Answers
[tex]Given: AD \parallel BCAD∥BC and AD=CB[/tex]
To Prove: [tex]AB \parallel DCAB∥DC[/tex]
1. [tex]AD \parallel BCAD∥BC , AD=CB[/tex]
Reason: Given
2. AC = AC
Reason: Reflexive Property of Equality
3. [tex]\angle 2 = \angle 3∠2=∠3[/tex]
Reason: If Lines are parallel, then Alternate Interior Angles are Equal).
4. [tex]\Delta ACD \cong \Delta CABΔACD≅ΔCAB[/tex]
Reason: SAS
5. [tex]\angle 1 = \angle 4∠1=∠4[/tex]
Reason: CPCTE
6. [tex]AB \parallel DCAB∥DC[/tex]
Reason: If Alternate Interior Angles are Congruent, then Lines are Parallel.
Answer:
The missing Statements and reasons are given below
Statement >> Reason
4. CB ≅ BC >> reflexive property of congruence
5. ∠ABC ≅ ∠DCB and ∠ACB ≅ ∠DBC >> Alternate interior angles theorem
6. ΔACB ≅ ΔDBC >> ASA congruence
7. AB ≅ DC and AC ≅ DB >> CPCTC
Related Questions
Only the a) part please!!!!
Answers
[tex](i)\\\\2A = \begin{pmatrix}3x \times 2 & 1 \times 2 & 5 \times 2\\0\times 2 & 2x \times 2 & -3 \times 2\end{pmatrix} = \begin{pmatrix}6x & 2 & 10\\0 & 4x & -6\end{pmatrix}\\\\\\(ii)\\\\2A + B = C\\\\\implies \begin{pmatrix}6x & 2 & 10\\0 & 4x & -6\end{pmatrix} + \begin{pmatrix}y & 0 & -4\\1 & -3y & 2\end{pmatrix} = \begin{pmatrix}31& 2 & 6\\1 & 17& -4\end{pmatrix}[/tex]
[tex]\implies \begin{pmatrix}6x+y & 2+0 & 10-4\\0+1 & 4x-3y & -6+2\end{pmatrix} = \begin{pmatrix}31 & 2 & 6\\1 & 17& -4 \end{pmatrix}\\\\\\\implies \begin{pmatrix}6x+y & 2 & 6\\1 & 4x-3y & -4\end{pmatrix} = \begin{pmatrix}31 & 2 & 6\\1 & 17& -4 \end{pmatrix}\\\\\text{System of equations},\\\\6x +y =31,~~ 4x -3y = 17\\\\\\(iii)\\\\6x +y-31 =0 \\\\4x-3y -17=0\\\\\text{Solving by cross multiplication method}\\\\\\\dfrac x{1(-17) - (-31)(-3)} = \dfrac y{4(-31) - 6(-17)} = \dfrac 1{6(-3) - 4(1)}[/tex]
[tex]\implies \dfrac{x}{-17 -93} = \dfrac{y}{-124 +102} = \dfrac 1{-18-4}\\\\\\\implies -\dfrac{x}{110} = -\dfrac{y}{22} = -\dfrac 1{22}\\\\ \implies \dfrac{x}{110} = \dfrac{y}{22} = \dfrac 1{22}\\\ \\\text{Hence,}\\\\\\x=\dfrac{110}{22}=5,~~~~ y= \dfrac{22}{22} =1[/tex]
Answer:
(i)
[tex]2A=\left[\begin{array}{ccc}6x&2&10\\0&4x&-6\end{array}\right][/tex]
(ii) 6x+y=31; 4x-3y=17
(iii) (x, y) = (5, 1)
Step-by-step explanation:
(i)The matrix 2A is written by multiplying each element of A by 2.
[tex]2A=\left[\begin{array}{ccc}6x&2&10\\0&4x&-6\end{array}\right][/tex]
__
(ii)Variables are seen in elements (1, 1) and (2, 2) of the matrices A and B, so the simultaneous equations can be chosen from those elements of the equation 2A+B=C.
6x+y=314x-3y=17__
(iii)A graphing calculator shows the solution to be (x, y) = (5, 1).
Mr. Capp runs his own disc golf store every Saturday. The first customer of the day came in and bought
1 driver and 2 putters for $43. The second customer came in and bought 3 drivers and 1 putter for $69.
How much money does one driver and one putter cost at Mr. C's store?
Answers
Answer:
a driver costs $19, while a putter costs $12
Step-by-step explanation:
driver = d
putter = p
1d + 2p = 43
3d + 1p = 69
d + 2p = 43. eq 1
3d + p = 69. eq 2
make d the subject of the equation
d = 43 - 2p. eq 3
substitute the value of d in eq 3 in eq 2
3(43 - 2p) + p = 69
129 - 6p + p = 69
collect like terms
129 - 69 = 6p - p
60 = 5p
p = 12
substitute the value of p in eq 3
d = 43 - 2(12)
d = 43 - 24
d = 19
15,735 children visited a fun park in January and 32,012 children visitedit in February. How many children visited the fun park in 2 months?
Answers
A computer artist created a rectangular image measuring 50 millimeters by 120 millimeters. She then dilated the image by a scale factor of 2.5. What are the dimensions of the dilated image?
A
125 millimeters by 120 millimeters
B
52.5 millimeters by 122.5 millimeters
C
125 millimeters by 300 millimeters
D
20 millimeters by 48 millimeters
Answers
The dimensions of the dilated image is 125 millimeters by 300 millimeters.
An image is dilated if the dimensions of the image is resized in a way that does not change the shape of the image. When an image is dilated, it is made larger.
The scale factor is 2.5. This means that the dimensions are 2.5 larger. Dimensions of the dilated image : 50 x 2.5 and 120 x 2.5 = 125 mm by 300 mm
To learn more about dilation, please check: https://brainly.com/question/3457976
67-7x(12-3)
Evaluate
Answers
Answer:
67-63x
Step-by-step explanation:
Please, Help with this MATH question.
Answers
Ali uses 1.5 cups of flour to bake a dozen cupcakes. at this rate,how many cups of flour will she need to bake 30 cupcakes?
A.3.75c
B.3c
C.2.4c
D.2.75c
Answers
Answer:
A
Step-by-step explanation:
1.5 c flour = 12 cupcake
0.75 c flour = 6 cupcake
1.5 + 1.5 + 0.75 = 3.75 c flour
What is the slope of the line?
Answers
Answer:
(1,1)
Step-by-step explanation:
What is the angle, in degrees, when the coordinate is [tex](-\sqrt{2} /2), \sqrt{2} /2)[/tex] ? Pls help thanks
Answers
Answer:
135°
Step-by-step explanation:
seg AB=seg OB
tan ∠AOB = 1
∠AOB = 45°
∠AOC = 135°
Describe the type of correlation each scatter plot shows. Draw a trend line that
models each data set and find the equation of that trend line.
Answers
The correlation coefficients off both the scatter plots are mentioned above.
What is correlation?Correlation is a statistical measure that expresses the extent to which two variables are linearly related.The sample correlation coefficient is defined as[tex]${\displaystyle {\begin{aligned}r_{xy}&={\frac {\sum x_{i}y_{i}-n{\bar {x}}{\bar {y}}}{ns'_{x}s'_{y}}}\\[5pt]&={\frac {n\sum x_{i}y_{i}-\sum x_{i}\sum y_{i}}{{\sqrt {n\sum x_{i}^{2}-(\sum x_{i})^{2}}}~{\sqrt {n\sum y_{i}^{2}-(\sum y_{i})^{2}}}}}.\end{aligned}}}[/tex]
where [tex]{\displaystyle s'_{x}}[/tex] and [tex]{\displaystyle s'_{y}}[/tex] are the uncorrected sample standard deviations of
X and Y.
Given are the scatter plot graphs as shown.
For the graph {1}, the correlation coefficient is positive and is in range of between 0.7 to 0.8
For the graph {2}, the correlation coefficient is negative and is in range of between -0.4 to 0.45
Therefore, the correlation coefficients off both the scatter plots are mentioned above.
To solve more questions on correlation, visit the link below -
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HELP!...................................................
You start your Thanksgiving morning doing the Turkey Trot, a 5K run, with friends. Your mom said you need to be at the Thanksgiving celebration by 11:30am to help prepare the side dishes. In order to get there on time, you have to plan ahead. The Turkey Trot starts at 8:00am. You have allotted 1.25 hours after the trot to stretch, and get home. It takes you 0.75 hours to shower and get ready. The drive to the Thanksgiving dinner is 0.9 hours. At what speed (in km/hr) do you need to run the Turkey Trot in order to still be on time to Thanksgiving on time?
Answers
Answer:
1.6 hrs remaining, or 3.12 km/h
Step-by-step explanation:
Bub buys a t - shirt for $7.45. He pays with a $20 bill . How much change will he get
Answers
Answer:
12.55
Step-by-step explanation:
Please help find these values.
Answers
Answer:
3. x=14° y=7
4. x=29° y=3
Step-by-step explanation:
3. this is a 45 - 45- 90 triangle
so the side is a-a-a√2 ( two sides are the same)
4y-3=10+2y+1 -- collect like terms
4y-2y=10+1+3
2y=14
y=7
find the angle of the inside triangle
180-59-90 =
31°
we know the big triangle was a 45-45-90 angle
so x+31=45
x=45-31
x=14°
4. this is a square, all sides are same
5y+3y=24
8y=24
y=3
angle is 90°
x+x+9y+5=90
we know y=3 --substitute
x+x+9(3)+5=90
2x+27+5=90
2x=90-27-5
2x=58
x=58/2
x=29
Ms. Lopez wants to buy an ipod. The ticket price shows $225. But she only brought $146.50 to the store. What percent discount would she need so that the ipod sells at the exact amount she has in her pocket?
Answers
Answer: 65.11%
Step-by-step explanation:
Quick easy question
Answers
Answer:16
Step-by-step explanation:
144^0.5 = 12
400^0.5 = 20
a^2=b^2+c^2
20^2 = 12^2 +x^2
x^2 = 400-144= 256
x =16
Answer:
16
Step-by-step explanation:
Jeremy solved 35 problems, which is (5)/(7) of all his homework problems. How many problems are in his homework?
ASAP
Answers
Answer:
49
Step-by-step explanation:
make an equation:
5/7x=35
x=35*7/5
x=7*7
x=49
x is the total amount
A grocery store buys cereal using the cost function c(n) = { 2n when n < 100 1. 9n when 100 ≤ n ≤ 500 1. 8n when n > 500 where n is the number of boxes of cereal the grocery store buys and c(n) is the cost of the cereal. The grocery store then sells the cereal using the sales function s(c) = 1. 3c. What is the grocery store's sales from selling cereal if the grocery store buys 100 boxes and sells all of them?.
Answers
The grocery store's sales from selling cereal if the grocery store buys 100 boxes and sells all of them are $247
From the given function, we can see that the equivalent function for a number of 100 boxes is given as;
c(n) = 1.9n
If n = 100
c(100) = 1.9(100)
c(100) = 190
Hence the cost of 100 boxes will be $190
Given the sales function s(c) = 1. 3c, the grocery store's sales from selling cereal if the grocery store buys 100 boxes will be expressed as:
[tex]s(c) = 1. 3c\\s(190)=1.3(190)\\s(190)=$247[/tex]
Hence the grocery store's sales from selling cereal if the grocery store buys 100 boxes and sells all of them are $247
Learn more on functions here: https://brainly.com/question/17043948
ILL GIVE BRAINLIEST
Two machines are printing shirts. The first machine can produce 2,100 shirts in 140 minutes. The second machine can produce 2,400 shirts in 120 minutes. If the two machines work together, how long will it take them to produce 7,350 shirts? If necessary, round your answer to the nearest whole number.
Answers
Answer:
210
Step-by-step explanation:
so first i found out how many shirts each prints in a minute
the first machine produced 15/min
the second produced 20/min
now I added the 2 together and got 35
7,350/35 is 210
The number of hours required to paint a house varies indirectly to the number of painters. If 5 painters painted a house in 120 hours, how many painters would be required to paint a similar house in 50 hours?
Answers
The answer is 2 workers coz there can't be 2.08333... workers
I
Table for a linear equation
Fill in the table using this function rule.
y = 5x-2
X
y
Х
?
- 1
0
1
2
Answers
The sunglasses cost €70
The exchange rate is €1 = £0.895
Emad says, “The sunglasses cost less than £60"
b) Using a suitable approximation, show that Emad is wrong.
Answers
Answer:
70 * 0.895 = 62.65
OR
1 0.895
70 x
-Cross-multiply
[tex]\frac{70 * 0.895}{1}[/tex] = 62.65
please help me asap, i suck at math tbh :)
ty!
Answers
y intercepts: (0,-6)
Answer:
Y intercept = (0,-6)
X intercept = (9,0)
Step-by-step explanation:
To find the y-intercept of an equation, let x = 0 and then solve for y
6(0) - 9y = 54 (6 times 0 gives us 0)
0 - 9y = 54 (subtract 9y from 0 gives you -9)
-9y = 54 (divide both sides by -9, the left side cancels out and the right side gives you -6)
y = -6 and x = 0
To find the x-intercept of the equation just let y = 0 and then solve for x
6x - 9(0) = 54 (9 times 0 gives us 0)
6x - 0 = 54 (subtract 0 from 6x gives us 6x)
6x = 54 (divide both sides by 6, left side cancels, right side gives 9)
x = 9 and y = 0
At the craft store, Franklin bought a bag of red and brown marbles. He received 33 red marbles and 67 brown marbles. What percentage of the marbles were red?
Answers
Answer:
33% of the marbles were red
Pleaseee this is a grade and i need to get my 67 to a 70 or above
Answers
Answer: a. [tex]f(x)=3^{x}[/tex]
Step-by-step explanation:
You can plug in the x and y values to get [tex]f(x)=3^{x}[/tex]
If the probability that the Islanders will beat the Rangers in a game is 1/3, what is the
probability that the Islanders will win exactly three out of three games in a series
against the Rangers? Round your answer to the nearest thousandth.
Answers
Answer:
1/3 ^ 1/3 * 1/3 = (1/3)^3 = 1/27
simply the expresstion: 5+8 (3 + x )
Answers
Answer:
29+8x
Step-by-step explanation:
5+8(3+x)
Expand 8(3+x)
= 5+24+8x (add the numbers)
= 29+8x
35% of (blank) days is 7 days
Answers
Answer:
2.45 days.
Step-by-step explanation:
35% of 7 days is 2.45 days :) please thank.
This should be 20.
50% of 20 is 10. If you subtracted 15% from 10, you would get 3 which then makes it 7. Therefore, 35% of 20 days is 7 days.
How do you write an equation of a line so that it is parallel or perpendicular to a given point??
Answers
The equation of a line so that it is perpendicular to a given point will be
y-y0=[tex]\frac{-1}{m}[/tex] (x - xo)
The equation of a line so that it is perpendicular to a given point will be
y-y0=m (x - xo)
The standard equation of the line is better written in point-slope form expressed as:
y-y0=m(x - xo)
where: m is the slope of the given line (x0, y0) is any point of the giuven line.
m is the slope of the given line
(x0, y0) is any point on the given line
If the given slope of the line is m, the slope of the line perpendicular will be expressed as -1/m
The equation of a line so that it is perpendicular to a given point will be
y-y0=[tex]\frac{-1}{m}[/tex] (x - xo)
2 (x + 4) = 2 (-8 - x) - 2x
Answers
Answer:
x = -4
Step-by-step explanation:
Simplifying
2[x + 4] = 2[-8 + -1x] + -2x
Reorder the terms:
2[4 + x] = 2[-8 + -1x] + -2x
[4 * 2 + x * 2] = 2[-8 + -1x] + -2x
[8 + 2x] = 2[-8 + -1x] + -2x
8 + 2x = [-8 * 2 + -1x * 2] + -2x
8 + 2x = [-16 + -2x] + -2x
Combine like terms: -2x + -2x = -4x
8 + 2x = -16 + -4x
Solving
8 + 2x = -16 + -4x
Solving for variable 'x'.
Move all terms containing x to the left, all other terms to the right.
Add '4x' to each side of the equation.
8 + 2x + 4x = -16 + -4x + 4x
Combine like terms: 2x + 4x = 6x
8 + 6x = -16 + -4x + 4x
Combine like terms: -4x + 4x = 0
8 + 6x = -16 + 0
8 + 6x = -16
Add '-8' to each side of the equation.
8 + -8 + 6x = -16 + -8
Combine like terms: 8 + -8 = 0
0 + 6x = -16 + -8
6x = -16 + -8
Combine like terms: -16 + -8 = -24
6x = -24
Divide each side by '6'.
x = -4
Simplifying
x = -4
2( x + 4) = 2 (-8 -x) -2x
Use the distributive property to multiply 2 by x + 4.
2x + 8 = 2 (-8 -x) - 2x
Use the distributive property to multiply 2 by -8 -x.
2x + 8 = -16 -2x - 2x
Combine -2x and 2x to get -4x.
2x + 8 = -16 - 4x
Add 4x to both sides.
2x + 8 + 4x = -16
Combine 2x and 4x to get 6x.
6x + 8 = -16
Subtract 8 from both sides.
6x = -16 - 8
Subtract 8 from -16 to get -24.
6x = -24
Divide both sides from 6.
x = [tex]\frac{-24}{6}[/tex]
Divide by -24 by 6 to get -4.
x = -4.
The graph shows Kendra's morning run:
Which interval on the graph shows Kendra stopping to tie her shoes and stretch? (4 points)
A
B
C
D
Answers
The interval which is horizontal and has a slope of zero shows no distance was covered while time kept increasing, therefore, the interval that shows Kendra stopping to tie her shoes and stretch is: C.
Recall:
A horizontal line on a graph shows rise, and a slope of zero.Given the graph showing Kendra's morning run, where time running is plotted on the horizontal axis (x-axis) while distance run is plotted on the vertical axis (y-axis).
Thus, the interval which is horizontal and has a slope of zero shows no distance was covered while time kept increasing, therefore, the interval that shows Kendra stopping to tie her shoes and stretch is: C.Learn more about horizontal graphs on:
https://brainly.com/question/13483111