Consider the coordinate plane:
1. The origin is the point where Sharon and Jacob started - (0,0).
2. North - positive y-direction, south - negetive y-direction.
3. East - positive x-direction, west - negative x-direction.
Then,
if Jacob walked 3 m north and then 4 m west, the point where he is now has coordinates (-4,3);if Sharon walked 5 m south and 12 m east, the point where she is now has coordinates (12,-5).The distance between two points with coordinates [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex] can be calculated using formula
[tex]D=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}.[/tex]
Therefore, the distance between Jacob and Sharon is
[tex]D=\sqrt{(12-(-4))^2+(-5-3)^2}=\sqrt{16^2+8^2}=\sqrt{256+64}=\sqrt{320}=8\sqrt{5}\approx 11.18\ m.[/tex]
The amount of interest earned on a savings account varies directly with the amount of money saved. If $208 in interest is earned on $6,500 of savings, how much interest will be earned on $8,000 of savings over the same time period? $224 $240 $256 $272
Which transformations can be used to show that circle P is similar to circle Q?
Circle P: center (2, −3) and radius 4
Circle Q: center (2, 3) and radius 28
.
Select each correct answer.
Circle Q is a translation of circle P, 6 units up.
Circle P is a dilation of circle Q with a scale factor of 24.
Circle Q is a translation of circle P, 6 units left.
Circle Q is a dilation of circle P with a scale factor of 7.
Answer: The answer is below i am in k12 just took the test
Circle Q is a dilation of circle P with a scale factor of 7. "
Circle Q is a translation of circle P, 6 units up.
Step-by-step explanation:
Suppose Karel wants to be the least expensive babysitter in the neighborhood. How much should she charge?
Suppose Karel wants to charge the same hourly rate as most of the other baby-sitters. How much should she charge?
Suppose Karel wants her hourly rate to be higher than the rate of half of other baby-sitters, but lower than the hourly rate of the rest of the babysitters. How much should she charge?
In addition to the babysitting rates charged by others, what might Karel consider when she sets her rates?
To be the least expensive babysitter, Karel should charge less than $2.00. If she wants her hourly rate to be higher than half the babysitters but lower than the other half, she could charge slightly less than $2.75. Beyond these rates, Karel should consider factors like her own experience, the specific tasks she'll perform, and the hours she'll work.
Explanation:To determine how much Karel should charge for her babysitting services, we need to consider the other babysitting rates and find the midpoint. The other students charge the following amounts: Stephanie-$2.75, Jessica-$2.00, Michael-$3.00, Raoul -$2.50, Rolanda-$2.75, Harry -$2.25, Samuel-$2.25, Anita-$2.75.
To be the least expensive, Karel should charge less than the lowest rate, which is $2.00 charged by Jessica. So, Karel could charge $1.75, for example.
Now, suppose Karel wants to have an hourly rate higher than half the babysitters but lower than the other half. We need to organize the rates in ascending order, and then find the median value. If we do this, we find that the middle value (the median) is $2.75. Therefore, Karel could charge slightly less than this, for example, $2.70.
Lastly, Karel should also consider other factors when setting her rates. These might include her experience and skills as a babysitter, the average babysitting rates in her neighborhood or city, the specific tasks she'll be expected to perform, and the hours she'll be working.
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Find the dimensions of a rectangle whose area is 221 cm2 and whose perimeter is 60 cm. (enter your answers as a comma-separated list.)
The dimensions of a rectangle with an area of 221 cm² and a perimeter of 60 cm are found by solving a system of equations derived from the definitions of area and perimeter. The dimensions are 13 cm by 17 cm, or equivalently, 17 cm by 13 cm.
Explanation:To find the dimensions of a rectangle with an area of 221 cm2 and a perimeter of 60 cm, we will let the length be x and the width be y. The area of a rectangle is found by multiplying the length and width, so we have the equation x * y = 221. The perimeter is twice the sum of the length and width, so we have 2x + 2y = 60, which simplifies to x + y = 30.
To solve these equations, divide the perimeter equation by 2 to find y = 30 - x. Substituting this into the area equation gives x(30 - x) = 221. Expanding this and bringing all terms to one side provides a quadratic equation: x2 - 30x + 221 = 0. Solving this quadratic equation by factoring or using the quadratic formula gives the dimensions of the rectangle.
The solutions to the quadratic equation are x = 13 and x = 17. Since x and y are interchangeable as length and width, the two sets of possible dimensions for the rectangle are 13 cm by 17 cm and 17 cm by 13 cm.
The dimensions of the rectangle are [tex]17\ cm , 13\ cm[/tex]
To find the dimensions [tex]\( l \)[/tex] (length) and [tex]\( w \)[/tex] (width) of the rectangle given its area and perimeter, we start with the following equations:
1. Area equation:
[tex]\[l \times w = 221\][/tex]
2. Perimeter equation:
[tex]\[ 2l + 2w = 60 \][/tex]
Step-by-Step Solution:
The dimensions of the rectangle are [tex]{{17, 13} \) cm.[/tex]
From the perimeter equation, divide everything by [tex]2[/tex] to simplify:
[tex]\[l + w = 30\][/tex]
Now we have a system of equations:
[tex]\[\begincases}l \times w = 221 \\l + w = 30\end{cases}\][/tex]
Let's solve this system using substitution or elimination:
From [tex]\( l + w = 30 \)[/tex], we can express [tex]\( w \)[/tex] in terms of [tex]\( l \)[/tex]
[tex]\[w = 30 - l\][/tex]
Substitute [tex]\( w = 30 - l \)[/tex] into the area equation:
[tex]\[l \times (30 - l) = 221\][/tex]
[tex]\[30l - l^2 = 221\][/tex]
Rearrange this equation to form a quadratic equation:
[tex]\[l^2 - 30l + 221 = 0\][/tex]
Now, solve this quadratic equation using the quadratic formula [tex]\( l = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \), where \( a = 1 \), \( b = -30 \), and \( c = 221 \)[/tex]
[tex]\[l = \frac{-(-30) \pm \sqrt{(-30)^2 - 4 \times 1 \times 221}}{2 \times 1}\][/tex]
[tex]\[l = \frac{30 \pm \sqrt{900 - 884}}{2}\][/tex]
[tex]\[l = \frac{30 \pm \sqrt{16}}{2}\][/tex]
[tex]\[l = \frac{30 \pm 4}{2}\][/tex]
Calculate both possible values of [tex]\( l \)[/tex]
[tex]\[l = \frac{30 + 4}{2} = 17 \quad \text{or} \quad l = \frac{30 - 4}{2} = 13\][/tex]
Corresponding values of \( w \)
[tex]If\ \( l = 17 \), then \( w = 30 - 17 = 13 \)[/tex]
[tex]If\ \( l = 13 \), then \( w = 30 - 13 = 17 \)[/tex]
Therefore, the dimensions of the rectangle are [tex]\( 17 \) cm[/tex] by [tex]\( 13 \) cm.[/tex]
Verification:
[tex]Area: \( 17 \times 13 = 221 \) cm\(^2\)[/tex]
[tex]Perimeter: \( 2 \times (17 + 13) = 2 \times 30 = 60 \) cm[/tex]
Both conditions match the given area and perimeter, confirming that the dimensions are correct.
Given f(x)=3x^2+5 and g(x)=x−2 .
What is (fg)(x) ?
What is the sum of the geometric series
What is Y=x^2+6x+4 in vertex form?
PLEASE SOMEONE HELP ME ON THIS
Find the exact volume of the cylinder.
Eli and Karl each throw a basketball straight up in the air at the same time. Eli is standing on a deck and the height of his ball, in meters, is given by the function f(x)=−4.9x2+12x+2.5 , where x is the number of seconds after the ball is released from his hands.
Karl is standing on the ground and the height of his ball, in meters, is given by the function g(x)=−4.9x2+14x , where x is the number of seconds after the ball is released from his hands.
There is a moment when the basketballs are at the same height.
What is this height?
Enter your answer, rounded to the nearest tenth of a meter, in the box.
Answer:
Just took the K12 quiz, and like killdrone said in the comments, the correct answer is 9.8 m
Step-by-step explanation:
The height at which both basketballs are at the same height is approximately 16.3 meters.
Explanation:To find the moment when the basketballs are at the same height, we need to find the common height value for both functions.
Setting the functions equal to each other, we get: -4.9x^2 + 12x + 2.5 = -4.9x^2 + 14x
Simplifying the equation, we get 2x = 2.5, which means x = 1.25.
Substituting this value back into the original function for Eli, we get f(1.25) = -4.9(1.25)^2 + 12(1.25) + 2.5 = 16.325
Therefore, the height at which both basketballs are at the same height is approximately 16.3 meters.
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Triangle HIJ has been reflected to create triangle H'I'J'. Segment HJ= H'J'= 4, segments IJ = I'J' = 7, and angles J and J' are both 32 degrees. Which postulate or theorem below would prove the two triangles are congruent?
A. SSS
B. SAS
C. ASA
D. HL
Evaluate the function for
f(x) = x + 3 and g(x) = x2 − 2.
(f − g)(0)
(f − g)(0) =
To evaluate (f - g)(0), find f(0) and g(0) for the functions f(x) = x + 3 and g(x) = x^2 - 2, and then subtract the latter from the former. For f(0) we have 3, and for g(0) we have -2. Subtracting, we get (f - g)(0) = 5.
Explanation:To evaluate the expression (f - g)(0), it means we need to find the value of the function f at x = 0, subtract the value of the function g at x = 0, and combine them. Given the functions f(x) = x + 3 and g(x) = x^2 − 2, let's calculate their values at x = 0:
For f(x), we have f(0) = 0 + 3 = 3For g(x), we have g(0) = (0)^2 − 2 = 0 − 2 = −2Now, let's subtract g(0) from f(0):
(f - g)(0) = f(0) - g(0) = 3 - (-2) = 3 + 2 = 5
Therefore, the value of (f - g)(0) is 5.
which number is a common factor of 32,48,and 80?
Answer:
Step-by-step explanation:
The GCF is found by listing the factors of all the numbers and picking the largest one that occurs in each. The factors of your numbers are as follows:
32: 1, 2, 4, 8, 16, 32
48: 1, 2, 3, 4, 6, 8, 12, 16, 24, 48
80: 1, 2, 4, 5, 8, 10, 16, 20, 40, 80
Looking at those factors you can pick out anything you'd like: all the common factors, the greatest common factors, whatever you need.
Final answer:
The number 16 is a common factor of 32, 48, and 80, as it is the only number among the options given that divides evenly into all three numbers.
Explanation:
To find a common factor of 32, 48, and 80, we need to identify a number that divides evenly into all three numbers. A systematic way to do this is to list out the factors of each number and see which ones they have in common.
Factors of 32: 1, 2, 4, 8, 16, 32
Factors of 48: 1, 2, 3, 4, 6, 8, 12, 16, 24, 48
Factors of 80: 1, 2, 4, 5, 8, 10, 16, 20, 40, 80
From these lists, we see that the numbers 1, 2, 4, 8, and 16 are common factors of all three numbers. However, among the options provided (3, 9, 10, 16), 16 is the only number that appears in all lists and is therefore a common factor of 32, 48, and 80.
Donna Bakes biscuits on a rectangular cookie sheet that is 30 centimeters by 50 centimeters.Each biscuit had a diameterof 8 centimeters. What is the maximum number of biscuits donna can make on the sheet at once on the cookie sheet.
Donna can make a maximum of 94 biscuits on the rectangular cookie sheet at once.
Explanation:To find the maximum number of biscuits Donna can make on the rectangular cookie sheet, we need to calculate the area of the sheet and divide it by the area of each biscuit.
The area of the sheet is given by length x width, so it is 30 cm x 50 cm = 1500 cm².
The area of each biscuit is given by πr², where r is the radius (half the diameter) of the biscuit. In this case, the radius is 8 cm / 2 = 4 cm. So the area of each biscuit is π x 4 cm x 4 cm = 16π cm².
To find the maximum number of biscuits, we divide the area of the sheet by the area of each biscuit:
Maximum number of biscuits = Area of the sheet / Area of each biscuit = 1500 cm² / 16π cm² ≈ 94.25 biscuits.
Since we can't have a fraction of a biscuit, the maximum number of biscuits that Donna can make on the sheet at once is 94 biscuits.
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Need help on 8,9,10,11 and 12
You want to measure the length of a ribbon in inches. You only have a centimeter ruler. The length of the ribbon is 16 cm. Is the ribbon longer or shorter than 16 inches? How many inches long is it?
A certain animated movie earned $1.1 * 10^9 in revenues at the box office. The movie lasts 9.1*10^1 minutes. How much revenue was earned per minute of the movie?
To find the revenue per minute of the movie, divide the total revenue ( [tex]\$1.1 \times 10^9[/tex]) by the length of the movie ( [tex]9.1 * 10^1[/tex]). The trick is to divide the numerical portions and the power of ten portions separately. The answer is approximately [tex]\$1.20879 \times 10^7[/tex] per minute.
Explanation:The subject of this question is mathematics and it involves a concept called division in scientific notation. To find the revenue per minute for this movie, we'll divide the total earnings ($1.1 * 109) by the length of the movie in minutes (9.1 * 101).
Step 1: Place the two values with scientific notation over each other, akin to a typical division problem. This means $1.1 * 109 / 9.1 * 101.
Step 2: Divide the two numerical portions separately from the power of ten portions. This is dividing 1.1 by 9.1 and 109 by 101.
Step 3: The former (from step 2) gives you approximately 0.120879 and the latter simplifies to 108 (because when you divide with the same base, you subtract the exponents).
So the earnings per minute of this movie were approximately $0.120879 * 108, or $1.20879 * 107.
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16 POINTS. Find x and y intercepts and show work.
I’m looking for number six.
**Giving away 20 points**. I need to know the arc length for EF and the area of sector EOF please:) (also plz show work thanks!!)
Which graphic organizer would help you visualize important events in the history of the U.S. space program? timeline point-by-point diagram cause-and-effect chart Venn diagram
Answer with explanation:
If we have to visualize important events in the history of the U.S. space program, we have to keep following things in mind
Year Program
19... Satellite A
19.. On Moon ....
.... ............
...... .........
So, while scaling , we will keep year , that is time on any of the axis and program on another axis.
→→The Appropriate option will be
(a) Time line
Find the lateral area and the total area of the prism.
27 sq. ft.
36 sq. ft.
54 sq. ft.
Answer:
54 sq. ft.
Step-by-step explanation:
LA=ph or in other words Lateral Area= base perimeter * height
The perimeter of the base is 9 because 3+3+3=9.
The height is 6. So 6 * 9 = 54
What is the square root of -1
Which of the following pairs of numbers contains like fractions?
A. 6⁄7 and 1 5⁄7
B. 3⁄2 and 2⁄3
C. 3 1⁄2 and 4 4⁄4
D. 5⁄6 and 10⁄12
The polygons are similar. Find the value of x
△ABC∼△DEF , △ABC has a height of 20 inches, and △DEF has a height of 24 inches. What is the ratio of the area of △ABC to the area of △DEF ?
Starting time 2:15 elapsed time 45 minutes
Alvin financed $3,450 to buy a new car. If he made 36 payments of $138.50 each, how much interest did he pay on the loan? a. $153.60 b. $415.50 c. $1,536 d. $4,986
A publisher pays 6% royalty to a book writer for the first 1,000 copies sold, and 5% on any number of copies above 1,000. They will print 3,000 copies. Find the sale price of the book if the writer expects to be paid $5,000.
Which is the graph of the system x + 3y > –3 and y < 1/2x + 1?
The answer to this question is D.