the side length of the square is 1 unit, the perimeter of the tangram is \(4 + 2a + 2d + 2g + 2j = 4 + 2(\sqrt(2)) + 2(\sqrt(5)) + 2(\sqrt(10)) + 2(\sqrt(2)) =\) approximately \(22.88\) units.
What is the perimeter of the tangram?The tangram consists of seven flat shapes:
2 large right-angled triangles (hypotenuse a and legs b and c)
1 medium-sized right-angled triangle (hypotenuse d and legs e and f)
2 small right-angled triangles (hypotenuse g and legs h and i)
1 parallelogram (base j and height k)
1 square (side length l)
The formulas for the area of each shape are:
Area of a right-angled triangle = 1/2 x base x height \(= 1/2 \times b \times c\) (for the large triangles); 1/2 x e x f (for the medium triangle); 1/2 x h x i (for the small triangles).
Area of a parallelogram = base x height \(= j \times k.\)
Area of a square = side length^2 = l^2.
To find the area and perimeter of the tangram, you can add up the areas and perimeters of each shape.
An easier way to do this is to use a tangram template with measurements marked on it. Then you can simply add up the areas and perimeters of each shape using the given measurements.
Assuming that the side length of the square is 1 unit, the area of the tangram is \(1 + 1/2 + 1/2 + 1/2 + 1/2 + 1/2 + 1 = 5 units^2.\)
To find the perimeter of the tangram, you need to add up the lengths of all the sides.
Therefore, assuming that the side length of the square is 1 unit, the perimeter of the tangram is \(4 + 2a + 2d + 2g + 2j = 4 + 2(\sqrt(2)) + 2(\sqrt(5)) + 2(\sqrt(10)) + 2(\sqrt(2)) =\) approximately \(22.88\) units.
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Jennifer's dining room is 10 feet wide and 23 feet long. Jennifer wants to install wooden trim around the top of the room. The trim costs $0.85 per foot. How much will it cost Jennifer to buy enough trim?
Answer:
Step-by-step explanation:
Given room looks like a rectangular room.Let w be the wide and l be long of the rectangular room respectively.Given,w=10 feet and l=24 feet.
we know area of the rectangular room= l*w
So,area=10*23
area=230 sq.feet
Given,cost of trim=$0.85 per foot
So,total cost =230* 0.85
=195.5
So,Jennifer charges $195.5 to buy enough
What is the value of x?
Answer:
i think it might be C
Step-by-step explanation:
very sorry if it's wrong
Answer without referring back to the text. Fill in the blank. (Enter your answers as a comma-separated list. Enter all answers using the appropriate multiplicities. ) If y = 5 − x + x2 + 9ex is a solution of a homogeneous fourth-order linear differential equation with constant coefficients, then the roots of the auxiliary equation are ___
The roots of the auxiliary equation are 1.
To find the roots of the auxiliary equation for the given homogeneous fourth-order linear differential equation with constant coefficients, we need to substitute y = \(e^{rx}\) into the differential equation, where r is an unknown constant.
This substitution yields the characteristic equation.
Substituting y = \(e^{rx}\)into the differential equation gives us:
\(e^{rx}\) = 5 - x + \(x^2\) + 9\(e^x\)
Next, we divide both sides by e^x to simplify the equation:
e^(rx - x) = 5 - x + \(x^2\)
Simplifying further:
\(e^{rx - x}\) = \(x^2\) - x + 5
Taking the natural logarithm of both sides to remove the exponential:
rx - x = ln(\(x^2\) - x + 5)
Combining like terms:
(r - 1)x = ln(\(x^2\) - x + 5)
Now, for the equation to hold for all x, the coefficient of x on the left-hand side must be zero, giving us the auxiliary equation:
r - 1 = 0
Solving for r:
r = 1
Therefore, the roots of the auxiliary equation are 1 (with multiplicity 4) since it is a fourth-order differential equation.
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HELP!
ABD is a right angled triangle.
All measurements are given in centimetres.
C is the point on BD such that
CD = √3/3
AB=BD=√2/2
Work out the exact area, in cm², of the shaded region.
Answer:
Step-by-step explanation:
ABD is a right-angled triangle, then the area of the shaded part will be equal to (3 - √6)/12 cm².
What is the area?An object's area is how much space it takes up in two dimensions. It is the measurement of the number of unit squares that completely encompass the surface of a compact figure.
The squared unit, which is frequently expressed as inches, square feet, etc., is the accepted unit of area.
As per the given figure and data in the question,
From Δ ACD
Area of triangle will be, a = 1/2 × b × h
a = 1/2 × (√2/2) × (√3/3)
a = √6/12 cm²
From Δ ABD
The area of the triangle will be, a' = 1/2 × b × h
a' = 1/2 × (√2/2) × (√2/2)
a' = 1/4 cm²
The area of the shaded portion in the triangle, s = a' - a
s = 1/4 - √6/12
s = (3 - √6)/12 cm²
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What is the breakdown of this math problem? 8 2/5 - 6 7/10 =
let's first off, convert the mixed fractions to improper fractions.
\(\stackrel{mixed}{8\frac{2}{5}}\implies \cfrac{8\cdot 5+2}{5}\implies \stackrel{improper}{\cfrac{42}{5}}~\hfill \stackrel{mixed}{6\frac{7}{10}} \implies \cfrac{6\cdot 10+7}{10} \implies \stackrel{improper}{\cfrac{67}{10}} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{42}{5}-\cfrac{67}{10}\implies \cfrac{(2)42~~ - ~~(1)67}{\underset{\textit{using this LCD}}{10}}\implies \cfrac{84-67}{10}\implies \cfrac{17}{10}\implies 1\frac{7}{10}\)
Juana borrowed $10,686.00 from her parents to finance a vacabion. H interest was charged on the loan at 5.79% p.a., how much interest would she have to pay in 20 days?
Juana would have to pay approximately $29.40 in interest for the $10,686.00 loan over a 20-day period, assuming an annual interest rate of 5.79%.
The interest Juana would have to pay in 20 days can be calculated using the formula:
Interest = Principal × Interest Rate × Time
In this case, the principal amount is $10,686.00 and the interest rate is 5.79% per annum. To calculate the interest for 20 days, we need to convert the time to a fraction of a year. Since there are 365 days in a year, the time in years would be 20/365.
Using the formula and substituting the values:
Interest = $10,686.00 × 0.0579 × (20/365)
Calculating this expression, we find that the interest amount Juana would have to pay in 20 days is approximately $29.40.
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change fraction to decimal 4/9
Answer:0.44
Step-by-step explanation:
yw. :)
A leaf hangs from a branch 12 feet in the air. It falls to the ground at a rate of 0.25 feet per second. Which graph could represent the leaf’s height in feet as a function of time, in seconds, after leaving the branch?
Answer:
No graphs was presented but its the last one shown in the photo
The leaf's height as a function of time is determined as h(t) = 12 - 0.25t - 4.9t².
Equation for the motion of the leaf
The equation for the motion of the leaf is calculated as follows;
h = vt + ¹/₂gt²
where;
h is the height of fallv is the initial velocityt is the time of motionThe leaf's height as a function of time is given as;
h(t) = 12 - 0.25t - 4.9t²
Due to presence of gravity, the decline in the height of the leaf will be gradual.
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Factor 26r3s 52r5 â€"" 39r2s4. What is the resulting expression? 13(2r3s 4r5 â€"" 3r2s4) 13r2s(2r 4r3 â€"" 3s3) 13r2(2rs 4r3 â€"" 3s4) 13r2(26r3s 52r5 â€"" 39r2s4).
The resulting expression from the factorization of 26r³s + 52r^(5) - 39r²s⁴ is; 13r²(2rs + 4r³ - 3s⁴)
We want to factor the algebraic expression;
26r³s + 52r^(5) - 39r²s⁴
Now, we need to first find the highest common factor here and factorize out.
First of all for the letters;
The highest common factor of the letters is r²
Factors of 26 = 1, 2, 13, 26
Factors of 39 = 1, 3, 13, 39
Factors of 52 = 1, 2, 4, 13, 26, 52
The highest common factor for the 3 numbers is 13.
Thus,in total, the highest common factor for the algebraic expression is 13r².
Finally, we have;
13r²(2rs + 4r³ - 3s⁴)
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g town wants to study the relationship between weekly revenue and advertising expenditures. all measures are recorded in thousands of dollars. the summary output for the regression model is given below. anova df ss ms f significance f regression 20 24.5710256 1.22855128 15.12484836 1.8033e-17 residual 66 5.361004789 0.08122735 total 86 29.93203039 step 1 of 3 : what is the coefficient of determination for this model, r2 ? round your answer to four decimal places.
Therefore, the coefficient of determination for regression model is 0.8209, rounded to four decimal places.
The coefficient of determination, R-squared (r²), is a measure of how well a linear regression model fits the data. It tells us the proportion of the total variation in the response variable (y) that is explained by the linear regression model.
In order to calculate r², we first need to calculate the regression sum of squares (SSR) and the total sum of squares (SST). The regression sum of squares measures the amount of variation in the response variable that is explained by the regression model. The total sum of squares measures the total amount of variation in the response variable.
Once we have calculated SSR and SST, we can calculate r² as the ratio of SSR to SST. In this case, we are given the values of SSR and SST in the ANOVA table. We can calculate r² as:
r² = SSR/SST
= 24.5710256/29.93203039
= 0.8209 (rounded to four decimal places)
Therefore, the coefficient of determination, R-squared (r²), is 0.8209, which means that 82.09% of the total variation in the response variable is explained by the linear regression model. This is a relatively high value for r², which indicates that the model is a good fit for the data.
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Which value is the best estimate for
√
162
Answer:
12.7
Step-by-step explanation:
Fill in the missing number to write an equivalent ratio. Show your work.
3/8 = blank/24
Answer:9
Step-by-step explanation:
3/8=x/24
3/8=x/3*8
\(\frac{3}{8} =\frac{\frac{x}{3} }{8}\)
3=x/3
x=9
Answer:
First, we evaluate the amount that the portion has been multiplied by. We want to determine how many number 8's fit in to the number 24 because the bottom of the portion is 24.
The solution would be 3, because eight multiplied by 3 equals 24. Also because the bottom of the fraction has been multiplied by three, the top, known as the numerator, also needs to be multiplied by three. As a result, the top becomes 3 multiplied by 3, which equals 9. As a result, the portion is 9/24.
Step-by-step explanation:
3/8=?/24
3/8*3/3=9/24
9/24
____ =/8
3/3
A small box holds 60 hats. A large box holds 180% as many hats in the small box. How many hats does the large box hold.
Answer:
108
Step-by-step explanation:
Answer:108
Step-by-step:180/100×6=180080180×6=
Follow these steps to construct a triangle to represent the given information:
Draw a ray in the direction S 20° E from point P. Create a circle with radius 43.5. (Note that you'll be scaling down all the distances in miles by a factor of 10: 435 ÷ 10 = 43.5.) Label the point where the circle intersects the ray as C (Cali).
Draw a ray in the direction S 81° E from P. Mark an arbitrary point on this ray, and label it S.
Create a line through point S that is parallel to the north-south line through P.
Using the line passing through point S, draw a ray that is S 53° W.
Move point S along line PS until the ray S 53° W from S passes through point C. This position of S locates San Cristobal.
Paste a screenshot of your construction in the space below.
Answer:
i have to write something here so reading this is a waste of time.
A triangle can be constructed by different means such as:
A, B, C - angles or vertices.a, b, c - sides opposite to A,B,C, respectively, or their lengths.ha, hb, hc - altitudes (or sometimes heights) to the sides a,b,c.What is a Triangle?This refers to the plane figure that has three sides and angles.
Hence, we can see that in order to construct a triangle, they can be done by different means and the construction cannot be done for you, but the other means can include:
ma, mb, mc - medians to the sides a,b,c.la, lb, lc - bisectors of the angles A, B, C.Read more about triangles here:
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4 less than four times a number is equal to three times the same number plus 1
Answer:
True
Step-by-step explanation:
5 x 4 - 4 = 16
5 x 3 + 1 = 16
Jia spends $8 on 4 pounds of fruit. How much would he pay for one pound of fruit?
Answer:
2 dollars
Step-by-step explanation:
For 4 pounds of fruit he pays 8 dollars. If you use the unit rate it is 2 dollars for every one pound of fruit
Answer:
$2 per pound
Step-by-step explanation:
$8 / 4 pounds = $2 / 1 pound
please help i suck at math and I am in class
Answer:84.84m^2
Edit: I redid it doing the base separate and got 84.847 because Pythagorean theorem tells you the sides of the three triangles are 6.998 which is ever so slightly smaller than the base triangle.
Step-by-step explanation:
This is assuming the triangles are equal. 1/2bh gives you 21.21 for the triangle with the given height and then multiplying that by four for all the sides gives you 84.84m^2. The question doesn’t specify what type of pyramid it is so again I’m assuming it’s equal. Not 100% positive hope it can help at all.
Why are most personal loans much smaller than mortgages and home equity loans?.
Answer:
Most personal loans are smaller than mortgages and equity loans because the percentage of the interest rate on a home is higher than that of a personal loan.
Step-by-step explanation:
1 + 2 + (-5) + 4
A . -6
B . -5
C . 0
D . 2
E . 4
F . 12
Answer:
Option D. 2
Step-by-step explanation:
1+2+(-5)+4
= 1+2-5+4
= 1+2+4-5
= 7-5
= 2
Question Which of the following r-values represent the weakest linear correlation between independent (x) and dependent (y) variables? Select the correct answer below: -0.904 0 -0.312 O 0.558 0.870
The r - values that represents the weakest linear correlation is ;
-0.312 is the weakest negative correlation and 0.558 is the weakest positive correlation.
Given,
The r- values;-
- 0.904, -0.312, 0.558, 0.870
We have to find the r - values that represents the weakest linear correlation;
r- values represents correlation between two variables. The r- value lies from -1 to 1.
If r = -1 or close to -1, then it represents strong negative correlation.If -1 < r < 0 or close to -0.5, then it represents weak negative correlation.If r=0 or near to 0, then it represents no correlation.If 0 < r < 1 or close to 0.5, then it represents weak positive correlation.If r=1 or close to 1, then it represents strong positive correlation.So, here.
-0.904 is close to -1, so it represents strong negative correlation.
-0.312 is close to -0.5, so it represents weak negative correlation.
0.558 is close to 0.5, so it represents weak positive correlation
0.870 is close to 1, so it represents strong positive correlation.
Therefore,
The r - values that represents the weakest linear correlation is ;
-0.312 is the weakest negative correlation and 0.558 is the weakest positive correlation.
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Answer:
-0.312
Step-by-step explanation:
−0.312
The size of the correlation, r indicates the strength of the linear relationship between x and y. Values of r which are closer to −1 or to +1 indicate a stronger linear relationship between x and y.
I choose $9000 but I'm not sure and I just wanted to verify or an explanation to see if I'm right?
Answer:
Yea it's 9000
Step-by-step explanation:
6,000 is way too low, and 15,000 and 18,000 are way too high
What is the surface area of the three-dimensional figure formed by the net shown?
Answer:
336 cm²
Step-by-step explanation:
1 rectangle 24 cm by 12 cm
1 triangle with base 12 cm and height 8 cm (combining the two small triangles into 1 larger triangle)
SA = 24 cm * 12 cm + 12 cm * 8 cm / 2
SA = 288 cm² + 48 cm²
SA = 336 cm²
Which of the following is the correct sequence of project phases? O A. Concept - Planning - Definition O B. Definition - Planning - Performance O C. Postcompletion - Performance - Planning OD. Performance - Concept - Planning
The correct sequence of project phases is Definition - Planning - Performance. The correct answer is B.
This is the typical order of project phases in a traditional project management approach. It starts with the definition phase, where the project's goals, the scope, and the requirements are established.
Then comes the planning phase, where the project plan is developed, including the allocation of resources, scheduling, and budgeting.
Finally, the performance phase begins, during which the project activities are executed, monitored, and controlled to ensure the successful project completion.
Therefore the sequence of project phase is Definition - Planning - Performance The correct answer is B.
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A box is to be made out of a
rectangular piece of cardboard that is 12 inches wide and 16 inches long. Squares x inches on a side are cut out of the corners and the sides are bent upwards.
What is the length of the box?
Length of the resulting box will be of (16-x) inches
How to make a cuboid from a rectangle?A rectangle can be made into a cuboid by cutting squares of equal length from each corners and then joining the edges.
Given, length of cardboard= 16inches
Width of cardboard= 12 inches
If squares of side x is cut out of the corners and the sides are bent upwards to make a box,
The dimensions of the resulting box will be,
Length= (16-x) inches
Width= (12-x) inches
Height= x inches
Therefore the length of the resulting box will be of (16-x) inches.
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please help it should be ez for you guys ;-; brainiest to best answer :D
Answer:
1: -16/0 or undefined
2: 0
Step-by-step explanation:
Answer:
17
≈ 0.31
Step-by-step explanation:
Do the rise over run tactic for both of these points :
\(\frac{Y2 - Y1}{X2 - X1}\)
Substitute : (8,7) and (8, -9)
\(\frac{(-9 ) -8}{7-8}\)
\(\frac{-17}{-1}\)
\(17\)
Substitute : (-5, 8) and (4, 8)
\(\frac{8- 4}{8- (-5)}\)
\(\frac{4}{13}\)
≈ \(0.31\)
The formula for the area of a triangle is A=1/2bh, where b is the base of the triangle and h is the height of the triangle. The area of the triangular sail of a sailboat is 126ft^2. The base is 12 ft. Find the height of the sail.
(Show steps please)
Answer:
H=21ft
Step-by-step explanation:
Height=2•Area/Base
Area=126ft^2
Base=12ft.
H=2•126/12=21ft
H=21ft
Hope this helps :)
The following orders were placed during breakfast at The Egg-cellent Cafe last Tuesday morning. Use what you know about systems of linear equations to find the cost of each item. Assume that all items of the same name have the same unit price. Sales tax was not included in the total amounts.
Answer:
Step-by-step explanation:
What is y = 1.65x + 2.35 if x=14?
Answer:
y is 25.45
Step-by-step explanation:
y=1.65x+2.35 insert the unknown x
y=1.65(14)+2.35 open brackets by multiplication
y=23.1+2.35
y=25.45
A prism has a volume of 620 in.³ the length is 10 inches and the width is 2 inches what is the height of this prism?
Answer:
Volume= 620 inches3
Length= 10 inches
Width= 2 inches
Height=?
10×2×31
=620
The height is 31 inches
Find the area of a parallelogram with a base of 7 metres and a height of 8 metres. Show full working out
Answer:
\(56m^2\)
Step-by-step explanation:
Step 1: Area of Parallelogram Formula
A=bxh
Step 2: Plug in the information and solve
A=7mx8m
A=\(56m^2\)
Therefore the area of the parallelogram is \(56m^2\)
Answer:
56 Meters Squared
Step-by-step explanation:
Area of a Parallelogram is: \(A=b*h\)
We are given the base of 7 meters and the height of 8 meters.
\(A=7*8\\\\A=\boxed{56}\)
The area of the parallelogram is 56 square meters.