Step-by-step explanation:
Notes;(a+b)² = (a+b) × (a+b)
= a(a+b) × b(a+b)
= a² +ab + ba + b²
= a² + b² + 2ab
similarly , (a-b) = a² + b² - 2ab so , The question :-103² = (100 + 3)²
= 100² + 3² + (2×100×3)
= 10000 + 9 + 600
= 10609
Carter wants to ride his bicycle 28.7 miles this week. He has already ridden 17 miles.
If he rides for 3 more days, write and solve an equation which can be used to
determine m, the average number of miles he would have to ride each day to meet his
goal. What is the equation?
The equation that we need to solve and the solution is:
A = 11.7mi/3 = 3.9 mi
We conclude that he needs to ride an average of 3.9 miles per day.
What is the equation?
Here we know that Carter wants to ride his bicycle 28.7 miles this week, and he has already ridden 17 miles, so the distance left is:
D = 28.7 mi - 17mi = 11.7mi
Now, if he has 3 days to complete that distance, then the average distance that he needs to travel each day is given by the quotient:
A = 11.7mi/3 = 3.9 mi
So that is the equation that we need to solve and the solution, we conclude that he needs to ride an average of 3.9 miles per day.
learn more about quotients:
https://brainly.com/question/629998
#SPJ1
Can someone please help me I don’t understand and it’s a really important homework
Answer: Large Box: 18.75 kilograms
Small Box: 15.75 kilograms
Step-by-step explanation:
l=large box. s=small box
5l+3s=141
7l+9s=273
(5l+3s=141)*3
15l+9s=423 ==> subtract this equation
7l+9s=273 ==> subtract this equation
8l=150 ==> subtract the two above equations
l=150/8
l=18.75
5(18.75)+3s=141
93.75+3s=141
93.75+3s=141.00
3s=47.25
s=15.75
Large Box: 18.75 kilograms
Small Box: 15.75 kilograms
Help!!! I will give brainly
Answer:
The above image is the correct answerStep-by-step explanation:
In all three pictures, the data are correctly matching except this one..
~~
1)the local park measure 60m by 50m. part of the park is torn to install a sidewalk of uniform width about it, reducing the area of the park itself by 321m2. what quadratic equation represents the situation?
2)the length of a rectangle is 1m less than twice the width. The area of the rectangle is 120 m2. what quadratic equation illustrates the situation?
1)The neighborhood park is 60m by 50 m. The park is reduced in size by 321m2 as a portion of it is ripped up to create a uniform-width sidewalk around it. What quadratic equation best captures the circumstances?
2)A rectangle's length is 1 m less than twice its width. The rectangle has a 120 m2 area. What quadratic equation best describes the circumstances?
Answer for the first question is the quadratic equation is [tex]4x^{2} -220x+321=0\\[/tex].
Answer for the second question is The quadratic equation is [tex]x^{2} -x-120=0[/tex].
1)Let 'x' stand in for the sidewalk's width.
The area of the park is: [tex]A_{1} =60\times50[/tex]
The reduced area of the park measures
60-2x by 50-2x with area of [tex]A_{2} =(60-2x)(50-2x)[/tex]
[tex]A_{1} -A_{2} =321[/tex]
[tex]60\times50-(60-2x)(50-2x)=321[/tex]
[tex]3000-(60-2x)(50-2x)=321\\3000-(3000-120x-100x+4x^{2} )=321\\220x-4x^{2} =321\\4x^{2} -220x+321=0\\[/tex]
Therefore, the quadratic equation is [tex]4x^{2} -220x+321=0\\[/tex].
2) Given that,
Width=x.
length=2x-1
Area=120[tex]m^{2}[/tex]
We know area=length[tex]\times[/tex]width
120=x(x-1)
[tex]x^{2} -x=120\\x^{2} -x-120=0[/tex]
Therefore, The quadratic equation is [tex]x^{2} -x-120=0[/tex].
To learn more about quadratic equation visit: https://brainly.com/question/17177510
#SPJ9
find the equation of the line shown
[tex]format \: \: y = mx + c[/tex]
[tex]m = \frac{5 - 0}{10 - 0} = \frac{5}{10} = \frac{1}{2} [/tex]
[tex]c = 0 \: since \: the \: line \: passes \: through \: the \: origin \\ [/tex]
[tex](d) \: \: \: y = \frac{x}{2} [/tex]
In a coordinate plane, points A and B have coordinates (-2,4) and (3,3), respectively. What is the value of A B ?
A. √50
B. (1,7)
C. (5,-1)
D. 1,-1)
E. √26
The correct option is E. √26.
The distance between the points A and B is √26.
What is defined as distance formula?Algebraic representation that gives the distances between two points based on of those coordinates (see coordinate system). The distance formulas for points throughout rectangular coordinates in two- and three-dimensional Euclidean space are based on the Pythagorean theorem.
Now, as per the given question;
The coordinates of the points A and B are (-2,4) and (3,3).
The formula of distance formula is written as for the points A and B ia-
AB² = (x₂ - x₁)² + (y₂ - y₁)²
AB = √[(x₂ - x₁)² + (y₂ - y₁)²]
The coordinates of A and B are-
(x₁,y₁) = (-2,4) and (x₂,y₂) = (3,3).
Substituting the values in the formula;
AB = √[(3 + 2)² + (3 - 4)²]
AB = √[(5)² + (-1)²]
AB = √[25 + 1]
AB = √26
Therefore, the distance between the coordinates A and B is found to be √26.
To know more about the distance formula, here
https://brainly.com/question/661229
#SPJ4
Rotate the angle 90° counterclockwise. Then, translate it left 3 units. Finally, reflect it across the y-axis. What is the relationship between the original angle and the transformed angle? If you transform an angle with a sequence of reflections, rotations, or translations, is it still an angle?
The first image is before I rotate the angle, and the second image is after I rotate the angle.
Answer: In geometry, when you translate an object, it means that you have turned that object in a different direction. Hence a translated angle is an angle that has been turned in a different direction.
From the first option in part A, it is clear from the image that the angle didn't change. It moves 7 units from the positive to the negative part of the x-axis.
From Part B, the angles also do not change. Note that when an angle is rotated or translated, it does not modify the angles.
From Part C, what we have is the reflection of the angles. This means that both angles are equal because they are a reflection of each other.
From Part D, the two sets of parallel lines will remain parallel to each other also long as they are both translated as the same time.
From part E, although in each set of parallel lines, the two sets of lines remain equidistant to each other, the parallel line that is at an angle to the Y-axis will not intersect that which is at an angle to the x-axis if they are extended infinitely.
Step-by-step explanation: hope this helps alittle
Write the domain and range of each relation in interval notation, and then determine if each relation is a function or not.
Answer:
Step-by-step explanation:
Answer:
A: D:(-6,6)
B: D:(-7,5]
C: Not a function D: -5
D: Not a function D:(-4,4)
E: Not a function D:(0,∞)
F: D:[0,∞)
G: D:[-3,5)
H: D:(-4,2)
I: D:[-3,4]
J: Not a function D:(-3.-4)
K: D:(-∞,∞)
L: D:(-∞,∞)
what is -188.7 in scientific notation with the correct number of significant digits
Answer:
See below
Step-by-step explanation:
-1.887 x10^2 would be one answer
- 18.87 x 10^1 could be another
Answer:
Step-by-step explanation: Wowee! That's pretty hard.
Scientific Notation:
-1.887 × 102
E-Notation:
-1.887e2
Engineering Notation:
-188.7 × 100
Real Number:
-188.7
Hope this helps!
If 4 cosx²+4 sin x = 5, show that sinx = 1/2
Answer:
See proof below
Step-by-step explanation:
[tex]4cos^2(x) +4sin(x) = 5\\\\\sf Divide\; both \; sides\; by\; 4\\== > cos^2(x) + sin(x) = \dfrac{5}{4} .................(1)\\\\cos^2(x) + sin^2(x) = 1\\\\cos^2(x) = 1- sin^2(x) \\\\\textsf {Substituting into equation (1) }\\1-sin^2(x) + sin(x) = \dfrac{5}{4}\\\\\\sf Subtract\; 1\; from\; both \; sides\\\mathsf{-\sin^2(x) + \sin(x) = \dfrac{5}{4} - 1}\\\\ \dfrac{5}{4} - 1 = \dfrac{5}{4} - \dfrac{4}{4} = \dfrac{1}{4}\\[/tex]
[tex]\sf {-\sin^2(x) + \sin(x) = \dfrac{1}{4}\\[/tex]
[tex]\sf Subtract\; \dfrac{1}{4}\;from\;both\;sides\\[/tex]
[tex]{-\sin^2(x) + \sin(x) - \dfrac{1}{4} = 0\\\\[/tex]
Multiply throughout by -1
[tex]\sf \sin^2(x) - \sin(x) + \dfrac{1}{4} = 0\\\\[/tex]
Let u = sin(x). Substituting we get
[tex]\sf u^2 - u + \dfrac{1}{4} = 0[/tex]
This is a quadratic equation which can be solved using sum of squars
Note that
[tex]\sf (u - \dfrac{1}{2})^2 = u^2 -2\cdot \dfrac{1}{4}u + (\dfrac{1}{2})^2 \\= \sf u^2 - u + \dfrac{1}{4} = 0[/tex]
So
[tex]\sf (u - \dfrac{1}{2})^2 = 0\\Solution\; is \;u = \dfrac{1}{2}\\\\Substituting\sin(x) \;for\;u \;gives\\sin(x) = \dfrac{1}{2}[/tex]
PROVED
Find the ninth and tenth terms of each arithmetic sequence. 6,3,0,-3, . . . .
The ninth and tenth term of the given arithmetic sequence are: -18 and -21.
What is an arithmetic sequence?A series of numbers called an arithmetic progression or arithmetic sequence (AP) has a constant difference between the terms.
Now,
Given: 6, 3, 0, -3, ....; it is a decreasing AP.
Here, a = 6 (initial term) and d = -3 (common difference)
Thus, in the formula: [tex]a_n[/tex] = a + (n - 1) d, substituting these values:
=> [tex]a_n[/tex] = 6 + (n - 1)(-3)
For ninth term, n = 9
Thus, [tex]a_n[/tex] = [tex]a_9[/tex] = 6 + (9 - 1)(-3)
=> [tex]a_9[/tex] = 6 + (8)(-3)
=> [tex]a_9[/tex] = 6 -24
=> [tex]a_9[/tex] = -18
Similarly, for the tenth term, n = 10
Thus, [tex]a_n=a_{10}[/tex] = 6 + (10 -1) (-3)
=> [tex]a_{10}[/tex] = 6 + (9) (-3)
=> [tex]a_{10}[/tex] = 6 - 27
=> [tex]a_{10}[/tex] = -21
Hence, The ninth and tenth term of the given arithmetic sequence are: -18 and -21.
To learn more about arithmetic sequences, refer to the link: https://brainly.com/question/6561461
#SPJ4
9x-2-20x+5 =
9x-2+20x+5 =
Please solve both pls and thank you
Answer:
The first one would be -11x + 3
The second on would be 29x + 3
Step-by-step explanation:
For the first equation you add -2 to 5 so you have 9x+3-20x. Then you add the 9x to -20x which will leave you with -11x+3.
For the second equation you add the -2 to 5 and have 9x+3+20x. You add 9x to 20x which will leave you with. 29x+3
R = x²/y.
x = 3.8 × 105
y = 5.9 × 104
Work out the value of R.
Give your answer in standard form to an appropriate degree of accuracy.
The value of the expression R = x^2/y when y = 3.8 x 10^5 and x = 5.9 x 10^4 is 9.2 x 10^3
What are expressions?Expressions are mathematical statements that are represented by variables, coefficients and operators
How to evaluate the expression?The expression is given as
R = x^2/y
Where
y = 3.8 x 10^5
x = 5.9 x 10^4
Substitute y = 3.8 x 10^5 and x = 5.9 x 10^4 in the equation R = x^2/y
So, we have
R = (5.9 x 10^4)^2/3.8 x 10^5
Evaluate the exponent in the above equation
So, we have
R = 34.81 x 10^8/3.8 x 10^5
Evaluate the quotient in the above equation
So, we have
R = 9.16052631579 x 10^3
Approximate the above expression
So, we have
R = 9.2 x 10^3
Hence, the value of the expression R = x^2/y when y = 3.8 x 10^5 and x = 5.9 x 10^4 is 9.2 x 10^3
Read more about scientific notation at
brainly.com/question/27862246
#SPJ1
Find the distance between each pair of parallel lines with the given equations.)
y=-0.75 x-1
3 x+4 y=20
The distance between the given parallel lines is 4 units
In the given statement is :
The equations of the pair of each parallel lines is:
y=-0.75 x-1
3 x+4 y=20
To find the distance between each pair of parallel lines.
Two lines a₁x +b₁y + c₁=0 and a₂x+b₂y+c₂=0 are said to be parallel if a₁=a₂ , b₁=b₂.
As we know that distance between the parallel lines (d) is given as:-
d = [tex]\frac{c_{2}-c_{1} }{\sqrt{a^{2} +b^{2} } }[/tex]
Parallel lines equation as:
y=-0.75 x-1...(1)
3 x+4 y=20....(2)
Divide by -3 in equation (2)
Now, The equations is
-0.75x -y -1 =0
-0.75x -y +4 =0
Here,
a = -0.75 , b = -1, c1 = -1 , c2 = 4
Therefore, putting the values
[tex]d =\frac{4-(-1)}{\sqrt{(-0.75^{2} )+(-1)^{2} } } \\\\d=\frac{5}{\sqrt{0.5625+1} }\\ \\d = \frac{5}{\sqrt{1.5625} }[/tex]
d = 4 units
Hence, The distance between the given parallel lines is 4 units
Learn more about Parallel lines at:
https://brainly.com/question/2235918
#SPJ4
EASY POINTS WILL GIVE BRAINLIST 2 BEST ANSWER
12-x=15+3x
explain
Answer:
Step-by-step explanation:
Answer: x=-3/4
Step-by-step explanation:
12-x=15+3x
12-x+x=15+3x+x
12=15+4x
12-15=15-15+4x ==> isolate the variable x.
-3=4x
4x/4=-3/4
x=-3/4
In 2006,500 million songs were legally downloaded from the Internet. In 2004, 200 million songs were legally downloaded.
c. If this trend continues at the same rate, how many songs will be legally downloaded in 2020 ?
Number of songs that will be downloaded in 2020 = 2600 million
Given that in 2004, 200 million songs were downloaded and in 2006, 500 million songs were downloaded from the internet.
When we graph this trend, these data corresponds to the points (4,200) and (6, 500).
Also it will be a straight line. So its slope can be found.
Slope = [tex]\frac{y_2-y_1}{x_2-x_1} = \frac{500-200}{6-4}[/tex] = 300/2 = 150
This means that there is an increase of 150 million songs downloads pe year.
Also 2020-2006 = 14 years
So the number of songs downloaded in 2020 = Number of songs downloaded in 2006 + 14 x 150 = 500 + 14 x 150
= 500 +2100
= 2600 million
So 2600 million songs will be downloaded legally from the internet by 2020.
Learn more about slope at https://brainly.com/question/16949303
#SPJ4
Where did the formula for summing finite geometric series come from? Suppose the geometric series has first term a₁ and constant ratio r , so that S n= a₁ + a₁r+ a₁ r²+ . . +a₁ rⁿ⁻¹
c. Use part (b) to show that S n = a₁ - a₁ rⁿ / 1-r = a₁ (1-rⁿ ) / 1-r .
The formula to find the sum of an arithmetic sequence: Sn = n/2[2a + (n - 1)d], where a is the first term, n is the number of terms and d is the common difference.
1) Let's substitute the values into the formula.
S17 = 17/2[2(11) + (17 - 1)6]
S17 = 17/2[22 + (16)6]
S17 = 17/2[22 + 96]
S17 = 17/2[118]
S17 = 17/2 × 118
S17 = 1003
Therefore, the sum of the first 17 terms of this arithmetic sequence is 1003.
To know more about "Common difference"
Refer this link:
https://brainly.com/question/19601308
#SPJ4
Identify the pattern and find the next three terms. 100,117,134,151,168, ...........
The given sequence 100,117,134,151,168, ........... is in AP. The next three terms are 185, 202, 219..
What is the AP arithmetic progression sequence?The difference between two numerical orders is a constant value in Arithmetic Progression (AP). Another name for it is Arithmetic Sequence.
We'd emerge across a few fundamental words in AP that have been labeled as:
The first term (a)Common difference (d)Term nth (an)The total of first n terms (Sn)The AP can also be described in terms of common differences, as shown below.
The procedure for appraising an AP's n-th term is as follows: an = a + (n − 1) × dThe following is the arithmetic progression sum: Sn = n/2[2a + (n − 1) × d].Common difference 'd' of an AP: d = a2 - a1 = a3 - a2 = a4 - a3 = ...... = an - an-1.Now, the given sequence is; 100,117,134,151,168, ...........
The series comprises of five given terms.
Let the initial term be 'a₁' = 100.
The second term be 'a₂' = 117.
The third term be 'a₃' = 134.
And, the fourth term is 'a₄' = 151.
The AP must have the equal common difference. So,
d = a₃ - a₂
Substitute the values.
d = 134 - 117
d = 17
Thus, the computed common difference is 17.
or d = a₄ - a₃ (Substitute the values)
d = 151 - 134
d = 17
Since, a₃ - a₂ = a₄ - a₃
Thus, we can get to know that the given sequence is in AP.
Now, the 6th term is estimated as; a₆ = a₅ + d = 168 + 17
a₆ = 185
Similarly, the 7th term will be; a₇ = a₆ + d = 185 + 17
a₇ = 202
And, the 8th term will be calculated as; a₈ = a₈ + d = 202 + 17
a₈ = 219.
Therefore, it can be said that the given sequence is in AP next three terms be 185, 202, 219.
To know more about the arithmetic progression, here
https://brainly.com/question/16954227
#SPJ4
A red string of holiday lights blinks every 3 seconds. a blue string of holiday lights blinks every 4 seconds. how many times will they blink in one minute?
If a red string of holiday lights blinks every 3 seconds. a blue string of holiday lights blinks every 4 seconds, then the number of times the red and blue string of holiday lights will blink in one minute is equal to 20 and 15 respectively.
The number of times each string of holiday lights will blink can be determined by using division.
As we have to calculate the number of times they blink in one minute, we can convert one minute into seconds.
One minute = 60 seconds
Now, the number of times each string of light blinks can be calculated by dividing the total seconds by the seconds after which the light blinks
For the red string of holiday lights :
The number of times the light will blink in one minute = 60 ÷ 3 = 20
For the blue string of holiday lights :
The number of times the light will blink in one minute = 60 ÷ 4 = 15
Hence the red string of holiday lights will blink 20 times and the blue string of holiday lights will blink 15 times in one minute.
To learn more about division, click here:
https://brainly.com/question/28119824
#SPJ4
SOMEBODY, PLEASE HELP ASAP PLEASE PLEASE PLEASE
Jack earns 2 cents per second. Jack works 40 hours a week. Determine how many dollars per year jack earns.
Answer:
1 hour has 3600 seconds
to get how many dollars Jack earns we have to do this
3600 sec x $0.02 = $72
40 weeks x $72 = $2880
Answer:
$149,760
Step-by-step explanation:
As:
1 minute = 60 seconds1 hour = 60 minutes⇒ 1 hour = 60 × 60 seconds = 3600 seconds
As:
1 year = 52 weeksJack works 40 hours per week.⇒ 52 × 40 = 2080 hours per year
Therefore, the number of seconds Jack works per year is:
⇒ 2080 × 3600 = 7,488,000 seconds
If Jack earns $0.02 per second, then the number of dollars per year he earns is:
⇒ $0.02 × 7,488,000 = $149,760
What is the solution of the system? Use elimination. Check your answer in all three original equations.
x-y+z = -1
x+y+3z= -3
2x-y+2z = 0
By elimination, the solution of the system of equations, x - y + z = -1, x + y + 3z = -3 and 2x - y + 2z = 0, is (4 , 2 , -3).
Given:
x - y + z = -1 (equation 1)
x + y + 3z = -3 (equation 2)
2x - y + 2z = 0 (equation 3)
Using the elimination method, given the equations in x, y, and z, a variable should be eliminated by adding/subtracting the equations.
Subtracting equations 1 and 3 will eliminate the variable y.
2x - y + 2z = 0 (equation 3)
x - y + z = -1 (equation 1)
x + z = 1 (equation 4)
Adding equations 2 and 3 will eliminate the variable y.
x + y + 3z = -3 (equation 2)
2x - y + 2z = 0 (equation 3)
3x + 5z = -3 (equation 5)
Multiply equation 4 by -5 and add with equation 5.
x + z = 1 (equation 4)
⇒ -5x - 5z = -5
+ 3x + 5z = -3 (equation 5)
-2x = -8
x = 4
Substitute the value of x to either equation 4 or 5 and solve for z.
x + z = 1 (equation 4)
4 + z = 1
z = 1 - 4
z = -3
Finally, substitute the value of x and z to any of the first three equations, and solve for y.
x - y + z = -1 (equation 1)
4 - y + (-3) = -1
-y = -1 - 4 + 3
-y = -2
y = 2
Checking if the values x = 4, y = 2, and z = -3 satisfies all the three equation.
x - y + z = -1 (equation 1)
4 - 2 + (-3) = -1
-1 = -1
x + y + 3z = -3 (equation 2)
4 + 2 + 3(-3) = -3
-3 = -3
2x - y + 2z = 0 (equation 3)
2(4) - 2 + 2(-3) = 0
0 = 0
Hence, the solution of the system of equations is (4 , 2 , -3).
Learn more about solving systems of equations by elimination here: brainly.com/question/28405823
#SPJ4
HELP ME PLEASEeeeeee
Answer:
7.2
Step-by-step explanation:
7.4-0.2=7.2
Simplify each expression.
(-3)(-9)
An expression can be used in algebra to represent a value, and that value may rely on the values given to the variables that appear in the expression.
If the expression be (-3)(-9) then the value of (-3)(-9) is 27.
What is an expression?A mathematical expression is a finite combination of symbols that is well-formed in accordance with context-specific norms.In order to help establish the order of operations and other elements of logical syntax, mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping.An expression can be used in algebra to represent a value, and that value may rely on the values given to the variables that appear in the expression.Let (-3)(-9) be the given expression
We know the rule , (-) × (-) = (+)
(-3) × (-9) = +27
Therefore, the value of (-3)(-9) is 27.
To learn more about simplifying expressions, refer to:
https://brainly.com/question/723406
#SPJ4
Which of the following rounds most closely to 1?
1/5
4/5
4/8
2/3
Answer:
B. 4/5
Glad to help :)
PLS HELPP TY <3
At Point Pleasant Park, the Advanced Trail is 3.6 times as long as the Medium Trail, and the Medium Trail is 1.2 times as long as the Beginner's Trail. How many times as long as the Beginner’s Trail is the Advanced Trail? Write your answer as a decimal.(1 point)
The advanced trail is 4.32 times as long as the beginner's trail.
What is the length of the advanced trail?A decimal is a number that is made up of integers and non-integers. The whole numbers are separated from numbers that are not whole number by a decimal point. An example of a decimal is 1.2.
Let:
a represent the length of the advanced trail m represent the length of the medium trail b represent the length of the beginner's trail.The equation that represents the length of the medium trail: 1.2 x b = 1.2b
The equation that represents the length of the advanced trail: 3.6 x 1.2b = 4.32b
To learn more about decimals, please check: https://brainly.com/question/15287678
#SPJ1
During a certain 3 month period, a company reported a 3,500 profit. I cover the next 3 month period, the company period a 6000 profit for those months. By approximately what percent did the company profit increase?
A) 25%
B) 32%
C) 42%
D) 55%
E) 70%
The company profit approximately increased by E) 70%.
What is an approximation?An approximation is an equivalent value or number obtained by rounding off to the required significant figure.
The result obtained through approximation is not an exact value but is the nearest rounded value.
For instance, 71.4% can be approximated to 71% or 70%. 58 minutes can be rounded off or approximated to 1 hour.
Data and Calculations?Profit in 3 months = $3,500
Profit in 6 months = $6,000
Increase in profit = $2,500 ($6,000 - $3,500)
Percentage increase in profit = 71.43% ($2,500/$3,500 x 100)
71.43% ≈ 70%
Thus, the company profit approximately increased by E) 70%.
Learn more about approximation at https://brainly.com/question/201331
#SPJ1
PleAse help me with this
Step-by-step explanation:
let this number is x
a.(x-11)/2 +7Segment AB intersects the circle with center C . What statement correctly describes the relationship shown in the image?
Answer: Since the radius of the circle is perpendicular to AB, AB is tangent to the circle.
Step-by-step explanation:
Answer:
perpendicular and tangent
Step-by-step explanation:
Triangle J K L has vertices J(2,5), K(1,1) , and L(5,2) . Triangle N P Q has vertices N(-3,0), P(-7,1) , and Q(-4,4).
c. Write a logical argument using coordinate geometry to support the conjecture you made in part b .
It can be seen that QPN and JKL have: JK = QN; JL = QP; KL = NP
They are congruent triangles.
What do you mean by congruent?
Two figures are said to be "congruent" if they can be positioned perfectly over one another. Both of the bread slices are the same size and shape when stacked one on top of the other. Congruent refers to things that are exactly the same size and shape.In the triangle JKL, the sides can be calculated as following:
J(2;5); K(1;1)
=> JK = [tex]\sqrt{( ( 1 - 2 )^{2} + ( 1 - 5 )^{2} } = \sqrt{( -1 )^{2} + ( -4)^{2} } \\= \sqrt{ 1 + 16 } = \sqrt{17}[/tex]
J(2;5); L(5;2)
JL = [tex]\sqrt{( 5 - 2 )^{2} + ( 2 - 5 )^{2} } = \sqrt{3^{2} + ( -3)^{2} } \\[/tex]
= [tex]\sqrt{ 9 + 9 } = \sqrt{18} = 3\sqrt{2}[/tex]
K(1;1); L(5;2)
=> KL = [tex]\sqrt{ ( 5 - 1 )^{2} + ( 2 - 1 )^{2} } = \sqrt{4^{2} + 1^{2} } = \sqrt{ 1 + 16} = \sqrt{17}[/tex]
In the triangle QNP, the sides can be calculate as following:
Q(-4;4); N(-3;0)
=> QN = [tex]\sqrt{[ -3 - ( -4)^{2} ] + ( 0-4)^{2} } = \sqrt{1^{2} + 16 } = \sqrt{17}[/tex]
Q (-4;4); P(-7;1)
=> QP = [tex]\sqrt{ [ -7 - ( -4 )^{2} + ( 1 - 4 )^{2} } = \sqrt{( -3)^{2} + ( -3)^{2} } = \sqrt{9 + 9} = \sqrt{18} = 3\sqrt{2}[/tex]
N(-3;0); P(-7;1)
=> NP = [tex]\sqrt{[-7 -( -3)]^{2} + ( 1 - 0 )^{2} } = \sqrt{ - 4^{2} + 1 } = \sqrt{ 16 + 1} = \sqrt{ 17}[/tex]
It can be seen that QPN and JKL have: JK = QN; JL = QP; KL = NP
=> They are congruent triangles
Learn more about congruent
brainly.com/question/12413243
#SPJ4
Carol used the expression below to calculate the amount of money she would earn in one year at her part time job
12(
100+20)
The amount that she would earn in one year at her part time job is 1440
How to determine the amountNote that a function is an expression, rule or law that shows the relationship between a dependent and an independent variable.
Given the expression as;
12(100+20)
To determine the amount, we need to use the BODMAS rule by solving the bracket, we have
Amount = 12(100+20)
Amount = 12(120)
Expand the bracket
Amount = 1440
Thus, the amount that she would earn in one year at her part time job is 1440
Learn more about functions here:
https://brainly.com/question/17043948
#SPJ1
