Answers
[tex]\huge\begin{array}{ccc}BT=21\\DC=10.2\end{array}[/tex]
If BT is the midsegment of ΔMAH and DC is the midsegment of ΔBTH, then MA, BT and DC are parallel.
Therefore the segments form the proportion:
[tex]\dfrac{HM}{MA}=\dfrac{HB}{BT}=\dfrac{HD}{DC}[/tex]
BT is the midsegment of ΔMAH, therefore
[tex]HB=\dfrac{1}{2}HM[/tex]
DC is the midsegment of ΔBTH, therefore
[tex]HD=\dfrac{1}{2}HB=\dfrac{1}{2}\cdot\dfrac{1}{2}HM=\dfrac{1}{4}HM[/tex]
Substitute:[tex]\dfrac{HM}{42}=\dfrac{\frac{1}{2}HM}{BT}[/tex]
cross multiply
[tex]HM\cdot BT=42\cdot\dfrac{1}{2}HM[/tex]
divide both sides by HM
[tex]\boxed{BT=21}[/tex]
[tex]\dfrac{HM}{42}=\dfrac{\frac{1}{4}HM}{DC}[/tex]
cross multiply
[tex]HM\cdot DC=42\cdot\dfrac{1}{4}HM[/tex]
divide both sides by HM
[tex]\boxed{DC=10.5}[/tex]
Related Questions
In the triangle below, with right angle G, suppose that m/F= (3x-14)° and mZH=(5x-16)°.
Find the degree measure of each angle in the triangle.
Answers
The degree measure of each angle in the triangle is
∠H = 59°
∠F = 39°
Angle sum property of triangle says that sum of all the triangle is always equal to 180°
∠G is given to us as 90°
So by applying the property we an say that
90 + (3x - 14) + (5x - 16) = 180
8x = 180 - 90 + 14 + 16
8x = 120
x = 15
∠H = 5x - 16
∠H = 5*15 - 16
∠H = 75 - 16
∠H = 59°
∠F = 3x - 14
∠F = 3*15 - 14
∠F = 45 - 14
∠F = 39°
Therefore ∠H = 59° and ∠F = 39°
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A rectangular blacktop with a length of 5x and a width of 3x has been erected inside a rectangular !eld that has a length of 12x and a width of 7x.a. What is the area of the part of the !eld that is not blacktop?b. "ere is a circular fountain in the rectangular !eld that has a radius of 3x. What is the area of the part of the !eld that does not include the blacktop or the fountain? Factor your answer. Pls help
Answers
Answer:
Step-by-step explanation:
to find area of a rectangle we use (L)(W) so we do that here for both of these rectangles first find the area of the black top
5x(3x)
15x^2 is the area of the blacktop
The “!ield” area is next
12x(7x)
84x^2 is the area now we just subtract the two numbers by subtracting coefficients but keeping the rest the same
84x^2-15x^2
69x^2 is the area of the rectangle that is not black top
B- the foundtain we find with the area of circle formula r squared times pi
3x(3x)pi
9x^2pi
Now we just subtract this from the area of the rectangle
69x^2 -9x^2pi is the area
Hopes this helps please mark brainliest
a grocer stacks oranges in a pyramid-like stack whose rectangular base is 5 oranges by 8 oranges. each orange above the first level rests in a pocket formed by four oranges below. the stack is completed by a single row of oranges. how many oranges are in the stack?
Answers
The total number of oranges in the pyramidal stack is 78.
The oranges are stacked by the grocer in a pyramid like shape,
The base of the pyramid is rectangular with a size of 5 by 8 oranges,
So, total number of oranges in the base can be found as,
= 5 x 8
= 40 oranges.
One orange has four oranges below it. So, if there are 40 oranges in the base, the upper layer will have one row of oranges reduced from each side of the rectangular base.
So, every next level will have (L-1)(B-1) oranges, where L and B are the length and breadth of every preceding rectangle.
Hence, Oranges in level 1 = 4x8
Oranges in level 2 = 3x7
Oranges in level 3 = 2x6
Oranges in level 4 = 1x5
Hence, total oranges are, (40+21+12+5) oranges.
Total oranges stacked are 78 oranges.
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Latisha wants to buy pumpkins and autumn squash for a fall display. She has a budget of no more than $117 but wants to buy more than 10 vegetables for the decorations. The pumpkins are $5.50 each and the autumn squash are $3.50 each. Let p represent pumpkins and s represent squash. Which system of linear inequalities represents this scenario?
Answers
A system of linear inequalities that represents this scenario is given by:
p + s ≥ 10
5.50p + 3.50s ≤ 117
What is an inequality?An inequality simply refers to a mathematical relation that is typically used for comparing two (2) or more numerical data and variables in an algebraic equation based on any of the following inequality symbols:
Greater than (>).Less than or equal to (≤).Greater than or equal to (≥).Less than (<).In order to write a system of linear inequalities to represent the scenario, we would assign variables to the cost of the beginner class and advanced class, and then translate the word problem into algebraic equation as follows:
Let the variable p represent the number of pumpkins.Let the variable s represent the number of squash.Since Latisha cannot buy more than (≥) 10 vegetables, the inequality to represent this is as follows:
p + s ≥ 10
Since Latisha's budget cannot exceed (≤) $117, the inequality to represent this is as follows:
5.50p + 3.50s ≤ 117
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which multiplication table have 8 and 50
Answers
Answer:2
Step-by-step explanation:
2*4=8
2*25=50
In triangle ABC, side AB is one-third of the length of side AC. Side BC is 5 more than the length of side AC. The perimeter is 19. What is the length of side AC?
Answers
Answer:
AC = 6 units===========
GivenAB = AC/3BC = AC + 5P = 19AC = ?SolutionP = AB + AC + BCSubstitute and solve for ACAC/3 + AC + AC + 5 = 192 1/3 AC = 147/3 AC = 14AC = 14*3/7AC = 6Note:
Other sides are 2 and 11. This is not a correct question as sum of two smaller sides (2 + 6) is less than the longest one (11), hence there is no such possible triangle.
0.00147 In standard form
Answers
Answer:
It can be written as 1.47x10-³.Answer:
This is in Standard form. Did you mean scientific form?
1.47 x [tex]10^{-4}[/tex]
Step-by-step explanation:
You move the decimal so that the number is between 1 and 10. Then since in standard form the number is much less than 1.47, you determine how muhc less my how many places you need to move the decimal to put it back in standard form. Since you would need to move the decimal 4 places to the left, the exponent would be -4
the line passes through (6,6) and (-2,2)
Answers
Answer:
Step-by-step explanation:
slope=change in y over change in x
6-2=4
6--2=6+2=8
-4/-8=1/2
Mathematical induction
Answers
Yes this question can be proven by mathematical induction
What do you mean by induction in mathematics?
For each and every natural number n, a statement, theorem, or formula can be proved using the mathematical induction technique. By generalizing this into the "Principle of Mathematical Induction," which we would utilize to demonstrate any mathematical assertion.
Here, n ≥ 1
1/1.2 + 1/2.3 + 1/3.4 + .............. + 1/n(n +1)
We employ the idea of Sigma here.
S/1/r(r + 1) { r = 1 to n }
Sigma [1/(r + 1) - 1/(1/r)] { r = 1 to n }
put r = 1 \s1/1 - 1/(1 + 1) = 1 - 1/2
put r = 2 \s1/2 - 1/(2 +1) = 1/2 - 1/3
put r = 3 \s1/3 - 1/(3 +1) = 1/3 - 1/4
........................................................... put r = n 1/n - 1/(n + 1)
after adding
Sigma = [1/(r+1) - 1/(1/r)] {r = 1 to n } = 1 -1/2 + 1/2 -1/3 + 1/3 - 1/4 + ............1/n - 1/(n +1)
= 1 - 1/( n +1) = n/( n +1)
Consequently, 1/1.2 + 1/2.3 + 1/3.4 +... 1/n(n + 1) = n/(n + 1).
so it proved
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can someone help me really quick
Answers
Answer:
18$
Step-by-step explanation:
this is so i can reach twenty characters.
each face of a cube is painted either red or blue, each with probability 1/21/2. the color of each face is determined independently. what is the probability that the painted cube can be placed on a horizontal surface so that the four vertical faces are all the same color?
Answers
The probability that the vertical faces have the same color painted is 0.6875
There are 6 faces on a cube.
Each face of the cube will either be red or blue.
The probability that one face will have red color = probability that the face will have blue color = 1/2
It is given that the cube is placed on a horizontal surface and the 4 vertical faces have the same color.
The painting of the faces of the cube clearly follows a binomial distribution.
Therefore the probability to color the faces of a cube
= P(4 faces are red, 2 faces blue) + P(4 faces are blue, 2 faces red) + P(5 faces blue) + P(5 faces red) + P(All faces blue) + P(all faces red)
For any binomial distribution
ⁿCₓ X pˣ (1 - p)ⁿ⁻ˣ
where
n = no. of sample
x = random variable
p = probability of success
Hence we get
⁶C₄ X 0.5⁴ 0.5² + ⁶C₄ X 0.5⁴ 0.5² + ⁶C₅ X 0.5⁵ 0.5 + ⁶C₅ X 0.5⁵ 0.5
⁶C₆ X 0.5⁶ + ⁶C₆ X 0.5⁶
= 15 X 0.015625 + 15 X 0.015625 + 6 X 0.015625 + 6 X 0.015625 + 0.015625
= 0.6875
Therefore we get the probability of having the four vertical faces of the same color to be 0.6875.
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the mean selling price of senior condominium in green valley over a year was $215,000. the population standard deviation was $25,000. a random sample of 100 new unit sales was obtained. a. what is the probability that the sample mean selling price was more than $210,000?
Answers
The probability that the sample mean selling price was more than $210,000 is 0.9772.
The given values are:
The mean selling price(μ) = $215000
Standard deviation(σ) = $25000
The random sample (n) = 100
We have to find the probability that the sample mean selling price was more than $210000.
z-score with z-bar= 210000
z = (x-bar - μ) / (σ/ √n)
= ( 210000 - 215000) / (25000/ √100)
= -5000/ 2500
=-2
Using z-tables, the probability is:
Probability = P[z> -2]
= 1 - 0.0228
= 0.9772
Therefore the probability is 0.9772.
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what is ( 7 5/6 - 5 1/3 ) +1 1/9?
Answers
Answer:
i don't know
Step-by-step explanation:
K(15) = ?
Please find what k(15) is of the following graph below
Answers
1/7a + 1/7 = ?
YALL HELP I LOST MY NOTES
Answers
Step-by-step:
1)Combine multiplied terms into a single fraction
1/7a+ 1/7
1a/7+1/7
2)Multiply by 1
3)Combine fractions with a common denominator
Solution
a+1/7
Hope That helps!
Step-by-step
1/7a + 1/7
Multiply by a/a
1/7a + 1/7 * a/a
1/7a + a/7a
Combine the numerators over the common denominator.
1+a/7a
Which of the following is equivalent to 60 Superscript one-half?
Answers
Answer
[tex]60\sqrt{x} 2[/tex]
Step-by-step explanation:
Answer:
StartRoot 60 EndRoot
Step-by-step explanation:
Edge
dave is making a rectangular garden bed. after assembling it, he finds that the bed has a width of three-fourths of a foot and a length of nine and one-third feet. what is the area of the garden in square feet
Answers
The area of the garden is 7 square feet.
Define area.The area a rectangle occupies is the space it takes up inside the limitations of its four sides. The dimensions of a rectangle determine its area. In essence, the area of a rectangle is equal to the sum of its length and breadth. An example of a quadrilateral with equal and parallel opposite sides is a rectangle. It is a polygon with four sides and four angles that are each 90 degrees. A rectangle is a shape with only two dimensions. A rectangle's area (A) is calculated by multiplying its length ('a') by its breadth ('b'). Area of Rectangle is therefore equal to (a× b) square units.
Given,
Width = 3/4
Length = 9 + 1/3
Length = 28/3
Area:
Length × Width
3/4 × 28/3
84/12
7
The area of the garden is 7 square feet.
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Which answer choice shows 38.782 rounded to the nearest half? PLEASE HURRY IS DUE TODAY!!!!!!!!!!!
A. 38
B. 38.5
C. 39
D. 39.5
Answers
What is the equation of the line in slope-intercept form?
pls help me!
Answers
Answer:
y = [tex]\frac{4}{3}[/tex] x + 4
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
calculate m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (- 3, 0) and (x₂, y₂ ) = (0, 4) ← 2 points on the line
m = [tex]\frac{4-0}{0-(-3)}[/tex] = [tex]\frac{4}{0+3}[/tex] = [tex]\frac{4}{3}[/tex]
the line crosses the y- axis at (0, 4 ) ⇒ c = 4
y = [tex]\frac{4}{3}[/tex] x + 4 ← equation of line
The cost
C
, in £, of a monthly phone contract is made up of the fixed line rental
L
, in £, and the price
P
, in £, of the calls made. Enter a formula for the cost and, enter the cost if the line rental is £20 and the price of calls made is £15.
Answers
The formula for the cost if the line rental is £20 and the price of calls made is £15 will be 20 + 15p.
How to calculate the cost?It should be noted that an expression is used to illustrate the relationship given between the variables.
In this case, the monthly phone contract is made up of the fixed line rental and the price represented by p.
The appropriate expression to illustrate this information will be:
= Fixed cost + Calls made
= 20 + 15(p)
= 20 + 15p
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a company makes a bracelet containing magnets that they claim improves balance and overall athletic performance. researchers recruit volunteers for an experiment. the subjects will test the effectiveness of the bracelet by performing a variety of athletic challenges with and without the bracelet. each subject will do each challenge 333 times: wearing the actual bracelet, wearing a placebo bracelet, and wearing no bracelet at all. the order will be randomized for each activity, subjects won't know which bracelet is which. why did the researchers include the scenario where subjects wear no bracelet at all?
Answers
The researchers include the scenario where subjects wear no bracelet at all are when it comes to mosquitoes, volunteers in each block should live in similar conditions.
Define experiment.An experiment might involve giving a novel drug to rats to see how they respond to learning about it. When you visit a new coffee shop but are unsure of how the coffee will taste, that is an example of an experiment. the act of carrying out a test like that; experimenting. An experiment is a procedure used as part of the scientific method to test a hypothesis. The independent and dependent variables are the two most important variables in every experiment. To investigate the impact of the independent variable on the dependent variable, it is either controlled or altered.
Given,
A company makes a bracelet containing magnets that they claim improves balance and overall athletic performance. researchers recruit volunteers for an experiment.
The researchers include the scenario where subjects wear no bracelet at all are:
When it comes to mosquitoes, volunteers in each block should live in similar conditions.
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sarah owns a farm and has lots of dogs on her property. in the table below, she has listed each of her dogs by name and has classified them according to size and color. at random, she picks one of the dogs to take with her to the pet store. what is the probability the selected dog is medium and brown?
Answers
The probability the selected dog is medium and brown by Sarah is 6/49.
What is meant by the word probability?A field of mathematics that deals with the exploration of probabilities. The ratio of that number of alternatives in an exhaustive set all equally probable scenarios that cause a specific event to that same total number of conceivable outcomes.Probability = favourable outcome/ total outcome
The table for the given question is attached.
Total dogs owned by Sarah = 7.
Total medium sized dogs = 2.
Total brown coloured dogs = 3
Probability( medium sized ) = 2/7
Probability( brown coloured ) = 3/7
Probability( medium sized and brown coloured ) = (2/7)×(3/7)
Probability( medium sized and brown coloured ) = 6/49
Thus, the probability the selected dog is medium and brown is 6/49.
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Given the speeds of each runner below, determine who runs the fastest.
i cant figure this out and its due soon pls help me
Answers
The person who runs fastest is Zach.
How to find the speed?Ron runs 9 feet per second: 9 ft/s
Zach runs 410 feet in 49 seconds:
410/49 ft/s
=8.36 ft/s
= 8.4 ft/s (Approximately)
Katie runs 1 mile in 412 seconds:
1 mile = 5280 ft
5280/412 ft/s
=12.8 ft/s
Noah runs 870 feet in 1 minute:
= 870/60 ft/s
= 14.5 ft/s
Hence,
Ron 9 feet per seconds
Zach 8.4 feet per seconds
Katie 12.8 feet per seconds
Noah 14.5 feet per seconds
So, Zach is the fastest.
Therefore the fastest is Zach.
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Help me please image is attached I really appreciate it
Answers
An inequality to find the number of batches of rolls Liz can make is 13n/4 ≤ 26 and she cannot make more than 8 batches of rolls.
How to write and solve this inequality?In order to solve this word problem, we would assign a variable to the number of batches, and then translate the word problem into an algebraic inequality as follows:
Let the variable n represent the number of batches.
Since Liz has 26 tablespoons of yeast left in the jar and each batch of biscuits takes 3 1/4 -tablespoons, we have:
3 1/4 (n) ≤ 26
13n/4 ≤ 26
Cross-multiplying, we have:
13n ≤ 26 × 4
13n ≤ 104
n ≤ 104/13
n ≤ 8.
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Complete Question:
Liz wants to make several batches of biscuits. She has 26 tablespoons of yeast left in the jar and each batch of biscuits takes 3 1/4 -tablespoons. Write and solve an inequality to find the number of batches of rolls Liz can make.
In class, everyone took a handful of m&ms, so people had a mean of
37 with a standard deviation of 7. Ms G hands everyone 10 more
m&ms. What is the new mean?
Answers
whats the answer to "The x -intercept is" and how do i find it
Answers
The x-intercept of the function represented on the graph is 3
How to complete the blank of the x-intercept?The graph represents the given parameters
To determine the x-intercept of the graph, we set y = 0
This means that the x-intercept of the graph is the point, where the line of the graph crosses the x-axis
For the graph, we have
When y = 0, the function has a value of 3
This means that
x-intercept is 3
Hence, the x-intercept of the graph is 7
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How to solve: n-4= 5n + 1/2
Answers
n =
Explanation:
Multiply 2 on both sides
2n - 8 = 10n + 1
Make n the subject
8n = -9
n = -9/8 = -1 1/8
How do you graph this?
Answers
Reflection at point y = -6 will have coordinates as
preimage image
Q(0, -9) Q' (0, -6)
R(4, -9) R' (4, -6)
S(6, -8) S' (6, -5)
T(2, -8) T' (2, -5)
How to find the coordinatesThe transformation involve is reflection and this is a type of transformation that produces the mirror image of the preimage
The transformation rule to get the mirror image is (x, y) → (x, y + 3)
The coordinates are applied as follows
Q(0, -9) → (0, -9 + 3) → Q' (0, -6)
R(4, -9) → (4, -9 + 3) → R' (4, 6)
S(6, -8) → (6, -8 + 3) → S' (6, -5)
T(2, -8) → (2, -8 + 3) → T' (2, -5)
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Due today help please!!
Answers
The equation of line: y = 2x - 9
slope = 2
y-intercept = (0, -9)
The graph of the line y = 2x - 9 is as shown below.
In this question we have been given a point (6, 3) and slope m = 2
We need to find an equation of line passing through (6, 3) with slope m = 2
Using formula of the point-slope form:
(y - y1) = m(x - x1)
(y - 3) = 2(x - 6)
y - 3 = 2x - 12
y = 2x - 12 + 3
y = 2x - 9
This is slope-intercept form of equation of line.
slope = 2
y-intercept = -9
Therefore, the equation of line: y = 2x - 9
slope = 2
y-intercept = (0, -9)
The graph of the line y = 2x - 9 is as shown below.
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PLEASE HELP ASAP NEEDED SOON
Answers
They will require 4 (4/11) days to complete the remaining work together.
Time is the duration during which any activity or work happens or continues. Work is a task or set of activities to achieve a certain result
It takes Ann alone 10 days to translate a document.
Ann's work in one day = 1/10
In 2 days = 2 / 10
Work left = 8 / 10
Ben alone now takes 12 days to translate a document.
Ben's work in one day = 1/12
We will now use addition.
Combined work of both Ann and Ben in 1 day = 1 / 10 + 1 / 12 = 11 / 60
Time taken to complete the rest of the work = 8 / 10 ÷ 11 / 60
= 48 / 11 = 4.4 days.
As a result, they need 4 (4/11) days to finish the remaining work together.
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