Please help, I don't know how to do this.
Provide reasons for the proof.
Given: Angle 2 = angle 4
and angle 2 and angle 3 are supplementary
Prove: angle 1 = angle 3
Answers
To prove that angle 1 is equal to angle 3, we can use the given information and the properties of supplementary angles. Using substitution and algebraic manipulations, we can show that angle 1 is indeed equal to angle 3.
Explanation:To prove that angle 1 is equal to angle 3, we can use the given information and the properties of supplementary angles.
Given: angle 2 = angle 4 and angle 2 and angle 3 are supplementary.
Since angle 2 and angle 4 are equal, we can substitute angle 4 with angle 2 in the given statement, giving us angle 2 = angle 2. Now, since angle 2 and angle 3 are supplementary, their sum is 180 degrees. So angle 2 + angle 3 = 180 degrees. We can rewrite this equation as angle 2 = 180 - angle 3. Now, we can substitute angle 2 in the equation with angle 4 (which is equal to angle 2), giving us angle 4 = 180 - angle 3. Rearranging this equation, we get angle 3 = 180 - angle 4. Since angle 4 = angle 2, we can substitute angle 4 with angle 2 in the equation, giving us angle 3 = 180 - angle 2. Finally, since angle 3 = 180 - angle 2, and angle 2 = angle 4 (from the given information), we can conclude that angle 1 = angle 3.
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Final answer:
The geometry proof demonstrates that angle 1 is congruent to angle 3 by using properties of supplementary and congruent angles.
Explanation:
The student is asking for help with a proof in geometry, a branch of mathematics. The proof involves understanding the properties of supplementary angles and congruent angles. Here is a step-by-step explanation addressing the problem:
If angle 2 is congruent to angle 4 (Given), then by definition, angle 2 and angle 4 have the same measure.Since angle 2 and angle 3 are supplementary (Given), their measures add up to 180 degrees.Because angle 2 is congruent to angle 4, angle 4 must also be supplementary to angle 3, as it has the same measure as angle 2.Angles supplementary to the same angle are equal to each other. Therefore, angle 1, which is supplementary to angle 4, must be congruent to angle 3.Consequently, we have proven that angle 1 is congruent to angle 3.
Related Questions
A room has a length of 12.62 ft and a width of 10.2 ft. Find the perimeter of the room with the correct number of significant digits.
Answers
Answer:
45.6 ft
Step-by-step explanation:
The room is a rectangle. The perimeter of a rectangle is
perimeter = 2L + 2W
perimeter = 2(12.62 ft) + 2(10.2 ft)
perimeter = 25.24 ft + 20.4 ft
perimeter = 45.64 ft
Since 10.2 ft has only 3 significant digits, the answer must also have only 3 significant digits.
Answer: perimeter = 45.6 ft
What is 7.0717 million in figures. ?
Answers
7.0717 million
Lets see:
1 million = 1.000.000
So, 7.0717 million = 7.071.700
7.071.700 can be read as "seven million seventy one thousand and seven hunred"
If you wanna split it you can split in
seven million = 7 million
seventy one thousand = 71 thousand
seven hundred = 7 hundred
The seats at a football stadium are on a slope with gradient of 1/2. What is the height of the bottom seats?
Answers
Answer:
ANS IS 2m
Step-by-step explanation:
we can solve it by using coordinate geometry
Answer:
Height of the bottom seats is 2 meter.
Step-by-step explanation:
It has been given in the question seats are located on a slope having gradient [tex]\frac{1}{2}[/tex]
We have to find the height h of the bottom seats.
Since gradient = [tex]tan\theta=\frac{1}{2}[/tex]
Therefore, from the figure attached,
[tex]tan\theta =\frac{(12-h)}{20}[/tex]
[tex]\frac{1}{2}=\frac{(12-h)}{20}[/tex]
12 - h = [tex]\frac{20}{2}[/tex]
12 - h = 10
h = 12 - 10
h = 2 m
Therefore, height of the bottom seats if 2 m.
The function
y = 2x + 2 and
y = -x + k intersect at
the point (2,6). Find the
value of k.
Answers
Answer:
k=8
The problem:
The function y=2x+2 and y=-x+k intersect at the point (2,6).
Find the value of k.
Step-by-step explanation:
(2,6) is a point contained by both y=2x+2 and y=-x+k.
Let's see if it actually on y=2x+2.
x=2,y=6
y=2x+2
6=2(2)+2
6=4+2
6=6 is true so it (2,6) is on y=2x+2.
Now we want k such that (2,6) is on y=-x+k.
6=-2+k
Add 2 on both sides:
8=k
So k=8.
Answer:
k = 8
Step-by-step explanation:
y = 2x + 2
y = -x + k
2x + 2 = - x +k
3x = k - 2
x= 2 : k-2= 6
k = 8
the product of 3 and a number is the same as 30 less thrice that same number
Answers
Answer:
11
Step-by-step explanation:
So, we can say that
3 × X - 3 = 30
3 × X = 30+3
3 × X = 33
X = 33/3
X = 11
How many hours are equal to 150 minutes?
Answers
Answer:
2Hours and 30 mins. 2 1/2
Step-by-step explanation:
3x60=180 since there is 60 minutes in an hour There is no possible ways to get an exact number.
Answer:
2.5 hours
Step-by-step explanation:
Just divide your total number of minutes by 60, which is how many minutes are in an hour to receive your answer of 2.5!
Babatunde has a mass of 78kg. What would Babatunde weigh on the Moon? (The gravitational field strength on the Moon is 1.6N/kg.)
Answers
Answer:
Babatunde weigh on the Moon would be 124.8 N
Step-by-step explanation:
* The wight of an object on the earth is mg , where m is the the
mass of the object in kg and g is the acceleration of gravity which
is 9.8 m/s²
* The mass of an object on earth is the same as the mass of the
same object on the moon but the weight of the object on the
earth is different from the weight of the same object on the
moon because the gravity on the earth different from on the moon
* The wight on the moon is mg , where m is the the mass of the
object in kg and g is gravitational field strength on the Moon
which is 1.6 N/kg
∵ Babatunde has a mass of 78 kg
∵ The mass on the moon = the mass on the earth
∵ On the moon the gravitational field strength is 1.6N/kg
∵ Weight = mg
∴ Babatunde weigh = 78 × 1.6 = 124.8 N
* Babatunde weigh on the Moon would be 124.8 N
Babatunde's weight on the Moon is calculated by multiplying his mass (78 kg) by the Moon's gravitational field strength (1.6 N/kg), resulting in 124.8 newtons.
Explanation:Calculating Babatunde's Weight on the MoonTo calculate Babatunde's weight on the Moon, we use the formula for weight, which is the product of mass and gravitational field strength. On Earth, the average acceleration due to gravity is approximately 9.8 m/s², and on the Moon, it is about 1.6 N/kg. Babatunde's mass on Earth is 78 kg. Therefore, to calculate his weight on the Moon, we multiply his mass by the Moon's gravitational field strength.
Weight on the Moon = Mass × Gravitational field strength on the Moon
Weight on the Moon = 78 kg × 1.6 N/kg
Weight on the Moon = 124.8 N
Babatunde would weigh 124.8 newtons on the surface of the Moon, significantly less than his weight on Earth due to the Moon's lower gravitational pull.
Simplify the expression 3(x + 2)(x2 − x − 8). 3x3 + 3x2 − 30x − 48 3x3 + x2 − 10x − 16 3x3 − 30x2 − 12x − 48 3x3 − 4x2 − 30x − 4
Answers
Answer:
3x^3 + 3x^2 − 30x − 48
Step-by-step explanation:
3( x + 2 )( x^2 − x − 8 )
= ( 3( x + 2 ))( x^2 + − x + − 8 )
= ( 3( x + 2 ))( x^2 ) + ( 3( x + 2 ))( −x ) + ( 3( x + 2 ))( −8 )
= 3x^3 + 6x^2 − 3x^2 − 6x − 24x − 48
3x^3 + 3x^2 − 30x − 48
Answer:
The correct option is A) [tex]3x^3+3x^2-30x-48[/tex]
Step-by-step explanation:
Consider the provided expression.
[tex]3\left(x+2\right)\left(x^2-x-8\right)[/tex]
Distribute 3 as shown
[tex]\left(3x+6\right)\left(x^2-x-8\right)[/tex]
Distribute parentheses as shown.
[tex]3xx^2+3x\left(-x\right)+3x\left(-8\right)+6x^2+6\left(-x\right)+6\left(-8\right)[/tex]
[tex]3x^2x-3xx-3\cdot \:8x+6x^2-6x-6\cdot \:8[/tex]
[tex]3x^3-3x^2-24x+6x^2-6x-48[/tex]
Add and subtract like terms
[tex]3x^3+3x^2-30x-48[/tex]
Hence, the correct option is A) [tex]3x^3+3x^2-30x-48[/tex]
Renees car causes her $195 per month +9 cents per mile. How many miles can a dry so that her monthly car expenses are no more than $250?
Answers
Answer:
611 miles max
Step-by-step explanation:
250 = 0.09x + 195
-195 -195
55 = 0.09x
/0.09 /0.09
x=611.11111111111
because of the context of the question, you'd have to round up
x = 611
Hope this helps! If you have any questions ask! :)
A plane takes off and climbs steadily for 30 minutes until it reaches 40,000 feet. It travels at that altitude
for 2 hours until it begins to descend to land, which it takes 15 minutes at a constant rate. Draw a graph
of the situation
Answers
Answer: The graph is attached.
Step-by-step explanation:
We must design a graph so that the x-axis represents the Time in hours and the y-axis represents the Height in feet.
The plane takes off from this point:
[tex]A(0,0)[/tex].
We know that the plane climbs steadily for 30 minutes (which is 0.5 hours) until it reaches 40000 feet. Then, we can identify another point; this is:
[tex]B(0.5,\ 40000)[/tex]
It travels at that altitude for 2 hours (which indicates a horizontal line) and then it begins to descend to land, giving us another point:
[tex]C(2.5\ 40000)[/tex]
This takes 15 minutes (which is 0.25 hours) at a constant rate. Then, we get a final point:
[tex]D(2.75,\ 0)[/tex]
Knowing these points, we can draw the graph (Observe the image attached)
Which point lies below the x-axis and to the right of the
y-axis?
Answers
Answer:
Quadrant IV
Step-by-step explanation:
The points (x,y) such that
y < 0 and x>0, i.e. quadrant IV of the plane.
percent of each number
71.33 % of 54
Answers
Answer:
38.5182
Step-by-step explanation:
54 • 0.7133 is 38.5182.
What is the range of values for measurements 300 +2%
Answers
300+6 =306
Done!
The range of values for the measurement 300 ±2% is 294 to 306. This involves considering the concept of accuracy and precision in measurements.
Explanation:The question is asking for the range of measurements that can be made if the measurement is 300 units with a 2% uncertainty. In mathematical terms, an uncertainty of 2% means we can make measurements that are 2% less or 2% more than the given value.
First you must calculate 2% of 300 to find the value representing the uncertainty. This is (2/100) * 300 = 6. Hence, the measurement can be 6 units less than or more than 300.
Therefore, the range of measurements we can make is from (300 - 6) to (300 + 6). This results in a range of 294 to 306.
This concept is grounded in accuracy and precision. Accuracy describes the close proximity of a measurement to a specific value, while precision relates to the consistency of output using the same measurement process.
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How will i solve this equation, 3m/4 - m/12 = 7/8 step by step?
Answers
Answer:
m = 21/16 or 1.325
Step-by-step explanation:
1. 9m/12 - m/12 = 7/8 (find common denominator)
2. 8m/12 = 7/8 (subtract)
3. 64m = 84 (cross multiply)
4. m = 84/64 (solve for m)
5. m = 21/16 (simplify fraction)
~1.325
The value of m is 21/16 or 1.3125.
Given,
3m/4 - m/12 = 7/8
We have to solve for m step by step.
We have,
3m/4 - m/12 = 7/8
Step 1.
Find LCM between 4 and 12 and make 3m/4 and m/12 into one fraction.
LCM of 4 and 12 = 12
( 3 x 3m - m ) / 12 = 7 / 8
( 9m - m ) / 12 = 7 / 8
8m / 12 = 7 / 8
Step 2.
Multiply both sides by 12.
12 x 8m/12 = 12 x 7/8
8m = ( 12 x 7 ) / 8
8m = 84 / 8
Step 3.
Dividing 8 into both sides.
8m/8 = 84 / (8 x 8)
m = 84 / 64
m = 4 x 21 / 4 x 16
m = 21 / 16 or m = 1.3125
Thus the value of m is 21/16 or 1.3125.
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if a scale factor is grater than 1, then your figure gets
Answers
Answer:
multiplied
Step-by-step explanation:
Answer:
If a scale factor is greater than 1, then your figure gets bigger.
Step-by-step explanation:
For scale factors, you are multiplying the scale factor to get the desired outcome. If the scale factor is greater than 1, you are multiplying by a whole number, which would be ≥ the original number. If the scale is 1, then it would be = too the original number. If the scale factor is a fraction, then the figure would be scaled down.
~
Use the points shown on the graph to find the slope of the line
Answers
Answer:
-1.4 or -7/5
Step-by-step explanation:
Slope=y2-y1/x2-x1
Your two points are:
(-3,2) and (2,-5)
1) Plug in the values into the slope formula:
(-5-2)/(2--3)
2) Simplify:
-7/5
3) Write as decimal: - Optional
-1.4
The slope of the linear equation in the graph is -7/5.
How to find the slope of the line?If a linear equation passes through two points (x₁, y₁) and (x₂, y₂), then the slope of the line is:
a = (y₂ - y₁)/(x₂ - x₁)
In the graph we can see the two points (-3, 2) and (2, -5)
Replacing that in the formula for the slope we will get:
a = (-5 - 2)/(2 + 3) = -7/5
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pls help me out least question :)
Answers
Answer:
A
Step-by-step explanation:
PLEASE HELP which statement is true about the system x-3y=5 and y=x-7
A. (8,1) is NOT a solution to either equation so it is not a solution to the system
B. (8,1) is a solution to one equation but not the other one so it is not a solution to the system
C. (8,1) is a solution to both equations so it is a solution to the system
D. (8,1) is a solution to one equation but not the other one so it is a solution to the system
Answers
Answer: C
Step-by-step explanation:
x-3y=5, y=x-7 *solve it
the answer is (8,1)
so..
C. (8,1) is a solution to both equations so it is a solution to the system
The pair (8,1) satisfies both of the given equations, so it is indeed a solution to the system, making option C correct.
For the first equation:
8 - 3(1) = 5
8 - 3 = 5
5 = 5 (True)
For the second equation:
1 = 8 - 7
1 = 1 (True)
Since both equations are satisfied when x is 8 and y is 1, the pair (8,1) is indeed a solution to both equations and therefore a solution to the system.
Given the function, d(t) = 50t, the variable t represents which of the following? Select all that apply. input output function independent variable dependent variable
Answers
Answer:
Input
Independent variable
Step-by-step explanation:
we know that
Independent variables, are the values that can be changed or controlled in a given model or equation
Dependent variables, are the values that result from the independent variables
we have the function
[tex]d(t)=50t[/tex]
In this problem
This is a proportional relationship between the variables d and t
The function d(t) represent the dependent variable or the output
The variable t represent the independent variable or input
Answer:
Independent variable
Step-by-step explanation:
Given is a function
[tex]d(t) = 50t[/tex]
We have to find the independent and dependent variable in this equation
In scientific analysis, the independent variable is one which is changed to get some results for tests. Dependent variable is one which changes according to changes in independent variable
Here we find the term t is independent as it can be changed independently and d(t) can be analysed for various values of t
Thus the dependent variable [tex]d(t)[/tex] a function of t is tested for various values of independent variable t.
Is this equation an identity?
-5w − 8 = 1 − 2w
Answers
Answer:
-3w = 9
w = -3
yes, it is an identity
9. We measure time in hours.
Suppose 12 noon is represented by the integer 0.
a) Which integer represents 1 P.M. the same day?
b) Which integer represents 10 A.M. the same day?
c) Which integer represents 12 midnight the same day?
d) Which integer represents 10 P.M. the previous day?
Describe the strategy you used to find the integers.
Answers
Answer:
for a
the integer 1 will be represented by 1 pm the same day
for b
-2 will be represented by 10 am
for C:
12 midnight will be represented by 0
for D:
the integer 10 will be represented by that .
Using a number line, integers can be used to represent the following given day time in hours as shown in the diagram below:
a. Integer 1 represents 1 P.M.
b. Integer -2 represents 10 A.M.
c. Integer -12 represents 12 midnight.
d. Integer 10 represents 10 P.M.
Recall:
Integers are numbers that have no fractional parts. They are whole numbers.Integers includes 0, negative, and positive numbers.Integers on a number line has been shown below to illustrate how they can represent measure of time in hours if 12 noon is integer 0.
From the image given showing the integers on a number line, the following integers and their respective day time they represent are:
a. Integer 1 represents 1 P.M.
b. Integer -2 represents 10 A.M.
c. Integer -12 represents 12 midnight.
d. Integer 10 represents 10 P.M.
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What is the combined length of all the pieces Meg measured? Write an equation using a variable to show your work.
Lengths of wire
1 - 3 inches
2 - 5 inches
3 - 6 inches
3 - 7 inches
1 - 9 inches
Answers
Answer:
The combined length is 61 inches
Step-by-step explanation:
we know that
To find out the combined length of all the pieces Meg measured, multiply each measure by the number of pieces and then sum all the values
Let
x -----> the combined length
we know that
we have
1 piece of 3 inches
2 pieces of 5 inches
3 pieces of 6 inches
3 piece of 7 inches
1 piece of 9 inches
so
[tex]x=(1)(3)+ (2)(5)+(3)(6)+(3)(7)+(1)(9)\\x=3+10+18+21+9\\x=61\ in[/tex]
therefore
The combined length is 61 inches
what is the complete factorization of 36y^2 - 1?
Answers
Answer:
(6y + 1) (6y - 1)
Step-by-step explanation:
The binomial can be factored using the difference of squares formula.
:)
Completely validate answer:)
What is 456698 in word form
Answers
Answer:
four hundred and fifty six thousand six hundred and ninety eight
A cardboard box, which weighs 0.6 pounds empty, is filled with 15 bags of beans and a 4-pound bag of rice. the total weight of the box and the contents inside it is 25.6 pounds. One way to represent this situation is with the equation 0.6+15b+4=25.6 . In this situation, what does the solution to the equation represent?
Answers
Answer:
the weight of a bag of beans
Step-by-step explanation:
You have an equation representing the total weight of a box, 15 bags of beans, and a bag of rice. You want to know the meaning of the variable b in the equation ...
0.6 +15b +4 = 25.6
Sum of weightsEach term in the equation is the weight of something.
The first term (0.6) is the weight of the empty box.
The second term (15b) is the weight of 15 bags of beans. In this context, we assume the meaning of 'b' is the weight of 1 bag of beans.
The third term (4) is the weight of a bag of rice.
The term on the right of the equal sign (25.6) is the total of the other weights.
SolutionThe unknown value in the equation is the value of 'b', the weight of a bag of rice. When we solve for that value, we get ...
4.6 +15b = 25.6
15b = 21
b = 21/15 = 7/5 = 1.4
When this value is multiplied by bags, the result is pounds. That means the units of 'b' are "pounds per bag", the weight of one bag of rice.
The solution (b=1.4) represents the weight of one bag of rice.
The solution to the given equation represents the weight of one bag of beans. The variable 'b' represents this weight in the equation, and by solving, we can find this value.
Explanation:The equation 0.6+15b+4=25.6 represents a situation where a cardboard box, which is empty weighs 0.6 pounds, is filled with 15 bags of beans and a 4-pound bag of rice, leading to a total weight of 25.6 pounds. Here, the variable 'b' represents the weight of one bag of beans. To find this value, we rearrange the equation and isolate 'b', leading to the equation b=(25.6-0.6-4)/15. We then calculate the righthand side to get the weight of a bag of beans. The solution to the equation is the weight of one bag of beans.
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Hector got 12 out of 20 words right in a spelling test what percentage did he get wrong
Answers
Answer:
60% is the answer
Step-by-step explanation:
it becomes 3/5 then 6/10 and 6/10 = 60%
Answer:
8%
Step-by-step explanation:
6.) A kennel owner has 168 feet of fencing with which
to enclose a rectangular region. He wants to subdivide
this region into three smaller rectangles of equal
length. If the total area to be enclosed 832 ft-, what are
the possible dimensions of the region?
Answers
Answer:
The possible dimensions of the region are
52 ft by 16 ft
32 ft by 26 ft
Step-by-step explanation:
Let
x -----> the length of the rectangular region
y ----> the width of the rectangular region
we know that
The perimeter of a rectangle is equal to
[tex]P=2(x+y)[/tex]
Remember that
A kennel owner wants to subdivide this region into three smaller rectangles of equal length
so
we also have to take into account the divisions
[tex]P=2(x+y)+2y[/tex]
[tex]P=2(x+2y)[/tex]
we have
[tex]P=168\ ft[/tex]
[tex]168=2(x+2y)[/tex]
simplify
[tex]84=(x+2y)[/tex] -----> [tex]x=84-2y[/tex] -----> equation A
The total area to be enclosed is 832 ft^2
The area is equal to
[tex]A=xy[/tex]
so
[tex]832=xy[/tex] ----> equation B
substitute equation A in equation B
[tex]832=(84-2y)y[/tex]
[tex]832=84y-2y^2[/tex]
[tex]2y^2-84y+832=0[/tex]
Solve the quadratic equation by graphing
The solution are y1=16 ft, y2=26 ft
see the attached figure
For
[tex]y=16\ ft\\x=84-2(16)=52\ ft[/tex]
For
[tex]y=26\ ft\\x=84-2(26)=32\ ft[/tex]
therefore
The possible dimensions of the region are
52 ft by 16 ft
32 ft by 26 ft
To increase an amount by 7% what single multiplier would you use?
Answers
QUESTION:To decrease an amount by 7% what single multiplier would you use?
ANSWER: You want 7% less than 100%, so the answer is (100%-7%)=93% =0.93.
Hope this helped! Enjoy! :)
5. A group of four friends attended a movie togene.
Each friend bought a movie ticket and a bottle o
water. The total they paid was $30. If each movie
ticket cost $5.50, how much did each bottle of
water cost?
Answers
$30-$22=8
8 ÷4=2
Therfore each bottle of water costs $2.00
Number A is 5342. Number B is 11124 greater than A. Number C is 3104 less than B. What is the total value of numbers A,B and C?
Answers
Answer:
B - 16466
C - 13362
total value - 35170
Step-by-step explanation:
to find B add 11124 to 5342 (11124+5342=16466)
to find C subtract 3104 from 16466 (16466-3104=13362)
total value - add them all together