Here are the vertices of rectangle FROG: (-2,5),(-2,1),(6,5),(6,1). Find the perimeter of this rectangle. If you get stuck, try plotting the points on a coordinate plane. For the rectangle FROG, the perimeter is . Find the area of the rectangle FROG. For the rectangle FROG, the area is
Answers
Answer:
Part 1) The perimeter of rectangle is equal to 24 units
Part 2) The area of rectangle is equal to 32 square units
Step-by-step explanation:
Part 1) Find the perimeter of rectangle
we know that
The perimeter of rectangle is equal to
[tex]P=2(L+W)[/tex]
where
L is the length of rectangle
W is the width of rectangle
we have
[tex]F(-2,5),R(-2,1),O(6,1),G(6,5)[/tex]
Plot the figure to better understand the problem
using a graphing tool
see the attached figure
Remember that in a rectangle opposite sides are congruent and the measure of each interior angle is equal to 90 degrees
so
[tex]FG=RO=L\\RF=OG=W[/tex]
the formula to calculate the distance between two points is equal to
[tex]d=\sqrt{(y2-y1)^{2}+(x2-x1)^{2}}[/tex]
step 1
Find the distance FG
[tex]F(-2,5),G(6,5)[/tex]
substitute the values
[tex]d=\sqrt{(5-5)^{2}+(6+2)^{2}}[/tex]
[tex]d=\sqrt{(0)^{2}+(8)^{2}}[/tex]
[tex]FG=8\ units[/tex]
step 2
Find the distance RF
[tex]R(-2,1),F(-2,5)[/tex]
substitute the values
[tex]d=\sqrt{(5-1)^{2}+(-2+2)^{2}}[/tex]
[tex]d=\sqrt{(4)^{2}+(0)^{2}}[/tex]
[tex]RF=4\ units[/tex]
step 3
Find the perimeter
[tex]P=2(L+W)[/tex]
we have
[tex]FG=RO=L=8\ units\\RF=OG=W=4\ units[/tex]
substitute
[tex]P=2(8+4)=24\ units[/tex]
Part 2) Find the area of rectangle FROG
we know that
The area of rectangle is equal to
[tex]A=LW[/tex]
we have
[tex]FG=RO=L=8\ units\\RF=OG=W=4\ units[/tex]
substitute
[tex]A=(8)(4)=32\ units^2[/tex]
The area and the perimeter of the rectangle FROG is evaluated as:
Area(FROG) = [tex]32 \: \rm unit^2[/tex]Perimeter(FROG) = [tex]64\: \rm units[/tex]How to find the area and the perimeter of a rectangle?For a rectangle with length and width L and W units, we get:
Area of the rectangle = [tex]L \times W \: \rm unit^2[/tex]Perimeter of the rectangle = [tex]2(L + W) \: \rm unit^2[/tex]What is the distance between two points ( p,q) and (x,y)?The shortest distance(straight line segment's length connecting both given points) between points ( p,q) and (x,y) is:
[tex]D = \sqrt{(x-p)^2 + (y-q)^2} \: \rm units.[/tex]
The coordinates of the points of the rectangle FROG are given as:
F(-2,5), R(-2,1), G(6,5), and O(6,1) (from its plot, as given below)
FR and RO are length and width pair(we can call any one of them as length and other as width) of the considered rectangle as they are adjacent to each other.
We denote length of a line segment AB by |AB|
Thus, we get:
Length of the rectangle = |FR| = [tex]\sqrt{(-2-(-2))^2 + (1 - 5)^2 } = 4[/tex] unitsWidth of the rectangle = |RO| = [tex]\sqrt{(6-(-2))^2 + (1 - 1)^2 } = \sqrt{64} = 8 \: \rm units[/tex]Now with the help of length and width, we can evaluate its perimeter and area, as shown below:
Area(FROG) = [tex]L\times W = 4 \times 8= 32 \: \rm unit^2[/tex]Perimeter(FROG) = [tex]2(L + W) = 2(4 + 8) = 64\: \rm units[/tex]Learn more about distance between two points here:
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Related Questions
Which of the following rational numbers represents a repeating decimal 11 / 40 ,3/25, 25/48,or 7/32
Answers
[tex]\frac{25}{48}[/tex] represents repeating decimal
Solution:
We are asked to find the rational number that represents repeating decimal
A repeating decimal, also called a recurring decimal, is a number whose decimal representation eventually becomes periodic (i.e., the same sequence of digits repeats indefinitely)
Option 1
[tex]\frac{11}{40} = 0.275[/tex]
So here the decimal part is not repeating. So [tex]\frac{11}{40}[/tex] does not represent repeating decimal
Option 2
[tex]\frac{3}{25} =0.12[/tex]
So here the decimal part is not repeating. So [tex]\frac{3}{25}[/tex] does not represent repeating decimal
Option 3
[tex]\frac{25}{48} = 0.52083333333[/tex]
So here in decimal part "3" is repeating and goes on forever
So [tex]\frac{25}{48}[/tex] represents repeating decimal
Option 4
[tex]\frac{7}{32} = 0.21875[/tex]
So here the decimal part is not repeating. So [tex]\frac{7}{32}[/tex] does not represent repeating decimal
What makes a trapezoid an isosceles trapezoid?
Answers
Answer:
A: Its legs are congruent
Step-by-step explanation:
A trapezoid is a quadrilateral with exactly one pair of parallel sides. In a trapezoid the parallel sides are called bases. A pair of angles that share a base as a common side are called a pair of base angles. A trapezoid with the two non-parallel sides the same length is called an isosceles trapezoid.
An isosceles trapezoid is a trapezoid with two congruent sides and congruent base angles.
Explanation:An isosceles trapezoid is a trapezoid that has two congruent sides. In other words, the two non-parallel sides of an isosceles trapezoid are equal in length. The base angles of an isosceles trapezoid are also congruent. The parallel sides of an isosceles trapezoid are not equal in length.
For example, if a trapezoid has sides AB = 6 cm, BC = 5 cm, CD = 4 cm, and DA = 5 cm, then it is an isosceles trapezoid because sides BC and DA are congruent.
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Amaya used these steps to solve the equation 8x+4=9+4(2x−1). Which choice describes the meaning of her result, 4=5?
Answers
Answer:
No value of x makes the equation true.
Step-by-step explanation:
Here are the choices which are missing in the question:
a) Amaya made a mistake because 4 is not equal to 5
b) No value of x make the equation true.
c) All value of x make the equation true.
d) The solution is x= 4 or 5
Given equation is [tex]8x+4=9+4(2x-1)[/tex]
Now, solving the equation:
[tex]8x+4=9+4(2x-1)[/tex]
distributing 4 with both 2x and -1
⇒[tex]8x+4= 9+8x-4[/tex]
⇒[tex]8x+4= 5+8x[/tex]
Subtracting both side by 8x
∴ 4=5
The result indicate that equation has the same result and x has no value.
Answer:
No values of x make the equation true.
Help meeeeeee need by 12:50 for me it’s 12:30 nowwwwwwww WILL MARK BRAINLIEST!!
Answers
Answer:
Step-by-step explanation:
XW II Yz and XY is transversal
∠XYZ +∠ZYX = 180° {sum of co-interior angle is 180}
2x + 90 + 3x - 5 = 180
5x = 180 - 90 + 5
5x = 95
x = 95 / 5
x = 19
Read through the scenarios below and calculate the predicted change in kinetic energy of the object compared to a 100 kg ball traveling at 5 m/s.
A 1,000 kg ball traveling at 5 m/s would have ____ Kinetic energy
A 10 kg ball traveling at 5 m/s would have ____ kinetic energy
A 100 kg person falling at 5 m/s would have ____ Kinetic energy
Answers
10 times
tenth
the same
Step-by-step explanation:
K.E is directly proportional to mass thus if the mass increases or decreses "k" times, then so does the K.E
Answer:
1). 10 times more 2). 10 times less 3). the same
Step-by-step explanation:
Circle A and circle B are congruent. CD is a cord of both circles. if AB = 24 inches in the radius is 13 inches how long is CD A.10in B.26in C.12in D.9in
Answers
Option A
Length of CD is 10 inches
Solution:
The diagram is attached below
Given that, Circle A and circle B are congruent
CD is a cord of both circles
AB = 24 inches
Radius = 13 inches
To find: length of CD
Draw a straight line connecting A and C
AC represents the radius of circle. Also given that radius is 13 inches, So AC = 13 inches
Given in question that AB = 24 inches
Therefore from figure, AO = AB/2 = 24/2 = 12
AO = 12
Let "b" be the length of CO
Therefore, CD = CO + OD = b + b
AOC forms a triangle, so we can use pythogoras theorem
Pythagorean theorem, states that the square of the length of the hypotenuse is equal to the sum of squares of the lengths of other two sides of the right-angled triangle.
By above definition for triangle AOC
[tex]AC^2 = AO^2 + OC^2[/tex]
Substituting AC = 13 and AO = 12 and OC = b
[tex]13^2 = 12^2 + b^2\\\\b^2 = 169 - 144\\\\b^2 = 25\\\\b = 5[/tex]
Thus length of CD is:
CD = b + b = 5 + 5 = 10
Thus length of CD is 10 inches
Choose the solution set graphic until the correct one is displayed.
A.Infinite set of points on the line
B.Empty set
C.Points on negative x-axis
Answers
Final answer:
The solution set graphic is C - Points on negative x-axis.
Explanation:
The correct solution set graphic for this question is C - Points on negative x-axis.
To determine the solution set graphically, you would need to plot all the possible values of the equation or inequality on a coordinate plane. Option A - Infinite set of points on the line would represent a linear equation or inequality with multiple solutions. Option B - Empty set would mean that there are no solutions to the equation or inequality. Option C - Points on negative x-axis would indicate that the equation or inequality has solutions only on the negative x-axis.
To be labeled as a jumbo egg, the egg is supposed to weight 2.5 oz. However, when Desmond buys a carton of jumbo eggs, the weight of one is 2.4 oz. What is the percent error?
(Explain in a detailed way on how you got your answer)
Answers
The percent error is 4.17 %
Solution:
To be labeled as a jumbo egg, the egg is supposed to weight 2.5 oz
When Desmond buys a carton of jumbo eggs, the weight of one is 2.4 oz
To find: percent error
Percent error is the difference between a measured and known value, divided by the known value, multiplied by 100%
[tex]\% \text { error }=\frac{\text {approximate value}-\text {exact value}}{\text {exact value}} \times 100[/tex]
Here approximate value = 2.5 oz and exact value = 2.4 oz
[tex]\% \text { error }=\frac{2.5-2.4}{2.4} \times 100\\\\\% \text { error }= \frac{0.1}{2.4} \times 100 = 4.17[/tex]
Therefore percent error is 4.17 %
There are 30 chairs in the band room mr avery wants to have the same number of chairs in each row there must be more than 1 row and the number of chairs in each row must also be greater than the number of rows explain how mr avery could arrange the chairs
Answers
Final answer:
Mr. Avery can arrange the 30 chairs in 5 rows of 6 chairs each or 3 rows of 10 chairs each to satisfy the conditions of having more than one row and the chairs per row being greater than the number of rows.
Explanation:
Mr. Avery can arrange the 30 chairs in the band room in multiple configurations but must satisfy two conditions: there must be more than one row and the number of chairs in each row must be greater than the number of rows. To find such arrangements, we can look for factors of 30 that adhere to these conditions. One possible arrangement is 5 rows with 6 chairs in each row. This satisfies the conditions because there are more than one row, and the number of chairs per row (6) is greater than the number of rows (5).
Another possible arrangement could be 3 rows with 10 chairs each. Here, the condition is also met since there are more than one row and the number of chairs per row (10) is greater than the number of rows (3). Mr. Avery must ensure there's enough space to move around, so he may need to rearrange the chairs to provide adequate pathways between rows.
Mike is making a scale model of his favorite car. The actual car is 8 feet long and four feet wide. Mike wants his model to be 12 inches in length. Which of the following proportions could be used to find the width, w, of his model?
A:8/4=12/w B:8/4=w/12 C: 8/12=w/4 D:12/8=4/w
Answers
Answer:
A. 8/4=12/w
Step-by-step explanation:
8/4=12/x
8feet long 12 inches
---------------- = ----------------
4feet wide X because we dont know exact width
Answer:
A. 8/4=12/w
Step-by-step explanation:
Help me find 7x+6=41
Answers
Answer:
x=5
Step-by-step explanation:
Answer:
x=5
Step-by-step explanation:
what i did was..
41-6 = 30
30/7 = 5
x=5
Can someone EXPLAIN how I find cf on 10. Thx
Answers
Answer:
Step-by-step explanation:
parent function is the main function the start function and transformations are the new function so parent function is y = x^2 and the transformations is down for (due to the -) and left 3 (due to the +)
HOPE THIS HELPED ;3
Answer:
so....wya
Step-by-step explanation:
the sum of 3x and 14 equals the difference of 20 and 2x
Answers
Answer. 17<18
The sum of 3x + 14 equals 17x.
The difference between 20 - 2x equals 18x.
Therefore the equation is not equal to each other.
the world population in 2013 was about 7.125 billion. in 2003,it was about 6.357 billion. which number represents the increase in the world population between 2003 and 2013?
Answers
there was a 768million person increase in that decade
Answer:
768million
Step-by-step explanation:
what is the slope of the line x=2
Answers
Answer:
infinite
Step-by-step explanation:
The slope is the amount the line moves in y direction when you go move unit in the x direction. For a vertical line that is infinite...
Jerry needs to buy nails and screws for the construction site. Nails cost $2.75 per pound and screws cost $3.25 per pound. If he
only has $500 to spend on nails and screws, which inequality represents the situation where he buys x pounds of nails and y
pounds of screws?
A)
3.25x +2.75y s 500
B)
3.25x + 2.75y 2 500
2.75x + 3.25y s 500
D)
2.75x + 3.25y 2 500
Answers
Answer:
C) 2.75x+3.25y ≤ 500
Step-by-step explanation:
Here are the correct options given:
A) 3.25x +2.75y ≤ 500
B) 3.25x + 2.75y ≥ 500
C) 2.75x + 3.25y ≤ 500
D) 2.75x + 3.25y ≥ 500
Given: Nails cost is $2.75 per pound
Screw cost is $3.25 per pound
Jerry has only $500 to spend on nails and screws.
x represent quantity of nail bought and y represent quantity of screw bought.
As given we know that Jerry has only $500 to spend, so the total cost has to be less than or equal to $500. It cannot go more than $500.
Remember, Total cost= [tex]\textrm{cost of goods per pound}\times quantity[/tex]
Now, Inequality to represent the cost of buying nails and screw.
[tex]\$2.75\times x\ pounds+ \$3.25\times y\ pounds\leq \$ 500[/tex]
∴ [tex]2.75x+3.25y\leq 500[/tex]
A garden is rectangular with an area of 6/7 square miles. If the length of the garden is 3/5 miles, what is its width?
Answers
Answer:
Step-by-step explanation:
Area= length x width
area=6/7, length=3/5, width=?
6/7=3/5 x width
6/7 divided by 3/5= 6/7 x 5/3 (you have to multiply by the recipricol, or flip the fraction.)
6/7 x 5/3=30/21= 1 3/7=width
The area of a 2D form is the amount of space within its perimeter. The width of the rectangle is 10/7 miles.
What is an area?The area of a 2D form is the amount of space within its perimeter. It is measured in square units such as cm2, m2, and so on. To find the area of a square formula or another quadrilateral, multiply its length by its width.
The area of a rectangle is the product of its length and its width, therefore, the width of the rectangle can be written as,
Area = Length × Width
Width = Area / Length
Given the area of the rectangle is 6/7 square miles, while the length of the rectangle is 3/5 miles, therefore, the width of the rectangle is,
Width = (6/7)/(3/5)
Width = (6×5)/(7×3) = 10/7
Hence, the width of the rectangle is 10/7 miles.
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A factory runs nonstop for three 14 - hour shifts. The first shift starts at 9.00 AM. At what times does their third shift end?
Answers
Answer:
Step-by-step explanation:
3 fourteen hr shifts.....that (14 * 3) = 42 hrs....thats 1 day and 18 hrs
first shift starts at 9 AM......
one day later will make it 9 AM the next day....now we have the 18 hrs.....so from 9 AM to 9 PM is 12 hrs.....so we are at 9 PM and have 6 hrs left.....making the last shift end at 3 AM <==
3:00 pm is the time where does their third shift end.
What is Equation?Two or more expressions with an Equal sign is called as Equation.
Given that A factory runs nonstop for three 14 - hour shifts.
The first shift starts at 9.00 AM.
We need to find the times does their third shift end.
First shift:
9:00Am to 11:00Pm (14 hours)
second shift:
11:00pm to 1:00 am (14 hours)
Third shift
1:00 am to 3:00 pm (14 hours)
Hence, 3:00 pm is the times where does their third shift end.
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Solve for y in terms of x: 3y-2x=7
Answers
Answer will be: y=7/3+2x/3
Answer:
y = 2/3x + 7 / 3
Step-by-step explanation:
Step 1: Add 2x to both sides.
−2x+3y+2x=7+2x
3y=2x+7
Step 2: Divide both sides by 3.
3y / 3 = 2x+7 / 3
y= 2 / 3x + 7 / 3
5(2r+6)-12r ; Simplify
Answers
First, use distributive property:
5(2r+6)-12r The original expression; multiply 5 by 2r, and 5 by 6.
10r+30-12r Keep the -12r, just add it on to the end of the number(s) you found
Next, use communitive property:
10r+30-12r What we found in the previous step
-2r+30 Combine the like terms; 10r-12r=-2r, then place the 30 at the end
Done! Your answer is -2r+30.
Hope that helps!
What are the solutions to x2 + 8x + 7 = 0?
O
O
O
O
x=-8 and x = -7
x=-7 and x=-1
x = 1 and x = 7
x = 7 and x = 8
Answers
Answer:
x = - 1 and x = - 7
Step-by-step explanation:
Given
x² + 8x + 7 = 0 ← in standard form
(x + 1)(x + 7) = 0 ← in factored form
Equate each factor to zero and solve for x
x + 1 = 0 ⇒ x = - 1
x + 7 = 0 ⇒ x = - 7
The quadrilateral shown is a rhombus. What is m∠4?
Answers
Answer:
m∠4= 360-(m∠A+m∠1+m∠3+m∠C+m∠2)
Step-by-step explanation:
In the diagram. check attach image
m∠A + m∠B + m∠C + m∠D = 360º.
Every quadrilateral can be decomposed (cut apart) into two triangles, each of whose angles' measures sum to 180º.
m∠A + m∠1 + m∠ 3 = 180º
m∠C + m∠2 + m∠4 = 180º
m∠A+m∠1+m∠3+m∠C+m∠2+m∠4 = 360º
therefore :
m∠4= 360-(m∠A+m∠1+m∠3+m∠C+m∠2)
Solve. 5x−3/2=3x+8
–26
–19
13
19
Answers
Good morning,
Answer:
-19
Step-by-step explanation:
(5x−3)/2=3x+8 ⇌ 5x−3 = 2×(3x+8) ⇌ 5x−3 = 6x+16 ⇌ 6x-5x = -3-16
⇌ x=-19.
:)
Answer:
x = - 19
Step-by-step explanation:
Given
[tex]\frac{5x-3}{2}[/tex] = 3x + 8
Multiply both sides by 2 to clear the fraction
5x - 3 = 6x + 16 ( subtract 6x from both sides )
- x - 3 = 16 ( add 3 to both sides )
- x = 19 ( multiply both sides by - 1 )
x = - 19
Solve 6x - 2 = 4x + 13 for x.
15/2
112
3/12
Answers
Answer:
[tex]\large \boxed{x = \dfrac{15}{2}}[/tex]
Step-by-step explanation:
[tex]\begin{array}{rcll}6x - 2& = & 4x + 13 & \\6x & = & 4x + 15 & \text{Added 2 to each side}\\2x & = & 15 & \text{Subtracted 4x from each side}\\x & = & \mathbf{\dfrac{15}{2}}& \text{Divided each side by 2}\\\\\end{array}\\\large \boxed{\mathbf{x = \dfrac{15}{2}}}[/tex]
mr.james runs a petting zoo. he records the number of visitors each week,v, t weeks, after opening the petting zoo. according to the table what is the average rate of change over the interval [2,5]
a.57 visitors per month
b. 28 visitors per month
c. 36 visitors per month
d 19 visitors per month
Answers
Answer:
[tex]\large \boxed{\text{19 visitors/mo}}[/tex]
Step-by-step explanation:
The average rate of change is the change in the number of visitors divided by the change in the number of months.
1. Change in number of visitors
Change in visitors = 182 -125 = 57 visitors
2. Change in number of weeks
Change in time = 5 - 2 = 3 months
3. Average rate of change
[tex]\begin{array}{rcl}\text{Average rate of change} &= &\dfrac{\text{change in visitors}}{\text{change in months}}\\\\&= &\dfrac{\text{57 visitors}}{\text{3 mo}}\\\\& = & \textbf{19 visitors/mo}\\\end{array}\\\text{The average rate of change is $\large \boxed{\textbf{19 visitors/mo}}$}[/tex]
PLEASE HELP!!
identify the cross section shown.
a. octagon
b. rectangle
c. trapezoid
d. triangle
Answers
Answer:
c
Step-by-step explanation:
The figure is a triangular prism
It is like you take an iron sheet with the shape of a trapezoid to cut the figure
The bottom part of the "sheet match the triangular base of the prism
The top part of the"sheet match the middle point of the triangular top of the prism
Benson played 12 games of trivia. He had
a perfect score on every game and received
35 bonus points per game. He earned a
total of 1,260 points. How many points did
he earn per game not including the
bonus points?
Answers
Benson earned 70 points per game not including the bonus points.
Step-by-step explanation:
Given,
Games of trivia played = 12
Bonus points received per game = 35 points
Bonus points for 12 games = 35*12 = 420 points
Total points earned = 1260 points
Points earned in games = Total points - bonus points
Points earned in games = 1260 - 420 = 840 points
As he scored 840 points in 12 games, therefore,
12 games = 840 points
1 game = [tex]\frac{840}{12} = 70\ points[/tex]
Benson earned 70 points per game not including the bonus points.
Keywords: subtraction, division
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Find the greatest common factor of 10, 30,10,30,10, comma, 30, comma and 454545.
Answers
Answer:
GCF = 5
Step-by-step explanation:
Given:
The numbers are given as:
10, 30 and 45
A factor of a number is a number by which the given number is evenly divisible.
Example: 2 is a factor of 4 as [tex]4\div 2 =2[/tex]. So, 4 is evenly divisible by 2 and hence 2 is a factor of 4.
Now, factors of 10 = 1, 2, 5, 10.
Factors of 30 = 1, 2, 3, 5, 6, 10, 15, 30.
Factors of 45 = 1, 3, 5, 9, 15, 45.
So, the greatest common factor in all the three numbers is 5.
Hence, the greatest common factor of 10, 30 and 45 is 5.
About 4/5 of the weight of a pineapple is water. About how much water would you expect to find in 2 1/2 pounds of pineapple?
Answers
Answer:
2 pounds
Step-by-step explanation:
all you have to do is 2 1/2 x 4/5 because 4/5 is equal to 1. So if you multiply that by 2 1/2 you will get the answer
Find the other endpoint given one endpoint (-1,6) and the midpoint is (4,2)
Answers
Answer:
The required points of the given line segment are ( 9, - 2 ).
Step-by-step explanation:
Given that the line segment AB whose midpoint M is ( 4, 2 ) and point A is ( - 1, 6), then we have to find point B of the line segment AB -
As we know that-
If a line segment AB is with endpoints ( [tex]x_{1}, y_{1}[/tex] ) and ( [tex]x_{2}, y_{2}[/tex] )then the mid points M are-
M = ( [tex]\frac{ x_{1} + x_{2} }{2}[/tex] , [tex]\frac{ y_{1} + y_{2}}{2}[/tex] )
Here,
Let A ( - 1, 6 ), B ( x, y ) with midpoint M ( 4, 2 ) -
then by the midpoint formula M are-
( 4, 2 ) = ( [tex]\frac{ - 1 + x}{ 2}[/tex] , [tex]\frac{ 6 + y}{2}[/tex] )
On comparing x coordinate and y coordinate -
We get,
( [tex]\frac{ -1 + x}{2}[/tex] = 4 , [tex]\frac{ 6 + y}{2}[/tex] = 2)
( - 1 + x = 8, 6 + y = 4)
( x = 8 + 1, y = 4 - 6 )
( x = 9, y = -2 )
Hence the required points A are ( 9, - 2 ).
We can also verify by putting these points into Midpoint formula.