Answer:
domain = - 2, 1, 0, 1, 4, - 1
range = - 4, 3, 0, 4, 6, - 2
Step-by-step explanation:
x is domain
y is range
The graphs of lines a and b are shown on the coordinate
plane. Write the equation on the line provided for each line.
Then solve the system of equations using any method.
The equation of line a is.
The equation of line b is.
Solution
From the graph we got two equations of line -3x+ y -9 =0 and x+y-7 =0
and solution of these equations are x = -1/2 and y= 15/2
what is equation of line?An algebraic expression that represents a number of points which creates a line in the XY coordinate system or another coordinate plane.
What is the equation of lines shown in the graph?
we are given a graph containing two equations of line named a and b. The lines are plotted in XY coordinate system.
From the graph, we can detect two locations of point (5, 6) and (1, -6) for line a and detect two location of point (1, 6) and (6, 1) for line b.
As per the formula for equation of straight line, a line passes through two points can be written as y-y₁ = [(y₂-y₁) / (x₂-x₁)] × (x- x₁)
hence, line a can be written as (y- 6) = [(-6 -6) / (1-5)] × (x- 5)
y-6 = 3(x-5)
y-6 = 3x -15
y-3x -9 = 0
In the next, line b can be written as (y-6) = [(1-6) / (6-1)] × (x-1)
y-6 = -1(x-1)
y-6 = -x+1
x+ y -7 =0
now, we get two equations, -3x+ y -9 =0
x+ y - 7 =0
Solving these two equations by addition method, we get x= -1/2 and y = 15/2
To learn more about graph of straight-line visit:
https://brainly.com/question/2564656
#SPJ1
Which of the following sets of numbers could not represent the three sides of a triangles?
9,23,34
10,24,31
8,14,21
5,14,16
Answer:
pretty sure it's B. Let me know if im wrong
Step-by-step explanation:
pls help last test or semester half my grade pls pls pls i’ll give brainliest
Therefore , the solution of the given problem of function comes out to be satisfies the given function is x=9 and y=21.
What is function?Any input will only result in one or zero outcomes for the function. The expression does not define the function if there are several outputs for a given input. Each value of x must have only one output value of y variable in order for anything to be a function.
Here,
Given : A table of values of x and y
To find : the function is linear or not
Thus,
F(x) = y -3x =0
So,
Putting the values of x and y in given function
The value which satisfies the given function is x=9 and y=21.
Therefore , the solution of the given problem of function comes out to be
satisfies the given function is x=9 and y=21.
To know more about function , visit
brainly.com/question/13461298
#SPJ1
Four student government officers want to go to the state convention. It will cost them $100 for registration, $375 for transportation and food, and $41 per person for the hotel. There is $425 budgeted for the convention in the student government savings account. They can earn the rest of the money they need by having a car wash. If they charge $5 per car, how many cars must they wash in order to have enough money to pay for the trip?
cars___?
Answer:
$100 + $375 + $41(4) = $516
$516 - $425 = $91
$91 / $5 = 18.2 cars
Therefore, the four student government officers must wash 18 cars in order to have enough money to pay for the trip.
Select the correct answer.
Steve is trying to determine the proper rectangular pan to use for his banana bread recipe. He has four different pans that he can use, each with the same length and width but all with different heights.
Which of the following formulas will show how Steve can determine the height of a rectangular pan?
I believe it's A
I hope this helps and if I'm wrong I apologize
Use the figure to answer the question,
Triangle ABC is similar to triangle ABC.
B
Which series of transformations shows that ABC is similar to ABC1
A. Reflect ABC across line I and translate 2 units right.
B. Reflect ABC across line I and translate 6 units up
C. Reflect ABC across line I and dilate from point A by a factor of 2.
D. Reflect ABC across line I and dilate from point A by a factor of
On solving the provided question, we cans ay that - here in triangles, triangle ABC is congruent to triangle A`B`C`
What is triangle?Three sides and three vertices make up a triangle, which is a polygon. It is among the fundamental forms in geometry. Triangle ABC is the name given to a triangle with vertices A, B, and C. When the three points are not collinear, a unique plane and triangle in Euclidean geometry are found. A triangle is a polygon that has three sides and three corners. The spots where the three sides join end to end make up the triangle's corners. Three triangle angles added together equal 180 degrees.
Here,
two triangles are there
triangle ABC and triangle A`B`C`
AB =A`B`
BC = B`C`
AC =A`C`
So, by sss property
both are congruent
To know more about triangle visit:
https://brainly.com/question/2773823
#SPJ1
A rectangular room measures 10 feet by 120 inches. Tonya said the area of the room is 1200 square feet. What did Tonya do wrong?
Answer: Tonya's calculation is incorrect because she mixed units of measurement. She used feet to measure one dimension of the room (10 feet) and inches to measure the other dimension (120 inches) and then calculated the area as 10 x 120 = 1200 square feet.
Area is a measure of the amount of space inside a two-dimensional shape, and it's typically measured in square units. To calculate the area of a rectangular room, you multiply the length of the room by the width of the room,
However in this case, Tonya used different units of measurement for length and width (feet and inches), and therefore the answer is incorrect.
You would need to convert inches to feet before multiplying 10 feet by 120 inches to get the area.
120 inches = 10 feet
So, the correct calculation of the area would be 10 feet * 10 feet = 100 square feet
It's worth mentioning that before calculating any area or volume, it's important to make sure that all units of measurement are consistent and the same.
Step-by-step explanation:
Imagine a box with an ant at one corner. The ant wants to travel to the opposite corner by the most direct path. It must travel across the top of box at some stage. The top of the box is the light area. It cannot travel along the ground or under the box. (Hint : it does not have to travel along an edge)
The solution is Option A.
The shortest distance is given by the two hypotenuses of the triangles and the distance is X = 7.8 cm
What is a Triangle?A triangle is a plane figure or polygon with three sides and three angles.
A Triangle has three vertices and the sum of the interior angles add up to 180°
Let the Triangle be ΔABC , such that
∠A + ∠B + ∠C = 180°
The area of the triangle = ( 1/2 ) x Length x Base
For a right angle triangle
From the Pythagoras Theorem , The hypotenuse² = base² + height²
Given data ,
Let the shortest distance be represented as X
Let the first triangle be the first face of the rectangular box ΔABC
The length of the triangle AB = 3 cm
The height of the triangle BC = 2 cm
Now ,
For a right angle triangle
From the Pythagoras Theorem , The hypotenuse² = base² + height²
The measure of AC = √ ( 3² + 2² )
The measure of AC = √13 cm
And , the second triangle is the second face of the rectangular box ΔDEF
The length of the triangle DE = 4 cm
The height of the triangle EF = 2 cm
The measure of DF = √ ( 4² + 2² )
The measure of DF = √18 cm
Now , the shortest distance X = The measure of AC + measure of DF
Substituting the values in the equation , we get
The shortest distance X = √13 cm + √18 cm
The shortest distance X = 3.60 + 4.24
The shortest distance X = 7.8 cm
Therefore , the value of A is 7.8 cm
Hence , the shortest distance for the ant is 7.8 cm
To learn more about triangles click :
https://brainly.com/question/16739377
#SPJ1
a ball is thrown from the top row of seats in a stadium the function h(t)=-16t^2+80t+96 gives the height, in feet, of the ball t seconds after it is thrown. how long will it be before the ball hits the ground?
The number of seconds it takes ball to before hit the ground is 6 seconds.
What is the solution of a quadratic equation?The solutions to the quadratic equation are the values of the unknown variable x, which satisfy the equation. These solutions are called roots or zeros of quadratic equations. The roots of any polynomial are the solutions for the given equation.
Given that, a ball is thrown from the top row of seats in a stadium the function h(t)=-16t²+80t+96 gives the height, in feet, of the ball t seconds after it is thrown.
When ball hits the ground h=0
So, -16t²+80t+96=0
-16(t²-5t-6)=0
t²-5t-6=0
By using splitting middle term method, we get
t²-6t+1t-6=0
t(t-6)+1(t-6)=0
t-6=0 or t+1=0
t=6 or t=-1
Time can not be negative integer.
Therefore, the number of seconds it takes ball to before hit the ground is 6 seconds.
To learn more about the solution of quadratic equation visit:
https://brainly.com/question/18305483.
#SPJ1
A woman leaves home at 7 am and drives to New York City 200 miles away. If she averages 50 miles per hour, what time will she arrive at the city
Answer:
11 AM
Step-by-step explanation:
Mile Calculation:
200 miles away and 50 miles per hour.
200 divided by 50 is equal to 4
Answer:
Now, 7 am + 4 hours is equal to 11 AM.
Joshua's cousin pledged $12 for a charity walk if Joshua walked 3 miles how much did his cousin pay per mile
Which of the following points best represents the location of -1;
15.
ос
OD
Ов
ОА
+
-2
в с
0
on the number line?
D
2 +
2
A satellite dish is in the shape of a parabolic surface. Signals coming from a satellite strike the surface for the dish and are reflected to the focus, where the receiver is located. The satellite dish has a diameter of 14 feet and a depth of 3 feet. How far from the base of the dish should the receiver be placed? Round your answer to the nearest tenth.
Answer:
Given that we know the base of the parabola is at the origin, and that it is symetrical about the y-axis, we can simplify the equation to
y=ax2=14px2" role="presentation" style="display: inline-block; line-height: 0; text-indent: 0px; text-align: left; text-transform: none; font-style: normal; font-weight: normal; font-size: 16.66px; letter-spacing: normal; overflow-wrap: normal; word-spacing: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; margin: 0px; padding: 1px 0px; position: relative;">y=ax2=14px2y=ax2=14px2
which corresponds to the given equation a=14p" role="presentation" style="display: inline-block; line-height: 0; text-indent: 0px; text-align: left; text-transform: none; font-style: normal; font-weight: normal; font-size: 16.66px; letter-spacing: normal; overflow-wrap: normal; word-spacing: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; margin: 0px; padding: 1px 0px; position: relative;">a=14pa=14p given above.
Since y=6" role="presentation" style="display: inline-block; line-height: 0; text-indent: 0px; text-align: left; text-transform: none; font-style: normal; font-weight: normal; font-size: 16.66px; letter-spacing: normal; overflow-wrap: normal; word-spacing: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; margin: 0px; padding: 1px 0px; position: relative;">y=6y=6 when x=2" role="presentation" style="display: inline-block; line-height: 0; text-indent: 0px; text-align: left; text-transform: none; font-style: normal; font-weight: normal; font-size: 16.66px; letter-spacing: normal; overflow-wrap: normal; word-spacing: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; margin: 0px; padding: 1px 0px; position: relative;">x=2x=2,
6=a(2)2=4a" role="presentation" style="display: inline-block; line-height: 0; text-indent: 0px; text-align: left; text-transform: none; font-style: normal; font-weight: normal; font-size: 16.66px; letter-spacing: normal; overflow-wrap: normal; word-spacing: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; margin: 0px; padding: 1px 0px; position: relative;">6=a(2)2=4a6=a(2)2=4a
and
a=32" role="presentation" style="display: inline-block; line-height: 0; text-indent: 0px; text-align: left; text-transform: none; font-style: normal; font-weight: normal; font-size: 16.66px; letter-spacing: normal; overflow-wrap: normal; word-spacing: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; margin: 0px; padding: 1px 0px; position: relative;">a=32a=32
Thus we have
32=14p12p=2p=16" role="presentation" style="display: table-cell !important; line-height: 0; text-indent: 0px; text-align: center; text-transform: none; font-style: normal; font-weight: normal; font-size: 16.66px; letter-spacing: normal; overflow-wrap: normal; word-spacing: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 3.337em; min-height: 0px; border: 0px; margin: 0px; padding: 1px 0px; width: 10000em; position: relative;">32=14p12p=2p=1632=14p12p=2p=16
So, the receiver should be placed 16" role="presentation" style="display: inline-block; line-height: 0; text-indent: 0px; text-align: left; text-transform: none; font-style: normal; font-weight: normal; font-size: 16.66px; letter-spacing: normal; overflow-wrap: normal; word-spacing: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; margin: 0px; padding: 1px 0px; position: relative;">1616 of a foot, or 2 inches, above the base.
In 1965, the population of a country was 192 thousand to 3 significant figures.
In 2020, the population of that country was 366 thousand to 3 significant figures.
Work out the percentage increase in population. Give your answer correct to 2 significant figures.
The percent change in population is 90.65%.
What is percent?A percentage is a figure or ratio that can be stated as a fraction of 100. If we need to calculate the percentage of a number, we must divide it by its full value and then multiply it by 100. As a result, the percentage is one part in one hundred. "Per 100" is short for "per percent." It is represented by the symbol "%".
Given population of country in 1965 = 192 thousand = 1,92,000.
population of country in 2020 = 366 thousand = 3,66,000
the increase in population is = 366000 - 192000 = 1,74,000
the percentage increase = (100)(increase in population)/(1965 population)
the percentage increase = (100) (174000)/(192000)
the percentage increase = 90.625%
Hence the percent increase is 90.62%.
Learn more about percent;
https://brainly.com/question/28840349
#SPJ1
I need help, I know it gave me the answer but I don’t understand how it got (-3) someone explain please
Answer: h=14
Step-by-step explanation:
If x=-18, then
h=17+(-18)/6
h=17+(-3)
h=17-3
h=14
Answer:
Step-by-step explanation:
so, the calculation was : h = 17 + [tex]\frac{-18}{6\\}[/tex]
To subtract "[tex]\frac{-18}{6}[/tex] " we need to make it the same denominator as "17"
(it's not written but technically 17 = [tex]\frac{17}{1}[/tex] )
Yet, we see that [tex]\frac{-18}{6} =\frac{-3* 6}{1*6}[/tex]
We just need to remove both the 6 that are not useful here and :
[tex]\frac{-3*6}{1*6} =\frac{-3}{1}= -3[/tex]
We obtain h = 17 - 3 = 14
hope it helped :)
3/5 of carl's money is $27.00. how much is 1/2 of his money
Answer:
$22.5
Step-by-step explanation:
$27.00/3/5=45
45*1/2=$22.5
Which of the following tables represents a linear relationship that is also proportional
Answer picture below
Answer:
c=200+0.4Yd find determine equlibirum level investment is =400
Answer:im pretty sure its D
Step-by-step explanation:it goes through the origin
The density of a certain material is such that it weighs 6900 grams for every 4.5 quarts of volume. Express this density in pounds per cubic foot. Round your answer to the nearest whole number.
The density in terms of pounds per cubic foot is 101.2 pounds/ft³
What is the unitary method?The unitary method is a method in which you find the value of a unit and then the value of a required number of units.
Given here; 6900 g for every 4.05 quarts thus expressing in terms of pounds per cubic foot we get = 15.22/0.15039
= 101.2
Hence, The density in terms of pounds per cubic foot is 101.2 pounds/ft³
Learn more about the unitary method here:
https://brainly.com/question/22056199
#SPJ1
The distribution of the amount of money undergraduate students spends on books for a term is slightly right-skewed, with a mean of $400 and a standard deviation of S80. If a simple random sample of 100 undergraduate students is selected, what is the probability that these students spend, on average, more than $425 on books?
The probability that on average these students spend more than $425 on books is given as follows:
0.0009 = 0.09%.
How to obtain the probability using the normal distribution?The z-score of a measure X of a variable that has mean symbolized by [tex]\mu[/tex] and standard deviation symbolized by [tex]\sigma[/tex] is obtained by the rule presented as follows:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The z-score represents how many standard deviations the measure X is above or below the mean of the distribution, depending if the obtained z-score is positive or negative.Using the z-score table, the p-value associated with the calculated z-score is found, and it represents the percentile of the measure X in the distribution.By the Central Limit Theorem, the sampling distribution of sample means of size n has standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].The parameters for this problem are given as follows:
[tex]\mu = 400, \sigma = 80, n = 100, s = \frac{80}{\sqrt{100}} = 8[/tex]
The desired probability is one subtracted by the p-value of Z when X = 425, hence:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem:
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{425 - 400}{8}[/tex]
Z = 3.125.
Z = 3.125 has a p-value of 0.9991.
1 - 0.9991 = 0.0009 = 0.09%.
More can be learned about the normal distribution at https://brainly.com/question/25800303
#SPJ1
Which radicals are already in the simplest form?
Given that a function, g, has a domain of -20 ≤ x ≤ 5 and a range of -5 ≤ g(x) ≤ 45 and that g(0) = -2 and g(-9) = 6, select the statement that could be true for g. A. g(0) = 2 B. g(-4) = -11 C. g(7) = -1 D. g(-13) = 20
A function, g, has a domain of -20 ≤ x ≤ 5 and a range of -5 ≤ g(x) ≤ 45 and that g(0) = -2 and g(-9) = 6 then g(-13) = 20
What is a function?A relation is a function if it has only One y-value for each x-value.
Given a a function, g, has a domain of -20 ≤ x ≤ 5 and a range of -5 ≤ g(x) ≤ 45
and that g(0) = -2 and g(-9) = 6,
x=-20 then g(-20)=-5
x=-19 then g(-19)=-4
x=-18 then g(-18)=-3
x=-17 then g(-17)=-2
x=-16 then g(-16)=-1
x=-15 then g(-15)=0
x=0 then g(0)=-2
x=-9 then g(-9)=6
By observing this we can say that as x values are decreasing the function values are increasing and vice versa
So option D is correct
Hence, a function, g, has a domain of -20 ≤ x ≤ 5 and a range of -5 ≤ g(x) ≤ 45 and that g(0) = -2 and g(-9) = 6 then g(-13) = 20
To learn more on Functions click:
https://brainly.com/question/21145944
#SPJ1
An Uber company charges $7.50 for the first mile and $1.10 for each additional mile. What is the Uber rate for 9 miles? Use r for the total rate and m for total miles.
Answer:
r = 7.50 + (1.10 × (m - 1))
r = 7.50 + (1.10 × (9 - 1))
r = 16.40
The total uber rate for 9 miles is $16.3.
What is an expression?An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
Example: 2 + 3x + 4y = 7 is an expression.
We have,
First-mile charge = $7.50
Additional charges after the first mile = $1.10
The total charge for 9 miles.
r = 7.50 + 1.10 x 8
r = 7.50 + 8.8
r = $16.3
Thus,
The total rate for 9 miles is $16.3.
Learn more about expressions here:
https://brainly.com/question/3118662
#SPJ2
What is the multiplicative rate of change for the exponential function f(x)=2(5/2) in decimal form
The multiplicative rate of change for the exponential function is 0.4.
What is an exponential function?The exponential function in mathematics is represented by the symbols f(x)=exp or ex. The word, unless otherwise stated, normally refers to the positive-valued function of a real variable, though it can be extended to complex numbers or adapted to other mathematical objects like matrices or Lie algebras.
In mathematics, an exponential function has the following form: f (x) = an x, where x is a variable and an is a fixed amount known as the function's base. The transcendental number e, or roughly 2.71828, is the most often encountered exponential-function base.
Given: Exponential function [tex]$f(x)=2\left(\frac{5}{2}\right)^{-x}$[/tex]
To find The multiplicative rate of change for the exponential function.
Solution :
The general form of the exponential function is [tex]$f(x)=a b^x$[/tex]
where $b$ is the rate of change of the function.
First we write the given function In proper form:
[tex]$$\begin{aligned}& f(x)=2\left(\frac{5}{2}\right)^{-x} \\& f(x)=2\left(\frac{2}{5}\right)^x\end{aligned}$$[/tex]
The rate of change is [tex]$f(x)=a b^x$[/tex]
Therefore, The multiplicative rate of change for the exponential function Is $0.4$
To learn more about exponential function refer to:
brainly.com/question/12940982
#SPJ1
Make equivalent fractions with the LCD of 12:
5/6 + 1/4 =
5/12 + 1/12 =
10/12 + 3/12 =
7/12 + 4/12 =
11/12 + 5/12 =
Which one?
Answer:
All four are equivalent fractions with the LCD of 12
Step-by-step explanation:
compare the function rule f(x) = 3x +2 and the graph of g(x)
which statements are true? select two that apply.
-g(x) increases at a faster rate over the interval (-1,0)
-g(x) increases at a faster rate over the interval (1,2)
-g(x) increases at a faster rate over the interval (0,1)
-f(x) increases at a faster rate over the interval (2,3)
-f(x) increases at a faster rate over the interval (0,1)
-f(x) increases at a faster rate over the interval (1,2)
On solving the provided question we can say that - from the graphs n f (x) and g( x) are 1 and 5 .
What is graphs?Graphs are visual representations or charts used in mathematics to methodically express data or values. A relationship between two or more objects is frequently represented by a point on a graph. A non-linear data structure called a graph is made up of nodes, or vertices, and edges. Connect the nodes, also known as vertices. This graph comprises a set of vertices V= 1, 2, 3, 5, and a set of edges E= 1, 2, 1, 3, 2, 4, and (2.5), (3.5), (4.5). Statistics graphs (bar charts, pie charts, line charts, etc.) Exponential diagrams. triangle graph, a logarithmic graph
by graphs of the function f (x) and g( x)
[tex]lim f ( x) + lim g ( x )\\= -1 + 2 = 1\\ f ( -1 ) + lim g ( x)\\= 3 + 2\\= 5[/tex]
from the graphs n f (x) and g( x) are 1 and 5 .
To know more about graphs visit:
https://brainly.com/question/11950136
#SPJ1
Find the values at the 30th and 90th percentile for each data set
6283, 5700, 6381, 6274, 5700, 5896, 5972, 6075, 5993, 5581.
A student made two patterns to show multiplication of a decimal by powers of ten. the equations shown for both patterns are incorrect. pattern A
3.675. 10 =3.7650
3.675. 100= 3.67500
3.675.1,000= 3.675000
pattern B
3.675. 10=3.0675
3.675.0.01= 3.00675
3.675. 0.001= 3.000675
explain why the equations in each of the patterns are false. Include in your explanation the values that should appear on the right side of each equation in both patterns to make the equations true.
If a student made two patterns to show multiplication of a decimal by powers of ten. All the value are incorrect. The correct value are: 36.75, 367.5, 3,675, 36.75, 0.03675, 0.003675.
How to find the correct value?Pattern A
3.675×10 =3.7650 Incorrect
3.675×10 = 36.75 Correct
3.675× 100= 3.67500 Incorrect
3.675×100= 367.5 Correct
3.675×1,000= 3.675000 Incorrect
3.675×1,000 = 3,675 Correct
Pattern B
3.675×10=3.0675 Incorrect
3.675× 10= 36.75 Correct
3.675×0.01= 3.00675 Incorrect
3.675×0.01= 0.03675 Correct
3.675×0.001= 3.000675 Incorrect
3.675×0.001= 0.003675 Correct
The correct value are: 36.75, 367.5, 3,675, 36.75, 0.03675, 0.003675.
Learn more about correct value here: https://brainly.com/question/27242311
#SPJ1
Which statements are always true regarding the diagram? Select three options. m∠5 + m∠3 = m∠4 m∠3 + m∠4 + m∠5 = 180° m∠5 + m∠6 =180° m∠2 + m∠3 = m∠6 m∠2 + m∠3 + m∠5 = 180°
Answer:
m∠5+m∠6=180°
m∠2+m∠3=m∠6
m∠2+m∠3+m∠5=180°
Step-by-step explanation:
Verify each option
case A) we have
m∠5+m∠3=m∠4 ----> equation A
we know that
m∠3+m∠4=180° -----> by supplementary angles
m∠4=180°-m∠3 ----> equation B
substitute equation B in equation A
m∠5+m∠3=180°-m∠3
m∠5+m∠3+m∠3=180°
This equation is true when m∠2=m∠3
Therefore Is not always true
case B) we have
m∠3+m∠4+m∠5=180° ----> equation A
we know that
m∠3+m∠4=180° -----> by supplementary angles
m∠4=180°-m∠3 ----> equation B
substitute equation B in equation A
m∠3+(180°-m∠3)+m∠5=180°
m∠5=0°
This option is not true
case C) we have
m∠5+m∠6=180°
we know that
m∠5 and +m∠6 are supplementary angles
so
Their sum is always 180 degrees
Therefore this option is always true
case D) we have
m∠2+m∠3=m∠6 -----> equation A
we know that
m∠5+m∠6=180° ----> by supplementary angles
m∠6=180°-m∠5 ----> equation B
substitute equation B in equation A
m∠2+m∠3=180°-m∠5
m∠2+m∠3+m∠5=180°
Remember that the sum of the interior angles of a triangle must be equal 180 degrees
Therefore this option is always true
case E) we have
m∠2+m∠3+m∠5=180°
Remember that the sum of the interior angles of a triangle must be equal 180 degrees
This option is always true
Learn more about triangle angle here: brainly.com/question/996668
#SPJ1
How many rectangular faces are in a right triangular prism?
Answer: A right triangular prism is a 3-dimensional geometric shape that has a triangular base and three rectangular faces that connect the base to the top. A rectangular prism has three pairs of rectangular faces that are congruent, these faces are perpendicular to each other and connected by edges.
So, in a right triangular prism there are 3 rectangular faces which are the lateral faces (the one that connects the base and the top)
A triangular prism also has 3 triangular faces which are the base faces
So in total, a right triangular prism has 3 rectangular faces and 3 triangular faces.
Step-by-step explanation:
Prove that limx→2 x/1+x= 1/2 using the definition of limit