I need help finding the perimeter and area. Can you help me?Even for the 2 I did can you double check them and see if I'm right and if I'm wrong then can you fix them and give me the answers. Thank you for your help!
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SOLUTION:
Step 1:
In this question, we are given the following:
Step 2:
The perimeter of the figure is:
[tex]\begin{gathered} 24+\text{ 18 + 17 + 9 +7+9} \\ =\text{ 84 units} \end{gathered}[/tex]The area of the figure is calculated as thus:
[tex]\begin{gathered} (\text{ 18x 17) + ( 9 x 7)} \\ =\text{ }306+63 \\ =\text{ }369units^2 \end{gathered}[/tex]
Related Questions
<45Can a matrix with dimensions of 3 X 6 be added to another matrix with dimensions of 6 X 3?O yesO no
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No
1) Since when adding matrices they both must share the same number of rows and columns. Then we can not add matrices with different dimensions.
2) Hence, the answer is No
I have an online class and I need a little help please. I just need the domain and range.
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What is the product of (2x - 5)(2x + 5)?A. 4x²-25B. 4x2+20x-25C. 4x2² - 10D. 4x² + 20x-10
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Explanation
The product of (2x - 5)(2x + 5) can be seen below.
[tex]\begin{gathered} \left(2x-5\right)\left(2x+5\right) \\ =2x\left(2x+5\right)-5\left(2x+5\right) \\ =4x^2+10x-10x-25 \\ =4x^2-25 \end{gathered}[/tex]Use a calculator to evaluate each to the nearest thousandths. In 62
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A) 4.127
Explanation:
With your calculator search for the ln function and it will give you the direct answer
could someone help me with number 4? as long as A, B, C
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Part A.
To determine the volume of the barrel we use the formula for the volume of a cylinder:
[tex]V=r^2\pi h,[/tex]where r is the radius of the base of the cylinder and h is its height.
For the barrel:
[tex]\begin{gathered} h=27\text{ in, } \\ r=\frac{25\text{ in}}{2}=12.5in. \end{gathered}[/tex]Substituting the above values in the formula, we get:
[tex]V=13246.875in^3.[/tex]Answer part A:
[tex]V=13,246.875\imaginaryI n^3[/tex]Part B.
Recall that:
[tex]1\text{ gallon=231in}^3.[/tex]Answer part B: There are 231 cubic inches in 1 gallon.
Part C.
Diagram:
The barrel can contain 57 gallons of water, if it is at 2/3 of its capacity then there are
[tex]57gallons*\frac{2}{3}=38\text{ gallons}[/tex]of water inside the barrel.
Answer part C:
[tex]38\text{ gallons.}[/tex]the population of sweden is about 1 11/16 times as great as the populaiton of denmark. find the population of sweden if the populatio of denmark is about 5,190,000
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If the population of Sweden is about 1 11/16 times as great as the population of Denmark, and the population of Denmark is about 5,190,000, we get that the population of Sweden is about:
[tex](1\frac{11}{16})5,190,000=(\frac{27}{16})5,190,000=8,758,125[/tex]Answer: 8,758,125.
Determine which measure(s) of center would best reflect the data and explain how you know
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If we rearrage the data in ascending order,we get:
[tex]\begin{gathered} 9,10,10,10,10,10,10,10,11,11,11,11,11,11,12,12,12,12,12,13,13, \\ 13,13,14,14,14,14,15,15,15,15,15,15,15,16,17,17,17,17,17 \end{gathered}[/tex]notice that the median in this case is m = 13, while for the mean, we have:
[tex]\begin{gathered} \mu=\frac{9+7(10++6(11)+5(12)+4(13)+7(15)+16+5(17)}{40} \\ =\frac{9+70+66+60+52+56+105+16+85}{40}=\frac{519}{40}=12.98 \\ \mu=12.98 \end{gathered}[/tex]as we can see, the mean is nearly the same value as the median. This is evident since there are no outliers on the data. Thus, the median or the mean can be used to describe the dataset
Moore's Law predicts that the number of transistors that can be fit on a microchip willincrease by 41% every year. If microchips from a given year could hold about 949,000transistors, how many transistors could fit on a microchip 7 years later?If necessary, round your answer to the nearest whole number.transistors
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The equation of a exponential growth function is equal to:
[tex]y=a(1+r)^x[/tex]Where:
y = the number of transistors
x = the number of years = 7 years
a = the initial value = 949,000
r = the rate of change = 41% = 0.41
Substitute the values:
[tex]y=949000(1+0.41)^7=949000(1.41)^7=10514775.41[/tex]Round to the nearest whole number: 10,514,775
Answer: 10,514,775 transistors
find at least 3 possible measures for the height and the radius of a cylinder with a lateral area of 144pi square centimeters. which of your dimensions will give you the largest volume?
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The height and radius of cylinder with curved surface area is given by:
[tex]\begin{gathered} 2\pi rh=144\pi \\ rh=72 \end{gathered}[/tex]So the possible combinations can be:
[tex]\begin{gathered} r=9,h=8 \\ r=12,h=6 \\ r=24,h=3 \end{gathered}[/tex]The volumes for each dimension is:
[tex]\begin{gathered} V_1=\pi\times9^2\times8=648\pi \\ V_2=\pi\times12^2\times6=864\pi \\ V_3=\pi\times24^2\times3=1728\pi \end{gathered}[/tex]Hence the maximum volume is when r=24 and h=3.
Therefore it can be concluded if the product of radius and height is known, then the height should be as small as possible to maximize the volume of cylinder.
Write an addition equation or subtraction equation your choice to describe the diagram. I will attach a screenshot of the problem I am confused with.
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First, identify the length of each arrow and the corresponding sign:
Notice that the combination of both arrows represents the number -13.
Then, an equation that can be used to represent the same information as in the diagram, is:
[tex]-4-9=-13[/tex]So I got the first one answer thingy for the question right now I just need the other part
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The original price was $105.04 and the discount is 10%.
Calculate the discount:
10 * 105.04 / 100 = 10.50
The discount is $10.50
The final (sale) price is:
$105.04 - $10.50 = $94.54
1Find the 9th term of the geometric sequence whose common ratio is 1/2and whose first term is 6.
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General category: Sequences, Series, and Mathematical Induction
Sub-category: Formulas and Notation for Sequences and Series
Topic: Recursive Formulas and explicit Formulas.
Introduction:
Given a geometric sequence with the first term a_1 and the common ratio r, the nth term is given by the following formula:
[tex]a_n=a_1\cdot r^{n\text{ -1}}[/tex]Explanation:If we have a geometric sequence whose common ratio is 1/2 and whose first term is 6, then the nth term is given by the following formula:
[tex]a_n=6\cdot(\frac{1}{2})^{n\text{ -1}}[/tex]thus, if n= 9, we get:
[tex]a_9=6\cdot(\frac{1}{2})^{9\text{ -1}}[/tex]that is:
[tex]a_9=6\cdot(\frac{1}{2})^8[/tex]this is equivalent to:
[tex]a_9=\frac{6}{2^8}=\frac{6}{256}=\frac{3}{128}[/tex]we can conclude that the correct answer is:
Answer:The 9th term is:
[tex]\frac{3}{128}[/tex]TED BORROWED $1,200 FOR TWO YEARS AND HE MADE MONTHLY PAYMENTS. IF THE TOTAL FINANCE CHARGE IS $175.92 WHAT IS THE APR? ANNUAL PERCENT RATE?
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Given:
The borrowed amount is $1200.
The finance charge is $175.92
The period of time =2 years ( 24 months)
Required:
We need to find APR.
Explanation:
Let r be the APR.
The monthly interest rate is r/12.
[tex]Total\text{ amount =1200+175.92=1375.92}[/tex]P=1200 and t =24.
[tex]Total\text{ amount =P\lparen1+}\frac{r}{n}\text{\rparen}^{nt}[/tex][tex]1375.92=1200(1+\frac{r}{12})^{12\times2}[/tex][tex]1375.92=1200(1+\frac{r}{12})^{24}[/tex][tex]\frac{1375.92}{1200}=\frac{1200}{1200}(1+\frac{r}{12})^{24}[/tex][tex]1.1466=(1+\frac{r}{12})^{24}[/tex][tex]1.00571631955=1+\frac{r}{12}[/tex][tex]1.00571631955-1=\frac{r}{12}[/tex][tex]0.00571631955\times12=r[/tex][tex]0.06859583463=r[/tex]Multiply by 100, to find APR
[tex]6.86\text{ \%}=APR[/tex]Final answer:
[tex]APR=6.82\text{ \%}[/tex]
Find the area of the composite figure. First, find the area of the parallelogram. 12 cm Parallelogram Area = [?] cm2 :6 cm [ Triangle Area = [ ] cm2 L: 4 cm Total Area of Composite Figure = [] cm2 Enter
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ANSWER
• Parallelogram Area = 72 cm²
,• Triangle Area = 24 cm²
,• Area of composite figure = 96 cm²
EXPLANATION
The area of a parallelogram is the product between the length of the base and the height of the parallelogram,
[tex]A_{parallelogram}=b\cdot h[/tex]In this case, b = 12cm and h = 6cm,
[tex]A_{parallelogram}=12cm\cdot6cm=72cm^2[/tex]The area of a triangle of base b and height h is,
[tex]A_{triangle}=\frac{b\cdot h}{2}[/tex]In this case, b = 12cm and h = 4cm,
[tex]A_{triangle}=\frac{12\operatorname{cm}\cdot4\operatorname{cm}}{2}=\frac{48cm^2}{2}=24cm^2[/tex]The area of the composite figure is the sum of the areas of the two figures,
[tex]A_{figure}=A_{parallelogram}+A_{triangle}=72cm^2+24cm^2=96cm^2[/tex]The total area of the composite figure is 96 cm²
Find the distance between the two points.(-3, -1) (-1,-5) We have to use a^2 + b^2 = c^2
Answers
The formula between the distance (c) is,
[tex]c=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]Where,
[tex]\begin{gathered} a=(x_2-x_1) \\ b=(y_2-y_1) \end{gathered}[/tex]Given
[tex]\begin{gathered} (x_1,y_1)=(-3,-1) \\ (x_2,y_2)=(-1,-5) \end{gathered}[/tex]Therefore,
[tex]c=\sqrt{(-1--3)^2+(-5--1)^2}[/tex]Simplify
[tex]\begin{gathered} c=\sqrt{(-1+3)^2+(-5+1)^2}=\sqrt{2^2+(-4)^2}=\sqrt{4+16}=\sqrt{20}=\sqrt{4\times5} \\ c=\sqrt{4}\times\sqrt{5}=2\times\sqrt{5}=2\sqrt{5}=\:4.47213\approx4.5 \end{gathered}[/tex]Hence, the answer is
[tex]c=4.5[/tex]Choose the rule that represents the series of transio1.A8()-(-1.5=5) (-y)-(1-12:5)D. (y) - (-+6-)8 (L.)-(:6-7)
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We have:
A ( -3, 6 ) ; A' ( 3, -6 )
and
A (x,y) --> A' ( x + a, y + b )
So, A ( -3, 6 ) --> A' ( -3 + a, 6 + b ) or A ( -3, 6 ) --> A' ( 3, -6 )
Therefore:
[tex]\begin{gathered} -3+a=3 \\ -3+a+3=3+3 \\ a=6 \end{gathered}[/tex]and
[tex]\begin{gathered} 6+b=-6 \\ 6+b-6=-6-6 \\ b=-12 \end{gathered}[/tex]Answer: The rule is:
[tex](x,y)\rightarrow(x+6,y-12)[/tex]Which statement is an example of the identify property of multiplication?8x0=08x1=88•-1=-8-8•-1=-8What is another way to write-3•(4+7)?-3•4+7-3•4•7-3•4+4•7-3•4+(-3)•7Which property is represented by 5+(-8)=-8+5?IdentityAssociativeCommutativeDistributive
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Identity property of multiplication indicates that when the "1" is is multiplied with any other number, the answer will be the number.
From the question, the statement that is an example of identity property of multiplication is:
8 x 1=8
sin (B)= 0.9761 cos(c)= 0.7850
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1. sin (B)= 0.9761
B = sin^-1 ( 0.9761 ) = 77.45 degrees
2. cos(C)= 0.7850
C = cos ^-1 ( 0.7850 ) = 38.28 degrees
which checkpoint is furthests from sea level? explain (ill send the picture)
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The sea level is considered to have an elevation of zero feet.
To determine which checkpoint is furthest away from the sea level you have to calculate their absolute difference to zero and compare them:
Checkpoint A
[tex]\begin{gathered} d_A=|15.6-0| \\ d_A=15.6ft \end{gathered}[/tex]Checkpoint B
[tex]\begin{gathered} d_B=|17.1-0| \\ d_B=17.1ft \end{gathered}[/tex]Checkpoint C
[tex]\begin{gathered} d_C=|5.2-0| \\ d_C=5.2ft \end{gathered}[/tex]Checkpoint D
[tex]\begin{gathered} d_D=|-6.5-0| \\ d_D=6.5ft \end{gathered}[/tex]Checkpoint E
[tex]\begin{gathered} d_E=|-18.5-0| \\ d_E=18.5ft \end{gathered}[/tex]Ordered from closest to furthest the distance of each checkpoint from sea level is:
[tex]0The furthest checkpoint to sea level is Checkpoint E, which is 18.5ft awayWhich quadratic expression does NOT represents the model. ++++ + + + + + o x² + 58+4 (x + 4)(x + 1) 0 x² + 44+5
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By the given diagram:
Since,
[tex]x^2+5x+4=(x+4)(x+1)[/tex]Then, the quadratic expression that does NOT represent the model is:
[tex]x^2+4x+5[/tex]how do i od this linear equation in slope form
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y = -x + 4
The correct option is B
Explanation:Given the point (1, 3) and (3, 1)
The equation of a line is given as:
y = mx + b
Where m is the slope and b is the y-intercept.
To obtain the slope, we use the formula:
[tex]\begin{gathered} m=\frac{y_2-y_1}{x_2-x_1} \\ \\ =\frac{1-3}{3-1}=\frac{-2}{2}=-1 \end{gathered}[/tex]The equation now becomes:
y = -x + b
We can use the point (1, 3) to obtain the y-intercept. Using x = 1, and y = 3
3 = -1 + b
b = 3 + 1 = 4
Finally, we can write the equation as:
y = -x + 4
Find the real solutions of the equation by graphing. x^3-4x^2-20x=-48The real solutions of the equation are _____.
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Given the following equation:
[tex]x^3-4x^2-20x=-48[/tex]We will find the real solutions to the equation by graphing.
We will rewrite the given equation as follows:
[tex]x^3-4x^2-20x+48=0[/tex]The graph of the function will be as shown in the following figure:
As shown the function has 3 real solutions which are the x-intercepts
So, the answer will be:
[tex]x=-4,2,6[/tex]Use Cramer's Rule to find the solution of the system of linear equations, if a unique solution exists.–5x + 2y – 2z = 263x + 5y + z = –22–3x – 5y – 2z = 21(–1, –7, 2)(–6, –1, 1)(–1, 3, 1)no unique solution
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A system of three equations with three unknowns can be written in matrix form as shown below:
[tex]\begin{gathered} a_1x+b_1y+c_1z=d_1 \\ a_2x+b_2y+c_2z=d_2 \\ a_3x+b_3y+c_3z=d_3 \\ \Leftrightarrow \\ \begin{bmatrix}{a_1} & {b_1} & {c_1} \\ {a_2} & {b_2} & {c_2} \\ {a_3} & {b_3} & {c_3}\end{bmatrix}\begin{bmatrix}{x} & {} & \\ {y} & {} & \\ {z} & {} & {}\end{bmatrix}=\begin{bmatrix}{d_1} & & {} \\ {d_2} & {} & {} \\ {d_3} & {} & {}\end{bmatrix} \end{gathered}[/tex]Then, x, y, and z are given by the expressions:
[tex]x=\frac{\det(\begin{bmatrix}{d_1} & {b_1} & {c_1} \\ {d_2} & {b_2} & {c_2} \\ {d_3} & {b_3} & {c_3}\end{bmatrix})}{\det(\begin{bmatrix}{a_1} & {b_1} & {c_1} \\ {a_2} & {b_2} & {c_2} \\ {a_3} & {b_3} & {c_3}\end{bmatrix})},y=\frac{\det(\begin{bmatrix}{a_1} & {d_1} & {c_1} \\ {a_2} & {d_2} & {c_2} \\ {a_3} & {d_3} & {c_3}\end{bmatrix})}{\det(\begin{bmatrix}{a_1} & {b_1} & {c_1} \\ {a_2} & {b_2} & {c_2} \\ {a_3} & {b_3} & {c_3}\end{bmatrix})},z=\frac{\det(\begin{bmatrix}{a_1} & {b_1} & {d_1} \\ {a_2} & {b_2} & {d_2} \\ {a_3} & {b_3} & {d_3}\end{bmatrix})}{\det(\begin{bmatrix}{a_1} & {b_1} & {c_1} \\ {a_2} & {b_2} & {c_2} \\ {a_3} & {b_3} & {c_3}\end{bmatrix})}[/tex]Then, in our problem:
[tex]\begin{bmatrix}{-5_{}} & {2_{}} & {-2_{}} \\ {3_{}} & {5_{}} & {1_{}} \\ {-3_{}} & {-5_{}} & {-2_{}}\end{bmatrix}\begin{bmatrix}{x} & {} & \\ {y} & {} & \\ {z} & {} & {}\end{bmatrix}=\begin{bmatrix}{26_{}} & & {} \\ {-22_{}} & {} & {} \\ {21_{}} & {} & {}\end{bmatrix}[/tex]Therefore, x is equal to
[tex]\begin{gathered} \Rightarrow x=\frac{\det(\begin{bmatrix}{26_{}} & {2_{}} & {-2_{}} \\ {-22_{}} & {5_{}} & {1_{}} \\ {21_{}} & {-5_{}} & {-2_{}}\end{bmatrix})}{\det(\begin{bmatrix}{-5_{}} & {2_{}} & {-2_{}} \\ {3_{}} & {5_{}} & {1_{}} \\ {-3_{}} & {-5_{}} & {-2_{}}\end{bmatrix})},=\frac{-186}{31}=-6 \\ \Rightarrow x=-6 \end{gathered}[/tex]Therefore, x= -6
As for y,
[tex]\begin{gathered} y=\frac{\det(\begin{bmatrix}{-5_{}} & {26_{}} & {-2_{}} \\ {3_{}} & {-22_{}} & {1_{}} \\ {-3_{}} & {21_{}} & {-2_{}}\end{bmatrix})}{\det(\begin{bmatrix}{-5_{}} & {2_{}} & {-2_{}} \\ {3_{}} & {5_{}} & {1_{}} \\ {-3_{}} & {-5_{}} & {-2_{}}\end{bmatrix})}=\frac{-31}{31}=-1 \\ \Rightarrow y=-1 \end{gathered}[/tex]Thus, y= -1.
Finally solving for z:
[tex]\begin{gathered} z=\frac{\det (\begin{bmatrix}{-5_{}} & {2_{}} & {26_{}} \\ {3_{}} & {5_{}} & {-22_{}} \\ {-3_{}} & {-5_{}} & {21_{}}\end{bmatrix})}{\det (\begin{bmatrix}{-5_{}} & {2_{}} & {-2_{}} \\ {3_{}} & {5_{}} & {1_{}} \\ {-3_{}} & {-5_{}} & {-2_{}}\end{bmatrix})}=\frac{31}{31}=1 \\ \Rightarrow z=1 \end{gathered}[/tex]Hence, z=1
The answer is (-6, -1, 1)
Chose the line with the grater slope. L1L2 Cannot be determined
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step 1
Find the slope of the blue line
we need two points
so
looking at the graph
we take
(1,0) and (2,1)
m=(1-0)/(2-1)
m=1/1
m=1
step 2
Find the slope of the red line
we take the points
(0,1) and (1,0)
m=(0-1)/(1-0)
m=-1
step 3
Compare the values
1 is greater than -1
therefore
the blue line has a greater slopeDo you have the options for this question?
I just need the answer and the work to show
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SOLUTION:
Sum of the interior angles in a triangle is 180 degrees
So, A + B + C = 180
39 + 31 + C = 180
70 + C = 180
C = 180 - 70
C = 110
The size of angle C is 110 degrees.
Imagine you are in an argument with your sibling or friends about the size of the slice of pizza that you were both served. They say that it was unfair because you got a bigger piece. What information would you need to know about each slice of pizza in order to calculate which one had a larger area? Explain (Hint: remember the formula for the area of a sector of a circle!!)
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Ok, so
Remember that the formula of the area of a sector of a circle is given by:
[tex]A=\frac{1}{2}r^2\theta[/tex]Where r is the radius of the circle and Θ is the angle (in radians) of the sector.
Therefore, we would need to know the radius of the pizza, and the angle of each slice of pizza in order to calculate which one had a larger area.
A hot air balloon is rising. The expression 120 + 2t represents theheight of the hot air balloon in meters after t seconds. Use theexpression to find the height of the balloon after 15 s.Show your work. .
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We are told that the height of the ballon after t seconds is given by the equation
[tex]\text{height}=120+2t[/tex]and we are asked to find the height after 15 seconds.
To answer this question we simply put in t =15 in the above formula to get
[tex]\text{height}=120+2(15)[/tex]This gives
[tex]\text{height}=120+30[/tex][tex]\text{height}=150m[/tex]Hence, the height of the ballon after 15 s is 150m
.
What is the slope of the line below? * A. y = 3x - 10B. y = 2x + 2C. y = -x + 2D. None of the above
Answers
Apply the slope formula.
[tex]m=\frac{y2-y1}{x2-x1}[/tex]Where:
(x1,y1) = (3,-1)
(x2,y2)= (5,5)
Replacing:
[tex]m=\frac{5-(-1)}{5-3}[/tex][tex]m=\frac{5+1}{5-3}=\frac{6}{2}=3[/tex]The only option that has a slope =3
A. y=3x-10
Answer:
See below
Step-by-step explanation:
SLope is also = rise / run
from the two red points rise = 6 run = 2
6/2 = 3 = m = slope
1 What is the area of a square with side length of 4 4 1/4m m? 8 1/2m² O 17m²? O 18 1/16 m²? o 20 1/4 m²
Answers
1) Since the area of a square is given by:
[tex]S=a^2[/tex]2) Let's plug into that the measure of their sides, 4 1/4m let's turn this Mixed Number into an improper fraction to make our calculations easier:
[tex]4\frac{1}{4}=\frac{4\times4+1}{4}=\frac{17}{4}[/tex]Notice that we keep the denominator, and multiply it by the whole number and then add to that numerator to get this improper fraction. Now let's plug it into that formula
[tex]\begin{gathered} S=(\frac{17}{4})^2 \\ S=\frac{289}{16}^{} \end{gathered}[/tex]Now let's turn it back to a Mixed Number, dividing 289 by 16. Since the answers are all Mixed Numbers.
3) Hence, the answer is 18 1/16 m²
Find the slope of a line parallel to the given line: 5x + y = 3
Answers
Answer
Slope of a line parallel to the given line = -5
Explanation
Two parallel lines have the same slopes.
So, if we obtain the slope of one line, we will obtain the slope of the other line.
The slope and y-intercept form of the equation of a straight line is given as
y = mx + b
where
y = y-coordinate of a point on the line.
m = slope of the line.
x = x-coordinate of the point on the line whose y-coordinate is y.
b = y-intercept of the line.
So, we need to put the given equation of the line in the y = mx + b form to obtain m.
5x + y = 3
y = -5x + 3
Comaparing this with y = mx + b
m = slope = -5
Hope this Helps!!!