Final answer:
The correct equation to find the length of each of Liam's rectangular plots is x³ + 15x² - 100x - 2,688=0. This cubic equation must be solved to determine the actual length of each plot.
Explanation:
To solve the problem involving Liam's rectangular plots of land, you need to find the length x of each plot. Since the width is 5 yards less than the length, the width is x - 5 yards. With the number of plots being 20 + x, and the total area given as 2,688 square yards, you can set up an equation using the area of a rectangle (length times width) multiplied by the number of plots equal to the total area
The correct equation to determine the length of each plot is as follows:
X (width) × X (length) × (number of plots) = total area
(x) (x - 5) (20 + x) = 2,688
x(x - 5)(x + 20) = 2,688
x³ + 15x² - 100x = 2,688
This simplifies to the equation x³ + 15x² - 100x - 2,688 = 0, which corresponds to option three. Upon solving this cubic equation, you would find the length of each plot. However, the last options are not supported by the given information and should be solved for using the derived equation.
How do you do x ^4-4? What is the x values?
A grocer wants to make a 10 pound mixture of cashews and peanuts that he can sell for $3.64 per pound. If cashews cost $5.80 per pounds and peanuts cost $2.20 per pound how many pounds of each nuts must he mix?
The height and radius of a right cylinder are each 8 cm. what is its volume
If the domain is {0, 2, -6}, what is the range of y = -2x + 3?
The range of the function is {-1, 3, 15}.
What is the range of the function?The set of a function's potential output values is known as its range.
Given that, the domain of the function is {0,2,-6}.
The range is the set of the output of the functions for the given domain values.
The value of y for x = 0 is:
y = -2(0) + 3
y = 3
Similarly, the values of y for x = 2 and x = -6 are:
y = -2(2) + 3
y = -1, and
y = -2(-6) + 3
y = 15
Hence, the range of the function is {-1, 3, 15}.
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PLEASE HELP! WILL MARK BRAINLIEST!
What is the sum of the polynomials (m+n+3)(m+n+4)
Answer:
2m+2n+7
Step-by-step explanation:
Given: Two polynomial
[tex]P_1=m+n+3[/tex]
[tex]P_2=m+n+4[/tex]
We need to find the sum of polynomial.
[tex]Sum=P_1+P_2[/tex]
[tex]\Rightarrow (m+n+3)+(m+n+4)[/tex]
write like term together
[tex]\Rightarrow m+m+n+n+3+4[/tex]
Combine the like term
[tex]\Rightarrow 2m+2n+7[/tex]
Hence, The sum of two polynomial is 2m+2n+7
The area of a rectangular wall of a barn is 96 square feet. its length is 4 feet longer than twice its width. find the length and width of the wall of the barn?
Final answer:
To find the dimensions of the barn's wall, we set up the equation w x (2w + 4) = 96 and solved for w to find the width is 8 feet. Then, we used the width to find the length, which is 20 feet.
Explanation:
To solve the problem of finding the dimensions of the rectangular wall of the barn, we need to set up and solve an algebraic equation. Let's call the width of the wall w feet. According to the problem, the length is 4 feet longer than twice the width, so we can express the length as 2w + 4 feet.
The area of the rectangle is given by multiplying the length by the width. We know the area is 96 square feet, so our equation to solve is w × (2w + 4) = 96.
Expanding this equation gives us 2w^2 + 4w - 96 = 0. This is a quadratic equation that we can solve by factoring, completing the square, or using the quadratic formula.
Factoring the quadratic equation, we look for factors of -96 that add up to 4. These factors are 12 and -8. So, we can write our equation as (2w + 12)(w - 8) = 0.
Setting each factor equal to zero gives us two possible solutions for w: w = -6 or w = 8. Since width cannot be negative, we discard w = -6 and keep w = 8 feet. The length is then 2(8) + 4 = 16 + 4 = 20 feet.
Therefore, the width of the barn's wall is 8 feet, and the length is 20 feet.
police can estimate the speed of a vehicle before the brakes are applied using the formula 0.75d = s^2 / 30.25 where is the speed in miles per hour d is the length of the vehicle's skid marks. What was the approximate speed of a vehicle that left a skid mark measuring 160 feet?
1.about 36 miles per hour
2."" 60 ""
3."" 13 ""
4"" 54 ""
The answer would be ≈60mph, hence the answer is B.
A guy-wire is attached from the ground to the top of a pole for support. If the angle of elevation to the pole is 67° and the wire is attached to the ground at a point 137 feet from the base of the pole, what is the height of the pole (round to 2 decimal places)?
A)53.53 feetB)74.62 feetC)126.11 feetD)322.75 feet
Function f, shown below, is translated down 3 units and left 4 units to create function g. f(x)=3|x-2|-5. Fill in the values of a, h, and k to write function g.
Answer:
g (x) = 3lx+2l-8
Step-by-step explanation:
Carlosego made a mistake on the horizontal shift.
y = f (x + c) shifts the graph c units to the left.
Therefore, g (x) = 3lx - 2 + 4l - 8 is
g (x) = 3lx+2l-8
A company has found that the demand for its product varies inversely as the price of the product. when the price x is 3.5 dollars, the demand yy is 450 units. find a mathematical model that gives the demand y in terms of the price x in dollars.
The mathematical model that gives the demand, y, in terms of the price, x, is y = 1575/x.
Explanation:To find a mathematical model that gives the demand, y, in terms of the price, x, we can use the formula for inverse variation. Inverse variation is described by the equation y = k/x, where k is a constant. To find the value of k, we can use the given information: when x = 3.5, y = 450. Substituting these values into the equation, we get 450 = k/3.5. Solving for k, we find that k = 1575. Therefore, the mathematical model that gives the demand, y, in terms of the price, x, is y = 1575/x.
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On a coordinate grid, point P is at (2, 1) and point R is at (−6, −5). Points Q and S are a reflection of both points across the x-axis. What are the coordinates of Q and S?
Answer:
Q(2, −1), S(−6, 5)
Step-by-step explanation:
The original ordered pairs were (2, 1) and (−6, −5). When you reflect across the x-axis the x-coordinates of the two ordered pairs are the same, and the y coordinate is the opposite in sign (positive and negative).
so since the original ordered pairs were (2, 1) and (−6, −5), the reflected ordered pairs would be Q(2, −1), S(−6, 5) because the y-coordinates are different and the x-coordinates are the same.
Hope this helped fellow FLVS student!!
The coordinates are Q(2, −1) and S(−6, 5)
What is reflection of points?A reflection point occurs when a figure is constructed around a single point, known as the point of reflection or centre of the figure. For every point in the figure, another point is found directly opposite to it on the other side. Under the point of reflection, the figure does not change its size and shape.
Given that, On a coordinate grid, point P is at (2, 1) and point R is at (−6, −5). Points Q and S are a reflection of both points across the x-axis.
We know that, when you reflect across the x-axis, the x-coordinates of the two ordered pairs are the same, and the y coordinate is the opposite in sign (positive and negative).
So, since the original ordered pairs were (2, 1) and (−6, −5), the reflected ordered pairs would be Q(2, −1), S(−6, 5) because the y-coordinates are different and the x-coordinates are the same.
Hence, The coordinates are Q(2, −1) and S(−6, 5)
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Each trapezoid in the figure below is congruent to trapezoid ABDC.
What is the perimeter of hexagon ACEFGH?
1)28 cm
2)32 cm
3)36 cm
4)64 cm
Answer:
The answer is the second option
[tex]32\ cm[/tex]
Step-by-step explanation:
we Know that
Each trapezoid in the figure below is congruent to trapezoid ABDC
so
[tex]CE=AC=3\ cm[/tex]
[tex]EF=AB+CD=4+6=10\ cm[/tex]
[tex]FG=AC=3\ cm[/tex]
[tex]GH=AC=3\ cm[/tex]
[tex]AH=AB+BH=AB+CD=4+6=10\ cm[/tex]
the perimeter is equal to
[tex]P=AC+CE+EF+FG+GH+AH[/tex]
substitute the values
[tex]P=3+3+10+3+3+10=32\ cm[/tex]
Please help and show all work thank you!
Make this equation true by rearranging the numbers.... 26=74
Quadrilateral JPRAQuadrilateral JPRA is similar to quadrilateral KDEWquadrilateral KDEW . PR=27 mmPR=27 mm , DE=15 mmDE=15 mm , and WE=25 mmWE=25 mm .
What is AR?
Sakura speaks 150150150 words per minute on average in hungarian, and 190190190 words per minute on average in polish. she once gave cooking instructions in hungarian, followed by cleaning instructions in polish. sakura spent 555 minutes total giving both instructions, and spoke 270270270 more words in polish than in hungarian. how long did sakura speak in hungarian, and how long did she speak in polish?
Answer:
3 minutes polish 2 minutes hungarian
Step-by-step explanation:
I just did it on Kahn Academy, and this was correct.
Workers have 1600 m of fencing to enclose a rectangular area where a music festival will be held. The table represents a quadratic function that shows how the area of the rectangle formed by the fence depends on the length of the rectangle.
Length (m) Area (m²)
0 0
100 70,000
200 120,000
300 150,000
400 160,000
500 150,000
600 120,000
700 70,000
800 0
Select from the drop-down menu to correctly complete the sentence.
The x-coordinate of the vertex represents
the length that result in the largest possible area
the smallest possible area of the rectangle
the greatest possible length of any rectangle formed
the greatest possible area of a rectangle
This should get you a hundred on the 4.11 quiz. :)
The correct option is the x-coordinate of the vertex representing the length.
What is a quadratic equation?A quadratic equation is an equation whose leading coefficient is of second degree also the equation has only one unknown while it has 3 unknown numbers.
It is written in the form of ax²+bx+c.
As it is given that the perimeter of the rectangular fencing is 1600 m.
Now, since the shape of the fence is rectangular, therefore, the x-coordinate of the vertex represents the length that results in the largest possible area, while the y-coordinate is the width of the rectangular fencing.
Hence, the correct option is the x-coordinate of the vertex representing the length.
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Suppose the time it takes a data collection operator to fill out an electronic form for a database is uniformly distributed between 1.0 and 2.1 minutes. (a) determine the mean of x. (round your answer to 2 decimal places.)
Segment AB has endpoints A(–4, 6) and B(1, 4). After a dilation, centered at the origin, the image of A is (–6, 9). Without measuring the distance, explain how you could find the image of B
Answer:
To find the image of B, first find the scale factor for the dilation. The scale factor should be greater than 1 because the image of A is farther from the origin than A. Divide the coordinates of the image of A by the coordinates of A: –6/–4 = 3/2 and 9/6 = 3/2, so the scale factor is 3/2. Now, apply the dilation to B by multiplying the coordinates by 3/2 to get ((3/2)(1), (3/2)(4)), or (3/2, 6).
Step-by-step explanation:
8.04 A
Graph each pair of parametric equations.
(2 points each)
x = 3 sin3t
y = 3 cos3t
A coordinate graph is shown with the x axis scaled from -10 to 10 and the y axis scaled from -10 to 10.
x = 7 sin t + sin 7t
y = 7 cos t + cos 7t
A coordinate graph is shown with the x axis scaled from -10 to 10 and the y axis scaled from -10 to 10.
x = 2t
y = t + 5, -2 ≤ t ≤ 3
A coordinate graph is shown with the x axis scaled from -10 to 10 and the y axis scaled from -10 to 10.
x = 2t – 1
y = t2 + 5, -4 ≤ t ≤ 4
A coordinate graph is shown with the x axis scaled from -10 to 10 and the y axis scaled from -10 to 10.
x = 6 sin t
y = 6 cos t, 0 ≤ t ≤ 2π
A coordinate graph is shown with the x axis scaled from -10 to 10 and the y axis scaled from -10 to 10.
find the measure of side c.
The length of side AB (c) in triangle ABC is 31.38 m.
In triangle ABC, angle BCA is a right angle with a measure of 90 degrees, and angle CAB has a measure of 42 degrees.
The side BC has a length of 21 m and the side AB has a length of c.
To find the length of side c, we can use the trigonometric function sine.
By using the sine function and the given angle CAB, we can calculate the length of side c as follows:
c = AB = BC * sin(CAB) = 21 * sin(42) = 31.38 m
Therefore, The length of side AB (c) in triangle ABC is 31.38 m.
The probable question may be:
In triangle ABC, Angle BCA= 90 degree, angle CAB=42 degree, Side BC (a)=21 m, Side AB=c, find the measure of side c.
suppose you invest $500 in a savings account that pays 3.5% annual interest. when will the account contain $650
When dividing which number goes first in the calculator?
A packet contains 24 pens.
Henry and Alice share them in the ratio 3 : 5
How many does Alice receive?
What are the roots of the polynomial equation?
–12, 12
–4, 3
–3, 4
–1, 1
PLEASEEEEE HELP WILL MARK BRAINLIEST!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Triangle HJK is transformed to similar triangle H’J’K’:
What is the scale factor of dilation?
1/2
1/3
1/4
1/5
Answer:
The scale factor of the dilation is [tex]\frac{1}{4}[/tex]
Step-by-step explanation:
we know that
If two figures are similar, then the ratio of its corresponding sides is equal and this ratio is called the scale factor
Let
z------> the scale factor
so
[tex]z=\frac{K'J'}{KJ}=\frac{K'H'}{KH}=\frac{J'H'}{JH}[/tex]
substitute the values
[tex]z=\frac{K'J'}{KJ}[/tex] -----> [tex]z=\frac{1}{4}[/tex]
The scale factor is less than 1
therefore
The dilation is a reduction
Quadrilateral ABCD is inscribed in this circle.
What is the measure of angle C?
Enter your answer in the box. °
What number is 22 spaces to the right of negative 7?
Final answer:
By adding 22 to -7, we find that the number 22 spaces to the right of -7 on the number line is 15.
Explanation:
The question asks for the number that is 22 spaces to the right of negative 7 on a number line. To find this, you can simply add 22 to negative 7. Here's the calculation: -7 + 22 = 15. Therefore, the number that is 22 spaces to the right of negative 7 is 15. To determine the number that is 22 spaces to the right of -7 on the number line, we need to add 22 to -7. Moving 22 spaces to the right indicates an increase in value by 22. Therefore, when we add 22 to -7, we get the final answer of 15. This calculation reflects the concept that moving to the right on the number line corresponds to increasing the numerical value, while moving to the left corresponds to decreasing it. In this case, starting from -7 and moving 22 spaces to the right results in a value of 15. Hence, 15 is the number that is 22 spaces to the right of -7.
Please help i'll give you brainliest answer!
1. Astronomers measure large distances in light-years. One light year is the distance that light can travel in one year, or approximately 5.88 x 10^12 miles. Suppose a star is 9.8 x 10^1 light years from Earth. In scientific notation, approximately how many miles is it?
A. 5.88 x 10^13 miles
B. 5.76 x 10^14 miles
C. 5.88 x 10^12 miles
D. 9.8 x 10^12 miles
2. A 1,600.00 principal earns 7% annual interest, compounded semiannually (twice per year). After 33 years, what is the balance in the account?
A. $4,979.11
B. $14,920.54
C. $112,992.00
D. $15,494.70
Answer:
1. B. 5.76 × 10¹⁴ miles.
2. D. $15,494.70
Step-by-step explanation:
Question 1: We have,
Distance light traveled in one year = 5.88 × 10¹² miles.
Since, the star is 9.8 × 10¹ light years away.
So, we get,
Total number of miles the star is away = 5.88 × 10¹² × 9.8 × 10¹ = 57.62 × 10¹³ miles.
Hence, the total number of miles are 5.76 × 10¹⁴ miles.
Question 2: We have,
Principle amount, P= $1,600
Rate of interest, r = 7% = 0.07
Time period, t = 33 years
Moreover, the interest is compounded twice per year i.e. n=2.
Since, Amount = [tex]P(1+\frac{r}{n})^{nt}[/tex]
i.e. Amount = [tex]1600(1+\frac{0.07}{2})^{2\times 33}[/tex]
i.e. Amount = [tex]1600(1+\frac{0.035)^{66}[/tex]
i.e. Amount = [tex]1600(1.035)^{66}[/tex]
i.e. Amount = [tex]1600\times 9.68418}[/tex]
i.e. Amount = $15,494.70
Hence, the balance in the account is $15,494.70.