NO LINKS!!! Please assist me part 2a
Plot the points in the coordinate plane. Then determine whether AB and CD are congruent. Explain
Answers
Answer:
AB and CD are congruent.
Step-by-step explanation:
Given points:
A = (-4, 1)B = (-4, 8)C = (-2, -5)D = (5, -5)After plotting the given points (see attachment), we can easily determine that AB is 7 units and CD is 7 units. Therefore, AB and CD are congruent.
Alternatively, as points A and B share the same x-coordinate, the length of AB is the difference between the y-coordinates:
⇒ AB = 8 - 1 = 7 units
Similarly, as points C and D share the same y-coordinate, the length of CD is the difference between the x-coordinates:
⇒ CD = 5 - (-2) = 7 units
Finally, we can prove that AB and CD are congruent by calculating their lengths using the distance formula.
[tex]\boxed{\begin{minipage}{7.8 cm}\underline{Distance Formula}\\\\$d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$\\\\where $(x_1,y_1)$ and $(x_2,y_2)$ are the two endpoints.\end{minipage}}[/tex]
[tex]\begin{aligned}\implies AB & =\sqrt{(x_B-x_A)^2+(y_B-y_A)^2}\\& =\sqrt{(-4-(-4))^2+(8-1)^2}\\& =\sqrt{(0)^2+(7)^2}\\& =\sqrt{0+49}\\& =\sqrt{49}\\& =7\end{aligned}[/tex]
[tex]\begin{aligned}\implies CD & =\sqrt{(x_D-x_C)^2+(y_D-y_C)^2}\\ & =\sqrt{(5-(-2))^2+(-5-(-5))^2}\\ & =\sqrt{(7)^2+(0)^2}\\ & =\sqrt{49+0}\\ & =\sqrt{49}\\ & =7\end{aligned}[/tex]
Therefore, as AB = CD, this proves that AB and CD are congruent.
Related Questions
whats 26/7 as a mixed number
Answers
Answer:3 and 5/7
Step-by-step explanation:
An engineering school reports that 53% of its students are male (M), 37% of its students are between the ages of 18 and 20 (A), and that 31% are both male and between the ages of 18 and 20.
What is the probability of a random student being chosen who is a female and is not between the ages of 18 and 20?
Your answer should be to two decimal places.
Answers
The probability of a random probability of a random student being chosen who is a female and is not between the ages of 18 and 20 will be 0.06.
How to calculate the probability?From the information, 53% of its students are male (M), 37% of its students are between the ages of 18 and 20 (A), and that 31% are both male and between the ages of 18 and 20.
Probability to females = 100% - 53% = 47%
Therefore, the probability of a random student being male or between the ages of 18 and 20 will be:
= 37% - 31%
= 6%
Therefore, the probability of a random student being female or between the ages of 18 and 20 will be 6%.
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D(7,3) is the midpoint, (MP), of AB.
E(10, 4) is the MP of BC.
F(5,5) is the MP of AC
Find the coordinates of A, B, and C
Answers
vertex of A = (x1,y1) =(2,4)
vertex of B = (x2,y2)= (12,2)
vertex of c = (x3,y3) = (8,6)
Midpoint :
The midpoint is the middle point of a line segment. It is equidistant from both endpoints, and it is the centroid both of the segment and of the endpoints. It bisects the segment.
x= x1+x2/2
y=y1+y2/2
Now ,
D(7,3) is the midpoint of AB.
D (x',y') = (7,3)
vertex of A = (x1,y1)
vertex of B = (x2,y2)
x' = x1+x2/2
7 = x1+x2/2
14 = x1+x2 ...1
y' = y1+y2/2
3= y1+y2/2
6= y1+y2 .....2
E (x'',y'') = (10,4)
vertex of c = (x3,y3)
vertex of B = (x2,y2)
x''= x3+x2/2
y''=y3+y2/2
20= x3+x2 ....3
8 =y3+y2.......4
F (x''',y''') = (5,5)
vertex of c = (x3,y3)
vertex of A = (x1,y1)
10= x1 +x3 ...5
10 =y1+y3 .....6
For 1 & 3 & 5
14 = x1+x2 ...1
20= x3+x2 ....3
10= x1 +x3 ...5
Add all 1 & 3 & 5
44 = 2(x1+x2+x3)
22 = (x1+x2+x3) .....7
For 1 & 7
x3 = 8
For 3 & 7
x1 = 2
For 5&7
x2 = 12
For 2 , 4 & 6
6= y1+y2 .....2
8 =y3+y2.......4
10 =y1+y3 .....6
Add all 2 & 4 & 6
24 = 2 (y1+y2+y3)
For 2 & 8
y3 = 6
For 4 & 8
y1 = 4
For 6 & 8
y2 = 2
vertex of A = (x1,y1) =(2,4)
vertex of B = (x2,y2)= (12,2)
vertex of c = (x3,y3) = (8,6)
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esse rode his bike for 2 hours at a constant rate. During the first 1.5 hours, he rode 12 miles. How many miles did Jesse ride his bike during the last half hour? (Enter an exact number.)
mi
Answers
In the last half hour 4 miles did Jesse ride his bike.
What is distance?The distance of an object can be defined as the complete path travelled by an object .Distance is a scalar quantity that refers to "how much ground an object has covered" during its motion.
Given:
Jesse rode his bike for 2 hours at a constant rate.
First 1.5 hours, he rode 12 miles.
According to given question we have
1.5 hours=12 miles
1 hours=12/1.5
0.5 hours=12*0.5/1.5
0.5 hours=4 miles
Therefore, in the last half hour 4 miles did Jesse ride his bike.
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What is the slope of the line?
Answers
Answer: 3/-4
The slope is measured in terms of rise over run. Rise is how many units you go up or down from the point (0, 0). Run is how many units you go left to right from the point where rise left off. For this question, we go up 3 and to the left 4. SO that's a 3 on top and a -4 on the bottom.
I hope this helps! :) I'm a huge Algebra nerd!!! I love Algebra. :)
The area of this rectangle is 54 square inches. Create an equation to find the value of n. Length is 3(n-1) and the width is n+2
Answers
Value of n is 4
The area of a rectangle is equal to the product of its length and width.
we know ,
the area of rectangle, multiply the length, , and the width, ,
and set the product equal to the area.
area of rectangle = length * width
54 = 3(n - 1) * (n + 2)
54 =( 3n - 3) * (n + 2)
multiply ( 3n - 3) with (n + 2)
we get,
54 = [tex]3n^{2} + 6n - 3n -6[/tex]
54 = [tex]3n^{2} + 3n -6[/tex]
54 = 3([tex]n^{2} + n -2[/tex])
[tex]\frac{54}{3}[/tex] = ([tex]n^{2} + n -2[/tex])
18 = ([tex]n^{2} + n - 2[/tex])
[tex]n^{2} + n - 2[/tex] - 18 = 0
[tex]n^{2} + n - 20[/tex] = 0
solve them
[tex]n^{2} + 5n + 4n -20[/tex] = 0
n (n + 5) - 4 (n + 5) = 0
(n + 5)(n -4)
then we get,
n = -5 , n = 4
value of n should not be negative . so value of n is 4
Area of rectangle is the region occupied by a rectangle within its four sides or boundaries.
The area of a rectangle depends on its sides. Basically, the formula for area is equal to the product of length and breadth of the rectangle. Whereas when we speak about the perimeter of a rectangle, it is equal to the sum of all its four sides. Hence, we can say, the region enclosed by the perimeter of the rectangle is its area
Area of rectangle = Length x Breadth
A = lb
how to Factoring Quadratic Equation
Step 1: Consider the quadratic equation ax2 + b x + c = 0
Step 2: Now, find two numbers such that their product is equal to ac and sum equals to b.
(number 1)(number 2) = ac
(number 1) + (number 2) = b
Step 3: Substitute these two numbers in the formula given below:
(1/a) [a x + (number 1)] [a x + (number 2)] = 0
Step 4: Finally simplify the above equation.
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John's test grade is 5 points less than twice Ariana's test grade. If x represents Ariana's test grade, write an expression for John's test grade.
Answers
In linear equation, 2x - 5 is an expression for John's test grade.
What is linear equation in one variable?
The equation for a linear equation in one variable is written as ax+b = 0, where a and b are two integers, and x is a variable. This equation has only one solution. For instance, the linear equation 2x+3=8 only has one variable.A linear equation is an algebraic equation of the form y=mx+b, where m is the slope and b is the y-intercept, and only a constant and a first-order (linear) term are included. The variables in the preceding equation are y and x, and it is occasionally referred to as a "linear equation of two variables."Let Ariana's test grade = x
twice Ariana's test grade = 2x
then, John's test grade = 2x - 5
an expression for John's test grade = 2x - 5
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←
If a single fair die is rolled, find the probability of the following result.
An even number, given that the number rolled was 1.
Answers
Answer: so assuming this is a d6, it's 3/6
Step-by-step explanation:
on a d6, there are 6 sides (duh). three out of the six numbers are even, two four and six. so, three out of the six numbers you can roll are even.
How to do domain and range
Answers
Answer:
bjuk
Step-by-step explanation:
ftftrtt987652123456789
A quality control inspector has drawn a sample of 19 light bulbs from a recent production lot. If the number of defective bulbs is 1 or more, the lot fails inspection. Suppose 20% of the bulbs in the lot are defective. What is the probability that the lot will fail inspection? Round your answer to four decimal places.
Answers
The probability that the lot of the bulbs will fail inspection of the quality control inspector is 0.9856
How find the probability of the lot that will fail inspectionGiven data
p = 20%
sample drawn = 19 bulbs
20% of the bulbs in the lot are defective
n = 19
p = 20% = 0.20
if 20% of the bulbs are defective to find the non defective bulbs we solve as follows
q = 1 - p
= 1 - 0.20
= 0.80
Using binomial theorem,
[tex]P ( X = x) = (^n C _{x} ) * p x * (1 - p)n - x[/tex]
[tex]= 1 - P ( x < 1 )[/tex]
[tex]= 1 - P ( X = 0)[/tex]
[tex]= 1 - ( ^{19} C _{0} ) * 0.20^0 * (0.80)^{19}[/tex]
[tex]= 1 - 1 * 1 * 0.01441[/tex]
[tex]= 1 - 0.01441[/tex]
= 0.98559
= 0.9856 (to four decimal place)
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Joyce saved $150 on an item that was 35
%
off. What was the original price?
Write answer to the nearest cent.
Answers
$202.50 is your answer
17x12 help what do it equal
Answers
Answer:
Step-by-step explanation:
17
12
-----
do 7 x 2
14
then carry the 1
2x1 is 2 plus the 1 from before. it becomes 3
then do 1 x 7 then 1 x 1 but with an extra zero
so it becomes
17
12
---------
34
170
---------
then add it all together
34+170=204
Answer: 17*12=204
Step-by-step explanation: because of G O O G L E
Ken is playing with building blocks. He wants to put all 64 blocks into the same number of stacks. How many blocks could he put in each stack
Answers
Answer: He could put 8 blocks in 8 stacks
Step-by-step explanation:
Ken could put the blocks in stacks of 1, 2, 4, 8, 16, 32, or 64.
What is an expression?An expression contains one or more terms with addition, subtraction, multiplication, and division.
We always combine the like terms in an expression when we simplify.
We also keep all the like terms on one side of the expression if we are dealing with two sides of an expression.
Example:
1 + 3x + 4y = 7 is an expression.
3 + 4 is an expression.
2 x 4 + 6 x 7 – 9 is an expression.
33 + 77 – 88 is an expression.
We have,
To find out how many blocks Ken could put in each stack, we need to divide the total number of blocks by the number of stacks.
So we have:
Number of blocks = 64
Number of stacks = x
To find out how many blocks can be put in each stack, we can set up the following equation:
64 / x = y
where y is the number of blocks in each stack.
Solving for y, we get:
y = 64 / x
So if Ken wants to put all 64 blocks into the same number of stacks, he can put:
64 blocks in 1 stack
32 blocks in 2 stacks
16 blocks in 4 stacks
8 blocks in 8 stacks
4 blocks in 16 stacks
2 blocks in 32 stacks
1 block in 64 stacks
Therefore,
Ken could put the blocks in stacks of 1, 2, 4, 8, 16, 32, or 64.
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a. write a sequence too described the number of blocks needed to create the figure for each step.
b. how many blocks will be needed to create the next figure?
c. describe the sequence in words
3. in a sequence, the first term is 12 and the common difference is -5. find the 4th term of sequence
Answers
Using arithmetic sequences, it is found that:
a) The sequence is: [tex]a_n = 5 + 3(n - 1)[/tex].
b) 14 blocks will be needed to create the next figure.
c) The sequence means that the number of blocks start at 5 and increase by 3 each figure.
3) The 4th term of the sequence is of -3.
What is an arithmetic sequence?In an arithmetic sequence, the difference between consecutive terms is always the same, called common difference d.
The nth term of an arithmetic sequence is given by:
[tex]a_n = a_1 + (n - 1)d[/tex]
From the figure, we have that:
The Figure 1 has 5 dots.The Figure 2 has 8 dots.The Figure 3 has 11 dots.Hence the first term and the common ratio are given as follows:
[tex]a_1 = 5, d = 3[/tex]
The sequence is: [tex]a_n = 5 + 3(n - 1)[/tex], hence the sequence means that the number of blocks start at 5 and increase by 3 each figure.
For item b, the amount is:
[tex]a_4 = 5 + 3(4 - 1) = 14[/tex]
14 blocks will be needed to create the next figure.
For item 3, the sequence is given by:
[tex]a_n = 12 - 5(n - 1)[/tex]
Hence the 4th term is:
[tex]a_4 = 12 - 5(4 - 1) = -3[/tex]
The 4th term of the sequence is of -3.
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Solve the equation.
Question 1, 9.3.1
-6y+6= -2(4y + 4)
Solve
Answers
Solution : y = -7
One Variable in the linear equation :
The linear equation in one variable is an equation that is expressed in the form of ax+b = 0, where a and b are two integers, and x is a variable and has only one solution. For example, 2x+3=8 is a linear equation having a single variable in it. Therefore, this equation has only one solution, which is x = 5/2. Whereas if we speak about linear equations in two variables, it has two solutions.
-6y+6= -2(4y + 4)
-6y = -8y -8 -6
-6y +8y = -14
2y = -14
y = -14/2
y = -7
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Find the length of the segment AB with the endpoints as A(-3,7) and B(6,14).
Round to 1 decimal.
AB=
Answers
The length of AB is 11.40 units.
The length of two points can be calculated using the distance formulae.
The distance formulae comes under the Co-ordinate geometry section.
The distance between two points is measured by squaring the sum of the difference between the x and y co-ordinates and then applying the square root to the result.
Here the two points given are A(-3,7) and B(6,14).
The length of the line segment AB is = √(-3-6)²+(7-14)²
= √(-9)²+(-7)²
= √81+49
= √130
= 11.40 units
So, the length of line segment AB is 11.40 units.
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Marty placed $4000 into an account earning 4% simple interest. At the end of the year he moved the total amount to a new account earning 5% interest. Determine the amount of money Marty would have at the end of the second year.
Answers
Simple interest , 4368 is the amount of money Marty would have at the end of the second year.
What does the term "simple interest" mean?
Simple interest is calculated based on a loan's principal or the initial deposit into a savings account. Simple interest doesn't compound, therefore a creditor will only charge interest on the principal sum, and a borrower will never be required to pay further interest on the interest that has already accrued.P = $4000 R = 4% T = 1
then substitute the value into the formula = [tex]\frac{P * R * T }{100}[/tex]
= [tex]\frac{4000 * 4 * 1}{100}[/tex] = 160
So, the total amount is ( 4000 + 160) = 4160
Second year
P = 4160 , R = 5% T = 1
then substitute the value into the formula = [tex]\frac{P * R * T }{100}[/tex]
= [tex]\frac{4160 * 5 * 1}{100}[/tex] = 208
So, the total amount is ( 4160 + 208 ) = 4368
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from the graph of each parabola, determine whether the parabola opens upward or downward, and find the vertex, axis of symmetry, and range of the function. find the maximum and minimum value of the function and the intervals on which the function is increasing and decreasing. URGENT 20 POINTS!
Answers
A quadratic function is one that has the formula f(x)=ax2+bx+c, where a, b, c, and an are all real values and a 0 a 0. The conventional form of a quadratic function is this form.
The quadratic function's graph is a U-shaped curve known as a parabola.
Below is a graph of the equation y=x2y=x2; it is a parabola.
The parabola rises if a>0a>0 in f(x)=ax2+bx+cf(x)=ax2+bx+c. In this case, the vertex is the smallest or lowest point of the parabola.
The vertex of the y=x2y=x2 graph is (0, 0). (0,0).
The parabola opens downhill if a0a0 in f(x)=ax2+bx+cf(x)=ax2+bx+c is true. The maximal or highest point of the parabola in this instance is called the vertex.
The value of cc for an equation in standard form yields the graph's yy-intercept.
The axis of symmetry is the line that divides the parabola into two symmetric sections and runs through the vertex.
In the case of the graph y=ax2+bx+cy=ax2+bx+c, where a=0a=0, the equation for the axis of symmetry is x=b2ax=b2a.
The yy-axis, with x=0x=0, is the axis of symmetry in all of the graphs above. The axis of symmetry in the graphs below is different (marked in red.) As you can see, cc still provides the yy-intercept.
If you write a quadratic function like x=f(y)=ay2+by+cx=f(y)=ay2+by+c, instead of writing yy as a function of xx, you obtain a parabola with a horizontal axis of symmetry.
Hence, that the xx-intercept in this situation is cc. When aa is positive, the graph opens to the right; when aa is negative, it opens to the left.
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work this out please
Answers
Answer:
1/16
Step-by-step explanation:
32= 2^5
Thus:
(2^5) ^-4/5
= (2)^ - 4
= (16) ^ - 1
= 1/16
help meeeeeeeeeeeeeeee please !!
Answers
Answer: 59
Step-by-step explanation:
In simplest terms, Adam can see a√b feet farther than Pam. a = , b =
Answers
It is recommended that the expressions
d = 400 - 256 and
d = 256 - 400 be considered when attempting to determine how much farther Adam can see to the horizon.
The calculation for the expression is as follows:Since, the eye-level height of Pam is 256 feet above sea level, whereas the eye-level height of Adam is 400 feet above sea level.
Therefore, the formula that indicates how much farther Adam can see to the horizon should be taken to be
d = 400 - 256 and
d = 256 - 400.
This expression may be found by subtracting 400 from 256.
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CQ
Pam's eye–level height is 256 feet above sea level and Adam's eye–level height is 400 feet above sea level. What expression shows how much farther Adam can see to the horizon? In simplest terms, Adam can see a√b feet farther than Pam.
Answer:
A= 2 B= 6
Step-by-step explanation:
the dude above me is wrong
The first steps in writing f(x) = 3x2 – 24x + 10 in vertex form are shown.
f(x) = 3(x2 – 8x) + 10
(StartFraction negative 8 Over 2 EndFraction) squared = 16
What is the function written in vertex form?
f(x) = 3(x + 4)2 – 6
f(x) = 3(x + 4)2 – 38
f(x) = 3(x – 4)2 – 6
f(x) = 3(x – 4)2 – 38
Answers
The function is written in vertex form the equation for is mathematically given as
f(x) = 3(x – 4)2 – 38
This is further explained below.
What is the function written in vertex form?Generally, To convert the expression "f(x) = 3x2 – 24x + 10," which is in quadratic form, into vertex form, which will look like this "y = a(x-h)2 + k," you will need to apply the technique of completing the square. This will allow you to convert the expression. In the beginning, we shall separate the x2 and x terms.
y = 3(x² - 8x) + 10
We start with a negative eight, divide that number by two to obtain a negative four, and then we square that number, which gets us sixteen. We combine these so that it forms a perfect square, and then we remove 16 so that it is not altered in any way. We will get:
y = 3(x² - 8x + 16 - 16) + 10
y = 3((x - 4)² ) - 48 + 10
y = 3(x - 4)² - 38
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Answer: option D
Step-by-step explanation:
What is the size of the sample space for
the outcomes of rolling two 20 sided
dice?
Answers
Step-by-step explanation:
So, the total number of joint outcomes (a,b) is 6 times 6 which is 36. The set of all possible outcomes for (a,b) is called the sample space of this probability experimentUse the information and diagram below to find the value of y. (Type a number answer only.)
Use the information and diagram below to find the value of x. (Type a number answer only.)
Answers
Answer:
I never took the lesson but il try!
Step-by-step explanation:
so if y is 34° and x should be 54° if I am being correct!
2.12 rounded to the nearest hundedth.
Answers
Answer: 2.12
Step-by-step explanation:
it's in the hundredths place
2 . 1 2
ones tenths hundredths
HELP PLESSE i need to hrr it turned in 4 horus
Answers
Answer: 5358
Step-by-step explanation:
282
x 18
----------
2538
+282
-----------
5358
For how many positive integers n, is 3^n+81 the square of an integer?
Answers
The number of positive integers n, that satisfy 3^n+81 the square of an integer is infinite.
How to illustrate the information?Based on the information given, let 3n + 82 = p².
Therefore, 3n = p² - 81
= (p - 9)(p + 9)
Let p = 3q.
3n = (3q - 9)(3q + 9(
= 9(q - 3)(q + 4)
n = 3(q - 3)(q + 3)
n > 0 ; q >= 4 for n = 4, 5, 6....
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10. 1.4810 irrational number
Answers
Answer:
List A: 2√2, 3√2, 4√2, …
List B: 2π, 3π, 4π, …
List C: 2log35, 3log35, 4log35, …
Step-by-step explanation:
chapter 7 /pt3
10.Find the value of each trigonometric ratio.
Answers
At 7:00 am, here's what we know about two airplanes: Airplane #1 has an elevation of 28270 ft. and is descending at the rate of 550 ft/min. Airplane #2 has an elevation of 5270 ft. and is climbing at the rate of 700 ft/min.
(1) Let
t
represent the time in minutes since 7:00 am, and let
E
represent the elevation in feet. Write an equation for the elevation of each plane in terms of
t
.
plane #1:
E
(
t
)
=
plane #2:
E
(
t
)
=
(2) At what time will the two airplanes have the same elevation?
t
=
minutes after 7:00 am
(3) What is the elevation at that time?
E
=
feet
Question HelpQuestion 25: Message Message instructor
Answers
Using linear functions, it is found that:
1. The functions are given as follows:
E1(t) = 28270 - 550t.E2(t) = 5270 + 700t.2. They will have the same elevation after 18.4 minutes.
3. At that time, the elevation is of 18,150 feet.
What is a linear function?A linear function is modeled in slope-intercept form by:
y = mx + b
In which:
m is the slope, which is the rate of change, that is, by how much y changes when x changes by 1.b is the y-intercept, which is the value of y when x = 0, and can also be interpreted as the initial value of the function.For the functions in this problem, we have that:
The initial heights are the intercepts.The rates are the slopes, climbing positive and descending negative.Hence the functions are given as follows:
E1(t) = 28270 - 550t.E2(t) = 5270 + 700t.They will have the same elevation when:
E1(t) = E2(t)
28270 - 550t = 5270 + 700t
1250t = 23000
t = 23000/1250
t = 18.4.
They will have the same elevation after 18.4 minutes.
This elevation will be of:
28270 - 550(18.4) = 18150.
At that time, the elevation is of 18,150 feet.
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