ABCD is a quadrilateral, P Q R and S divide AB, CB, CD and AD in ratio 1:3 respectively. Prove that a//m. (Please hurry up, I will mark you as Brainliest)
Answers
Two lines are parallel if they are equidistant from one another. The following proves [tex]a || m[/tex]
[tex]Ratio = 1:3[/tex] means that:
[tex]BP=3PA[/tex]
[tex]BQ=3QC[/tex]
To prove that [tex]a || m[/tex] is to prove that side length SR and side length PQ are parallel because:
[tex]SR = a\\ PQ = m[/tex] --------- See attachment for quadrilateral
Considering [tex]\triangle ABC[/tex], we have: [tex]BP=3PA[/tex]
Divide both sides by PA
[tex]\frac{BP}{PA} = \frac{3PA}{PA}[/tex]
[tex]\frac{BP}{PA} = 3[/tex]
Similarly: [tex]BQ=3QC[/tex]
Divide both sides by QC
[tex]\frac{BQ}{QC} = \frac{3BQ}{QC}[/tex]
[tex]\frac{BQ}{QC} = 3[/tex]
So, we have:
[tex]\frac{BP}{PA} = \frac{BQ}{QC} = 3[/tex]
Express as ratios
[tex]BP:PA = BQ:QC = 3[/tex]
[tex]BP:PA \to[/tex] means point P divided side length BA into 3:1
[tex]BQ:QC \to[/tex] means point Q divided side length BC into 3:1
Thales Theorem states that: A line that divides any two sides of a triangle in the same ratio is parallel to the third side.
The third side of [tex]\triangle ABC[/tex] is [tex]AC[/tex].
This means that: [tex]PQ[/tex] is parallel to [tex]AC[/tex]
Since [tex]AC[/tex] is parallel to [tex]SR[/tex], then [tex]PQ[/tex] is parallel to [tex]SR[/tex]
i.e. [tex]SR || PQ[/tex]
Recall that:
[tex]SR = a\\ PQ = m[/tex]
Hence:
[tex]a || m[/tex] has been proved.
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Related Questions
mean marks of 100 students was 40.. It was discovered that 53 was misread as 83. Find the actual mean.
Answers
mean marks of 100 students was 40.. It was discovered that 53 was misread as 83. Find the actual mean.
Solution:-Total mean score = 40
[tex]mean \: = \frac{sum \: of \: observation}{number \: of \: observations} [/tex]
sum of observations
= mean × no of observations
= 40×100
= 4000
After the replacement, sum of new observation will be
=4000-83+53
= 3970
mean of new the observation will be
[tex] = \frac{3970}{100} [/tex]
[tex] = 39.7[/tex]
[Hence, the actual mean is 39.7]
What is the value of c ?
Answers
Answer:
the value of c is 70
Pls pls pls pls help me
Answers
Answer:
96 cm²
Step-by-step explanation:
Triangular face:
base = 8 cm
height = 6 cm
Area of triangle = [tex]\dfrac{1}{2}*b*h[/tex]
[tex]= \dfrac{1}{2}*8*6\\\\=4*6\\\\= 24 \ cm^{2}[/tex]
Area of 4 triangular faces = 4 * 24 = 96 cm²
Lucia quiere repartir 4/5 litros de leche entre sus dos hijos en partes iguales. ¿Cuánto le dará a cada hijo?
Answers
17. Test Practice which represents the number that is ten more than two
thousand, seventy?
A 280
® 2,008
© 2,080
0 2,800
Answers
Answer:
2,080
Step-by-step explanation:
Two thousand and seventy is written as 2,070.
Ten more than 2,070 would be 2,080 as you're just adding on 10.
Hope this helps :)
Match the arc or central angle to the correct measure based on the figure below.
Answers
Answer:
a. 50 degrees
b. 130 degrees
c. 180 degrees
d. 230 degrees
a. 50°
b. 130°
c. 180°
d. 230°
what is geometry?geometry, the department of mathematics deals with the shape of individual objects, spatial relationships among various objects, and the properties of surrounding space.
various shapes in geometry have different angle measures. as an example: A triangle is a 3-sided shape and the sum of its 3 interior angles is 180˚ A square, rectangle or quadrilateral are 4-sided shapes, and the sum of their four interior angles is 360˚
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Please help explanation if possible
Answers
Answer:
y = | x-5|
Step-by-step explanation:
y = |x-h| +k where (h,k) is the center of the "v"
The "v" is located at (5,) so h=5 and k = 0
y = | x-5| +0
What are the x-intercepts of the graph of the function below?
y= x^2+3x – 28
A. (6,0) and (4,0)
B. (-7,0) and (-4,0)
C. (7,0) and (-4,0)
D. (-7,0) and (4,0)
Answers
I did the math
Graph the line that passes through the points (-3,-6) and (8,-6)and determine the equation of the line.
Answers
Answer:
Y = -6
Step-by-step explanation:
x1 y1 x2 y2
-3 -6 8 -6
(Y2-Y1) (-6)-(-6)= 0 ΔY 0
(X2-X1) (8)-(-3)= 11 ΔX 11
slope= 0
B= -6
Y = -6
3 cm
20 cm
4 cm
Find the volume of the rectangular prism.
[?] cm
Enter
Answers
Answer:
240cm^3
Step-by-step explanation:
3cmx20cmx4cm=240cm^3
the perimeter of a right angled triangle is 60 cm and its area is 120cm².find the lengths of the triangle.
Answers
Step-by-step explanation:
The area of triangle given as 120 cm2
Area of Triangle = 1/2 x b x h = 120
therefore bxh = 240
240 can be factorized as 10 x 24
The perimeter of the triangle is given as 60
so the other side has to be 26 cm
As this is a right angle triangle it should satisfy pythagoras theorem
(10)2 + (24)2 = (26)2
100+576 =676
Hence the sides of the triangle are 10 cm, 24 cm and 26 cm
Simplify 7(A - 6).
A - 6
7A - 6
7A - 42
Answers
Answer:
7A-42
Step-by-step explanation:
What is the perimeter of a square which has the same area as a circle with circumfrence of 4π
Answers
Answer:
Perimeter square = 8 sqrt(pi)
Step-by-step explanation:
The perimeter of a square is 4*s
The area of a circle is Area = pi * r^2
The circumference of a circle is C = 2*pi * r
C = 4 pi
4pi = 2*pi * r
r = 2
So the area of the circle is pi * r^2 = pi * 2^2 = 4pi
The square has the same area
Area = 4*pi
Square = 4*pi
s^2 = 4*pi
s = sqrt(4*pi)
s = 2*sqrt(pi)
The perimeter = 4 * 2 * sqrt(pi)
The perimeter = 8 * sqrt(pi)
The graph of y vx is translated 5 units to the left and 7
units up. What is the equation of the graph that results from
this translation?
Answers
y=-1.4x
Step-by-step explanation:
divide the change in y by the change in x to find the gradient,
7 divided by -5 [as the translation is to the left].
there might be a y intercept value, c as in
y=mx + c but with the given information without thee starting points it is hard to find
The required equation of the graph that results from the translation is y = √(x + 5) + 7.
What is translation on the coordinate plane?Translation on a coordinate plane is a transformation that moves an object or figure from its original position to a new position in a straight line. It is also called a "slide." In translation, all points of the object are moved by the same distance in the same direction.
Here,
To shift the graph of the function y = √x to the left by 5 units, we need to replace x with x + 5 in the equation. This will give us the graph of y = √(x + 5).
To shift the graph 7 units up, we need to add 7 to the entire function. This will give us the final equation of the translated graph:
y = √(x + 5) + 7.
Therefore, the equation of the graph that results from the translation is y = √(x + 5) + 7.
Learn more about translation here:
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Zero is_______greater than any negative integer.
always
never
sometimes
Answers
Answer:
always
Step-by-step explanation:
Zero is always greater than any negative integer.
All the negative integers lie to the left of 0 on the number line. This implies that zero is always greater than any negative integer.Perform the indicated operation.
Help
5/8 + 7/12
5/24
1/5 24
1/2
Answers
Answer:
29/24 or 1 5/24
Step-by-step explanation:
5/8 + 7/12
~Have common denominators
15/24 + 14/24
~Add
29/24
Best of Luck~
The height of a triangle is 5cm more than half the base of the triangle. The area of the triangle is 6cm^2. Find the base and height of the triangle
Answers
Answer:
Base = 2 cm and height = 6 cm.
Step-by-step explanation:
Area = 1/2 * base + height
Let b be the base and h = height of the given triangle, then
6 = b/2 * h
6 = b/2(b/2 + 5)
b^2/4 + 5b/2 - 6 = 0
b^2 + 10b - 24 = 0
(b + 12)(b - 2) = 0
b = 2 (we neglect the negative b = -12)
So h = b/2 + 5 = 2/2 + 5 = 6.
1. Ms. Rogers earns $___ each month. She pays 25% of her earnings, or $____ in federal taxes and 6% of her earnings, or $____ in state taxes. She pays ____ % of her earnings, or $____ for insurance. After these deductions, Ms. Rogers takes home $_____
131.76
8
175.68
549
2,196
1,339.56
Answers
Answer:
2,196; 549; 131.76; 8; 175.68; 1339.56
Step-by-step explanation:
2,196 is the biggest number, so use that as the first number.
.25x2196=549
.06x2196=131.76
.08x2196=175.68
2196-(549+131.76+175.68)=1339.56
Write the integer represented by H. List its opposite and absolute value.
Answers
Answer:
The integer represented by H is -2
Its opposite is 2 and the absolute value is also 2
Answer:The integer represented by H is -2
Step-by-step explanation:
4(v+4)–7=17 please help me
Answers
Answer:
v = 2Step-by-step explanation:
4(v+4)–7=17
=> 4(v + 4) = 17 + 7
=> 4v + 16 = 24
=> 4v = 24 - 16
=> 4v = 8
[tex] = > v = \frac{8}{4} [/tex]
=> v = 2 (Ans)
Answer:
v=2
Step-by-step explanation:
4(v+4)–7=17
Distribute
4v+16 -7 = 17
Combine like terms
4v +9 =17
Subtract 9 from each side
4v+9-9=17-9
4v = 8
Divide by 4
4v/4 = 8/4
v=2
Find th slope of the line passing through the points (5,8) and (6,12)
Answers
Answer:
Slope= 4
Step-by-step explanation:
y2-y1/x2-x1
5=x1 8=y1 etc.
12-8/6-5
=4/1
Answer:
The slope of the line is 4.
Step-by-step explanation:
To solve for the slope of the line, use the rise over run formula. The rise over run formula is a measure of how much something changes vertically compared to how much it changes in the horizontal direction. The rise over run formula calculates the difference between the two points in the vertical direction (rise) and then divide it by the difference in the horizontal direction (run). The formula looks like [tex]\frac{rise}{run}[/tex], but in terms of finding a slope, it looks like [tex]\frac{y_{2}-y_{1} }{x_2-x_1}[/tex].
For finding the slope of this line with the points (5,8) and (6,12), start by writing down the information given from the question.
[tex]y_2=12[/tex]
[tex]y_1=8[/tex]
[tex]x_2=6[/tex]
[tex]x_1=5[/tex]
Next, plug in the information given from the question into the formula, and the formula will look like [tex]\frac{12-8}{6-5}[/tex]. Then, simplify the equation, which will look like [tex]\frac{4}{1}=4[/tex]. The final answer will be 4.
Suppose a graph passes the horizontal line test: No horizontal line can be drawn that touches the graph in more than one location. Does this mean that the graph represents a function? If not, is there anything special about a graph that passes the horizontal line test? Share your ideas with a classmate.
Answers
Answer:
Step-by-step explanation:
If a function passes the horizontal line test, then we may conclude that the inverse of the function exists and can be found.
Choose the correct description of the graph of the compound inequality:
x-3<-9 or x+5>equal to 12
Answers
Answer:
C
Step-by-step explanation:
x - 3 < -9
simplifies to x < -6, which is to the left with an open circle
x + 5> 12
simplifies to x > 7, which is to the right a closed circle
PLS HELP ME ON THIS QUESTION I WILL MARK YOU AS BRAINLIEST IF YOU KNOW THE ANSWER PLS ANSWER THE QUESTION WITH A STEP BY STEP EXPLANATION!!
A sample of 100 U.S. architects are asked to use a new pencil and express their opinions on the pencil. The population in this study is ________________.
A. all pencils used by the architects
B. all U.S. architects
C. the 100 U.S. architects
D. all pencils
Answers
i think the correct answer is C
Answer:
C
Step-by-step explanation:
Find the measure of the missing angles.
b =
C=
Answers
Answer:
Angle C and Angle B 61 degree as Angle 119 is supplementary to angle B and C (180-119=61)
PLEASE HELP 46 POINTS!!!
Answers
Answer:
Step-by-step explanation:
a) Input = -9 ⇒ x = -9
y = x² + 3
Plugin x = (-9),
y = (-9)² + 3
= 81 + 3 {(-9)² = -9 * (-9) = 81}
y = 84 ---> Output
y = √x - 2
= √-9 - 2 { i² = -1}
[tex]= \sqrt{3*3 * i^{2}}-2\\\\=3i -2[/tex]
y = 3i - 2 ------> Output
b) Output = 0
y = x² + 3
x² + 3 = 0
x² = -3
[tex]x = \sqrt{-3}=\sqrt{3i^{2}}\\\\x = i \sqrt{3}[/tex]
y = √x -2
0 = √x - 2
√x = 2
Take square,
[tex](\sqrt{x})^{2}=2^{2}\\\x = 4[/tex]
Someone please helppp
Answers
Answer:
true
Step-by-step explanation:
y = 5x+6
To find the inverse, exchange x and y
x = 5y+6
Solve for y
x-6 = 5x+6-6
x-6 = 5x
Divide by 5
x/5 - 6/5 = 5y/5
1/5x - 6/5 = y
The inverse is (x-6)/5
NEED HELP ASAP!
Slove for x.
A.4
B.10
C.8
D.7
Answers
i think it 10 because the angle your looking at is x is 7
monday through friday a baker uses 1 1/4 sacks of flour when baking cakes. will the baker use more than or less than 5 sacks of flour from monday through friday?
Answers
Answer:
more than 5 sacks
Step-by-step explanation:
1 1/4 sack of flour per day
5 days
5 * 1 1/4
Change to an improper fraction
5 * (4*1+1)/4
5 * 5/4
25/4
Change to a mixed number
6 1/4 sacks
Answer:
more than
Step-by-step explanation:
1 1/4 = mon - fri
1 1/4 * 5 (days) = 6.25
I hope this helped !6.25 > 5
a circle has a radius of 8.5cm correct to the nearest 0.1cm.
the lower bound of the area of the circle is pπ cm².
the upper bound of the area of the circle is qπ cm².
find the value of p and the value of q.
Answers
Answer:
The area of the circle is exactly π times the square of its radius. If you are given that the radius is within 0.1cm of 8.5cm, i.e. lies between 8.4 cm and 8.6 cm, its square will lie between p=8.4² = 70.56 and q=8.6² = 73.96 cm².
Answer:
The area of the circle is exactly π times the square of its radius. If you are given that the radius is within 0.1cm of 8.5cm, i.e. lies between 8.4 cm and 8.6 cm, its square will lie between p=8.4² = 70.56 and q=8.6² = 73.96 cm².
Step-by-step explanation:
thanks for question dear
