Answer:
[tex]Area = 0.25 \ m^2[/tex]
Step-by-step explanation:
Force = 1500N , Pressure = 6000
[tex]Pressure = \frac{Force}{Area }[/tex]
[tex]6000 = \frac{1500}{Area }[/tex]
[tex]6000 \times Area = 1500\\\\Area = \frac{1500}{6000} \\\\Area = \frac{1}{4} = 0.25 \ m^2[/tex]
Universal Studios is looking to expand in Ontario. The new theme park will be located equidistant to
Newmarket, N (2,8), Markham, M (7,3) and Vaughan, V (-2, 0). Determine the location of the new
theme park if it is located at the point of intersection of the perpendicular bisectors.
===============================================
Explanation:
For now, we're only going to consider Newmarket and Markham, which are points N and M respectively.
Let's find the slope of line NM through use of the slope formula.
m = (y2-y1)/(x2-x1)
m = (3-8)/(7-2)
m = -5/5
m = -1
Line NM has a slope of -1. Its perpendicular slope is +1 or just 1.
Rule: If the slopes multiply to -1, then the lines are perpendicular.
Or you can apply the negative reciprocal rule to go from -1 to 1.
We'll keep this perpendicular slope in mind for later.
----------------
Now let's find the midpoint of points N and M.
Add up the x coordinates and divide by 2: (x1+x2)/2 = (2+7)/2 = 4.5
Do the same for the y coordinates: (y1+y2)/2 = (8+3)/2 = 5.5
The midpoint of N and M is at (4.5, 5.5)
The perpendicular line must go through these two points. I'm going to skip a few steps here, but basically we go from y = mx+b to y = x+1 after plugging in those x,y values and the perpendicular m we found earlier.
--------------------
In short, the perpendicular bisector for line segment NM is the equation y = x+1.
If you follow the same steps as the previous two sections, but you apply them for points M and V instead, then you should find that the perpendicular bisector is y = -3x+9. I'm skipping steps here as well.
----------------------
At this point, we have the system of equations
[tex]\begin{cases}y = x+1\\y = -3x+9\end{cases}[/tex]
Let's use substitution to solve for x and y
y = x+1
-3x+9 = x+1
-3x-x = 1-9
-4x = -8
x = -8/(-4)
x = 2
y = x+1
y = 2+1
y = 3
So together, x = 2 and y = 3 pair up to get the ordered pair solution (x,y) = (2,3)
This is the location where the theme park should be placed. Let's say that C = (2,3). I'm using C for center.
You can use the distance formula to confirm that segments CN, CM and CV are all the same length, which would verify that point C is equidistant from all the other points. Furthermore, it means that points N, M and V are all on the same circle centered at C.
I know it says not to use a graph, but it still helps to see what's going on. Also, it's a handy way to confirm the answer. I used GeoGebra to make the graph. See the diagram below.
Side note: you only need 2 perpendicular bisectors to find point C. You could use three, but that's overkill since they all intersect at the same location.
Please Help!!!! Please!!!!!!!!
9514 1404 393
Answer:
see attached
Step-by-step explanation:
I found it easiest to draw arcs of radii AB and AC centered at A, and arcs of radii DB and DC centered at D. The intersection points of those arcs mark the points B' and C'. These are points B and C reflected across line AD.
Joining A, B', C', and D will make a figure symmetrical about AD.
Its due in 20 mins
Will mark brainliest
Answer:
a) 20 km away fro the starting point.
b) The bearing from P to R is 80°.
c) Q is 60 km North P.
d) Q is - 60 km west of P
Step-by-step explanation:
Stating Facts in the Question:
P to Q is 80 km and bearing 330°
It turned around, Q to R is 60 km and bearing 250°.
a) Picture a number line (Look at the first image)
You go 80 to the right. You turn around and go 60 to the left.
80 - 60 = 20
20 km away fro the starting point
b) Picture a number line (Look at the second image)
P to Q is bearing 330°
Q to R is 60 km is bearing 250°
P to Q is red
Q to R is blue
330° - 250° = 80°
The bearing from P to R is 80°
c) P to Q is 60 km
The plane went forward or North so the answer is 60 km.
Q is 60 km North P.
d) Q to P is 60 km
Q is not to the west of P
Q is - 60 km west of P
Of the marbles in a bag, 4 are yellow , 4 are white , and 5 are green . Sandra will randomly choose one marble from the bag. Fill in the blanks in parts a and b. The probability that Sandra will choose a marble from the bag is
Answer:
Probability[Random choose marble is green] = 5 / 13
Step-by-step explanation:
Given:
Number of yellow marble in bag = 4
Number of white marble in bag = 4
Number of green marble in bag = 5
Find:
Probability[Random choose marble is green]
Computation:
Probability of an event = Number of favourable outcome / Number of total outcome
Probability[Random choose marble is green] = 5 / [4 + 4 + 5]
Probability[Random choose marble is green] = 5 / 13
the slope of line (-1,1) (2,-5)?
Answer:
slope = 4/3
Step-by-step explanation:
(-1 , 1) = (x1 , y1)
(2 , 5) = (x2 , y2)
slope (m) = y2 - y1/x2 - x1
=5 - 1/2 - (-1)
=4 /2+1
=4/3
I need help in this (￣▽￣)
Answer:
Step-by-step explanation:
a=-2.9
b=-2 5/8=-21/8=-2.625
c=-7/3=-2.333333
35/48*100 fraction into percentage.
Answer:
729167
Step-by-step explanation:
Now we can see that our fraction is 72.916666666667/100, which means that 35/48 as a percentage is 72.9167%.
How do you solve this?
Answer:73825
Step-by-step explanation:
Shuts shield grid
Answer:
[tex]j=8[/tex]
Step-by-step explanation:
Special right triangles:
The sides of all 30-60-90 triangles are in the proportion [tex]x:x\sqrt{3}:2x[/tex], where [tex]2x[/tex] is the hypotenuse of the triangle and [tex]x[/tex] is the side directly opposite to the 30 degree angle.
Since the base of the triangle is directly opposite to the 30 degree angle, the hypotenuse, j, must be equal to [tex]4\cdot 2=\boxed{8}[/tex]
Basic trig:
[tex]\sin 30^{\circ}=\frac{4}{j},\\j=\frac{4}{\sin 30^{\circ}}=\boxed{8}[/tex]
Simplify -|-7 + 4|. please helppppp
Answer: -3
Step-by-step explanation:
-l-7+4l = -l-3l = - 3
ll means anything inside there is positive, so for example if -3 was in there, l-3l = 3
Answer:
- 3
Step-by-step explanation:
-|-7 + 4|
Simplify inside the absolute values first( like parentheses)
-|-3|
Take the nonnegative value for the absolute value
- 3
Please help I’ll give branliest
Answer:
optin d) 8
Step-by-step explanation:
[tex]2 \times 2 \times 2 = 2^3[/tex] [tex]= 8[/tex]
Help for brainliest
Find h.
9 ft
h = [?] ft
Answer:
[tex]\sqrt{77}[/tex] ft
Step-by-step explanation:
Hi there!
Notice how we can create a right triangle in the cone, where the base is 2 ft (4/2=2), the height is h and the hypotenuse is 9 ft.
Using these values, we can solve for h with the Pythagorean theorem: [tex]a^2+b^2=c^2[/tex] where a and b are the two legs of a right triangle and c is the hypotenuse.
Plug in 2 and h as a and b and 9 as c:
[tex]2^2+h^2=9^2\\4+h^2=81\\h^2=81-4\\h^2=77\\h=\sqrt{77}[/tex]
I hope this helps!
Luke's tyre pressure gauge shows a reading which is 8% higher than the actual pressure.
What is the actual pressure when Sue's gauge shows 39.42?
Answer:
so for this we do
39.42*1.08=42.5736
Hope This Helps!!!
Convert the following decimal to fraction 3.04
Answer:
3 1/25
Step-by-step explanation:
3.04
Do the decimal part first
.04 = 4/100
Reduce - cancel out 4
1/25
Put back the whole number
3 1/25
Answer:
3 [tex]\frac{1}{25}[/tex]
Step-by-step explanation:
I agree with the previous answer :
You need to do it part by part.
0.04 is equal to [tex]\frac{4}{100}[/tex]
[tex]\frac{4}{100}[/tex] simplified (we divide by 4 with both the denomantor and the numerator.) =
[tex]\frac{1}{25}[/tex]
And we still have those 3 wholes that we had in the beginning.
Now we add.
3 + [tex]\frac{1}{25}[/tex] = 3 [tex]\frac{1}{25}[/tex]
Which table of ordered pairs represents a proportional relationship?
х
-2
4
-6
y
4
16
36
х
-4
-6
-8
y
-8
-12
-18
o
х
-3
-5
-7
y
5
3
1
O
х
-3
-6
-9
y
12
24
36
Answer:
x=-3×-5×-7
-3×-5=15
15×-7=-105
=-105
Solve for x.
3x + 10
3x +
x = [?]
Answer: x = 28
Step-by-step explanation:
3x+10+3x+2=180
6x+12=180
6x=168
x = 28
Answer:
x=28
Step-by-step explanation:
Since both lines going up are parallel, we can label the angle to the left of the angle with the measure of 3x+10 3x+2. These angles are supplementary as they are on different sides of the same line. This means that:
(3x+10)+(3x+2)=180
6x+12=180
6x=168
x=28
Triangle N P O is shown. Line O N extends through point M to form exterior angle P N M. Angle N P O is 38 degrees. Angle P O N is 39 degrees. Exterior angle P N M is x degrees.
Which statement about the value of x is true?
x > 38
x < 39
x < 77
x > 103
Answer:
77
Step-by-step explanation:
i took the test
Answer:
c
Step-by-step explanation:
logo y = x means: log base b of y equals x.
True
False
If you meant to write [tex]\log_{b}(y) = x[/tex] then the statement is true.
As a more concrete example, something like [tex]\log_3(81) = 4[/tex] would be read out as "log base 3 of 81 is equal to 4".
Select all the correct answers.
Which expressions are equivalent to the given expression?
Answer:
6√7=15.874507866387543=√252
Step-by-step explanation:
hope this is helpful
The expression that are equivalent to √252 are [tex]252^{\frac{1}{2} }[/tex] and 6√7.
How to find equivalent expression?
Applying the surd rule,
√a = [tex]a^{\frac{1}{2} }[/tex]
Hence,
[tex]\sqrt{252}=252^{\frac{1}{2} }[/tex]
using surd rule, we can also decompose √252
Therefore,
√252 = √36 × 7 = 6√7
Hence, the equivalent expression of √252 are as follows:
[tex]252^{\frac{1}{2} }[/tex]6√7learn more on expression here: https://brainly.com/question/27768447
#SPJ2
Help please !!!!!!!!!!!!
=============================================================
Explanation:
Ignore the rows that are labeled "stock ABC" and "stock MNO".
We only focus on the top row (gains and losses) and the "stock JKL" row.
Multiply each gain or loss with its corresponding probability in decimal form. Use negative values to represent a loss
-25*0.15 = -3.755*0.65 = 3.2545*0.20 = 9Add up those results to get the final answer: -3.75+3.25+9 = 8.50
-----------------------
Here's another way to get the answer.
Let's say you had a 10 by 10 grid of graph paper.
Shade exactly 15 tiny squares in red to represent a loss of $25 (note that 15/100 = 15%)Shade exactly 65 squares in blue to represent a gain of $5 (65/100 = 65%)Shade the remaining 20 squares in green to represent a gain of $45This can be thought of as like a dart board. Imagine throwing 1000 darts at this grid (maybe do so blindfolded to give each square an equal chance; if you land outside the grid then re-throw the dart). Theoretically, the probability of landing in the red area is 15/100 = 0.15, so we expect about 1000*0.15 = 150 darts will land there out of the 1000 thrown total. Each of those 150 darts in the red area represents a loss of $25. So we have a loss of 150*25 = 3750 dollars. We'll write this as -3750.
We also expect 0.65*1000 = 650 darts to have a gain of $5. That means 650*5 = 3250 is earned here. Furthermore, 0.20*1000 = 200 darts land in the green squares to get us $45 per attempt. So that's another 45*200 = 9000 dollars.
Overall, we would get -3750+3250+9000 = 8500 in profit.
Divide this over the 1000 dart throws and we end up with an expected value of 8500/1000 = 8.50
Keep in mind that this dart game or thought experiment is depending on theoretical probabilities. If you actually do this game, then your empirical probabilities will likely differ slightly from the theoretical values. However, the more trials you conduct, the closer your empirical probabilities should get to the theoretical ones.
Suppose y varies directly with x, and y = 45 when x = 3. What is the value of y when x = -6?
Answer:
y=-90
Step-by-step explanation:
y = kx
45 = k 3
k = 15
~~~~~~~~~~~~
y = 15*-6
y=-90
Answer:
36
We should write a formula for their relationship:
Y = x+42. <- this is what a direct varieation is I believe.
So, when x is -6, y is +42 aka 36
a=v2/rSolve the formula for r.
Answer:
r =v2 /a
Step-by-step explanation:
a=v2/r
ra=v2
r =v2 /a
Answer:
r = [tex]\frac{v^2}{a}[/tex]
Step-by-step explanation:
Given
a = [tex]\frac{v^2}{r}[/tex] ( multiply both sides by r to clear the fraction )
ar = v² ( divide both sides by a )
r = [tex]\frac{v^2}{a}[/tex]
Please answer quickly, simple geometry
OPTION C IS THE CORRECT ANSWER.
Jude studied a total of 20.5 hours over a period of 5 days. On average, how many hours did Jude study each day
Answer:
4.1 hours each day
Step-by-step explanation:
20.5 ÷ 5
= 4.1
Therefore 4.1 hours was spent on studying each day.
How many solutions does this have?
y=5x+-2
y=5--2x
Answer:
one solution (2.333, 9.6666)
Step-by-step explanation:
The ys have to be equal for there to be 1 solution. Let's see if they are. Equate the ys. - -2x becomes 2x
5x +-2 = 2x + 5 Write the left with 1 sign
5x - 2 = 2x + 5 Subtract 2x from both sides
2x 2x
3x - 2 = 5 Add 2 to both sides
2 2
3x = 7 Divide by 3
x = 7/3
x = 2 1/3
y = 5x - 2
y = 5(2 1/3) - 2
y = 11 2/3 - 2
y = 9 2/3
help help help help help
Step-by-step explanation:
press the picture to see the answer I swear it has a solution too
Solve the problem.
An initial investment of $930 is appreciated for 19 years in an account that earns
6% interest, compounded continuously. Find the amount of money in the
account at the end of the period.
$1275.35
$22,067.28
$12,424,545.93
$2907.89
Answer:
$2907.89
General Formulas and Concepts:
Symbols
e (Euler's number) ≈ 2.71828Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightAlgebra i
Compounded Continuously Formula: [tex]\displaystyle A = Pe^{rt}[/tex]
P is principle amountr is ratet is timeStep-by-step explanation:
Step 1: Define
Identify variables
P = 930
t = 19
r = 6% = 0.06
Step 2: Find Interest
Substitute in variables [Compounded Continuously Formula]: [tex]\displaystyle A = 930e^{19 \cdot 0.06}[/tex][Exponents] Multiply: [tex]\displaystyle A = 930e^{1.14}[/tex]Evaluate exponents: [tex]\displaystyle A = 930(3.12677)[/tex]Multiply: [tex]\displaystyle A = 2907.89[/tex]What percent is represented by the shaded area?
Answer:91%
Step-by-step explanation:
X 8. From the given Venn-diagram, list the elements of the following sets, a) U b) XU Y and XUY c) X Y and X d) X - Y and X-Y e) Y - X and Y - X 11 15
Answer:
where is the Venn diagram plz insert Venn diagram then I should solve
Pleaseeeeee help meee
Answer:
Surface area of sphere = 1,344.8 m² (Approx)
Step-by-step explanation:
Given:
Volume of sphere = 1,476π m³
Find;
Surface area of sphere
Computation:
Volume of sphere = [4/3]πr³
1,476π = [4/3]πr³
1,476 = [4/3]r³
[1,476][3/4] = r³
1,107 = r³
r = 10.35 m (Approx.)
Surface area of sphere = 4πr²
Surface area of sphere = 4(3.14)(10.35)²
Surface area of sphere = 4(3.14)(107.1225)
Surface area of sphere = 1,345.45
Surface area of sphere = 1,344.8 m² (Approx)
Name five whole numbers that can be expressed as the difference of two perfect squares. Show the math!
