The area of the polygon become 24.5.
According to the statement
We have to find that the area of the polygon.
So, For this purpose, we know that the
Polygon is a plane shape (two-dimensional) with straight sides.
Area is defined as the total space taken up by a flat (2-D) surface or shape of an object.
From the given information:
The given vertices are:
J(-3,\ 4),\ K(4,\ 4),\ L(3,-3)
And then the base of the polygon become:
Base = [tex]\sqrt{(x_{1} - x_{2})^{2} + (y_{1} - y_{2})^{2} }[/tex]
Then
Base = [tex]\sqrt{(-3 - 4)^{2} + (4 -4)^{2} }[/tex]
Base = 7
Then
Height = [tex]\sqrt{(y_{1} - y_{2})^{2} +(z_{1} - z_{2})^{2} }[/tex]
Height = [tex]\sqrt{(4 - 4)^{2} +(4 - (-3))^{2} }[/tex]
Height = 7
Then the area of the polygon becomes:
Area = 1/2 *Base*Height
Area = 1/2 *7*7
Area = 1/2*49
Area = 24.5
Thus, The area of the polygon become 24.5.
Learn more about Polygon here
https://brainly.com/question/1592456
#SPJ9
URGENTT ! PLEASE HELP :3
Write a function rule for each relation below.
1)
X:
-2
-1
0
1
2:
Y
-2
2
6
10
14
Answer:
x | y
-2. -2
-1. 2
0. 6
1. 10
2. 14
how many numbers do we have between each number on Y? 4
Step 1
this you have to use this data to make your function
f(x)=4X
Always you have to use the spaces times X
Step 2
We have to calculate what do we need to satisfy the function, in this case we have to add 6
f(x)=4x+6
When a ball is bounced on a smooth surface, the angles formed by the path of the ball are congruent. If the path of a ball forms a 53^{\circ} angle with the floor, find \(m \angle A B C\).
The ball hits the surface at 43.5° and bounces back at 43.5°.
What is a system of equations?A system of equations is two or more equations that can be solved to get a unique solution. the power of the equation must be in one degree.
Given that When a ball is bounced on a smooth surface, the angles formed by the path of the ball are congruent.
If the path of a ball forms a 53 angle with the floor, find the angle with the floor, x
Let the angle with the floor, x
Using, to find x, setup the equation:
x+ 53 +x=180
2x+ 53 =180
2x = 127
x= 43.5°
Therefore, the ball hits the surface at 43.5° and bounces back at 43.5°.
Learn more about equations here;
https://brainly.com/question/10413253
#SPJ4
What is the Term for an answer that was obtained in a fair or controlled test
Can someone pls help me I need to know if I am correct
If you have the fraction - 8/5 (the negative sign is not on either 8 or 5) it means that both numbers are negative right?
Answer:
Yes, that means the whole fraction is negative.
Also for future note, if the negative is on the top or bottom, the fraction will still be negative. Unless it says to simplify.
Hope this helps!
It takes Andrea 12.5 hours to drive 875 miles. What was her average Speed?
Answer:
70 miles per hour
Step-by-step explanation:
take 875mi and divide by how long it took: 12.5 hours
Question
Find the sum.
(1−5q)+2(2.5q+8)
Answer:
[tex]1 - 5q + 5q + 16 \\ = 17[/tex]
Find the 17 th term of each sequence. a₁₆ = 1/5, d= 1/2
7/10 is 17th term of sequence a₁₆ = 1/5, d= 1/2.
Given the 16th term and the common difference, we add the common difference from the 16th term to determine the 17th term:
a₁₇ = a₁₆ + d
= 1/5 + 1/2
= 7/10
How to solve an equation?To solve linear equations, utilize the steps that are provided below.
Remove parentheses from each side of the equation and combine similar terms to make it simpler.To separate the variable term on one side of the equation, use addition or subtraction.To find the variable, use division or multiplication.The common denominator can be multiplied by each side of the equation to eliminate fractions.Lets take an example of solve z for 7z – (3z – 4) = 12
Here is no multiplication or division, so this will be easy to solve
⇒ 7z – (3z – 4) = 12
⇒ 7z – 3z + 4 = 12
⇒ 4z = 12 – 4
⇒ 4z = 8
⇒ z = 8/4
⇒ z = 2
See, that was so simple, using the mentioned methods, every linear equation can be solved easily.
Learn more about linear equations
brainly.com/question/14323743
#SPJ4
Hurry please i need these done Asap?Jessica is making matching book bags for her 4 friends. 1 7/8 yards of fabric.
Moon and stars- 7 1/2
softballs- 7.4
stripes- 7 3/5
tie-dye- 7.9
Indicate which of the fabrics Jessica can and cannot use to make all of the book bags for her friend.
moons and stars can or cannot
softballs can or cannot
stripes can or cannot
tie-dye can or cannot
The fabric that she cannot use is the softballs.
Which fabric can she not use?A proper fraction is a non-integer that is made up of a numerator that is smaller in value than the denominator. A mixed fraction is a fraction that is made up of an integer and a proper fraction. An example of a mixed fraction is 1 7/8.
The first step is to determine the total amount of fabric needed for the 4 friends : 1 7/8 x 4
15/8 x 4 = 60 /8 = 7 1/2 yards
The second step is to convert the mixed fractions to decimals, by dividing the numerator by the denominator and adding the integer.
7 1/2 = 7.5
73/5 = 7.6
The fabric that cannot be used as the fabrics that are less than 7.5 yards.
To learn more about fractions, please check: https://brainly.com/question/10354322
#SPJ1
Given point Y is between X and Z, where XY = 12 and XZ = 48, What is YZ?
Answer: 36
Step-by-step explanation:
XZ=XY+YZ
48=12+YZ
48-12=12-12+YZ
YZ=48-12
YZ=36
Δ A B C has vertices A(-3,3), B(2,5) , and C(4,-3) . What are the coordinates of the centroid of ΔA B C ? Explain the process you used to reach your conclusion.
The coordinates of the centroid of Δ ABC is y = -1/3x + 2.
What is meant by the slope of the line?
The slope of the line is the rise-to-run ratio or the rise divided by the run. It expresses the slope of a line in the coordinate plane. Finding the slope of a line is similar to determining the slope between two points.
The midpoint D of AC is (-3+4/2, 3-3/2) or (1/2, 0).
Note that DB is a line that connects the vertex B and D, the midpoint of AC.
The slope of the line DB is ((5-0)/(2-1/2)) or 10/3.
The equation of DB is
y - 5 = 10/3 (x - 2)
simplifying the above equation, we get
y - 5 = 10x/3 - 20/3
y - 5 + 5 = 10x/3 - 20/3 + 5
y = 10x/3 - 5/3
Use the same method to find the equation of the line between point A and the midpoint of BC.
Therefore, the coordinates of the centroid of Δ ABC is y = -1/3x + 2.
To learn more about the slope of the line refer to:
https://brainly.com/question/16949303
#SPJ4
The sum of three consecutive even integers is 18 more than five-halves the smallest integer. What is the product of the smallest and largest integer?
The product of the smallest and largest integer is 672
What is the product of the smallest and largest integer?Represent the smallest even integer with x.
So, the other even integers are x + 2 and x + 4
The sum is represented as
x + x + 2 + x + 4 = 18 + 5/2x
Evaluate the like terms
3x + 6 = 18 + 5/2x
Evaluate the like terms
1/2x = 12
Multiply by 2
x = 24
The largest integer is x + 4
So, we have
x + 4 = 24 + 4
x + 4 = 28
The product of the smallest and largest integer is
Product = 24 * 28
Evaluate
Product = 672
Hence, the product of the smallest and largest integer is 672
Read more about consecutive integers at:
https://brainly.com/question/10853762
#SPJ1
In a company, the penalty for being late for work in one month
follows the table below.
Late the first 3 times
$10 total
For every additional time $8 per time
If Jane paid $42 for the penalty last month, how many times
was she late for work?
___times
You are choosing between two health clubs. Club A offers membership for a fee of $28 plus a monthly fee of $28. Club B offers membership for a fee of $23 plus a monthly fee
of $29. After how many months will the total cost of each health club be the same? What will be the total cost for each club?
Answer:
Step-by-step explanation:
True or False?
4 and 1/4 are opposites
A brick path is being installed around a circular pond. The pond has a circumference of 68 feet. The outer edge of the path is going to be 4 feet from the pond all the way around. What is the approximate circumference of the path? Round to the nearest hundredth.
The approximate circumference of the path Round to the nearest hundredth is 93.12 feet.
What is circumference of circle?A circle's outside boundary is called the circumference and can be measured, or calculated, by using
Circumference = 2πr
where r is the radius of circle.
Now it is given that,
circumference of pond = 68 feet
⇒ 2πr = 68
⇒ r = 34/π
⇒ r = 10.82 feet
Now it is also given that, The outer edge of the path is going to be 4 feet from the pond all the way around
⇒ Radius of path, R = r + 4
⇒ Radius of path, R = 10.82 + 4
⇒ R = 14.828
So,circumference of the path = 2πR
⇒ circumference of the path = 2π*14.828 = 93.119 feet
⇒ circumference of the path Round to the nearest hundredth = 93.12 feet
Thus, the approximate circumference of the path Round to the nearest hundredth is 93.12 feet.
To learn more about circumference of circle :
brainly.com/question/13663465
#SPJ4
PLEASE HELP
PLEASE SHOW HOW U CHECKED UR WORK
The expression is simplified to s = -5/ 4
What are algebraic expressions?Algebraic expressions are expressions composed of terms, variables, constants, factors and coefficients.
They are also made up of mathematical operations such as addition, subtraction, multiplication, division, etc
Given the expression;
42 = 14{ 4 + 4/ 5s}
Divide both sides by 14
42/14 = 14{ 4 + 4/ 5s}/14
3 = 4 + 4/ 5s
3 = 20 + 4s/5
cross multply
15 = 20 + 4s
collect like terms
15 - 20 = 4s
-5 = 4s
Make 's' the subject
s = -5/ 4
Thus, the expression is simplified to s = -5/ 4
Learn more about algebraic expressions here:
https://brainly.com/question/4344214
#SPJ1
For all x,(x-7)²= ?
A x²-49
B x² + 49
C x² - 14x - 49
D x² - 14x + 49
E x² + 14x - 49
Answer:
I'm pretty sure the answer is E
x^2(3x-1)^4 integrate by parts
Answer:
[tex]81x {}^{6} - 108 { \times }^{5} + 54 { \times }^{4} - 12 { \times }^{3} + { \times }^{2} [/tex]
Determine a base and a height
Answer:
base : 7 units
height : 4 units
What is the area of the figure below?
The area of the figure is 289 square unit
What is Area of a Rectangle ?The area of a rectangle can be calculated by multiplying the length and the width of the shape.
Given that
L = 20 - xB = 3x + 8A = LBBut the length and the width have two equal opposite sides. The shape is a square
20 - x = 3x + 8
20 - 8 = 3x + x
12 = 4x
x = 12/4
x = 3
L = 20 - 3 = 17
B = 3(3) + 8
B = 9 + 8
B = 17
A = 17 x 17
A = 289 square unit
Therefore, the area of the figure is 289 square unit
Learn more about Area here: https://brainly.com/question/25292087
#SPJ1
What is the solution of the equation 3⁻ˣ = 1/243 ?
Answer:
well done .....I hope it's helpful
For the past 4 years, Jesse has grown 3 inches each year. He is now 15 years old and is 5 feet 6 inches tall. He predicts that when he is 20 years old, he will be 6 feet 9 inches tall. What would you tell Jesse about his prediction?
He estimates that he will stand 6 feet 9 inches tall when he is 20 years old. His prediction is correct.
How to check Jesse's prediction?Given: Growth per year = 3 inches
Height at 15 yrs of age = 5'6''
Height at 20 yrs of age = 6'9''(predicted)
We know that Jesse grows 3 inches every year.
In 5 years(15yrs - 20yrs) his growth = 5 × 3 = 15 inches.
At 15 years(present) height = 5'6''
At 20 years (future) height = 5'6'' + 15'' = 6'9'' (since, 1ft = 12 inches)
Thus, Jesse's prediction is correct
To learn more about feet and inches, refer to:
https://brainly.com/question/8019254
#SPJ4
Write the component form of →PQ .
The vector PQ is given by the addition of the components of the two vectors i.e. →PQ = →Q + →P
Vector is a quantity having magnitude as well as direction and is used to denote the mathematical and geometrical direction of the given quantity.
For example : Velocity, Displacement etc.
Let us first assume that,
P(x,y,z) and Q(u,v,w)
Now, we need to find the vector PQ
→PQ = →Q + →P
= (ui + vj + wk ) + (xi + yj + zk)
= (ui + xi ) +(vj + yj) + (wk +zk)
= (u+x) i + (v + y) j + (w + z)k
= →PQ
For example : Let P(1,2,1) and Q ( -1, -2,4)
Then, →PQ = →Q + →P
= (1i + 2j + 1k ) + (-1i + (-2)j + 4k)
= (1-1) i + (2 -2) j + (1 + 4)k
= oi+0j +5j
= 5j
Hence, the vector PQ is given by the addition of the components of the two vectors.
To learn more about Vectors, here
https://brainly.com/question/24256726
#SPJ4
Suppose we draw a single card from a deck of 52 fair playing cards. what is the probability of drawing an ace or a two?
The probability of getting an Ace is 1/13.
Probability of an event = number of favorable outcomes for the event/number of all possible products.
First, let's calculate the number of all possible outcomes. Randomly picking the cards could result in each of the 52 being selected. So, there are 52 possible outcomes.
But if you want an Ace in your desired event, you have four options—ace of Spades, Ace of Clubs, Ace of Hearts, and Ace of Diamonds. Therefore, the number of favorable outcomes for Aces = 4.
Therefore,
The probability of getting an Ace with a deck of 52 cards = 4/52 = 1/13.
More problems related to the concept of probability are given in the link below.
https://brainly.com/question/26900823?referrer=searchResults
#SPJ4
What is the value of x?
6
O 7
08
09
Answer:
7
Step-by-step explanation:
5x + 3 = 38
5x + 3 - 3 = 38 - 3
5x = 35
5x ÷ 5 = 35 ÷ 5
x = 7
Select the values that make the inequality s ≤ 6 s≤6 true. (Numbers written in order from least to greatest going across.) -2 1 3 5 5.9 5.99 5.999 6 6.001 6.01 6.1 7 9 11 14
The numbers that makes the inequality s ≤ 6 true include:
-2,1, 3, 5, 5.9, 5.99, 5.999. 6How to interpret inequality graphInequality graphs are graphs made to represent inequality equations.
the equation s ≤ 6 is interpreted to be the value of s that is less than or equal to 6.
From the interpretation, any value from 6 downwards is the correct answer. Hence we have the correct numbers listed as:
-2,1, 3, 5, 5.9, 5.99, 5.999. 6Other numbers above 6 are wring and do not fit in
Read more on inequalities here: https://brainly.com/question/11613554
#SPJ1
Which inequalities have no solution?
X>X
-3x < -3x
-4+X>-2+X
X-2
In mathematics, an inequality is a relation which makes a non-equal comparison between the two numbers or other mathematical expressions. Inequalities have no solution are X>X, -4+X>-2+X.
What do you mean by inequality?An inequality compares two values, showing if one is less than, greater than, or simply not equal to the another value.
The a ≠ b says that a is not equal to bThe a < b says that a is less than bThe a > b says that a is greater than b (those two are known as strict inequality)The a ≤ b means that a is less than or equal to bThe a ≥ b means that a is greater than or equal to b.Inequalities are governed by following properties. All of these properties also hold if all of non-strict inequalities (≤ and ≥) are replaced by their corresponding strict inequalities (< and >) and — in case of applying a function — monotonic functions are limited to the strictly monotonic functions.
From the above equations, the inequalities having no solutions are,
X>X
-4+X>-2+X
To know more about inequality visit: https://brainly.com/question/20383699
#SPJ9
A student has some 1 bills and 5 bills in his wallet. He has a total of 15 bills that are worth 47 . How many of each type of bill does he have?
If a student has some 1 bills and 5 bills in his wallet and he has a total of 15 bills that are worth 47, then the number of 1 bills he has is equal to 7 and the number of 5 bills he has is equal to 8.
The number of bills of each type can be calculated by forming a system of equations.
Consider x to be the number of 1 bills and y to be the number of 5 bills.
The first equation can be given as,
x + y = 15
The second equation can be given as,
x + 5y = 47
The two equations can be solved by using the substitution method:
By rearranging the first equation the value of x can be calculated to be,
x + y = 15
x = 15 - y
Putting this value of x in the second equation,
x + 5y = 47
15 - y + 5y = 47
4y = 47 - 15
4y = 32
y = 32 ÷ 4
y = 8
The value of x can be determined by putting y = 8 in the first equation,
x + y = 15
x + 8 = 15
x = 15 - 8
x = 7
Hence, the number of 1 bills and 5 bills are equal to 7 and 8 respectively.
To learn more about the substitution method, click here:
https://brainly.com/question/25869125
#SPJ4
Question 2
Find the unit rate.
If there are 8 teaspoons for every 4 cups in a recipe. How many
teaspoons are there in one cup?
teaspoons
