Answers
answer: A. (6;2;0)
Details are in the attachment.
Related Questions
3.1 Q19
Mona has 440 yards of fencing to enclose a rectangular area. Find the dimensions of the rectangle that maximize the enclosed area. What is the maximum area?
Answers
x + x + y + y = 440
2x + 2y = 440
Divide by 2 through ...
x + y = 220
y = 220 - x
Area = xy
Area = x(220 -x) = 220x - [tex] x^{2} [/tex]
Given that that max length of x will be -b/2a
a = -1 b = 220
x = [tex] \frac{-220}{-2} [/tex] = 110
x = 110
y = 220 - 110 = 110
Therefore max area = 110 x 110 = 12100 square yards
What is the 7th term in the geometric sequence described by this explicit formula?
A. 15,625
B. 156,250
C. 1,000,000
D. 31,250
Answers
The 7th term in the geometric sequence described by this explicit formula will be 31,250 so option (D) will be correct.
What is geometrical progression series?A geometric progression is a sequence in which any element after the first is obtained by multiplying the previous element by a constant which is called a common ratio denoted by r.
For example, the sequence 1, 4, 16, 64,… is a geometric sequence with a common ratio of r = 4.
Given explicit formula is
[tex]a_{n}[/tex] = 2 × [tex]5^{(n-1)}[/tex]
Where n represents a number of terms and [tex]a_{n}[/tex] is an nth term in the GP series.
By substituting n = 7 into the formula
[tex]a_{7}[/tex] = 2 × [tex]5^{(7 - 1)}[/tex]
[tex]a_{7}[/tex] = 2 × 5⁶
[tex]a_{7}[/tex] = 2 × 15625 = 31250 hence, it will the correct answer.
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A triangle has 3 sides, 10000, 1000, 10x. Find 10x. What 2 numbers can x be between.
answer format: ?<X<?
please help!!!!!!!!!!
Answers
a) 10000 < 1000 +10x
.. 1000 < 100 +x
.. 900 < x
b) 1000 < 10000 +10x
.. 100 < 1000 +x
.. -900 < x
c) 10x < 10000 +1000
.. x < 1100
x can be between 900 and 1100
Mya has a raised garden bed in the shape of a rectangular prism. The bed is 8 feet long, 3 2/3 feet wide, and 2 feet high. Part A: Belinda wants to make a raised garden bed that covers the same area as Mya’s, but the space she has is only 3 feet wide. How long should her garden bed be? Part B: Find the volume of Mya’s gardening bed. Suppose Belinda’s garden bed is the same height as Mya’s. Will Belinda’s bed have the same volume? Explain. Part C: A small bag of soil contains 2 cubic feet. How many bags of soil should Mya buy if she wants to fill her garden bed completely? Show your work. Part D: Belinda already has 22 bags of soil. Use your answer to Part C to find the depth to which she can fill her garden bed
Answers
[tex]\frac{88}{3}=x*3[/tex]
Divide both sides by 3:
88/3 ÷ 3 = 3x ÷ 3
88/3 * 1/3 = x (remember that when dividing fractions you flip the second one, 3/1, and multiply)
88/9 = x
Belinda's garden would need to be 88/9, or 9 7/9, feet long to have the same area as Mya's.
Part B)
The volume of Mya's garden is found by multiplying length by width by height. Another way of looking at this is the area of the base multiplied by the height.
8(3 2/3)(2) = (8/1)(11/3)(2/1) = 176/3 = 58 2/3 cubic feet.
The volume of Belinda's garden would still be the area of the base multiplied by the height; since the area of her garden is the same as the area of Mya's garden, as well as the heights being the same, then yes, hers would have the same volume:
(9 7/9)(3)(2) = (88/9)(3/1)(2/1) = 528/9 = 58 2/3
Part C)
We divide the volume of Mya's bed, 58 2/3 cubic feet, by 2 to find out how many bags:
(58 2/3) ÷ 2 = (176/3) ÷ (2/1) = (176/3) * (1/2) = 176/6 = 29 1/3 bag. We can't purchase 1/3 of a bag so she will need to purchase 30 bags.
If Belinda has purchased 22 bags, that is 44 cubic feet of soil. We divide this volume of soil by the area of her bed to find the height it will reach:
44 ÷ (88/3) = (44/1) ÷ (88/3) = (44/1) * (3/88) = 132/88 = 1 1/2 feet.
walter loves to paint. Every week day, he paints for 20 minutes. Every weekend day, he paints for 60 minutes. How many minutes does he spend painting in one week??
Answers
So Walter spends 220 minutes painting a week!
Hope this helps!
♤MidnightQueen
How do you multiply two scientific notation values? Explain the steps you would take to find the product of 6.7 × 106 and 3.2 × 105 written in scientific notation.
Answer is: Calculate the product of the coefficients and powers separately. Apply the product of powers rule to add the exponents. The product is not in scientific notation because the coefficient is greater than 10. Change the coefficient by moving the decimal one place to the left and increasing the exponent by one.
Answers
The answer to the above is
2.144 * 10^12
In scientific notation the product is written as [tex](2.144)\times10^{12}[/tex].
Given,Two scientific notation values are [tex]6.7\times10^6[/tex] and [tex]3.2 \times10^5[/tex].
We have to explain the steps to find the product of these values.
Scientific notation:Scientific notation is a widely used floating-point system in which numbers are expressed as products consisting of a number between 1 and 10 multiplied by an appropriate power of 10.
For the product of the above values we multiply coefficients separately like
[tex](6.7\times3.2=21.44)[/tex]
and powers of 10 separately
[tex](10^6\times10^5=10^{11} )[/tex].
So,
[tex]6.7\times10^6 \times 3.2\times10^5=(6.7\times3.2)\times(10^6\times10^5)[/tex].
[tex]6.7\times10^6 \times 3.2\times10^5=(21.44)\times10^{11}[/tex]
Or, in scientific notation form,
[tex]6.7\times10^6 \times 3.2\times10^5=(2.144)\times10^{12}[/tex].
Hence, in scientific notation the product is written as [tex](2.144)\times10^{12}[/tex].
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Malia is placing a barrier around the edge of a circular path with the diameter of 13 M the barrier are in length of 2.5 M.
what is the best approximation of how many pieces of a barrierd malia will need? used 3.14 for approximate for pi
Answers
(40.82 m)/(2.5 m) = 16.328
16 may be the best approximation of the number of pieces Malia will need. 17 pieces will make a barrier that is longer (larger diameter) than is needed.
Find the image of O (0,0) after two reflections, first across L1 and then across L2: L1: y = 2 L2: x = -3
Answers
[tex]S_x(x,y)\rightarrow(x,-y+2k)[/tex] reflection about horizontal line y=k
[tex]S_y(x,y)\rightarrow(-x+2h,y)[/tex] reflection about vertical line x=h
So for O(0,0), h=-3, k=2
First reflection about L1: y=2
(x,y)->(x, -y+2(k)) =>
O(0,0)->O'(0,-0+2(2) = O'(0,4)
Second reflection about L2: x=-3
(x,y)->(-x+2h,y) =>
O'(0,4)->O''(0+2(-3),4) = O"(-6,4)
Answer: after both reflections, the position of image is O"(-6,4)
Final answer:
After reflecting the origin (0,0) first across the line y=2, and then across the line x=-3, the final image of the point is at (-6,4).
Explanation:
The reflection of a point in the Cartesian coordinate system can be found using certain rules, depending on the line of reflection.
For the first reflection across L1: y = 2, imagine that every point has to move in a perpendicular motion to this line until it is on the opposite side but the same distance from L1.
The origin (0,0) will move up to (0,4) because it is 2 units away from y=2 and needs to move another 2 units up to be an equal distance on the opposite side of the line.
Next, for the reflection across L2: x = -3, use the same principle, but horizontally.
The point (0,4) is 3 units away from the line x=-3.
Reflecting over this line, you would move (0,4) to the left by 6 units (twice the distance from the line), giving us a final position of (-6,4).
The final position of the point O (0,0) after the two reflections is (-6,4).
Triangle ABC has vertices A(0,0), B(3,2), and C(0,4). This triangle may be classified as ?..?
1) equilateral
2) isosceles
3) right
4) scalene
Btw it wasn’t number 2 because that one was inaccurate.
Answers
The triange may be classified as (2) isosceles triangle
How to classify the triangle?The vertices are given as:
A(0,0), B(3,2), and C(0,4)
Calculate the side lengths using:
d = √(x2 - x1)^2 +(y2 - y1)^2
So, we have:
AB = √(3 - 0)^2 +(2 - 0)^2
AB = √13
AC = √(0 - 0)^2 +(4 - 0)^2
AC = 4
BC = √(3 - 0)^2 +(2 - 4)^2
BC = √13
Side lengths BC and AB are equal
i.e. AB = BC = √13
Hence, the triange may be classified as (2) isosceles triangle
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If the arrival of major road vehicles can be described by the poisson distribution, and the peak hour volume is 1000 veh/hr. the value of the critical gap is 4 seconds. the expected number of available gaps during the peak hour is equal to:
Answers
expected no. of vehicles per 4 minute interval = 1000/(3600/4) = 10/9 = λ
Using the poisson distribution, probability that no vehicles within the 4 second interval
P(0)= λ ^0 e^(- λ )/ 0!
= (10/9)^0 e^(-10/9) / 1
= e^(-10/9)
= 0.3292 (approx.)
In an hour, there are n=3600/4=900 such intervals, each with probability of p=0.3292 occurring.
Applying binomial distribution,
expected number of gaps
=np
=900*0.3292
= 296.3
Answer: the expected number of gaps is 296 (to the nearest unit).
Note: in fact, the actual expected number will be higher because gaps do not line up at 4 second intervals. If a vehicle passes at the 1 second of the interval, a gap can commence at the next second. Therefore the expected value could/should be slightly higher.
WILL GIVEBRAINLIEST AND 25 PTS PLEASE HURRY!!!Which lines are the directrices of the ellipse?
x = −4.25 and x = 8.25
x = −3.25 and x = 9.25
y = −4.25 and y = 8.25
y = −3.25 and y = 9.25
Answers
Answer:
The directrix of the ellipse is:
x= -3.25 and x=9.25
Step-by-step explanation:
As we know that for any ellipse equation of the type:
[tex]\dfrac{(x-h)^2}{a^2}+\dfrac{(y-k)^2}{b^2}=1[/tex] and a>b
The directrix is given by:
[tex]x=h\pm \dfrac{a}{e}[/tex]
where,
[tex]e=\sqrt{1-\dfrac{b^2}{a^2}}[/tex]
Here we have the equation of parabola as:
[tex]\dfrac{(x-3)^2}{5^2}+\dfrac{(y-2)^2}{3^2}}=1[/tex]
Hence, we have:
[tex]h=3,\ k=2,\ a=5,\ b=3\\\\and\\\\e=\sqrt{1-\dfrac{3^2}{5^2}}\\\\e=\sqrt{1-\dfrac{9}{25}}\\\\e=\sqrt{\dfrac{25-9}{25}}\\\\\\e=\sqrt{\dfrac{16}{25}}\\\\e=\dfrac{4}{5}[/tex]
Hence, we have: the directrix as:
[tex]x=3\pm \dfrac{5}{\dfrac{4}{5}}\\\\\\x=3\pm \dfrac{25}{4}\\\\Hence, x=9.25\ and\ x=-3.25[/tex]
Hence, the equation of directrix is:
x= -3.25 and x=9.25
Answer:
B
Step-by-step explanation:
On edge
The Harlowe school district gives awards to its schools based on overall student attendance. The data for attendance are shown in the table, where Low represents the fewest days attended and High represents the most days attended for a single student.
School Low High Range Mean Median IQR σ
High School A 98 180 82 158 148 55.5 35.2
High School B 105 180 75 145 124 48.5 28.2
High School C 102 180 78 169 151 53.5 31.3
Part A: If the school district wants to award the school that has the most consistent attendance among its students, which high school should it choose and why? Justify your answer mathematically. (5 points)
Part B: If the school district wants to award the school with the highest average attendance, which school should it choose and why? Justify your answer mathematically.
Answers
Part B: High school A has the highest average attendance, because it has higher mean (82) than B and C. Mean is mathematically the same as average, total number of days attended by all students divided by the number of students.
A circular rug has a radius of 3 ft. What is the circumference of the rug? Use 3.14 for mc014-1.jpg.
9.32 ft
9.42 ft
18.64 ft
18.84 ft
Answers
We must use a certain formula to find the circumference of anything circular.
The formula is:
C = 2 × pi × r
We know that pi = 3.14 approximately and the radius is 3 feet.
Substitute:
C = 2 × 3.14 × 3
C = 6.28 × 3
C = 18.84 ft
ANSWER:
The circumference of the circular rug is 18.84 ft. (Last option)
The circumference of a circular rug with a radius of 3 feet is equal to 18.84 feet.
Given the following data:
Radius of circular rug = 3 feet.π = 3.14.How to calculate the circumference of a circle?Mathematically, the circumference of a circle is calculated by using this formula:
Circumference = 2πr
Where:
r is the radius of a circle.
Substituting the given parameters into the formula, we have;
Circumference = 2 × 3.14 × 3
Circumference = 18.84 feet.
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What is the surface area of the right cone below?
Answers
[tex]A= \pi r(r+ \sqrt{h^2+r^2} )[/tex]
Here Radius, r= 6 units
To find the height of cone, we use Pythagorean theorem.
c²=a²+b²
Put values
15²=6²+h²
225=36+h²
h²=189
Put values in formula.
A=6π(6+√189+36)
A=6π+(6+√225)
A=6π(6+15)
A=126π units²
Answer:
Te correct option B.
Step-by-step explanation:
The surface area of a cone is
[tex]A=\pi r(r+l)[/tex]
Where, r is the radius and l is slant height.
From the given figure it is noticed that the radius of the cone is 6 and slant height is 15.
The surface area of cone is
[tex]A=\pi \times 6\times (6+15)[/tex]
[tex]A=\pi \times 6\times 21[/tex]
[tex]A=126\pi[/tex]
The area of the cone is 126π units². Therefore option B is correct.
I need help with this part plz help it's the last part
Answers
What is the formula for finding compound interest
Answers
where
A = is the final amount
[tex] P_{0} [/tex] is the initial principal
r is the rate as a decimal
n is the number of times compounded in a year
t is the time in years
Caitlyn has a credit card with a spending limit of $1500 and an APR (annual percentage rate) of 18%. During the first month, Caitlyn charged $375 and paid $250 of that in her billing cycle. Which expression will find the amount of interest Caitlyn will be charged after the first month?
Answers
The interest that will be charged after the first month is $1.875, calculated by multiplying the remaining balance of $125 by the monthly interest rate of 1.5%.
Explanation:The subject at hand is centered around the concept of credit card interest calculation. In Caitlyn's case, the remaining balance after her payment is $375 - $250 which equals $125. This is the amount that will incur interest.
The APR (annual percentage rate) is 18%, but we must first convert this to a monthly rate by dividing by 12, which equals 0.015 (or 1.5%). The interest charged after the first month is calculated by multiplying the remaining balance by the monthly interest rate. Therefore, the formula to calculate the interest is $125 * 0.015, which equals $1.875.
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Zakai cuts a piece of birthday cake as shown below.
What is the volume of the piece of cake?
Answers
Which number line shows the solution to
11x + 14 < –8?
Answers
Answer:
D!!
Step-by-step explanation:
Hope it helps!!
The solution to the inequality 11x + 14 < -8 is x < -2. On a number line, this would be a circle at -2 with a line extending to the left.
Explanation:To find the solution to the inequality 11x + 14 < –8, we will first subtract 14 from both sides, which gives us:
11x < -8 - 14
This simplifies to 11x < -22.
Next, we divide both sides by 11 for: x < -2
The solution is x < -2. On a number line, this would be represented by a circle around -2 (not filled in, because the inequality does not include 'equal to') with a line extending to the left (indicating 'less than').
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A line has a slope of –3 and a y-intercept of (0, –1). What is the equation of the line that is parallel to the given line and passes through the point (–3, 1)?
A.
y = –3x – 8
B.
y = 3x + 10
C.
y = –3x + 4
Answers
a line parallel to that one, will have the same exact slope of -3.
now, we know about this other parallel line that it runs through -3,1, and of course, since is parallel, it has a slope of -3
[tex]\bf \begin{array}{ccccccccc} &&x_1&&y_1\\ &&(~ -3 &,& 1~) \end{array} \\\\\\ % slope = m slope = m\implies -3 \\\\\\ % point-slope intercept \stackrel{\textit{point-slope form}}{y- y_1= m(x- x_1)}\implies y-1=-3[x-(-3)] \\\\\\ y-1=-3(x+3) \implies y-1=-3x-9\implies y=-3x-8[/tex]
Find all real numbers X such that 4x+2>14 AND -21x+1>22
Answers
To solve the system of inequalities, we find the values of x that satisfy both conditions: x > 3 and x < -1.
Explanation:To solve this problem, we need to find the values of x that satisfy the given inequalities:
4x+2 > 14
-21x+1 > 22
For the first inequality, subtracting 2 from both sides gives us:
4x > 12
Dividing both sides by 4, we get:
x > 3
For the second inequality, subtracting 1 from both sides gives us:
-21x > 21
Dividing both sides by -21 (and flipping the inequality sign), we get:
x < -1
Therefore, the values of x that satisfy both inequalities are:
x > 3 and x < -1
A cone is cut parallel to its base. Write the best name for the plane section (or cross section).
Answers
Final answer:
A cone cut with a plane parallel to its base forms a circular cross section, a concept that is part of the study of conic sections.
Explanation:
When a cone is cut with a plane parallel to its base, the cross section or plane section that is created is a circle. This concept falls under the study of conic sections, which also includes other shapes like ellipse, parabola, and hyperbola, all of which are formed by the intersection of a plane with a cone. If the cut is made closer to the apex, the circle will be smaller, and if it's made closer to the base, the circle will be larger, but all such cross sections remain circular as long as the cut is parallel to the base.
write a congruence statement for the pair of triangles zyb
Answers
Which of the following is a polynomial function in standard form with zeros at 0, 2, and 4?
Answers
x(x² - 6x + 8)
x³ - 6x² + 8x
Answer:
polynomial x³ -6x² +8x .
Step-by-step explanation:
Given : polynomial function in standard form with zeros at 0, 2, and 4.
To find : Which of the following is a polynomial function.
Solution : we have given that
zeros at 0, 2, and 4.
x = 0 .
x = 2
x = 4
(x -0)(x -2) (x -4).
x (x-2)(x-4).
x( x² -4x -2x +8).
x (x² -6x +8).
x³ -6x² +8x .
Therefore, polynomial x³ -6x² +8x .
The distance from Boulder City, NV to Santa Fe, NM is around 600 miles. If a map has a scale of 0.3 in for every 30 mi, how far is the scale distance between Boulder City, NV and Santa Fe, NM?
Answers
600 divided by 30 = 20 units
each unit is 0.3 inches
20*0.3 = 6
6 inches
Answer:
6 inches.
Step-by-step explanation:
The distance between two cities is around = 600 miles.
Map has a scale of 0.3 inches = 30 miles.
Therefore, on the scale 1 inches = [tex]\frac{30}{0.3}[/tex] miles
= 100 miles
Since on the map, 100 miles = 1 inches
The distance of 600 miles = [tex]\frac{600}{100}[/tex]
= 6 inches
The scale distance between cities is 6 inches.
Which word best describes the degree of overlap between the two data sets? none moderate low high Two line plots with the same scale and interval, from zero to sixty, with tick marks every five units. The plots are stacked vertically for comparison. Each plot has fifteen data values. Values appear as x marks above the line. Upper plot data values are one x mark above thirty, two x makrs above thirty-five, four x marks above forty, four x marks above forty-five, one x mark above fifty, two x marks above fifty-five, and one x mark above sixty. Lower plot data values are three x marks above five, four x marks above ten, three x marks above fifteen, two x marks above twenty, one x mark above twenty-five, one x mark above thirty, and one x mark above thirty-five.
HURRY PLEASE
Answers
min: 11q1 13q2 15q3 16max: 17iqr 3range: 6mean: 14.43
Lower data set: 11, 12, 13, 14, 14, 15, 15, 15, 15, 16, 16, 16, 17, 17
min: 11q1 14q2 15q3 16max: 17iqr 2range: 6mean: 14.71
I think that the degree of overlap is HIGH.
Answer:
High
Step-by-step explanation:
beth is making brownies. She makes 3 batches of brownies on saturday and 4 batches on sunday. she uses 1/4 cup of butter in each batch. how much butter does beth use? explain
Answers
Tally up the total number of batches.
= 3 batches + 4 batches
= 7 batches
STEP 2:
Multiply the total number of batches by the amount of butter used in one batch (which is 1/4 cup).
= 7 batches * 1/4 cup per batch
= 7 * 1/4
= (7*1)/4
= 7/4
= 1 3/4 cup of butter
Beth used 1 3/4 cup of butter to make a total of 7 batches of cookies.
Hope this helps! :)
The five members of the Traynor family each buy train tickets. During the train ride, each family member buys a boxed lunch for $6.50. If the total cost of the trip is $248.50, what is the price of each train ticket? Enter your answer in the box.
Answers
248.5 - 32.5 = 216
216/5 = 43.2
each ticket is $43.20
Elliot buys a 5 pound package of ground beef for 12.50 varna buys a package of ground beef for 7.50 at the same unit price. What is the weight of the package
Answers
Varna's package weighs 3 pounds, priced at $7.50, matching Elliot's $12.50 package with 5 pounds at same unit price.
To find the weight of Varna's package of ground beef, we can set up a proportion based on the unit price.
Elliot's package:
Price: $12.50
Weight: 5 pounds
Varna's package:
Price: $7.50 (same unit price as Elliot's)
Weight: Let's call it x pounds
We can set up the proportion:
[tex]\[\frac{12.50}{5} = \frac{7.50}{x}\][/tex]
Now, we can cross multiply:
[tex]\[12.50x = 5 \times 7.50\]\[12.50x = 37.50\][/tex]
Now, let's solve for \( x \):
[tex]\[x = \frac{37.50}{12.50}\]\[x = 3\][/tex]
So, the weight of Varna's package of ground beef is 3 pounds.
Complete question:
Elliot buys a 5 pound package of ground beef for 12.50
1)varna buys a package of ground beef for 7.50 at the same unit price. 2)What is the weight of the package
how many even 2-digit numbers have an odd number as the sum of their digits?