Question:
What is the perimeter of the path, in miles?
Answer:
35 miles
Step-by-step explanation:
Given
Let the corners be ABCD
[tex]A = (-2,2)[/tex]
[tex]B = (1,2)[/tex]
[tex]C = (1,-2)[/tex]
[tex]D = (-2,-2)[/tex]
First, we calculate the perimeter of the corners in units.
This is done by calculating the distance between the corners.
Distance is calculated as:
[tex]D = \sqrt{(x_2 - x_1)^2 +(y_2 - y_1)^2 }[/tex]
For AB:
[tex](x_1,y_1) = (-2,2)[/tex]
[tex](x_2,y_2) = (1,2)[/tex]
[tex]D_1 = \sqrt{(1 - (-2))^2 +(2 - 2)^2 }[/tex]
[tex]D_1 = \sqrt{(1 +2)^2 +(0)^2 }[/tex]
[tex]D_1 = \sqrt{3^2}[/tex]
[tex]D_1 = 3[/tex]
For BC
[tex](x_1,y_1) = (1,2)[/tex]
[tex](x_2,y_2) = (1,-2)[/tex]
[tex]D_2 = \sqrt{(1 - 1)^2 +(-2 - 2)^2 }[/tex]
[tex]D_2 = \sqrt{(0)^2 +(-4)^2 }[/tex]
[tex]D_2 = \sqrt{16 }[/tex]
[tex]D_2 = 4[/tex]
For CD:
[tex](x_1,y_1) = (1,-2)[/tex]
[tex](x_2,y_2) = (-2,-2)[/tex]
[tex]D_3 = \sqrt{(-2 - 1)^2 +(-2 - (-2))^2 }[/tex]
[tex]D_3 = \sqrt{(-3)^2 +(-2 +2)^2 }[/tex]
[tex]D_3 = \sqrt{9 +0^2 }[/tex]
[tex]D_3 = \sqrt{9 }[/tex]
[tex]D_3 = 3[/tex]
For DA
[tex](x_1,y_1) = (-2,-2)[/tex]
[tex](x_2,y_2) = (-2,2)[/tex]
[tex]D_4 = \sqrt{(-2 - (-2))^2 +(2 - (-2))^2 }[/tex]
[tex]D_4 = \sqrt{(-2 +2)^2 +(2 +2))^2 }[/tex]
[tex]D_4 = \sqrt{0^2 +4^2 }[/tex]
[tex]D_4 = \sqrt{4^2 }[/tex]
[tex]D_4 = 4[/tex]
The perimeter P in units is:
[tex]P = D_1 + D_2 + D_3 + D_4[/tex]
[tex]P = 3+4+3+4[/tex]
[tex]P = 14[/tex]
Given that:
[tex]1\ units = 2.5\ miles[/tex]
Multiply both sides by 14
[tex]14 * 1\ units = 14 * 2.5\ miles[/tex]
[tex]14 \ units = 35\ miles[/tex]
Hence, the perimeter is 35 miles
PLEASE HELPPPP
Activity
In this activity, you will create a function from two points that satisfy it.
A linear function passes through the points (-2,3) and (-3,5). Complete the following tasks to find the equation of the function.
Part A
To find the equation, first find the rate of change. What is the rate of change for the linear function that passes through the two points?
Answer: The line representing the function has its y-intercept at 40. So, the initial value of the function graphed is 40.
Step-by-step explanation:
The equation of the line passing through the points (-2,3) and (-3,5) will be 2x + y + 1 = 0 and the rate of change is negative 2.
What is the linear system?A Linear system is a system in which the degree of the variable in the equation is one. It may contain one, two, or more than two variables.
A linear function passes through the points (-2,3) and (-3,5). Complete the following tasks to find the equation of the function.
Then the equation of the line passing through the points (-2,3) and (-3,5) will be
[tex]\begin{aligned} y - 5 &= \dfrac{5-3}{-3 + 2} (x + 3)\\\\y - 5 &= -2 (x + 3)\\\\y - 5 &= -2x -6\\\\2x + y + 1 &= 0 \end{aligned}[/tex]
The rate of change is negative 2.
More about the linear system link is given below.
https://brainly.com/question/20379472
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A factory produces 80,000 candies each day. They produce equal quauntities of four flavors cherry lemon orange and strawberry. The candies are mixed together during packaging . What is the probabillity that a randomly selected cany is orange
Answer: [tex]\dfrac14[/tex]
Step-by-step explanation:
Given: The factory produces equal quantities of four flavors cherry lemon orange and strawberry.
Let orange candy= cherry = lemon = strawberry = x
Total candies = x + x + x + x= 4x
The probability that a randomly selected candy is orange = [tex]\dfrac{x}{4x}=\dfrac14[/tex]
Hence, the probability that a randomly selected candy is orange = [tex]\dfrac14[/tex]
3(x+4) what is this question?
Answer:
Step-by-step explanation:
3×x+4×3
3x+12
Answer:
Step-by-step explanation:
The first step would be to multiply out the bracket. So, using this example we would times each item inside the bracket by 3.
As a result we would get: 3x + 12 = 18
Then we would need to move the 'x' value to one side of the equation and the rest of the equation to the other side. To move '12' onto the other side of the = sign we need to subtract 12 from both sides.
This would then bring us to: 3x = 6
Finally, to find the value of 'x' we then need to divide both side of the equation by 3.
Resulting in the final answer of x = 2
Expressed answers As reduced fraction. Find the trig value.
Tan A=
Answer:
The value of tan A: 40/9
i.e.
tan A = 40/9
Step-by-step explanation:
Given
Hypotenuse = 41
To determine
m ∠ A = ?
Using the trigonometric ratio
tan A = opposite / adjacent
Here:
Opposite of m ∠ A = 40Adjacent of m ∠ A = 9Thus, substituting opposite = 40 and adjacent = 0 in the equation
tan A = opposite / adjacent
tan A = 40/9
Therefore, the value of tan A: 40/9
i.e.
tan A = 40/9
Solve the system of linear equations by elimination.
-3.x – 5y = -7
-4x + 5y = 14
Answer:
(- 1, 2 )
Step-by-step explanation:
Given the 2 equations
- 3x - 5y = - 7 → (1)
- 4x + 5y = 14 → (2)
Add the 2 equations term by term to eliminate y , that is
- 7x + 0 = 7
- 7x = 7 ( divide both sides by - 7 )
x = - 1
Substitute x = - 1 into either of the 2 equations and solve for y
Substituting into (1)
- 3(- 1) - 5y = - 7
3 - 5y = - 7 ( subtract 3 from both sides )
- 5y = - 10 ( divide both sides by - 5 )
y = 2
solution is (- 1, 2 )
Answer:
( -1, 2)
Step-by-step explanation:
Since this is asking for elimination, you will need to line up x or y to be the opposite amount:
-3x -5y = -7
-4x + 5y = 14
(notice -5y and 5y are already opposite, therefore no further actions are needed to line them up.)
Next step is to add both equations up to eliminate y and to find x:
-7x = 7
x = -1
After finding x, plug the x back into either one of the equations to solve for y. If you are unsure, you can plug it into the other equations to double check.
If you chose to do equation 1:
-3(-1) -5y = -7
3 -5y = -7
-5y = -10
y = 2
If you chose to do equation 2:
-4(-1) + 5y = 14
4 + 5y = 14
5y = 10
y = 2
After finding x and y, you will find the point ( -1, 2)
how do i graph the equation y= -4x - 1
9514 1404 393
Answer:
see attached
Step-by-step explanation:
Find the y-values corresponding to x-values of 0 and 1, then plot those points and draw a line through them.
For x=0, ...
y = -4·0 -1 = -1 . . . . the point is (0, -1) . . . the y-intercept
For x=1, ...
y = -4·1 -1 = -5 . . . . the point is (1, -5)
The attached graph shows these points and the line through them.
hiii please help! i’ll give brainliest if you give a correct answer tysm!
Answer:
1/5
Step-by-step explanation:
The volume is found by multiplying the height, width, and length. So to find the height, you need to divide 1/100 by 1/4 and 1/5.
1/100 divided by 1/5 = 1/20
1/20 divided by 1/4 = 1/5
Hope this helps :)
What is the missing number in this pattern?
0, 7, 26, 63, 124, 215, 342, __
Find the missing value.
Hint: Use the number line to find the missing value.
Answer: Missing value is 6
Step-by-step explanation: -9+6=-3
Michelle lives 4.5 miles from work. Kelly lives 5.6 kilometers from work. Staci lives 4,200 meters from work. Kyle lives 670,000 centimeters from work.
Answer:
Michelle < Staci < Kelly < Kyle
Kyle is the greatest distance from work, while Michelle is the closest to work.
Step-by-Step Explanation:
1 kilometer = 0.62137119 mile(s)
4.5 miles = 0.62137119 × 4.5 = 2.79617036 kilometers
4,200 meters = 4.2 kilometers
670,000 centimeters = 6.7 kilometers
So,
Michelle = 2.8 kilometers (rounded up)
Kelly = 5.6 kilometers
Staci = 4.2 kilometers
Kyle = 6.7 kilometers
So,
Michelle < Staci < Kelly < Kyle
Kyle is the greatest distance from work, while Michelle is the closest to work.
Hope this helps! ^^
6. Here is an octagon.
3 in
4 in 3 in
→
3 in
a. While estimating the area of the octagon, Lin
reasoned that it must be less than 100 square
inches. Do you agree? Explain your reasoning.
b. Find the exact area of the octagon. Show your
reasoning.
4 in
3 in
Answer:
a). Yes. Area will be less than 100 square in.
b). Area of octagon = 82 in²
Step-by-step explanation:
From the picture attached,
a). Octagon is inscribed in a square having one side = 10 inches.
Since, octagon is obtained by cutting off the four equal corners of the square,
Area of octagon will be less than the area of the square.
Area of square = (side)²
= 10²
= 100 in²
Therefore, area of octagon will be less than 100 in²
b). Since, corner cut off from the square are equal in shape and area,
Area of one corner (right angle triangle) = [tex]\frac{1}{2}(\text{Base})(\text{Height})[/tex]
= [tex]\frac{1}{2}(3)(3)[/tex]
= 4.5 in²
Area of 4 corners = 4.5 × 4 = 18 in²
Area of octagon = Area of square - Area of 4 corners removed
= 100 - 18
= 82 in²
Simplify: x + (x-y) + y + (y-x )
Answer:
x + y
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightAlgebra I
Terms/CoefficientsStep-by-step explanation:
Step 1: Define
x + (x - y) + y + (y - x)
Step 2: Simplify
Combine like terms (x): x - y + y + yCombine like terms (y): x + yKieran, Jermaine and Chris play football.
Kieran has scored 8 more goals than Chris.
Jermaine has scored 5 more goals than Kieran.
Altogether they have scored 72 goals.
How many goals did they each score?
Step-by-step explanation:
Find an equation that explains the problem. We can see how many goals the players have scored in comparison to each other. The person with the fewest goals is Chris. Let us say he score x goals. Then we can see that Kieran has scored 8 more than Chris, i.e. x + 8. Jermaine scored 5 more goals than Kieran, therefore x + 8 + 5 = x + 13. Now we have the amount of goals each person scored relative to each other. The total number of goals scored was 72, thus all of these amounts must equal 72.
x + (x + 8) + (x + 13) = 72
Now we can rearrange and solve for x.
3x + 21 = 72
3x = 51
x = 17
Is the relation shown in the arrow diagram a function? Explain
A)Yes: Ench input has only one output
B)Yes;Each output has only one input
C)No, Each input has only one output
D)No, The output 32 has two inputs
Answer: A yes. Each input has only one output.
Step-by-step explanation:
functions are determined by each input only having one output.
Answer:
Answer is A
Step-by-step explanation:
determine the intercept of the line.
Answer:
Y Intercept : (-3, 0)
X Intercept : (0, -1.2)
If your expression contains square roots, during which step of PEMDAS do you solve them?
Answer:
E
Step-by-step explanation:
"If the expression has exponents or square roots, they are to be performed after parentheses and other grouping symbols have been simplified and before any multiplication, division, subtraction and addition that are outside the parentheses."
PLEASE HELP ASAP WILL GIVE 75 POINTS AND BRAINLIEST TO FIRST ANSWER!!!!
Imagine you work at a cola processing plant doing data entry and produce counts. You are doing an empty can count and come up with 1,000 cans. However, the computer system says there are 10,000 cans. After visually confirming that there are only 1,000, you check to see who last entered the value in the computer and discover it is your boss Ms. Strictlend. After triple checking your count you realize Ms. Strictlend made a mistake.
Write an email to Ms. Strictlend. Address her as you would a professional and explain the problem including the mistake she most likely made. Use as many words as you need to communicate the information without being fired.
Answer:
Step-by-step explanation:
Dear Ms Striclend,
I don’t think you meant to, but you made a mistake putting in the value for the computer system. Can you please explain to me how you made the mistake?
Thanks!
my name
HELP ASAP!! omg someone smart answer the question please i dont get it. ill give brainliest if ur right
Answer:
Length 3
Width 3
Height 4
Step-by-step explanation:
Length x Width x Height
3 x 3 x 4 = 36 cm :)
Answer:
Combinations could include:
2, 3, 6
6, 6, 1
3, 3, 4
4, 9, 1
In the diagram (triangle)PRQ~ (Triangle) DEF
FIND m
Answer:
Angle R is equal to 35 and DE is equal to 48
Step-by-step explanation:
In similar triangles, like these, the angles will always be the same to its correspondent. Angle E in the other triangle is 35 degrees so R, its corresponding angle, will be the same. So therefore R is 35.
This is not the same case for sides. There will always be a ratio between both triangles. The ratio in this case is 1.2 to 1. So multiply RP (DE's corresponding side), by 1.2. You will get 48. So therefore DE is equal to 48.
Hope this helped! Please mark me as brainliest!
Scott will run at least 25 miles this week. so far he has run 16 miles . what are possible numbers of additional miles he will run?
use t for the additional miles he will run.
write your answer as an inequality solved for t.
Hello please help me !!!!!
Answer:
negative 4 and negative 1
3(x+5x-5)
another give away
rate me...
Answer:
18x-15
Step-by-step explanation:
solve the inequality
1/3x+8≤11
Answer:
x ≤ 9
Step-by-step explanation:
First, Isolate the variable by subtracting 8.
1/3x<= 3
Multiply both sides by 3
x<= 9
Answer:
x≤9
Step-by-step explanation:
Step 1: Subract 8 from both sides.
1/3x+8-8≤11-8
1/3x ≤3
Step 2: Multiply both sides by 3.
3*(1/3x)≤(3)*(3)
x≤9
Help me out please and thank you
Answer:
I got B
75+20+85=180
The orbit of a comet in a video game can be defined by the equation (x - 56)^2/150 + (y - 28)^2/256 = 1. Which of the following is true about the path of the comet on the screen?
Check all that apply.
The major axis is horizontal.
The center is at (–56, –28).
The length of the major axis is 32 units.
The length of the minor axis is 150 units.
One of the foci is approximately .
Answer:
C & E
Step-by-step explanation:
Answer:
C.) The length of the major axis is 32 units.
E.) One of the foci is approximately
Step-by-step explanation:
A student has a container with a volume of 1.5 liters. She estimates the volume to be 1.8 liters. By what percent is the students estimate off?
Answer:
20%
Step-by-step explanation:
Write the equation of a line that passes through (2, 4) with a slope of 2.
Answer:
y=2x is it I think because the y intercept is the origin
Can’t pls help me with this question
Answer:
Let
Total number of people (T)=1600
those satisfied with the car (t) =720
The percentage of the satisfied people(S)= number of satisfied people divided by the total number of people who took part in the survey, multiplied by 100
=> S=(T/t)*100
S=(720/1600)*100
S=45%
Step-by-step explanation:
Felix bought a new pair of pants for $27.98. If the sales tax is 6%, how much did he spend in total?
Answer:
$29.66
Step-by-step explanation:
6% taxes is 1.68 , 27.98+ 1.68= $29.66
Sales tax:
[tex]\\ \tt\longmapsto 0.06(27.98)[/tex]
[tex]\\ \tt\longmapsto 1.67[/tex]
Total=
27.98+1.67=29.65$Complete the pairs of corresponding parts if △RST ≅ △TXY.
RT =
TX
XY
TY
Answer:
RT is corresponding to TY
Hence, we conclude that:
RT = TYStep-by-step explanation:
Given
△RST ≅ △TXY
It means the triangles △RST and △TXY are congruent to each other.
We know that congruent triangles have equal corresponding parts.
Please check the attached graph.
From the graph, it is clear that:
RT is corresponding to TY.ST is corresponding to XY.RS is corresponding to TX.We need to determine RT
as
RT is corresponding to TY
i.e. RT = TY
Hence, we conclude that:
RT = TY