Find the area of an isosceles trapezoid with legs 16 and bases 15 and 29
Answers
The diagram represents the interpretation of the question for proper clarity.
To be able to obtain the are of the Isosceles trapezoid, we have to find the height first.
To find the height, we are going to use the Pythagoras theorem. Thus, we have:
[tex]\begin{gathered} (\text{Hypotenuse)}^2=(\text{Opposite)}^2+(\text{Adjacent)}^2 \\ 16^2=h^2+7^2 \\ 256=h^2+49 \\ 256-49=h^2 \\ 207=h^2 \\ h=\sqrt[]{207} \\ h=14.3875 \end{gathered}[/tex]The area of the Isosceles Trapezoid is given as:
[tex]A=\frac{1}{2}(a+b)h[/tex]Thus, we have:
[tex]\begin{gathered} A=\frac{1}{2}(15+29)14.3875 \\ A=\frac{1}{2}\times44\times14.3875 \\ A=316.53\text{ square unit} \end{gathered}[/tex]Hence, the area of the Isosceles trapezoid is 316.53 square unit
Related Questions
2. All three points displayed are on the line. Findan equation relating x and y(3,3) (6,9)
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As we can see there are three points on the line
As the two points
(4.5,6) is the answer.
simplify each of the following
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Hi, can you help me to solve this problem, please!!
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We are given the graph of a function and we are asked to determine the y-intercept. To do that we need to have into account that the y-intercept is the point where the graph crosses the y-axis. From the graph we notice that the graph touches the yaxis in the following point:
Therefore, the y-intercept is y = -2.
Part IExplain why there must be a sequence of rigid transformations that will map ∆A'B'C' exactly onto ∆DEF. Find and perform one such sequence of rigid transformations. Describe the sequence of rigid transformations you performed. The triangles are in the image
Answers
The Solution:
Given the figure below:
Step 1:
We shall explain why there is a sequence of rigid transformations that map triangle A'B'C' onto triangle ABC.
There is a sequence of rigid transformations because the lengths of the triangles are the same.
Step 2:
We shall describe the sequence transformations that are performed.
The transformation is 4.5 units to the right and then 3 units up.
Mackenzie already knew 1 appetizer recipe before starting culinary school, and she will learn1 new appetizer recipe during each week of school. After how many weeks of culinaryschool will Mackenzie know a total of 40 appetizer recipes?
Answers
Mackenzie already knew 1 appetizer recipe before starting culinary school, and she will learn 1 new appetizer recipe during each week of school.
After how many weeks of culinary school will Mackenzie know a total of 40 appetizer recipes?
SOLUTION
Mackenzie already knew 1 appetizer recipe before starting culinary school, and she will learn 1 new appetizer recipe during each week of school.
That is 2 appetizers per week
40 appetizers ===40 / 2 = 20 weeks
If SU=b+18 and SW=4b, find the value of b that makes quadrilateral TUVW a parallelogram.WVUTSb=Submit
Answers
If we want to make quadrilateral TUVW a parallelogram, we need to set the next equality SU= SW.
This is given because diagonals on a parallelogram bisect each other.
Now, we need to replace:
SU= SW.
b + 18 = 4b
Solve for b:
18 = 4b - b
18 = 3b
6 =b
Hence, the correct answer is b=6.
A group of students want to build three identical rectangular gardens, each of
which has a width of x ft. The gardens will be arranged in one of two ways, as
showr by the plans below. The students have 480 ft of fencing and plan to build
a fenc around each of the three gardens. They will also install lighting for the
garders.
Plan A
Plan B
X
x
X
X
X
1. Suppose that the students use all of the fencing. Given that the width of a
small rectangular garden is x ft, write an expression in terms of x for the length
of one of the small rectangular gardens in Plan A. Then write an expression
in terms of x for the length of one of the small rectangular gardens in Plan B.
Explain.
Answers
So, here we have the following figures for each plan:
We're given that the students have 480 ft of fencing, and they want to build a fence around each of the three gardens.
If "x" represents the width, we could say that "y" represents the large.
To find an expression for the length of one of the small rectangular gardens in plan A, remember that the perimeter of a rectangle is defined as the sum of the measures of all its sides. So, the total fence in the plan A is given by the expression:
[tex]4x+6y=480[/tex]We could solve this equation in terms of x to find the value of y:
[tex]\begin{gathered} 6y=480-4x \\ y=\frac{480-4x}{6}\to y=80-\frac{2}{3}x \end{gathered}[/tex]Now, we're asked to find an expression for the length of one of the small rectangular gardens in plan A.
So, the perimeter of one rectangle will be the substraction between 480 and the perimeter of the other two small rectangles:
[tex]\begin{gathered} 480-(x+x+y+y+y+y) \\ 480-2x-4y \end{gathered}[/tex]But we know that y = 80 - 2/3x, so:
[tex]\begin{gathered} L=480-2x-4(80-\frac{2}{3}x) \\ L(x)=480-2x-320+\frac{2}{3}x \\ L(x)=160-\frac{4}{3}x \end{gathered}[/tex]So that's the expression for the length of one of the small rectangular gardens in plan A.
Now, for plan B, we got that the total length of the three gardens is,
[tex]5x+5y=480[/tex]If we solve for y:
[tex]\begin{gathered} 5y=480-5x \\ y=96-x \end{gathered}[/tex]And, the perimeter of one rectangle will be the substraction between 480 and the perimeter of the other two small rectangles:
[tex]\begin{gathered} L=480-(3x+3y) \\ L=480-3x-3y \end{gathered}[/tex]But, we know that y=96-x, so:
[tex]\begin{gathered} L(x)=480-3x-3(96-x) \\ L(x)=480-3x-288+3x \\ L(x)=192 \end{gathered}[/tex]That means that the value of the length in the plan B is constant.
The graph shows a relationship between the size of 18 households and the average amount of time, in hours, each member of the householdspends on chores per week.O31234567Household MembersWhich equation best models this data set?
Answers
Solution
Step 1:
Pick the two points where the line passes through.
The points are: (3, 4.25) and ( 8, 2.5)
Step 2:
[tex]\begin{gathered} \frac{y\text{ - 4.25}}{x\text{ - 3}}\text{ = }\frac{2.5\text{ - 4.25}}{8\text{ - 3}} \\ \\ \frac{y\text{ - 4.25}}{x\text{ - 3}}\text{ = }\frac{-1.75}{5} \\ \\ \frac{y\text{ - 4.35}}{x\text{ - 3}}\text{ = -0.35} \\ \\ y\text{ - 4.25 = -0.35x + 1.05} \\ \\ y\text{ = -0.35x + 1.05 + 4.25} \\ \\ y\text{ = -0.35x + 5.3} \\ \end{gathered}[/tex]
which expression represents the value of sin C- cos C?
Answers
From the diagram, sinC= cosB = s
cosC=sinB = r
Therefore, sinC - cosC = s - r . Third option.
Use the distributive property to remove the parentheses.-7(-4u³+6-3x²)
Answers
Given:
The given expression is,
[tex]-7(-4u^3+6-3x^2)[/tex]Required:
To use the distributive property to remove the parentheses.
Answer:
We have the given expression,
[tex]-7(-4u^3+6-3x^2)[/tex]Using the distributive property to remove the parentheses, we will multiply each term inside the parentheses by -7.
Therefore, we get,
[tex]\begin{gathered} -7(-4u^3+6-3x^2) \\ \Rightarrow-7\times(-4u^3)+(-7)\times(6)-(-7)\times(3x^2) \\ \Rightarrow28u^3-42+21x^2 \end{gathered}[/tex]Final Answer:
Using the distributive property, we get the expression,
[tex]28u^3-42+21x^2[/tex]If the width of a rectangle is 3x, what is the length?
Answers
Given:
Area of the rectangle is defined as
[tex]A(x)=3x^2+21x[/tex]Width of the rectangle = 3x
Required: Length of the rectangle
Explanation:
The formula to find the area of a rectangle is
Area = Length x Width
Plug the given values into the formula.
[tex]\begin{gathered} 3x^2+21x=l\cdot3x \\ l=\frac{3x^2+21x}{3x} \\ =\frac{3x^2}{3x}+\frac{21x}{3x} \\ =x+7 \end{gathered}[/tex]So, the length of the rectangle is x + 7.
Final Answer: The length of the rectangle is x+7.
Please Help me with this problem so I can help my son better understand.I have attached an image of what were working on.
Answers
Given,
[tex]\begin{gathered} (2x^4+x^3-4x^2+3)+(4x^4-2x^3-x^2+10x+2) \\ 6x^4-x^3-5x^2+10x+5^{} \end{gathered}[/tex]For the standard deviation how do you transfer 10,074 to 100.37 For the sample variance how do you make 10,074 to 10,074
Answers
We have a calculation of the sample standard deviation and the sample variance.
The standard deviation is calculated with the following formula:
[tex]\sigma=\frac{1}{n-1}\sum ^n_{i=1}(x_i-M)^2[/tex]M: sample mean.
The standard deviation in this case has he value:
[tex]\sigma=\sqrt[]{\frac{30,222}{3}=\sqrt[]{10,074}\approx100.37}[/tex]Key to calculate the square root.
7(7-2x)>-35. solve for the variable
Answers
Solve for the variable
7 (7-2x) > -35
Dividing into 7
(7 (7-2x)) / 7 > -35/ 7
(7/7) (7-2x) > -35/ 7
(7-2x) > -35/7
(7-2x) > -5
-2x > -5 -7
-2x > -12
x > -12 /-2
x > 6
Answer x > 6
For the following equation, determine the values of the missing entries. Reduce all fractions to lowest terms.x = y²Note: Each column in the table represents an ordered pair. If multiple solutions exist, you only need to identify one..AnswerXy0Correct√516100-2√2Key
Answers
we have the equation
[tex]x=y^2[/tex]Complete the table
For x=0
substitute in the equation
[tex]\begin{gathered} 0=y^2 \\ y=0 \end{gathered}[/tex]For y=√5
[tex]\begin{gathered} x=(\sqrt{5})^2 \\ x=5 \end{gathered}[/tex]For x=16
[tex]\begin{gathered} 16=y^2 \\ y=\pm4 \end{gathered}[/tex]For x=100
[tex]\begin{gathered} 100=y^2 \\ y=\pm10 \end{gathered}[/tex]For y=-2√2
[tex]\begin{gathered} x=(-2\sqrt{2})^2 \\ x=8 \end{gathered}[/tex]Sketch the graph of the exponential function f(x)=3x−3.Which graph is the correct representation of the function?
Answers
Solution:
Given the function:
[tex]f(x)=3^x-3[/tex]The graph of the function is:
CORRECT OPTION:
y=2/3x+8yput in standard form
Answers
Explanation
the standard form is
[tex]Ax+By=C[/tex]Step 1
order the terms
[tex]\begin{gathered} y=\frac{2}{3}x+8y \\ 0=\frac{2}{3}x+8y-y \\ 0=\frac{2}{3}x+7y \\ \frac{2}{3}x+7y=0 \end{gathered}[/tex]If you are to pack this prism with unit cubes of the appropriate unit fraction edge lengths what would be the appropriate length of the edge of a unit cube? why? ၇ ? 2 3 2 4 А. 4 yd Byd 1 6 yd С. 4 yd 17 yd
Answers
Volume V = LxLxL
then
Volume = 6 yd x 2 3/4 yd x 1 1/2 yd
. = 6x (2 + 3/4) x ( 1 + 1/2 )
. = 12 + 4.5 x ( 1 + 1/2 )
. = 12 + 12•1/2 + 4.5 + 4.5•1/2
. = 18 + 6.75
. = 24.75 cubic yards
Now find length l of cubic unit
6 yd is divided by 1/2
1 1/2 yd. Is divided by 1/2
2 3/4 is divided by 1/2
Then minimum unit cube is 1/2 x 1/2 x 1/2
Then answer is
Option A ) 1/2
.
.
Word Problem " I need help solving this problem using quadratic equations.I need to show all work, If I can get step by step understanding I can then possibly start to solve the others on my own.
Answers
From the present question we will need to find the greatest common divisor between 144, 90, and 36 because the greatest common divisor will be the largest number of backpacks they can pack with numbers of pencils, note pads, and granola bars evenly.
From this information, to find the greatest common divisor, we must factorize the numbers. It means to write them as multiplication of prime numbers, as follows:
[tex]\begin{gathered} 144=2\times2\times2\times2\times3\times3=2^4\times3^2 \\ 90=2\times3\times3\times5=2^1\times3^2\times5^1 \\ 36=2\times2\times3\times3=2^2\times3^2 \end{gathered}[/tex]From this, we can see that all of the numbers have in their factorization the number 2 at least once, and the number 3 at least twice. From this, we know that they can be rewritten as follows:
[tex]\begin{gathered} 144=(2\times3^2)\times2^3=18\times2^3 \\ 90=(2\times3^2)\times5^1=18\times5^1 \\ 36=(2\times3^2)\times2^1=18\times2^1 \end{gathered}[/tex]It means that the greatest common divisor is 18, and from this, the largest backpacks they will be able to pack will be 18.
Determine which regions contain cube roots of -1. Check all that apply.on real axison imaginary axisquadrant 1quadrant 2quadrant 3quadrant 4
Answers
One of the cubic root of -1 is -1 itself.
The other two roots are imaginary numbers, and we can find them drawing an equilateral triangle in an unitary circle, with one vertex being the root (-1, 0):
What is at 6% interest And what is at 14% interest
Answers
The rule of the simple interest is
[tex]I=\text{PRT}[/tex]P is the initial amount
R is the rate in decimal
T is the time
Let her put $x in the account of 6%, and $y in the account of 14%
Since the amount in the 14% is more by 900, then
[tex]y=x+900\rightarrow(1)[/tex]Let the first account has I1 interest and the second amount has I2 interest
[tex]I_1=x(R_1)(1)[/tex]Since R1 = 6%
Change it to decimal by dividing it by 100
[tex]R_1=\frac{6}{100}=0.06[/tex]Then
[tex]\begin{gathered} I_1=x(0.06)(1) \\ I_1=0.06x \end{gathered}[/tex]Since R2 = 14%, then
[tex]\begin{gathered} I_2=y(\frac{14}{100})(1) \\ I_2=0.14y \end{gathered}[/tex]Since the total interest is $209, then add I1 and I2 and equate the sum by 209
[tex]0.06x+0.14y=209\rightarrow(2)[/tex]Substitute y in equation (2) by equation (1)
[tex]0.06x+0.14(x+900)=209[/tex]Simplify the left side
[tex]\begin{gathered} 0.06x+0.14(x)+0.14(900)=209 \\ 0.06x+0.14x+126=209 \end{gathered}[/tex]Add the like terms on the left side
[tex]\begin{gathered} (0.06x+0.14x)+126=209 \\ 0.2x+126=209 \end{gathered}[/tex]Subtract 126 from both sides, then divide the 2 sides by 0.2 to find x
[tex]\begin{gathered} 0.2x+126-126=209-126 \\ 0.2x=83 \\ \frac{0.2x}{0.2}=\frac{83}{0.2} \\ x=415 \end{gathered}[/tex]Substitute x in equation (1) by 415
[tex]\begin{gathered} y=900+415 \\ y=1315 \end{gathered}[/tex]6% is $415
14% is $1315
suppose a company is testing the flexibility of new type of fiberglass by creating a diving board out of the fiberglass machine
Answers
The three equations are as you are using:
[tex]\begin{gathered} a+b+c=116 \\ 8a+4b+c=448 \\ 27a+9b+c=972 \end{gathered}[/tex]So by solving the system of linear equations:
[tex]\begin{bmatrix}{1} & {1} & {1} \\ {8} & {4} & {1} \\ {27} & {9} & {1}\end{bmatrix}\begin{bmatrix}{a} & {} & {} \\ {b} & {} & \\ {c} & & {}\end{bmatrix}=\begin{bmatrix}{116} & {} & {} \\ {448} & {} & \\ {972} & & {}\end{bmatrix}[/tex]Now i'm telling you to use transformation and then solve it. it'll be easy for you:
The first transformation is:
[tex]R_2-8R_1=R_2[/tex]Then:
[tex]R_3-27R_1=R_3_{}_{}[/tex]And then
[tex]R_3-\frac{9}{2}R_2=R_3[/tex]Then you'll get:
[tex]\begin{gathered} a+b+c=116 \\ -4b-7c=-480 \\ \frac{11}{2}c=0 \end{gathered}[/tex]If C is the temperature in degrees celsius and f is the temperature in degrees Fahrenheit, then 9C=5(F-32). If the temperature is 45 degrees celsius what is the corresponding temperature in degrees Fahrenheit
Answers
Given:
The relation between f and c is:
[tex]9C=5(F-32)[/tex]The temperature is 45 degrees celsius.
Find-:
The temperature in degrees Fahrenheit
Explanation-:
Temp. in degrees Fahrenheit
[tex]9C=5(F-32)[/tex]Temp. Is:
[tex]C=45\text{ }[/tex][tex]\begin{gathered} 9C=5(F-32) \\ \\ 9\times45=5(F-32) \\ \\ F-32=\frac{9\times45}{5} \\ \\ F-32=9\times9 \\ \\ \end{gathered}[/tex]So, the temp. In degree Fahrenheit is:
[tex]\begin{gathered} F-32=9\times9 \\ \\ F-32=81 \\ \\ F=81+32 \\ \\ F=113 \end{gathered}[/tex]So, the temperature is 113 degrees fahrenheit.
Find the ratio of the areas of the two circles
Answers
Explanation
the area of a circle is given by:
[tex]\begin{gathered} \text{Area}=\text{ }\pi r^2 \\ or \\ \text{Area}=\text{ }\pi(\frac{D^2}{4}) \end{gathered}[/tex]then
Step 1
find the area of the circles
a)let radius= r=10 m
replace
[tex]\begin{gathered} \text{Area}=\text{ }\pi r^2 \\ \text{Area}=\pi(10m)^2 \\ \text{Area}=100\pi(m^2) \end{gathered}[/tex]b) let
diameter= 24 m
replace
[tex]\begin{gathered} \text{Area}=\text{ }\pi(\frac{D^2}{4}) \\ \text{Area}=\text{ }\pi(\frac{(24)^2^{}}{4}) \\ \text{Area}=\text{ }\pi(\frac{(24)^2^{}}{4}) \\ Area_2=144\text{ }\pi \end{gathered}[/tex]Step 2
now, find the ratio of the areas
so
[tex]\begin{gathered} \text{ratio}=\text{ }\frac{Area_1}{Area_2_{}} \\ \text{replace} \\ \text{ratio}=\frac{100\pi}{144\pi} \\ \text{ratio}=\frac{50}{72}=\frac{25}{36} \\ \text{ratio}=\frac{25}{36} \end{gathered}[/tex]I hope this helps you
what is the word form of each decimal 0.02
Answers
two hundredths
this is because 0.02 = 2/100
or 2 x 1/100
2 = two and 1/100 = hundredths
cosb= A. cosb B. sina C. cosa OD. sinb [sin (a + b) + sin(a - b)] OOO MONETHE
Answers
Answer: B. sin a
Explanation
• Expression,
[tex]_{---}\cos b=\frac{1}{2}\left[\sin\left(a+b\right)+\sin\left(a-b\right)\right][/tex]If we use the properties we get that:
[tex]2\sin a\cos b=\left[\sin\left(a+b\right)+\sin\left(a-b\right)\right][/tex]Then:
[tex]\sin a\cos b=\frac{1}{2}\left[\sin\left(a+b\right)+\sin\left(a-b\right)\right][/tex]write the equation of line that has a slope 3/5 and passes through the point (-10,-16)
Answers
It is required to find the equation of the line with a slope 3/5 and passes through (-10,-16)
The general equation of the line is y = mx + b
Where m is the slope and b is a constant
Given : the slope = m = 3/5
So, the equation will be:
[tex]y=\frac{3}{5}x+b[/tex]Find the value of b using the given point ( -10 , -16 )
[tex]\begin{gathered} -16=\frac{3}{5}\cdot-10+b \\ -16=-6+b \\ b=-16+6=-10 \end{gathered}[/tex]So, the equation of the line is:
[tex]y=\frac{3}{5}x-10[/tex]The cost before tax for an order of CDs from Music & More store was $214.60. If the store ordered 20 equally priced CDs, and the total shipping and handling fee was $15.00, what was the cost of one CD?$9.98$11.48$14.31$10.73
Answers
Okay, here we have this:
Considering the provided information, we are going to calculate the total cost of one CD, so we obtain the following:
First we will calculate the total cost of the 20 CDs by adding the total taxes and shipping that had to be paid:
Total Cost=$214.60+$15.00
Total Cost=$229.60
Unitary Cost=Total cost / Quantity
Unitary Cost=$229.60/20
Unitary Cost=$11.48
Finally we obtain that the cost of one CD is $11.48
We found the correlation coefficient for the comparison between height and weight in babies to be -0.12. That meanscorrelation is strongthe taller the baby, the heavier the babythe taller the baby, the lighter the babyHeight and weight of babies are independent
Answers
Answer:
The taller the baby, the lighter the baby
Explanation:
A correlation coefficient is a number between -1 and 1. The correlation is strong when it is a number closer to -1 or closer to 1 and the relation is independent when it is a number closer to 0.
In this case, we get that the correlation coefficient is -0.12, so there is a weak negative correlation. The negative means that when one variable increases, the other decrease, so the taller the baby, the lighter the baby.
Then, the answer is:
The taller the baby, the lighter the baby
Each equation below is followed by several stories. Select all of the stories that can be represented by the equation. If none of the stories can be represented, select "None of the above". (a) 5x = 10 Isabel had x cards. Then her friend gave her 5 cards. Isabel now has 10 cards, Isabel has 5 packs of cards. Each pack has x cards. Isabel has 10 cards. Isabel has 5 friends. Each friend gave her x cards. This gave Isabel 10 cards. Isabel had x cards. Then she gave her friend 5 cards. Isabel now has 10 cards. 1 None of the above Next Question Check Answer