Yasmin has some identical rectangular tiles.
Each tile is L’cm by W'cm.
Using 9 of her tiles, Yasmin makes rectangle ABCD, shown in the diagram below.
Diagram NOT
accurately drawn
The area of ABCD is 1620 cm²
Work out the value of L and the value of W.
B
Diagram NOT
accurately drawn
Answers
The dimensions L and W, considering the area of the rectangle, are given as follows:
L = 6.1 cm.W = 4.9 cm.How to obtain the area of a rectangle?The area of a rectangle of dimensions L and W is given by the multiplication of these dimensions, as follows:
Considering the image shown at the end of the answer, with the composition of the smaller rectangles, the dimensions of the large rectangle are given as follows:
Width: 5W = 4L.Length: L + W.Hence the expression for the area of the rectangle is given as follows:
5W(L + W) = 1620.
From the width relation, we have that:
5W = 4L
W = 0.8L.
Hence the length is obtained as follows:
5W(L + W) = 1620.
5 x 0.8L(L + 0.8L) = 1620
7.2L³ = 1620
L = (1620/7.2)^(1/3) -> cubic root
L = 6.1 cm.
W = 0.8L = 0.8 x 6.1 = 4.9 cm.
Missing InformationThe problem is given by the image shown at the end of the answer.
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Related Questions
arch
Convert the following equation
into slope-intercept form.
-8x + y = -9
0
y = [? ] x + [
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Enter
0
Answers
The slope-intercept form of the given equation is y = 8x - 9
What is slope intercept form?
Using a straight line's slope and the location of its y-axis intersection, the slope-intercept equation can be used to determine the general equation of the line. Y = mx + b is the equation in slope-intercept form.
The slope-intercept form is y=mx+b, where
m is the slope and
b is the y-intercept.
Here, we have
Given equation = -8x + y = -9
Rewrite in slope-intercept form.
Add 8x on both sides of the equation and we get
y = -9 + 8x
y = 8x - 9
Hence, the slope-intercept form of the given equation is y = 8x - 9
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A 4-pint carton of soy milk costs $0.96. What is the price per cup?
Answers
The cost of per cup milk cartons is $ 0.24
Given price of a 4 pint carton = $ 0.96
thus to calculate the price of 1 carton
we would have to use unitary method
in unitary method ,
the cost of multiple or the cost of an item is given and we are supposed to find the cost of a single or multiple items respectively.
Here since the cost of 4 pint cartons are given
we will find the cost of 1 carton by dividing :
the cost of 4 pint cartons / number of cartons
thus we will get 0.96/4 = $ 0.24
Thus the cost of 1 carton is $ 0.24
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Elisa is driving at a speed of 65 miles per hour. Let h represent the number of hours that Elisa drives at this speed. Write an algebraic expression to represent the number of miles that Elisa travels during this time.(I NEED HELP NOW , I AM IN RISK OF A WHOOPING)
Answers
We have
Elisa travels 65 miles per hour
h is the number of hours
the al
What is the value of the expression below? 64 + 16 A. 4 C. - 4 B. 1 D. 8
Answers
We want to find the value of the expression:
[tex]\frac{64}{16}[/tex]Since 2 is a common factor of both numerator and denominator, we divide by 2s:
[tex]\frac{64}{16}=\frac{32}{8}=\frac{16}{4}=\frac{8}{2}=\frac{4}{1}=\text{ 4}[/tex]The answer is 4. (Option A)
The tree diagram below represents the relationships between the sets and subsets of real numbers. Real Numbers Rational Numbers {..., V2, e, , ...) ? Non-integer Rational Numbers {0, 1, 2, 3, ---) Whole Number Opposites Which group of numbers could replace the question mark in the tree diagram
Answers
The diagram starts with Real Numbers which comprehend all numbers except for complex numbers.
The second level is formed by rational numbers and irrational numbers.
The third level is formed by subsets of rational numbers non-integers rational numbers and integers rational numbers.
Therefore, the right answer is C. -7, 8, -4, since these numbers are rational and integers.convert 62°F to degree Celsius if necessary round to the nearest 10th of a degreeC=5/9 (F-32)F=9/5 C + 32
Answers
Given the following question:
Using the formula:
[tex]undefined[/tex]Hello, is it possible to help me understand this question a little better?
Answers
1) Since the degree of the denominator is lower than the numerator's we can divide these expressions through long division that way:
As we can see in each step the aim is to cancel the leading coefficient.
2) Note that a Long Division, has a way to write its answer so we can tell that this is the answer:
[tex]\frac{3x^3-4x^2+5x-2}{3x+2}=\quad x^2-2x+3-\frac{8}{3x+2}[/tex]Note that the remainder is written above the divisor on the final answer.
Marks wants to paint a mural. He had 1 1/5 gallons of yellow paint, 1 1/6 gallons of green paint and 7/8 gallon of blue paint. Mark plan to use 3/4 gallons of each paint color. How many gallons of paint will he have left painting the mural?
Answers
Yello paint: 1 1/5
Green paint: 1 1/6
Blue paint: 7/8
After using 3/4 of each paint color, we have
- Yellow:
[tex]\begin{gathered} 1+\frac{1}{5}-\frac{3}{4} \\ \frac{5}{5}+\frac{1}{5}-\frac{3}{4} \end{gathered}[/tex]The least common multiple of 5 and 4 is 20, then...
[tex]\begin{gathered} \frac{5\cdot4}{5\cdot4}+\frac{1\cdot4}{5\cdot4}-\frac{3\cdot5}{4\cdot5} \\ \frac{20}{20}+\frac{4}{20}-\frac{15}{20} \\ \frac{20+4-15}{20} \\ \frac{9}{20} \end{gathered}[/tex]So, for yellow paint, we will have 9/20 gallons
- Green:
[tex]\begin{gathered} 1+\frac{1}{6}-\frac{3}{4} \\ \frac{6}{6}+\frac{1}{6}-\frac{3}{4} \end{gathered}[/tex]The LCM of 6 and 4 is 12
[tex]\begin{gathered} \frac{6\cdot2}{6\cdot2}+\frac{1\cdot2}{6\cdot2}-\frac{3\cdot3}{4\cdot3} \\ \frac{12}{12}+\frac{2}{12}-\frac{9}{12} \\ \frac{12+2-9}{12} \\ \frac{5}{12} \end{gathered}[/tex]So, for green paint, we will have 5/12 gallons
- Blue:
[tex]\frac{7}{8}-\frac{3}{4}[/tex]LCM of 4 and 8 is 8
[tex]\begin{gathered} \frac{7}{8}-\frac{3\cdot2}{4\cdot2} \\ \frac{7}{8}-\frac{6}{8} \\ \frac{7-6}{8} \\ \frac{1}{8} \end{gathered}[/tex]So, for blue paint, we will have 1/8 gallons
Now, we add them upp in order to obtain our anwser:
[tex]\frac{9}{20}+\frac{5}{12}+\frac{1}{8}[/tex]The LCM of 8, 12 and 20 is 120
[tex]\begin{gathered} \frac{9\cdot6}{20\cdot6}+\frac{5\cdot10}{12\cdot10}+\frac{1\cdot15}{8\cdot15} \\ \frac{54}{120}+\frac{50}{120}+\frac{15}{120} \\ \frac{54+50+15}{120} \\ \frac{119}{120} \end{gathered}[/tex]In conclusion, he will have left 119/120 gallons of paint
A pet store has 8 cats, 12 dogs, and 3 rabbits. The ratio 8:23 compares Irby Pets 1 dogs to cats 2 cats to dogs 3 rabbits to cats 4 cats to all animals
Answers
The ratio for each animal between the stores is the divition of pet store with Irby Pets so:
For cats is going to be:
[tex]\frac{8}{2}=4[/tex]So the ratio is 4:1
for dogs is going to be:
[tex]\frac{12}{3}=4[/tex]So the ratio is again 4:1
So the total ratio will be 4:1
If cos A = 35/37 and sin B = 9/41 and angles A and B are in Quadrant I, find the valueof tan(A - B).
Answers
The given expression is tan(A - B)
Since tan (A - B) is equal to
[tex]\tan (A-B)=\frac{\tan A-\tan B}{1+\tan A\tan B}\rightarrow(1)[/tex]Since the values of cos A and sin B are
[tex]\begin{gathered} \cos A=\frac{35}{37} \\ \sin B=\frac{9}{41} \end{gathered}[/tex]We will use the rules
[tex]\begin{gathered} \tan ^2A=\sec ^2A-1\rightarrow(2) \\ \cot ^2B=\csc ^2B-1\rightarrow(3) \end{gathered}[/tex]csc B = 1/sin B, cot B = 1/tan B, sec A = 1/cos A
[tex]\begin{gathered} \csc B=\frac{1}{\frac{9}{41}}=\frac{41}{9} \\ \sec A=\frac{1}{\frac{35}{37}}=\frac{37}{35} \end{gathered}[/tex]Substitute the value of csc B in rule (3) to find cot B
[tex]\begin{gathered} \cot ^2B=(\frac{41}{9})^2-1 \\ \cot ^2B=\frac{1600}{81} \\ \sqrt[]{\cot^2B}=\pm\sqrt[]{\frac{1600}{81}} \\ \cot B=\frac{40}{9} \end{gathered}[/tex]Reciprocal it to find tan B
[tex]\tan B=\frac{1}{\cot B}=\frac{9}{40}[/tex]Substitute the value of sec A in rule (2) to find tan A
[tex]\begin{gathered} \tan ^2A=(\frac{37}{35})^2-1 \\ \tan ^2A=\frac{144}{1225} \\ \sqrt[]{\tan^2A}=\pm\sqrt[]{\frac{144}{1225}} \\ \tan A=\frac{12}{35} \end{gathered}[/tex]Substitute the values of tan A and tan B in rule (1) above
[tex]\begin{gathered} \tan (A-B)=\frac{\frac{12}{35}-\frac{9}{40}}{1+(\frac{12}{35})(\frac{9}{40})} \\ \tan (A-B)=\frac{165}{1508} \end{gathered}[/tex]The value of tan(A - B) is 165/1508
A shirt retails for $22.40. A 10% tax is then applied to the original. What is the final price after tax? $20.16 $24.64 $22.50 $32.40 $22.30
Answers
To solve this question, follow the steps below.
Step 01: Find the value of the tax.
If a tax of 10% is applied, then the tax is:
[tex]\begin{gathered} tax=\frac{10}{100}*22.40 \\ tax=2.24 \end{gathered}[/tex]Step 02: Find the final price.
The final price is the original price + tax.
Then, the final price is:
[tex]\begin{gathered} final\text{ }price=22.40+2.24 \\ final\text{ }price=24.64 \end{gathered}[/tex]Answer: $24.64.
The length of a rectangle is 2 meters less than 3 times the width. The perimeter is 60 meters. Find the width.The width ismeters.
Answers
Step 1
Let x= the width
[tex]3x-2=length[/tex](because the length is 2 meters less than 3 times the width)
Step 2
The perimeter of a rectangle is given as;
[tex]\begin{gathered} P=2length+2width \\ P=2(3x-2)+2x \\ P=60 \end{gathered}[/tex][tex]\begin{gathered} 60=6x-4+2x \\ 60=8x-4 \\ 60+4=8x \\ x=8m \end{gathered}[/tex]Answer;
[tex]Width=8m[/tex]Identify the factors of the expression x^3 +4x^2-16x-64.
Answers
Solution:
Consider the following polynomial:
[tex]x^3+4x^2-16x-64[/tex]By grouping terms, we get that the above polynomial is equivalent to the following expression:
[tex](x^3+4x^2)+(-16x-64)[/tex]Now, we can apply common factor:
[tex]x^2(x^{}+4^{})-16(x+4)[/tex]again, applying a common factor, we get:
[tex](x^2-16)(x+4)[/tex]Note that the left factor is a difference of squares, therefore, the above expression is equivalent to:
[tex](x-4)(x+4)(x+4)[/tex]this is equivalent to:
[tex](x-4)(x+4)^2[/tex]So that, we can conclude that the factors of the given expression are:
[tex](x-4)[/tex]and
[tex](x+4)^{2^{}}[/tex]and we can conclude that:
[tex]x^3+4x^2-16x-64=(x-4)(x+4)^2[/tex]Septima invests $3,000 in an account with an annual interest rate of 5.2% compounded monthly for 3 years.What is the return on investment for Septima's account?16.8%1.3%14.4%5.3%
Answers
Given:
Principal, P=$3000
Interest rate, r=0.052
Years, t=3 years
To find the return amount is compounded monthly:
Using the formula,
[tex]\begin{gathered} A=P(1+\frac{r}{12})^{12t}_{} \\ =3000(1+\frac{0.052}{12})^{12\times3} \\ =3000(1+0.00433)^{36} \\ =3505.30 \end{gathered}[/tex]Hence, the return amount on investment is $3505.30.
In percentage,
The return on investment is,
[tex]\begin{gathered} \frac{3505.3}{3000}\times100=16.84 \\ \approx16.8\text{ \%} \end{gathered}[/tex]Hence, the answer is 16.8%.
You must show your work.
Answers
Using Euler’s formula, how many edges does a polyhedron with 9 faces and 14 vertices have? Thank you
Answers
Solve the Euler's formula above to E (Edges)
[tex]\begin{gathered} \text{Substract 2 in both sides of the equation;} \\ \\ F+V-2=E+2-2 \\ F+V-2=E \\ \\ \text{ Rewrite the equation:} \\ \\ E=F+V-2 \end{gathered}[/tex]Use the given data;
Faces; F=9
Vertices: V=14
[tex]\begin{gathered} E=9+14-2 \\ E=21 \end{gathered}[/tex]The polyhedron has 21 edgesIn summery, explain in your own words the steps to SOLVE for x.
Answers
To solve for x in any specific equation, we need to isolate x in one side of the equation. we can do that by adding, subtracting, multiplying, or dividing by a specific number on both sides of the equation.
For example:
X + 3 = 7
X + 3 - 3 = 7 - 3
X = 4
We solve for x when we subtract 3 on both sides of the equation.
how to determine maximum or maximum point without using a graph
Answers
you could calculate the derivative and equalize it to zero,then you can evaluate the function in the boundary points of the domainand compare them to the ones found in the last step to find the maximum of a given function.
13. Michael found that the difference
between two numbers is 259.
What could the two numbers be?
How did you find the numbers?
Answers
The numbers whose difference are calculated could be 300 and 41
How to determine the two numbers?From the question, we have the following statement that can be used in our computation:
The difference between two numbers is 259
Represent the two numbers with x and y
So, we have the following representation
x - y = 259
Make x the subject of the formula
This gives
x = 259 + y
Assume y is 41
So, we have
x = 259 + 41
Evaluate the sum
x = 300
Hence, the numbers are 300 and 41
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Please help with this . I am really stuck on it.The graph shows how time required to ring up a customer is related to the number of items being purchased.If it takes 80 seconds to ring up a customer, how many items are purchased?
Answers
First, we have to find the slope of the line. Let's use the points (30, 60) and (40, 80). Using the slope formula, we have.
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]Let's replace the points.
[tex]m=\frac{80-60}{40-30}=\frac{20}{10}=2[/tex]Then, we use one point, the slope, and the point-slope formula to find the equation.
[tex]\begin{gathered} y-y_1=m(x-x_1) \\ y-60=2(x-30) \\ y-60=2x-60 \\ y=2x-60+60 \\ y=2x \end{gathered}[/tex]Then, we use this equation to find the items purchased for 80 seconds.
[tex]y=2\cdot80=160[/tex]Therefore, if it takes 80 seconds to ring up a customer, the number of items purchased is 160.1) Find the equation of the line through the points (-2, 5) and (3, 1). Also, graph this line.
Answers
Answer
The equation of the line is
y - 5 = -0.8 (x + 2)
We can then simplify further
y - 5 = -0.8x - 1.6
y = -0.8x - 1.6 + 5
y = -0.8x + 3.4
Explanation
The general form of the equation in point-slope form is
y - y₁ = m (x - x₁)
where
y = y-coordinate of a point on the line.
y₁ = This refers to the y-coordinate of a given point on the line
m = slope of the line.
x = x-coordinate of the point on the line whose y-coordinate is y.
x₁ = x-coordinate of the given point on the line
So, for this, we just need to solve for the slope and use one of the two points given to find the equation of the line.
For a straight line, the slope of the line can be obtained when the coordinates of two points on the line are known. If the coordinates are (x₁, y₁) and (x₂, y₂), the slope is given as
[tex]Slope=m=\frac{Change\text{ in y}}{Change\text{ in x}}=\frac{y_2-y_1}{x_2-x_1}[/tex]For this question,
(x₁, y₁) and (x₂, y₂) are (-2, 5) and (3, 1)
x₁ = -2
y₁ = 5
x₂ = 3
y₂ = 1
[tex]\text{Slope = }\frac{1-5}{3-(-2)}=\frac{-4}{3+2}=\frac{-4}{5}=-0.8[/tex]Recall
y - y₁ = m (x - x₁)
m = slope = -0.8x
(x₁, y₁) = point = (-2, 5)
x₁ = -2
y₁ = 5
y - y₁ = m (x - x₁)
y - 5 = -0.8 (x - (-2))
y - 5 = -0.8 (x + 2)
We can then simplify further
y - 5 = -0.8x - 1.6
y = -0.8x - 1.6 + 5
y = -0.8x + 3.4
Hope this Helps!!!
solve the polynomials in standard form1) y=4x^4+7x^3-2x^3+5x^52) y=(x-3)^2-3(x-4)
Answers
The standard form of a polynomial contains no like terms and the exponents are in descending order (largest to smallest).
[tex]\begin{gathered} y=4x^4+7x^3-2x^3+5x^5 \\ \text{Std Form:} \\ y=5x^5+4x^4+7x^3-2x^3 \end{gathered}[/tex]Question 3 of 5Select the correct answer from each drop-down menu.The graph of function p represents the profit, in dollars, from concert ticket sales when the tickets are sold for x dollars each.
Answers
In order for the concert to make money, the graph must be above the x-axis, because they y-axis represents the profit. This happens in the interval:
[tex](20,120)[/tex]For the concert to lose money, the graph must be below the x-axis. This happens in two intervals:
[tex](0,20)\cup(120,\infty)[/tex]Jessica was just offered a position as the Head Makeup Consultant. As a manager she will not earncommission or overtime. Her starting salary will be $38,500 per year and is based on a 40 hour workweek paid biweeklyDetermine Jessica's hourly rate. Will Jessica earn more as an hourly paid employee or manager?How much more or less? Show work for credit.
Answers
Assuming there are 52 woking weeks in a year (Since it is the standard used by companies). And in week Jessica can have a maximum of 40 hours, we can conclude that;
[tex]\begin{gathered} \text{Hourly rate (H) =}\frac{38,500\text{ per year}}{52\text{ we}eks\text{ per year (40 hours per we}ek\text{)}} \\ \text{Hourly rate (H) = }\frac{38,500}{52(40)} \\ H\text{ = 18.51} \end{gathered}[/tex]Therefore Jessica's hourly rate is $18.51.
And by calculating her salary per year if she is paid hourly, let us again assume that there are 52 working weeks in a year and she works 8 hours per day 5 times a week as the standard working hours. We get;
[tex]\begin{gathered} \text{Yearly Salary (paid by hour) = 18.51/hour x 52 w}eeks\text{ x 8 hours/day x 5 days/w}eek \\ \text{Yearly Salary (paid by hour) = 18.51 x 52 x 8 x 5} \\ \text{Yearly Salar (paid by hour) = 38,500.80} \end{gathered}[/tex]Therefore Jessica's salary per year if she is paid hourly is $38,500.80, so there is a $0.80 difference between her initial salary.
Select the correct choice and fill in the blank if necessary
Answers
Given
[tex]f(x)=\frac{x+6}{x-7}[/tex]Recall
The horizontal line test can be used to determine if a function is one-to-one given a graph. Simply superimpose a horizontal line onto a graph and see if it intersects the graph at more than one point. If it does, the graph is not one-to-one and if it only intersects at one point, it will be one-to-one.
The graph
It passed the horizontal line test, therefore is one to one function
Part B
[tex]f(x)=\frac{x+6}{x-7}[/tex]Step 1
Replace f(x) with y
[tex]y=\frac{x+6}{x-7}[/tex]Step 2
Inter change y and x
[tex]x=\frac{y+6}{y-7}[/tex]Step 3
Make y the subject
[tex]\begin{gathered} x=\frac{y+6}{y-7} \\ x(y-7)=y+6 \\ xy-7x=y+6 \\ xy-y=6+7x \\ y(x-1)=6+7x \\ divide\text{ both sides by x-1} \\ y=\frac{6+7x}{x-1} \end{gathered}[/tex]Step 4
Replace y with f^-1
[tex]f^{-1}(x)=\frac{6+7x}{x-1}[/tex]The final answer
[tex]f^{-1}(x)=\frac{6+7x}{x-1}[/tex]Simple probabilityYou draw a card at random from a deck that contains 3 black cards and 7 red cards.If necessary, round your answer to 2 decimal places.
Answers
The question says you draw a card at random from a deck that contains 3 black cards and 7 red cards.
What is the probability of drawing a black card?
Recall,
Probability = Number of possible outcome
Number of favorable outcome
There are 3 favorable outcomes (the 3 black cards)
There are 10 possible outcomes ( the 3 + 7 = 10 cards)
Therefore,
P(draw a black card) = 3/10
P(draw a black card) = 0.30 (to 2 decimal places)
In how many ways can a committee of three men and two women be formed from a group of eight men and seven women?
Answers
By counting principle rule, we have
[tex]\begin{gathered} \text{three men out of eight} \\ \binom{8}{3} \end{gathered}[/tex][tex]\begin{gathered} \text{two women out of seven} \\ \binom{7}{2} \end{gathered}[/tex]Then the ways a committee of three men and two women can be formed is
[tex]\binom{8}{3}\cdot\binom{7}{2}=1176[/tex]Therefore, there are 1176 possible ways.
Question 3 1 pts A pair of designer sneakers was purchased for $120. Since they were purchased their price has increased by 15%. What is the new price, in dollars?
Answers
The new price after the increase of 15%
=120(100 + 15)%
=120 * 115%
= 120 * 115/100
= 138
The new price is $138
A data set of monthly expediture rounded to the nearest dollar and cure at coffee shop by a sample of 700 household has a minimum value of 4 and a maximum value of 210 suppose we want to group these data into 6 classes of equal with assuming we take the lower limit of the 1st class as one and the upper limit of the sick class as 210 determine the class limit boundaries and midpoint for a group quantitive data table
Answers
EXPLANATION
Number of households = 700
Minimum value = $4
Maximum value = $210
Dividing this by the upper limit by by the needed number of classes: 210/ 6 = 35
The width of each class is 35.
Class width = 35
Class Limits Lower Boundary Upper Boundary Class midpoint
1 to 35 0.5 35.5 36/2 = 18
36 to 70 35.5 70.5 106/2= 53
71 to 105 70.5 105.5 176/2= 88
106 to 140 105.5 140.5 246/2= 123
141 to 175 140.5 175.5 316/2= 158
176 to 210 175.5 210.5 386/2= 193
How would I solve this. Since I’m not sure what formula I could be using to solve this or how?
Answers
Answer:
[tex]\begin{gathered} a)\text{ 23 \%} \\ b)\text{ w\lparen t\rparen= 90e}^{0.23t} \end{gathered}[/tex]Explanation:
a)We have the general representation as follows:
[tex]w(t)\text{ = ae}^{kt}[/tex]when t = 3, we have the value doubling
Thus: w(t) = 2 * 90 thousand = 180 thousand megawatts
Thus:
[tex]\begin{gathered} 180\text{ = 90e}^{3k} \\ e^{3k}\text{ = 2} \\ k\text{ = }\frac{ln\text{ 2}}{3}\text{ = 0.231} \end{gathered}[/tex]This means we have the continuous growth rate at 23%
b) Writing w as a function of t, we have it that:
[tex]w(t)\text{ = 90e}^{0.23t}[/tex]