The Perimeter of the polygon = 22.43 units.
How to Determine the Perimeter of a Polygon?Given the vertices of the polygon as:
U(-2,4)V(3,4)W(3,-4)The perimeter of the polygon is the sum of all its sides, UV + VW + UW.
Apply the distance formula, d = [tex]\sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}[/tex] to find the length of each of the three sides of the polygon as shown below:
UV = √[(3−(−2))² + (4−4)²]
UV = √[(5)² + (0)²]
UV = √25
UV = 5 units
VW = √[(3−3)² + (4−(−4))²]
VW = √64 = 8 units
UW = √[(−2−3)² + (4−(−4))²]
UW = √89 = 9.43 units
Perimeter of the polygon = 5 + 8 + 9.43
Perimeter of the polygon = 22.43 units
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Consider the polynomials:
A(x) = (3-x)2² - (x-3) (7x+4)-18+2x²
B(x) = (3x + 2)² - (x - 1)²
1) Develop and reduce A (x).
2) Factorize A (x) and B (x).
3) Solve the equation A (x)= B(x)
4) Prove that B (X) -3 = 2x(4x+7) , then solve the equation B(x) =3
Answer:
1) -5x² + 13x + 6
2) B(x) =(4x + 1 )(2x + 3)
A(x) = (5x +2)(3-x)
Step-by-step explanation:
1) Expand the equation by using distributive property. Then simplify by combining the like terms.
A(x) = (3 -x)2² - (x -3)(7x+ 4) - 18 + 2x²
= (3 - x)4 - [x*7x + x*4 - 3*7x - 3*4] - 18 + 2x²
= 3*4 - x*4 - [7x² + 4x - 21x - 12] - 18 + 2x²
= 12 - 4x - 7x² - 4x + 21x + 12 - 18 + 2x²
= 2x² - 7x² -4x - 4x + 21x + 12 + 12 - 18
= -5x² + 13x + 6
B(x) = (3x + 2)² - (x - 1)²
Identities:
(a + b)² = a² + 2ab + b² ; Here a =3x & b = 2
(m -n)² = m² - 2mn + n² ; Here m = x & n = 1
2) B(x) = (3x)² + 2*3x*2 + 2² - [x² - 2*x*1 + 1]
= 9x² + 12x + 4 - [x² - 2x + 1]
= 9x² + 12x + 4 - x²+ 2x - 1
= 9x² - x² + 12x + 2x + 4 - 1
= 8x² + 14x +3
Product = 8*3 = 24
Sum = 14
Factors = 2 , 12 {2*12 = 24 & 2 +12= 14}
= 8x² + 2x + 12x + 3 {Rewrite the middle term}
= 2x(4x + 1) + 3(4x + 1)
= (4x + 1 )(2x + 3)
A(x) = - 5x² + 13x + 6
= -5x² + 15x -2x + 6
= 5x(-x +3) +2 (-x + 3)
= (5x +2)(3-x)
4) B(x) - 3 = 8x² + 14x + 3 - 3
= 8x² + 14x
= 2x *4x + 2x *7
=2x(4x + 7)
Hence proved.
B(x) = 3
8x² + 14x + 3 = 3
8x² + 14x + 3 - 3 = 0
8x² + 14x = 0
2x(4x + 7) = 0
2x = 0 or 4x + 7 = 0
x = 0 or 4x = -7
[tex]\sf x = \dfrac{-7}{4}[/tex]
x = 0 or [tex]\sf \dfrac{-7}{4}[/tex]
The coordinates of A and B are (3k, 8) and (k, -3) respectively. Given that the gradient of the line segment AB is 3, find the value of k.
Step-by-step explanation:
gradient = slope or several other words.
it describes how strongly a line (or tangent to a bent curve) is going up or down or ... if it is changing at all.
it is represented by the ratio
(y coordinate change / x coordinate change)
when going from one point on the line to another.
in our case, when going from A to B we have
x changes by -2k (from 3k to k).
y changes by -11 (from 8 to -3).
so, the gradient or slope is
-11/-2k = 3
11/2k = 3
11 = 3×2k = 6k
k = 11/6
A = (33/6, 8) = (11/2, 8)
B = (11/6, -3)
I need assistance with this problem.
Answer: it is upside down
Step-by-step explanation:
cant see the problem
As a fundraiser for the Lax Team, they plans to sell tees with the school logo. The company ducing the fees charges $125 for the design and set up plus $5 per tee. The lax members will sell tees for $10 each. How many do they need to sell to break even? PLEASE HELP
The company must produce 25 t-shirts to break even.
Here, we are given that a company producing t-shirts charges $125 for the design and set up plus $5 per tee.
This means-
fixed cost of producing the t-shirts = $125
Variable cost of producing a t-shirt = $5
Let x be the number of t-shirts produced
Thus, the total cost of producing t-shirts will be-
Total cost = 125 + 5x
Further, the selling price of 1 t-shirt = $10
Thus, selling price of x t-shirts = $10x
Now, at the break even point, the profit is 0, this implies-
Selling price = cost price
⇒ 10x = 125 + 5x
10x - 5x = 125
5x = 125
x = 125/5
x = 25
Thus, the company must produce 25 t-shirts to break even.
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A sidewalk that is 2 ft wide surrounds a rectangle that is 4 ft by 6 ft what's the area of the sidewalk in square feet
The area of a sidewalk that surrounds a rectangle of 4 ft by 6 ft is 56 ft²
The given situation can be depicted in the attached picture.
Recall the formula to calculate the area of a rectangle:
A = l ⨉ w
Where:
l = length
w = wide
In the attached picture, the area of the sidewalk is the one with green color.
Notice that:
Area of sidewalk = area of bigger rectangle – area of smaller rectangle
Parameters of the bigger rectangle:
l = 6 + 2 + 2 = 10 ft.
w = 4 + 2 + 2 = 8 ft.
Area of bigger rectangle = 10 x 8 = 80 ft²
Parameters of the smaller rectangle:
l = 6 ft.
w = 4 ft.
Area of bigger rectangle = 6 x 4 = 24 ft²
Hence,
Area of sidewalk = 80 - 24 = 56 ft²
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25 point to who gets these problems plus thank
Cameron's current service charge of $0.95 per song, and the new service charge of $0.89 per song and $12 fee for joining, gives;
Formula for finding the number of songs that makes the cost of both services the same is; 0.95•s = 12 + 0.89•sComputing the value of s that satisfies the above equation gives the number of songs at which the cost of both service is the same as 200 songs The interpretation is the the cost of either service is the same when 200 songs are downloadedHow can the equation that gives the required number of songs be found?To Formulate
The charges for songs on the current music service is, C1 = 0.95•s
The charges for the new download service is, C2 = 12 + 0.89•s
Where the $12 is the joining fee
When the cost is the same for both service, we have;
C1 = C2
Which gives;
0.95•s = 12 + 0.89•sThe equation to represent when the cost for both service is the same is therefore;
0.95•s = 12 + 0.89•s
Computing;
The number of songs that gives the same costs is therefore;
0.95•s = 12 + 0.89•s
12 = 0.95•s - 0.89•s = 0.06•s
s = 12 ÷ 0.06 = 200
The number of songs at which the cost of each option will be the same is s = 200 songsInterpreting the solution;
The interpretation is, the cost of songs downloaded on both service will be the same, when 200 songs are downloaded.
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Ramon has $4896 in his bank account. he has been depositing the same amount of money monthly for 2 years. how much money did ramon deposit monthly?
Answer:
Ramon deposited $204 monthly
Step-by-step explanation:
Step 1: Firstly convert 2 years to month
1 year = 12 month
∴ 2 years = 24 month
Step 2: Divide $4896 by 24
➟ 4896 ÷ 24
➟ 204
2. Why does this
equation have no
solutions?
3(4x12) = 2(6x + 8)
The equation 3(4x + 12) = 2(6x + 8) has no solution because the variable x was neglected as it equals 0.
How to calculate the value?It should be noted that the equation given is illustrated as:
3(4x + 12) = 2(6x + 8)
Open the parentheses
12x + 36 = 12x + 16
Collect like terms
12x - 12x = 16 - 36
0 = -20
Therefore, it has no solution.
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Answer the 2 questions in photo [ Brainliest + 20 points ]
( you don’t have to answer both just at least one of them please)
A restaurant serves breakfast, lunch, anddinner. The restaurant offers a daily special.To estimate the percentage of customers who order the daily specials, the restaurant selected a random sample of customers who had lunch during 2 month period. From the results, the restaurant determined that 25% of these customers ordered the daily
special. Which statement about the sample it true?
1) no generalizations can be made because the sample size is too small.
2)the same shows that exactly 25% of the customers ordered the daily specials
3) the sample might not be representative of the population behave it only survey lunch customers.
4) the sample percentage is the percentage of customers who order daily specials
Answer:
nnk;'/mnhjjfn;h;;vhxpycoyyoly,
Step-by-step explanation:
I]o]ogi-gogoig]gogh]o]v]b]bob]b]k k k lgg]goghjppkngghhjjl
No generalizations can be made because the sample size is too small. Therefore, the correct option is option A.
What is restaurant?A restaurant is an institution of business which prepares and provides clients with food and beverages. Although many restaurants now provide take-out as well as food delivery services, meals are often served and consumed on the premises.
A restaurant serves breakfast, lunch, and dinner. The restaurant offers a daily special. To estimate the percentage of customers who order the daily specials, the restaurant selected a random sample of customers who had lunch during 2 month period. From the results, the restaurant determined that 25% of these customers ordered the daily special. No generalizations can be made because the sample size is too small.
Therefore, the correct option is option A.
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In ΔOPQ, o = 1.2 inches, p = 3.2 inches and ∠Q=37°. Find the area of ΔOPQ, to the nearest 10th of a square inch.
SILL GOVE BRIANLIST TO BEST ANSWER
WHATS the volume of the prism ?
Answer:
629.3 cm3
Step-by-step explanation:
This is known as a rectangular prism aka cuboid.
The formula for the volume is Length x width x height
so 14.5x7x6.2 = 629.3 cm cubed
What is the equation of a line that contains the points (5, 0) and (5, −2)?
a) x = 5
b) x = 0
c) y = 0
d) y = 5
Thank you!
The equation of the line is x = 5
How to find the equation of a line?The equation of a line can be represented in slope intercept form as follows:
y = mx + b
where
m = slopeb = y-interceptTherefore, let's find the slope and y-intercept
(5, 0)(5, - 2)
m = -2 - 0 / 5 - 5
m = -2 / 0
m = infinity
Hence, It is a vertical line, since the x is the same for both of them, and it is equal to both times.
Therefore, the equation of the line is x = 5
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ya Williams-
set to the inequality
Solve the inequality.
-1.5(4x+1) > 45-25(x+1)
1. For parentheses:
Distribute
2. If necessary:
Combine Terms
3. Apply properties:
Add
Multiply
Subtract
Divide
4. To start over:
Reset
English
V
KE'NAIYA
The solution to the inequality using William's template is x > 21.5/19
How to determine the solution to the inequality using William's template?The inequality expression is given as
-1.5(4x + 1) > 45 - 25(x + 1)
For parentheses: Distribute
So, we have
-6x - 1.5 > 45 - 25x - 25
2. If necessary: Combine Terms
So, we have
19x > 21.5
3. Apply properties: Divide both sides by 19
x > 21.5/19
Hence, the solution to the inequality using William's template is x > 21.5/19
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Can y’all please help me on question 23 please
Answer:
x<-5/4 or x>2
Step-by-step explanation:
-4x -11 > 5
+11 +11
-4x>5
/ /
-4 -4 Switch the sign when divided by a negative.
x<-5/4
8x - 7 > 9
+7 +7
8x>16
/ /
8 8
x>2
WILL GIVE BRAINLIEST need help asap
What will be the location of the y value of R' after using the translation rule (x + 4, y - 7), if the pre-image R is located at ( -17, -3)
The location of the y value of R' after using the translation rule is -10
What will be the location of the y value of R' after using the translation rule?The translation rule is given as:
(x + 4, y - 7)
The pre-image of R is located at (-17, -3)
Rewrite as
R = (-17, -3)
When the translation rule is applied, we have:
R' = (-17 + 4, -3 - 7)
Evaluate
R' = (-13, -10)
Remove the x coordinate
R'y = -10
Hence, the location of the y value of R' after using the translation rule is -10
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for each positive integer $n$, the mean of the first $n$ terms of a sequence is $n$. what is the $2008^{\text{th}}$ term of the sequence?
B(4015) is the [tex]2008^{th[/tex]term of the sequence.
What is the sequence?
A sequence is an enumerated group of particulars in mathematics where reiterations are permitted and order is important. analogous to a set, it has members( also called rudiments, or terms). The length of the series is the number of rudiments( potentially horizonless). A list of particulars in a particular order, generally figures, is called a sequence.Since the mean of the first terms is, the sum of the first terms is n². Thus, the sum of the first 2007 terms is 2007² and the sum of the first 2008 terms is 2008² Hence, the 2008th term of the sequence is
2008² - 2007² = (2008 + 2007) (2008 - 2007) = 4015
Note that n² is the sum of the first n odd integers.
From inspection, we see that the sum of the sequence is n². We also notice that n² is the sum of the first n odd integers.
Because 4015 is the only odd integer, B is the answer.
B(4015) is the [tex]2008^{th[/tex]term of the sequence.
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he first step in simplifying the expression: (1.8 x 10^5) - (2.6 x 10^3)
a
Addition and subtraction requires the terms to be "like terms" with the same power of the base 10, so you would need to change the second number to (0.026 x 10^5).
b
Addition and subtraction do not require any changes, so you would just subtract (2.6 - 1.8) and (10^(5-3))
c
Addition and subtraction do not require any changes, so you would just subtract (1.8 - 2.6) and (10^(5-3))
d
Addition and subtraction requires the terms to be "like terms" with the same power of the base 10, so you would need to change the second number to (2600 x 10^5).
Using scientific notation, the first step in simplifying the expression is given by:
a. Addition and subtraction requires the terms to be "like terms" with the same power of the base 10, so you would need to change the second number to (0.026 x 10^5).
What is scientific notation?A number in scientific notation is given by:
[tex]a \times 10^b[/tex]
With the base being [tex]a \in [1, 10)[/tex].
For two numbers in scientific notation to be added or subtracted, they need to have the same exponent, which removes options b and c.
Moving the second number for 10^3 to 10^5 would be equivalent to a multiplication by 100, hence we have to divide by 100 at the base, that is:
2.6 x 10^3 = (2.6/100) x 10^5 = 0.026 x 10^5.
Hence option a is correct.
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Which is equivalent to the fraction represented by point M on the number line?
From the calculation below, the equivalent to the fraction represented by point M on the number line is [tex]\frac{1}{4}[/tex].
How do we determine the fraction equivalent?On the number line, it can be observed that there are eight points starting from the first point after 0 up to 1.
Since M is on the second point on the number line, we can have:
P = Point at which M is located on the number line = 2
T = Total number of points on the number line = 8
Therefore, we have:
[tex]M =\frac{P}{T}[/tex]
[tex]M=\frac{2}{8}[/tex]
[tex]M =\frac{1}{4}[/tex]
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At the beginning of the day the stock market goes down 50 1/2 points and stays at this level for most of the day. At the end of the day the stock market goes up 120 3/4 points from the low at the beginning of the day. What is the total change in the stock market from the beginning
The total change in the stock market from the beginning based on the information will be 171 1/4 points.
How to illustrate the information?It should be noted at the beginning of the day the stock market goes down 50 1/2 points and stays at this level for most of the day and at the end of the day the stock market goes up 120 3/4 points from the low at the beginning of the day.
Therefore, the total change in the stock market from the beginning will be the difference between the fractions that are given. This will be:
= 120 3/4 - (- 50 1/2)
= 120 3/4 + 50 1/2
= 171 1/4
Therefore, the total change in the stock market from the beginning based on the information will be 171 1/4 points.
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is i get one point each 5 minutes how long until i get 50 points?
Answer:
250 minutes.
Step-by-step explanation:
1/5=50/x
cross product
5*50=1*x
250=x
f(x)= 4x - 2
find x if f(x)=2
Answer:
1
Step-by-step explanation:
a) Flip the equation
4x - 2 = 2
b) Add 2 to both sides
4x - 2 + 2 = 2 + 2
4x = 4
c) Divide both sides by 4
4x/4 = 4/4
x = 1
HELP!!!!!!!!!!!!! 30 points that is all my points
1) Unit Rate of the given options are;
$0.05 for 1 ounce
24 bottles per case
16 ounces per bottle
2) Rate of the given options are;
5 bottles for $5
$1 per 16 ounces
What is the Unit Rate?A unit rate (or unit ratio) describes how many units of the first type of quantity corresponds to one unit of the second type of quantity. For example, if you ran 70 yards in 10 seconds, you ran on average 7 yards in 1 second.
Meanwhile, a rate is the ratio between two different units of measure.
Thus;
1) Unit Rate of the given options are;
$0.05 for 1 ounce
24 bottles per case
16 ounces per bottle
2) Rate of the given options are;
5 bottles for $5
$1 per 16 ounces
3) The option that is neither a unit rate nor a rate is; 36 bottles
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A store sells a package of 50 paper plates for $2.50 and a package of 80 paper plates for $4.00. Which of the following statements is correct? Multiple choice question. A) The unit prices are the same. B) The package of 50 paper plates has the lower unit price. C) The package of 80 paper plates has the lower unit price. D) The package of 50 paper plates has the higher unit price.
Answer:
A) The unit prices are the same.
Step-by-step explanation:
First convert dollars to cents to make the calculation easier
Package of 50 paper plates costs $2.50
$2.50 = 2.50 x 100 = 250¢
So the unit price, which is the price per paper plate = 250/50 = 5¢
Package of 80 paper plates costs $4.00
$4.00 = 4.00 x 100 = 400¢
So the unit price, which is the price per paper plate = 400/80 = 5¢
So the unit prices of both packages are the same
2- (-4)= what is the answere
Answer:
The answer is 6.
Step-by-step explanation:
A negative and a negative makes a positive when the problem is written as
x - (-x)
So 2 - (-4) equals 2 + 4
which is simply 6
Answer:
6
Step-by-step explanation:
Two negatives cancel out a positive.
2-(4) should turn into 2 +4
2+4 =6
the model represents a polynomial of the form ax2 bx c. an algebra tile configuration. 4 tiles are in the factor 1 spot: 3 x , 1 negative. 2 tiles are in the factor 2 spot: 1 x, negative. 8 tiles are in the product spot in 4 columns with 2 rows. first row: 3 x squared, 1 negative x. second row: 3 negative x, 1 . which equation is represented by the model? 3x2 – 4x – 1
The Quadratic equation modeled is [tex]3x^{2} -4x+1=(3x-1) (3x-1)[/tex].
Quadratic equation as an equation of degree 2, meaning that the highest exponent of this function is 2. The standard form of a quadratic is [tex]y=ax^{2} +bx+c[/tex], where a, b, and c are numbers and a cannot be 0.
the given equation Much easier to understand with the symbol [tex]3x^{2} -4x+1=(3x-1) (3x-1)[/tex]
[tex]3x^{2} -4x+1= 9x^{2} -6x+1\\6x^{2} -2x=0[/tex]
That is how I interpreted the "tile" set up.
Now count up the factors:
These are (4 -x) and ( x +1) factor of Quadratic equation.
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resolver esto
2x - 3y = 7
4x + y = 7
Ayuda es para hoy ;-; si t sale el resultado deben de cambiarlo y ver si salio ;-;
If a train is going 3 miles in a hour how much will it go into 2 3/4 a hour
Answer: 8.25 miles in 2 3/4 hours
Step-by-step explanation:
(a) The marked price of a bicycle is Rs 2,000. If the shopkeeper allows some discount and a customer bought it for Rs 1921 including 13% VAT, how much amount was given as the discount?
The amount of the discount that was given is $300.
What is the discount given?A discount reduces the price of an item. When a discount is given, the item becomes cheaper. VAT is value added tax. VAT increases the price of an item.
The equation that can be used to represent the total cost of the bicycle is:
Total cost after VAT and discount = (1 + VAT) x (marked price - discount)
1921 = (1 + 0.13) x (2,000 - d)
1921 = 1.13 x (2,000 - d)
In order to determine the value of discount, take the following steps:
Divide both sides of the above equation by 1.13
1921 / 1.13 = 2000 - d
1,700 = 2,000 - d
Combine similar terms: 2000 - 1700 = d
Add similar terms together: d = 300
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4) Mr. Carter loves underwater diving. His house
boat is 250 feet above sea level. After jumping from
that level, he ended up at 650 feet below sea level.
What was the total distance that Mr. Carter traveled
from his boat to where he ended up?
Answer:
he traveled 900 feet
Step-by-step explanation:
250 + 650 = 900
Mr. Carter traveled a total distance of 900 feet from his boat to where he ended up.
Here, we have to find the total distance that Mr. Carter traveled from his boat to where he ended up, we need to calculate the sum of the distances above and below sea level.
The distance above sea level is 250 feet (his house boat's level), and the distance below sea level is 650 feet (where he ended up after jumping).
Total distance traveled = Distance above sea level + Distance below sea level
Total distance traveled = 250 feet + 650 feet
Total distance traveled = 900 feet
Mr. Carter traveled a total distance of 900 feet from his boat to where he ended up.
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