What is the perimeter of the rectangle shown on the coordinate plane, to the nearest tenth of a unit?
13.4 units
17.9 units
26.8 units
40.0 units
Answers
see the attached figure to better understand the problem
Let
x------> the length side of a rectangle
y-------> the width side of a rectangle
we know that
the perimeter of a rectangle is equal to the formula
[tex]P=2x+2y[/tex]
in this problem
[tex]AB=DC=x[/tex]
[tex]AD=BC=y[/tex]
Step 1
Find the distance AB
[tex]A(-6,4)\\B(2,8)[/tex]
we know that
the distance's formula between two points is equal to
[tex]d=\sqrt{(y2-y1)^{2} +(x2-x1)^{2}}[/tex]
substitute the values
[tex]d=\sqrt{(8-4)^{2} +(2+6)^{2}}[/tex]
[tex]d=\sqrt{(4)^{2} +(8)^{2}}[/tex]
[tex]dAB=\sqrt{80}\ units[/tex]
Step 2
Find the distance BC
tex]B(2,8)\\C(4,4)[/tex]
we know that
the distance's formula between two points is equal to
[tex]d=\sqrt{(y2-y1)^{2} +(x2-x1)^{2}}[/tex]
substitute the values
[tex]d=\sqrt{(4-8)^{2} +(4-2)^{2}}[/tex]
[tex]d=\sqrt{(-4)^{2} +(2)^{2}}[/tex]
[tex]dBC=\sqrt{20}\ units[/tex]
Step 3
Find the perimeter
we know that
the perimeter of a rectangle is equal to the formula
[tex]P=2x+2y[/tex]
[tex]P=2AB+2BC[/tex]
we have
[tex]dAB=\sqrt{80}\ units=8.9\ units[/tex]
[tex]dBC=\sqrt{20}\ units=4.5\ units[/tex]
substitute the values of the distance in the formula
[tex]P=2*8.9+2*4.5=26.8\ units[/tex]
therefore
the answer is
The perimeter of the rectangle is equal to [tex]26.8\ units[/tex]
Related Questions
A total of 15000 is to be divided between jon and wendy with jon to receive 2500 less than wendy how much will she receive
Answers
j = w - 2500
w - 2500 + w = 15,000
2w - 2500 = 15,000
2w = 15,000 + 2,500
2w = 17500
w = 17500/2
w = 8750 <=== what wendy receives
j = w - 2500
j = 8750 - 2500
j = 6250...what Jon receives
Wendy will get $8750.
We have a total of 15000 that is to be divided between Jon and Wendy with Jon to receive 2500 less than Wendy how much will she receive.
We have to determine how much money will Wendy receive.
A total of 20 chocolates are to be divided between you and your brother such that you will get 6 more chocolates than your brother. How many chocolates will your brother get?Assume your brother gets x number of chocolates.
Then, you will get - x + 5.
Therefore -
x + x + 6 = 20
2x = 14
x = 7
According to the question -
Assume that Wendy receives $x.
Then Jon will receive $(x - 2500).
Then -
x + x - 2500 = 15000
2x = 17500
x = 8750
Hence, Wendy will get $8750.
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Solve for x.
2x−45=x+4
Answers
Which of the following inequalities is equivalent to 8 ≤ x.
Answers
Answer:
The answer is D
Step-by-step explanation:
IS THIS TRUE OR FALSE
A dilation is a function because every point on the pre-image corresponds to exactly one point on the image.
Answers
Help please me thanks
Answers
In how many distinct ways can the letters in engineering be arranged?
Answers
So the answer is
11!=39916800
Suppose you had d dollars in your bank account. You spent $22 but have at least $28 left. How much money did you have initially? Write and solve an inequality that represents this situation.
A) d + 22 ≤ 28; d ≤ 72
B) d – 22 > 28; d > 50
C) d + 22 ≥ 28; d ≥ 72
D) d – 22 ≥ 28;d ≥ 50
Answers
28 + 22 = 50
So the answer would be
B. d – 22 > 28; d > 50
I hope this helped : )
Answer:
D) d – 22 ≥ 28;d ≥ 50
Step-by-step explanation:
Let d represents the initial money ( in dollars ) in the account,
So, after spending $ 22 the remaining amount = initial amount - $ 22 = (d-22) dollars,
According to the question,
The remaining amount ≥ $ 28
⇒ d - 22 ≥ 28
Adding 22 on both sides, ( additive property of inequality ),
⇒ d ≥ 50
Hence, the required inequality and its solution would be,
d - 22 ≥ 28; d ≥ 50
Option 'D' is correct.
What affect does "h" have on the parent function y = 1/x ?
h < 0 moves the graph to the left, h > 0 moves the graph to the right.
Vertical stretch by a factor of |h|
h > 0 moves the graph up, h < 0 moves the graph down.
h > 0 reflects the graph across the y-axis.
Answers
[tex]y= \frac{1}{x-h} [/tex] (moves right)
If a vertical stretch by a factor of |h|, then [tex]y = \frac{h}{x} [/tex]
If h moves the graph up or down, [tex]y= \frac{1}{x} +h[/tex] (moves up)
[tex]y= \frac{1}{x} -h[/tex] (moves down)
[tex]y= \frac{1}{-hx} [/tex] and h = 1
20 P[OINTS!!!!!! ppppppllllllllllleeeeeeeeeeeeeeeaaaaaaaassssssseee help asap!!!!!!!
A quadrilateral is shown on the graph:
What effect will a reflection about the x-axis have on the quadrilateral? Be sure to address how it could impact the angles, side lengths, and congruency between the original pre-image and the image.
Answers
Answer:
The angles and side length would remain the same, the only thing that would change is the cornents, therefore the original pre image and the image would be congruent.
Step-by-step explanation:
The gas tank in Ms. Brown's car holds a total of 15 gallons. At any given time, how many gallons, g, will Ms. Brown have to pump into her car to fill her tank given the fraction of the tank,f, already filled?
A. g = 15f
B. g = f15/f
C. g = 15−15f
D. g = 15-15/f
Answers
Answer:
c cause i took the sat practice
The number of gallons (g) that Ms. Brown have to pump into her car to fill her tank will be g = 15 – 15f. Then the correct option is C.
What is a fraction number?A fraction number is a number that represents the part of the whole, where the whole can be any number. It is in the form of numerator and denominator.
The gas tank in Ms. Brown's car holds a total of 15 gallons.
At any given time.
The number of gallons (g) that Ms. Brown have to pump into her car to fill her tank given the fraction of the tank, f, already filled will be
The gas in a tank will be
⇒ 15f
Then number of gallons (g) will be
⇒ 15 – 15f
Then the correct option is C.
More about the fraction number link is given below.
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The graph of a linear function h contains the points given in the table below.
Find h^-1. x y
-2,4
-1,2
1,-2
2,-4
a.h^-1(x)=2x
b.h^-1(x)=-2x
c.h^-1(x)=1/2x
d.h^-1(x)=-1/2x
Answers
y=-2x
inverse x=-2y
y= -1/2x
Answer:
h-1(x) = -x
Step-by-step explanation:
Lydia is trying to prove that a quadrilateral in a coordinate plane is a square. First, she uses the slope formula to prove that there are two pairs of parallel sides. Next, she uses the distance formula to prove that all sides are equal. What additional step must Lydia perform before reaching a conclusion that the quadrilateral is a square?
A) Use the distance formula to prove that the diagonals of the quadrilateral are not equal.
Eliminate
B) Use the slope formula to prove that four right angles exist as a result of perpendicular sides.
C) Use the midpoint formula to prove that the diagonals of the quadrilateral do not bisect each other.
D) Use the Pythagorean Theorem to prove that the diagonals of the quadrilateral are twice the length of each side.
Answers
Its B
Answer:
slope
Step-by-step explanation:
Is this function even, odd, or neither?
Answers
when a function is odd, the symmetry is with respect to the origin, meaning, the graph to the right-side of the y-axis, is a mirror image of the one on the left-bottom-upside-down. So, you take a photo of the right-side graph,flip it over the x-axis, and then flip it again over the y-axis.
now, this one shows neither of those behaviours.
Answer:
The given function is neither even nor odd.
Step-by-step explanation:
A function is an even function if
[tex]f(-x)=f(x)[/tex]
A function is an odd function if
[tex]f(-x)=-f(x)[/tex]
From the given graph it is clear that graph is passing though the points (-3,2), (-1,2), (0,1/2), (1/2,0), (1,-1), (2,-1) and (3,1).
Here,
[tex]f(3)=1[/tex]
[tex]f(-3)=2[/tex]
[tex]f(-3)\neq f(3)[/tex] and [tex]f(-3)\neq -f(3)[/tex]
Since [tex]f(-x)\neq f(x)[/tex] and [tex]f(-x)\neq -f(x)[/tex], therefore the given function is neither even nor odd.
A boat takes 3.6 h to travel downstream from its dock to a fishing hole. If the water were still, it would have taken 4.5 h to make the trip. Let x represent the speed of the boat and let y represent the speed of the water.
(a) Write an expression for the distance traveled in moving water, using 3.6 h for the time. Then write an expression for the distance traveled as if in still water, using 4.5 h for the time.
(b) Set the expressions in Part (a) equal to each other. Then solve the equation for y. Show your work.
(c) What percent of the boat’s speed is the water current?
Answers
t1 = 3.6 h
t2 = 4.5 h
x = speed of boat
y = speed of water
Required:
a) Expression of distance traveled with moving water with 3.6h
Expression of distance traveled with moving water with 4.5h
b) Solve for y
c) Percent of boat's speed is the water current
Solution:
Working formula: distance = velocity*time
a) For travelling downstream, we get the equation
d = (x +y)*3.6
For travelling upstream, we get the equation
d = (x-y)*4.5
b) Setting the distance as equal for travelling upstream or downstream, we arrive at the equation of
(x+y)*3.6 = (x-y)*4.5
3.6x + 3.6y = 4.5x - 4.5y
8.1y =0.9x
y = x/9
c) percentage = 1/9*100% = 11.1%
ANSWERS: a) d = (x+y)*36; d = (x-y)*4.5
b) y = x/9
c) 11.1%
Suppose that a number written as a decimal has an infinite number of non–repeating digits after the decimal point. what is this number called?
Answers
When a number has an infinite number of non-repeating digits, which is called a non-terminating decimal value, then such number is an irrational number such as 1.3127...
Irrational number are real numbers which cannot be expressed in the form of p/q ; that is they cannot be expressed accurately as a ratio.They are characterized as having repeating decimal values as well as non-terminating decimal digits. When a number has unending or infinite number of non-repeating digits, it is said to be non-terminating, hence, such number is called an irrational number.
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Use the formula C = 2πr and π= 3.14 to find the circumference of a circle with a radius of 5 meters.
A.15.7 m
B.78.5 m
C.3.140 m
D.31.4 m
E.34.54 m
Answers
Just put into a calculator
Hope I helped :)
Bob ate 10 carrots and 7 hershey's kisses and the total calories were 263. fred ate 4 carrots and 8 hershey's kisses and the total calories were 230. how many calories are in a carrot and a hershey's kiss? (the answer is not a scientific truth, only made up numbers!!!)
Answers
let c the calories in carrot
let h the calories in hershey's kisses
4c + 8h = 230 eq 1
10 c + 7 h = 263 eq 2
to solve the solution we multiply eq 1 by 10
we multiply eq 2 by 4
40 c + 80 h = 2300
40c + 28 h = 1052
we subtract the two equations we get
52 h = 1248
h= 24
and so in replacing h = 24 in the equation we get c = 9.5
Find the roc of the volume of a cube with respect to the length of its side s when s = 25.
Answers
V=25³=15625
Volume of a cube with the length of the side equal to 25 is 15625
The radius of a cylindrical construction pipe is 2ft . if the pipe is 23ft long, what is its volume? use the value 3.14 for π , and round your answer to the nearest whole number. be sure to include the correct unit in your answer.
Answers
Which scientist arrived at a fairly accurate calculation of the value of pi?
Answers
The sum of the circumference of a circle and the perimeter of a square is 16. find the dimensions of the circle and square that produce a minimum total area. (let x be the length of a side of the square and r be the radius of the circle.)
Answers
Let x = the length of a side of the square.
The sum of the circumference of the circle and the perimeter of the square is 16.
Therefore
2πr + 4x = 16
That is
[tex]r = \frac{2}{ \pi } (4-x)[/tex] (1)
The combined area of the circle and the square is
[tex]A = \pi r^{2} + x^{2}[/tex] (2)
From (1), obtain
[tex]A = \pi . \frac{4}{ \pi ^{2}}(4-x)^{2} + x^{2} = \frac{4}{ \pi } (4-x)^{2}+x^{2} [/tex]
In order for A to be minimum, A' = 0.
That is,
[tex]- \frac{8}{ \pi } (4-x)+2x=0 \\x(2+ \frac{8}{ \pi } ) = \frac{32}{ \pi } \\ x =2.2404[/tex]
The second derivative should be positive in order for A to be minimum.
A'' = 8/π + 2 > 0 , so the condition is satisfied.
The graph shown below confirms this.
From (1), obtain
r = (2/π)*(4 - 2.2404) = 1.1202
Answer:
r = 1.12 and x = 2.24
When rewriting y = 2x + 1 in function notation, what do you replace with f(x)?
Answers
So it becomes f(x)=2x+1
f(x) = 2x +1
Solve for x. 9≤17−4x Enter your answer, as an inequality, in the box.
Answers
9 - 17 ≤ 17 - 17 - 4x
-8/-4 ≤ - 4x/-4
x≤ 2
hope this helps
The first thing you need to do is get rid of the 17 to leave -4x isolated..
so subtract -17 from 9 = -8 ≤-4x divide -4 from both sides = x≤2
What is 187.023 in word form
Answers
some integers are whole numbers? true or false
Answers
The composition do,0.75(x,y) ∘ do,2(x,y) is applied to △lmn to create △l''m''n''. which statements must be true regarding the two triangles? check all that apply. ∠m ≅ ∠m'' △lmn ~ △l''m''n'' △lmn ≅ △l''m''n'' the coordinates of vertex l'' are (-3, 1.5). the coordinates of vertex n'' are (3, -1.5). the coordinates of vertex m'' are (1.5, -1.5).
Answers
Answer:
A. ∠M ≅ ∠M''
B. △LMN ~ △L''M''N''
E. The coordinates of vertex N'' are (3, -1.5).
Step-by-step explanation:
Transformation involves changing the position and size of a shape.
The true statements are:
[tex]\mathbf{\angle m \cong \angle m"}[/tex].[tex]\mathbf{\triangle lmn \sim \triangle l"m"n"}[/tex].The coordinates of n" are [tex]\mathbf{N" = (3,-1.5)}[/tex].The coordinates of the triangle are:
[tex]\mathbf{L = (-1, 2)}[/tex]
[tex]\mathbf{ M = (-1, -1)}[/tex]
[tex]\mathbf{N = (2, -1)}[/tex]
The transformation rule is given as:
[tex]\mathbf{do, 0.75(x,y)\circ,2(x,y)}[/tex]
The transformation rule is a dilation by a factor of 0.75, and then a factor of 2.
Uniform dilation changes the size of a shape, but the angles remain unchanged. This means that:
[tex]\mathbf{\angle l \cong \angle l"}[/tex].[tex]\mathbf{\angle m \cong \angle m"}[/tex].[tex]\mathbf{\angle n \cong \angle n"}[/tex].[tex]\mathbf{\triangle lmn \sim \triangle l"m"n"}[/tex]The above highlights means that:
The angles of both triangles are congruentThe triangles are similarNext, we apply the rule on the coordinates of the triangle
[tex]\mathbf{L" = 0.75 \times 2 \times (-1,2)}[/tex]
[tex]\mathbf{L" = (-1.5,3)}[/tex]
[tex]\mathbf{M" = 0.75 \times 2 \times (-1,-1)}[/tex]
[tex]\mathbf{M" = (-1.5,-1.5)}[/tex]
[tex]\mathbf{N" = 0.75 \times 2 \times (2,-1)}[/tex]
[tex]\mathbf{N" = (3,-1.5)}[/tex]
Hence, the true statements are:
[tex]\mathbf{\angle m \cong \angle m"}[/tex].[tex]\mathbf{\triangle lmn \sim \triangle l"m"n"}[/tex].The coordinates of n" are [tex]\mathbf{N" = (3,-1.5)}[/tex].Read more about transformations at:
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Geometry! What describes line FI?
Answers
Both equations in a system of linear equations have y-intercepts at (0,2). is it possible for this system to have only one solution?
Answers
Both equations in a system of linear equations have y-intercepts at (0,2) but it is not possible for this system to have only one solution because it depends on another point as well.
Given :
Both equations in a system of linear equations have y-intercepts at (0,2).
The following steps can be used in order to determine the system have only one solution or not:
Step 1 - According to the given data, both equations in a system of linear equations have y-intercepts at (0,2).
Step 2 - The equation of a line is given by:
[tex]\dfrac{y-y_1}{x-x_1}=\dfrac{y_2-y_1}{x_2-x_1}[/tex]
Step 3 - From the above steps, it can be concluded that it does not say that the system to have only one solution because it depends on another point as well.
For more information, refer to the link given below:
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Should your calculator be in radians or degrees for physics
Answers
Identify the segment bisector of JK
Answers
Answer:
A segment whose length is 9 units.
Step-by-step explanation:
A segment whose length is 9 units.
All we have is a bisection that divides equally segment JK in two parts. And M is the Midpoint what reassures us that JM=MK, so plugging in:
3x+15=8x+25
3x-8x=25-15
-5x=10
5x=-10
x=-2
JM=3(-2)+15 =9
MK=8(-2)+25=9
Answer:
Step-by-step explanation: