The cost of one bag of pretzel is $ 1.80
The cost of one bag of granola bars is $ 3.15
What is an Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the cost of one pretzel be represented as x
Let the cost of one granola bar be represented as y
Now , the equation will be
4 bags of pretzels and 2 boxes of granola bars for $13.50
Substituting the values in the equation , we get
4x + 2y = 13.50 be equation (1)
And , 1 bag of pretzels and 5 boxes of granola bars for $17.55
Substituting the values in the equation , we get
x + 5y = 17.55 be equation (2)
Multiply equation (2) by 4 , we get
4x + 20y = 70.2 be equation (3)
Subtracting equation (1) from equation (2) , we get
18y = 56.70
Divide by 18 on both sides of the equation , we get
y = $ 3.15
So , the cost of one granola bar is $ 3.15
Substituting the value of y in equation (1) , we get
4x + 2 ( 3.15 ) = 13.50
4x + 6.30 = 13.50
Subtracting 6.30 on both sides of the equation , we get
4x = 7.20
Divide by 4 on both sides of the equation , we get
x = $ 1.80
So , the cost of one pretzel is $ 1.80
Hence , the equations are solved
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What is the domain of f(x) = 5x – 7?
{x | x > –7}
{x | x < –7}
{x | x > 0}
{x | x is a real number}
Answer:
{x:x is a real number}
Since any value can replace x to give an integer.
{x:x is a real number}
N a carton of a dozen eggs of which four are cracked, how many ways could you select 3 cracked and 2 good if you randomly select 5 eggs
The number of ways we can select 3 cracked and 2 good is 1200 ways.
Given there are 5 eggs in which 3 eggs are cracked and 2 eggs which are good.
We have to find the number of ways we can select 3 cracked and 2 good eggs from 5 eggs.
Number of ways can be found through permutations.
The factorial of n equals the product of n with the smaller factorial..
Permutations is the technique of calculating various ways in which objects from a set may be selected, generally without replacement, to form subsets.
n[tex]P_{r}[/tex]=n!/(n-r)!
So the number of ways will be 5[tex]P_{3}[/tex]*5[tex]P_{2}[/tex]
([tex]5P_{3}[/tex] for cracked eggs and [tex]5C_{2}[/tex] for good eggs)
=5!/(5-3)!*51/(5-2)!
=5*4*3*2!/2!*5*4*3!/3!
=5*4*3*5*4
=1200
Hence there are 1200 ways through which 3 cracked and 2 good eggs can be selected from 5 eggs.
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The table represents a linear function.
A two column table with six rows. The first column, x, has the entries, negative 2, negative 1, 0, 1, 2. The second column, y, has the entries, negative 2, 1, 4, 7, 10.
What is the slope of the function?
–3
–2
3
4
The slope of given data is a -3.
According to the statement
we have given a some data and we have to find the slope of the data.
So, data given is:
x, has the entries, negative 2, negative 1, 0, 1, 2.
y, has the entries, negative 2, 1, 4, 7, 10.
and we have to find the slope of the data
So, we know that it is a data represent in the graph then
We know that a there is a graphical representation of data.
A graph is the representation of the data on the vertical and horizontal coordinates so we can see the trend of the data.
And when we observe this data then we see that the there is some increase the y axis value as compare to the x axis values.
So,
For each unit of run in the x-values, there is an increase of 3 in the y-values. The slope is rising over Run so 3/1 = 3
So, The slope of given data is a -3.
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Answer: the answer is a -3
Step-by-step explanation:
What is the total surface area of a regular square based pyramid which has a slant height of 10 units and base side lengths of 6 units?
360 square inches
420 square inches
216 square inches
200 square inches.
168 square inches.
The total surface area of a regular square pyramid having slant height of 10units and base length of 6 units is 168 square inches which is fifth option.
Given that slant height is 10 units and base lengths of 6 units.
We are required to calculate total surface area of regular square pyramid.
We know that total surface area of regular square based pyramid is equal to [tex]s^{2} +s\sqrt{s^{2} +4h^{2} }[/tex] in which s is side of base length and h is slant height of regular square pyramid.
Total surface area=[tex]6^{2} +6\sqrt{6^{2} +4*10^{2} }[/tex]
=36+6[tex]\sqrt{36+400}[/tex]
=36+6[tex]\sqrt{436}[/tex]
=36+6*20.88
=36+125.28
=161.28
Nearest option is 168 square inches.
Hence the total surface are of regular square based pyramid is option 5 which is 168 square inches.
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If B P ⊥ P C , what is m B C ^ ? 180 90 60
The measure of angle BC (m ∠BC) is 90°
Perpendicular linesFrom the question, we are to determine the measure of angle BC
From the given information, we have that
B P ⊥ P C
This means line BP is perpendicular to line PC
The angle between two perpendicular lines is 90°
Hence, the measure of angle BC (m ∠BC) is 90°.
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5. You are a game manufacturer. You and your team are trying to
find the best pair of dice for a new board game you have made. You
are examining the possible results of using one 6-sided die and
one 10-sided die and rolling them together. If the random variable
is defined as the sum of the two dice when rolled, which of the following
values are included in the random variable?
0
16
1
14
10
17
All of the above
The values that are included in the random variable of the experiment that include rolling one 6-sided die and one 10-sided die are 10, 14 and 16
How to determine the values in the random variable?The experiment elements are given as:
One 6-sided dieOne 10-sided dieThe sample spaces of both dice are:
6-sided = {1, 2, 3...., 6}
10-sided = {1, 2, 3...., 10}
When the outcomes of both dice are added, we have:
Sample space = {2, 3, 4, 5, 6, 7, 8, 9, .............. 16}
Minimum = 2
Maximum = 16
This means that the values that are included in the random variable are in the range 2 - 16 i.e. starting from 2 and ending in 16
Hence, the values that are included in the random variable of using one 6-sided die and one 10-sided die and rolling them together are 10, 14 and 16
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Whales evolved in the early Cambrian and include transitional species such as Kutchicetus and Rodhocetus.
False, Whales evolved in the early Cambrian and include transitional species such as Kutchicetus and Rodhocetus.
What animals evolved during Cambrian period?
Animals include, from left: Dinomischus, Ottoia, Halucinoginia, Wiwaxia, Trilobites, Archeocyathans, Microdictyon, Canadia, and Pikia. Two larger Anomolocarus are seen in the distant background.When did animals evolve in the Cambrian?
The Cambrian explosion happened more than 500 million years ago. It was when most of the major animal groups started to appear in the fossil record, a time of rapid expansion of different forms of life on Earth.What long lived group of arthropods went extinct at the end of the Permian?
The trilobites, a group of extinct arthropods, as well as the closely related eurypterids, first appeared in the Permian. The Paleozoic Era saw the extinction of rugose and tabulate corals.Learn more about Cambrian animals evolved.
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The complete question is -
True or false . Whales evolved in the early Cambrian and include transitional species such as Kutchicetus and Rodhocetus.
Study the following data set.
{8,15,9,18,9,17,22,10,11,9,13}
What is the quarterfinal range of the data set?
The interquartile range of the data set is 8
How to solve for the interquartile rangeTo do this we have to arrange in ascending order
= 8,9,9,9,10,11,13,15,17,18,22
Q2 = The median of the data is 11.
We have to find the median of the half before 11 and the median of the half after 11.
We would have
8,9,9,9,10
Q1 = 9
And 13,15,17,18,22
Q3 = 17
The interquartile range is
Q3 - Q1
= 17 - 9
= 8
The interquartile range of the data set is 8
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Correct question
Study the following data set.
{8,15,9,18,9,17,22,10,11,9,13}
What is the interquartile range of the data set?
A super sundae ice cream cone has a radius of 0. 5 in and a depth of 4 in. A wonderful waffle cone has a radius 0. 9 in and a depth of 3 in. Which cone holds more ice cream?
The wonderful waffle cone holds more ice cream than super sundae cone.
In this question,
The ice cream cone is the shape of hemisphere at the top and cone shape at the bottom.
Volume of ice cream cone = volume of hemisphere + volume of cone
Volume of ice cream cone = [tex]\frac{2}{3}\pi r^{3} +\frac{1}{3} \pi r^{2} h[/tex]
Volume of super sundae cone:
Radius of hemisphere = height of hemisphere = 0.5 in
Depth of the ice cream cone = 4 in
Volume of super sundae cone = [tex]\frac{2}{3}\pi (0.5)^{3} +\frac{1}{3} \pi (0.5)^{2} (4)[/tex]
⇒ [tex]\frac{2}{3}(3.14)(0.125) +\frac{1}{3} (3.14)(0.25)(4)[/tex]
⇒ 0.2616+1.0466
⇒ 1.3082 ≈ 1.31 cubic in.
Volume of wonderful waffle cone:
Radius of hemisphere = height of hemisphere = 0.9 in
Depth of the ice cream cone = 3 in
Volume of wonderful waffle cone = [tex]\frac{2}{3}\pi (0.9)^{3} +\frac{1}{3} \pi (0.9)^{2} (3)[/tex]
⇒ [tex]\frac{2}{3}(3.14)(0.729) +\frac{1}{3} (3.14)(0.81)(3)[/tex]
⇒ 1.526+2.5434
⇒ 4.0694 ≈ 4.07 cubic in.
Thus volume of wonderful waffle cone > volume of super sundae cone.
Hence we can conclude that the wonderful waffle cone holds more ice cream than super sundae cone.
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Tyler's playlist has 36 songs. Noah’s playlist has one quarter as many songs as Tyler's playlist. How many songs are on Noah’s playlist?
Answer: 9
Step-by-step explanation:
Answer:
9 songs
Step-by-step explanation:
a quarter is basically a fourth of a number so you need to just divide the number by four
I NEED THE ANSWER TO D please provide
Answer:
y = 2/5x -4
Step-by-step explanation:
Point-Slope Form formula
y - y1 = m (x - x1)
slope = m = 2/5
(-5, -6)
y - -6 = 2/5 (x - -5)
y + 6 = 2/5x + 2
y = 2/5x - 4
patrickJMT
Use Newton's method to approximate the zero of the function f(x)=x^3-4x+33 to five decimal places. Round any intermediate calculations, if needed, to no less
than six decimal places, and round your final answer to five decimal places.
A rectangular swimming pool with a length of 18m and width of 8m is surrounded by a concrete patio. The patio is a uniform 3m width around the entire pool. What is the area of the patio
The area of the patio is 192 [tex]m^{2}[/tex]
What is area?An object's area is how much space it takes up in two dimensions. It is the measurement of the quantity of unit squares that completely cover the surface of a closed figure. The square unit, which is frequently expressed as square inches, square feet, etc., is the accepted unit of area.
The word "area" refers to a free space. A shape's length and width are used to compute its area.
Length of swimming pool=18 m
Width of swimming pool=8 m
Area of swimming pool= 18*8 = 144[tex]m^{2}[/tex]
Width of patio=3m
Total length of swimming pool=18+2(3)=24 m
Total width of swimming pool=8+2(3)=14 m
Total area=24*14=336 [tex]m^{2}[/tex]
Area of patio= total area - Area of swimming pool
=336-144
=192 [tex]m^{2}[/tex]
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please help! Which system of inequalities represented by the graph?
Answer: B
[tex]x + 2y \leq 4 \textrm{ and } 3x + y \leq 4[/tex]
Step-by-step explanation:
Insert the values of x and y for any point in the heavily shaded region and see if it satisfies both inequalities
We can see that the origin (0,0) is inside the shaded region so use these values because they are the easiest to compute
Plug in x = 0 and y = 0 into the first inequality
0 + 2.0 = 0 which is greater than 5.
So we can eliminate both A and D since they both contain incorrect inequalities
Now, test the second inequality with x = 0 and y = 0
For B we get
3.0 + 0 = 0 which is indeed less than 4
C is not applicable since 0 is not greater-than-equal to 4
Hence B is the correct solution
This can be verified using a graphing tool (see image)
A certain quadratic function has the factors
3,
(x+2)，
and
(x - 5)
. What are the zeros of this function?
a. x=2 and x=-5
b. x=2, x=5, and x=-3
c. x=-2 and x=5
d. x=-2, x=5, and x=3
[tex]f(x) = 3(x + 2)(x - 5)[/tex]
[tex]solving \: f(x) = 0 \\ 3(x + 2)(x - 5) = 0 \\ (x + 2)(x - 5) = \frac{0}{3} \\ (x + 2)(x - 5) = 0 \\ x + 2 = 0 \: \: \: \: \: \: \: \: \: \: x - 5 = 0 \\ x = - 2 \: \: \: \: \: \: \: \: \: \: x = + 5[/tex]
Option CFind the perimeter of the triangle whose coordinates are A (2, 2), B (3, 3), and C (4, 2)
The perimeter of the triangle whose coordinates are A (2, 2), B (3, 3), and C (4, 2) is 4.828
Finding the perimeter of a triangle with vertices?We can determine the perimeter of a triangle with vertices by utilizing the distance formula.
Given that, we have the vertices (x₁,y₁), (x₂, y₂), (x₃, y₃). Then the length of each sides can be expressed as follows:
SIde AB = [tex]\mathbf{\sqrt{(x_1 -x_2)^2 +(y_1 -y_2)^2}}[/tex]
Side AC = [tex]\mathbf{\sqrt{(x_1 -x_3)^2 +(y_1 -y_3)^2}}[/tex]
Side BC = [tex]\mathbf{\sqrt{(x_2 -x_3)^2 +(y_2 -y_3)^2}}[/tex]
Replacing the values of the coordinates into the given formula above the perimeter of the triangle is 4.828
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The diameters of bolts produced in a machine shop are normally distributed with a mean of 5.34 millimeters and a standard deviation of 0.03 millimeters. Find the two diameters that separate the top 8% and the bottom 8%. These diameters could serve as limits used to identify which bolts should be rejected. Round your answer to the nearest hundredth, if necessary.
Using the normal distribution, we have that:
The diameter that separates the top 8% is of 5.38 mm.The diameter that separates the bottom 8% is of 5.30 mm.Normal Probability DistributionThe z-score of a measure X of a normally distributed variable with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The z-score measures how many standard deviations the measure is above or below the mean. Looking at the z-score table, the p-value associated with this z-score is found, which is the percentile of X.The mean and the standard deviation for this problem are given, respectively, by:
[tex]\mu = 5.34, \sigma = 0.03[/tex]
The 8th percentile separates the bottom 8%, that is, X when Z = -1.405, hence:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]-1.405 = \frac{X - 5.34}{0.03}[/tex]
X - 5.34 = -1.405 x 0.03
X = 5.30.
The 92th percentile separates the top 8%, that is, X when Z = 1.405, hence:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]1.405 = \frac{X - 5.34}{0.03}[/tex]
X - 5.34 = 1.405 x 0.03
X = 5.38.
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At a coffee shop, the manager recorded the number of customers who visited the store at the end of each hour. The graph shows the recordings for a 24-hour period. The function describing this graph is a transformation of the parent sine function, y=sin(x)
Which value is closest to the amplitude of the transformed function?
O 83 customers
O 27 customers
O 54 customers
O 30 customers
Answer:
Step-by-step explanation:
The amplitude of a sine function is equal to one-half the distance between the maximum and minimum values of the function.
In this case, the maximum value is approximately 84 customers, and the minimum value is approximately 30 customers
Therefore, the value that is closest to the amplitude of the transformed function is 27 customers.
One of the criticisms of the Social Readjustment Rating Scale is that it does NOT take into account:
What is one major limitation of the Social Readjustment Rating Scale?
The Social Readjustment Rating Scale has severe limitations, despite being a helpful tool for the research of life transition and disease. The current measure cannot be used to assess the impact of various life changes (such as positive or negative ones) on the development of sickness.Learn more about Social Readjustment Rating Scale brainly.com/question/13044228
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Find the sum. express the answer in scientific notation. (1.54 times 10 superscript 6 baseline) (6.15 times 10 superscript 6 baseline) 7.69 times 10 superscript 6 9.471 times 10 superscript 6 7.69 times 10 superscript 12 9.471 times 10 superscript 12
The sum of the numbers is 7.69 * 10^6
How to evaluate the sum?The expression is given as:
(1.54 times 10 superscript 6 baseline) (6.15 times 10 superscript 6 baseline)
Rewrite properly
(1.54 * 10^6) + (6.15 * 10^6)
Factor out 10^6
(1.54 + 6.15) * 10^6
Evaluate the sum
7.69 * 10^6
Hence, the sum of the numbers is 7.69 * 10^6
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Answer:
a
Step-by-step explanation:
Find the sum. Express the answer in scientific notation.
(1.54 times 10 Superscript 6 Baseline) + (6.15 times 10 Superscript 6 Baseline)
7.69 times 10 Superscript 6
9.471 times 10 Superscript 6
7.69 times 10 Superscript 12
9.471 times 10 Superscript 12
What is quadratic equations by factoring
The concept of factoring quadratic equations simply is one of the ways to solve for the zeroes of the quadratic equation.
What is quadratic equations by factoring?The concept of factoring quadratics is a technique which is characterized by expressing the quadratic equation ax2 + bx + c = 0 as a product of its associated linear factors as (x - f)(x - g), in which case, f and g are the roots of the quadratic equation ax2 + bx + c = 0.
Factoring is an important concept that helps express equations of any type in simpler forms The mode of operation of the factoring works such that, the polynomial is rewritten in a simpler form and consequently, expressed as a product of it's linear factors.
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Write a function of the geometric sequence with a starting term of 8 and a common ratio of 2. Find the fourth term.
The expression that represents well the geometric sequence is [tex]f(n) = 8 \cdot 2^{n-1}[/tex] and the value of the fourth term is 64. (Correct choice: B)
How to analyze geometric sequencesGeometric sequences are exponential expressions with discrete domain, whose form is presented and explained below:
[tex]f(n) = a \cdot r^{n-1}[/tex], where a, r are real numbers and n is a natural number. (1)
Where:
Value of the starting term.Common ratio of the series.According to the statement, we know that the first term of the geometric sequence is 8 and between any two consecutive terms there is a common ratio of 2. If we know that a = 8, r = 2 and n = 4, then the fourth term of the series by means of (1) is:
[tex]f(4) = 8 \cdot 2^{4-1}[/tex]
f(4) = 8 · 8
f(4) = 64
The expression that represents the geometric sequence is [tex]f(n) = 8 \cdot 2^{n-1}[/tex] and the value of the fourth term is 64.
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Find the lateral surface area of the
following prism:
5 cm
5 cm
apothem = 3.44 cm
cm
5 cm
10 cm
5 cm
LSA = [?] cm2
The laterals surface area of the given hexagonal prism is: 250 cm².
How to Find the Lateral Surface Area of Hexagonal Prism?Lateral surface area = 5ah, where:
a = edge length of the baseh = height of the prism.Given the following:
a = 5 cm
h = 10 cm
Lateral surface area of the hexagonal prism = 5ah = 5(5)(10)
Lateral surface area of the hexagonal prism = 250 cm²
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A scale model of a rectangular building lot measures 7 feet by 5 feet. If the actual house will be built using a scale factor of 12, what is the area of the actual building lot?
The area of the actual building lot is 5040 square ft
Scale factorsThis factors are used to enlarge or diminish the given figure. Given the scale model of a rectangular building lot measures 7 feet by 5 feet. If the actual house will be built using a scale factor of 12, the new length and width is expressed as:
Length = 12 * 7 = 84ft
Width = 5*12=60 ft
Determine the area
Area = 84 * 60
Area = 5040 square feet
Hence the area of the actual building lot is 5040 square ft
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PLEASE HELP
If BC DA, then which segment is the shortest side?
The length of the shortest side is DC
How to determine the shortest side?As a general rule in triangle;
The smallest angle in a triangle is opposite the shortest side.
Similarly, the largest angle in a triangle is opposite the largest side.
From the given figure of triangles, the smallest angle is angle CBD with a measure of 47 degrees.
The side opposite this angle is side length DC
Hence, the length of the shortest side is DC
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A piece of PVC material weighs 0.063 pounds per cubic inch. What's the weight of a 36-inch piece of PVC pipe with an outside diameter of 0.82 inches and an inside diameter of 0.75 inches?
The weight of a 36-inch piece of PVC pipe is 0.20 pounds
How to determine the weight of a 36-inch piece of PVC pipe?The given parameters about the 36-inch piece of PVC pipe are
Height, h = 36 inches
Outside diameter, D = 0.82 inches
Inside diameter, d= 0.75 inches
The volume of the PVC pipe is then calculated as:
V = πh(D/2)^2 - πh(d/2)^2
Substitute the known parameters in the above equation
V = 3.14 * 36 * (0.82/2)^2 - 3.14 * 36 * (0.75/2)^2
Evaluate the quotients
V = 3.14 * 36 * 0.41^2 - 3.14 * 36 * 0.375^2
Evaluate the exponents
V = 3.14 * 36 * 0.1681 - 3.14 * 36 * 0.140625
Evaluate the products
V = 19.002024 - 15.89625
Evaluate the difference
V = 3.105774 cubic inches
From the question, we have:
Weight = 0.063 pounds per cubic inch
So, the total weight is
Total weight = 3.105774 cubic inches * 0.063 pounds per cubic inch
Evaluate the product
Total weight = 0.195663762 pounds
Approximate
Total weight = 0.20 pounds
Hence, the weight of a 36-inch piece of PVC pipe is 0.20 pounds
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What is an appropriate display to show the spread of 150 test scores for Mrs. Hansen's last science test?
(ignore my answer, i didn't mean to click it)
The appropriate display to show the spread of 150 test scores for Mrs. Hansen's last science test is: b. box and whisker plot.
What is box and whisker plot?Box and whisker plot which is also called box plot can be defined as the plot that show a graphical presentation of data set by helping to display the data set or data score .
Hence a graphical presentation display to show the spread of 150 test scores for Mrs. Hansen's last science test is option B which is Box and whisker plot .
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Using the diagram below, what is the measure of ZE?
A. 130°
B. 50°
C. 65°
D. 25°
Given: 1. ACAB-ACED
2. AB ED
1 mile = 5280 ft
The measure of angle E is (b) 50°
How to determine the angle measure?The given parameters are:
ΔCAB is similar to ΔCEDAB and ED are parallelThe similarity of the triangles implies that:
angle C = angle Cangle A = angle Eangle B = angle DFrom the figure, we have:
angle A = 50
Substitute angle A = 50 in angle A = angle E
angle E = 50
Hence, the measure of angle E is (b) 50°
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Prove by induction:
5| (21^n+9)
It's kind of self-evident. Any power of 21 will have a 1 in the units place, and adding 9 to it makes it 0 and hence the number is divisible by 5.
To prove the claim by induction, first establish the base case. I assume [tex]n\in\Bbb N[/tex], so for [tex]n=1[/tex] we have
[tex]21^1 + 9 = 21 + 9 = 30[/tex]
and of course 30 = 5×6 is divisible by 5.
Assume the claim is true for [tex]n=k[/tex], that [tex]5 \mid 21^k + 9[/tex]. This means that for some integer [tex]\ell[/tex], we can write
[tex]21^k + 9 = 5\ell[/tex]
Now the induction step: when [tex]n=k+1[/tex], we have
[tex]21^{k+1} + 9 = \bigg(21\times(21^k + 9) - 9\times21\bigg) + 9 \\\\ ~~~~~~~~~~~~~~ = 21\times5\ell - 9\times20 \\\\ ~~~~~~~~~~~~~~= 5\times(21\ell - 9\times4)[/tex]
which is divisible by 5. QED
Can someone help me with this problem pleaseee having a lot of trouble doing this!!!
1003 more square feet of wallpaper for the living room than the family room when family room is with dimensions (l = 3x, b = 3x, h = x), living room is with dimensions (l = 5x, b = 3x, h = x) and doors are with dimension (b =3, h = 7) {where x = 8}. This can be obtained by forming equations for the given figures.
What is the expression of square feet of wallpaper for family room?Given that,
dimensions (l = 3x, b = 3x, h = x) and there is one door (b =3, h = 7)
expression of square feet of wallpaper for family room,
⇒ area of four walls - area of one door= [(3x)(x)+(3x)(x)+(3x)(x)+(3x)(x)] - [3×7]
=[3x²+3x²+3x²+3x²] - 21
=12x² - 21 square feet
What is the expression of square feet of wallpaper for living room?
Given that,
height and width are same as of the family room but length is 5 times more than height [length = 5(height) ⇒ l = 5x]
dimensions (l = 5x, b = 3x, h = x) and there is two doors (b =3, h = 7)
expression of square feet of wallpaper for family room,
area of four walls - area of two doors= [(3x)(x)+(5x)(x)+(3x)(x)+(5x)(x)] - 2[3×7]
=[3x²+5x²+3x²+5x²] - 2(21)
=16x² - 42 square feet
What is the total amount of wallpaper needed?
total amount of wallpaper needed
⇒wallpaper for family room + wallpaper for living room = 12x²-21 + 16x²-42
=28x²-63 square feet
How much more square feet the living room will require more than family room when x = 8?Family room ⇒ 12x²-21 = 12(8²)-21 = 768-21=747 square feet Living room ⇒ 16x²-42 = 16(8²)-42 = 1792-42 = 1750 square feet
Area of wallpaper of living room - area of wallpaper of family room
= 1750 - 747
= 1003 square feet
Hence 1003 more square feet of wallpaper for the living room than the family room when family room is with dimensions (l = 3x, b = 3x, h = x), living room is with dimensions (l = 5x, b = 3x, h = x) and doors are with dimension (b =3, h = 7) {where x = 8}.
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