Answers
We have been given a figure and we need to find its area.
To determine the area we will divide the figure into known shapes. From the division into shapes, we have a square and a trapezoid.
[tex]Area\text{ of the figure = Area of the square + Area of the trapezoid}[/tex][tex]\begin{gathered} Dimensions\text{ of the square:} \\ length\text{ = 12 ft} \\ Area\text{ of the square = length}^2 \\ \\ Area\text{ of the square = 12}^2 \\ \\ Area\text{ of the square = 144 ft}^2 \end{gathered}[/tex][tex]\begin{gathered} Dimensions\text{ of the trapezoid:} \\ base\text{ 1 = 10 ft, base 2 = 12 ft} \\ height\text{ = 6 ft} \\ \\ Area\text{ of trapezoid = }\frac{1}{2}(10\text{ + 12\rparen}\times\text{ 6} \\ \\ Area\text{ of trapezoid = }\frac{1}{2}\times22\text{ }\times6\text{ = 11}\times6 \\ \\ Area\text{ of trapezoid = 66 ft}^2 \end{gathered}[/tex][tex]\begin{gathered} Area\text{ of the figure = 144 + 66} \\ \\ Area\text{ of the figure = 210 ft}^2 \end{gathered}[/tex]
Related Questions
Place the following from least to greatest 9square root of 6square root of 101.53.14159
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[tex]\begin{gathered} \sqrt[]{6}=2.44\cdots \\ \sqrt[]{10}=3.16\cdots \end{gathered}[/tex]
Therefore, the given number ordered from least to greatest is:
[tex]1.5,\sqrt[]{6},3.14159,\sqrt[]{10},9[/tex]Five CDs cost $80 . If each CD costs the same, how much does one cost
Answers
solution:
5 CDs ----> $80
1 CDs ----> x
then
[tex]x=\frac{80}{5}=16[/tex]answer: one CD cost $16
For her cell phone plan heather pays 30 dollars per month plus 0.05 per text. She wants to keep her cell phone bill under 60 dollars per month. Which inequality represents the number of texts t heather can send each month while staying within her budget?
Answers
The inequality represents the number of texts t heather can send each month while staying within her budget is t<600.
Given, heather pays 30 dollars per month plus 0.05 per text.
She wants to keep her cell phone bill under 60 dollars per month.
hence texts she can send = 0.5 × 600
= $30
hence for $30 heather can text upto 600 texts.
so, cell phone plans + text
= $30 + $ 30
= $60
so, the inequality represents the number of texts t heather can send each month while staying within her budget is t<600
Hence the inequality is t<600
Learn more about Inequality here:
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this one is super hard
Answers
Answer:
16, 767
Explanation:
The second term of the sequence is
23 * 3 = 69
the third term is
23* 3 *3 = 207
the fourth term is
23 * 3* *3 *3
the fifth term is
23 *3* *3 *3 *3
the sixth term is
23 *3* *3 *3 *3 * 3
the seventh term is
23 *3* *3 *3 *3 * 3* 3 = 16767
which is our answer!
Find the unknown angle measure. 33 mZFGH: mZGFH: mzGHF: 33° х F 28 H
Answers
m∠FGH =33º, m∠GFH =119º and m∠GHF= 28º
1) Since the sum of all interior angles of any triangle is always equal to 180º, we can write:
m∠f + m∠H + m∠G = 180º Plug it into that the following measures
x +33º +28º= 180º
x + 61º = 180º
x = 180 -66
x =119º
2) Then we can write:
m∠FGH =33º, m∠GFH =119º and m∠GHF= 28º
Need help with this homework Part 2) construct the line that is perpendicular to the directrix and passes through the focus. This line will be the axis of symmetry of the para bola what are the coordinates of the point of intersection,A, of the access of symmetry and directrix of the parabola
Answers
After following the instructions in part A, the result is
In general, the equation of a horizontal line is y=a, with 'a' a constant. In our case, the line has to be 6 units below F; then y=4-6=-2. The equation of the directrix is y=-2
Part 2)
In Geogebra, go to Tools->Construct->Perpendicular Line; then, click on point F and line y=-2. A new line should appear on your screen, then go to Tools->Points->Intersect and select both lines. After naming the intersection point as 'A', the result is
The answer to part 2) is A=(6,-2)
The steps below show the incomplete solution to find the value of n for the equation 4n − 2n + 4 = −1 + 17:Step 1: 4n − 2n + 4 = −1 + 17 Step 2: 4n − 2n + 4 = 16 Step 3: 2n + 4 = 16Which of these is most likely the next step? (5 points)2n = 122n = 42n = 82n = 20
Answers
In this case, we'll have to carry out several steps to find the solution.
Step 01:
Data:
4n − 2n + 4 = −1 + 17
Step 02:
We must apply the algebraic rules to find the solution.
Step 1: 4n − 2n + 4 = −1 + 17
Step 2: 4n − 2n + 4 = 16
Step 3: 2n + 4 = 16
2n + 4 = 16
2n = 16 - 4
2n = 12
The answer is:
2n = 12
Rangers wanted to estimate the total number of elk in region of Montana. they tagged 12 elk and sent them back to the area. two months later the Rangers observed 4 of the tagged elk out of 25 total Elk observed. estimate the size of the elk population in that region of Montana
Answers
Total number of elks tagged = 12
Number of a sample of the tagged elks from 25 total Elk observed = 4
Total number of 25 Elk observed = 12/4 = 3
Size of the elk population in the region of Montana = 3 x 25
= 75
i need help with -1=-4/7t
Answers
The equation is:
[tex]-1\text{ = -}\frac{4}{7}\text{ t}[/tex]To find t you need to isolate t.
First, pass the 7 multiplying and the 4 dividing:
[tex]-1\cdot\frac{7}{4}=-t[/tex]Finally, pass the minus sign:
[tex]-t\text{ = (-1)}\cdot t=-1.\frac{7}{4}\Rightarrow\text{ t = (-1)}\cdot\frac{7}{4}\frac{1}{(-1)}=\frac{7}{4}[/tex]Math help question one and two
Answers
We can determine that the option D is better fit of equation model which calculated as follows :
First, insert the value x to the formula (y)
y = 0.07(100) + 0,94
y = 7 + 0,94
y = 7,94
Given the bone chips (x) is 100, then the bone tools (y) is 8.
The value of bone tools (y) which is 8 is the result of rounded of value (y) 7,94.
2. The answer for question no. 2 is B
The equation models the line of best fit for data is y = -0,35x + 31,6
We can prove it as follows :
First step is value of race (x) of the first column which given by 1 to the formula .
y = -0,35(1) + 31,6
y = -0,35 + 31,6
y = 31,25
Next, we check that given the value of the Time (y) of Race (x) value of 1 is 31,1.
Hence, it shows that the equation models the line of best fit for data is y = -0,35x + 31,6
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Jaden and Lola are hosting events that are catered by the same company. Jaden plans to have 82 adults and 96 children attend, so the total projected cost of his meals is $5,664. Lola has 65 adults and 49 children on his guest list, so she will pay the caterer $4,002. How much does the caterer charge for each meal?
Answers
Let's use the variable x to represent the cost of one adult meal, and y to represent the cost of one child meal.
If the cost of 82 adult meals and 96 children meals is $5,664, we can write the following equation:
[tex]82x+96y=5664[/tex]If the cost of 65 adult meals and 49 children meals is $4,002, we can write the equation:
[tex]65x+49y=4002[/tex]To solve this system, let's solve the second equation for y and then use its value in the first equation:
[tex]\begin{gathered} 65x+49y=4002 \\ 49y=4002-65x \\ y=\frac{4002-65x}{49} \\ \\ 82x+96y=5664 \\ 82x+96(\frac{4002-65x}{49})=5664 \\ 82x+7840.653-127.347x=5664 \\ -45.347x=-2176.653 \\ x=48 \\ \\ y=\frac{4002-65\cdot48}{49} \\ y=18 \end{gathered}[/tex]Therefore every adult meal costs $48 and every child's meal costs $18.
Nick used a rope to make a rectangle and a circle below. If 10 cm rope was left, what was the original length of the rope? cm 10 cm 7 cm
Answers
To find the original length of the rope, we must find the length of rope used in the rectangle and in the circle, and add it to the length of rope that was leftover.
The length of rope used in the rectangle would be the perimeter of the rectangle, the perimeter of the rectangle is the sum of all his sides.
Perimeter of a rectangle = side + side + side + side
[tex]\text{Perimeter rectangle= 10+7+10+7=34 cm}[/tex]The question gives us the perimeter of the circle, 20 cm this measure was the length of rope used in the circle.
[tex]\text{Perimeter circle= 20 cm}[/tex]Now the total length of the rope was: The sum of the perimeters of both rectangle and circle and the length of rope that was left.
Total length rope = 34 + 20 + 10 = 64 cm
A computer system was purchased by a small business for $12,000 and, for tax purposes, is assumed to have a salvage value of $2,000 after 8 years. If its value is depreciated linearly from $12,000 to $2,000, find the linear equation that relates the value V in dollars to the time t in years. A video production company is planning to produce instructional videotape. The producer estimates that it will cost $84,000 to shoot the video and $15 per unit to copy and distribute the tape. The wholesale price of the tape is $50 per unit. How many units must be manufactured and sold each month for the company to break even?
Answers
Second question
In order to break even,
total revenue must be equal to total cost. In this case, there is no profit
Let x represent the number of units of tape that would be manufactured to break even.
From the information given,
cost of shooting the video = 84000
If the cost of producing a unit is $15, it means that the cost of x units would be 15x
The total cost of producing x units is
15x + 84000
The wholesale price of the tape is $50 per unit. It means that the revenue from selling x units would be 50x
To break even, it means that
15x + 84000 = 50x
50x - 15x = 84000
35x - 84000
x = 84000/35
x = 2400
2400 units must be manufactured and sold each month for the company to break even
Brady creates the graph below to keep track of the approximate height of the grass on hislawn over timeWhat is the dependent variable in the situation?Brady's Lawnthe number of days it takes for the grass togrow an inchthe height of the grass, in inchesthe number of inches the grass grows eachdayHeight of Grass (inches)the amount of time that has passed. In days2468 10 12 14 16 18 20Time (days)
Answers
Answer:
The height of the grass, in inches
Explanation:
The dependent variable is the variable whose value changes whenever the other variable (independent) changes.
From the graph, the height of the grass (in inches) depends on the time in days.
Therefore, the dependent variable in this situation is the height of the grass, in inches
Use a properly of equality to solve this equation: 4.5x = 18
Answers
To solve the equation you can use the property of the multiplicative inverse, like this
[tex]\begin{gathered} 4.5x=18 \\ \frac{1}{4.5}\cdot4.5x=18\cdot\frac{1}{4.5} \end{gathered}[/tex]Dividing by 4.5 into both sides of the equation is the same as multiplying by the multiplicative inverse of 4.5 on both sides of the equation
[tex]x=\frac{18}{4.5}[/tex]Therefore,
[tex]x=4[/tex]Janelle invests in a piece of art that cost 600 British Pounds. A study found that art appreciates in value at a rate of 3.97% per year. Assuming this pattern continues, how much, in British Pounds, will Janelle's piece of art be valued at after 10 years? Round your answer to the hundredths place.
Answers
Step-by-step explanation:
The art piece originally costs £600.
And it appreciates at a rate of 3.97% each year.
And we want to find the value of the art after 10 years.
We can write an exponential function to model the situation. The standard exponential function is given by:
[tex]f(t)=a(r)^t[/tex]Where t is the time in years.
Since it appreciates at a rate of 3.97% each year, the value after each year will be (100% + 3.97%) or 103.97%.
103.97% = 1.0397. So, r = 1.0397:
[tex]f(t)=a(1.0397)^t[/tex]Our a is the initial value. Therefore:
[tex]f(t)=600(1.0397)^t[/tex]Then the value of the piece of art after 10 years is:
[tex]f(10)=600(1.0397)^{10}=885.58793\approx885.59[/tex]Hence, It will be worth about £885.59 after 10 years.
Hi I want to double check if I’m right, thank you
Answers
Solution
The whole shape is a trapezoid
a= 10 , b = 10 +7+7 = 24 , h = 9
Formula
[tex]A=\frac{1}{2}(a+b)h[/tex][tex]\begin{gathered} A=\frac{1}{2}(10+24)9 \\ A=\frac{1}{2}(34)9 \\ A=153units^2 \end{gathered}[/tex]The correct answer is 153
To start a new business Beth deposits $1500 at the end of each six-month period in an account that pays 8%, compounded semiannually. How much will she have at the end of 9 years?
Answers
The amount Beth deposit every six-month is A = $1500.
The rate percent is 8% or 0.08.
The time after which futre value determined is t = 9 years.
Determine the rate percent for semi-annually.
[tex]\begin{gathered} i=\frac{0.08}{2} \\ =0.04 \end{gathered}[/tex]Determine the value of time (t) for semi-annualy.
[tex]\begin{gathered} n=2\cdot9 \\ =18 \end{gathered}[/tex]The formula for the future value is,
[tex]FV=\frac{A}{i}\lbrack(1+i)^n-1\rbrack[/tex]Substitute the values in the formula to determine the future value.
[tex]\begin{gathered} FV=\frac{1500}{0.04}\lbrack(1+0.04)^{18}-1\rbrack \\ =37500\lbrack(1.04)^{18}-1\rbrack \\ =38468.11933 \\ =38468.12 \end{gathered}[/tex]So answer is 38468.12
Supposed to 25% of the time Danny eat out twice a month 30% of the time he eats out once a month and 45% of the time he doesn’t eat out at all in a given month what is the expected value for the number of times daily eats out during a month
Answers
Answer
Expected value = 0.8 times per month
Explanation
The mean of the probability distribution is called expected value and it is given as
E(X) = Σxᵢpᵢ
where
xᵢ = each variable = Number of times Danny eats out
pᵢ = probability of each variable
n = number of variables
p = probability of one variable
We need to set up the probability distribution first
xᵢ | pᵢ
2 | 0.25
1 | 0.30
0 | 0.45
E(X)
= (2 × 0.25) + (1 × 0.30) + (0 × 0.45)
= 0.5 + 0.3 + 0
= 0.8
Hope this Helps!!!
A group of biologists is surveying the mice population in a forest. The equatio n=75 times 3t gives the total number of mice, n, t years after the survey began. What does the number 3 mean in the situationA: the common difference B: The original population of miceC: the common ratioD: the slop
Answers
I think the equation should be
[tex]n=75\cdot3^t[/tex]where 3 is the common ratio of the exponential function
so the answer is C.
Solve for 2. Enter the solutions from least to greatest.x^2 - 3x - 40 = 0lesser x = [ ]greater x = [ ]
Answers
In this case, we'll have to carry out several steps to find the solution.
Step 01:
Data
x^2 - 3x - 40 = 0
x1 = ?
x2 = ?
Step 02:
Quadratic equation:
roots:
x² - 3x - 40 = 0
(x - 8)(x + 5) = 0
x1 = 8
x2 = -5
The answer is:
lesser x = -5
greater x = 8
what is the ratio 250 pieces of red construction paper and 114 blue construction paper
Answers
Answer
Check Explanation
Explanation
We need to find the ratio of red construction paper to blue construction paper.
250 : 114
Divide both sides by 2
125 : 57
That's how far we can go, since there is no number that can divide these two numbers.
Hope this Helps!!!
Sketch a graph of g (x) = V (x-3) + 2 Label at least 4 points including X-and y-intercepts, explain
Answers
The equation is given as
[tex]g(x)=\sqrt[]{x-3}+2[/tex]To find the coordinates of the equation,
Hence the graph of the equation is
Susan is making a pennant in the shape of a triangle for her senior class photo. She wants the base length of this triangle to be 4 inches. The area of the pennant must be at least 12 square inches. (The pennant has to be seen in the photo.) Write an Inequality that describes the possible heights (in inches) of the triangle. Use h for the height of the triangular pennant.
Answers
Susan is making a pennant in the shape of a triangle for her senior class photo. She wants the base length of this triangle to be 4 inches. The area of the pennant must be at least 12 square inches. (The pennant has to be seen in the photo.) Write an Inequality that describes the possible heights (in inches) of the triangle. Use h for the height of the triangular pennant.
Remember that
the area of the triangle is
[tex]A=\frac{1}{2}b\cdot h[/tex]we have
b=4 in
at least -----> is greater than or equal to
so
[tex]A\ge12\text{ in2}[/tex]therefore
[tex]\begin{gathered} \frac{1}{2}\cdot(4)\cdot h\ge12 \\ \text{solve for h} \\ 2h\ge12 \\ h\ge6\text{ in} \end{gathered}[/tex]the height of triangle must be greater than or equal to 6 inches
What is the measurement of the exterior angle in the diagram below?A. 100B. 30C. 70D. 88
Answers
Describe the rotation:A) 180 degreesB) 90 degrees counterclockwise C) 90 degrees clockwise
Answers
The image 1 is rotated 90 degree clockwise to get image 2.
4. A cylinder has a volume of 198 cm^3,and itsbase has an area of 22 cm^2.What is theheight of the cylinder?Please hurry
Answers
1) Let's find out the height of that cylinder, by plugging it into the formula:
[tex]\begin{gathered} V=\pi\cdot r^2\cdot h \\ 198\text{ =}\pi\cdot rh \\ \end{gathered}[/tex]2) The Base area is given by:
[tex]\begin{gathered} A_B=\pi\cdot r^2 \\ 22=\pi\cdot r^2 \\ \frac{22}{\pi}=\frac{\pi}{\pi}r^2 \\ r=\sqrt[]{\frac{22}{\pi}} \end{gathered}[/tex]So now let's plug that radius
[tex]undefined[/tex]A sailmaster decides to stitch a strip of binding right round the edge of a sail which is the shape of a right- angled triangle. The vertical and horizontal edges of the sail are 6.5m and 2.6m respectively. What length of binding is needed for the job?
Answers
First, we will use the Pythagorean theorem to compute the hypotenuse:
[tex]\begin{gathered} h^2=(6.5m)^2+(2.6m)^2 \\ =42.25m^2+6.76m^2 \\ =49.01m^2. \end{gathered}[/tex]Then:
[tex]h\approx7.0m.[/tex]Therefore, the sail master will need:
[tex]6.5m+2.6m+7m=16.1m[/tex]of blinding.
Answer: 16.1m
A complex number zı has a magnitude z1] = 2 and an angle 6, = 49°.=Express zy in rectangular form, as 21 == a +bi.Round a and b to the nearest thousandth.21 =+iShow Calculator
Answers
Complex numbers can be written in two forms:
[tex]\begin{gathered} z=a+b\cdot i \\ z=r\cdot e^{i\theta} \end{gathered}[/tex]Where a and b are known as the real and the imaginary part and r and theta are the magnitude and the angle of the number. In this case we are given these last two quantities and we have to find a and b. One way to do this is recalling an important property of the exponential expression above:
[tex]e^{i\theta}=\cos \theta+i\sin \theta[/tex]Then the exponential form of a number is equal to:
[tex]z=r\cdot e^{i\theta}=r\cdot(\cos \theta+i\sin \theta)=r\cos \theta+i\cdot r\sin \theta[/tex]And since we are talking about the same number then this expression must be equal to that given by a and b:
[tex]a+i\cdot b=r\cos \theta+i\cdot r\sin \theta[/tex]Equalizing terms without i and those with i we have two equations:
[tex]\begin{gathered} a=r\cos \theta \\ b=r\sin \theta \end{gathered}[/tex]Now let's use the data from the exercise:
[tex]\begin{gathered} r=\lvert z_1\rvert=2 \\ \theta=\theta_1=49^{\circ} \end{gathered}[/tex]Then we have:
[tex]\begin{gathered} a=2\cdot\cos 49^{\circ} \\ b=2\cdot\sin 49^{\circ} \end{gathered}[/tex]Using a calculator we can find a and b:
[tex]\begin{gathered} a=1.312 \\ b=1.509 \end{gathered}[/tex]Then the answers for the two boxes are 1.312 and 1.509
I need help on this I can’t remember how to do it
Answers
Answer:
[tex]g(x)=7^{\frac{x}{3}}+1[/tex]Explanation:
The function f(x) is given as:
[tex]f(x)=7^x+1[/tex]If a function, f(x) is horizontally compressed by a factor of k units, the transformation rule is:
[tex]f(x)\to f(kx)[/tex]Therefore, if f(x) is transformed to g(x) through a horizontal compression by a factor of 1/3, the function g(x) is:
[tex]g(x)=7^{\frac{x}{3}}+1[/tex]