Triangles A B C and N M Q are shown. Sides B C and N M are congruent. Angles A B C and Q N M are congruent. Angles B C A and N M Q are both right angles.
Nessa proved that these triangles are congruent using ASA. Roberto proved that they are congruent using AAS. Which statement and reason would be included in Roberto’s proof that was not included in Nessa’s proof?
Given: AngleB ≅ AngleN; BC ≅ NM; AngleC is right; AngleM is right
Prove: TriangleABC ≅ TriangleQNM
AngleA ≅ AngleQ because of the third angle theorem.
AB ≅ QN because they are both opposite a right angle.
BC ≅ NM because it is given.
AngleC ≅ AngleM because right angles are congruent.
Answers
What would be included to prove both triangles are congruent by the AAS theorem is: B. AB ≅ QN because they are both opposite a right angle.
What is the AAS Congruence Theorem?The AAS congruence theorem states that two triangle are congruent if both have two pairs of corresponding congruent angles and a pair of non-included corresponding congruent sides.
In the image given, since AB and QN both lie opposite a right triangle, then they are congruent to each other.
Therefore, to prove both triangles are congruent by AAS theorem, what would be included is: B. AB ≅ QN because they are both opposite a right angle.
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Answer:
AngleA ≅ AngleQ because of the third angle theorem
Step-by-step explanation:
right on edge
Related Questions
Triangle A B C has centroid G. Lines are drawn from each point through the centroid to the midpoint of the opposite side to form line segments A F, B D, and C E. The length of line segment A G is 19 x + 14 and the length of line segment D G is 9 x + 2.
G is the centroid of triangle ABC.
What is the length of GF?
units
Answers
A triangle is a three-edged polygon with three vertices. It is a fundamental form in geometry. The length of GF is 254 units.
What is a triangle?A triangle is a three-edged polygon with three vertices. It is a fundamental form in geometry. The sum of all the angles of a triangle is always equal to 180°.
Since a centroid of a triangle divides the median into a ratio of 2:1. Therefore, the ratio of AG: DG is,
AG / DG = 2/1
(19x+14)/(9x+20) = 2/1
19x + 14 = 18x + 40
19x - 18x = 40 - 14
x = 26
Assuming the triangle is an equilateral triangle, therefore, the length of GF will be,
GF = DG = 9x+20
GF = DG = 9(26) + 20
GF = 254 units
Hence, the length of GF is 254 units.
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Answer: 26 units
Step-by-step explanation: Trust Me!!!
The answer is correct on Edge. I just got it right!
A parabola with a vertex at (0,0) has a focus along the negative part of the x-axis.
Which could be the equation of the parabola?
y2 = x
y2 = –2x
x2 = 4y
x2 = –6y
Answers
The equation of the parabola in standard form whose vertex is (0, 0) and a focus along the negative part of the x-axis is equal to x² = - 6 · y. (Correct choice: D)
How to determine the best equation of the parabola based on given characteristics
In accordance with the statement, we find that the parabola has its vertex at the origin, therefore it is horizontal and its vertex constant (C) is negative as its focus is in the negative part of the x-axis. Therefore, the equation of the parabola in standard form has the following form:
x² = C · y, for C < 0. (1)
In consequence, the equation of the parabola in standard form whose vertex is (0, 0) and a focus along the negative part of the x-axis is equal to x² = - 6 · y.
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Which of the following is correct equation for the trend line in the scatter plot? A. Y= 2/5 x -2 B. Y= 5x-1 C. Y= 5x +5 D. Y= -x+5
Answers
The equation for the trend line in the scatter plot will be Y= 5x-1. Option B is correct.
What is a scatter plot?In an effort to demonstrate how much one variable is influenced by another, scatter plots are used to depict data points on a horizontal and vertical axis.
When there is no connection between two variables, it is called a zero correlation. For instance, there is no correlation between IQ level and the quantity of tea consumed.
The graphs are attached in the attachment.
The equation for the trend line in the scatter plot will be Y= 5x-1.
Hence, option B is correct.
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Write each expression as a difference.
a+5
Answers
The equivalent expression of a + 5 is -(-a - 5)
How to rewrite the expression?The expression is given as:
a + 5
Multiply by 1
1 * (a + 5)
Express 1 as -1 * -1
-1 * -1 * (a + 5)
Open the bracket
-1 * (-a - 5)
This gives
-(-a - 5)
Hence, the equivalent expression of a + 5 is -(-a - 5)
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write the following linear equations into the standard form Ax+ by=c
DETERMINE the values of A,B and C.
Answers
Answer:
Step-by-step explanation:
1). 7x - 2y = 5 , A = 7 , B = 2 , C = 5
2). 4x - y = 1 , A = 4 , B = - 1 , C = 1
3). 5x - 2y = 3 , A = 5 , B = - 2 , C = 3
4). 4x - 3y = 3 , A = 4 , B = - 3 , C = 3
5). 2x + y = 15 , A = 2 , B = 1 , C = 15
Two cyclists start at the same time from opposite ends of a course that is 45 miles long. One cyclist is riding at 14 mph and the second cyclist is riding at 16 mph. How long after they begin will they meet
Answers
If the distance is 45 miles and speed of both cyclist is 14 and 16 miles per hour then they will take time of 1.5 hour to meet.
Given First cyclist is riding at 14 miles per hour and second at 16 miles per hour. The distance is 45 miles.
We know that speed is the distance covered by an object in a particular period of time.
Speed=distance/time.
It is expressed as kilometers per hour or miles per hour, etc.
If both riders are riding towards each other then the speed will be 16+14 =30 miles per hour.
Distance=45 miles.
Time =distance/speed
=45/30
=1.5
Hence if first cyclist is riding at 14 miles per hour and second is riding at 14 miles per hour and the distance is 45 miles then they will meet after 1.5 hours.
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The total cost of owning a home for 6 years is $120,000. The
rent for a comparable home is $1500 per month. If you had invested the
down payment for the home, you could have earned $10,000 in interest.
After 6 years, how much more, in dollars, is the cost of owning compared
to the cost of renting?
Answers
After 6 years, the difference between owning the house and renting is $12,000.
What is the difference in owing and renting the house?
The first step is to determine the total cost of renting the house for six years.
Total cost of renting the house = rent per month x number of years x number of months in a year
1500 x 12 x 6 = $108,000
Difference = cost of owning - cost of renting
$120,000 - $108,000 = $12,000
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2/5 (1/3x - 15/8) - 1/3(1/2 - 2/3x)
Answers
Your question presented was: [tex]\frac{2}{5} (\frac{1}{3} x-\frac{15}{8} )-\frac{1}{3} (\frac{1}{2} -\frac{2}{3}x)[/tex]
Okay, lets distribute this problem and break it into two parts. We will distribute 2/5 and -1/3 to the numbers in parenthesis. This is the distributive property.
Step 1.
[tex]\frac{2}{5} (\frac{1}{3} x-\frac{15}{8} )[/tex] when distributed is [tex]\frac{2}{15} x - \frac{30}{40}[/tex]
Please note that -1/3 can be rewritten as + -1/3. So you must distribute the negative.
Step 2.
[tex]\frac{-1}{5} + \frac{2}{9} x[/tex]
So..lets put the 2 parts of the equation together
[tex]\frac{2}{15} x - \frac{30}{40}[/tex] + [tex]\frac{-1}{5} + \frac{2}{9} x[/tex] can be simplified by getting the common denominator.
You can only add like terms, so those fractions with x can only be combined with x.
Step 3.
Lets reformat while we're at it
[tex]\frac{6}{45} x + \frac{10}{45} x -\frac{30}{40} -\frac{8}{40}[/tex]
We got 45 because the LCM (Lowest Common Multiple) of 15 and 9 was 45. We multiplied both sides of the fraction by 3 for 2/15x and we multiplied by 5 on both parts of the fraction for 2/9x.
Now we combine.
Step 4.
[tex]\frac{16}{45}x-\frac{38}{40}[/tex]. We can still simplify!
Step 5.
-38/40 can be simplified by a common factor, 2! So our final answer is
[tex]\frac{16}{45}x-\frac{19}{20}[/tex]
I hope this helps you, heart if it helps.
What is the expression of g(x) when we perform the following sequence of transformations onto the parent function fx=x2+2x:
a) Compress horizontally by a factor of 3 with respect to its axis of symmetry
b) Shift right 1 unit
Answers
The transformed function is:
[tex]g(x) = ( (x + 1)/3 - 2)^2 + 2*( (x + 1)/3 - 2)[/tex]
How to get the function g(x)?
The parent function is:
[tex]f(x) = x^2 + 2x[/tex]
Here the axis of symmetry is at:
[tex]x = -2/2*1 = -1[/tex]
So first we need to apply a horizontal compression by a factor of 3 with respect to the line x = -1.
Here we can, for the moment, define a new variable that is zero when x = -1, let's define:
z = x + 1.
x = z - 1
Writing our function in terms of z, we get:
[tex]f(z) = (z - 1)^2 + 2*(z - 1)[/tex]
Now we can apply a compression by a factor of 3 around the origin. Then we have:
[tex]f(z/3) = (z/3 - 1)^2 + 2*(z/3 - 1)[/tex]
Returning to the original variable, we have:
[tex]f((x+1)/3) = ( (x + 1)/3 - 1)^2 + 2*( (x + 1)/3 - 1)[/tex]
Now we want to shift it one unit to the right, then we have:
g(x) = f( (x + 1)/3 - 1)
Replacing the actual function we get:
[tex]g(x) = f((x+1)/3 - 1) = ( (x + 1)/3 - 1 - 1)^2 + 2*( (x + 1)/3 - 1 - 1)\\\\g(x) = ( (x + 1)/3 - 2)^2 + 2*( (x + 1)/3 - 2)[/tex]
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2/x+3/y=9/x;4/x+9/y=21/xy(x=0,y=0)
Answers
The solution to the equations 2/x+3/y=9/xy; and 4/x+9/y=21/xy are x = 1, and y = 3.
What is a linear equation?It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.
If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.
The complete question is:
Solve for x and y:
2/x+3/y=9/xy; and 4/x+9/y=21/xy x ≠ 0, y ≠ 0
We have two equations:
2/x+3/y=9/xy;
4/x+9/y=21/xy
Solving substitution method:
[tex]\rm \dfrac{4}{\dfrac{9-2y}{3}}+\dfrac{9}{y}=\dfrac{21}{\dfrac{9-2y}{3}y}[/tex]
y = 3
x = 1
Thus, the solution to the equations 2/x+3/y=9/xy; and 4/x+9/y=21/xy are x = 1, and y = 3.
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can anyone help me with this problem?
Answers
Answer:
a1
Step-by-step explanation:
Just add the numerators if both fractions to get: a + 1 = a1
Answer:
a+1
Step-by-step explanation:
Well if you have the same denominator, which in this case you do, it's equal to b, you can simply add the numerators. This gives you the expression [tex]\frac{a+1}{b}[/tex] so the numerator is a+1
What is the solution to the equation startfraction negative 3 d over d squared minus 2 d minus 8 endfraction startfraction 3 over d minus 4 endfraction = startfraction negative 2 over d 2 endfraction?
Answers
Answer: C / d=1
Step-by-step explanation:
Just did it
Answer: C
Step-by-step explanation: Just took the quiz
Davion wants to buy 4 tickets to a basketball game. He sees that there is a discount for$25 off his entire purches at check out, so the tickets would him $215 before tax. what was the original price of each tickets?
Answers
The original price of each tickets is; $60 per ticket
What is the original Price?We are told that $215 is what it costs after the discount. Thus, we add the amount taken off, back on to get;
$215 + $25 = $240
Now, since he wants to buy 4 tickets, then we divide the amount above by 4 to get the cost of each individual ticket.
Original Cost of each individual ticket = 240/4 = $60
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Question 3 of 10 True or False? A circle could be circumscribed about the quadrilateral below.
95, 80, 85, 100
Answers
True, a circle can be circumscribed about the quadrilateral described in the task content.
What is the condition to circumscribe a circle about a quadrilateral?It follows from the task content that quadrilateral in discuss has angles; 95, 80, 85 and 100.
By convention, it follows that circles can be circumscribed about only cyclic quadrilaterals in which case their opposite angles are supplementary. Hence, since opposite angles of the quadrilateral are supplementary (i.e amount to 180). Then, True, the circle can be circumscribed about the quadrilateral.
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What is the inverse of the function f(x) = 1/9x+2
Answers
Hello,
f(x) = 1/9x + 2 ⇔ y = 1/9x + 2 ⇔ 1/9x = y - 2 ⇔ x = 9(y - 2)
x = 9y - 18
⇒ f⁻¹(x) = 9x - 18
[tex]\frak{Hi!}[/tex]
[tex]\orange\hspace{300pt}\above3[/tex]
If we have a function, we can find its inverse if we do the
following-:
[tex]\tiny\bullet[/tex] replace f(x) with y.
[tex]\boldsymbol{\sf{y=\displaystyle\frac{1}{9}x+2}}[/tex]
[tex]\tiny\bullet[/tex] switch the places of x and y
[tex]\boldsymbol{\sf{x=\displaystyle\frac{1}{9}y+2}}}[/tex]
[tex]\bullet[/tex] solve for y
[tex]\boldsymbol{\sf{x\times9=\frac{1}{9}y\times9+2\times9}}[/tex]
[tex]\boldsymbol{\sf{9x=y+18}}[/tex]
[tex]\boldsymbol{\sf{-y=-9x+18}}[/tex]
[tex]\boldsymbol{\sf{y=9x-18}}}[/tex]
[tex]\boldsymbol{\sf{f(x)^{-1}=9x+18}}[/tex]
[tex]\orange\hspace{300pt}\above3[/tex]
What is the least possible value of (x+4)(x+5)+[tex]\frac{10^{6} }{x(x+9)} ,[/tex] where x is a positive real number?
Answer choice: 2017, 2018, 2019, 2020, 2021
Explain in High School Mathematics terminology. Do not attempt if your not 98% sure
Answers
The least possible value of the expression is 2020
How to determine the value of the expression?The expression is given as:
[tex](x + 4)(x + 5) + \frac{10^6}{x(x + 9)}[/tex]
Next, we plot the expression on a graph (see attachment)
From the attached graph, the minimum value of the expression is 2020 under the domain of x > 0
Hence, the least possible value of the expression is 2020
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if x=2 y=4 a=3 b=6 and c=2 find the value of
xty=5
2a+5b-4c
(4c-3b)a÷2
5x2square+4y2squre-5
Answers
Answer:
I didnt know but i worked it out and searched it up and i got this
Step-by-step explanation:
(2a+4c-5b+2a+5b-4c)
Find the length of UC
Answers
Answer:
18
Step-by-step explanation:
Entire length =105 + 82 =187
subtract 22
subtract 96
subtract 51 result =18
4. Write the trinomial represented by each rectangle of algebra tiles. Then, determine the
dimensions of each rectangle
Answers
The trinomial represented by the algebraic tiles is x^2 + 4x + 3
How to determine the trinomial?On the horizontal axis, we have:
1 row under the big square.
This represents x + 1
On the vertical axis, we have:
3 columns beside the big square.
This represents x + 3
So, we have:
(x + 1) * (x + 3)
Expand
(x + 1) * (x + 3) = x^2 + x + 3x + 3
Evaluate
(x + 1) * (x + 3) = x^2 + 4x + 3
Hence, the trinomial represented by the algebraic tiles is x^2 + 4x + 3
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I am not able to solve this question
Answers
Answer:
Choice A
Step-by-step explanation:
[tex] \rm \: a {}^{2} \cdot \{ a \ { {}^{ (\frac{2}{3}) } \}}^{ - 1} [/tex]x^-1 = 1/x[tex] \rm \: a {}^{2} \{ \cdot \: \cfrac{1}{a {}^{ \frac{2}{3} } \ } \}[/tex]
Applying Distributive property;
[tex] \rm \: a {}^{2 \times \cfrac{2}{3} } [/tex][tex] \rm \: a {}^{ \cfrac{4}{3} } [/tex]Choice A is accurate.
Evaluate the given question
Answers
The value of the given expression is 1/16
Exponential functionsGiven the exponential function below as shown;
(1/2)^4
This means the product of 1/2 in 4 places. This can be expressed as;
(1/2)^4 = 1/2 * 1/2 * 1/2 *1/2
(1/2)^4 = 1/4 * 1/4
(1/2)^4 =1/16
Hence the value of the given expression is 1/16
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PLEASE HELP!!!!!!!!!!!!!!!!!!!! ASAP PLEASE!!!!!!!!!!!!!!!!!!!!!!!
Answers
Answer:
729
Step-by-step explanation:
I have not done this in some time so the terms may be a bit unconventional, but they work. The key to this is multiplying by -3.
1*(-3) = -3
-3*(-3) = 9
And so on.
1, -3, 9, -27, 81, -243, 729
The heart rate of 10 adults is measured and the results are 83, 87, 90, 92, 93, 100, 104, 111, 115, 121. Find the interquartile range of the data set.
Answers
The interquartile range of the data set is 21.
Given that the heart rate of 10 adults is measured and the results are 83, 87, 90, 92, 93, 100, 104, 111, 115, 121.
The interquartile range shows the extent of the middle half of the distribution. Quartiles segment any distribution, ordered from low to high, into four equal parts. The interquartile range (IQR) contains the second and third interquartile ranges, the central half of the dataset.
The value of quartile 1 is Q₁=90
The value of quartile 3 is Q₃=111
So, the interquartile range is
IQR=Q₃-Q₁
IQR=111-90
IQR=21
Hence, the interquartile range of the data set 83, 87, 90, 92, 93, 100, 104, 111, 115, 121 is 21.
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The length of a rectangle is 6 less than twice the width. If the perimeter is 60 inches, find the length and width.
Answers
Answer:
w = 12
l = 18
Step-by-step explanation:
Hello!
Recall the perimeter of a rectangle is twice the sum of the length and the width of the rectangle.
[tex]P = 2(l + w)[/tex]Let w be the width. The length is 6 less than twice the width. That means, l is 2w - 6.
Plug it into the formula and solve, given that P is 60.
Solve for w[tex]P = 2(l + w)[/tex][tex]60 = 2(2w - 6 + w)[/tex][tex]60 = 2(3w - 6)[/tex][tex]60 = 6w - 12[/tex][tex]72 = 6w[/tex][tex]w = 12[/tex]The width is 12 inches. We can plug in 12 for 2w - 6 to find the length.
Solve for l[tex]l = 2w - 6[/tex][tex]l = 2(12) - 6[/tex][tex]l = 24 - 6[/tex][tex]l = 18[/tex]The length is 18 inches.
The width is 12 inches, and the length is 18 inches.
What package of toothpaste has the lower unit price?
Package Price Unit Price
6.2 oz $2.95
8.0 oz $3.13
Answers
Answer:
6.2 oz is lower
Step-by-step explanation:
Math 2 Of high school
Answers
Answer:
B. BC = 18 so ∆ABC ～ ∆DEF by SASStep-by-step explanation:
[tex] \bf \cfrac{AB}{DE} = \cfrac{BC}{EF} [/tex]
[tex] \bf \cfrac{15}{10} = \cfrac{BC}{12} [/tex][tex]\bf \cfrac{3}{2} = \cfrac{BC}{12} [/tex][tex]\bf BC = \cfrac{3}{2} \times 12 [/tex][tex]\bf 3 \times 6[/tex][tex]\bf BC = 18[/tex][tex] \bf \angle B = \angle \: E[/tex]So, ∆ABC ～ ∆DEF by SAS.
------------------------------------GOE
ASSI
Collect Data from Our Solar System
Fill in the table. To obtain each planet's distance from the sun and orbital period, click its name.
DONE
"include all given digits
Distance from the sun (au)
Orbital Period (years)
Venuss
Sun
9.72.a
Mercury Venus Earth
Mars
Orbital Period: 0.616 years
Jupiter Saturn Uranus Neptune
ΝΑ
ΝΑ
Answers
Answer:
Mercury - 0.39 and 0.242
Venus - 0.72 and 0.616
Earth - 1 and 1
Mars - 1.52 and 1.88
Uranus - 19.18 and 84.00
Neptune - 30.06 and 165.00
The distance between Mercury, Venus, Earth, Mars, Uranus, and Neptune from the sun is 0.39, 0.72, 1, 1.52, 19.18, and 30.06 respectively.
What is Distance?The length along a line or line segment between two points on the line or line segment.
Distance=√(x₂-x₁)²+(y₂-y₁)²
The distance between each planet from the sun will be given as
Mercury - 0.39 and 0.242
Venus - 0.72 and 0.616
Earth - 1 and 1
Mars - 1.52 and 1.88
Uranus - 19.18 and 84.00
Neptune - 30.06 and 165.00
Hence, the distance between Mercury, Venus, Earth, Mars, Uranus, and Neptune from the sun is 0.39, 0.72, 1, 1.52, 19.18, and 30.06 respectively.
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Copy the figure below onto a separate sheet of paper. Find the image of the figure under reflections in line m and then line t. In the box below, descibe the new location of point F in relation to lines m and t.
Answers
The image of the figure under reflections in line m and then line t is shown below.
What is a transformation of geometry?A spatial transformation is each mapping of feature shapes to itself, and it maintains some spatial correlation between figures.
Reflection does not change the size and shape of the geometry.
The image of the figure under reflections in line m and then line t.
The reflection of the square DEFG will be given in the figure.
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Two farmers bought a total of 230 cows and a year later found out that the first farmer had 10% more cows than in the beginning, whereas the second had 20% increase. The total number of cows at the end of the observed period was 263. How many cows did each have in the beginning?
Answers
In the beginning, they have 50 and 180 cows respectively.
How to find the total number of cows?The two farmers bought a total of 230 cows .
A year later the first farmer had 10% more cows than in the beginning.
Therefore,
let
x = number of cow he has initially.
A year later the percentage increase = 0.1x
whereas the second had 20% increase. Therefore,
let
y = number of cow he has initially.
A year later percentage increase = 0.2y
Hence,
x + y = 230
1.1x + 1.2y = 263
1.1x + 1.1y = 253
1.1x + 1.2y = 263
0.2y = 10
y = 10 / 0.2
y = 50
x = 230 - 50
x = 180
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Find the coordinates of the circumcenter 0,0 4,0 4,-3
Answers
The coordinates of the circumcenter of triangle having coordinates of (0,0),(4,0),(4,-3) are (1,-17/6).
Given The coordinates of triangle are (0,0),(4,0),(4,-3).
Let the triangle be ABC.
Let the coordinates of the circumcenter be D(x, y).
We know that the length of circumcenter from the corner points are equal to each other.
In this way AD=BD=DC
AD=[tex]\sqrt{(x-0)^{2} +(y-0)^{2} }[/tex]
=[tex]\sqrt{x^{2} +y^{2} }[/tex]
DC=[tex]\sqrt{(4-x)^{2} +(-3-y)^{2} }[/tex]
BD=[tex]\sqrt{(4-x)^{2} +(0-y)^{2} }[/tex]
=[tex]\sqrt{(4-x)^{2} +y^{2} }[/tex]
AD=DC
[tex]\sqrt{x^{2} +y^{2} }[/tex]==[tex]\sqrt{(4-x)^{2} +(-3-y)^{2} }[/tex]
Squaring both sides we get
[tex]x^{2} +y^{2}=16+x^{2} -8x+9+3y+3y+y^{2}[/tex]
8x-6y=25--------------------1
DC=BD
[tex]\sqrt{(4-x)^{2} +(-3-y)^{2} } =\sqrt{(4-x)^{2} +y^{2} }[/tex]
8x+6y=-9---------------------2
Solve equation 1 and 2
Add both equations
8x-6y+8x+6y=25-9
16x=16
x=1
put the value of x in 1
8x-6y=25
8*1-6y=25
-6y=25-8
y=-17/6
Hence the coordinates of circumcenter is (1,-17/6).
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