In the diagram shown, M, N and P are collinear and QM=QN as shown. If mMQN = 48" and
mNQP = 33. Justify why QNP must be isosceles.
Answers
Answer/Step-by-step explanation:
Let's find the measure of the angles of ∆QNP.
∆QMN is am isosceles ∆, because it has two equal sides. Therefore, its base angles would be the same. Thus:
m<MNQ = ½(180 - 48) (one of the base angles of ∆QMN)
m<MNQ = ½(132) = 66°
Next, find m<QNP
m<QNP = 180° - m<MNQ (linear pair angles)
m<QNP = 180° - 66° (Substitution)
m<QNP = 114°
Next, find m<P
m<P = 180 - (m<QNP + m<PQN) (sum of ∆)
m<P = 180 - (114 + 33)
m<P = 180 - 147
m<P = 33°
Thus, in ∆QNP, there are two equal angles, namely, <P and <PQN.
An isosceles ∆ had two equal base angles. Therefore, ∆QNP must be an isosceles ∆.
An isosceles triangle is that the triangle must have two sides of equal length.
Triangle QNP is isosceles triangle because, QN = PN
In triangle QMN,
Since, QM = QN
So, ∠QMN = ∠QNM
By property of triangle:
∠MQN + ∠QNM + ∠QMN = 180
48 + 2 ∠QNM = 180
∠QNM = [tex]\frac{180-48}{2}[/tex] = 66 degree
So, ∠QMN = ∠QNM = 66 degree
from figure,
∠QNM + ∠QNP = 180
∠QNP = 180 - 66 = 114 degree.
In triangle QNP,
∠QNP + ∠PQN + ∠QPN = 180
∠QPN = 180 - 33 - 114 = 33 degree
Since, ∠QNP = ∠QPN = 33 degree
Therefore, triangle QNP is isosceles triangle.
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Related Questions
4
Noah has a bag of candies
that he splits between
himself and 3 friends. His
brother then gives him 8
more candies. If he now has
36 candies, how many were
in the bag to begin with?
Explanation too please
Answers
Answer:
28
Step-by-step explanation:
36 - 8 = 28
Answer:
112
Step-by-step explanation:
36-8= 28. then 28 x 4 = 112 candies total
A carpenter has boards of length 24 36 and 42 inches they must be cut into smaller boards of equal length with no scrap wood left over . What is the longest lenght of boards can he cut
Answers
The longest he can cut is 6 inches
Answer:6 inches
Step-by-step explanation:
Which system of linear equations has the ordered pair (4, –5) as a solution? 2 x minus 5 y = negative 30 and 7 x + 4 y = negative 19 6 x minus y = negative 29 and 8 x + 3 y = negative 17 3 x minus 2 y = 22 and 2 x + 9 y = negative 37 5 x minus 6 y = 49 and x + 8 y = negative 27
Answers
Answer:
c
Step-by-step explanation:
i took test
The ordered pair (4, -5) satisfies the equation
3x- 2y= 22
What is Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides. LHS = RHS is a common mathematical formula.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given:
We have ordered pair (4, -5)
First equation, 2x - 5 y= -30
So, 2(4)- 5(-5)= 8 + 25= 33
Second equation,7 x + 4 y = -19
So, 7(4)+4(-5)= 28 -20= 8
Third equation, 6x - y= -29
So, 6(4) +5= 24+ 5 = 29
Fourth equation, 8 x + 3 y= -37
So, 8(4) + 3(-5)= 32 - 15 = 17
Fifth equation, 3x- 2y= 22
3(4)- 2(-5)= 12 + 10 = 22
sixth equation, 2x+ 9y = -37
2(4) + 9(-5)= -37
seventh equation, 5x- 6y= 49
5(4) - 6(-5)= 20 + 30 = 50
eight equation, x+ 8y= -27
4+ 8(-5)= -36
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Help me out? Please! Thank you!
Answers
Answer:
A
Step-by-step explanation:
pls give brainliest
A varies inversely as the square of B. If A is 1 when B is 3, find A when B is 5
Answers
Answer:
0.36
Step-by-step explanation:
A= K/B^2
K= A × B^2
K= 1 × 3^2
K= 1×9
K= 9
Therefore if B is 5 then A can be calculated as follows.
K= A × B^2
9= A × 5^2
9= A × 25
9= 25A
A= 9/25
A= 0.36
Hence A is 0.36
what is ─6d – 10 = 10 – 4d solved for the variable
Answers
Answer:
d = -10
Step-by-step explanation:
(d is the variable)
-6d - 10 = 10 - 4d
+4d +10
-2d = 20
-2d/-2 20/-2
d = -10
:)
Answer:
d = 2
Step-by-step explanation:
Simplify both sides.
6d − 10 = 10 − 4d
6d + −10 = 10 + −4d
6d − 10 = −4d + 10
6d − 10 + 4d = −4d + 10 + 4d
10d − 10 = 10
10d − 10 + 10 = 10 + 10
10d = 20
20 ÷ 10 = 2
Find the m TFS.
Answer choices are:
12 degrees
76 degrees
64 degrees
52 degrees
Answers
Gina already owns 2 necklaces , and additional necklaces are priced at 1 for a dollar. How much money does Gina need to spend on new necklaces in order
to own a total of 18 necklaces?
Answers
Answer:
16 dollars
Step-by-step explanation:
she already owns 2 necklaces
18-2=16
1 necklace =1 dollar
16x1=16
Answer:
16 dollars.
Step-by-step explanation:
She already has 2 necklaces. For a total of 18 necklaces, she needs to pay for 16 more. One is 1 dollar so do 16 x 1 to find the amount of payment required.
Hope it helps!
which sentence most accurately describes how to solve for perimeter multiplying dividing subtracting or adding all sides of the polygon
Answers
Answer:
Is there supost to be an image or options orrr?....
Step-by-step explanation:
Nicole is buying some souvenir keychains for her friends. Her total bill is $11.40. If the keychains are $0.95 each, how many keychains did she buy?
pleaseeeeeeeeeeeeeeeeeeee helpppppppppppp
Answers
Answer:
12 keychains
Step-by-step explanation:
$11,40 : $0,95 = 12
If a water dispenser pours 2 1/3 gallons a minute. How long does it take to pour 6 gallons in mixed number form?
Answers
Answer:
Step-by-step explanation:
3 1/2
When graphed, which line will have the
greatest rate of change?
a. y = 5x
b.
y = 3x
y = 0.3x
C.
Answers
Answer:
the answer is y=5y , because the larger b , the larger rate of change
instructions: the polygons in each pair are similar. find the missing side length.
Answers
Answer:
it's 19
Step-by-step explanation:
18 - 3 = 15
so the difference between them is 15
so since you wanna fine the "?" on the right, you would add 4+15, which gives you 19
(also 3 and 4 four are only one number apart, so you could have just added (+1) to 18) :)
what is the image point of (-6,1) after a translation left 2 units and down 3 units
Answers
Answer:
(-8, -2)
Step-by-step explanation:
Subtract 2 from -6, so -6 -2 which gives -8.
Subtract 3 from 1 so, 3-1 = -2.
Answer:I just had to do this in Math class and the answer is (-8,-2)
Step-by-step explanation:
The half-life of radioactive radium (226Ra) is 1599 years. What percent of a present amount of radioactive radium will remain after 275 years?
Answers
Answer:
88.76%
Step-by-step explanation:
Given that :
Half life of radium = 1599 years
Percentage that will remain after 275 years
Using the relation :
y = Ae^kt
Where ; A = mass of radium and t = half life = 1599, A = initial mass
By 1599, the mass of radium will be half its initial
Hence,
y = initial / 2 = A /2
A/2 = Ae^kt
To obtain the value of k
0.5 = e^1599k
In0.5 = 1599k
k = (In0.5)/1599
k = - 0.0004335
Hence,
y = Ae^-0.0004335t
Amount of radium. After 275 years : t = 275
y = Ae^-0.0004335*275
y = A0.8876191
y = 0.8876191 of intial amount
Hence, 0.8876191 * 100%
= 88.76%
can answer this
1/2 + 2/5=
Answers
Answer:
9/10 or 0.9.
Step-by-step explanation:
1/2 + 2/5 =
5/10 + 4/10 =
5 + 4/10 =
9/10
Answer:
9/10 or 0.9
Step-by-step explanation:
1/2 + 2/5 =
1 × 5 + 2 × 2/2 × 5
5 + 4 = 10
9/10 or 0.9
In Fraction = 9/10
In Decimal = 0.9
Thus, The answer is 9/10 or 0.9
-TheUnknownScientist
find the measure of BE step by step
Answers
Answer:
BE = 49 cm
Step-by-step explanation:
Use Pythagorean theorem
(hypotenuse)² = (base)² + (leg)²
ΔDEF,
DE² + EF² = FD²
DE² + 63² = 65²
DE² + 3969 = 4225
DE² = 4225 - 3969
DE² = 256
DE = √256 = √(16*16)
DE = 16 cm
ΔCBD,
BC² + BD² = CD²
56² +BD² = 65²
3136 + BD² = 4225
BD² = 4225 - 3136
BD² = 1089
BD = √1089 = √(33*33)
BD = 33 cm
BE = BD + DE
= 33 + 16
BE = 49 cm
1. On Monday, Sarah
started reading her book
that has 26 chapters. On
Monday, she read 9/26 of
her book. On Tuesday she
read 6/26 of her book. How
much does she have left to
read?
Answers
Answer:
Sara have 11 chapters left to read.
Step-by-step explanation:
Total chapters Book has = 26
On Monday Sarah read = [tex]\frac{9}{26}\ of \ 26 \ chapters = \frac{9}{26}\times \ 26 \ chapters=9 \ chapters[/tex]
On Tuesday Sarah read = [tex]\frac{6}{26}\ of \ 26 \ chapters = \frac{6}{26}\times \ 26 \ chapters=6 \ chapters[/tex]
Total Chapters read by Sarah = [tex]9+6= 15 \ chapters[/tex]
Chapters left to read by Sarah = [tex]26-15 = 11 \ chapters[/tex]
So, Sara have 11 chapters left to read.
Find the value of X
Answers
divide by 5 on both sides :
x=8
Answer : x=8
A square has a side 9cm length . What is its area?
Answers
Answer:
81
Step-by-step explanation: A square has all sides the same so you just multiply 9×9
Have a great day and a awsome thanks giveing brake :)
If the Miami Marlins won 14 of their first 27 games and the team continued to win at the
same rate, how many games would they win in a 162-game season?
c. 98 games
d. 56 games
a. 84 games
b. 70 games
Answers
:)if it is wrong sorry
This type of problem can be solved in various ways such as in terms of ratios and fractions, Let us go with fractions.
What is a fraction?A fraction is written in the form of p/q, where q ≠ 0.
Fractions are of two types they are proper fractions in which the numerator is smaller than the denominator and improper fractions where the numerator is greater than the denominator.
Given, Miami Marlins won 14 of their first 27 games.
So, their win rate in decimal is,
= 14/27.
= 0.518.
∴ In 162 games at the same rate, Miami Marlins will win,
162×0.518.
= 84 games.
So, after playing 162 games they'll win 84games.
learn more about fractions here :
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An ant is walking at a speed of 42 centimeters in 5 minutes.
Part A
At what rate did the ant walk?
Part B
A slug moved a distance of 30 centimeters. It moved at a rate that was 2.4 centimeters per minute slower than the ant. For how many minutes was the slug moving?
Answers
Answer:
Part A. the ant walked at a speed of 8.4 centimeters per minute.
Part B. the slug was moving for 5 minutes because 8.4 minus 2.4 is 6 and 6 times 5 is 30.
Step-by-step explanation:
dont tell me the Answer but walk me through the steps plz
Answers
Answer:
Find the multiplies of 2
Answer please ;)ANSWER PLEASE!!!!!!!!
Answers
Answer:
y intersect is -4 and x intersect is between 6 and 7...
Step-by-step explanation:
which is a correct statement about the description to less than the quotient of a number cubed and 16 increased by 8 when n equals 4
Answers
Answer
12
Step-by-step explanation:
Get equation: (n^3/16) + 8
Substitute: ((12)^3/16) + 8
Solve: 64/16 + 8
4 + 8
= 12
When does a parabola open upward?
a.
when p is negative
c.
when p is positive
b.
when h is positive
d.
when h is negative
Please select the best answer from the choices provided
A
B
C
D
Answers
Answer:
C - When p is positive
Step-by-step explanation:
Just took the test
Martha's mother is 4 times older than Martha. Martha mother is 36 years old. Which equation can be used to find Martha's age, a?
Answers
Answer:
4a = 36
Step-by-step explanation:
multiply a by 4 to get the mom's age. it can also be 1/4 (36) = a
Answer:
m=4a, m=36, 36/4=a
Step-by-step explanation:
M= Martha's mom's age, a=martha's age.
Create and solve an additional word problem using the following numbers:
Answers
Word Problem: Sophie and Joan need to determine whether or not they have enough paint to paint the walls of their bedroom. They need 2 6/7 gallons of paint in order to cover the entire room. Sophie has brought 5/6 of a gallon of paint. What is the minimum amount of paint Joan needs to bring in order to paint the entire wall?
Answer: 2 1/42 gallons
Solving Steps:
2 6/7 - 5/6 (needs to be simplified)6/7 x 6/6 = 36/425/6 x 7/7 = 35/4236/42 - 35/42 = 1/422 + 1/42 = 2 1/42Final Answer: 2 1/42 gallonsI hope this helps!! :)
someone helpppp pleaseeee
Answers
Answer:
138
Step-by-step explanation:
G + H = 180 {G, H are linear pair}
12x + 6 + 4x - 2 = 180
12x + 4x + 6 - 2 = 180
16x + 4 = 180
16x = 180 - 4
16x = 176
x = 176/16
x = 11
G = 12x + 6
= 12*11 + 6
= 132 + 6
= 138
Which value of x makes the following equation true?
6.5(x - 2) = -0.5x + 29
A. 9
B. 6
C. 5
D. 8
Answers
Answer:
The value of x that will make this equation true is 50.
0.5 times 50=25 -8 = 17
0.2 times 50= 10 +7 = 17
Therefore, your answer is 50.
Step-by-step explanation:
Know ur meme ;)