The figure to the right shows the graph y= 3^-x and three inscribed rectangles. What is the sum of the areas of the rectangles?
Answers
Based on the calculations, the sum of the areas of the rectangles is equal to: A. 0.25 square unit.
How to calculate the area of a rectangle?Mathematically, the area of a rectangle can be calculated by using this formula;
A = LW
Where:
A represents the area of a rectangle.l represents the length of a rectangle.w represents the width of a rectangle.By critically observing the figure (see attachment), we can logically deduce the following information:
Width of rectangle A = 2 units
Width of rectangle B = 2 units.
Width of rectangle C = 4 units.
Next, we would determine the length and area of each of the rectangle.
The length of the first rectangle is given by:
Length of rectangle, y = 3^-x
Length of rectangle, y(0) = 3⁻⁰ = 1 units.
Length of rectangle, y = 3^-x
Length of rectangle, y(2) = 3⁻² = 0.11 unit.
Area of first rectangle = 2(0.11)
Area of first rectangle = 0.22 square unit.
For the second rectangle, we have:
Length of second rectangle, y = 3^-x
Length of second rectangle, y(4) = 3⁻⁴ = 0.012 unit.
Area of second rectangle = 2(0.012)
Area of second rectangle = 0.025 square unit.
For the third rectangle, we have:
Length of third rectangle, y = 3^-x
Length of third rectangle, y(8) = 3⁻⁸ = 0.00015 unit.
Area of third rectangle = 4(0.00015)
Area of third rectangle = 0.0006 square unit.
Now, we can calculate the sum of the areas of the rectangles:
Total area = 0.22 square unit + 0.025 square unit + 0.0006 square unit.
Total area = 0.246 ≈ 0.25 square unit.
Total area of rectangle = 0.25 square unit.
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Complete Question:
Figure 3 shows the graph of y = 3^−x and three inscribed rectangles. What is the sum of the areas of the rectangles?
[a] 0.25
[b] 0.50
[c] 2.45
[d] 6.26
[e] 12.68
Related Questions
Approximate √18 to the nearest tenth and plot
the number on a number
line.
Answers
Answer: 4.2
Step-by-step explanation:
√18=
4.24=
4.24=4.2
Example 8
A school received a shipment of laptops and tablets purchased for $35,100 for their new
computer lab. Each tablet cost $375 and each laptop cost $850. If the school ordered 3 times as
many laptops as tablets, then which of the following is the number of laptops in the shipment?
Answers
The shipment contained 12 tablets and 36 laptops.
What is an equation?An equation is used to show the relationship between numbers and variables. An equation can be linear, quadratic depending on the degree.
Let x represent the number of tablets and y represent the laptop.
Each tablet cost $375 and each laptop cost $850, hence:
375x + 850y = 35100 (1)
Also:
y = 3x (2)
From both equations:
x = 12, y = 36
The shipment contained 12 tablets and 36 laptops.
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Several batches of stew were made yesterday. Each batch required 1 and two-thirds pounds of meat. All together, 10 and StartFraction 5 over 6 EndFraction pounds of meat was used. Janice tried to find the number of batches of stew made. Her work is shown below.
Answers
Answer:
Step-by-step explanation:
Answer:
no of batches of street made is 2345
srry i don't know
Step-by-step explanation:
Maggie has a container in the shape of a right prism. the formula for its surface area is sa = ph 2b. solve for h. h = sa minus two times b over p h = sa plus two times b over p h = sa plus p over two times b h = sa minus p over two times b
Answers
The value of the height of the right prism is given by the formula, h = (SA - 2B) / P. It is gained by using the surface area of the right prism.
What is the right prism?
A right prism is a three-dimensional closed figure with 6 faces, 8 corners and 12 edges. It is called a right prism because, in this prism, the angle between the base and the sides is 90 degrees. All the faces of a right prism are rectangular, hence sometimes also called a right rectangular prism.
Calculation of h for the right prism
We know the surface area of the right prism is given by:
SA = Ph + 2B
Ph + 2B = SA
Subtracting 2B from both sides of the above equation, we have,
Ph + 2B - 2B = SA - 2B
Ph = SA - 2B
Dividing both sides of an equation by P, we get,
(Ph) / P = (SA - 2B) / P
h = (SA - 2B) / P
Hence, the value of h can be found using the formula, h = (SA - 2B) / P
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There are 140 cars in a parking lot. Keisha looks at 15 cars and sees that two of them are red. Aproximately, how many red cars are in the parking garage?
Answers
Write down the inequality described by "negative three groups of x is less than two", and solve for x
Answers
Answer:
- 3x < 2
x < - 1
Explanation and Check part below
Explanation and Check part belowHope this helps :)
Step-by-step explanation:
1. To solve, first isolate the variable by doing the inverse operation which is in this case dividing by - 3 on both sides of the equation.
- 3x < 2
- 3 -3
x < - 1
2. Graph it if needed with an open dot because - 1 is not part of the set of solutions.
<--------○
<----l----l-----l----->
-2 -1 0
Check:
1. Substitute x with any number less than - 1 and solve.
- 3 (- 2) < 2
-6 < 2
True statement.
9. Bus A arrives every 12 minutes and Bus B arrives every 15 minutes. Both buses arrive
together at 9am, what time do they next arrive together
Answers
============================================================
Explanation:
12 = 3*4
15 = 3*5
The GCF of 12 and 15 is 3
LCM of x and y = (x*y)/(GCF of x and y)
LCM of 12 and 15 = (12*15)/(GCF of 12 and 15)
LCM of 12 and 15 = (12*15)/(3)
LCM of 12 and 15 = 60
-------------------
We can confirm this by listing out the multiples of each
multiples of 12 are: 12, 24, 36, 48, 60, 72, ...
multiples of 15 are: 15, 30, 45, 60, 75, ...
-------------------
Since the LCM is 60, this means their schedules line up every 60 minutes, aka 1 hour.
If they arrive together at 9 AM, then their next arrival time together is 10 AM which is the final answer.
Can someone help me with these? ASAP please
Answers
a. Length of AB = 7 units
Length of CDS = 3 units
Line segment AB and line segment CD are not congruent.
b. Length of AB = 7 units
Length of CD = 7 units
Line segment AB and line segment CD are congruent.
c. Length of AB = 9 units
Length of CD = 7 units
Line segment AB and line segment CD are not congruent.
How to Find the Length of a Segment?Given two points on a coordinate plane, where the two points are on a horizontal or vertical line, the distance between the two points is the absolute difference between their coordinates.
a. Given:
A(10, -4)
B(3, -4)
C(-1, 2)
D(-1, 5)
Length of AB = |10 - 3| = |7|
Length of AB = 7 units
Length of CD = |5 - 2| = |3|
Length of CDS = 3 units
Line segment AB and line segment CD are not congruent.
b. Given:
A(-5, 6)
B(-5, -1)
C(-4, 3)
D(3, 3)
Length of AB = |6 - (-1)| = |7|
Length of AB = 7 units
Length of CD = |-4 - 3| = |-7|
Length of CD = 7 units
Line segment AB and line segment CD are congruent.
c. Given:
A(8, 3)
B(-1, 3)
C(5, 10)
D(5, 3)
Length of AB = |8 - (-1)| = |9|
Length of AB = 9 units
Length of CD = |10 - 3| = |7|
Length of CD = 7 units
Line segment AB and line segment CD are not congruent.
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estimate the square root of 60 to one decimal place
Answers
I need some help with my math please: Triangles ABD and ACE are similar right triangles. Which ratio best explains why the slope of AB is the same as the slope of AC?
Answers
Answer:
The second answer is the correct one I believe
Answer:
second one
Step-by-step explanation:
multiply or divide write your answer in simplest form 3/6 x 7/10
Answers
Answer:
0.35
Step-by-step explanation:
3/6=1/2
7/10=0.7
1/2=0.5,0.5×0.7
=0.35
Answer: 7/20
Step-by-step explanation:
3/6*7/10= 0.35
First write down the decimal number divided by 1 like this:
0.35
1
As we have 2 digits after the decimal point in the numerator, we need to multiply both the numerator and denominator by 102 = 100, so that there is no decimal point in the numerator
0.35 × 100
1 × 100
=
35
100
Since the greatest common factor of 35 and 100 is 5, we can simplify the fraction and show the same amount
35 ÷ 5
100 ÷ 5
=
7
20
Therefore, 0.35 as a fraction is 7/20
the data to the right represent the top speed (in kilometers per hour) of all the players (except goaltenders) in a certain soccer league. find (a) the number of classes, (b) the class limits for the second class, and (c) the class width.
Answers
Liam is 3 years older than his little sister Carin. Together they're 31 years old. How old is Liam? Solve the problem with an equation
Answers
Answer: Liam is 17
Step-by-step explanation: 17-14= 3. 17 + 14 = 31
Write an equation for a cubic function that has been reflected across the x-axis, shifted
right 3 units and shifted up 1 unit.
y = x³
Answers
Does the following expression have a value greater than 2? - 3+ (+4) +2
Answers
Yes, the resulting value of the expression is 3 which is greater than 2.
Expression:
Expression is defined as a combination of terms that are combined by using mathematical operations such as subtraction, addition, multiplication, and division.
An expression contains the following:
Constant: A constant is a fixed numerical value.
Variable: A variable is a symbol that doesn't have a fixed value.
Term: A term can be a single constant, a single variable, or a combination of a variable and a constant combined with multiplication or division.
Coefficient: A coefficient is a number that is multiplied by a variable in an expression.
Given,
Expression = -3 + (+4) + 2
Here we need to check the resulting value of the expression is greater than 2 or not.
For that, first we have to simplify the given expression,
Then,
=> -3 + ( 4 + 2)
=> -3 + 6
=> 3
Now, we have know that 3 is greater than 2.
So, the expression is greater than 2.
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how to solve? …………….
Answers
Solution:
[tex]3(2x+3)[/tex]
Hope this helps!
HELP !!!
Point (2,6) is 2/3 of the way from A to B. If A has coordinates (-8, 6), what are the coordinates of B?
Answers
The coordinates of the point B are (-5, 6)
How to determine the coordinates of the point B?The given parameters are
A = (-8, 6)
Point = (2, 6)
Proportion = 2/3
Because the y coordinates are the same, we can make use of only the x coordinate
So, we have
Point = Proportion * (B - A)
This gives
2 = 2/3 * (B + 8)
Multiply through by 3/2
So, we have
3 = B + 8
Subtract 8 from both sides
B = -5
Hence, the coordinates of the point B are (-5, 6)
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Round 3,487,967 to the nearest ten thousands
Answers
Answer:
3,490,000
Step-by-step explanation:
3,487,967 = (87967) The 7 rounds up so the 8 would become 9.
a store normally sells windows at $100 each. This week the store is offering one free window for each purchase of 4. Dave needs 7 windows and Doug needs 8. How much money will they save if they purchase together rather than separately?
Answers
They will save $100 if they purchase together rather than separately.
If this week, the store is offering one free window for each purchase of 4, then the price of 5 windows will be just equal to the price of 4.
1 window = $100
5 windows = 4 x $100 = $400
If
Dave needs 7 windows
Doug needs 8 windows
total they need together = 7+8 = 15 windows.
Buying at the offer of $400/5 windows,
they should buy 3 sets of 5 windows.
3 x 5 = 15
cost when bought together : 3 x $400
cost when bought together : $1200
If they bought separately,
Dave : 7 = 5 + 2
cost = $400 + 2($100)
cost = $600
Doug : 8 = 5 + 3
cost = $400 + 3($100)
cost = $700
cost when bought separately : $600 + $700
cost when bought separately : $1300
compare the two total costs and to determine how much they will save.
$1300 - $1200 = $100
They will save $100 if they purchase together rather than separately.
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question 15(multiple choice worth 1 points) (03.02 lc) abcd is a rectangle. what is the value of x? rectangle with length 56 m, width x m, and diagonal 65 m 9 meters 28 meters 33 meters 65 meters
Answers
The width of the rectangle is: 33m, by Pythagoras theorem.
What is Pythagoras Theorem?The Pythagorean Theorem describes a fundamental relationship between a right triangle's three sides in Euclidean geometry. According to this statement, the areas of the squares on the other two sides add up to the size of the square whose side is the hypotenuse.Now,
given:
Length of rectangle = 56m (say, l)Diagonal = 65m (say, d)TO find: Width of rectangle = ? (say, w)
Finding:
BY Pythagoras theorem, in the rectangle ABCD,
For l = AB, w = BC and d = AC,
=> l² + w² = d²
Ob substituting the values, we get: 56² + w² = 65²
=> w² = 65² - 56²
=> w² = 4225 - 3136
=> w² = 1089
=> w = 33m
Hence, for the given values of rectangle, the width of the rectangle is 33m by Pythagoras Theorem.
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8 as a product of three primes
Answers
Answer: 2x2x2 or 2 cubed
Step-by-step explanation: 2x2=4 2x4=8
URGENT!! ILL GIVE BRAINLIEST! 100 POINTS
Maria wanted to bring back 5 million grams of sand from her trip to the beach. Each grain of sand weighs approximately 6.7 x 10^-7 kg. How heavy is the bag of sand that Maria brings home?
Answers
Answer:
3.35kg
Step-by-step explanation:
Answer:
Multiply (5,000,000 x 6.7 x 10^-7) = (5 x 10^6) x (6.7 x 10^-7) = (5 x 6.7) x (10^(6 + - 7)) = 33.5 x 10^-1 = 3.35 kg
Step-by-step explanation:
multiple choice question. with explanation needed.
Answers
Answer: 4
Step-by-step explanation:
A projectile with an initial velocity of 48 feet per second is launched from a building 190 feet tall. the path of the projectile is modeled using the equation h(t) = â€""16t2 48t 190.approximately when will the projectile hit the ground?1.5 seconds3.2 seconds5.3 seconds6.2 seconds
Answers
The time for the projectile to hit the ground from the given position is 1.5 s, which is obtained using the concept of time period and velocity of a projectile.
What is a projectile?
A projectile is defined as an object that has the force of gravity as the only force occurring on it. Acceleration in the projectile motion always acts vertically.
Calculation of the time taken by projectile to hit the ground
The given parameters:
The starting velocity of the projectile, u = 48 ft / s
Height of the projectile, h = 190 ft
Model of the projectile path, h(t) = - 16(t)2 + 48t + 190 —-- 1
When the projectile hits the ground, the final velocity, v = 0
differentiating equation 1 w.r.t t, we get,
(dh(t)) / (dt) = - 32t + 48
Putting dh(t) / dt = 0, we have,
- 32t + 48 = 0
32t = 48
t = 48 / 32
t = 1.5 s
Hence, the time taken by the projectile to hit the ground is 1.5 s.
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hello ! how's you're day, I hope it's doing good Im proud of ur work !
Answers
Answer:
thanks, I needed That
Step-by-step explanation:
brainliest
b. Find the change in temperature if the temperature rises from -18°F to 15°F.
Answers
The change in temperature is 33°F.
According to the question we have been given that there are two temperature readings which are, -18°F and 15°F.
We need to find the change in temperature that is we need to find the difference. And for that we will use distance formula.
The formula to find the distance between the two numbers p and q is
= |p-q|
Here , p = -18°F and q = 15°F
Putting the required values in the above formula we get
= |-18 - 15| °F
= |-33| °F
= 33°F
Hence the change in temperature is 33°F.
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Find the coordinates of the centroid of the triangle with the given vertices. (Lesson 5-2)
X(-11,0), Y(-11,-8), Z(-1,-4)
Answers
The triangle with vertices located at X(-11 , 0), Y(-11 , -8), and Z(-1 , -4) has its centroid located at (-23/3 , -4).
The centroid of a triangle is the point inside the triangle where the three medians intersect. The median of a triangle is the line the connects the midpoint of a side and the opposite vertex.
To get the centroid of a triangle, use the formula given by:
C(x , y) = [(x1 + x2 + x3)/3 , (y1 + y2 + y3)/3]
where C is the centroid of the triangle located at (x , y)
x1, x2, and x3 are the x-coordinate of the vertices of the triangle
y1, y2, and y3 are the y-coordinate of the vertices of the triangle
Let Point 1(x1 , y1) = X(-11 , 0)
Point 2(x2 , y2) = Y(-11 , -8)
Point 3(x3 , y3) = Z(-1 , -4)
Plug in the values in the formula.
C(x , y) = [(x1 + x2 + x3)/3 , (y1 + y2 + y3)/3]
C(x ,y) = [(-11 + -11 + -1)/3 , (0 + -8 + -4)/3]
C(x ,y) = (-23/3 , -12/3)
C(x ,y) = (-23/3 , -4)
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Algebra 1
1.1 Evaluating Expressions
Evaluate each using the values given.
1) z−5+ x; use x = 1, and z = -3
Answers
Evaluating Expressions-
z−5+ x= -7
x = 1, and z = -3
z−5+ x=-3 + (-5) + 1
= -3-5+1=-7
to assess an algebraic expression way to find the price of the expression while the variable is changed by using a given range.
to evaluating expression, we replacement the given range for the variable within the expression and then simplify the expression the use of the order of operations
What does “Evaluating Expressions” suggest?
Simplification of expressions can be performed with the help of operations’ order. It consists of changing the variable to discover the expression’s fee. The given number is substituted to evaluate expressions. After this, one needs to simplify it primarily based at the order of the operations
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Tanisha and some friends are going to the movies. At the theater, they sell a bag of
popcorn for $5.50 and a drink for $4. How much would it cost if they bought 4 bags
of popcorn and 6 drinks? How much would it cost if they bought p bags of popcorn
and d drinks?
Answers
Hope this helps!
which of the following statements is not correct? fewer students in the sample listed volleyball as their favorite sport than football. more students in the sample listed lacrosse as their favorite sport than basketball. more students in the sample listed basketball as their favorite sport than volleyball. the highest percentage of teenagers in the sample listed soccer as their favorite sport.
Answers
The highest percentage of teenagers in the sample listed soccer as their favorite sport. this option is correct .
What does a statistical pie chart mean?
A pie chart, often known as a circle chart, is a visual representation of the various values of a specific variable or a means to summarize a set of nominal data (e.g. percentage distribution). This kind of chart consists of a circle with numerous segments. A certain category is represented by each segment.Pie charts are circular charts with segments that each indicate a value and are used in data handling. Pie charts have portions (or "slices") that depict varying sizes of values. For instance, an entire class is represented by the circle in this pie chart.In this question pie chart is showing data of games .
So. by observing the chart we can say that ,
the highest percentage of teenagers in the sample listed soccer as their favorite sport.
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