PLEASE HELP!!! 20 POINTS!!!! WILL MARK YOU BRAINIEST!!! Two isosceles triangles share the same base. Prove that the medians to this base are col linear. (There are two cases in this problem: vertices are on the same side of the base and vertices are on the opposite sides of the base!)
Answers
Answer:
Given: Two Isosceles triangle ABC and Δ PBC having same base BC. AD is the median of Δ ABC and PD is the median of Δ PBC.
To prove: Point A,D,P are collinear.
Proof:
→Case 1. When vertices A and P are opposite side of Base BC.
In Δ ABD and Δ ACD
AB= AC [Given]
AD is common.
BD=DC [median of a triangle divides the side in two equal parts]
Δ ABD ≅Δ ACD [SSS]
∠1=∠2 [CPCT].........................(1)
Similarly, Δ PBD ≅ Δ PCD [By SSS]
∠ 3 = ∠4 [CPCT].................(2)
But, ∠1+∠2+ ∠ 3 + ∠4 =360° [At a point angle formed is 360°]
2 ∠2 + 2∠ 4=360° [using (1) and (2)]
∠2 + ∠ 4=180°
But ,∠2 and ∠ 4 forms a linear pair i.e Point D is common point of intersection of median AD and PD of ΔABC and ΔPBC respectively.
So, point A, D, P lies on a line.
CASE 2.
When ΔABC and ΔPBC lie on same side of Base BC.
In ΔPBD and ΔPCD
PB=PC[given]
PD is common.
BD =DC [Median of a triangle divides the side in two equal parts]
ΔPBD ≅ ΔPCD [SSS]
∠PDB=∠PDC [CPCT]
Similarly, By proving ΔADB≅ΔADC we will get, ∠ADB=∠ADC[CPCT]
As PD and AD are medians to same base BC of ΔPBC and ΔABC.
∴ P,A,D lie on a line i.e they are collinear.
Related Questions
please help im being timed
jeremy recived a bill with a balance due of $25.60. after an error was corrected, the new balance due was 1/4 of the original balance due, what is his new balance due
Answers
Answer:
6.40$
Step-by-step explanation:
HOPE THIS HELPS
PLZZ MARK BRAINLEIST
In right triangle DEF, ∠E is a right angle, m∠D=26∘, and DF=4.5.
sin26∘≈0.44
cos26∘≈0.90
tan26∘≈0.49
What is the measurement of EF?
If necessary, round your answer to two decimal places, like this: 42.53
Answers
The table contains data on the number of people visiting a historical landmark over a period of one week. Which type of function best models the relationship between the day and the number of visitors?
A. A quadratic function with a positive value of a
B. A square root function
C. A linear function with a positive slope
D. A quadratic function with a negative value of a
Answers
Hence , it is to be quadratic function where a has to be less than zero.
Given that ,
The table contains data on the number of people visiting a historical landmark over a period of one week.
We have to find,
The relationship between the day and the number of visitors.
According to the question,
[tex]y = a\sqrt{x} + b[/tex]
And where x = no. of days = 1
y = no. of visitors = 45
45 = a [tex]\sqrt{1}[/tex] + b
45 = a + b
And When x = 2 and y = 86
86 = [tex]a\sqrt{2} + b[/tex]
Solving the equation for the values of a and b.
From equation 1
45 - a = b
Put the value of b in equation 2
86 = [tex]a\sqrt{2}[/tex] + 45 - a
86 - 45 = [tex]a \sqrt{2} - a[/tex]
41 = a ([tex]\sqrt{2} - 1[/tex] )
[tex]a = \frac{41}{\sqrt{2} - 1 }\\\\a = \frac{41}{0.41}[/tex]
a = 100
Put the value of a = 100
45 = 100 + b
45 - 100 = b
b = -55
The required equation is y = 100[tex]\sqrt{x}[/tex] -55.
When x = 4
[tex]y = 100\sqrt{2} - 55\\\\ y = 100 ( 1.4 ) - 55\\\\y = 140 - 55\\\\y = 85[/tex]
And when x = 5
[tex]y = 100\sqrt{5} - 55\\\\y = 223.5 - 55\\\\y = 168.60[/tex]
y = 168 ( approx )
Therefore, 168 ≠ 158
Since the function rises less and less in later stage , it can not be a first order function.
So, it is to be quadratic function where a has to be less than zero.
For more information about quadratic equation click the link given below.https://brainly.com/question/2263981
Help pwease :( will give brainliest.
Answers
Answer:
a. $7
b. $x
c. $20
d.$5y
e.$x + $5y
please help me it’s urgent
Answers
Step-by-step explanation:
i hope i didnt answer too late i see that ot says 7 min remaining but oh well
the answer
equation: (7x-13)+(x+29)+(3x + 5) = 180 (the reason why i put = to 180 is because every triangle adds up to 180 degrees)
first of all add the numbers: 29-13+5 = 21--- then add variables: 7x+3x+x= 11x
you get ur equation as: 11x + 21 = 180--- 180-21=11x---159=11x--- 159/11=14 9/20
x = 14 9/20 permiter = 88.15 + 43.45 + 48.35 = 179.95
really hope this helps :) good luck
Composition and inverse
Consider the functions
Answers
How can you drop two eggs the fewest amount of times, without them breaking?
Answers
Answer:
Possible
Step-by-step explanation:
This is done on any floor, the highest or the lowest. Simply drop the egg from one inch above your foot and it will not break. every answer above is wrong. The only way, having 2 eggs, is to starts from the 2º floor.
the rectangle below is being enlarged by a scale factor of 3.5. what is the area of the new drawing?
Answers
Answer:
122.5^2
Step-by-step explanation:
3.5 x 2 = 7
3.5 x 5 = 17.5
7 x 17.5 =122.5 ft^2 (a=hl^2)
Which number on the number line is 4 less than 6?
Answers
Answer:
2
Step-by-step explanation:
6-4=2
Answer:
2
Step-by-step explanation:
2 is the answer
Choose the value to make the equation true.
70.9 divided by = 7.09
1
10
100
1,000
Answers
Answer:
10
Step-by-step explanation:
I hope this helped!
Answer:
10
Step-by-step explanation:
70.9 ÷ 7.09 = 10
-TheUnknownScientist
The value of V8 is between which two integers?
7 and 9
49 and 81
2 and 3
3 and 4
Answers
♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️
[tex] \sqrt{4} < \sqrt{8} < \sqrt{9} [/tex]
Thus :
[tex]2 < \sqrt{8} < 3[/tex]
So √8 is between 2 and 3 ,
Which means option three is the correct answer.
♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️
After eating dinner at a restaurant, Alex's bill before tax is $78.00. The sales tax rate is 8%. Alex decides to leave a 20% tip for the waiter based on the pre-tax am
Answers
Answer:
$99.84Step-by-step explanation:
Step one:
given data
we are told that before tax the bill is pretax= $78
the tax is 8%
and he left 20% of the pretax for the attendant.
Step two:
let us find the amount he paid for eating with tax
=8/100*78
=0.08*78
=$6.24
with tax the meal cost is
= 78+6.24
=$84.24
let us solve for the tip he left (note: it is 20% of the pretax)
=20/100*78
=0.2*100
=$15.6
the tip is $15.6
Step three:
the total amount he paid after eating plus tax and tip is
78+6.24+15.6
=$99.84
Answer:
99.84
Step-by-step explanation:
Shelby mixes a 25% bleach solution with 5 cups of a 10% bleach solution, resulting in a 20% bleach solution. The table shows the amount of each solution used. A table titled Bleach Solution showing Cups, Bleach concentration, and Total. The first row shows 10 percent Bleach with 5, 0.10, and 0.5. The second row shows, 25 percent bleach, with x, 0.25, and 0.25 x. The third row shows Mixture, with 5 plus x, 0.20, and 3. What is the value of x? 1 3 10 24 Mark this and ret
Answers
Answer: 10
Step-by-step explanation:
Answer:
c
Step-by-step explanation:
You want to build a fence around a rectangular yard that is 15 ft. Wide and 25 ft. Long. Find the perimeter of the yard. If fencing costs $6.25 per foot, how much will the fence cost?
Answers
Answer:
$500
Step-by-step explanation:
25*2=50
15*2=30
15(2)+25(2)=80
80(6.25)=500
Fill in the chart below using the information for Credit Card Finance. Mike starts with $1299.99 and an APR of 18% and makes no new purchases. The minimum payment is always 7%.
Answers
Answer:
Step-by-step explanation:
Step one:
given data
P= $1299.99
r=18%= 0.18
minimum rate r= 7%
t=1year
say the account is on simple interest the maximum payment is when the APR is 18%
A=P(1+rt)
A= 1299.99(1+0.18*1)
A= 1299.99(1.18)
A=1533.9882
$1533.9882
The minimum amount is when APR ia 7%
A=P(1+rt)
A= 1299.99(1+0.07*1)
A= 1299.99(1.07)
A=1390.9893
$1390.9893
Find the area of the trapezoid.
bı = 5, b2 = 7, h = 4
The area is
square units
Answers
Answer:
24 square units
Step-by-step explanation:
Students had two options for lunch, either a taco salad or a hot dog.
The ratio of taco salads to hot dogs is 3:1.
If a total of 80 lunches were served, how many were hot dogs?
Answers
Answer:
ok, so the answer would be 27 hot dogs and 53 tacos salads
Step-by-step explanation:
Last year, the number of students enrolled in a school was 847. If this number increases by 9% the next year, how many students will there be?
Answers
Answer:
Original answer: 923.23
Can't have a fraction of a student, so I'd probably say 923
Step-by-step explanation:
Initial students: 847
Interest: 9%
You want 109%
Multiply: 847(1.09)
(-1,0)
(-1,3)
Find the rate
Answers
Answer:
The answer is 3/0, which is undefined/∞
Step-by-step explanation:
3-0=3
-1+1=0
3/0= undefined or ∞
A manufacturing company produces x units this week and wants to increase its weekly output by 135 units by next week. The company hopes to make 1450 units next week. Which equation can be used to find x?
Answers
Answer:
x + 135 = 1450
Step-by-step explanation:
It says that they are trying to increase the output by 135 so you have the variable to show how much they have to make to reach there goal of 1450 next week
I hope this helped you!
PLZ HELP!!! I NEED THIS ASAP!!
Triangles ACD and BCD are isosceles. Angle BAC has a measure of 17 degrees and angle BDC has a measure of 52 degrees. The measure of angle ABD is __ degrees
A-163
B-142
C-76
D-159
E-141
Answers
Answer:
D-159
Step-by-step explanation:
The required measure of angle ABD is 142°. Option B is correct.
Given that,
Triangles ACD and BCD are isosceles. Angle BAC has a measure of 17 degrees and angle BDC has a measure of 52 degrees.
The triangle is a geometric shape that includes 3 sides and the sum of the interior angle should not greater than 180°
Here,
According to the question,
ΔBDC,
∠BDC + ∠BCD + ∠DBC = 180
52 + 52 + ∠DBC = 180
∠DBC = 180 - 104
∠DBC = 76°
Now,
∠ABD = 360 - ∠DBC / 2
∠ABD = [360 - 76] / 2
∠ABD = 284/2
∠ABD = 142°
Thus, the required measure of angle ABD is 142°. Option B is correct.
Learn more about triangles here:
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PLEASE HELP ME (20 POINTS)
Answers
Answer:
Not always.
Step-by-step explanation:
https://brainly.com/question/18051242?referrer=fromSearch
Click an item in the list or group of pictures at the bottom of the problem and, holding the button down, drag it into the
correct position in the answer box. Release your mouse button when the item is place. If you change your mind, drag
the item to the trashcan. Click the trashcan to clear all your answers.
For the right triangle shown, the lengths of two sides are glven. Find the third side. Leave your answer in simplified,
radical form.
B.
с
a
b
b = 9, C = 16
415
6 8
910
lab
Answers
Answer:
a = 5√7
Step-by-step explanation:
Sides of a right triangle follow the Pythagoras theorem,
By Pythagoras theorem,
(AB)² = (BC)² + (AC)²
c² = a² + b²
If b = 9 and c = 16,
(16)² = a² + 9²
256 = a² + 81
a² = 256 - 81
a = √175
a = 5√7
Therefore, measure of third side a = 5√7
Using the slope and the y-intercept, graph the line represented by the following equation. Then identify the figure showing that graph.
2y+4=0
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The graph will be Option C. passing through the point y = -2
The equation of line is y = -2 and the graph will be passing through the point y = -2
What is an Equation of a line?
The equation of a line is expressed as y = mx + b where m is the slope and b is the y-intercept
And y - y₁ = m ( x - x₁ )
y = y-coordinate of second point
y₁ = y-coordinate of point one
m = slope
x = x-coordinate of second point
x₁ = x-coordinate of point one
The slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )
Given data ,
Now , the equation of the line is given by
2y + 4 = 0
Subtracting 4 on both sides , we get
2y = -4
Divide by 2 on both sides , we get
y = -2
Therefore , the equation of line is y = -2
So , the line graph will be having a straight line 2 units down on the negative y-axis
Hence , the equation of line is y = -2 and the graph will be passing through the point y = -2
To learn more about equation of line click :
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Problem 1:
1. Define the variable:
1. Trini needs more than 51
cubic feet of soil to top up
his raised garden. Each bag
of soil contains 1.5 cubic
feet. Write and solve an
inequality to find how many
bags of soil Trini needs.
2. Write the inequality:
5 times b greater than 51
3.
Solve the inequality
4. Interpret the solution
Answers
Answer:
1) The variable is x
2) [tex]1.5x > 51[/tex] Solving the inequality we get x>34
3) [tex]5b > 51[/tex], solving the inequality we get b>10.2
Step-by-step explanation:
1. Define the variable:
The variable is x
2) Trini needs more than 51 cubic feet of soil to top up his raised garden. Each bag of soil contains 1.5 cubic feet. Write and solve an inequality to find how many bags of soil Trini needs.
[tex]1.5x > 51[/tex]
Solving the inequality
[tex]x>\frac{51}{1.5}\\x>34[/tex]
Solving the inequality we get x>34
3) Write the inequality:
5 times b greater than 51
[tex]5b > 51[/tex]
4) Solving the inequality
[tex]5b > 51\\b>\frac{51}{5}\\b>10.2[/tex]
So, solving the inequality we get b>10.2
Please help easy questions (:
Answers
Answer:
1. x=66
2. x=-3
Step-by-step explanation:
1. x\6-2=9
add 2 to both sides
x\6=11
multiply both sides by 6
x=66
2. -7(3x-4)=91
distribute -7 into parenthesis
-21x+28=91
subtract 28 from both sides
-21x=63
divide both sides by -21
x=-3
Answer:
1: 66 2: -3
Step-by-step explanation:
9+2=11
11=x/6
x=66
-21x+28=91
91-28 = -21x
63=-21x
x = -3
What is -4.5 = 1.5 - x
Answers
Answer:
x=6
Step-by-step explanation:
help pleaseee and explain!!
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Answer:
D
Step-by-step explanation:
Its an abs value so you have to solve twice. Once for d - 3.5 < or equal to 1.5 which equals 5. You also have to solve for d - 3.5 > or equal to -1.5 which equals 2. So on the graph it has to be less than 5 and greater than 2 so you just connect the two and draw the line over the numbers in between the 2 and 5.
Help please!!!!!! And explain ur answer.. I will mark as BRAINLIEST.
Answers
Answer:
The total earning of commission on sales of 85, 000 will be:
[tex]3500+1050=4550[/tex]
Step-by-step explanation:
Total sales earning = 85,000As salesperson earns 5% commission the first 70,000.
[tex]\frac{5}{100}\:\times \:70\:000=3500[/tex]
As the salesperson earns 7% commission on the sales over 70,000.
As 15000 is the sales earning on which he will get commission 7%.
Because
85,000 - 70,000 = 15000So the 7% earning of salesperson will on 15000 will be:
[tex]\:\frac{7}{100}\:\times \:15\:000=1050[/tex]
Therefore, the total earning of commission on sales of 85, 000 will be:
[tex]3500+1050=4550[/tex]
Help me asap
The hanger image below represents a balanced equation. Write an equation to represent the image.
Answers
Answer:
1/5 + 2/5 = 3/5
Step-by-step explanation:
your welcome
Answer:
1/5+z=3/5
Step-by-step explanation: