The equation of this parabola in vertex form is y = ( -1/2) x² - 0.5
What are Functions?In mathematics, a function is an expression, rule, or law that describes the relationship between one variable (the independent variable) and another variable (the dependent variable) (the dependent variable). In mathematics and the physical sciences, functions are indispensable for formulating physical relationships.
We are given that Focus (0,-1), Directrix is the line y=0
so, we have a vertical parabola open downward
Remember that the distance from the vertex to the directrix must be the same that the distance from the vertex to the focus
This means that the vertex is the point (0,-0.5)
The midpoint between the focus and the directrix
Find out the value of p (focal distance)
p=0.5
The equation of the parabola is given by
y =( -1/2) x² - 0.5
The vertex is (0,-0.5)
The value of p=0.5
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given a and b, determine the least-squares error in the least-squares solution of ax equals b.
The least-squares error in the least-squares solution of ax = b is given by the equation:
[tex]||b - ax||^2 = (b - ax)^T(b - ax) = b^Tb - 2a^Tbx + a^Tax[/tex]
The least-squares solution is the value of x that minimizes this error. This occurs when the derivative of the error with respect to x is equal to zero, and the second derivative is positive.
To find the least-squares solution, we take the derivative with respect to x and set it to zero:
[tex]-2a^T(b - ax) = 0\\a^Tb = a^Tax[/tex]
This gives us the normal equation, which is the equation that x must satisfy in order to minimize the error. The solution of this equation is:
[tex]x = (a^Ta)^-1a^Tb[/tex]
This is the least-squares solution of the equation ax = b, and it is the value of x that minimizes the least-squares error. The least-squares error is given by the equation:
[tex]||b - ax||^2 = b^Tb - 2a^Tbx + a^Tax = b^Tb - a^T(a(a^Ta)^-1a^Tb) = b^Tb - a^T(a^Tb)[/tex]
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A school is planning a car wash to raise $540.
• There will be 6 teams.
• Each team will wash 3 cars per hour.
• The car wash will last 6-½ hours.
• Each team will take two 15-minute breaks. How much should the school charge per car to raise exactly $540?
The car wash made $600 since "there will be 8 teams" meaning 8 * $75.
Find the solution?The length of the car wash will be five and a half hours, with two 15-minute breaks for each team.
Thus, each team works for five hours.
Two automobiles will be washed per hour by each team.
Ten vehicles per squad, then.
[5*2]
Given that "there will be 8 teams," 80 vehicles will be washed (assumed to be in a continuous line of vehicles) [10*8].
The charge must be $600/80=$7.50 each car in order to make $600.
Check (extremely important): "each crew will wash two cars per hour," meaning that each team will earn $15 per hour; "the car wash will run five and a half hours," and "each team will take two 15-minute breaks." As a result, five times $15 equals $75 earned each team.
The car wash made $600 since "there will be 8 teams" meaning 8 * $75.
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Algebra question pls help
All of them thxxxx
Pat does a lot of traveling in her car, she keeps records on how often she fills her car with petrol. The table alongside shows the frequencies of the number of days between refills. Estimate the likelihood that:
A) there is a four day gap between refills.
B) there is at least a four day gap between refills.
At least 4 days means 4 or more; in this example, 4, 5, or 6
a 17/190 ≈ 0.089
b 24/190 ≈ 0.126
How often she fills her car with petrol?Step 1:
At least 4 days means 4 or more; in this example, 4, 5, or 6. So
Estimated Probability (Car Refill Gaps)
in general ,estimated probability observe =The frequency of a particular
outcome/The no: of times an
experiment is
repeated
This particular task observes=The no: of time a 4 day refill gap occurs/
The total frequency of refill gap
days
Case a total of 190 refill gap days occurred. Of those 17 were 4 days gap
Estimated probability in these case 17/190 or 0.089
This particular task observe= The no : of times 4 day or more refill gap
occurs/The total frequency of refill gap
day
Case a total of 190 refill gap day occurred of these 24 were 4+ day gap
Estimated probability in these case 24/190 or 0.126
Step 2:
a 17/190 ≈ 0.089
b 24/190 ≈ 0.126
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What is the formula for area and perimeter of a hexagonal?
For a regular Hexagon , the formula for Area of hexagon is [tex]\frac{3\sqrt{3} s^{2} }{2}[/tex] and Perimeter of Hexagon is [tex]6s[/tex] .
What is a Regular Hexagon ?
A regular hexagon is defined as a closed shape polygon that has six equal sides and six equal angles.
The area of the regular hexagon is the space that is enclosed by all of the six sides .
let the side length of the regular polygon be = "s" ;
So , the Area will be denoted by = [tex]\frac{3\sqrt{3} s^{2} }{2}[/tex] ;
and the perimeter of regular hexagon is represented as = the sum of all six sides , that is "6s" .
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A complex number is a number that can be written in the form a bi, where a and b are real numbers. in the complex number 4 2i, 4 is the part. in the complex number 4 2i, 2 is the part.
In the complex number 4 + 2i, 4 is the real part. In the complex number 4 + 2i, 2 is the imaginary part.
Complex numbers are those that are represented as a+ib, where a and b are actual numbers and i is an imaginary number termed a "iota."
Imaginary numbers are those that don't exist in reality. An imaginary number produces a negative value when squared. It is shown as Im (). Example: The numbers 2, 7, and 11 are all fictitious.
The two parts of the complex number are called the real part and the imaginary part. The imaginary part is identified by its multiplier of i.
In the given number, the 2 is multiplied by i, so 2 is the imaginary part. The other part, 4, is the real part.
Therefore, In the complex number 4 + 2i, 4 is the real part. In the complex number 4 + 2i, 2 is the imaginary part.
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In the complex number 4+2i, the real part is 4 and the imaginary part is 2. In the complex number 4+2i, 4 is the real part and 2 is the imaginary part.
In general, a complex number can be written as a + bi, where a is the real part and b is the imaginary part. For example, in the complex number 3 + 4i, the real part is 3 and the imaginary part is 4.
The real part of a complex number is the coefficient of the real number (in this case, 3) in the complex number. The imaginary part of a complex number is the coefficient of the imaginary unit i in the complex number.
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find the exact length of the curve y=sqrt(x-x^2)+sin^-1(sqrt(x))
The exact length of the curve y=sqrt(x-x^2)+sin^-1(sqrt(x)) is 2.527.
The exact length of the curve y=sqrt(x-x^2)+sin^-1(sqrt(x)) can be calculated using the formula for arc length.
This formula states that the length of a parametric curve from t=a to t=b is equal to the integral of the square root of the sum of the squares of the respective derivatives of x and y, evaluated from a to b.
Using this formula, the length of the curve y=sqrt(x-x^2)+sin^-1(sqrt(x)) can be calculated by integrating the square root of (1-2x)^2 + (1/sqrt(x))^2 from 0 to 1. This yields a length of approximately 2.527.
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1. Suppose that the water level of a lake is 35 feet and that it is receding at a rate of 1.5 feet per day.
a. Write an equation for the water level, L, after D days.
b. In how many days will the water level be 20 feet?
2. Tina babysits after school and charges a flat fee of $3, plus $5 per hour.
a. Write an equation for the cost ,C, after H hours of babysitting.
b. What do the slope and the y-intercept represent in this problem situation?
c. How much money will Tina make if she babysits 5 hours?
3. An electrician charges $25 for a service call plus $50 per hour of service.
a. Write an equation in slope intercept for the cost ,C, after H hours of service
b. What will be the total cost for 8 hours of work?
c. If an electrician earned $225, how many hours did the repair last?
1a) An equation for the water level, L, after D days is L = 35 - 1.5D.
1b) Using the above equation, in 10 days, the water level will be 20 feet.
2a) An equation for the cost, C, after H hours of babysitting by Tina is C = 3 + 5H.
2b) The slope for this problem represents the variable charge per hour while the y-intercept represents the total charge for H hours of babysitting, C.
2c) Based on the above equation, if Tina babysits for 5 hours, she will make $28.
3a) An equation in slope-intercept for the cost, C, after H hours of service by the electrician is C = 25 + 50H.
3b) The electrician's total cost for 8 hours of work is $425.
3c) If an electrician earned $225, the repair lasted 4 hours.
What is an equation?An equation is a statement describing two mathematical expressions as equal or equivalent using the equation symbol (=).
1) Water level of a lake = 35 feet
Receding rate per day = 1.5 feet
Let L = water level and D = days
For the water level, L, to become 20 feet, it will take 10 days (D)
L = 35 - 1.5D
20 = 35 - 1.5D
1.5D = 15
D = 10
2) Fixed fee = $3
Variable fee per hour = $5
Let the charge of babysitting for H hours = C
Equation:C = 3 + 5H
For 5 hours of babysitting, Tina will make C = 3 + 5(5) = $28
3) Fixed charge for a service call = $25
Variable cost per hour of service = $50
An Equation in slope intercept:
C = 25 + 50H
For 8 hours of work, the total cost, C = 25 + 50(8) = $425
Total earnings = $225
The number of repair hours = 4 ($225 - $25/$50)
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What is the McCandless method?
The McCandless method has four steps divide the stage, assign lights, use color and fill the empty spaces.
Setting up the McCandless method for a thrust stage involves several steps.
To light a thrust stage using the McCandless method, divide the space into separately illuminated sections as the first step. The size of the stage will determine how you do it, but there should be enough areas for uniform lighting throughout.
Assign lights to each part of your stage once you've divided it into lighting segments. Three lights per section is the traditional norm, although you should use as many or as few as necessary to provide a consistent effect.
Use color: After placing your lights in each region, you may use gels to balance out their hues. To balance out the shadows on the performers' faces, the McCandless technique recommends a mix of warm and cold hues.
Fill in the blanks: At this stage, your lighting setup should be clear enough for you to understand how it affects your actors and see any potential issues. Use smaller lights, such as Fresnels, to tone down any unnaturally lit areas and blend the performers' looks.
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The process of McCandless method is explained below.
According to the theory of "Into the Wild", the process of McCandless method calls for a combination of warm and cool colors to balance out the shadows on the actors' faces.
And here we know that for a double McCandless system, then you can achieve this by making two of the lights warm and the other two cool.
Here you can also have all your lights be similar, neutral colors.
Apart from this, we have the following steps to do it:
We have to choose the right type of visualization.
And then we have to declutter your visualization.
And then we have to focus your audience's attention.
And the final steps is to think Like a Designer.
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How many single receptacles can be installed in a two-gang box that is made using two single-gang boxes that are ganged together
Two single receptacles can be installed in a two-gang box made up of two single-gang boxes ganged together.
A two gang-box is a square electrical box, also called a double-gang box, houses two devices. The two gang-box have a combination switch/outlet or a pair of switches/outlets inside that can control two lighting circuits.
A two-gang box made up of two single-gang boxes which are ganged together can install two single receptacles- receptacles refer to the openings in the gang box into which electronics can be plugged.
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Find the slope of the following graph and write your result in the empty box.
Answer:
slope = 2
Step-by-step explanation:
calculate the slope m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (2, 3) and (x₂, y₂ ) = (4, 7) ← 2 points on the line
m = [tex]\frac{7-3}{4-2}[/tex] = [tex]\frac{4}{2}[/tex] = 2
Gente me ajuda no projeto de matemática quanto é 3743÷250=???
let u = <5, 6>, v = <-2, -6>. find -2u + 5v.
The graph of a linear function passes through the two given points on the coordinate plane.
(5,12)
(8,21)
What is the rate of change of the function?
Answer:
2
Step-by-step explanation:
Point c is at (1, 2)
point d is at (2, 4)
rate of change formula
(f(d) - f(c))/2 - 1
f(2) = 4
f(1) = 2
4-2/1 = 2
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10. How Long Ago Was 2 Million Seconds In Terms Of Days?
By using the unit conversion method, 2 million seconds converted to days are equal to 23 days.
A unit conversion expresses the same aspect as another unit of measurement. For example, time can be expressed in minutes rather than hours, and distance can be represented from miles to kilometers, feet, or any other unit of measurement.
In this situation, you need to convert between seconds and days:
A day consists of 24 hours. Therefore, the fraction 24 hours/day is equal to 1. There is no value change when multiplying a number by 1. The same holds true for the conversion factors 1 hour/60 minutes and 1 minute/60 seconds.
If you multiply 2,000,000 seconds (2 million seconds) by these conversion factors, you will change the seconds to days:
2,000,000 sec. x (1 min/60 sec.) x (1 hour/60 min) x (1 day / 24 hours)
Therefore, all that is required is to divide 2,000,000 by the product of 60, 60, and 24.
(2,000,000) / (60*60*24) = 2,000,000 / 86,400 = 23.148 days ≈ 23 days
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Find the equation of the quadratic on which the points (0, 7) and (2, 11) lay.
Answer:
y = 2x + 7
Step-by-step explanation:
someone please help asap please
Answer:
[tex]21[/tex]
Step-by-step explanation:
[tex]\textrm{If y varies directly with x we can write this relationship as}[/tex]
[tex]y = k \cdot x[/tex]
[tex]\textrm{k is referred to as the constant of proportionality.}[/tex]
[tex]\textrm{Substituting these values into the above equation we get}[/tex]
[tex]3 = k \cdot 2[/tex]
[tex]So\; k = \dfrac{3}{2}[/tex]
[tex]\mathrm{When }[/tex] [tex]x = 14,[/tex]
[tex]y = \dfrac{3}{2} \cdot 14[/tex]
[tex]y = 21[/tex]
The line plots represent data collected on the travel times to school from two groups of 15 students. A horizontal line starting at 0, with tick marks every two units up to 28. The line is labeled Minutes Traveled. There is one dot above 10,16,20, and 28. There are two dots above 8 and 14. There are three dots above18. There are four dots above 12. The graph is titled Bus 14 Travel Times. A horizontal line starting at 0, with tick marks every two units up to 28. The line is labeled Minutes Traveled. There is one dot above 8, 9,18, 20, and 22. There are two dots above 6, 10, 12,14, and 16. The graph is titled Bus 18 Travel Times. Compare the data and use the correct measure of variability to determine which bus is the most consistent. Explain your answer. Bus 14, with an IQR of 6 Bus 18, with an IQR of 7 Bus 14, with a range of 6 Bus 18, with a range of 7
PLEASE HELP I NEED TO SUBMIT BY 11:15 am today
The correct option regarding which bus has the least spread among the travel times is given as follows:
Bus 14, with an IQR of 6.
How to obtain the measures of spread?First we consider the dot plot, which shows the number of times that each observation appears in the data-set.
Then we consider the interquartile range, which gives the difference between the third quartile and the first quartile of the data-set.
The interquartile range is a better measure of spread compared to the range of a data-set, as it does not consider outliers.
For groups of 15 students, we have that:
The first half is composed by the first seven students, hence the first quartile is the fourth dot, which is the median of the first half.The second half is composed by the last seven students, hence the first quartile is the eleventh dot, which is the median of the first half.The quartiles for Bus 14 are given as follows:
Q1 = 12.Q3 = 18.Hence the IQR is of:
IQR = Q3 - Q1 = 18 - 12 = 6.
The quartiles for Bus 18 are given as follows:
Q1 = 9.Q3 = 16.Hence the IQR is of:
IQR = Q3 - Q1 = 16 - 9 = 7.
Hence Bus 14 is the more consistent bus, due to the lower IQR.
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Answer: i dont know why my previous question was deleted for being unclear but lets forget it, The correct answer one be option 2 or B.
Step-by-step explanation:
i had got it right on the test
IfMNO~ QRS, find x. Round to the nearest tenth.
MN = 10
NO=x
QR=5
RS 7
Answer:
x = 14
Step-by-step explanation:
given Δ MNO and Δ QRS are similar then the ratios of corresponding sides are in proportion , that is
[tex]\frac{NO}{RS}[/tex] = [tex]\frac{MN}{QR}[/tex] ( substitute values )
[tex]\frac{x}{7}[/tex] = [tex]\frac{10}{5}[/tex] = 2 ( multiply both sides by 7 to clear the fraction )
x = 7 × 2 = 14
or Jeffrey and his friends are preparing for an epic snowball fight. They make 85 snowballs before Jeffrey's dad calls them in for lunch. After lunch, they make more snowballs. In all, Jeffrey and his friends make 153 snowballs. Which equation can you use to find the number of snowballs s Jeffrey and his friends make after lunch?
The equation that can be used to find the number of snowballs Jeffrey and his friends make after lunch is = 153 snowballs - 85 snowballs
How to find the number of snowballs ?The number of snowballs that Jeffrey and his friends made after lunch, can be found by the formula :
= Number of total snowballs made - Number of snowballs made before the boys went to lunch
Number of total snowballs made = 153 snowballs
Number of snowballs made before the boys went to lunch = 85 snowballs
The equation for the number of snowballs Jeffrey and his friends make after lunch is :
= 153 snowballs - 85 snowballs
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Rahul bought a sweater and saved rs20 when a discount of 25% was given. what was the price of the sweater before the discount ?
Answer: To find the price of the sweater before the discount, you need to determine how much the discount saved Rahul and divide that amount by the discount rate.
The discount saved Rahul 20 / 0.25 = 80 rupees.
So, the price of the sweater before the discount was 80 + 20 = 100 rupees.
Step-by-step explanation:
The gym has a ratio of 7 basketballs for every 6 soccer balls. There are 24 soccer balls. How many basketballs are in the gym?
Answer:
28
Step-by-step explanation:
step 1: put into fraction form (but it's a ratio)
[tex]\frac{6s}{7b} =\frac{24s}{Xb}[/tex] -> ( s = soccer ) (b = basketball)
step 2: find out the ratio between 6 soccer balls and 24 soccer balls
(the difference is 24 divided by 6, with is 4)
step 3: multiply the basketballs by that ratio
(7b * 4 = 28b)
Therefore, the answer is 28 basketballs.
sketch the solid whose volume is given by the iterated integral. 1 0 1− x 0 3 − 3z dy dz dx 0
The solid is a rectangular prism with a triangular cut-out.
The volume of the solid is given by the iterated integral 1 0 1− x 0 3 − 3z dy dz dx 0. The integral is taken over a three-dimensional rectangular region with x-coordinates between 0 and 1-x, y-coordinates between 0 and 3, and z-coordinates between 0 and 3-3z.
This describes a rectangular prism with length 1-x, width 3 and height 3-3z. However, the triangular cut-out is defined by the equation of the plane z = y/3. It's a triangular region in the zy-plane, with a height of 3 and a base of 3x. This triangular cut-out is "slicing" the rectangular prism from the corner (x,0,0) to the corner (x,3,3x/3) in the xyz-plane.
The final shape is a rectangular prism with a triangular cut out from the corner, with a base on the xy-plane and the vertex on the z-axis. The height, width and length of the rectangular prism are 3, 3 and 1-x respectively.
This type of iterated integral is useful to calculate the volume of a solid with complex boundaries, it's also easy to visualize the shape of the solid by looking at the limits of integration.
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using the pencle plot the point (4, -3)
Answer:
Step-by-step explanation: go to the x axis that goes left to right and go to the #4 and then go down 3
x + y= -3 graphing lines in standard form find the y intercept and slope
The slope intercept form of the line is y=mx+c where m is the slope of the line and c is the y-intercept is +3
What is meant by slope?
Slope is a numerical representation of how inclined a line is with respect to the horizontal.The slope of any line, ray, or line segment in analytical geometry is defined as the ratio of the vertical to the horizontal distance between any two points on the line, ray, or segment.A line's lope is determined by how steeply it slopes from LEFT to RIGHT.The slope of a line is determined by dividing its rise, or vertical change, by its run, or horizontal change.No matter which two places along the line you choose, the slope of a line is always constant.The slope-intercept form of an equation is used whenever the equation of a line is expressed in the form y = mx + b.Change the equation x−y=3 in slope intercept form:
x + y = 3
⇒y = x - 3
⇒y= + x−3
Hence, the slope of the line x + y= -3 is m= - 1 and the y+intercept is +3.
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Interpreting the meaning of the derivative in context Due to the tide, the water level rises and falls daily in Buzzard's Bay. D gives the depth of the water, in meters, t hours after midnight on a certain day. What is the best interpretation for the following statement? The value of the derivative of D at t = 8 is equal to -0.5. Choose 1 answer At 8 a.m. the water level decreased at a rate of 0.5 meters per hour. At 8 a.m. the water level decreased at a rate of 0.5 meters. At 8 a.m. the water level was 0.5 meters below sea level. D Until 8 a.m. the water level decreased at a rate of 0.5 meters per hour.
The value of the derivative of D at t = 8 is equal to -0.5 is At 8 a.m. the water level decreased at a rate of 0.5 meters per hour.
A function that has a derivative at each point in its domain is referred to as a differentiable function of one real variable in mathematics.
In other words, a graph of a differentiable function has a non-vertical tangent line at each interior point in its domain. A differentiable function has no break, angle, or cusp and is smooth (it is locally well approximated as a linear function at each interior point).
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the organizer of a potluck dinner sends 6 people a list of 10 different recipes and asks each person to bring one of the items on the list. if all 6 people randomly chose a recipe from the list, what is the probability that at least 2 will bring the same thing?
The probability of at least two people bringing the same item is 0.19.
The probability of two people bringing the same item can be calculated using the formula P(A∩B) = P(A) × P(B). In this case, P(A) and P(B) are both 1/10, since each person has the same chance of choosing any one of the 10 items on the list. Therefore, the probability of two people bringing the same item is 1/100. To calculate the probability of at least two people bringing the same item, we can use the formula P(A∪B) = P(A) + P(B) - P(A∩B). In this case, P(A∪B) = 1/10 + 1/10 - 1/100 = 0.19. Therefore, the probability of at least two people bringing the same item is 0.19.
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A set of sides that creates a right triangle has sides in a ratio of 5 : 12 :13. Find two different sets of sides in feet that would create a right triangle using this ratio.
Answer:
10 : 24 : 26
15 : 36 : 39
Step-by-step explanation:
You can multiply all numbers in the ratio to find equivalent ratios that would function as different sets of sides because it's just a larger version of the 5: 12 : 13 triangle
In the diagram below, right ∆ is the image of right ∆ after a dilation centered at the
origin, with (0,0), (3,0), (4.5,0),(0,6) and (0,4).
Determine and state the scale factor.
The scale factor of the dilation is 1.5.
What is scale factor?Scale factor is a numerical value used to describe the relationship between two different measurements. It is used to compare two measurements of the same type, such as length, area, or volume. The scale factors are used in many mathematical equations and can be used to enlarge or reduce an image or object. For example, a scale factor of two would cause a two-dimensional object to double in size while a scale factor of one-half would cause the object to halve in size.
This can be determined by dividing the length of the sides of the original triangle by the length of the sides of the image triangle. For example, the length of the side of the original triangle connecting (0,0) and (3,0) is 3, and the length of the side of the image triangle connecting (0,0) and (4.5,0) is 4.5. Dividing 4.5 by 3 gives 1.5, which is the scale factor.
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Hi, could someone please help me with this shape I have to find the perimeter and the area of that shape But I have no clue Where to start from, so could anybody help me figure this out this is very important to me, and please do not Try to give me the wrong answer because I really need the right answer!!
Answer: I think that you will have to times each side by 2 that whould equal 16.
Step-by-step explanation:
