The longer route is 4 miles further than the shorter route.
What is meant by the Pythagorean theorem?According to the concept, the square of the hypotenuse of a right triangle equaled the square of the other sides. The formula is
[tex]c^{2} = a^{2} + b^{2}[/tex],
where c is the hypotenuse length and a and b are the other two sides' lengths.
Calculate the difference between the longer route and the shorter route:
By using the Pythagorean theorem,[tex]c^{2} =a^{2} +b^{2}[/tex]
Your hypotenuse is the straight path from Crimson to Sunshine, and your legs are the roadways to and from Happy Ville. [tex]c^{2} =6^{2} +8^{2}[/tex]
Take the square root of both sides of the equation to eliminate the exponent on the left side: [tex]c=\pm \sqrt{6^{2}+8^{2}}[/tex]
Raise 6 to the power of 2:[tex]c=\pm \sqrt{36+8^{2}}[/tex]
Raise 8 to the power of 2: [tex]c=\pm \sqrt{36+64}[/tex]
Add 36 and 64: [tex]c=\pm \sqrt{100}[/tex]
Rewrite 100 as [tex]10^{2}[/tex]
[tex]c=\pm \sqrt{10^{2}}[/tex]
Pull terms out from under the radical, assuming positive real numbers.
[tex]c=\pm 10[/tex]
So the distance between Crimson and Sunshine is 10 miles.It asks for the shortest path, either to Happy ville and then to Sunshine (through the legs) or to Sunshine immediately (hypotenuse),
Legs = 6+8 = 14
Hypotenuse = 10
So getting straight to Sunshine would be faster than going to Happyville than Sunshine because going straight to Sunshine is 10 miles against 14 miles for going to Happyville than sunshine.The longer path was 14 miles, while the shorter way was 10 miles, so subtract the two.14−10 = 4Hence, the longer route is 4 miles further than the shorter route.
Learn more about the Pythagorean theorem here:brainly.com/question/20545047
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2 4/5 divided by (6 divided by 2 1/2)
i really need help this is from my little sister she is in 4th grade and doesn't know how to do this.....
2 4/5÷(6÷2 1/2)
2 4/5÷2 2/5
1 1/12
Evaluate the following expressions for x = 2. –9. 2(4 – x) –9. 2(4 – (2)) –9. 2(2) Evaluate the following expression for x = 2. -36. 8 9. 2x.
Answer:
Evaluate the following expressions for x = 2. –9. 2(4 – x) –9. 2(4 – (2)) –9. 2(2)
= -18.4
Evaluate the following expression for x = 2. -36. 8 9. 2x.
= -18.4
Answer:
Both are -18.4
Step-by-step explanation:
Please help me with #5 !?
Answer:
4/15
Step-by-step explanation:
to find out the portion that is shaded we can do the following:
1 - (1/3 + 2/5)
now we want a common denominator, we can use 15:
15/15 - (5/15 + 6/15) → 15/15 - 11/15
the answer is 4/15
Answer:
1 over 3 is the answer have a nice night
I need help can I have how to do it and some work so I can do it.
Answer:
(-1,-2) OR x = -1 and y = -2
Step-by-step explanation:
y = 3x + 1
y = -x -3
so you would first multiply everything on y = -x -3 by 3 and get 3y = -3x -9
so then you would add 3y = -3x -9 to y = 3x + 1 ( to eliminate the x )which would be 4y = -8 then divide by 4 and get y = -2
then you plug in y = -2 into any one of the equations but to make it easier i am going to plug it into y = -x -3 so now it would be -2 = -x - 3 then, add 2 to both sides which would be 0 = -x -1 then add 1 to both side 1 = -x then multiply both sides by -1 and get x = -1
SO your answer would be (-1,-2) OR x = -1 and y = -2 ( both of them are correct but it depends on what the teacher taught you)
1. Heaven hasn markers. Miley has marker fewer than twice the number of
markers Heaven has. Write and simplify an expression for the total number of
markers they have.
Answer:
hey are you new i love this app so much a get my answers right evarytime but i dont have any folowers but thats okay its the thaught that counts wright
(5r+2)(3r-4 WHAT IS THE PRODUCT
Answer:
152−14−8
Step-by-step explanation:
Answer: The product is: 9r-28
Step-by-step explanation:
(5r+2)(3r-4)
5r x 3r = 15r
5r x -4 = -20r
2 x 3r = 6r
2 x -4 = -8
Put it all together:
15r-20+6r-8
Then simplify:
9r-28
Please Help Me Quickly As Soon As Possible, I Have A Test. I Will Give Out Brainly.
The equation to show the depreciation at the end of x years is
[tex]f(x) = 1500 - 200x[/tex]
Data;
cost of machine = 1500annual depreciation value = xLinear EquationThis is an equation written to represent a word problem into mathematical statement and this is easier to solve.
To write a linear depreciation model for this machine would be
For number of years, the cost of the machine would become
[tex]1500 - 200x[/tex]
This is properly written as
[tex]f(x) = 1500 - 200x[/tex]
where x represents the number of years.
For example, after 5 years, the value of the machine would become
[tex]f(x) = 1500 - 200x\\f(5) = 1500 - 200(5)\\f(5) = 1500 - 1000\\f(5) = 500[/tex]
The value of the machine would be $500 at the end of the fifth year.
From the above, the equation to show the depreciation at the end of x years is f(x) = 1500 - 200x
Learn more on linear equations here;
https://brainly.com/question/4074386
Simplify to create an equivalent expression.
3n + 2(-2n-1)
Answer: -n -2
Step-by-step explanation:
distribute the 2
3n+ -4n-2
combine like terms
-n -2
Solution:
3n + 2(-2n - 1)=> 3n + (-4n - 2)=> 3n - 4n - 2=> -n - 2The simplified expression is -n - 2.
Find the area of the polygon
A) 59 square units
B) 65 square units
C) 72 square units
D) 83 square units
Answer:
B) 65 square units
Step-by-step explanation:
Triangle[SUT]=4.8/2=16
Trapezoid [SUQR]=(8+6).7/2=49
16+49=65
Jada walks up to a tank of water that can hold up to 10 gallons. When it is active, a drain
empties water from the tank at a constant rate, When Jada first sees the tank, it contains 7 gallons of water. Three minutes later, the tank contains 5 gallons of water.
A. At what rate is the amount of water in the tank changing? Use a signed number, and
include the unit of measurement in your answer.
B. How many more minutes will it take for the tank to drain completely?
C. How many minutes before Jada arrived was the water tank completely full?
Answer:
Part A)The amount of water in the tank is changing at -2/3 gallons per minute.
Part B) it will take 7.5 minutes for the tank to drain completely.
Part C) The water tank was completely full 4.5 minutes before Jada arrived.
Step-by-step explanation:
Information fetching:
Tank of water can hold up-to 10 gallons.
When it is active, a drain empties water from the tank at a constant rate.
7 gallons of water present in the tank when Jade first saw
5 gallons of water left after 3 minutes
Part A) At what rate is the amount of water in the tank changing?
As the gallons were decreased from 7 to 5 in three minutes. It means in three minutes, 2 gallons were decreased.
So, gallons per minute change would be -2/3 gallons per minute. Hence, the amount of water in the tank is changing at -2/3 gallons per minute.
Note: negative sign indicates the number of gallons of water are decreasing.
Part B) How many more minutes will it take for the tank to drain completely.
Let 'm' be the number of minutes will it take for the tank to drain completely.
As,
(2/3 gallons per minute) (m minutes) = 5 gallons
So,
m = 5 (3/2)
= 15/2
= 7.5 minutes
So, it will take 7.5 minutes for the tank to drain completely.
Part C) How many minutes before Jada arrived was the water tank completely full
As tank of water can hold up to 10 gallons. So, the tank of water is full when there is 10 gallons of water. So, this is 3 gallons of water more than the total 7 number of gallons at the time when Jada arrived.
As Jada arrived when the tank had left 7 gallons.
Let 'm' be the number of minutes before Jada arrived when the water tank was completely full.
So,
(2/3) (m) = 3
m = 3(3/2) = 9/2
= 4.5 minutes
So, the water tank was completely full 4.5 minutes before Jada arrived.
Which statement correctly describes this expression? 2m^3 -11
Answer:
Option A is the correct answer
Step-by-step explanation:
A. The difference of twice the cube of a number and 11
Work out, giving your answer in its simplest form:
32 + 2
응
help
Step-by-step:
[tex]3\frac{1}{2}+2\frac{3}{5} = \frac{7}{2} + \frac{13}{5} = \frac{35}{10}+\frac{26}{10} = \frac{61}{10}.[/tex]
Explaination:
Use [tex]a\frac{x}{y} = \frac{a.y+x}{y}[/tex] to convert a mixed number to a fraction.
Use [tex]\frac{a}{b} +\frac{x}{y} = \frac{a.y}{b.y}+\frac{b.x}{b.y} = \frac{a.y+b.x}{b.y}[/tex] to calculate the sum of two fractions with different denominators.
Hope this help!
Solve the equation. − 12 + ( − 32 ) =
Answer: -44
Step-by-step explanation: First you do add -32 to both sides of the equation, then yo add it all together... Hope this helped :)
Answer:
-12+(-32)= -44
Step-by-step explanation:
negative numbers plus a negative number would result in a smaller negative number. So -12 + -32 would be -44.
The table shows the scores of two teams at the end of the first half of a trivia challenge.
How many more points did the Huskies score than the Bobcats?
Answer: [tex]3x-4[/tex]
Step-by-step explanation:
Difference = Huskies - Bobcats
Hence,
[tex](5x-3)-(2x-7)\\=5x-3-2x+7\\=3x+4[/tex]
Whats the zeros and the vertex !
Answer:
The vertex is (0,3), and the zeroes are at -1 and -7
Step-by-step explanation:
Since the function is going upward, the vertex is the minimum value
So the vertex is (0,3)
The zeros of a function are where the function touches the x-axis, or when y is 0.
We can find the zeros by making y (or f(x)) 0.
(x+4)^2-9=0
x^2+8x+16-9=0
x^2+8x+7=0
Factoring
(x+1)(x+7)=0
The zeroes are at -1 and -7.
if f(x)=3x-12 what is f(-2)
Step-by-step explanation:
f(-2) = 3(-2) - 12
→ -6 - 12 = -18 ans.
hope this helps you !
is the point(-1,4) a function
Answer:
Yes. This relation is a function.
Step-by-step explanation:
Since there is one value of y for every value of x in (−1,4), this relation is a function.
A total feet of snow falls over three days. On the first day, 1/6 of the total snow falls. One the second day, 7/12 of the total snow falls. Complete the table to list the amount of snow of snow, in inches, that falls each day. Use paper to show your thinking. Plzzzzzzzzzzzz help plz
Answer:
If it wants to know the total on day 3, then the answer is 3/12, or 1/4 (fully simplified).
Step-by-step explanation:
1/6 + 7/12 = 3/4
This means that you would need 1/4 more inches of snow. 3/12 is the answer before simplification, and 1/4 is the fully simplified answer.
A school needs 1,800 notebooks for next year. If the notebooks come in packages of 90, how many packages should the school buy?
Answer:
20 packages
Step-by-step explanation:
the school needs 1800 notebooks, since the notebooks come in packages of 90 each. there will be a total of 20 packages.
formula
1800/90
= 20
Answer:
20
Step-by-step explanation:
Let x be the number of packs the school should buy.
1800[tex]\geq[/tex]90x
/90 /90
20[tex]\geq[/tex]x
Mr.O’Donnell bought 3 shirts for x dollars. He also bought shoes for $100. If he spent $160, how much did each shirt cost
Answer:
$20
Step-by-step explanation:
3x + 100 = 160
3x = 60
x = 20
Find value of x when y = 1
Answer:
x = 3.2
Explanation:
when y = 1
1 = x²-2x-3
x²-2x-3-1 = 0
x²-2x-4 = 0
using the formula: [tex]x = \frac{ -b \pm \sqrt{b^2 - 4ac}}{2a}[/tex][tex]x = \frac{ 2 \pm \sqrt{(-2)^2 - 4(1)(-4)}}{2*1}[/tex]
[tex]x = 1 + \sqrt{5}[/tex]
x = 3.236
x = 3.24 in 2 decimal places
x = 3.2 in nearest tenth
the radius of a circle is 9 times of the radius of a smaller circle. the area of the smaller circle is 50 square cenimeters. what is the area of the larger circle
Answer:
4050 cm²
Step-by-step explanation:
This is a question of scale factors:
The radius of the larger circle is 9× that of the smaller circle;
This is the linear scale factor of the enlargement of the smaller to larger circle;
The scale factor of the area pertains to 2 dimensions so the scale factor will be the square of the linear scale factor, which is:
9² = 81
The area of the larger circle is found by the area of the smaller circle multiplied by this number:
50 × 81 = 4050
$360,000 is what percent of $600,000?
My sister and ate some of a chocolate bar she had 1/4 and I had 5/8 how much of the chocolate bar did we eat
Answer:
7/8
Step-by-step explanation:
1/4 times 2/2 = 2/8. you would have to do this because the only way you can add fractions is if they have the same denominator. so 2/8 + 5/8= 7/8
Answer:
You ate 7/8 of the chocolate bar.
Step-by-step explanation:
First, we need to change 1/4 and 5/8 so that they have the same denominators (bottom numbers).
There's a common multiple of 8.
What you do to the bottom needs to be done to the top.
1 x 8 = 8
1 x 5 = 5
5/8
Your amount of chocolate stays the same.
4 x 2 = 8
1 x 2 = 2
2/8 is how much the sister had,
Finally, add the two fractions together.
2/8 + 5/8 = 7/8
You ate 7/8 of the chocolate bar.
Hope this helps, have a good day! :D
Is triangle ABC= triangle DEF?
Answer:
cannot be determined
Step-by-step explanation:
you know they are similar triangles because their angles are congruent, but you cannot determine if they are the same because you are not given that any of their sides are congruent
Find the measures of the numbered angles in the rhombus.
there is four angles I need someone plz help
keeping in mind that in a rhombus the diagonals always meet at right-angles, Check the picture below.
If d-6c=4 and 2d-9c=20, find the value of d/c
Answer:
7
Step-by-step explanation:
You get the value of c and d as follow
c=4
d=28
now,
d/c=28/4=7
so,
the value of d/c here is 7
HELP HELP HELP HELP help pls help
Answer:
supplementary
Step-by-step explanation:
angles that are over 90° that over all equal to 180° are supplementary. 156° is over 90° and adding 24° is simple math, meaning 156+24=180
hope this helps
10. Mr. Larsen ran out of gas 10
kilometers from the nearest gas
station. He walked 4.2 km and stopped
to rest. Then, he walked 2.1 km before
resting again. How much farther does
he have to walk?
F
G
1.1 km
3.7 km
4.7 km
5.3 km
H)
J
Answer:
3.7 km further to walk
Step-by-step explanation:
Distance to travel to gas station = 10km
Distance remaining is (10km - distances walked)
(10km - 4.2km - 2.1km)
(10km - 6.3km)
3.7 km further to walk
PLEASE HELP (image attached)
Answer:
1: 3 choice 2: choice 1
Step-by-step explanation:
6x+9+5x-20 = 11x -11
x-8 - 3x - 3 = -2x-11
