Final answer:
The jogger runs a total distance of 224 meters, which includes running along the width and length of the park and taking a shortcut diagonally across the park.
Explanation:
To calculate the total distance the jogger runs, we must add the distances from each leg of the jogger's path. Starting from the southeast corner, the jogger runs the width of the park (28 meters) to the west, and then the length of the park (96 meters) to the north, reaching the northwest corner. The shortcut from the northwest corner directly back to the southeast corner, where her car is parked, is the hypotenuse of the resulting right-angled triangle. To find the length of this hypotenuse, we use the Pythagorean theorem (a² + b² = c²), where the sides of the rectangle serve as 'a' and 'b'.
Let's calculate the hypotenuse:
a = 28 m (width)
b = 96 m (length)
c = √(a² + b²) = √(28² + 96²)
c = √(784 + 9216)
c = √10000
c = 100 m
Now, we sum up all the distances:
28 m (west along the width)
96 m (north along the length)
100 m (shortcut diagonally)
Total distance = 28 m + 96 m + 100 m = 224 meters
Thank you so much
I need the help
Answer:
g(x) is translated 6 units down from f(x)
Step-by-step explanation:
given a function f(x) then f(x) + c represents a vertical translation
• If c > 0 then vertical translation up ↑
• If c < 0 then vertical translation down ↓
Y=7 X=2 what is the value of x when y =21
Step-by-step explanation:
x might equal 6 because 21 divided by 7 is 3 so u multiply 3 by 2. You get 6. i think x equals 6. Hope this is right and hope this helped!
Answer:
6
Step-by-step explanation:
y times 3 equals 21 because 7 times 3 equals 21 so:
x times 3 equals 6 because 2 times 3 equals 6
Annette has 5more dimes than quarters, the total amount is $3.30. How many of each coin does she have?
A
Step-by-step explanation:the answer is you have 8 quarter and 13 dimes .
Because you have 5 more dimes than quarters which will equal 3 dollars and 30 cents
Annette has a total of 5 coins according to the total money she has.
Given that,
Annette has 5more dimes than quarters, the total amount is $3.30. How many of each coin does she have is to be determined.
In mathematics, it deals with numbers of operations according to the statements. There are four major arithmetic operators, addition, subtraction, multiplication and division,
Here,
let the number of dimes be x
Now a number of quarters is x - 5
Accoding to the question,
x + x - 5 = 3.30
2x = 3.30 + 5
2x = 8.30
x = 4.15
Now,
here
number of dimes has approximately = 4
number of quarters = x - 5 = 4 - 5 = -1 (value is negative which is not possible). = 0
Thus, Annette has a total of 5 coins according to the total money she has.
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Triangle ABC was dilated to triangle A'B'C'. What was the magnitude of the dilation?
A) 1
B) 2
C) 3
D) 4
Answer:
B) 2
Step-by-step explanation:
If you start from the origin and go to point B, you went up 2, and to the left 1. Now if you go from the origin to B', you went up 4, and to the left 4. Lets compare the ratios.
2/1 and 4/2
You had to multiply the first ration by 2 to get to the second ratio.
Solve the following problems: Given: ∆AFD, m ∠F = 90° AD = 14, m ∠D = 30° Find: Area of ∆AFD
We have the triangle 30° - 60° - 90°.
The sides are in proportion: 2 : √3 : 1
(look at the picture).
[tex]2a=14[/tex] divide both sides by 2
[tex]a=7[/tex]
[tex]a\sqrt3=7\sqrt3[/tex]
The area of a trinagle AFD:
[tex]A_{\Delta}=\dfrac{1}{2}(7)(7\sqrt3)=\boxed{\dfrac{49\sqrt3}{2}}[/tex]
Given that (2,9) is on the graph of f(x) find the corresponding point for the function f(x+2)
Answer:
The corresponding point for the function f(x+2) is (0,9)
Step-by-step explanation:
The point (2,9) lies on the graph of f(x). And we have to find the corresponding point for the function f(x+2).
Whenever we add some constant "c" in x then the graph of the function shifts left by 'c' units.
We can see that, 2 has been added with x . Hence, the graph of the function will shift left by 2 units.
Therefore, the corresponding point for the function f(x+2) is given by
(2-2,9)
= (0,9)
William is 1/6 as old as his father but 5 years older than his sister Mary. If the sum of all their ages is 51, how old is William?
Answer: William is 7 years old
Hope this helps, I can take the time to explain if needed:)
By creating a system of equations from the information given and solving for William's age, we determine that William is 7 years old.
The question presents a typical age-related algebra problem. We have three unknowns: William's age, his father's age, and his sister Mary's age. To solve this problem, we need to set up a system of equations based on the information provided.
Let's let W stand for William's age, F for his father's age, and M for Mary's age.
The first piece of information tells us that William is 1/6 as old as his father, so F = 6W.
The second piece says that William is 5 years older than his sister Mary, so W = M + 5.
Lastly, we know that the sum of all their ages is 51, so W + F + M = 51.
Now, we'll substitute F and M from the first two equations into the third equation:
W + 6W + (W - 5) = 51
This simplifies to:
8W - 5 = 51
Adding 5 to both sides gives us:
8W = 56
Dividing both sides by 8, we find:
W = 7
Therefore, William is 7 years old.
Emily and a friend bought 2 tickets to see a soccer game each ticket costs 8.25 dollars the friends paid a toatal of 24.50 dollars which included a parking fee what percent increase represents the change when the parking fee is included?
Answer:
48 percent increase
Step-by-step explanation:
write the equation if the line that passes through (4,5) and has a slope of m=3
Answer:
y = 3x - 7
Step-by-step explanation:
The point-slope formula for a straight line is
y – y₁ = m(x – x₁)
x₁ = 4; y₁ = 5; m = 3 Substitute the values
y – 5 = 3(x - 4) Remove parentheses
y – 5 = 3x - 12 Add 5 to each side
y = 3x - 7
The graph is a straight line with a y-intercept at y = -7 and a slope = 12/4 = 3.
How do I solve this math problem?
Answer: 4x² + 4x - 2 - [tex]\frac{3}{2x+3}[/tex]
Step-by-step explanation:
You can use either synthetic or long division. I am using synthetic division:
2x + 3 = 0 ⇒ x = [tex]-\frac{3}{2}[/tex]
[tex]-\frac{3}{2}[/tex] | 4 10 4 -6
| ↓ -6 -6 3
4 4 -2 -3 ← -3 is the remainder
↓ ↓ ↓
4x² +4x -2 ← factored polynomial
ANSWER ASAP!!!!
Three of the choices are ways to express 0.50. Which is NOT?
A. 1 half
B. 5 hundredths
C. 5 tenths
D. 50 hundredths
Answer:
B
Step-by-step explanation:
5 days 6 hours 20 minutes minus 3 days 8 hours 40 minutes plz help will make brainliest
Answer:
1 day 21 hours 40 minutes
Step-by-step explanation:
5 days 6 hours 20 minutes
- 3 days 8 hours 40 minutes
============================
We will need to borrow minutes from the hours because we don't have enough.
1 hour = 60 minutes
6-1 = 5 hours
20 +60 = 80 minutes
5 days 5 hours 80 minutes
- 3 days 8 hours 40 minutes
==========================
We will need to borrow hours from the days because we don't have enough.
1 day = 24 hours
5 -1 =4 days
5 + 24 = 29 hours
4 days 29 hours 80 minutes
- 3 days 8 hours 40 minutes
==========================
1 day 21 hours 40 minutes
Answer:
1 day 21 hours 40 minutes
Step-by-step explanation:
you have to convert the days to hours, then convert the hours to minutes then subtract
4 days 29 hours 80 minutes - 3 days 8 hours 40 minutes = 1 day 21 hours 40 minutes
PLZ MARK BRAINIEST
how to write slope-intercept form through (-1,3) and a slope of -1
The slope-intercept form:
[tex]y=mx+b[/tex]
m - slope
b - y-intercept
We have the slope m = -1 and the point (-1, 3). Substitute:
[tex]3=(-1)(-1)+b[/tex]
[tex]3=1+b[/tex] subtract 1 from both sides
[tex]2=b\to b=2[/tex]
Answer: y = -x + 2PLEASE HELP ME
And show work
Answer:
The snow cone in a cup will hold more.
Step-by-step explanation:
Traditional snow cone:Firstly, to find the area of the cone you need to know the formula:
[tex]\frac{1}{3}\pi r^{2} h[/tex]
So simply plug the values in:
[tex]\frac{1}{3}\pi 4^{2} 13[/tex]
= 217.81 = 218cm³
Snow cone in a cup:To find the area of a cylinder, you need to remember the formula:
The radius is half the diameter so:
Radius = 8 ÷ 2 = 4
[tex]\pi r^{2} h[/tex]
So simply plug these values in:
[tex]\pi 4^{2} 5[/tex]
= 251.33 = 251cm³
So this means that because the snow cone in a cup is 251cm³ whereas the traditional snow cone is only 218cm³, the snow cone in a cup will hold more.
Complete the equation of the graphed linear function in point-slope form. y – (–2) = (x – ) The graph of the function goes through point 1, negative 2 and point 2, 2.
Answer:
[tex]y-(-2) = 4(x-1)[/tex]
Step-by-step explanation:
Point-slope form of the equation of a straight line is:
[tex]y-y_0 = m(x-x_0)[/tex] (1)
The two points given in the problem are:
[tex](x_0,y_0)=(1,-2)\\(x_1,y_1)=(2,2)[/tex]
So, the slope of the line is given by:
[tex]m=\frac{y_1 -y_0}{x_1 -x_0}=\frac{2-(-2)}{2-1}=\frac{4}{1}=4[/tex]
And substituting into eq.(1), we find:
[tex]y-(-2) = 4(x-1)[/tex]
What is the circumference of the circle? r=6.4
Answer:
C = 40.2124
Step-by-step explanation:
The formula for circumference is
C = 2*pi*r
where r is the radius.
Substitute what we know.
C = 2 * pi * 6.4
C = 12.8 * pi
If we use substitute pi in, we get
C = 40.2124
In a candy store, a $12.00 jar of candy is labeled, "35% off." what is the sale price of the jar of candy?
Answer:I belive the sale price is $11.65
Step-by-step explanation:
$12.00-$0.35
sorry if im wrong
This week, Jamyra spent a total of 100 minutes studying. This total was 8 more than four times the amount of minutes she studied last week. How many minutes did Jamyra spend studying last week?
Answer: 23 minutes
Step-by-step explanation:
4x + 8 = 100
100 is 8 more than 4 times of minutes than last week.
X = minuted she studied last week.
Find x
4x = 100 - 8
4x = 92
x = 92/4
x = 23 minutes
Based on the problem, we form an equation 4x + 8 = 100 to represent the given situation. After solving this equation, we find that Jamyra spent 23 minutes studying last week.
Explanation:The question is asking about the amount of time that Jamyra spent studying last week based on the information provided about this week. It's given that Jamyra spent 100 minutes studying this week and that this total was 8 more than four times the amount of minutes she studied last week.
We can form an equation from this information: 4x + 8 = 100, where 'x' is the time Jamyra spent studying last week. Subtract 8 from both sides to get 4x = 92.
Then, divide both sides of the equation by 4 to isolate 'x', and we get x = 23.
So, Jamyra spent 23 minutes studying last week.
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Two cars leave towns
950
kilometers apart at the same time and travel toward each other. One car's rate is
16
kilometers per hour less than the other's. If they meet in
5
hours, what is the rate of the slower car?
Final answer:
The speed of the slower car is 87 km/h. This was calculated by setting up an equation with the sum of the distances traveled by both cars after 5 hours, which is 950 km, and solving for the speed of the faster car first, then finding the speed of the slower car.
Explanation:
To determine the rate of the slower car in a scenario where two cars travel toward each other from 950 kilometers apart and meet in 5 hours, we set up an equation based on the relative speeds and distances covered. Let the speed of the faster car = v km/h; therefore, the speed of the slower car would be (v - 16) km/h, since it's given that the slower car travels 16 km/h less than the faster one.
The sum of the distances traveled by both cars when they meet after 5 hours is 950 km. We can express this with the equation: 5v + 5(v - 16) = 950.
Solving for v:
Subtracting 16 km/h from the faster car's speed gives us the slower car's speed:
v - 16 km/h = 103 km/h - 16 km/h = 87 km/h.
Therefore, the rate of the slower car is 87 km/h.
q supp r and m q =22 degrees
Answer:
<R = 158
Step-by-step explanation:
Supplementary angles equal 180 degrees.
<Q + <R =180
22 + <R = 180
Subtract 22 from each side
22-22 + <R = 180-22
R = 158
Answer:
Option 2 - [tex]\angle R=158^\circ[/tex]
Step-by-step explanation:
Given : [tex]\angle Q[/tex] supp [tex]\angle R[/tex] and [tex]\angle Q=22^\circ[/tex]
To find : [tex]\angle R[/tex] ?
Solution :
Supp means the supplementary angle.
We know that,
The sum of two supplementary angle is 180°.
i.e. [tex]\angle Q+\angle R=180^\circ[/tex]
Substitute [tex]\angle Q=22^\circ[/tex],
[tex]22+\angle R=180^\circ[/tex]
[tex]\angle R=180-22[/tex]
[tex]\angle R=158[/tex]
Therefore, [tex]\angle R=158^\circ[/tex]
So, option 2 is correct.
Which of the following does not represent a function? graph of a sine wave function graph of a line with a negative slope and a y intercept of negative 5 graph of a positive parabola oriented about the y axis with y intercept negative 6 graph of an absolute value function oriented about the x-axis
If you are 14 years old now, which equation could be used to solve for your age, Y, 22 years from now?
14*Y=22
14+22=Y
14-22=Y
14+Y=22
Answer:
14+22=Y
Step-by-step explanation:
Since it is 22 years from now, you would add 22 to your current age, 14, to get Y, the age.
The correct equation to find your age 22 years from now, if you are currently 14, is 14 + 22 = Y. Solving the equation gives Y equals to 36.
Explanation:The correct equation that can be used to solve for your age, Y, in 22 years if you are currently 14 years old then the second option i.e., equation 14 + 22 = Y is the correct answer.
This equation represents an addition where you add the number of future years (22 years) to your current age (14 years old). When you solve this equation, Y equals to 36, which would be your age 22 years from now, assuming you're currently 14 years old.
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Suppose that y varies directly with x, and y = 10 when x = 5. What direct variation equation relates x and y? What is the value of y when x = 2?
The constant of variation is usually given using the letter k.
To find K you would divide Y by x, so the equation becomes k = Y/x.
First find k using the first y and x values provided:
k = 10/5 = 2
Now you know k, you can solve for y when x = 2:
using the equation k =y/x, replace k and x with the known values and solve for y:
2 = y/2
y = 2*2
y = 4
Answer: Linear equation y=2x
Step-by-step explanation:
If x=2
Then y=2(2)
y=4
a store has some sale on let supplies the price of each item is marked down 25% the store also offers a coupon for 5 off for when you check out write an expression that represents the final price after a customer uses the coupon
What is the solution of 14=y-10
Answer:
24
Step-by-step explanation:
Just Add 10 to both sides (The rule is that in equations, what you do to one side, must be done to the other
[tex]14=y-10\\14+10=y-10+10\\24=y[/tex]
Answer:
24
Step-by-step explanation:
14 = y - 10
Addition property of equality: You can add the same value to both sides.
14 + 10 = y - 10 + 10
Add: 24 = y
y = 24
Solution means the value of the variable.
in the diagram, HE ||GF. Find DF
Answer:
WOwwwzerzzzzZZZZZZZZZZZZZZZZZZZZ
evaluate each using the values given.
(z)(yx)^2+z; use x=2,y=2, and z=2
A.40
B.36
C. 34
D. 35
Put the values of x = 2, y = 2 and z = 2 to the expression (z)(yx)²+z:
[tex](2)(2\cdot2)^2+2=(2)(4)^2+2=(2)(16)+2=32+2=34[/tex]
Answer: C. 34An old billionaire is writing his will, and deciding how to distribute his nine estates among his three children. He wants to give each child at least one estate, and he does not want to give any two of his children the same number of estates. In how many possible ways can he distribute his estates?
The old billionaire can distribute his nine estates among his three children in one possible way, with the conditions that each child must receive at least one estate no two children can receive the same number of estates.
Explanation:This is a combinatorics problem in mathematics, specifically a variety problem. The billionaire has nine estates and three children. The conditions are that each child must receive at least one estate and no two children can receive the same number of estates.
Considering these conditions, the estates can be distributed in the following way: The first child can receive one estate, the second two, and the third child six. This is just one way to distribute the estates; there are several other combinations possible given the constraints.
To calculate the total number of possible distributions, we must consider all combinations. However, with the given constraints, there is only one possible way to distribute the estates among the three children.
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There are 18 possible ways for the billionaire to distribute his estates among his three children, ensuring that each child receives at least one estate and no two children receive the same number of estates.
Explanation:To distribute the nine estates among the three children, we can use combinatorics.
Step 1: We give each child one estate each. This leaves us with six estates.
Step 2: We need to divide these six estates among the three children in such a way that no two children receive the same number of estates.
Case 1: If we distribute the six estates as 4-1-1 (four estates to one child, one estate to each of the other two children), we have 3 options to choose the child who receives four estates. Once that is chosen, there are 2 options for the child who receives one estate, and the remaining child will automatically receive one estate. So, in this case, we have 3 * 2 = 6 options.
Case 2: If we distribute the six estates as 3-2-1 (three estates to one child, two estates to another, and one estate to the remaining child), we have 3 options to choose the child who receives three estates. Once that is chosen, there are 2 options for the child who receives two estates and one option for the child who receives one estate. So, in this case, we have 3 * 2 * 1 = 6 options.
Case 3: If we distribute the six estates as 3-1-2 (similar to Case 2, but switching the number of estates for two of the children), we also have 6 options.
Therefore, the total number of possible ways to distribute the estates is 6 + 6 + 6 = 18.
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write a story problem that represents 528 divided by 24
Answer:
Micheal owns a farm. On that farm he plants 528 oranges. After harvest, he decides to pack all of his oranges into crates to sell. If he has 24 crates, how many oranges should he pack into each crate? Will there be too many oranges in which there will be some left over?
Step-by-step explanation:
Addison plays 1/2 of a song in 1/4 of a minute. How minutes will she need to play a full song?
Answer:
30 minutes
Step-by-step explanation:
She plays 1/2 of a song in 1/4 of a minute so that would be 15 minutes because if you divide 60 by 4 you would get 15. You would multiply 15 by 2 because if she plays a full song you multiply 1/2 by 2 to get a whole. So she will need 30 minutes to play a full song