are also known as a system of equations.
Family A Family B Total Cost
Adults 2 2 $62
Children 1 4 $70
Let the ticket cost per child = x
Let the ticket cost per adult = y
Equations:2x + 2y = 62 ... Equation 1
x + 4y = 70 ... Equation 2
Multiply Equation 1 by 2
4x + 4y = 124 ... Equation 3
Subtract Equation 2 from Equation 3:
4x + 4y = 124
-
x + 4y = 70
3x = 54
x = 18
= $18
From Equation 2, Substitute x = 18:
x + 4y = 70
18 + 4y = 70
4y = 52
y = 13
= $13
Learn more about simultaneous equations at https://brainly.com/question/15165519
#SPJ1
Question Completion:Another family of one adult and four children pays $70.
If Mark reads 18 pages less than originally planned, he will need 5 more days to complete the book. If he reads 24 pages less than originally planned, he will need 8 more days to finish. How many pages are in the book?
Answer: Let's denote the original number of pages Mark planned to read as "P".
From the first statement, we know that P - 18 pages will take 5 more days, which means P pages will take 5 days less, or 5 - 5 = 0 days.
From the second statement, we know that P - 24 pages will take 8 more days, which means P pages will take 8 days less, or 8 - 8 = 0 days.
So, we have two equations:
P - 18 = 5 * X
P - 24 = 8 * Y
Where X and Y are the number of pages Mark reads per day.
Since X and Y are equal, we can substitute one of them for the other:
P - 18 = 5 * (P - 24) / 8
Expanding the right side and solving for P, we find that P = 288 pages.
Step-by-step explanation:
Nate wants to buy a CD for $1000 that earns 3% APR and is compounded
quarterly for 5 years. He will be taxed on 20% of the interest that he earns.
What is the total amount of interest Nate will earn, after taxes?
O A. $40. 96
O B. $51. 20
O c. $161. 18
O D. $128. 94
SUBMIT
Help apex!
D. $128.94. is the total amount of money Nate will earn after taxes when he buys a CD for $1000 The formula for compound interest is:
A = P * (1 + r/n)^(nt), where A is the amount after t years, P is the principal amount, r is the interest rate as a decimal, n is the number of times interest is compounded per year, and t is the number of years.
We can use this formula to calculate the amount of money Nate will have after 5 years:
A = 1000 * (1 + 0.03/4)^(4 * 5) = 1000 * (1 + 0.0075)^20 = 1000 * 1.1629 = 1162.9
The interest earned is 1162.9 - 1000 = $162.9.
And the amount of interest taxed is 20% of $162.9, which is 20% * $162.9 = $32.58.
So, the total amount of interest earned after taxes is $162.9 - $32.58 = $130.32.
Therefore, the correct answer is D. $128.94.
To know more about Compound Interest
https://brainly.com/question/28020457
#SPJ4
Find the value of x. to 89° 118° 104° x°
Answer:
x = 49
Step-by-step explanation:
We can find the sum of the interior angles of a polygon using the formula
[tex]S_{n}=(n-2)*180[/tex], where n is the number of sides the polygon has.
Because the figure in the picture is a trapezoid and has four sides, we can find the sum of all the interior angles in the polygon by substituting 4 for n:
[tex]S_{4}=(4-2)*180\\ S_{4}=2*180\\S_{4}=360[/tex]
Since we know that the sum of all the angles in the trapezoid is 360, we can find x by subtracting the sum of the angles already given from 360:
[tex]x+118+104+89=360\\x+311=360\\x=49[/tex]
in the given figure AB || CD PROVE THAT p+q+r = 180
As per the figure, the angle equation p + q + r = 180 is proved.
In geometry, an angle is defined as the figure formed by two rays, called the sides of the angle, sharing a common endpoint, called the vertex of the angle. When two lines are parallel, the angles opposite to each other are called corresponding angles.
In the given figure AB || CD, we are asked to prove that the sum of angles p, q, and r is equal to 180 degrees. This can be proven using the concept of corresponding angles.
Since lines AB and CD are parallel, the angles opposite to each other are equal, i.e., p = r. Therefore, the sum of angles p and r can be represented as 2p.
Furthermore, since lines AB and CD are parallel, the alternate interior angles are equal. This means that angle q is equal to angle p.
Therefore, the sum of all three angles, p, q, and r, can be represented as 2p + q.
And since we know that p = q, we can simplify this to 3p.
Finally, since the sum of angles in a triangle is always 180 degrees, we know that
=> 3p = 180 degrees.
Solving for p, we find that p = 60 degrees.
Therefore, the sum of angles p, q, and r is equal to
=> 2p + q = 2 * 60 + 60 = 180 degrees,
which proves the statement p + q + r = 180 degrees.
To know more about angle here.
https://brainly.com/question/4316040
#SPJ4
Give the domain and range of G.
Write your answers using set notation.
Domain of function = {-3 , -4}
Range of function = {4 , -1 , -4}
What is domain and range of a function?The domain of a function is the set of values that we are allowed to plug into our function. This set is the x values in a function such as f(x). The range of a function is the set of values that the function assumes. This set is the values that the function shoots out after we plug an x value in.
Given,
points on graph of a function are
(-3 , 4) , (-3 , -1) , (-4 , -4)
Range is set of y-values,
Range = {4 , -1 , -4}
Domain is set of x - values
Domain = {-3 , -4}
Hence, Domain and range of function are {-3 , -4} and {4 , -1, -4} respectively.
Learn more about domain and range here:
https://brainly.com/question/28135761
#SPJ1
Work out the volume of the cuboid below.
Remember to give the correct units.
13 m
5m
13 m
3 m
Answer:
195m^3
Step-by-step explanation:
Volume of a rectangle = Length x Width x Height
L = 5m
W = 3m
H = 13m
V = 5m x 3m x 13m
V = 195m^3
It took 2 electricians 5 days to wire a house. How long would it take 10 electricians?
Answer:
1 day
Step-by-step explanation:
Assuming all the electricians work at the same rate, we can use the formula:
(time x workers) = constant
So, if 2 electricians took 5 days, we have:
(5 x 2) = (time x 10)
Simplifying, we get:
10 = time x 10
Dividing both sides by 10, we get:
time = 1
Therefore, it would take 10 electricians 1 day to wire the house.