Superman is working at the Daily Planet Newspaper P(100, 40). He needs to fly to stop a bank robbery at B(40. 80) and then bring the criminals to jail at (130, 105). Finally he needs to fly back to the Daily Planet to get back to work as "Clark Kent'. What is the total distance for the trip?
Given:
Superman is working at Daily Planet Newspaper P(100, 40).
Bank robbery at B(40,80).
Criminals to jail at C(130, 105).
Then fly back to the Daily Planet.
To find:
The total distance for the trip.
Solution:
Distance formula:
[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
Using distance formula, the distance between Daily Planet Newspaper P(100, 40) and place of bank robbery at B(40,80) is
[tex]PB=\sqrt{(40-100)^2+(80-40)^2}[/tex]
[tex]PB=\sqrt{(-60)^2+(40)^2}[/tex]
[tex]PB=\sqrt{3600+1600}[/tex]
[tex]PB=\sqrt{5200}[/tex]
[tex]PB=20\sqrt{13}[/tex]
Similarly,
Distance between place of bank robbery at B(40,80) and jail at C(130,105) is
[tex]BC=\sqrt{\left(130-40\right)^2+\left(105-80\right)^2}[/tex]
[tex]BC=5\sqrt{349}[/tex]
Distance between jail at C(130,105) and Daily Planet Newspaper P(100, 40) is
[tex]CP=\sqrt{\left(100-130\right)^2+\left(40-105\right)^2}[/tex]
[tex]CP=5\sqrt{205}[/tex]
Total distance for the trip = PB+ BC +CP
[tex]Trip=2\sqrt{13}+5\sqrt{349}+5\sqrt{205}[/tex]
[tex]Trip=7.2111+93.4077+71.5891[/tex]
[tex]Trip=172.2079[/tex]
[tex]Trip\approx 172.21[/tex]
Therefore, the total distance for the trip is about 172.21 units.
Help Me Pls I Will Give Brainliest
Answer:
Hi!
My name is Euijin :D and the answer is:
600$
Step-by-step explanation:
I Divided 12 and 0.02 and got 600
Look at points C and D on the graph: A coordinate plane graph is shown. Point C is at negative 5 comma negative 1. Point D is at 0 comma 3. A segment connects the two points. What is the distance (in units) between points C and D? Round your answer to the nearest hundredth.
the answer choices are
A.5.50
B.6.40
C.9.00
D.41.00
Answer:
6.40 cus I got it right ona test
Step-by-step explanation:
Answer:
B: 6.40
Step-by-step explanation:
x=3
y=5
find the value of
2x squared + 3y squared
{2×3}×{2×3} +{3×5}×{3×5}
36+225=261
Evaluate 2 + 3n if n = 5
Answer:
your awnser is n=1 if i wrong just message me but I'm positive that is the awnser
10 points
1. The retail price of an electric toothbrush is $40. What is the price after
a markdown of 30%?*
Answer:
The answer is 12
Step-by-step explanation:
. What is the 11th term of the geometric sequence {1,000,000; 100,000; 10,000; …}?
what is vertex of the graph of the function below y=x^2-10x+21
Answer:
(-4,5)
Step-by-step explanation:
Answer:
Step-by-step explanation:
it is (5,-4) the first answer is backwards
Kaelyn has 14 coins I have a value of $1.20. She only has dimes and nickels. How many nickels does Kaelyn have?
Answer:
10 dimes would be $1.00 and 4 nickels is $.20. That equals $1.20 and 14 coins.
Kaelyn has 4 nickels
2
Type the correct answer in each box.
What are the values of x and y that make the equations true?
Equation A
(x + yi) + (4 – 7i) = 3 – 4i
Equation B (t + yi) - (-6 + 14i) = 18 + 2i
In equation A, I =
and y =
.
In equation B, 1 =
and y =
Reset
Next
Answer:
Equation A: x = -1 and y = 3
Equation B: x = 12 and y = 16
Step-by-step explanation:
In the complex numbers (a + bi) and (x + yi)
(a + bi) + (x + yi) = (a + x) + (b + y)i(a + bi) - (x + yi) = (a - x) + (b - y)iEquation A
∵ (x + yi) + (4 – 7i) = 3 – 4i
∴ (x + 4) + (y - 7)i = 3 - 4i
→ Compare the real parts and compare the imaginary parts
∴ x + 4 = 3 and y - 7 = -4
∵ x + 4 = 3
→ Subtract 4 from both sides
∴ x + 4 - 4 = 3 - 4
∴ x = -1
∵ y - 7 = -4
→ Add 7 to both sides
∴ y - 7 + 7 = -4 + 7
∴ y = 3
Equation B
∵ (x + yi) - (-6 + 14i) = 18 + 2i
∴ (x - -6) + (y - 14)i = 18 + 2i
→ (-)(-) = (+)
∴ (x + 6) + (y - 14)i = 18 + 2i
→ Compare the real parts and compare the imaginary parts
∴ x + 6 = 18 and y - 14 = 2
∵ x + 6 = 18
→ Subtract 6 from both sides
∴ x + 6 - 6 = 18 - 6
∴ x = 12
∵ y - 14 = 2
→ Add 14 to both sides
∴ y - 14 + 14 = 2 + 14
∴ y = 16
Answer: In equation A, -1 and 3 . In equation B, 12 and 16 .
picture below
Step-by-step explanation:
PLEASE HELP DUE IN HOUR!!!!!!!
Which is the best statement regarding an operating characteristic curve? A. As the fraction defective increases, the probability of accepting the lot also increases. B. As the fraction defective decreases, the probability of accepting the lot also decreases. C. As the lot tolerance percent defective decreases, the consumer's risk also decreases. D. As the AQL decreases, the producer's risk also decreases.
Answer:
D. As the AQL decreases, the producer's risk also decreases.
Step-by-step explanation:
The characteristic curve is the graph that shows the relation between two variables.
Operating characteristic curve helps in the selection of sampling plans that are effective in reducing risks.
In case of an operating characteristic curve, as the AQL decreases, the producer's risk also decreases.
Option D is correct
Please help me solve this problem
Answer:
x=2
Step-by-step explanation:
because if you put the equation as in x+11=6x+1 and do the equation you'll get x=2
Answer this please!
Answer:
Its the second option
Step-by-step explanation:
Answer:
c reflection on the y axis by 2 units
Step-by-step explanation:
Carolina goes to a paintball field that charges an entrance fee of \$18$18dollar sign, 18 and \$0.08$0.08dollar sign, 0, point, 08 per ball. The field has a promotion that says, "Get \$10$10dollar sign, 10 off if you spend \$75$75dollar sign, 75 or more!" Carolina wonders how many paintballs she needs to buy along with the entrance fee to get the promotion.
Let BBB represent the number of paintballs that Carolina buys.
1) Which inequality describes this scenario?
Choose 1 answer:
Choose 1 answer:
(Choice A)
A
18+0.08B \leq 7518+0.08B≤7518, plus, 0, point, 08, B, is less than or equal to, 75
(Choice B)
B
18+0.08B \geq 7518+0.08B≥7518, plus, 0, point, 08, B, is greater than or equal to, 75
(Choice C)
C
18+0.08B \leq 1018+0.08B≤1018, plus, 0, point, 08, B, is less than or equal to, 10
(Choice D)
D
18+0.08B \geq 1018+0.08B≥10
Answer:
carolina needs to buy at least 713 paintballs to get $10 off
Step-by-step explanation:
Entrance fee = $18
Fee per ball = $0.08
The field has a promotion that says, "Get $10 off if you spend $75 or more"
Let B represent the number of paintballs that Carolina buys.
18 + 0.08B ≥ 75
Subtract 18 from both sides
0.08B ≥ 75 - 18
0.08B ≥ 57
Divide both sides by 0.08
B ≥ 57 / 0.08
B ≥ 712.5
Approximately
B ≥ 713
carolina needs to buy at least 713 paintballs to get $10 off
moby sold half his toy cars collection, and then bought 12 more cars the next day. He now has 48 toy cars. how many toy cars did he have to start with?
Answer:he 36
Step-by-step explanation:
Answer:
The answer should be72 toy cars.
Step-by-step explanation:
Step 1:
48-12
= 36
= 36 multiplied by 2
= 72
What equation is graphed in this figure?
y-4= = -⅓(x+2)
y-3= ⅓(x + 1)
y+ 2 = -3(x - 1)
y - 5 = 3 (x - 1)
Answer:
y - 5 = 3(x - 1)
Step-by-step explanation:
Let the equation of the line passing through a point (x', y') and slope 'm' is,
y - y' = m(x - x')
Since slope of a line passing through two points [tex](x_1, y_1)[/tex] and [tex](x_2,y_2)[/tex] is represented by,
m = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]
Therefore, slope of the line passing through (0, 2) and (1, 5) is,
m = [tex]\frac{5-2}{1-0}[/tex] = 3
Now equation of the line passing through a point (1, 5) and slope = 3 will be,
y - 5 = 3(x - 1)
Option (4) is the answer.
Answer:
y−5=3(x−1)
Step-by-step explanation:
write each fraction as a ratio in simplest form.
Answer:
Step-by-step explanation:
5) 6:18 = 1:3
6) 10:12 = 5:6
7) 12:28 = 6:14 = 3:7
8) 18:24 = 6:8 = 3:4
9) 16:20 = 8:10 = 4:5
10) 15:9 = 5:3
11) 5:30 = 1:6
12) 14:10 = 7:5
13) 6:16 = 3:8
14) 20:35 = 4:7
Hope this helps
plz mark as brainliest!!!!!
Answer:
Step-by-step explanation:
5) 6 : 18 = [tex]\frac{6*1}{6*3} = 1 : 3[/tex]
6) [tex]10 : 12 = \frac{2*5}{2*6} = \frac{5}{6}= 5 : 6[/tex]
7) [tex]12 : 28 =\frac{4*3}{4*7}=\frac{3}{7}= 3:7[/tex]
[tex]8) 18:24 =\frac{6*3}{6*4}=\frac{3}{4} = 3 : 4\\\\\\9)16 : 20 =\frac{4*4}{4*5}=\frac{4}{5}=4:5\\\\\\10) 15:9=\frac{5*3}{3*3}=\frac{5}{3}=5:3\\\\\\11)5:30 =\frac{5*1}{5*6}=\frac{1}{6}=1:6\\\\\\12)14:10=\frac{2*7}{2*5}=\frac{7}{5}=7:5\\\\\\13)6:16=\frac{2*3}{2*8}=\frac{3}{8}=3:8\\\\\\14)20:35=\frac{5*4}{5*7}=\frac{4}{7}=4:7\\\\[/tex]
To reduce to simplest form, find Greatest Common Factor of the two numbers and divide both numbers by the GCF
21 = 3 * 7
9 = 3 * 3
GCF = 3
[tex]\frac{21}{9}=\frac{3*7}{3*3}=\frac{7}{3}=7:3[/tex]
Find the sum
[tex](5a { }^{2} +7ab - 3b {}^{2} ) + (3a {}^{2} - ab - 6b {}^{2}) [/tex]
possible answers:
A:
[tex]2a {}^{2} + 8ab + 3b {}^{2} [/tex]
B:
[tex]8a {}^{2} + 7ab - 3b {}^{2} [/tex]
C:
[tex]8a {}^{2} + 6ab - 9b {}^{2} [/tex]
D:
[tex]12a {}^{2} + 2ab - 9b {}^{2} [/tex]
Simplify the expression.
14 - 3z + 8 + 2
Answer: 24-3z
Step-by-step explanation: 14+8+2=24-3z
Hello guys i am in secondary school y8 and need help on my school work due tomorrow please could you help me out.
hii!! i used an online calculator so i could help you quicker, but the area is 60, and the height is 12.
hope this helps!! <3
ayudaaaaaaaaaaaaaaaaa
Peter needs to measure the slope of a cone-shaped pile of
sand. The vertical distance from the pile's peak to its base is
2.5 meters and the horizontal distance from its peak to its edge
is 5 meters. What is the slope of the pile of sand?
(Enter your answer as a decimal rounded to the nearest tenth)
Answer:
The slope of the pile of sand is 0.5
Step-by-step explanation:
Since slope = vertical distance/horizontal distance.
Here, the vertical distance from the pile's peak to its base is 2.5 meters and the horizontal distance from its peak to its edge is 5 meters.
So, we calculate the slope as
slope = vertical distance/horizontal distance where vertical distance = vertical distance from the pile's peak to its base = 2.5 meters and horizontal distance = horizontal distance from its peak to its edge = 5 meters.
slope = vertical distance/horizontal
slope = 2.5 meters/5 meters
slope = 0.5
So, the slope of the pile of sand is 0.5
Find the value of x in the questions?
Answer
10
Step-by-step explanation:
Slope is-2, and (5,3) is on the line
Answer:
Step-by-step explanation:
cant see the picture :)
Need help with 15 and show the work
Answer:
D
Step-by-step explanation:
In 2 hours they wash 8 cars total so...
8
16
24
The extra time is 15 mins for 2 cars
(3-х)
-Чx
What is the awnser for this ?
Answer:
-1x or 1x
Step-by-step explanation:
Does anyone know these answers? 50 pts to you if u do.....don't steal from me.
y = -2x + 3
y = -x + 10
y = 4x + 10
y = 3/2x - 2
y = -1/2x - 1
y = x + 5
y = 25x + 5
y = .99x + 1.99
y = x - 2
y = -1.50 + 1.50
y = 42x + 27
y = -1/3x - 2
now i am in my phone can see the photo
sometimes in the computer don't appear the picture
I need help on answering this question.
Answer:
The value of m is 3 because (5^4)^3 = 244140625 and 5^12 = 244140625 also, this means they are both equal to each other. Another way of getting the correct answer is just seeing what times 4 will get you 12, as you can see
3 x 4 = 12.
So yea the answer is M = 3.
Step-by-step explanation:
The polynomial p(x)=3x^3-5x^2-4x+4p(x)=3x 3 −5x 2 −4x+4p, left parenthesis, x, right parenthesis, equals, 3, x, cubed, minus, 5, x, squared, minus, 4, x, plus, 4 has a known factor of (x-2)(x−2)left parenthesis, x, minus, 2, right parenthesis. Rewrite p(x)p(x)p, left parenthesis, x, right parenthesis as a product of linear factors.
Answer:
(3x-2)(x-2)(x+1)
Step-by-step explanation:
Here, given a factor of 3x^3 -5x^2 -4x + 4, we want to fully express the polynomial as a product of its linear factor
To find the other factors, we shall divide the polynomial by the given factor
That will be;
3x^3-5x^2-4x + 4/(x-2)
we use long polynomial division here
Please check attachment for the division
The division yields 3x^2 + x - 2
what is left is to factorize the expression above
That will be;
3x^2 + 3x -2x - 2
= 3x(x + 1) -2(x + 1)
So we have (3x-2)(x + 1)
So the complete factorization will be;
3x^3-5x^2-4x + 4 = (x-2)(3x-2)(x+1)