At 7 a.m. Gene left Austin and headed south at 10 miles per hour. At 8 a.m. Anne left from the same place and headed south on the same road. If Anne was 60 miles ahead by 3 p.m. on the same day, what was her speed?
Anne's speed is 20 miles per hour. If she returned home by the same path 7 hours and 30 minutes after she left, her average speed for the entire trip is 18.67 miles per hour while her average velocity is zero.
To answer this question, we need to calculate Anne's speed based on the information given. Gene started at 7 a.m. traveling at 10 miles per hour. By the time Anne starts at 8 a.m., Gene has already covered 10 miles (since he travels for 1 hour). The time from 8 a.m. to 3 p.m. is 7 hours. Both Anne and Gene travel the same path for these 7 hours, but Anne is 60 miles ahead of Gene by 3 p.m. Therefore, we need to calculate the total distance Gene traveled in 8 hours, add 60 miles to that distance, and then divide by 7 to find Anne's speed.
First, we determine Gene's total travel distance by 3 p.m., which is 10 miles/hour * 8 hours = 80 miles. Anne is 60 miles ahead, meaning she traveled 80 miles + 60 miles = 140 miles in 7 hours. Thus, Anne's speed is 140 miles \/ 7 hours = 20 miles per hour.
For part (c), if Anne returned home by the same path 7 hours and 30 minutes after she left, the total trip time would be 15 hours (7 hours to 3 p.m. and another 7 hours and 30 minutes back). Since the round trip distance is 140 miles out and 140 miles back, the total distance is 280 miles. Her average speed is total distance divided by total time, hence 280 miles / 15 hours = 18.67 miles per hour. The average velocity for the round trip is zero because she ends up at the starting point, so the overall displacement is zero.
Write an equation of the line that is parallel to 2x + 4y = 6 and passes through the point (6, 4).
Find the distance between the two points. (2, 5) and (–1, –5)
How do you combine like terms of #-10+7x+24-2x#?
(05.07 mc) mandy needs to paint all the faces and the base of a model pyramid she made for her history project. the dimensions of the pyramid are shown here. what is the total surface area of the pyramid? a square pyramid is shown. the side of the square is 10 inches. the height of the triangular faces is 9 inches.
Answer:
280
Step-by-step explanation:
i n e e d p o i n t s
A total of 243 adults and children are at a movie theater. There are 109 more adults than children in the theater. If eh represents the number of adults and b represents the number of children, which system of equations could be used to find the number of adults and the number of children in the theater?
The system of the equations representing the situation is a+b = 243 and
a-b = 109 and values of a and b are 176 and 67 respectively.
What is a system of equations?A system of equations is a collection of two or more equations with a same set of unknowns.
Given that, A total of 243 adults and children are at a movie theater. There are 109 more adults than children in the theatre. If a represents the number of adults and b represents the number of children,
Establishing the equations according to the given situation,
a+b = 243......(i)
a-b = 109.......(ii)
Adding the equations, we get,
2a = 352
a = 176
Therefore, b = 67
Hence, The system of the equations representing the situation is a+b = 243 and a-b = 109 and values of a and b are 176 and 67 respectively.
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Evaluate the expression for = −3 and = 5.
r^{-4} s^2
Compare the functions shown below:
f(x) = −3x − 5
g(x)
cosine function with y intercept at 0, negative 3 h(x) = 2 cos(2x − π) + 4
Which function has the greatest y-intercept?
a. f(x)
b. g(x)
c. h(x)
d. all three functions have the same y-intercept
Find all y-intercepts:
1. For f(x): when x=0 you have that f(0)=-3·0-5=-5, then y-intercept is a point (0,-5).
2. For g(x): from the task conditions you have that g(x) is cosine function with y intercept at 0, negative 3, then y-intercept is a point (0,-3).
3. For h(x): when x=0 you have that h(0)=cos(2·0-π)+4=cos(-π)+4=-1+4=3, then y-intercept is a point (0,3).
As you can see the greatest y-intercept has function h(x).
Answer: correct choice is C.
Answer:
C
Step-by-step explanation:
I just took the test. :)
Out of the 180 students at a summer camp, 72 signed up for canoeing. There were 23 students who signed up for trekking, and 13 of those students also signed up for canoeing.
Use a two-way table to organize the information and answer the following question:
Approximately what percentage of students signed up for neither canoeing nor trekking?
72%
40%
54%
98%
The recommended space needed for certain plant is 2 ft.² you want to plant 32 of this plants in a square garden .what is the length of each side of the garden if you follow the recommendation?
The square of a positive number decreased by twice the number is 48. Find the number
Let the required positive number is x.
The square of the number is [tex]x^2[/tex]
Now, we have been given that square of a positive number decreased by twice the number. It means we have
[tex]x^2-2x[/tex]
Now, it is equal to 48. Hence, we have
[tex]x^2-2x=48\\ x^2-2x-48=0\\ x^2-8x+6x-48=0\\ x(x-8)+6(x-8)\\ (x-8)(x+6)=0\\ x=8,-6[/tex]
The number is positive, Hence, we have [tex]x=8[/tex]
Therefore, the required number is 8
Determine the equation of the line given by the graph.
A) y = 2x + 4
B) y = 4x + 2
C) y = 1/2x − 2
D) y = −2x + 4
The equation of the given line is y=2x+4. Therefore, option A is the correct answer.
From the given graph coordinates on the line are (-2, 0) and (0, 4).
What is slope of a line?The slope of the line is the ratio of the rise to the run, or rise divided by the run. It describes the steepness of line in the coordinate plane.
Slope of a line, m= 4/2 = 2
Put m=2 and (-2, 0) in y=mx+b
0=2(-2)+b
b=4
Substitute m=2 and b=4 in y=mx+b
That is, y=2x+4
The equation of the given line is y=2x+4. Therefore, option A is the correct answer.
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Where does Pythagorean identity come from and how does it relate to right triangles
Crater Lake Oregon is a roughly circular lake. The lake basin formed about 7000 years ago when the top of a volcano exploded in an immense explosion. Hillman Peak, Garfield Peak, and Cloudcap are three mountain peaks on the rim of the lake. The peaks are located in a coordinate plane at H(-4,1), G(-2,-3), and C(5,-2). Find the coordinates of the center of the lake.
Answer:
The coordinates of the center of the lake are [tex](\frac{-1}{3},\frac{-4}{3})[/tex].
Step-by-step explanation:
It is given that Hillman Peak, Garfield Peak, and Cloudcap are three mountain peaks on the rim of the lake. The peaks are located in a coordinate plane at H(-4,1), G(-2,-3), and C(5,-2).
If we joint these points, then we get a triangle and the center of a triangle is known as centroid.
The formula for centroid of a triangle is
[tex]Centroid=(\frac{x_1+x_2+x_3}{3},\frac{y_1+y_2+y_3}{3})[/tex]
The centroid of the triangle H(-4,1), G(-2,-3), and C(5,-2) is
[tex]Centroid=(\frac{-4-2+5}{3},\frac{1-3-2}{3})[/tex]
[tex]Centroid=(\frac{-1}{3},\frac{-4}{3})[/tex]
Therefore the coordinates of the center of the lake are [tex](\frac{-1}{3},\frac{-4}{3})[/tex].
A french fry stand at the fair serves their fries in paper cones. The cones have a radius of 222 inches and a height of 666 inches. It is a challenge to fill the narrow cones with their long fries. They want to use new cones that have the same volume as their existing cones but a larger radius of 444 inches. What will the height of the new cones be?
To find the height of the new cone with a larger radius that maintains the same volume, we calculate the volume of the original cone and solve for the new height using the cone volume formula.
Explanation:The student wants to find out the new height of the cone with a larger radius while maintaining the same volume as the original cone. The volume of a cone is given by the formula V = 1/3 πr²h. To find the height of the new cone, we'll use the volume of the original cone as the constant value.
Let's first calculate the volume of the original cone:
V_original = 1/3 π(222²)(666)Now, let's set up an equation with the new radius to solve for the new height (h_new):
1/3 π(444²)(h_new) = V_originalh_new = (V_original) / (1/3 π(444²))By substituting the V_original from step 1 into step 3, we can solve for h_new. The result will be the height of the new cone with a radius of 444 inches that has the same volume as the original cone.
Javier is 175% heavier than his brother . if javier brother weigh 80 pounds how much do javier weigh
You choose 3 bananas from a group of 9. In how many ways can this be done?
Assuming the order of selection doesn't matter:
[tex] \displaystyle
\binom{9}{3}=\dfrac{9!}{3!6!}=\dfrac{7\cdot8\cdot9}{2\cdot3}=84 [/tex]
For Jack's birthday, his mom is taking him and 12 friends to the zoo. If she pays $11 for each ticket using her credit card, what impact will it have on the available credit left on her credit card?
The impact on Jack's mom's available credit after purchasing zoo tickets for Jack and 12 friends at $11 each will be a reduction of $143.
When Jack's mom pays $11 for each zoo ticket for him and his 12 friends, she will be purchasing a total of 13 tickets (one for Jack plus 12 for his friends). To calculate the total cost, multiply the number of tickets by the price per ticket:
Number of tickets: 13 (Jack + 12 friends)Price per ticket: $11Total cost: 13 tickets × $11 per ticket = $143The total impact on her credit card's available credit will be a reduction of $143. If she had some available credit limit before this purchase, we just subtract this amount from her available credit to determine the new available credit.
What is the total amount and the amount of interest earned on $6,500 at 6% for 25 years?
Answer:
Total amount earned after 25 years=$27,897.16
Step-by-step explanation:
Step 1: Express formula for calculating total amount
The total amount after 25 years can be expressed as;
A=P(1+r)^n
where;
A=total amount after 25 years
P=principal amount
r=annual interest rate
n=number of years
Step 2: Substitute values in the expression
In our case;
P=$6,500
r=6%=6/100=0.06
n=25 years
replacing in the original expression;
A=6,500(1+0.06)^25
A=27,897.16
Total amount earned after 25 years=$27,897.16
Final answer:
The total amount after 25 years will be $27,897.16, and the amount of interest earned on a $6,500 investment at a 6% annual interest rate will be $21,397.16.
Explanation:
To calculate the total amount and interest earned on $6,500 at 6% for 25 years, we'll assume that the interest is compounded annually. The formula to calculate the total amount with compound interest is:
A = P(1 + r/n)^(nt)
Where:
A is the amount of money accumulated after n years, including interest.P is the principal amount (the initial amount of money).r is the annual interest rate (in decimal).n is the number of times that interest is compounded per year.t is the time the money is invested or borrowed for, in years.Let's plug the values into the formula:
A = $6,500(1 + 0.06/1)^(1*25)
A = $6,500(1 + 0.06)^25
A = $6,500(1.06)^25
A = $6,500 * 4.29187072
A = $27,897.16
The total amount after 25 years will be $27,897.16.
To find the interest earned, subtract the principal from the total amount:
Interest = A - P
Interest = $27,897.16 - $6,500
Interest = $21,397.16
The amount of interest earned will be $21,397.16.
Find the slope of the line graphed below
Find the perimeter of the polygon on this picture. I don’t know how to do this. Plz help
If matrix A is a 6 × 5 matrix, which order of matrix can be multiplied by matrix A?
Answer:
5 x n, where n is any natural number.
Step-by-step explanation:
If A is a 6 x 5 matrix, it means that A has 6 rows and 5 columns, this means that if a matrix B can be multiplied by A, then each one of its columns must have 5 entries. Therefore, B has to be a matrix with 5 rows and it might have any arbitrary number of columns, in other words B is a 5 x n matrix, where n must be a natural number bigger than 1.
Let v1 = (-6,4) and v^2 = (-3,6). Compute the following
V^1 * V^2
Find the dimensions of a rectangle whose width is 6 miles less than its length and whose area is 55 square miles.
Which item produces the magnetic field in the electromagnet?
I’m sorry if the picture is blurry but try please! :)
Thank you all
Image option 2 will produce the magnetic field in the electromagnetism.
What is Magnetic field?The portion of space near a magnetic body or a current-carrying body in which the magnetic forces due to the body or current can be detected.
Given that figures,
In figure option 2 there are wires given and as we know when there is current flowing in a body or wire it will create an electric field as well as magnetic field.
Hence, image option 2 is the correct option.
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In the ancient chinese proverb, there are more than how many different ways to breathe
Answer: 40
What we all know is that there is only one way to breath (inhaling and exhaling) For the ancient Chinese, as cited on ancient proverb there are forty (40) ways. These different ways promote relaxation thru breathing on the lower stomach.
each of the circles below has an area of 196 pi square units find the perimeter of the rectangle
Answer:
Step-by-step explanation:
Alright lets get started.
We have given the area of each circle as 196 pi square units.
since the area of the circle =[tex]\pi*radius^2[/tex]
so,the radius of the circle :
[tex]196\pi =\pi r^2[/tex]
[tex]r^2=196[/tex]
[tex]r=14[/tex]
therefore the diameter of the circle will be [tex]2*radius=2*14=28[/tex]
the perimeter of the rectangle=[tex]2*(length+ width)[/tex]
the length of the rectangle will be addition of diameters of the circle=[tex]28+28=56[/tex]
breadth of the rectangle is equal of the diameter =28
Perimeter of the rectangle =[tex]2*(56+28)=168[/tex]
Answer 168 units.
The perimeter of the given rectangle is 168 units
Given that area of each of the circles are [tex] 196 \pi [/tex] sq units and we know that the area of circle [tex]=\pi r^{2}[/tex] using this radius of the circle will be
[tex]\pi r^{2} =196\pi\\ r^{2} = 196\\ \\ r=14[/tex]
So, the diameter of the circle is twice the radius which is
[tex]2\times r\\ 2\times 14 =28 [/tex]
Here we can see that length of rectangle is equal to twice the diameter of the circle and breadth is equals to twice the radius
[tex]length= 28+28=56[/tex]
[tex]breadth = 2\cdot14=28[/tex]
How to find the perimeter of the given rectangle ?
To find the perimeter we use the formula
Perimeter of rectangle = [tex]2\cdot(length + breadth)[/tex]
On solving we get ,
[tex]2\cdot(56 +28)\\ 168 units[/tex]
Therefore, The perimeter of the given rectangle is 168 units
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A parabolic archway is 12 meters high at the vertex. at a height of 10 meters, the width of the archway is 8 meters. how wide is the archway at ground level?
We found the width at ground level to be approximately 19.6 meters.
We start by assuming the equation of the parabola to be of the form y = ax² + bx + c.
Since the vertex of the parabolic arch is at (0, 12), we know that c = 12. Next, we use the condition that at y = 10 meters, the width is 8 meters, meaning the points (4, 10) and (-4, 10) lie on the parabola. Plugging these into the equation:
For (4,10): 10 = a(4)² + b(4) + 1210 = 16a + 4b + 1216a + 4b = -2 (1)Solving for the same with (-4,10) is unnecessary as it results in the same equation. Next, we use the vertex form y = a(x - h)² + k ⇨ y = a(x - 0)² + 12 ⇨ y = ax² + 12.
From equation (1), we have 16a + 4b = -2. Since the vertex form tells us there is no 'b' term in the simplest form, 'b' must be 0. Thus, 16a = -2 ⇨ a = -1/8.
The equation of the parabola is therefore y = -(1/8)x² + 12.
To find the width at ground level (y = 0):
0 = -(1/8)x² + 12(1/8)x² = 12x² = 96 ⇨ x = ±√96 = ±4√6 ≈ ±9.8 meters.Thus, the total width of the arch at ground level is approximately 2 × 9.8 = 19.6 meters.
The perimeter of a rectangular floor is 50 feet. find the dimensions of the floor if the length is four times the width.
The dimensions of the rectangle are width = 5 feet and length = 20 feet.
What is the perimeter of the rectangle?The perimeter of a rectangle is defined as the addition of the length and width.
The perimeter of a rectangle = 2(L + W)
Where W is the width of the rectangle and L is the length of the rectangle
We have been given that the perimeter of a rectangular floor is 50 feet.
The length is four times the width.
Let the width of the rectangle is x
So the length of the rectangle = 4x
The perimeter of a rectangle = 2(L + W)
50 = 2(4x + x)
50 = 2(5x)
50 = 10x
10x = 50
x = 50 /10
Apply the division operation,
x = 5
So the length of the rectangle = 4(5) = 20 feet
Therefore, the dimensions of the rectangle are width = 5 feet and length = 20 feet.
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Anyone know this geometry question? Will give brainiest