If DM = 26 and point G lies on the perpendicular bisector of DM¯¯¯¯¯¯¯, what is the value of r? Segment D M with point G between the endpoints. Segment D G has length R plus 3, and segment G M has length 4R minus 28. A. 10 B. 13 C. 30 D. 52
Answers
Applying the segment addition postulate, the value of r is determined as: A. 10.
What is the Perpendicular Bisector?A perpendicular bisector is a line segment which divides another line segment into two equal parts, that is, the segments formed have equal lengths.
Since point G lies on the perpendicular bisector of segment DM, therefore:
DG = GM
Given the following:
DM = 25
GM = 4r - 28
DG = r + 3
Therefore:
DG + GM = DM [segment addition postulate]
Substitute
r + 3 + 4r - 28 = 25
Combine like terms
5r - 25 = 25
5r = 25 + 25
5r = 50
5r/5 = 50/5
r = 10
Thus, applying the segment addition postulate, the value of r is determined as: A. 10.
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Related Questions
The cost to download data for a certain mobile phone plan is modeled by c(x), where x represents the total number of gigabytes downloaded. The mobile phone company plans to raise the rate per gigabyte by $2. 50, and charge 20% more if the number of gigabytes downloaded is 5 or more. Identify a function for the new rates
Answers
The new cost function for downloading data is as follows:
C(x) = { 14.50x if 0 <= x < 2
20.50x if 2 <= x < 5
24.60x if x >= 5 }
Option D is correct.
Here, we have, the new cost function for downloading data based on the given conditions.
If 0 <= x < 2 gigabytes:
The original cost function is C(x) = 12x.
After raising the rate by $2.50, the new cost function for this range becomes C₁(x) = (12+ 2.50)x = 14.50x.
If x >= 2 gigabytes:
The original cost function is C(x) = 18x.
After raising the rate by $2.50, the new cost function for this range becomes C₂(x) = 18x + 2.50x = 20.50x.
If x >= 5 gigabytes (20% more):
The original cost function is C(x) = 18x.
After raising the rate by $2.50 and charging 20% more, the new cost function for this range becomes C₃(x) = [1.20 * (18+ 2.50)]x = 24.60x.
Now, we need to combine these functions to get a single function for the new rates:
For 0 <= x < 2 gigabytes: C(x) = C₁(x) = 14.50x
For 2 <= x < 5 gigabytes: C(x) = C₂(x) = 20.50x
For x >= 5 gigabytes: C(x) = C₃(x) = 24.60x
So, the new cost function for downloading data is as follows:
C(x) = { 14.50x if 0 <= x < 2
20.50x if 2 <= x < 5
24.60x if x >= 5 }
Option D is correct.
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For any correlation, people often assume that change in one quantity causes change in the second quantity. This is not always true. For each situation, do you think that change in the first quantity causes change in the second quantity? What else may have affected the change in the second quantity?
number of miles driven and fuel expenses
Answers
For the given situation, we can clearly say that the change in one quantity will also cause a change in the second quantity.
Correlation is a relationship between the values of two variables. A scatter plot is a useful tool for displaying data about two variables as a series of points in the x and y plane and determining whether there is a correlation between the variables.
Causality means that one event causes another. Well-designed experiments can only determine causality. In such experiments, similar groups receive different treatments, and the results of each group are examined.
The collected data on the number of miles driven and fuel expenses. we found that number of miles driven tended to be lower when fuel expenses were high, and the number of miles driven tended to be higher when fuel expenses sales were high.
We do not conclude that more fuel expenses mean fewer miles driven. Likely, an Increased in fuel expenses and the number of miles driven may be caused by a third factor, car mileage. So, the present case is a case of negative correlation.
Negative correlation: y decreases as x increases.
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Find the measures of the angles or sides in each triangle.
The ratio of the three sides is 5: 3: 6 and the perimeter is 98 centimeters.
Answers
Interior angles in triangles are all equal to 180 degrees. A triangle's angles are equal to the sum of the angles at each of its three vertices. The sides of the triangle are 35cm, 21cm, and 42cm.
How to measures the angles of the triangle?
Due to the fact that one outside angle of a triangle is equal to the sum of its other two angles, all of its angles add up to 180 degrees. In other words, the third angle must be added to the other two angles in the triangle (the ones that add up to generate the outer angle) to form a 180-degree angle.
The perimeter of the triangle = 98cm
The ratio of the 3 sides is 5: 3: 6
Take it as 5x, 3x, 6x
where, x is the scaling factor
5x + 3x + 6x = 98
simplifying the above variables, we get
14x = 98
x = 7
The sides of the triangle are
5x = 5 × 7 = 35 cm
3x = 3 × 7 = 21 cm
6x = 6 × 7 = 42 cm
Therefore, the sides of the triangle exists 35 cm, 21 cm and 42 cm.
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Select the expressions that are equivalent to -5(-9f + 7) - 7.
-42f + 45
-9f-42
(-9f + 7)-5-7
45f - 42
Answers
Answer:
The answers are 45f - 42 and -42+45f
Step-by-step explanation:
-5(-9f + 7) - 7
45f (-35 -7)
45f -42
also
-42 + 45f
Let triangle ABC be a right triangle, and let H be the point on the side AB so that CH is perpendicular to AB.
Prove that (x+h)^2 + (y+h)^2 = (a+b)^2
(I would like a detailed answer)
Answers
Katelynn and Petra both commute to work. Katelynn's commute on the bus takes 15 minutes more than 1/3 as many minutes as Petra's commute by car. It takes Katelynn 45 minutes to get to work. Write an equation to determine how many minutes it takes Petra to get to work.
Help! 100 points.
Answers
Answer:
2) (1/3)x + 15 = 45
Step-by-step explanation:
Given that,
→ Katelynn's commute takes 15 minutes more than 1/3 as many min as Petra's.
→ It takes Katelynn 45 minutes.
Then the equation will be,
→ (1/3) times + 15 = 45
→ (1/3)x + 15 = 45
Hence, option (2) is correct.
Find the slope of the line through each pair of points. (-5,-7) and (0,10)
Answers
The slope of the line through each pair of points. (-5,-7) and (0,10) is 17 / 5
What is the slope of an equation?A line's slope often indicates the steepness and direction of the line. By calculating the difference between the coordinates of the two locations, (x1,y1) and (x2,y2), it is simple to calculate the slope of a straight line between them. The letter "m" is frequently used to denote slope.
The given points are (-5,-7) and (0,10)
Formula to calculate slope is - y2 - y2 / x2 - x1
= 10 + 7 / 0 + 5
= 17 / 5
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Which of the following best describes the number π?
O Positive Integer
O Negative Rational Number
O Whole Number
O Positive Irrational Number
Answers
Answer:
Positive Irrational Number
Step-by-step explanation:
The whole numbers are the numbers without fractions and it is a collection of positive integers and zero. Integers are the numbers that can be positive, negative or zero, but cannot be a fraction. All rational numbers can be expressed as a fraction whose denominator is non-zero. Whereas, pi cannot be expressed in the fraction of two integers and has no accurate decimal value, so pi is an irrational number.
Find the value of x?
Answers
Answer: 70º
Step-by-step explanation: isosceles triangle (2 equal sides) means 2 equal angles
Answer:
Hi,
Answer 111
Step-by-step explanation:
This shape (a kite) has an axis of horizontal symmetry
What is the value of cos(B) in the diagram?
Answers
Answer:
11/61
Step-by-step explanation:
Cos is equal to Adjacent over hypotenuse
For angle B, the adjacent side is side BC which is 11 units long
the hypotenuse is 61
11/61
Arysville purchased new textbooks for its three elementary schools. about how many more books did they purchase for oak hill than elm street and woodland combined? textbooks purchased for marysville elementary schools elm street oak hill woodland 4,432 12,398 5,912
Answers
Using basic mathematical operations such as addition and subtraction, they purchase 2054 more books for Oak Hill than Elm Street and Woodland combined.
Elm Street = 4,432 books
Oak Hill = 12,398 books
Woodland = 5,912 books
Using addition, we can determine how many books are purchased for Elm Street and Woodland combined by adding their values.
Elm Street + Woodland
4,432 + 5,912 = 10,344
Using subtraction, determine how many more books did they purchase for Oak Hill than Elm Street and Woodland combined.
Oak Hill - (Elm Street + Woodland)
12,398 - 10,344 = 2054 books
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Begging for help atp!!!! PLEASE
Answers
The range of the graph is 0 <= y <= 12
How to determine the range of the graph?The graph represents the given parameter
On the graph, we have the following observations
Minimum y value = 0
Maximum y value = 12
The range of the graph is represented as
Minimum y value <= y <= Maximum y value
So, we have
0 <= y <= 12
Hence, the range of the graph is 0 <= y <= 12
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Estimate the uncertainty in the momentum of an electron whose location is uncertain by a distance of 2 angstroms. what is the uncertainty in the momentum of a proton under the same conditions?
Answers
Δp≥5.2755∗10−25ms−1
According to the Heisenberg uncertainty principle, we have
δx∗δp≥ℏ2
Since Δx=1angstrom=10−10m,
Δp≥6.626∗10−344∗3.14∗10−10
Δp≥5.2755∗10−25ms−1
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given aright triangle with legs a and b, hypnoses c, find the length of side c if a=2(sqr)3, c=2b
Answers
The length of the hypotenuse c is 6
How to determine the length of c?The given parameters are
Legs = a and b
Hypotenuse = c
a = 2√3
c = 2b
Make b the subject in c = 2b
b = 1/2c
By Pythagoras theorem, we have:
c^2 = a^2 + b^2
This gives
c^2 = (2√3)^2 + (1/2c)^2
Evaluate the exponents
c^2 = 12 + 1/4c^2
Evaluate the like terms
1/3c^2 = 12
This gives
c^2 = 36
Take the square roots
c = 6
Hence, the length of the hypotenuse c is 6
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Each interior angle measure equals each exterior angle measure??
Answers
Answer:
No, they must sum up to give 360 degrees so it's not possible for them to be equal, if they are equal like 180 degrees each, there won't be a polygon formed!
8-3(k+2)=2-3k
My teacher doesn't teach very well I need help its 10th-grade algebra
Answers
Answer:
Step-by-step explanation:
8-3k-6 = 2-3k (distribute -3 to (k+2))
-3k+2 = 2-3k (8-6 is 2)
2 = 2 (subtract 3k from both sides)
2 = 2 means all real numbers
Answer:
0
Step-by-step explanation:
Distribute
8-3(k+2)=2-3k
8-3k+2=2-3k
subtract
8-6=2
2-3k+2=3k
rearrange
-3k+2=3k
I dont feel like typing the rest, watch khan academy
(ill take your email if you want to review on the weekend)
Word problem involving average rate of change
Answers
Answer: A. -2.2 B. -2.7
Step-by-step explanation: To find the rate of change is y2-y1/x2-x1.
For A y2=184.3, y1=140.3 x2=0 and x1=20. 184.3-140.3 will give you 44. 0-20 is -20. So 44 divided by -20 is -2.7.
For B its the same thing: y2=109.3, y1=28.3, x2=30, and x1=60. 109.3-28.3 is 81 and 30-60 is -30. 81 divided by -30 is -2.7.
On a number line, point A is at coordinate -2. Point B is at coordinate 0. Fine the coordinate that is the midpoint from A to B.
Answers
Answer:
The midpoint of the line segment AB
is at (−1, 0).
Step-by-step explanation:
Midpoint Formula:In a general sense the midpoint formula for a line segment whose endpoints are
[tex] \sf ( x_1 + x_2) (y_1 + y_2)[/tex]
would be the mean of the abscissa and the ordinate as seen in the formula below:
[tex] \sf \: (x_m, \: y_m) = ( \frac{x_1 + x_2}{2} , \frac{y_1 + y_2}{2} )[/tex]
When the line segment lies on one axis, then the there would be only one non-zero value in the ordered pair.
Assuming that the line segment AB
is in the x-axis, then the coordinates of the points would be:
[tex] \sf \: A(−2, 0)B(0,0)[/tex]
To get the midpoint, substitute the points above in the formula for the midpoint:
[tex] \sf \: (x_m, \: y_m) = ( \frac{x_1 + x_2}{2} , \frac{y_1 + y_2}{2} ) \\ \sf \: = ( \frac{ - 2 + 0}{2} ),0 \\ \sf \: = ( \frac{ - 2}{2} ), 0 \: \: \: \: \: \: \: \: \\ \sf \: ( - 1, 0)[/tex]
The midpoint of the line segment AB
is at (−1, 0).
Find the slope of the line through each pair of points. (0,0) and (2,6)
Answers
The slope of the line through each pair of points (0,0) and (2,6) is 3.
What is the slope of the line?The increase divided by the run, or the ratio of the rise to the run, is how a line's slope is calculated. It gives information about the line's slope in the coordinate plane. Finding the slope between two locations and calculating the slope of a line are related tasks.
The following formula is used to determine slope:
The slope of the line between two points is given by y2 - y1 / x2 - x1.
Given the points are -
(0,0) and (2,6)
The slope of the line passing through the points is -
= 6 - 0 / 2 - 0
= 6/2
= 3
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Solve the following X + 8 < 3 or -8x < -40
Answers
Answer:
Not 100% sure. Hope it helps you
Find the slope of the line.
d. the line containing (-3,3) and (4,3)
Answers
The slope of the line containing (-3,3) and (4,3) is Zero (0).
The slope of a straight line can be written as follows,
m = [tex](y_{2} - y_{1} )/(x_{2} - x_{1} )[/tex] equation1
The line is containing the points (-3,3) and (4,3). So, we can write
[tex]y_{2}[/tex] = 3 , [tex]y_{1}[/tex] = 3 , [tex]x_{2}[/tex] = 4 , and [tex]x_{1}[/tex] = -3 .
On substituting the values of variables in equation1, we will get
m = ( 3-3 ) / ( 4-(-3) ) = (0/7) = 0.
As the slope of a line is Zero (0), so we can conclude that the given line is a straight line.
Here:
m = the slope of the line
( [tex]x_{1}[/tex] , [tex]y_{1}[/tex] ) are the first coordinates.
( [tex]x_{2}[/tex] , [tex]y_{2}[/tex] )are the second coordinates.
The slope of the line containing (-3,3) and (4,3) is Zero (0).
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How many fixed points are there for the function f(x)= x^5
Answers
To calculate the fixed point for the given function that is f(x)= x^5
The value of ‘x’ can take from one to infinity that means the range is (1,infinity)
Therefore,
The function can be represented as: [tex]f(x)= x^5[/tex]
The interval of the variable 'x' is: [tex]0 < x <[/tex]∝ (infinity)
And finally the range of the variable 'x' as: (1, 32,......,infinity)
What is the fixed point?
Fixed points are those points which do not change when they are mapped with different functions. It is also called as invariant points. The fixed point method is used for the calculation of those function which are in the form of constant.
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What is the equation of each line in slope-intercept form?
a. the line parallel to 4 x+2 y=7 through (4,-2) ,
Answers
The slope-intercept form is y = 1/2x - 4 for line perpendicular to 4 x+2 y=7 through (4,-2) ,
How to solve an equation?To solve linear equations, utilize the steps that are provided below.
Remove parentheses from each side of the equation and combine similar terms to make it simpler.To separate the variable term on one side of the equation, use addition or subtraction.To find the variable, use division or multiplication.The common denominator can be multiplied by each side of the equation to eliminate fractions.Lets take an example of solve z for 7z – (3z – 4) = 12
Here is no multiplication or division, so this will be easy to solve
⇒ 7z – (3z – 4) = 12
⇒ 7z – 3z + 4 = 12
⇒ 4z = 12 – 4
⇒ 4z = 8
⇒ z = 8/4
⇒ z = 2
See, that was so simple, using the mentioned methods, every linear equation can be solved easily.
In an equation, perpendicular lines have the opposite reciprocal slope. In other words, if a line's slope is a positive fraction, its reciprocal slope is negative.
Here given that 4 x+2 y=7
can also be written as
y = -2x + 7/2
Here -2 is the slope and 7/2 is the y-intercept
To find a perpendicular line to the following equation, use the opposite reciprocal slope and point, then solve using the point-slope formula.
y - y₁ = m(x - x₁)
We have, m = 1/2, x₁ = 4and y₁ = -2
y - (-2)= 1/2(x - 4)
y + 2= 1/2x - 2
y = 1/2x - 4
We have the slope-intercept form y = 1/2x - 4 of a line perpendicular to 4 x+2 y=7 through (4,-2)
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A rabbit population in a forest doubles each month. The Department of Natural Resources estimates that the forest contains 525 rabbits at the start of the first month. Write an explicit formula describing the number of rabbits an, in the forest n months later.
Answers
Answer: [tex]525(2)^{n-1}[/tex]
Step-by-step explanation:
We can represent this as a geometric sequence with first term 525 and common ratio 2.
Select the correct answer.
Based on the end behavior, which is the graph of function f?
f(x) = x³ x² – 2x
Answers
Answer:
The answer and explanations are in the pictures.
Step-by-step explanation:
∠A and \angle B∠B are complementary angles. If m∠A=(3x-8)∘ and m∠B=(x+26)∘ then find the measure of ∠A
Answers
Answer:
m∠B = 26°
Step-by-step explanation:
∠A and ∠B being complementary means m∠A + m∠B = 90°
4x + 24 + 3x - 4 = 90
7x + 20 = 90
7x = 70
x = 10
m∠B = (3•10 - 4)° = 26°
Answer:
m∠A = 46°
Step-by-step explanation:
∠A and ∠B are complementary angles (Given)-> m∠A + m∠B = 90°-> (3x - 8)° + (x + 26)° = 90°-> (3x - 8 + x + 26)° = 90°-> (4x + 18)° = 90°-> 4x + 18 = 90-> 4x = 90 - 18 -> 4x = 72-> x = 72/4-> x = 18 (3x - 8)° = (3*18 - 8)° = (54 - 8)° = 46°-> m∠A = 46°A doggy daycare charges a $90 fee plus $15 each day to board a dog. the puppy palace charges $35 per day to board a dog. the cost to board the dog at each site is for a full day. how many days must someone board their dog for the total cost at a doggy daycare to be less expensive than puppy palace?
Answers
Answer:
5 days
Step-by-step explanation:
Answer:
All of theses are correct.
4.5
4 1/2
9/2
About 5.
What is the equation of the line that passes through (0,-5) and (-3,-12)?
Answers
Answer:
-20
Step-by-step explanation:
If you rotate point (4,2) 90°C and 180°C about the origin, how do the x - and y -coordinates change?
Answers
R (-90°) = (x, y) — > (y, -x) is the x - and y -coordinates change.
How is a point rotated with respect to the origin?
Rotational direction: clockwise or counterclockwise. Rotations that are positive are counterclockwise. Clockwise rotations are negative rotations. The following rule is used, for instance, to rotate the point (2, 5) 90 degrees counterclockwise around the origin.As it turns out, however, I don’t need to look at options. I can tell you that a clockwise rotation of 90° of a point about the origin is actually considered a rotation of -90°.
(For positive rotations are counterclockwise, while negative rotations are clockwise.) The rule for the type of rotation you speak of is
R (-90°) = (x, y) — > (y, -x)
One more point, if I may. It appears that you copied this problem verbatim right out of a textbook.
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Wall Ab is covered in a mirror. If you stand at point C and look at point D, what point on wall BF will you see in the mirror? Label the point E and determine the distance from B to E.
Answers
The distance from B to E is 4/3 when wall AB covered in a mirror.
The virtual image created by reflection in a plane mirror is the mirror image of an object or two-dimensional figure; it is the same size as the original but different, unless the object or figure has reflection symmetry.
Angle ∠1 = Angle ∠2
So Triangle ADC = Triangle EBD
A line of reflection is required to accomplish a geometry reflection; the two figures' consequent orientations are opposing. Comparable distances separate the corresponding regions of the figures from the line of reflection. Ordered pair rules appear on the x-axis as (x, -y), the y-axis as (-x, y), and the line y=x as follows (y, x).
tan ADC = AC / AD
= 2/3
tan EBD = BE/BD
= x/2
if Triangle ADC = Triangle EBD
than AC / AD = BE / BD
2/3 = x/2
x = 4/3
Thus , when wall AB is covered in mirrors, the distance from B to E is 4/3.For point E see the attachment below -
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