A conjecture and the paragraph proof used to prove the conjecture are shown. Given: angle 2 is congruent to angle 3. Prove: angle 1 and angle 3 are supplementary. A horizontal line. Two rays extend from upper region of the line diagonally down to the left and right and intersect the line forming interior angles labeled as 2 and 3 and an exterior angle labeled as 1. Drag an expression or statement to each box to complete the proof. Put responses in the correct input to answer the question. Select a response, navigate to the desired input and insert the response. Responses can be selected and inserted using the space bar, enter key, left mouse button or touchpad. Responses can also be moved by dragging with a mouse. ∠1 and ∠2 form a linear pair, so ∠1 and ∠2 are supplementary by the Response area. Therefore, m∠1+ Response area = 180° by the definition of supplementary. It is given that ∠2≅ Response area, so m∠2=m∠3 by the Response area. By substitution, m∠1+m∠3=180°, so ∠1 and ∠3 are supplementary by the definition of supplementary. angle congruence postulatelinear pair postulatem∠2m∠3∠3∠2
Answers
The fill up of the missing points are:
∠1 and ∠2 form a linear pair, so ∠1 and ∠2 are supplementary by the Linear Postulate theorem. Therefore, m∠1+m∠2 = 180° by the definition of supplementary. It is given that ∠2≅ ∠3, so m∠2=m∠3 by the Congruence Postulate theorem. By substitution, m∠1+m∠3=180°, so ∠1 and ∠3 are supplementary.What is the angles about?Using the image attached, one can see that m<1 and m<2 creates a kind of linear pair hence one can say they are both supplementary using the law of LINEAR POSTULATE THEOREM.
Based on the fact that the supplementary angles add up to 180 degrees, therefore:
m<1 + m<2 = 180 - will be equation 1
Since the interior angles m<2 and m<3 are known to be equal based on the CONGRUENCE POSTULATE THEOREM. Therefore
m<2 = m<3 --- will be equation 2
Then place eqn. 2 into eqn. 2
m <1 + m <3 = 180
This connote that m<1 and m<3 are supplementary.
Hence, The fill up of the missing points are:
∠1 and ∠2 form a linear pair, so ∠1 and ∠2 are supplementary by the Linear Postulate theorem. Therefore, m∠1+m∠2 = 180° by the definition of supplementary. It is given that ∠2≅ ∠3, so m∠2=m∠3 by the Congruence Postulate theorem. By substitution, m∠1+m∠3=180°, so ∠1 and ∠3 are supplementary.Learn more about the angle from
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Related Questions
What expression is equivalent to (square root)
Answers
Answer:
C.) [tex]x^{\frac{3}{2} } y^{\frac{19}{2} }[/tex]
Step-by-step explanation:
To simplify the expression, you need to:
1.) Rewrite [tex]\sqrt{xy^{3} }[/tex]
-----> [tex]\sqrt{x} = x^{\frac{1}{2} }[/tex]
2.) Distribute the exponents
-----> When an exponent is raised to another exponent, they should be multiplied
3.) Create common denominators
4.) Combine the variables
-----> When two variables with exponents are being multiplied, the exponents should be added
A solid lies between planes perpendicular to the x-axis at x0 and x. The cross-sections perpendicular to the axis on the interval 0x are squares with diagonals that run from the parabola to the parabola. Find the volume of the solid.
Answers
The volume of the solid is 900 cubic unit given that the solid lies between planes perpendicular to the x-axis at x = 0 and x = 19, the cross sections perpendicular to the x-axis on the interval 0 ≤ x ≤ 15 are squares with diagonals that run from the parabola y = - 2√x to the parabola y = 2√x. This can be obtained by finding the area of the square using the length of the diagonal.
What is the volume of the solid?
Given that, diagonals that run from the parabola y = - 2√x to the parabola y = 2√x
The length of the diagonal,D = 2√x - (-2√x)
D = 4√x
Using Pythagoras theorem,D² = s² + s², where s is the side of the square
(4√x)² = 2s²
16x = 2s²
s² = 8x
s² is the area
Area A = 8xThus,
volume V = ∫A dx, 0 ≤ x ≤ 15V = [tex]\int\limits^{15}_0 {8x} \, dx[/tex]
V = [tex]8\int\limits^{15}_0 {x} \, dx[/tex]
V = 4 (15² - 0)
V = 4×225
⇒ V = 900 cubic unit
Hence the volume of the solid is 900 cubic unit given that the solid lies between planes perpendicular to the x-axis at x = 0 and x = 19, the cross sections perpendicular to the x-axis on the interval 0 ≤ x ≤ 15 are squares with diagonals that run from the parabola y = - 2√x to the parabola y = 2√x.
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Disclaimer: The question was given incomplete on the portal. Here is the complete question.
Question: A solid lies between planes perpendicular to the x-axis at x = 0 and x = 19. The cross sections perpendicular to the x-axis on the interval 0 ≤x ≤ 15 are squares with diagonals that run from the parabola y = - 2√x to the parabola y = 2√x. Find the volume of the solid.
provide the answer by sketching the graph on the image below
Answers
The attached graph is the graph of the function f(x) = -2sin(x)
How to sketch the graph?The function is given as:
f(x) = -2sin(x)
The above function is a sine function that has an amplitude of 2
Next, we plot the graph of the sine function f(x) = -2sin(x) using a graphing calculator
See attachment for the graph of f(x) = -2sin(x)
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Find the term that must be added to the equation x2+6x=7 to make it into a perfect square.
Answers
To make x² + 6x = 7 a perfect square, we add 16 to the equation.
In the question, we are asked for the term that must be added to the equation x² + 6x = 7, to make it into a perfect square.
The given equation can be shown as:
x² + 6x = 7,
or, x² + 6x - 7 = 0.
To make it a perfect square, we need to find the b² term as per the 2ab term for the formula, (a + b)² = a² + 2ab + b², where a is x.
This can be shown as:
x² + 6x - 7 = 0,
or, x² + 2(x)(3) - 7 = 0, where we get b = 3.
Thus, b² = 3² = 9, can be obtained by adding 16 to the equation, as -7 + 16 = 9.
Thus, we add 16 to both sides of the equation, to get:
x² + 2(x)(3) - 7 + 16 = 16,
or, x² + 2(x)(3) + 9 = 16,
or, (x + 3)² = 16, which gives us the required perfect square.
Thus, to make x² + 6x = 7 a perfect square, we add 16 to the equation.
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Can someone help me please
Answers
The simplified form of the expression is x-4 + 2/x-2
Synthetic division of equationGiven the following fraction below
f(x) = x^2 + 2x - 6/x-2
Using the long division as shown below;
x + 4
x-2 | x^2 + 2x - 6
x^2 - 2x
_________________
4x - 6
4x - 8
___________________
2
Hence the simplified form of the expression is x-4 + 2/x-2
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When given an inverse variation, how do you find k?
Answers
Which is the equation of the function? f(x) = 3|x| + 1 f(x) = 3|x – 1| f(x) = 1/3|x| + 1 f(x) = 1/3|x – 1|
Answers
The equation of the function is −3<x<1. See the explanation below.
What is the solution to the above?Given the graph of function f is a parabola,
Thus, equation of parabola is y=(x+3)(x+1)
⇒y=x² +4x+3
⇒y−3+2²
= x²+2× x ×2+2²
⇒y+1=(x+2)²
We can rewrite this as
(x+2)² =4× (1/4) ×(y+1)
Comparing the above equation to the equation of a parabola, (x−h)² =4a(y−k), where (h,k) is the coordinates of vertex of parabola, we have,
(h,k)≡(−2,−1)
Hence, the x coordinate of the vertex is −2 which lies in the interval −3<x<1
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(‼️‼️I WILL MARK BRAINLIEST PLEASE HELP‼️‼️)Dilate the figure by the scale factor. Then enter
the new coordinates.
K = 5
(-3,-1)
A
(-1,-4) C
B(2,-2)
A' ([?], [ ])
B' ([ ], [ ])
C' ([ ], [ ])
Answers
Answer:
A' (-15, -5)
B' (10, -10)
C' (-5, -20)
Answer:
A ' (-15, -5)
B ' (10, -10)
C ' (-5, -20)
Step-by-step explanation:
The scale factor is [tex]K=5[/tex]. This tells us to multiply each coordinate, of each point, by the scale factor (5) to get the dilated points.
Point A is at [tex](-3,-1)[/tex] and moves to [tex]A ' (-15, -5)[/tex] after multiplying the x and y coordinates by 5. The same applies to points B and C as well.
Point B moves from [tex](2,-2)[/tex] to [tex]B' (10,-10)[/tex] because [tex]2*5=10[/tex] and [tex]-2*5=-10[/tex]. This also means that Point C moves from [tex](-1,-4)[/tex] to [tex]C' (-5,-20)[/tex] because [tex]-1*5=-5[/tex] and [tex]-4*5=-20[/tex].
The dilation rule can be written as [tex](x, y)[/tex] → [tex](5x, 5y)[/tex]
As a result of the dilation, triangle A'B'C' has sides that are 5 times longer compared to the corresponding sides of triangle ABC.
Simplify 7 1/5 5 A B C D
Answers
Answer:
C. 7
Step-by-step explanation:
The answer is 7. Use the power of a power property. To use it you have to multiply the power inside the parenthesis to the one outside of the parenthesis. 1/5 * 5 = 1. Since the power is 1, you do not need to write the power.
Hope this helps!
What is the solution of StartFraction negative 8 Over 2 y minus 8 EndFraction = StartFraction 5 Over y + 4 EndFraction minus StartFraction 7 y + 8 Over y squared minus 16 EndFraction?
Answers
The solution of the fraction given as -8/(2y - 8) = 5/(y + 4) - (7y + 8)/(y² - 16) is determined as 4 or - 0.25.
What is fraction?A fraction represents a part of a whole or, more generally, any number of equal parts.
A fraction can also be described as how many parts of a certain size there are, in a given whole.
Solution of the fractionThe fraction given can be written as follows;
-8/(2y - 8) = 5/(y + 4) - (7y + 8)/(y² - 16)
simplify as follows;-8/(2y - 8) = 5/(y + 4) - (7y + 8)/(y - 4)(y+4)
-8/(2y - 8) = [5(y - 4) - (7y + 8)] /(y-4)(y + 4)
-8/(2y - 8) = (5y - 20 + 7y + 8)/(y-4)(y + 4)
-8/(2y - 8) = (12y - 12)/(y-4)(y + 4)
cross and multiply both sides of the equation;
-8((y-4)(y + 4)) = (12y - 12)(2y - 8)
-8(y² - 16) = 24y² - 96y - 24y + 96
-8y² + 128 = 24y² - 120y + 96
0 = 32y² - 120y - 32
solve the quadratic equation using formula method;
a = 32, b = -120, c = - 32
y = 4 or -0.25
Thus, the solution of the fraction given as -8/(2y - 8) = 5/(y + 4) - (7y + 8)/(y² - 16) is determined as 4 or - 0.25.
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y=6
for the eqution
[tex]\frac{-8}{2y-8} =\frac{5}{y+4} -\frac{7y+8}{y^{2}-16 } \\[/tex]
Which are correct representations of the inequality –3(2x – 5) < 5(2 – x)? Select two options.
x < 5
–6x – 5 < 10 – x
–6x + 15 < 10 – 5x
A number line from negative 3 to 3 in increments of 1. An open circle is at 5 and a bold line starts at 5 and is pointing to the right.
A number line from negative 3 to 3 in increments of 1. An open circle is at negative 5 and a bold line starts at negative 5 and is pointing to the left.
Answers
The correct statements are –6x + 15 < 10 – 5x and a number line from negative 3 to 3 in increments of 1. An open circle is at 5 and a bold line starts at 5 and is pointing to the right.
Inequality expressionInequality are expressions not separated by an equal sign. Given the inequality expression:
–3(2x – 5) < 5(2 – x)
Expand
-6x +15 < 10 - 5x
Collect the like terms
-6x+5x < 10 - 15
-x <-5
x > 5
Hence the correct statements are –6x + 15 < 10 – 5x and a number line from negative 3 to 3 in increments of 1. An open circle is at 5 and a bold line starts at 5 and is pointing to the right.
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The table gives an inequality and a number to multiply both sides of the inequality by. Identify the new, true inequality.
A: (-16 > -4) (-16 < -4) (-16 = -4)
B: (40 > 8) (40 < 8) (40 = 8
C: (-45 > 15) (-45 < 15) (-45 =15)
D: (35 > -20) (35 < -20) (35 = -20)
Multiplying both sides of an inequality by a negative number (does not change) (reverses) the inequality symbol.
Answers
Multiplying both sides of an inequality by a negative number reverses the inequality symbol.
How to determine the true inequalities?The table of values is given as:
A: (-16 > -4) (-16 < -4) (-16 = -4)
B: (40 > 8) (40 < 8) (40 = 8
C: (-45 > 15) (-45 < 15) (-45 =15)
D: (35 > -20) (35 < -20) (35 = -20)
In the above list of inequalities, the true inequalities are
-16 < -4 --- because -16 is less than -4
40 > 8 --- because 40 is greater than 8
-45 < 15 --- because -45 is less than 15
35 > -20 --- because 35 is greater than -20
Lastly, when an inequality is multiplied or divided by a negative number, the inequality sign changes
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Answer:
-16 < -4
40 > 8
-45 < 15
35 > -20
Reverses
Step-by-step explanation:
hope this helps
The function f has the property that, for all x, 5(f)x=f(5x). If f(20)=40, what is the value of f(4)?
Answers
Using the given property, we conclude that:
f(4) = 8
What is the value of f(4)?
We know that our function has the property:
5*f(x) = f(5*x)
Now, we also know that:
f(20) = 40
Notice that we can rewrite:
f(20) = f(5*4)
Using the above property, we know that:
f(20) = f(5*4) = 5*f(4) = 40
Using the last part:
5*f(4) = 40
f(4) = 40/5 = 8
f(4) = 8
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Solve the equation below by factorising.
2m^2- 11m + 5 = 0
Answers
Answer:
[tex]m_{1} =1/2\\m_{2} =5[/tex]
Step-by-step explanation:
[tex]2m^{2} -11m+5=0[/tex]
[tex](2m-1)(m-5)=0[/tex]
[tex]2m-1=0\\2m=1\\m_{1} =1/2[/tex]
[tex]m-5=0\\m_{2} =5[/tex]
Hope this helps
HELPPP PLEASEEEE
Other than translation, what transformation is used to create this frieze pattern?
horizontal reflection
glide reflection
vertical reflection
90° rotation
Answers
Answer:
I think glide reflection
Step-by-step explanation:
a certain video on yt had explained the examples of similar look alike this picture
12.) tan L
A)
C)
√6
2
√6
w
L
√
V10
B)
D)
2
√6
√10
2
√10
M
N
Answers
Answer: [tex]\frac{\sqrt{6}}{2}[/tex]
Step-by-step explanation:
By the Pythagorean theorem,
[tex]2^2 + (MN)^2 = (\sqrt{10})^2\\\\4+(MN)^2 = 10\\\\(MN)^2 = 6\\\\MN=\sqrt{6}\\\\\implies \tan L=\frac{\sqrt{6}}{2}[/tex]
How would I solve this?? My math course didn't teach me anything related to this sort of problem..
Answers
Answer:
See below
Step-by-step explanation:
The larger is
7-6 = 1 unit bigger than the smaller....and this unit = 24 gallons
each unit is 24 gallons
larger barrel holds 24 * 7 = 168 gal
smaller barrel holds 24 * 6 = 144 gal
Answer:
Small barrel=144 large barrel=168
Step-by-step explanation:
The ratio is 6 to 7 so lets assign x as a factor.
6x=Small barrel (S)
7x=Large barrel (L)
7x-6x=x
x is the difference so x is 24
x=24
6*24=144=S
7*24=168=L
help please its khan academy
Answers
i’m not sure if this is correct but it seems like it
help me please 10 POINTS
Answers
x/2+y=4/5. x+y/2=7/10
Answers
Answer:
x = 2/5
y = 3/5
Step-by-step explanation:
**Disclaimer** Hi there! I assumed the question to be a system of equations. The following answer is a method for solving a system of equations. Thus, if it is not, please let me know and I will modify my answer.
Given information:
[tex]\frac{x}{2}+y=\frac{4}{5}[/tex]
[tex]x+\frac{y}{2} =\frac{7}{10}[/tex]
Eliminate fractions by multiplying 10 on both sides of the first equation:
[tex]10*\frac{x}{2}+10*y=10*\frac{4}{5}[/tex]
[tex]5x+10y=8[/tex]
Eliminate fractions by multiplying 10 on both sides of the second equation:
[tex]10*x+10*\frac{y}{2} =10*\frac{7}{10}[/tex]
[tex]10x+5y=7[/tex]
Current system:
[tex]5x+10y=8[/tex]
[tex]10x+5y=7[/tex]
Multiply the second equation by 2:
[tex]5x+10y=8[/tex]
[tex]20x+10y=14[/tex]
Subtract the first equation from the second equation:
[tex](20x+10y)-(5x+10y)=14-8[/tex]
[tex]20x+10y-5x-10y=6[/tex]
[tex](10y-10y)+20x-5x=6[/tex]
[tex]0+15x=6[/tex]
[tex]\boxed{x=\frac{2}{5} }[/tex]
Substitute the x value back to one of the equations to get the y value:
[tex]x+\frac{y}{2} =\frac{7}{10}[/tex]
[tex](\frac{2}{5}) +\frac{y}{2} =\frac{7}{10}[/tex]
[tex](\frac{2}{5}) +\frac{y}{2}-\frac{2}{5} =\frac{7}{10}-\frac{2}{5}[/tex]
[tex]\frac{y}{2} =\frac{3}{10}[/tex]
[tex]\frac{y}{2}*2 =\frac{3}{10}*2[/tex]
[tex]\boxed{y=\frac{3}{5} }[/tex]
Hope this helps!! :)
Please let me know if you have any questions
The answer is x = 2/5, y = 3/5 or (2/5, 3/5)
First, in order to avoid fractional values during calculation, multiply both equations by 10 to simplify.
10 (x/2 + y) = 10 (4/5) ⇒ 5x + 10y = 810 (x + y/2) = 10 (7/10) ⇒ 10x + 5y = 7Multiply the 1st equation by 10 and 2nd equation by 5.
3. 10 (5x + 10y) = 10 (8) ⇒ 50x + 100y = 80
4. 5 (10x + 5y) = 5 (7) ⇒ 50x + 25y = 35
Subtract : 3rd equation - 4th equation
50x + 100y - 50x - 25y = 80 - 3575y = 45y = 3/5Now, substitute for x in the 1st equation to find y.
x/2 + 3/5 = 4/5x/2 = 1/5x = 2/5Which table represents a linear function? Which quadratic function is represented by the graph?
Answers
The first table is a quadratic function while the second table is a linear function.
How to Interpret Function Tables?
1) For the first table, we have;
x y
0 5
1 0
2 -3
3 -4
4 -3
x = 2 and x = 4 have same value of y = -3 and as such it will be a Quadratic Function.
y = x² - 6x + 5
2) For the second table, we have;
x y
2 5
5 14
6 17
8 23
10 29
This table is a Linear function because slope is same and equal to 3 all through. Thus, the equation is y = 3x - 1
3) For the third table, we have;
x y
-3 8
-2 4
-1 2
0 1
1 0.5
This is an exponential function because equation can be modelled by;
y = 2⁻ˣ
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If light travels at 10,000 km in 3.0 x 10² seconds,
how long will it take light to travel one meter?
(1 km = 1 x 10³ m)
PLEASE HELP ME
Answers
Answer:
1000xm
Step-by-step explanation:
1 meter = 3.2808 feet, hence. 9.8424 x 10^8 feet in 1 second. 1 foot in x seconds. hence it takes 1 / (9.8424 x 10^8) = 0.10168 x 10^(-8) seconds. ➡️1km = 1000xm⬅️
It will take light approximately 3.0 x 10⁻⁵ seconds to travel one meter.
To find out how long it will take light to travel one meter, we need to convert the given distance of 10,000 km to meters and the time of 3.0 x 10² seconds to seconds.
Given:
Distance traveled by light = 10,000 km
Time taken by light = 3.0 x 10² seconds
To convert km to meters, we know that 1 km = 1 x 10³ m, so:
10,000 km = 10,000 x 1 x 10³ m = 1 x 10⁷ m
Now, we can find the time taken to travel one meter by dividing the total time by the total distance:
Time taken to travel one meter = Total time / Total distance
Time taken to travel one meter = (3.0 x 10² seconds) / (1 x 10⁷ m)
To simplify the expression, we can cancel out one factor of 10 from the numerator and denominator:
Time taken to travel one meter = (3.0 x 10) / (1 x 10⁶ m)
Now, we get the final answer:
Time taken to travel one meter = 3.0 x 10⁻⁵ seconds
So, it will take light approximately 3.0 x 10⁻⁵ seconds to travel one meter.
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What numbers are zeros of g(x) = x^2 - 2x - 4? take your time if you need to!
Answers
Answer:
[tex]x = 1 + \sqrt5, x = 1 - \sqrt5[/tex]
Step-by-step explanation:
Hello!
We can solve the quadratic by using the quadratic formula.
Standard form of a quadratic: [tex]ax^2 + bx + c = 0[/tex]
Quadratic Formula: [tex]x = \frac{-b\pm\sqrt{b^2 - 4ac}}{2a}[/tex]
Given our Equation: [tex]g(x) = x^2 - 2x - 4[/tex]
a = 1b = -2c = -4Plug the values into the equation and solve.
Solve[tex]x = \frac{-b\pm\sqrt{b^2 - 4ac}}{2a}[/tex][tex]x = \frac{-(-2)\pm\sqrt{(-2)^2 - 4(1)(-4)}}{2(1)}[/tex][tex]x = \frac{2\pm\sqrt{4 +16}}{2}[/tex][tex]x = \frac{2\pm\sqrt{20}}{2}[/tex][tex]x = \frac{2\pm\sqrt{4 * 5}}{2}[/tex][tex]x = \frac{2\pm(\sqrt4 * \sqrt5)}{2}[/tex][tex]x = \frac{2\pm2\sqrt5}{2}[/tex][tex]x = 1 + \sqrt5, x = 1 - \sqrt5[/tex]A store sells about 30 pants each week for Nu 800 each. The owner expects to lose one sale each week for every increase in price of Nu 40. a) Write an expression to represent the i) new price of a pant after n Nu 40 price increases. ii) expected number of pants that will be sold weekly after n price increases. b) Write a function to represent the expected weekly sales as a function of the number of price increases of Nu 40. c) Use the function to determine the price that will maximize totally sales.
Answers
The new price after the price increase of Nu 40 will be Nu 840.
How to calculate the price?The price of a pant after n Nu 40 price increases will be:
= 800 + 40
= 840
The expected weekly sales as a function of the number of price increases will be:
= n - 1) × 800
= (30 - 1) × 800
= 29 × 800
= 23200
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urgent please help!!!!! will give brainliest
Answers
Answer: Read the explanation
Step-by-step explanation:
If the points of a figure are all moved the same, they are congruent.
Point A is moved 9 points right, and 7 points down.
Point B is moved 9 points right, and 7 points down.
Point C is moved 9 points right, and 7 points down.
So, they are congruent.
A prism has volume 100cm^3 and length 8cm. If the cross-section is an equilateral triangle, find the length of a side of the triangle.
Answers
Answer:
5.373 cm
Step-by-step explanation:
Divide the volume by the length to find the area of the equilateral triangle
100/8 = 12.5
Area of equilateral triangle = sqrt(3) / 4 * s^2 = 12.5
s^2 = 12.5 *4 / sqrt3
s = 5.373 cm
There are 20 red and blue marbles in a bag. s marbles are red how many are blue?
Answers
Answer:
Step-by-step explanation:
Step-by-step explanation:
15 r blue marbles
20- 5 = 15
What are the solutions of the equation (2x 3)2 8(2x 3) 11 = 0? use u substitution and the quadratic formula to solve.
Answers
Answer:
Step-by-step explanation:
Solve the equation by completing the square
Answers
Answer:
Below.
Step-by-step explanation:
x^2 + 4x = 18
x^2 + 4x + (2)^2 = 15 + 2^2
x^2 + 4x + 4 = 18 + 4
(x + 2)^2 = 22
x + 2 = +/- √22
x = -2 + √22 and x = -2 + √22
x = 2.7 and -6.7 to nearest tenth.
PLEASE HELP IM STUCK
Answers
Step-by-step explanation:
[tex] \frac{y2 - y1 }{x2 - x1} = \frac{3 - - 2}{5 - 0} = \frac{5}{5} = 1[/tex]
Hey there!
Here, given;
The points are; (0,-2) and (5,3).
Now, simply use slope formula.
slope(m)
y?-yl
7
^ 4.2
Put all values.
3+2
m
Simplify them to get answer.
3
Therefore the slope is 1.
Hope it helps…