Points P, Q, R, and S are collinear. Point Q is between P and R, R is between Q and S, and PQ =RS. If PS = 21 and PR = 16, what is the value of QR? QR = (Simplify your answer.)
Answers
Greetings from Brasil...
→ Collinear points = points belonging to the same line
→ PQ is said to be equal to RS. Let’s call this distance X
→ let's call QR Y
With this information and the figure in the annex we can conclude that:
refer to attached
PQ = X
QR = Y
RS = PQ = X
then
PR = PQ + QR
16 = X + Y i
PS = PR + RS
21 = 16 + X
X = 5 putting in i
16 = X + Y
16 = 5 + Y
Y = 11
So,
PQ = 5QR = 11RS = 5
Collinear points are points on the same line.
The value of QR is 11
From the question, we have:'
Q between P and RR between Q and SThis means that:
[tex]\mathbf{PR = PQ + QR}[/tex]
[tex]\mathbf{QS = QR + RS}[/tex]
[tex]\mathbf{PS = PR + RS}[/tex]
The given parameters are:
[tex]\mathbf{PS = 21}[/tex]
[tex]\mathbf{PR = 16}[/tex]
[tex]\mathbf{PQ = RS}[/tex]
Substitute the above values in [tex]\mathbf{PS = PR + RS}[/tex]
[tex]\mathbf{21= 16 + RS}[/tex]
Solve for RS
[tex]\mathbf{RS = 21- 16}[/tex]
[tex]\mathbf{RS = 5}[/tex]
This means that:
[tex]\mathbf{PQ = RS = 5}[/tex]
Substitute 5 for PQ in [tex]\mathbf{PR = PQ + QR}[/tex]
[tex]\mathbf{PR = 5+ QR}[/tex]
Substitute [tex]\mathbf{PR = 16}[/tex] in [tex]\mathbf{PR = 5+ QR}[/tex]
[tex]\mathbf{16 = 5+ QR}[/tex]
Solve for QR
[tex]\mathbf{QR = 16 - 5 }[/tex]
[tex]\mathbf{QR = 11}[/tex]
Hence, the value of QR is 11
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Related Questions
Which best describes and corrects the error in finding the difference?
Answers
Answer:
The first answer choice.
Answer: The opposite of -12 should be added.
7 - (-12) = 7 + 12 = 19
Step-by-step explanation:
The 2 minus signs cancel out and make the 12 positive so 7 - (-12) = 19.
If these two trapezoids are similar, what is the measure of the missing angle?
90°
1150
900
65°
Answer:
degree.
Answers
the answer is would have to be 900
The measure of the missing angle in the similar trapezoid is 90°.
In the given trapezoid the measure of angles are 90°, 115°, 90° and 65°.
What are similar figures?Similar figures mean when two figures are of the same shape but are of different sizes. In other words, two figures are called similar when they both have a lot of the same properties but still may not be identical.
Given that, the two trapezoids are similar
Here, the measure of the missing angle in the other trapezoid is 90°
Therefore, the measure of the missing angle in the similar trapezoid is 90°.
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Given f(x) = 2x + 1, find the range value if the domain value is 1.75.
Answers
Given:
The function is
[tex]f(x)=2x+1[/tex]
To find:
The range value if the domain value is 1.75.
Solution:
Domain is the set of input values and range is the set of output values.
Here, range value if the domain value is 1.75. It means the value of function f(x) at x=1.75.
Substitute x=1.75 in the given function.
[tex]f(1.75)=2(1.75)+1[/tex]
[tex]f(1.75)=3.5+1[/tex]
[tex]f(1.75)=4.5[/tex]
Therefore, the required range value is 4.5.
I need help ASAP, due in an hour. Will give 5 stars and brainiest to the first person.
Answers
Answer:
5n is a term= true
3m and 5n are NOT like terms=true
these are the correct answers
Step-by-step explanation:
these are the wrong ones
a variable would be m or n
coefficients would be 3 and 5
Which represents a function? A 2-column table with 5 rows. The first column is labeled x with entries negative 10, negative 5, 0, 5, 10. The second column is labeled y with entries 84, 31.5, 4, 1.5, 24. A mapping diagram shows a relation, using arrows between domain and range for the following ordered pairs: (8, negative 4), (negative 2, 10), (negative 2, negative 7). In the domain, the number 3 does not have a relation to a number in the range. A series of ordered pairs: (4, 5), (6, negative 2), (negative 5, 0), (6, 1)
Answers
Answer:
The 1st table represents a function
Step-by-step explanation:
Just trust me on this I took the quiz on edge 202 and got it right
the graph is
x | Y
--------------
-5 | -22
--------------
0 | -2
------------
3 | 10
Which statements are biconditional? Check all that apply.
All triangles and rectangles are polygons.
Sam bakes cookies or he bakes bread.
If it is fashionable, then this store sells it.
If the sun rises in the east, then it is morning, and if it is morning, the sun rises in the east.
Victoria will play outside if and only if the weather is nice.
Answers
The statements that are biconditional include:
If the sun rises in the east, then it is morning, and if it is morning, the sun rises in the east.Victoria will play outside if and only if the weather is nice.What is a biconditional statement?A biconditional statement combines a conditional statement with its inverse. As a result, one conditional is true if and only if the other is also true. It frequently employs the phrase "if and only if" or the abbreviation "if." The double arrow indicates that the conditional must be true in both directions.
Examples are that if and only if the polygon is a quadrilateral, it has four sides. If and only if the polygon has four sides, it is a quadrilateral. If and only if the quadrilateral is a square, it has four congruent sides and angles.
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4 solve the equation below 5 =g/4
Answers
Answer:
g = 20
Step-by-step explanation:
multiply both sides by 4 to get g = 20
Answer:
g=20
Step-by-step explanation:
multiply both sides by 4
Aaron puts $1,000 in an account that pays 10% interest compounded quarterly. He leaves it in the account for six months. Estimate how much interest he earns.
Answers
Answer: $50.63 --- Interest
Step-by-step explanation:
Step 1
Using the formulae
A = P(1 + r/n)^nt
Where
A = principal + interest Amount
P = Principal Amount = $1000
t = Time in years= 6months = 0.5 years
n = number of compounding periods= quarterly =4
Step 2
6 months = 6/12 = 0.5 years
Rate = 10 % = 0.1
A = P(1 + r/n)^nt
= 1000 ( 1 + 0.1/4)^(4 x 0.5)
=1000(1 +0.025)^2
= 1000(1.025)^2
= 1000 x 1.050625
A= $1,050.625
but A = principal + interest Amount
Interest = A- Principal=$1,050.625-$1,000
=$50.625
whats 4x4 +65x67-5+8+9=
Answers
4,383 I hope I got that right, Hope it helps!
which expressions are equivalent to 2? Choose ALL that apply. 6 6 6 6 6 6 2.2.2.2.2.2 2.6 4.16 12 - 12 8.8
Answers
Answer:
2,4,6,8,12,16
Because it is 2 times 3 equals 6
2 times 1 equals 2
2 times 2 equals 4
2 times 8 equals 16
2 times 3 equals 6
2 times 4 equals 8
2 times 6 equals 12
and they are all a factor of 2
Help me answer
Expand 3p(p+5)
Answers
Answer:
3p² + 15p
Step-by-step explanation:
We use distributive property to distribute 3p to each of the terms:
3p · p = 3p²
3p · 5 = 15p
3p² + 15p
Hey there!☺
[tex]Answer:\boxed{3p^2+15p}[/tex]
[tex]Explanation:[/tex]
[tex]3p(p+5)[/tex]
Let's expand.
[tex]3p(p+5)\\\text{After Expanding: }3p^2+15p[/tex]
So the answer is [tex]3p^2+15p[/tex].
Hope this helps!
What is shrek’s ultimate life form
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shrek himself is the ultimate life form
Answer:
This is Shreks ultimate form.
Step-by-step explanation:
This is Shreks ultimate form.
Solve the equation below. -1/5x-18=2
Answers
1
5
x
5
1
x to
x
5
5
x
.
−
x
5
−
1
8
=
2
−
5
x
−18=2
2 Add
1
8
18 to both sides.
−
x
5
=
2
+
1
8
−
5
x
=2+18
3 Simplify
2
+
1
8
2+18 to
2
0
20.
−
x
5
=
2
0
−
5
x
=20
4 Multiply both sides by
5
5.
−
x
=
2
0
×
5
−x=20×5
5 Simplify
2
0
×
5
20×5 to
1
0
0
100.
−
x
=
1
0
0
−x=100
6 Multiply both sides by
−
1
−1.
x
=
−
1
0
0
x=−100
given a right-angled triangle with perimeter 18. The sum of the squares of the three side lengths is 128. What is the area of the triangle ?
Answers
Answer:
9units²
Step-by-step explanation:
A triangle has 3 sides. Let the length of the three sides be a, b, c.
If the perimeter of the triangle is 18, then;
P = a+b+c
a+b+c = 18... 1
If the sum of the squares of the three side lengths is 128, this means;
a²+b²+c² = 128... 2
Since the triangle is also right angled, according to Pythagoras theorem;
c² = a²+b²... 3 (taking c as the hypotenuse)
Substitute equation 3 into 2;
(a²+b²)+c² = 128
c²+c² = 128
2c² = 128
c² = 128/2
c² = 64
c = √64
c = 8
Substituting c = 8 into 1
a+b+c = 18
a+b+8=18
a+b = 10 ...... 3
Substituting c = 8 into 2
a²+b²+c² = 128
a²+b²+8² = 128
a²+b²+64 = 128
a²+b²= 64..... 4
Solve equation 3 and 4 simultaneously;
a+b = 10
a²+b²= 64
From 4; a = 10-b
Substitute a = 10-b into 4;
(10-b)²+b² = 64
100-20b+b²+b² = 64
2b²-20b+100-64 = 0
2b²-20b+36 = 0
Divide through by 2:
b²-10b+18 = 0
b = 10±√10²-4(18)/2
b = 10±√100-72/2
b =( 10±√28)/2
b =(10±√4×7)/2
b = (10±2√7)/2
b = 5±√7
Hence b = 5+√7
If a+ b = 10
a+(5+√7 ) = 10
a = 10-(5+√7)
a = 10-5-√7
a = 5-√7
Area of the triangle A = 1/2 ab
A = 1/2 × (5+√7) × (5-√7)
A = 1/2 × (25-5√7+5√7-7)
A = 1/2 × (25-7)
A = 1/2 × 18
A = 9
Hence the are of the triangle is 9units²
A mathematical sentence without an equal sign. pick from one of these: Absolute Value Distributive Property Equation Evaluate Equivalent Simplify Expression Integers Like Terms Inequality Reciprocal Coefficient Variable Solution Ratio
Answers
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expression
Step-by-step explanation:
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Find the coordinates of the midpoint of XY for X(-2,3) and T(-8,-9)
Answers
Answer:
Midpoint of XY = ( - 5, - 3)
Step-by-step explanation:
[tex]Midpoint \: of \: XY \\ = \bigg( \frac{ - 2 + ( - 8)}{2}, \: \frac{3 + ( - 9)}{2} \bigg) \\ = \bigg( \frac{ - 2 - 8}{2}, \: \frac{3 - 9}{2} \bigg)\\ = \bigg( \frac{ - 10}{2}, \: \frac{ - 6}{2} \bigg)\\ Midpoint \: of \: XY = ( - 5, \: - 3)[/tex]
. Jane made a door frame for the house but does not have a tool to measure the angles. How can she check that the corner is 90 degrees?
Answers
Answer:
She needs to measure the length of the diagonal and two sides of the frame. Then she needs to find the square of each measure. If the sum of the squares of the two smaller sides equals the square of the diagonal, then she created a right triangle.
Step-by-step explanation:
edg 2022
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Answers
Answer:
The anwser is 6.01176470588
Add then divide.
Evaluate
(7.3 X 10) + (2.4 X 107)
(4 X 104)
Answers
Answer:
6.0 x 10^2
Step-by-step explanation:
(7.3 X 10) + (2.4 X 10^7)
(4 X 10^4)
= 73 + 24000000
40000
= 24000073
40000
= 6.0 x 10^2
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x=2
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Here are two five-pointed stars. A student said, “Both figures A and B are polygons. They are both composed of line segments and are two-dimensional. Neither have curves.” Do you agree with the statement? Explain your reasoning.
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Answer:A
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Bcnitsreksbeux
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Or 0.03
M is between L and N. If LN = 91 and LM = 23, find MN.
Answers
Answer:
MN = 68
Step-by-step explanation:
LN = 91
LM = 23
Points L, M, and N are collinear, therefore, according to the segment addition postulate, the following can be deduced:
LM + MN = LN
23 + MN = 91 (Substitution)
Subtract 23 from both sides
23 + MN - 23 = 91 - 23
MN = 68
Which function has an inverse that is a function?
b(x) = x^2 + 3
d(x) = -9
m(x) = -7x
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The box-and-whisker plot below
shows the test scores for the last
quiz. What is the interquartile range?
IS
40
50
60
70
80
90
100
Answers
Answer:
Interquartile range = 40
Step-by-step explanation:
interquartile range = Q3-Q1
It has 7 numbers, in order to make it even we remove the middle number (70) to make two sets of quartiles
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The sum of five consecutive integers is five. What is the product of the five integers?
Answers
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So the sum is always divisible by 5, for any value of n
Step-by-step explanation:
A line segment has the endpoints U(4,8) and V(4, 6). Find the coordinates of its midpoint M.
Write the coordinates as decimals or intogor
Answers
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Step-by-step explanation:
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How to solve 2m - 3 = 13
Answers
Answer:
m=8
Step-by-step explanation:
Answer: m=8
Step-by-step explanation:
2m-3=13
Add 3 to -3 and 13 to cancel the number without a variable
-3+3=0 13+3=16
2m=16
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2/2=0 16/2=8
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Answers
Answer:the answer is 7.5 if you need to round it up it’ll be 8 if you need it as a fraction it’ll be 7 1/2
Step-by-step explanation: