6. In the diagram below, suppose that point M and point N are the midpoints of PQ and RQ, respectively, and PN = RM.a. Find the coordinates of point M and Point Nb. Using the distance formula) write and simplify an equation expressing the fact that PN=RM.c. Use the equation you found in part (b) to express b in terms of a alone (solve for b) What does this tell you about Triangle PQR?
Answers
a)
The formula for calculating the coordinates midpoint between two points is expressed as
midpoint = (x1 + x2)/2, (y1 + y2)/2
Considering point M, the coordinates of the endpoints are
P(0, 0), Q(2b, 2c)
Considering point N, the coordinates of the endpoints are
R(2a, 0), Q(2b, 2c)
Finding the midpoint of PQ or coordinates of point M, we have
x1 = 0, y1 = 0
x2 = 2b, y2 = 2c
M = (0 + 2b)/2, (0 + 2c)/2 = 2b/2, 2c/2
M = (b,c)
Finding the midpoint of RQ or coordinates of point N, we have
x1 = 2a, y1 = 0
x2 = 2b, y2 = 2c
N = (2a + 2b)/2, (0 + 2c)/2 = 2(a + b)/2, 2c/2
N = ((a + b), c))
b)
The formula for calculating the distance beween two points is expressed as
\(\text{distance = }\sqrt[]{(x2-x1)^2+(y2-y1)^2}\)For PN, the coordinates are P(0, 0), N(a + b), c
x1 = 0, y1 = 0
x2 = a + b, y2 = c
Thus,
\(\begin{gathered} PN\text{ = }\sqrt[]{(a+b-0)^2+(c-0)^2}\text{ = }\sqrt[]{(a+b)^2+c^2} \\ PN\text{ = }\sqrt[]{a^2+2ab+b^2+c^2} \\ PN\text{ = }\sqrt[]{b^2+2ab+a^2+c^2} \end{gathered}\)For RM, the coordinates are R(2a, 0), M(b, c)
x1 = 2a, y1 = 0
x2 = b, y2 = c
\(RM\text{ = }\sqrt[]{(b-2a)^2+(c-0)^2}=\sqrt[]{(b-2a)^2-x^2}\)Related Questions
x f(x) −5 1 −4 0 −3 1 −2 2 −1 3 0 4 1 5 2 6 3 7 What are the vertex and range of the function?
Answers
The vertex is the turning point of a function while the range is the interval of the value of the function thus vertex of the given function is at (-4,0) while the range is [0,6].
What is the range and domain of a function?A function's range is the set of all values that the function accepts, and its domain is the set of all values for which the function is defined.
The domain is for the independent variable while the range is for the dependent variable.
As per the given function,
x f(x) −5 1 −4 0 −3 1 −2 2 −1 3 0 4 1 5 2 6
The graph of this function has been plotted below,
The vertex is the point where the function is changing its sign of slope or turning point.
It is clear that at (-4,0) it is changing its slope of sign therefore (-4,0) will be the vertex.
The range is the interval where the function exists since the given function goes from y = 0 to y = 6 so [0,6] will be the range of the function.
Hence "The vertex is the turning point of a function while the range is the interval of the value of the function thus vertex of the given function is at (-4,0) while the range is [0,6]".
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Will mark brainist if you can help
Answers
Answer:
2/5 or 40 percent
Step-by-step explanation:
All we need to solve this problem are the total number of boys and the total number of girls. Since we already know how many boys there are (6) , let's start by finding the girls, which is marked as b. Looking at the chart, we can tell that
8 + a = b
but we don't know what a is yet. How about we find that out first? If we look vertically, we can see that
a + 4 = 5
so
a = 1.
Now, we can find b.
b = 9
To find the probability of selecting a boy, we have to divide the number of boys by the total number of people.
boys/total = 6 / 15
Simplifying, we get the answer
2/5.
A repeated-measures design would be appropriate for which of the following situations?
A researcher would like to study the effect of advanced training on sales figures.
A researcher would like to compare individuals from at least two populations.
The effect of a new initiative is studied in a small group of individuals with rare skills.
None of these situations
Which of the following is an independent-measures design?
Different participants perform in each condition.
Each participant is tested twice, once in each condition.
All participants perform in every condition.
None of these situations
Answers
The design of the experiment is an indication of the allocation of the
participants in the experiment to different groups.
The responses are;
First Part: A repeated-measures design is appropriate for; A researcher would like to study the effect of advanced training on sales figures.Second Part: An independent-measures design is one in which; Different participants perform in each condition.Reasons:
First Part:
A repeated-measures design is a testing procedure used during an
investigation that makes use of the same group or sample set, but taking
measurement of the members of the set under two different conditions or
at two different times.
Therefore;
A repeated-measures design would be appropriate in the situation where; A researcher would like to study the effect of advanced training on sales figures.
Second Part:
An independent-measures design is one that compares the properties
within two samples, such that the information in the population is not
required. It is a between-groups design, such that different participants
are used for the different conditions of the independent variable.
Therefore;
The option that is an independent-measures design is; Different participants perform in each condition.
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(a) Describe in words a sequence of transformations that maps AABC to
AA"B"C".
(b) Write an ordered-pair rule for each transformation in the sequence.
Answers
Answer:
(x, y) ⇒ (-x, -y) . . . . . . . reflection across the origin(x, y) ⇒ (x +3, y +1) . . . translation 3 right a 1 upStep-by-step explanation:
You want a sequence of transformations that maps ∆ABC to ∆A'B'C' where the vertices are A(-5, 3), B(-2, 3), C(-4, 1), A'(8, -2), B'(5, -2), and C'(7, 0).
Orientation and scalingSegment AB is a 3-unit line segment directed to the right. Segment A'B' is a 3-unit line segment directed to the left. This means there is no dilation involved in the transformation. At least, the figure has been reflected left-to-right.
Point C is below segment AB, while point C' is above segment A'B'. This means the figure has also been reflected top-to-bottom.
Together these reflections can be accomplished by either of reflection across the origin, or rotation 180° about the origin.
TranslationThe reflected figure would leave A' at (5, -3). Its location at (8, -2) means the figure has also been translated to the right and up.
Translation to the right has been by 8 -5 = 3 units.
Translation up has been by -2 -(-3) = 1 unit.
(a) Description of transformationsTriangle ABC can be transformed to triangle A'B'C' by ...
reflection across the origintranslation 3 units right and 1 unit up(b) Transformation rulesThe corresponding ordered-pair rules for these transformations are ...
reflection: (x, y) ⇒ (-x, -y)translation: (x, y) ⇒ (x +3, y +1)__
Additional comment
The single transformation that will accomplish the mapping is ...
(x, y) ⇒ (3 -x, 1 -y) . . . . . reflection across the point (3/2, 1/2)
In the diagram, m ZXYZ = 115° and mZWXY = 45°
Х
Answers
Answer:
m∠XWY = 70°
Explanation:
Two opposite interior angle sum up to one exterior angle on a straight line.
============
? + 45° = 115°
? = 115° - 45°
? = 70°
Answer:
The value of angle XWY = 70°
Step-by-step explanation:
=> angle XYZ + angle XYW = 180° { linear pair }
=> angle XYW + 115° = 180°
=> angle XYW = 180° - 115°
=> angle XYW = 65°
Now angle WXY + angle XWY + angle XYW = 180° { sum of angles of a triangle is 180° }
=> 45° + 65° + angle XWY = 180°
=> angle XWY + 110° = 180°
=> angle XWY = 180° - 110°
=> angle XWY = 70°
Sarah is three times old as Henry. Henry is twice as old as Maria. Maria is 4 years old. How old is Sarah?
Answers
Answer:
24 years old
Step-by-step explanation:
maria is 4 so henry is 8 because its x2 the sarah is 24 because 8x3=24 :)
√₂
You invested $7000 between two accounts paying 5% and 8% annual interest, respectively. If the total interest
earned for the year was $500, how much was invested at each rate?
was invested at 5% and $ was invested at 8%.
Save
>
Answers
Answer:
$2000 was invested at 5% and $5000 was invested at 8%.
Step-by-step explanation:
Assuming the interest is simple interest.
Simple Interest Formula
I = Prt
where:
I = interest earned.P = principal invested.r = interest rate (in decimal form).t = time (in years).Given:
Total P = $7000P₁ = principal invested at 5%P₂ = principal invested at 8%Total interest = $500r₁ = 5% = 0.05r₂ = 8% = 0.08t = 1 yearCreate two equations from the given information:
\(\textsf{Equation 1}: \quad \sf P_1+P_2=7000\)
\(\textsf{Equation 2}: \quad \sf P_1r_1t+P_2r_2t=I\implies 0.05P_1+0.08P_2=500\)
Rewrite Equation 1 to make P₁ the subject:
\(\implies \sf P_1=7000-P_2\)
Substitute this into Equation 2 and solve for P₂:
\(\implies \sf 0.05(7000-P_2)+0.08P_2=500\)
\(\implies \sf 350-0.05P_2+0.08P_2=500\)
\(\implies \sf 0.03P_2=150\)
\(\implies \sf P_2=\dfrac{150}{0.03}\)
\(\implies \sf P_2=5000\)
Substitute the found value of P₂ into Equation 1 and solve for P₁:
\(\implies \sf P_1+5000=7000\)
\(\implies \sf P_1=7000-5000\)
\(\implies \sf P_1 = 2000\)
$2000 was invested at 5% and $5000 was invested at 8%.
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If two opposite sides of a square are increased by 8 meters and the other sides are decreased by 5 meters, the area of the rectangle that is formed is 68 square meters. Find the area of the original square.
Answers
Answer:
21
Step-by-step explanation:
8 * 2 = 16
5 * 2 = 10
68 - 16 = 52 - 10 = 42.
The perimeter of the square is 42.
42 / 4 = 10.5. 10.5 is the length of a side.
10.5 * 2 = 21.
on a recent day, 8 dogs were worth $9 and 24 dogs worth $27. write a chart for the proportion and write an equation the for formulas y=kx
Answers
Answer: y=1.125x
Step-by-step explanation:
Fill in the blank using the scaling factor that makes the number sentence true. 5.3 × > 5.3 0.886 or 1.00 or 1.003
Answers
The given options, the only value greater than 1 is 1.003. Therefore 0.886, which is less than 1 and makes the inequality true.
The given number sentence is 5.3 × > 5.3, where we need to find the scaling factor that makes the inequality true. To do this, we can divide both sides of the inequality by 5.3. This gives us:
5.3 × x > 5.3 ÷ 5.3 × k
We need to find the value of k that makes the inequality true. Simplifying the right-hand side of the equation, we get:
5.3 ÷ 5.3 × k = k × 1 = k
Substituting this into our equation, we get:
5.3 × x > k
We know that 5.3 × 1 = 5.3, which means that k must be greater than 1 to satisfy the inequality. Among the given options, the only value greater than 1 is 1.003. However, this value would make the inequality too large, so it is not the correct answer.
The correct answer is therefore 0.886, which is less than 1 and makes the inequality true.
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Michael is paid $9 per hour to work at the movie theater and $7 per hour when he helps his aunt at her bakery. Michael cannot work more than 32 hours in a week, but he wishes to earn at least $251 each week. Which weekly work schedule is within Michael’s constraints?
8 hours at the movie theater and 25 hours at the bakery
15 hours at the movie theater and 20 hours at the bakery
19 hours at the movie theater and 12 hours at the bakery
21 hours at the movie theater and 8 hours at the bakery
Answers
Answer: the answer is C
Edg. 2021
Answer:
C
Step-by-step explanation:
edg 2021
What is the solution to the system of equations using the graph
Answers
Paul says that (3.14 x 10^5) + (2.53 x 10^4) = 5.67 x 10^5. Is Paul correct? i need a explaining
Answers
Answer: It’s not correct, the equality is false. The reasoning behind this is the equality is the left-hand and right-hand side are different when you do the math.no
DON'T SOLVE IT
I know the answer. I just need to know the TOPIC in geometry.
What is the topic???
Answers
Answer:
Triangles in Geometry
Step-by-step explanation:
Help me solve these two problems! Show the work
Answers
Answer:
see explanation
Step-by-step explanation:
2
4x² + 64 ← factor out the common factor of 4 from each term
= 4(x² + 16)
3
(a - 10)² = 121 ( take square root of both sides )
a - 10 = ± \(\sqrt{121}\) = ± 11 ( add 10 to both sides )
a = 10 ± 11
then
a = 10 - 11 = - 1
a = 10 + 11 = 21
Graph the equation y = 3x - 6
Select two points to graph the line.
Answers
Answer:
y intercept is -6 put your first point on that y intercept
Step-by-step explanation:
from -6 rise 3 and run 1 (to the right )
whats that point ? (0,2)
from that point 2.... run 1 ( to the right and up 3) that will take from x4 to y6
(0,2) (4,6) Two points
y2 -y1 = 6
x2-x1 =2
6/2 simplified is 3/1
Make sense?
1.
Anthony has a sink that is shaped like a half-sphere. The sink has a volume of 3000/3 π, in^3?. One day, his sink
clogged. He has to use one of two cylindrical cups to scoop the water out of the sink. The sink is completely
full when Anthony begins scooping.
(a) One cup has a diameter of 5 in, and a height of 6 in. How many cups of water must Anthony scoop
out of the sink with this cup to empty it? Round the number of scoops to the nearest whole
number. Show all your work.
(b) One cup has a diameter of 6 in, and a height of 6 in. How many cups of water must he scoop out of
the sink with this cup to empty it? Round the number of scoops to the nearest whole number.Show all your work
Answers
Answer:
a) 27
b) 19
Step-by-step explanation:
a) Calculate the volume of the the cup using volume of cylinder equation: \(V = \pi r^{2} h\)
Where V = Volume, r=radius, and h=height. Your answer should be in cubic inches (\(in^3\)).
You're given diameter, so use equation \(d/2 = r\) to find radius.
Substituting these equations will give you: \(V = \pi (d/2)^2 h\)
However, the given volume of the sink is 3000/3\(\pi\) or 1000\(\pi\), meaning that you should modify your results to match this value. Do not substitute \(\pi\) for 3.14..., leave it as a symbolic value. Your final V of the cup should = 37.5 \(\pi\)
Divide the volume of the sink by the volume of the cup. This number will be the amount of cups needed to empty it. In equation form:
\(Vsink / V cup =\) # of cups.
Note the the \(\pi\) will cancel each other out, so there's not need to factor that in.
b) Repeat the steps above with the new d (diameter) value.
I neeeed help plz question 4
Answers
C))x+6y=10
A tennis supply store pays a wholesaler $90 for a tennis racquet and sells it for $144. What is the markup rate?
As a percent
Answers
Find the quotient and express the answer in scientific notation. 302 ÷ (9.1 x 10^4 )
Answers
The quotient of 302 ÷ (9.1 x \(10^4)\) in scientific notation is approximately 3.31868131868 x \(10^1\)
How to find the quotientDividing 302 by 9.1 gives:
302 ÷ 9.1 ≈ 33.1868131868
Now, to express this result in scientific notation, we need to move the decimal point to the appropriate position to create a number between 1 and 10. In this case, we move the decimal point two places to the left:
33.1868131868 ≈ 3.31868131868 x\(10^1\)
Therefore, the quotient of 302 ÷ (9.1 x \(10^4\)) in scientific notation is approximately 3.31868131868 x\(10^1\)
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Please help!! what's the answer
Answers
Answer:
B 244
Step-by-step explanation:
You can split up the polygon into two separate rectangles, one smaller one on top and one bigger one below.
Area of smaller rectangle = 6 × (14-8)
= 36
Area of bigger rectangle = 26 × 8
= 208
Total area of polygon = 36 + 208
= 244
4 granola bars are shared equally between 8 people what fraction of a granola bar does each person receive
Answers
Answer:
1/2 of a granola bar
Step-by-step explanation:
Answer: a half of a granola bar
help me asap. my exam is tomorrow.
Answers
The total surface area of the doghouse is 1452 ft²
What is surface area?The area occupied by a three-dimensional object by its outer surface is called the surface area.
The dog house has many surfaces including the roofs . The total surface area is the sum of all the area of the surfaces.
area of the roof part = 2( 13×11) + 2( 12× 10)×1/2
= 286 + 720
= 1006 ft²
surface area of the building
= 2( lb + lh + bh) -bh
= 2( 10× 11 + 10×8 + 11×8) - 10×11
= 2( 110+80+88)-110
= 2( 278) -110
= 556 -110
= 446ft²
The total surface area = 1006 + 446
= 1452 ft²
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Which represents the solution set of the inequality 5x-9321?
O xs"?
23
O x
O x26
O x56
Answers
• Jason runs 8 miles in an hour and bikes 12 miles in an hour.
. This week, he runs a total of 3 hours and bikes a total of 6 hours.
Answers
He also bikes a total of 126 = <<126=72>>72 miles this week.
In total, Jason runs and bikes a total of 24+72 = <<24+72=96>>96 miles this week.
Amiya Kettey
Reflection of a Point
Oct 01, 11:38:14 PM
Watch help video
What is the image of (0, -6) after a reflection over the line y = 2?
Submit Answer
Answers
Answer:
(0,10)
Step-by-step explanation:
Answer:
(0,10)
Step-by-step explanation:
See picture
To find the number in a square, add the numbers in the two circles
connected to it.
Fill in the missing numbers.
Answers
The missing values in the quantitative reasoning given are : -2, 13 and 9
Given the rule :
square = circle + circleWe can deduce that :
circle = square - circleFor the left circle :
circle = -6 - (-4) = -6 + 4 = -2
For the right circle :
circle = 11 - (-2) = 11 + 2 = 13
For the left square :
square = 13 + (-4)
square = 13 -4 = 9
Therefore, the missing values are : -2, 13 and 9
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1. For infant girls, the mean body length at 10 months is 72 centimeters with a standard deviation of 3 centimeters. The 75th percentile for a 10 month-old girl is ____ centimeters? (Round to one decimal place)
Answers
Using the normal distribution, the 75th percentile for a 10 month-old girl is 74 centimeters.
Normal Probability DistributionThe z-score of a measure X of a normally distributed variable with mean \(\mu\) and standard deviation \(\sigma\) is given by:
\(Z = \frac{X - \mu}{\sigma}\)
The z-score measures how many standard deviations the measure is above or below the mean. Looking at the z-score table, the p-value associated with this z-score is found, which is the percentile of X.The mean and the standard deviation are given, respectively, by:
\(\mu = 72, \sigma = 3\)
The 75th percentile is X when Z = 0.675, hence:
0.675 = (X - 72)/3
X - 72 = 3 x 0.675
X = 74.
The 75th percentile for a 10 month-old girl is 74 centimeters.
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What's the meaning of –(–3)?
Answers
Answer:
+3
Step-by-step explanation:
if your subtracting a negitive it means your adding and its now a positive
-(-3) is equal to a positive 3
Which of the following best describes a semi-regular tessellation?
A) An arrangement of repeating shapes
B) An arrangement of more than one repeating shape with no spaces or overlapping between shapes
C) An arrangement of one repeating shape with no spaces or overlapping between shapes
D) An arrangement of non-repeating shapes
Answers
An arrangement of more than one repeating shape with no spaces or overlapping between shapes is a semi-regular tessellation
Given data ,
Let the semi-regular tessellation be represented as A
Now , the value of A is
A semi-regular tessellation is a tiling of the plane by two or more regular polygons in such a way that every vertex has the same configuration of polygons in the same order
Therefore , an arrangement of more than one repeating shape with no spaces or overlapping between shapes
Hence , the semi-regular tessellation is solved
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