[tex] = > 6a - 2b[/tex]
[tex] = > 6(5) - 2(7)[/tex]
[tex] = > 30 - 14[/tex]
[tex] = > 16[/tex]
You are tasked with finding the dimensions of an empty rectangular swimming pool. The goal is to calculate the amount of water needed to fill the pool. What would be the appropriate tool for taking the required measurements?
Please help! will mark brainlest
A. a ruler
B. a protractor
C. a compass
D. a measuring tape
Answer:
Its D
Step-by-step explanation:because the ruler is small and the other tools are not for it porpuse
100 points! Please show your work :)
Answer:
7.76 minutes
Step-by-step explanation:
The +51 is regardless (being the y intercept) so it does not affect our answer. If the employee has to drive one mile (x=1) it will take 7.76 + 51 min to get there. If they have to drive 0 miles (x=0) it will only take 51 min. This is a difference of 7.76. You really just need to take the slope (I just used this example to make it make more sense) as x is the number of miles the employee has to drive, and therefore that times 7.76 would be how much longer it would take to drive to work.
LORAN is a long range hyperbolic navigation system. Suppose two LORAN transmitters are located at the coordinates (−60,0) and (60,0), where unit distance on the coordinate plane is measured in miles A receiver is located somewhere in the first quadrant. The receiver computes that the difference in the distances from the receiver to these transmitters is 100 miles.
What is the standard form of the hyperbola that the receiver sits on if the transmitters behave as foci of the hyperbola?
LORAN follows an hyperbolic path.
The equation of the hyperbola is: [tex]\mathbf{\frac{x^2}{2500} + \frac{y^2}{1100} = 1}[/tex]
The coordinates are given as:
[tex]\mathbf{(x,y) = (-60,0)\ (60,0)}[/tex]
The center of the hyperbola is
[tex]\mathbf{(h,k) = (0,0)}[/tex]
The distance from the center to the focal points is given as:
[tex]\mathbf{c = 60}[/tex]
Square both sides
[tex]\mathbf{c^2 = 3600}[/tex]
The distance from the receiver to the transmitters is given as:
[tex]\mathbf{2a = 100}[/tex]
Divide both sides by 2
[tex]\mathbf{a = 50}[/tex]
Square both sides
[tex]\mathbf{a^2 = 2500}[/tex]
We have:
[tex]\mathbf{b^2 = c^2 - a^2}[/tex]
This gives
[tex]\mathbf{b^2 = 3600 - 2500}[/tex]
[tex]\mathbf{b^2 = 1100}[/tex]
The equation of an hyperbola is:
[tex]\mathbf{\frac{(x - h)^2}{a^2} + \frac{(y - k)^2}{b^2} = 1}[/tex]
So, we have:
[tex]\mathbf{\frac{(x - 0)^2}{2500} + \frac{(y - 0)^2}{1100} = 1}[/tex]
[tex]\mathbf{\frac{x^2}{2500} + \frac{y^2}{1100} = 1}[/tex]
Hence, the equation of the hyperbola is: [tex]\mathbf{\frac{x^2}{2500} + \frac{y^2}{1100} = 1}[/tex]
Read more about hyperbolas at:
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Triangles PQR and XYZ are similar. What is the length of XZ?
.Factor 20x2 + 68x - 160
Answer:
4(5x-8) (x+5)
Step-by-step explanation:
4(5x^2+17x-40)
4(5x-8) (x+5)
which rule explains why these triangles are congruent?
SAS
SSS
AAS
ASA
These triangles cannot be
proven congruent.
What is this answer need reply ASAP
Answer:
how many boxes is the line on
Use the y- and x- intercepts to write the equation of the line. y-intercept (0, -6), x-intercept (-2, 0)
Hi there! :)
We are given 2 points. It means we can use the following formula to find the slope:
m=[tex]\frac{y2-y1}{x2-x1}[/tex]
m=[tex]\frac{0-(-6)}{-2-0\\} \\\frac{0+6}{-2}\\\frac{6}{-2} \\-3[/tex]
So the slope is -3
First, let's write the equation of the line in point-slope form.
y-y1=m(x-x1)
y-(-6)=-3(x-0)
y+6=-3(x+0)
y+6=-3x+0
y=-3x+0-6
y=-3x-6
Hope this helps!
~Just an emotional teen who listens to her favorite song "Try Everything"
[tex]SilentNature[/tex]
In Bobby's grade, 679 students are enrolled in health and 21 students are not. What percentage of the students in the school are enrolled in health? Write your answer using a percent sign (%).
97.07%
Step-by-step explanation:
total number of students is
696+21=717
696/717×100=97.07
answer is 97.07%
??
What is the asnwer plsssss
The arc length is 7/2 pi.
Solve the following two problems using Calculus. Show all of your work on a separate sheet of paper, making clear how you arrived at all your solutions. Please be aware that you are using similar thinking for both of these problems, but you are solving for maximum area in Part A and minimum cost in Part B. Enjoy
A. If the materials for the fence cost $12 per foot, find the dimensions of the
corral for the largest possible area that can be enclosed with $2400 worth of fence.
B. If he only requires an area of 288 square feet for his vegetable garden, find the minimum cost of putting up this fence, if the cost per foot is $10. Indicate the dimensions of the garden that will minimize the cost.
9514 1404 393
Answer:
A. 50 ft square
B. 12√2 ft square
Step-by-step explanation:
These problems are basically the same, so have the same solution. The rectangle with maximum area for a given perimeter will have the same shape as the one with minimum perimeter for a given area.
We can find it generically. Let p represent the perimeter of a rectangular area with one side that measures x. The area will be ...
A = x(p/2 -x) = -x^2 +(p/2)x
The area will be maximized when dA/dx = 0:
dA/dx = -2x +p/2 = 0
p/2 = 2x . . . . . add 2x
x = p/4 . . . . . . divide by 2
The other dimension is ...
p/2 -x = p/2 -p/4 = p/4
The dimensions of the maximum area for perimeter p are ...
p/4 × p/4 . . . . . . . a square
__
A.$2400 worth of fence at $12 per foot is 2400/12 = 200 ft of fence. The largest possible area that can be enclosed will have dimensions of 200 ft/4 = 50 ft square:
50 ft × 50 ft
__
B.The perimeter of the garden will be at its shortest when the shape of the garden is square.
√(288 ft²) = 12√2 ft
The dimensions of the garden that will minimize the cost are ...
12√2 ft × 12√2 ft
Help me please i've been stuck on this question for hours.
Answer:
a) x^3 b) y^5
Step-by-step explanation:
you can combine the x's and y's to make a exponent equal to the number of x's or y's.
sin⁻¹(-[tex]-\frac{\sqrt{3} }{2}[/tex]
Answer:
240,300
[tex] \frac{4\pi}{3} . \: \: \frac{5\pi}{3} [/tex]
4. The effects of a certain anesthesia on patients is modeled by the rational function listed below. The
constants A and B are determined by factors such as body mass, age, etc. Suppose a patient who is
about to undergo surgery requires the constants to be A=36 and B=9. If t represents the number of
hours from the time the anesthesia enters the blood stream, and the function describes the percent
concentration needed for the anesthesia to be effective; how long can a surgery take if the percent
concentration needed for the patient to be sedated but not dead is between 4 and 6 percent? Explain
your reasoning and how you found your solution.
Model:C(t)= At/T^2+B
Answer: you will need 10
Step-by-step explanation:
I had the same problem on my hw this is what i got tell i think its correct:
Edit:
C(t)=At/T^2+B
a=36
b=9
t= how long it takes to enter blood stream
c=36/t^2 + 9
I found T to be 6 becuase I searched it up so
36/6^2=36/36=1
c=9+1
C=10
New awnser is 10
Determine the equation of the line passing through the point below having the corresponding slope.
Point: ( -20, -34)
Slope: m =9/5
Write your answer as an equation in the form y=mx+b
Answer:
Step-by-step explanation:
-34 = (9/5)(-20) + b
b = -34 + 36 = 2
y = (9/5)x + 2
Multiply.
[−2 3/11⋅(−4)]⋅(1 13/20)⋅(−10)
What is the product?
Answer:
[tex]{ \rm{ \{ - 2 \frac{3}{11} \times ( - 4) \}. \{1 \frac{13}{20} \times ( - 10) \} }} \\ \\ = { \rm{9 \frac{1}{11} \times - 16 \frac{1}{2} }} \\ \\ { \boxed{ \rm{ \: = - 150 \: \: }}}[/tex]
(1 point) Use the graph below to find exact values of the indicated derivatives, or state that they do not exist. If a derivative does not exist, enter dne in the answer blank. The graph of f(x) is black and has a sharp corner at x = 2. The graph of g(x) is blue.
Let h(x) = f(g(x)). Find
A. h'(1) =
B. h'(2) =
C. h'(3) =
Derivatives can be calculated from graphed functions.
The values of the derivatives are:
The given parameter is:
[tex]\mathbf{h(x) = f(g(x))}[/tex]
Start by calculating the equations of f(x) and g(x)
Graph f(x)
The slopes of f(x) are: 3/2 and -3/2
So, the equations are:
[tex]\mathbf{f(x) = \frac{3}{2}x,\ 0 \le x \le 2}[/tex]
[tex]\mathbf{f(x) = -\frac{3}{2}x,\ x \ge 2}[/tex]
Graph g(x)
The slope of g(x) is: -1/2
So, the equation is:
[tex]\mathbf{g(x) = -\frac 12x}[/tex]
For x = 1 and x = 2, we have:
So, we have:
[tex]\mathbf{h(x) = f(g(x))}[/tex]
Where:
[tex]\mathbf{f(x) = \frac{3}{2}x\ 0 \le x \le 2}[/tex] and [tex]\mathbf{g(x) = -\frac 12x}[/tex]
[tex]\mathbf{h(x) = f(g(x))}[/tex] becomes
[tex]\mathbf{h(x) = \frac{3}{2}(-\frac{1}{2}x)}[/tex]
Open brackets
[tex]\mathbf{h(x) = -\frac{3}{4}x}[/tex]
Differentiate
[tex]\mathbf{h'(x) = -\frac{3}{4}}[/tex]
So:
[tex]\mathbf{h'(1) = -\frac{3}{4}}[/tex]
[tex]\mathbf{h'(2) = -\frac{3}{4}}[/tex]
For x = 3, we have:
[tex]\mathbf{h(x) = f(g(x))}[/tex]
Where:
[tex]\mathbf{f(x) = -\frac{3}{2}x\ x \ge 2}[/tex] and [tex]\mathbf{g(x) = -\frac 12x}[/tex]
[tex]\mathbf{h(x) = f(g(x))}[/tex] becomes
[tex]\mathbf{h(x) = -\frac{3}{2}(-\frac{1}{2}x)}[/tex]
[tex]\mathbf{h(x) = \frac{3}{4}x}[/tex]
Differentiate
[tex]\mathbf{h'(x) = \frac{3}{4}}[/tex]
Substitute 3 for x
[tex]\mathbf{h'(3) = \frac{3}{4}}[/tex]
Hence, the values of the derivatives are:
[tex]\mathbf{h'(1) = -\frac{3}{4}}[/tex], [tex]\mathbf{h'(2) = -\frac{3}{4}}[/tex] and [tex]\mathbf{h'(3) = \frac{3}{4}}[/tex]
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Onyango slept at 2040 h on Thursday and woke up after 5 h 20 minutes. At what time did he wake up? A. 2.00 p.m. B. 2.40 a.m. C. 2.40 p.m. D. 2.00 a.m.
Answer:
Your answer is C.
Step-by-step explanation:
Answer:d.2:00am
20:40 is 8:40 pm in regular time. if you add five hours to the it will be 1:40am and add another 20 minutes it will end up being 2:00am
Which table shows a proportional relationship between x and y?
A.
x y
2 4
3 6
4 9
B.
x y
3 4
9 16
15 20
C.
x y
4 12
5 15
6 18
D.
x y
1 4
2 8
3 15
Answer:
c is the answer
Step-by-step explanation:
A football coach must order 9 new jerseys. The jerseys cost $23.79 each.
What is the total cost for the jerseys?
Answer:
9 x 23.79 = $214.11
In one season a basketball player missed 45% of her free throws. How many free throws did she attempt if she made 176 free throws?
Step-by-step explanation:
she missed 45%, so that means she made 55% of her free throws.
and these 55% correlate to the absolute number of 176 successful throws.
so,
55% = 176
1% = 55%/55 = 176/55
100% = 1%×100 = 176×100/55 = 320
so, she attempted 320 free throws in total.
Let g(x) = (x - 2)2. Find x such that g(x) = 25.
Answer:
x = 14.5
can also be written as;
x = 29/2
Step-by-step explanation:
8.70 divided by 0.46
Answer:
18.91304348
Step-by-step explanation:
Just divide it and you get the answer. When you divide something by a decimal, it acts more like multiplying and less like dividing lol (cuz the answer is bigger than the other 2 numbers)
On Friday, 0.325 of the students in
Keisha's math class were absent. What
percent of the students were absent?
Look at picture for choices!! Quick!!
Please help me thank you!!
Answer:
what the hell
Step-by-step explanation:
Leon and Thomas have the same number of cherries. Leon eats 5 of his cherries and has 12 cherries left. Thomas eats 9 of his cherries. How many cherries does Thomas have left?
34-18-(-23) write as a single number
Answer: 39
Step-by-step explanation: 34-18=16+23=39. Remember, 2 negatives equals a positive.
Answer: 39 cus 34-18=16+23=39
Step-by-step explanation:
On Mrs. Sean's desk,
there are pink and yellow
markers. The ratio of pink
markers to total markers
is 1:3. If there are 16
yellow markers, then how
many markershare pink?
Since the ratio of pink markers to total markers is 1:3, then there are 8 pink markers.
Number of yellow markers given = 16
Based on the information given, therefore, the pink markers will be half of the yellow markers. This will be:
= 1/2 × 16
= 8 markers
Therefore, the total markers will be:
= 8 + 16 = 24
In conclusion, pink markers will be 8/24 = 1/3. Therefore, the number of pink markers is 8.
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Ajar contains 3 red and 5 green balls identical in all aspects except color. If two balls are drawn at random, then the probability that the two balls drawn are not green is
Answer:
3/28.
Step-by-step explanation:
Total of 8 balls in the jar.
Prob (first one not green (= that its red) = 3/8
Prob ( Second one is also red) = 2/7.
So probability that both are not green = 3/8 * 2/7
= 6/56
= 3/28.
A ball is thrown vertically upward from the top of a 100-foot tower, with an initial velocity of 20 ft/sec. Its position function is s(t) = -16t^2 + 20t + 100. What is its velocity in ft/sec when t = 1 second?
The velocity of the ball in ft/sec, when t = 1 second is equal to -12 ft/sec.
Given the following data:
Displacement = 100 feetTime = 1 secondsPosition function = [tex]s(t) = -16t^2 + 20t + 100[/tex]To calculate the velocity of the ball in ft/sec, when t = 1 second:
Mathematically, the velocity of an object or physical body is equal to the differentiation of it's position function.
Velocity = s'(t)
Velocity = [tex]s(t) = -16t^2 + 20t + 100[/tex]
[tex]Velocity = -32t + 20[/tex]
Substituting the value of time (t), we have:
[tex]Velocity = -32(1) +20\\\\Velocity =-32+20[/tex]
Velocity = -12 ft/sec
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