Find the image of O (0,0) after two reflections, first across L1 and then across L2: L1: y = 2 L2: x = -3
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).
A used bookstore will trade 2 of its books foe of yours, If Val brings in 18 books to trade,how many books can she get from the store
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??
I need help with this part plz help it's the last part
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
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
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
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
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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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?
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.
What is the formula for finding compound interest
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?
Subtract 1.05 from a certain number. Multiply the difference by 0.8, add 2.84 to the product then divide the sum by 0.01 and get 700. What is the number?
Answer:
6.25
Step-by-step explanation:
I go to rsm and this answer worked
A cone is cut parallel to its base. Write the best name for the plane section (or cross section).
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.
A bag contains 15 red candies, 20 blue candies, and 10yellow candies. What is the probability of drawing a red candy? A blue candy? Something besides a yellow candy?
The probability of drawing a red, blue, and a candy that is not yellow from the bag is 1/3, 4/9, and 7/9 respectively.
Explanation:The question involves the concept of probability in mathematics, with a scenario of drawing candies from a bag. The total number of candies in the bag is 45 (15 red + 20 blue + 10 yellow).
The probability of drawing a red candy is the number of red candies divided by the total number of candies, which is 15/45 or 1/3.
The probability of drawing a blue candy is the number of blue candies divided by the total number of candies, which is 20/45 or 4/9.
If we want to find the probability of drawing something other than a yellow candy, this is essentially the sum of the probabilities of drawing a red or blue candy. This is 35 out of 45 (15 red candies + 20 blue candies), which reduces to 7/9.
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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
You are selling items from a catalog for a school fundraiser. Select two inequalities that you can use to find the range of sales that will earn you at least $40 and at most $50. Then find the range of sales. Let x represent the amount of sales (in dollars).
The range of sales that will earn at least $40 and at most $50 is represented by the inequalities x >= 40 and x <= 50. Hence, the range of possible sales is x such that 40 <= x <= 50.
Explanation:The subject of this question is inequalities and the concept of a range of numbers in mathematics. Here, we're looking at a range of sales values that will result in the organizer earning between $40 and $50.
The two inequalities that represent this scenario are: x >= 40 and x <= 50.
To find the range of sales, we look at the values that satisfy both conditions. Therefore, the range of sales is all the sales amounts (x) such that: 40 <= x <= 50. This means that any amount of sales that is greater than or equal to $40 and less than or equal to $50 will meet the criteria.
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Which of the following is a polynomial function in standard form with zeros at 0, 2, and 4?
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 .
A triangle has 3 sides, 10000, 1000, 10x. Find 10x. What 2 numbers can x be between.
answer format: ?<X<?
please help!!!!!!!!!!
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?
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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Find all real numbers X such that 4x+2>14 AND -21x+1>22
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
Marge cut 16 pieces of tape for mounting pictures on poster board. Each piece of tape was 3/8 inch long. How much tape did Marge use?
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
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.
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
What is the surface area of the right cone below?
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.
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.
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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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.
The sum of two numbers is 46 and the difference is 14. What are the numbers?
Which number line shows the solution to
11x + 14 < –8?
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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how many even 2-digit numbers have an odd number as the sum of their digits?
A graduated cylinder is filled with 36π of liquid. The liquid is poured into a different cylinder that has a radius of 3 cm. What will the height of the liquid be in the new cylinder?
Answer:
The height of the liquid in the new cylinder = 4 cm
Step-by-step explanation:
∵ The volume of the liquid = 36π cm³
∵ It poured into a cylinder that has radius 3 cm
∵ The volume of any cylinder = πr²h
∴ The volume of the liquid in the cylinder = π(3)²h = 9πh
- Where h is the height of the liquid inside the cylinder
∴ 9πh = 36π ⇒ divide both sides by π
∴ 9h = 36 ⇒ h = 36/9
∴ h = 4 cm
∴ The height of the liquid in the new cylinder = 4 cm
The height of the liquid in the new cylinder will be 4 cm. The term height is frequently used to describe someone's or something's height.
What is the height?Height is defined as the vertical distance between an object's top and bottom. It is measured in centimeters, millimeters, meters, and other units.
From the given conditions;
The volume of the liquid is, [tex]\rm V_L=36 \pi \ cm^3[/tex]
The radius of the cylinder is,[tex]\rm r=3 cm[/tex]
The volume of the cylinder is found as;
[tex]\rm V= \pi r^2 h \\\\ \rm V= \pi (3)^2 h \\\\ \rm V=9\pi h[/tex]
The height of the liquid is in the new cylinder is found as;
The volume of cylinder = Volume of liquid
[tex]\rm 9 \pi h= 36 \pi \\\\ \rm h=\frac{36}{9} \\\\ h= 4 \ cm[/tex]
Hence the height of the liquid in the new cylinder will be 4 cm.
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