Line r has a slope of -6. Line s is parallel to line r. What is the slope of line s?
Thank you.
Answer:
-6
Step-by-step explanation:
Because two lines that are parallel have the same slope
A ballroom dance couple has learned 8 different routines and is going to perform 6 of them at a local competition. How many different ways could they arrange their performance?
The ballroom dance couple can arrange their performance in 28 different ways by selecting 6 routines out of the 8 they have learned.
To solve this problem
The idea of combinations can be used.
The number of ways to select k items from a set of n items is given by the formula for combinations:
C(n, k) = n! / (k! * (n - k)!)
In this case, n = 8 (the total number of routines they have learned) and k = 6 (the number of routines they will perform).
Using the formula, we can calculate:
C(8, 6) = 8! / (6! * (8 - 6)!)
= 8! / (6! * 2!)
The factorial function is represented in this case by the exclamation symbol (!).
The sum of all positive integers from 1 to n is the factorial of the number n.
Calculating the factorials involved:
8! = 8 * 7 * 6 * 5 * 4 * 3 * 2 * 1 = 40,320
6! = 6 * 5 * 4 * 3 * 2 * 1 = 720
2! = 2 * 1 = 2
Plugging in these values:
C(8, 6) = 40,320 / (720 * 2)
= 40,320 / 1,440
= 28
Therefore, the ballroom dance couple can arrange their performance in 28 different ways by selecting 6 routines out of the 8 they have learned.
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Factorise and Simplify :
a) 6p - 7q/12p - 14q
b) 6x⁵ - 8x²/2x
c) 10a + 15b/5
d) p² - 6q + 8/3p - 6
guys please help! please
a) We can factor out a common factor of two from the denominator and a half from the numerator: (6p - 7q)/(12p - 14q) = (3p - 7q/2)/(6p - 7q)
b) The numerator and denominator can be factored to provide a common factor of2x²: (6x⁵ - 8x²)/(2x) = 2x³ - 4
c) A common factor of 5 may be extracted from the numerator: (10a + 15b)/5 = 2a + 3b
d) By grouping factors, we may factor the numerator: p² - 6q + 8/3p - 6 = [(p² - 6q) + 8]/[3(p - 2)] = (p - 2)(p - 4)/(p - 2) = p - 4 (where p ≠ 2)
Factorising is the process of employing brackets to represent an expression as the product of its components. We do this by eliminating any elements that are shared by all of the expression's terms. Maths. Algebra. We must eliminate any factors that are shared by each word in an expression before we can factorize it. Expanding brackets is the process's reverse.
Finding an expression's highest common factor (HCF), or the largest number or letter that each term can be split by, is necessary to ensure that it has been properly factorized. Otherwise, there will still be common factors inside the bracket, preventing the expression from being properly factorized.
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A rectangular prism measures 3 ft by 6 ft by 5 ft. If the dimensions of the box were all quadrupled, how would the surface area of the box change?
1.The new surface area would be 16 times the original surface area.
2.The new surface area would be quadruple the original surface area.
3.The surface area would not change.
4.The new surface area would be 12 times the original surface area.
To determine how the surface area of a rectangular prism changes when all dimensions are quadrupled, we need to compare the original surface area to the new surface area.
The original surface area of the rectangular prism is given by:
SA_original = 2lw + 2lh + 2wh
where l, w, and h represent the length, width, and height of the prism, respectively.
In this case, the dimensions of the original box are:
Length (l) = 3 ft
Width (w) = 6 ft
Height (h) = 5 ft
Substituting these values into the formula, we have:
SA_original = 2(3)(6) + 2(3)(5) + 2(6)(5)
= 36 + 30 + 60
= 126 square feet
Now, if we quadruple all the dimensions of the box, the new dimensions would be:
Length (l_new) = 4(3) = 12 ft
Width (w_new) = 4(6) = 24 ft
Height (h_new) = 4(5) = 20 ft
The new surface area of the enlarged box is given by:
SA_new = 2(l_new)(w_new) + 2(l_new)(h_new) + 2(w_new)(h_new)
= 2(12)(24) + 2(12)(20) + 2(24)(20)
= 576 + 480 + 960
= 2016 square feet
Comparing the original surface area (SA_original = 126 sq ft) to the new surface area (SA_new = 2016 sq ft), we can see that SA_new is 16 times greater than SA_original.
Therefore, the correct answer is:
1. The new surface area would be 16 times the original surface area.
50 Points! Multiple choice geometry question. Photo attached. Thank you!
The value of angle BCD is determined as 108⁰.
option B is the correct answer.
What is the value of angle BCD?The value of angle BCD is calculated by applying intersecting chord theorem, which states that the angle at tangent is half of the arc angle of the two intersecting chords.
Also this theory states that arc angles of intersecting secants at the center of the circle is equal to the angle formed at the center of the circle by the two intersecting chords.
arc AB = m∠ACB
m∠ACB = 72⁰
The value of angle BCD is calculated as follows;
angle BCD = 180 - 72⁰ (sum of angles in a circle)
angle BCD = 108⁰
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Suppose that the volume, V,
of a right circular cylinder is
1280 cubic centimeters and
the radius of its base is
8 centimeters. What is the
height of the cylinder?
D
Answer:
[tex]\huge\boxed{\sf h \approx 6.4\ cm}[/tex]
Step-by-step explanation:
Given data:Volume = v = 1280 cm³
Radius = r = 8 cm
π = 3.14
Required:Height = h = ?
Formula:V = πr²h
Solution:Put the given data in the above formula.
Finding height of cylinder.
1280 = (3.14)(8)²(h)
1280 = (3.14)(64)(h)
1280 = 200.96 (h)
Divide both sides by 200.961280 / 200.86 = h
h ≈ 6.4 cm[tex]\rule[225]{225}{2}[/tex]
Your professor has offered to give you $100, starting next year, and after that growing at 3% for the next 20 years. You would like to calculate the value of this offer by calculating how much money you would need to deposit in the local bank so that the account will generate the money you would need to deposit in the local bank so that the account will generate the same cash flows as he is offering you. Your local bank will guarantee a 6% annual interest rate so long as you have money in your account.
1. How much money will you need to deposit into your account today?
2. Using an excel spreadsheet, show explicitly that you can deposit this amount of money into the account, and every year withdraw what your brother has promised, leaving the account with nothing after the last withdrawal.
3. Change the bank annual interest rate from 6% to 10% what is the difference?
To calculate the amount of money needed to deposit into the account today, we can use the concept of present value. The present value represents the current value of future cash flows, taking into account the time value of money.
1. To calculate the present value of the cash flows, we can use the formula for the present value of an annuity:
PV = C * (1 - (1 + r)^(-n)) / r
Where PV is the present value, C is the cash flow per period, r is the interest rate per period, and n is the number of periods.
In this case, the cash flow per period is $100, the interest rate per period is 6% (0.06), and the number of periods is 20.
Plugging in the values into the formula:
PV = 100 * (1 - (1 + 0.06)^(-20)) / 0.06
Calculating this value gives us the amount of money needed to deposit into the account today.
2. To show explicitly using an Excel spreadsheet, you can set up a column for each year, starting from year 0 (the present year) to year 20. In the first row, enter the initial deposit amount calculated in step 1. In the subsequent rows, use a formula to calculate the value for each year by adding the interest earned and subtracting the annual withdrawal of $100. The last value in year 20 should be zero, indicating that the account will have no remaining balance after the last withdrawal.
3. If the bank's annual interest rate changes to 10%, you would need to recalculate the present value using the new interest rate. Repeat step 1 with the new interest rate of 10% (0.10) to find the updated amount of money needed to deposit into the account today. Compare this value with the previous amount calculated with a 6% interest rate to determine the difference.
Solve for z. z² = 36 Enter your answer in the box. z =
Answer:
Step-by-step explanation:
z=6
100 Points! Geometry question. Photo attached. Determine whether each pair or figures is similar. If so, write the similarity statement and scale factor. If not, explain your reasoning. Please show as much work as possible. Thank you!
The figures are similar because the ratio of segment BC to segment EF is equal to the of segment AB to segment DE.
The scale factor is equal to 3/2.
What are the properties of similar triangles?In Mathematics and Geometry, two (2) triangles are said to be similar when the ratio of their corresponding side lengths are equal and their corresponding angles are congruent.
Additionally, the lengths of corresponding sides or corresponding side lengths are proportional to the lengths of corresponding altitudes when two (2) triangles are similar.
Based on the side, angle, side (SAS) similarity theorem, we can logically deduce the following:
Scale factor = BC/EF = AB/DE
Scale factor = 9/6 = 6/4
Scale factor = 3/2 = 3/2 (similar)
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10 cm
15 cm
17 cm
5 cm
What is the volume of this figure?
6 cm
10 cm
The Volume of Trapezoidal prism is 420 cm².
From the given figure we can write the dimension of the prism as
a = 5, b=15, c= 15, d= 15
h= 7 and l = 6 cm
Now, Volume of Trapezoidal prism
= 1/2 (a+b) x h x l
= 1/2 (5+15) x 7 x 6
= 1/2 x 20 x 42
= 10 x 42
= 420 cm²
Thus, the Volume of Trapezoidal prism is 420 cm².
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which of the following is the slope of the line with equation -7x=6+3y
Answer:
Slope = -7/3
Step-by-step explanation:
-7x = 6 + 3y is in the standard form of a line, whose general equation is
Ax = C + By (it's sometimes written in terms of C and is Ax + By = C, but in this problem, it's written in terms of Ax).
We can find the slope of the line by converting from standard form to slope-intercept form, whose general equation is y = mx + b, where
m is the slope,and b is the y-intercept.Step 1: Subtract 6 from both sides:
(-7x = 6 + 3y) - 6
-7x - 6 = 3y
Step 2: Divide both sides by 3 to isolate y:
(-7x - 6 = 3y) / 3
-7/3x - 2 = y
Thus, the slope of the line is -7/3
Answer: Therefore the slope is [tex]-\frac{7}{3}[/tex].
Step-by-step explanation:
We can rewrite the equation -7x=6+3y in slope-intercept form y = mx + b, where the m is the slope of the line, and b is the y-intercept.
-7x = 6 + 3y
-6 -6
-7x - 6 = 3y
[tex]\frac{-7x}{3}-\frac{6}{3} =\frac{3y}{3}[/tex]
[tex]\frac{-7}{3}x-2 =y[/tex]
Therefore the slope is [tex]-\frac{7}{3}[/tex].
A custom cake baker charges a flat fee for each job, plus an hourly rate for the
number of hours the job takes to complete. The total amount of her bill to the customer can be expressed by 40 + 25h
where h is the hours it takes for the job.what does the coefficient of h, in the expression represent
The coefficient h in the expression means the time taken for the job to be completed in hours.
How to find the value of the coefficient in the expression?The custom cake baker charges a flat fee for each job, plus an hourly rate for the number of hours the job takes to complete. The total amount of her bill to the customer can be expressed by 40 + 25h where h is the hours it takes for the job.
Therefore, the coefficient h in the expression can be interpreted as follows:
total amount of bills = 40 + 25h
where
40 dollars is the flat fee for each job
Then the coefficient h means the hourly rate for the time taken for the job to be completed.
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A jogger running around a rectangular park takes a shortcut back to his car by running 53 meters from one corner to the opposite corner. If the park is 45 meters long, what is the width?
Answer:
28 meters Aprox
Step-by-step explanation:
To find the width of the rectangular park, we can use the Pythagorean theorem. The diagonal running from one corner to the opposite corner forms a right triangle with the length and width of the park.
Given:
Length of the park (L) = 45 meters
Diagonal distance (d) = 53 meters
Using the Pythagorean theorem:
d² = L² + W²
(53 meters)² = (45 meters)² + W²
2809 = 2025 + W²
W² = 2809 - 2025
W² = 784
Taking the square root of both sides:
W ≈ √784
W ≈ 28
Therefore, the width of the rectangular park is approximately 28 meters.
WILL GIVE BRAINLIEST TO THE CORRECT ANSWER!!
This scale drawing shows a enlargement in a figure.
What is the value of x?
Enter your answer in the box.
X =
Answer:
18
Step-by-step explanation:
is a 1/3 scale
6-12-?
8-16-24
simple :)
I need some help with this
The solution of the given expression is,
x = 1/2.
The given expression is,
[tex]36^{3x} = 216[/tex]
Since we know that,
As the name indicates, exponents are utilized in the exponential function. An exponential function, on the other hand, has a constant as its base and a variable as its exponent, but not the other way around (if a function has a variable as its base and a constant as its exponent, it is a power function, not an exponential function).
Now we can write it as,
⇒ [tex]6^{2^{3x}} = 6^3[/tex]
⇒ [tex]6^{6x}} = 6^3[/tex]
Now equating the exponents we get,
⇒ 6x = 3
⇒ x = 3/6
⇒ x = 1/2
Hence,
Solution is, x = 1/2.
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carlos tiene 18 años y juan 42en cuantos años la edad de juan sera el doble de la de carlos es ese entonces
In 6 years Juan will have the double of Carlos age.
When Juan will have double of Carlos's age?The ages of each one are:
Carlos = 18 years old.
Juan = 42 years old.
In x years, they will have:
C = 18 + x
J = 42 + x
Carlos will have the double of Juan's age when:
J = 2*C
Replacing the equations we will get the linear equation:
42 + x = 2*(18 + x)
Solving for x we will get:
42 +x = 36 + 2x
Solving for x:
42 - 36 = 2x - x
6 = x
So Juan will have the double of Carlos age in 6 years.
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50 Points! Multiple choice algebra question. Photo attached. Thank you!
Answer:
B. Similar
Step-by-step explanation:
The two spheres are similar, but not congruent. They have the same shape, but different sizes.
The scale factor between the two spheres is 9/6= 3/2, which means that the radius of the larger sphere is 3/2 times the radius of the smaller sphere.
The box contains some green and yellow counters. 7/4 of the box is green counters. There are 24 yellow counters . How many green counters are there?
Considering the definition of an equation and the way to solve it, there are 84 green counters in the box.
Definition of equationAn equation is the equality existing between two algebraic expressions connected through the equals sign in which one or more unknown values appear.
The solution of a equation means determining the value that satisfies it. To solve an equation, keep in mind:
When a value that is adding, when passing to the other member of the equation, it will subtract.If a value you are subtracting goes to the other side of the equation by adding.When a value you are dividing goes to another side of the equation, it will multiply whatever is on the other side.If a value is multiplying it passes to the other side of the equation, it will pass by dividing everything on the other side.Amount of green countersKnowing that:
7/9 of the box is green counters.1-7/9= 2/9 of the bok are yellow counters.There are 24 yellow counters.the equation in this case is:
2/9 × total counters on the box =24
Solving:
total counters on the box =24÷ 2/9
The first step in dividing by a fraction is to find the reciprocal (reverse the numerator and denominator) of the second fraction.
Then, the two numerators and the two denominators must be multiplied and, if necessary, the fractions are simplified.
total mountain bikes =24× 9/2= 24/1× 9/2
total mountain bikes =(24×9)/ (1×2)
total mountain bikes =216/2
total mountain bikes =108
Then, there are 108 green and yellow counters in the box.
So, the amount of green counters in the box is calculated as:
Amount of green counters= 7/9× 108
Amount of green counters= 7/9× 108
Amount of green counters= 84
Finally, there are 84 green counters in the box.
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Write a equation to calculate d for any star
The required equation to find the distance of any star from the Sun is d = 1/ tan [tex]\theta[/tex].
Given that, the astronomer is finding the distance(d) of star to the sun in astronomical unit (AU) and tan [tex]\theta[/tex] = 0.000001389.
To find the equation by using the trigonometric function that is
tan a = perpendicular / base.
By using the data and the tangent trigonometric function, the equation is
tan [tex]\theta[/tex] = 1/d.
On simplifying gives,
Thus, d = 1/tan [tex]\theta[/tex].
Hence, the required equation to find the distance of any star from the Sun is d = 1/ tan [tex]\theta[/tex]
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I am so lost please help
Answer:
(a) - [tex]y=-2x+18[/tex]
(b) - [tex]y=\frac{1}{2} x-\frac{9}{2}[/tex]
Step-by-step explanation:
Given the equation of a line, which we'll call line 1, find the following.
(a) - The equation of a line, which we'll call line 2, that is parallel to line 1 and travels through the point (9,0)
(b) - The equation of a line, which we'll call line 3, that is perpendicular to line 1 and travels through the point (9,0)
Given:
[tex]3y+6x=-6[/tex]
(1) - Write the equation of line 1 in slope-intercept form
[tex]\boxed{\left\begin{array}{ccc}\text{\underline{Slope-Intercept Form:}}\\y=mx+b\\\bullet \ m \ \text{is the slope of the line}\\\bullet \ b \ \text{is the y-intercept of the line}\end{array}\right}[/tex]
[tex]3y+6x=-6\\\\\Longrightarrow 3y=-6-6x\\\\\Longrightarrow y=-\frac{6}{3} -\frac{6}{3}x \\\\\therefore \boxed{y=-2x-2}[/tex]
Thus, we can conclude the slope of line 1 is -2.
(2) - Answering part (a)
To find a line that is parallel to line 1, the slopes must be the same, -2. Use the point-slope form for a line to find the equation for line 2.
[tex]\boxed{\left\begin{array}{ccc}\text{\underline{Point-Slope Form:}}\\y-y_1=m(x-x_1)\\\bullet \ m \ \text{is the slope of the line}\\\bullet \ (x_1,y_1) \ \text{is a point the line passes through}\end{array}\right}[/tex]
[tex]y-y_1=m(x-x_1); \ \text{Recall that} \ m=-2 \ \text{and} \ (x_1,y_1)=(9,0)\\\\\Longrightarrow y-0=-2(x-9)\\\\\therefore \boxed{\boxed{ y=-2x+18}}[/tex]
Thus, the equation for line 2 is found.
(2) - Answering part (b)
To find a line that is perpendicular to line 1, the slope of line 3 must be the opposite-reciprocal of line 1's. Once again, use the point-slope form of a line to find the equation of line 3.
[tex]y-y_1=m(x-x_1); \ \text{Recall that} \ m=\frac{1}{2} \ \text{and} \ (x_1,y_1)=(9,0)\\\\\Longrightarrow y-0=\frac{1}{2}(x-9)\\\\\therefore \boxed{\boxed{ y=\frac{1}{2} x-\frac{9}{2} }}[/tex]
Thus, the equation of line 3 is found.
Describe the Transformations for 4 and 5
If h(x) = f(–x), this is saying that your graph will be reflected over the y-axis. In other words, the x-values of every point on the graph of y=f(x) will be switched to the opposite sign. The graph will be flipped over sideways.
For example, if (1,-4) is a point on y=f(x), then y=h(x) will have (–1,-4) on it.
If h(x) = –f(x), this is saying that your graph will be reflected over the x-axis. In other words, the y-values of every point on the graph of y=f(x) will be switched to the opposite sign. The graph will be flipped upside-down.
For example, if (1,–4) is a point on y=f(x), then y=h(x) will have (1,4) on it.
While you are given the equation for f(x) in each exercise, the function f(x) does not impact the transformation at all. What is said above is true for all functions.
If you want to graph them, then for 4:
f(x) = -3 - x
h(x) = f(-x) = -3 + x
For #5:
f(x) = 1/3 x + 1
h(x) = -f(x) = -1/3 x - 1
10. Given m AC = 85%,
find m
AEC
AEC =
and m2ABC = E
A
B
The measure of angle AEC is 225 degree.
Given ABCD square then all sides are equal and all angles are of 90°
AB=BC=CD=DA
and also CDE is an equilateral triangle
CD=DE=EC and all angles are of 60°
Now, In ΔADE, ∵AD=AE ⇒ ∠DAE=∠AED
∠ADE=∠ADC-∠EDC=90°-60°=30°
By angle sum property of triangle
∠ADE+∠DAE+∠AED=180°
30°+2∠AED=180°
2∠AED=150°
∠AED=75°
and, ∠EAB = ∠DAB-∠DAE = 90°-75° = 15°
Reflex angle ∠AEC= 360°-∠AED-∠DEC
=360° - 75° -60°
=225°
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The complete and correct question is attached below:
find the surface area
The surface area of the cylinder is: 156π.
Here, we have,
given that,
the cylinder has:
radius = 6 in
height = 10 in
now, surface area of the cylinder is:
SA = 2πrh + πr²
here, we have,
SA = 2π *6 * 10 + π6²
= 120π + 36π
= 156π
Hence, The surface area of the cylinder is: 156π.
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a) Su-Lo scored 45% in her test out of 80.
what mark did she
score?
Answer:
Step-by-step explanation:
To calculate Su-Lo's score on the test, we can multiply her percentage by the total marks for the test.
Su-Lo scored 45% out of 80, so her score can be calculated as follows:
Score = Percentage × Total marks
Score = 45% × 80
To find the score, we need to convert the percentage to a decimal by dividing it by 100:
Score = (45/100) × 80
Score = 0.45 × 80
Score = 36
Therefore, Su-Lo scored 36 marks on the test.
The distribution of scores on a history test is close to normal. The scores are adjusted so that the mean score is about =75
and the standard deviation is =5
. What percent of the scores fall between 65 and 75?
13.5%
27.0%
47.5%
The percentage of scores that fall between 65 and 75 is approximately [tex]2 \times 34 = 68%.[/tex]%
To determine the percentage of scores that fall between 65 and 75, we can use the properties of the normal distribution.
Mean score = 75
Standard deviation = 5
We know that the normal distribution is symmetric around the mean, and approximately 68% of the data falls within one standard deviation from the mean.
This means that about 34% of the scores fall between the mean and one standard deviation above the mean.
To calculate the percentage of scores between 65 and 75, we need to determine how many standard deviations away from the mean 65 and 75 are.
For 65:
(65 - 75) / 5 = -2
For 75:
(75 - 75) / 5 = 0
From the calculations, we can see that 65 is 2 standard deviations below the mean, and 75 is at the mean.
Since the distribution is symmetric, we can consider the percentage of scores between the mean and one standard deviation above the mean (34%) and double it to account for the scores between the mean and one standard deviation below the mean.
Therefore, the percentage of scores that fall between 65 and 75 is approximately 2 [tex]\times[/tex] 34% = 68%.
However, none of the given answer options match the calculated result. Therefore, none of the provided answer options accurately represent the percentage of scores between 65 and 75 based on the given information.
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100 Points! Geometry question. Photo attached. Write the equation of the parabola with the given conditions. Please show as much work as possible. Thank you!
Answer:
[tex](y - 4)^2 = -8(x - 2).[/tex]
Step-by-step explanation:
The equation of a parabola with a vertical axis of symmetry, vertex (h, k), and focus (h+a, k) is given by:
[tex](y - k)^2 = 4a(x - h)[/tex]
In this case, the vertex is (2, 4) and the focus is (0, 4).
Comparing this to the general equation, we have h=2, k=4, and h+a=0.
From h+a=0, we can solve for a:
a=-h = -2
Substituting the values of h, k, and p into the equation, we get:
[tex](y - 4)^2 = 4(-2)(x - 2)[/tex]
Simplifying further:
[tex](y - 4)^2 = -8(x - 2)[/tex]
Therefore, the parabola equation is[tex](y - 4)^2 = -8(x - 2).[/tex]
Which of the following correctly order from least to greast 0.75,3/5,70%
− 4 p − ( 5 p − 4 ) ≤ −4p−(5p−4)≤ 7 p + 10 + 3 p 7p+10+3p
Answer:
To solve the inequality −4p − (5p − 4) ≤ 7p + 10 + 3p, we can simplify and isolate the variable p. Let's work through the steps:
Step 1: Distribute the negative sign (-) inside the parentheses:
-4p - 5p + 4 ≤ 7p + 10 + 3p
Simplifying further:
-9p + 4 ≤ 10p + 10
Step 2: Group like terms by adding 9p to both sides of the inequality:
-9p + 9p + 4 ≤ 10p + 9p + 10
Simplifying further:
4 ≤ 19p + 10
Step 3: Subtract 10 from both sides of the inequality:
4 - 10 ≤ 19p + 10 - 10
Simplifying further:
-6 ≤ 19p
Step 4: Divide both sides of the inequality by 19:
-6/19 ≤ 19p/19
Simplifying further:
-6/19 ≤ p
So the solution to the inequality is p ≥ -6/19.
A rhombus with horizontal
diagonal length 2 centimeters
vertical diagonal length 3 centimeters.
Find the area of the rhombus-shaped keychain.
3 cm2
5 cm2
6 cm2
12 cm2
The area of the Rhombus-shaped keychain is 3 square centimeters.
The area of the rhombus-shaped keychain,
we can use the formula:
Area = (diagonal1 * diagonal2) / 2
Given that the horizontal diagonal has a length of 2 centimeters and
the vertical diagonal has a length of 3 centimeters,
we can substitute these values into the formula:
Area = (2 * 3) / 2
= 6 / 2
= 3 cm^2
Therefore, the area of the rhombus-shaped keychain is 3 square centimeters.
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The rectangle below has an area of
15
�
4
+
35
�
3
+
20
�
2
15k
4
+35k
3
+20k
2
15, k, start superscript, 4, end superscript, plus, 35, k, cubed, plus, 20, k, squared.
The width of the rectangle is equal to the greatest common monomial factor of
15
�
4
,
35
�
3
,
15k
4
,35k
3
,15, k, start superscript, 4, end superscript, comma, 35, k, cubed, comma and
20
�
2
20k
2
20, k, squared.
What is the length and width of the rectangle?
Three rectangles of different sizes make up a larger rectangle. The larger rectangle's length is labeled length. The larger rectangle's width is labeled width. The smaller rectangle on the left has fifteen k to the fourth power inside it. The smaller rectangle in the middle has thirty five k cubed inside it. The smaller rectangle on the right has twenty k squared inside it.
Three rectangles of different sizes make up a larger rectangle. The larger rectangle's length is labeled length. The larger rectangle's width is labeled width. The smaller rectangle on the left has fifteen k to the fourth power inside it. The smaller rectangle in the middle has thirty five k cubed inside it. The smaller rectangle on the right has twenty k squared inside it.
Width
=
Width=start text, W, i, d, t, h, end text, equals
Length
=
Length=start text, L, e, n, g, t, h, end text, equals
The width of the rectangle is 5k² and the length of the rectangle is 3k² + 7k + 4.
How to explain the informationThe greatest common monomial factor of 15k⁴, 35k³, and 20k² is 5k². So the width of the rectangle is 5k².
The area of the rectangle is the product of its length and width. So the length of the rectangle is the area divided by the width. The area is 15k⁴ + 35k³ + 20k² and the width is 5k². So the length is:
= (15k⁴ + 35k³ + 20k²) / (5k²)
= 3k² + 7k + 4.
Therefore, the width of the rectangle is 5k² and the length of the rectangle is 3k² + 7k + 4.
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