Answer:
k = 1/2
Step-by-step explanation:
direct variation equation is y = kx where 'k' is the constant of variation
substitute 36 for 'y' and 72 for 'x' to get:
36 = 72k
solve for 'k' to get:
k = 36/72 or k = 1/2
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]
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per
A man deposited $80,000.00 in
bank at a 12% compound interest
annum. How much did the man have
in the bank at the second year?
e
Using the compound interest formula, the amount of money in the man's bank account in the second year is $100352
The compound interest relationship is computed using the relation :
Final amount = P(1 + r)^tP = principal ; r = interest rate ; t = periodPlugging the values into the formula :
Final amount = 80000(1 + 12%)²
Final amount = 80000(1 + 0.12)²
Final amount = 80000(1.12)²
Final amount = $100352
Therefore, the final amount in the second year is $100352
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does anyone know this math problem??
Answer:
y = -7
Step-by-step explanation:
NO LINKS OR ASSESSMENT!!!!
Answer:
See below and attachedStep-by-step explanation:
1. There are infinite number of lines going from only one point (2, 5)
No definite solution for line A.2. This is a proportional relationship, since line passes through the origin. The slope is -3.
The line B is:
y = -3x3. Points (-3, -2) and (3, 10)
The slope:
m = (10 + 2)/(3 + 3) = 2The y - intercept:
10 = 2*3 + b ⇒ b = 4The line C is:
y = 2x + 44. The rate of change is m = 2.5
The y- intercept:
1 = 2*2.5 + b ⇒ - 4The line D is:
y = 2.5x - 45. Line E has a slope of 4, no sufficient info to conclude.
y = 4x + b, with any value of b6. Line F has m = -3/4 and passes through (8, -1).
The y -intercept is:
-1 = 8(-3/4) + b ⇒ b = 5The line F is:
y = -3/4x + 57. G is not a linear relationship as the function increases exponentially with common ratio of 3.
1/2(x+24)=21 (distributive property) thanks
Answer:
x=18
Step-by-step explanation:
since x+24 is in parenthesis, we need to distribute 1/2 to all the parts inside the parenthesis.
1/2 * x = 1/2x
1/2 * 24= 12
1/2x+12=21
subtract 12 from both sides
1/2x= 9
divide 1/2 from both sides
x=18
so your answer would be x=18
Hi there!
»»————- ★ ————-««
I believe your answer is:
[tex]\frac{1}{2}(x+24)=21 \rightarrow \frac{1}{2}x + 12 = 21\\\\x = 18[/tex]
»————- ★ ————-««
Here’s why:
⸻⸻⸻⸻
[tex]\frac{1}{2}(x+24) = 21\\\rule{150}{0.5}\\\\\rightarrow \frac{1}{2}*x = \frac{1}{2} \\\\\rightarrow \frac{1}{2} * 24 = 12\\\\\rightarrow \frac{1}{2}x + 12 = 21\\\\\rightarrow \frac{1}{2}x + 12 - 12 = 21 - 12\\\\\rightarrow \frac{1}{2}x = 9\\\\\rightarrow (\frac{1}{2}x)2 = 9 * 2\\\\\rightarrow\boxed{x = 18}[/tex]
⸻⸻⸻⸻
»»————- ★ ————-««
Hope this helps you. I apologize if it’s incorrect.
What is the value of x?
4
ISNDNDMSLWLWKXDJSNKWKEDLC
1.Which of the following is equivalent to 0.00648
2. What is the decimal equivalent of 8.3 x 10*6
3. What is the decimal equivalent of 9.7 x 10*5
4. Write 0.501 in scientific notation
5. Which of the following is equivalent to 4.99 x 10*-4
Answer:
D) 6.48 x 10⁻³
Step-by-step explanation:
to get an exponent of -3 means you move the decimal point three spaces to the right
2) 8,300,000
3) 970,000
4) 5.01 x 10⁻² (picture) 5.01 x 10⁻¹ (question)
5) 0.000499
the greatest common factor of 12 and 26 pls explain the steps
Step-by-step explanation:
12- 2*6
26- 2*13
gcf =2
the least greatest common factor is 2
find the length of x rounded to nearest hundredth please!!
Answer:
4.00 pls give brainliest
Step-by-step explanation:
Hello turkshcutie11!
[tex] \huge \boxed{\mathfrak{Question} \downarrow}[/tex]
Find the value of x.
[tex] \large \boxed{\mathfrak{Answer \: with \: Explanation} \downarrow}[/tex]
It's given that the triangle in the figure is a right triangle (a triangle with one angle as 90°). So, we can use the pythagoras property to solve this question.
__________________
Given sides :-
5 units (base)3 units (altitude)x units (hypotenuse)__________________
Using pythagoras property...
Hypotenuse ² = Base² + Altitude ²
x² = 5² + 3²
x² = 25 + 9
x² = 34
x = √34
x = 5.83 units (1st option).
__________________
Hope it'll help you!
ℓu¢αzz ッ
All items or people of interest in an experiment is called
Answer: a population
Step-by-step explanation:
Step-by-step explanation:
I think your answer is Population
The super discount store s having a sale and all the clearance items are 40% off. which of the following are correct ways to find the price of an item that is normally $25.00?
A. Multiply $25.00 by 40 B. Multiply $25.00 by 0.4
C. Multiply $25.00 by 0.4 and subtract that amount from $25.00
D. Multiply $25.00 by 0.6
Answer:
Answer is C.
Step-by-step explanation:
Write an explanation to a friend about how you
would estimate 17 1/5 / 3 4/5.
Answer:
67/5
Step-by-step explanation:
17 1/5
17x5= 85 + 1= 86/5
3 4/5
3x5=15+4= 19/5
86/5 - 19/5=
86-19= 67/5
hope this helps!
find the product what is 9.874×7= ?
Can someone help me and explain this to me step by step?
Answer: 11/9
Step-by-step explanation:
First, convert two to 18/9. This is still equal to two but this makes it easier to answer the problem, because both of the terms have the same denominator. Now, since both of them have the same denominator, all you need to do is subtract the numerators, and put that over the denominator of 9. 18-7=11. So the answer is 11/9. This is an improper fraction, though you could also make it into a mixed number: 1 and 2/9.
Answer:
11/9
Step-by-step explanation:
Add a one under the 2. So that it becomes 2/1. Now you have the expression, 2/1 - 7/9. To subtract fractions, you need the denominators of the two fractions to be the same. We can put 9 as the common denominator. All you have to do in order for 2/1 to have 9 as its denominator, is to multiply 9 for both the numerator and denominator; 2/1 x 9/9 = 18/9. After that, your new expression would be 18/9 7/9. Just subtract across, 18 - 7 = 11, keep the denominator 9. The answer should be 11/9
9 is the cube root of (a) 343 (b) 729 (c) 629 (d) 81
Answer:
(b) 729
Step-by-step explanation:
9 × 9 × 9 = 9^3 = 729
Thus, 9 is the cube root of 729
Answer the question below, and then fill in the blanks if necessary.
Can the distributive property be used to rewrite
3 + (8 + 4) ?
Answer:
acoording to the picture given, it is possible be cause there is a multiplication operation before the parenthesis.
Step-by-step explanation:
distribut the 3 to each number in the parenthesis:
(3 * 8) + (3 * 4) = 24 + 12 = 36
what is 100 divided by 5, (the answer) x 3 (the answer) x 79 (the answer) - 4
NO LINKS PLEASE! First to answer correct gets Branliest!!!
Answer:
4736
Step-by-step explanation:
1) 100 divided by 5 is 20
2) 20 times 3 is 60
3) 60 times 79 is 4740
4) 4740 subtract from 4 is 4736
5) Answer is 4736
Answer:
4736
Step-by-step explanation:
5*20 = 100
20*3 = 60
60*79 = 4740
4740 - 4 = 4736
A caterer charges 5500 plus 530 per guest to cater a wedding. Walt and Traci don't want to spend more than $8000 on catering Write
and solve an inequality in terms of the number ofguests, 9 that can be invited.
Answer:
x = 250
Step-by-step explanation:
What are the odds of winning a game, if the probability of losing the game is 5 /13 ?
Answer:
Step-by-step explanation:
If divided: 0.38461538461
If percent: 38.4615%.
Brainliest rn:D
The odds of winning the game is [tex]\frac{8}{13}[/tex].
What is probability?Probability is the measure of happening and non-happening of the outcomes of a random experiment.
What is the sum of probabilities?The sum of all the probabilities of all the elementary events of an experiment is always 1.
According to the given question.
We have
The probability of losing the game is [tex]\frac{5}{13}[/tex]
Since, we know that the sum of all the probabilities of all elementary events of an experiment is always 1.
Therefore,
Probability of winning the game + Probability of losing the game = 1
⇒ Probability of winning the game + [tex]\frac{5}{13} =1[/tex]
⇒ Probability of winning the game = [tex]1 - \frac{5}{13}[/tex]
⇒ Probability of winning the game = [tex]\frac{13-5}{13}[/tex]
⇒ Probability of winning the game = [tex]\frac{8}{13}[/tex]
Hence, the odds of winning the game is [tex]\frac{8}{13}[/tex].
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A living room is a compound shape made of two rectangles like the one
below. How many square feet of carpet would you need to cover the entire room?
Answer:
Step-by-step explanation:
702
What is the y-intercept of the line y =
= {x-5
-5?
[tex]\large y=\dfrac{1}{2} x-{\boldsymbol5}^{\sf /y -intersept} \\\\ \rm Answer : B)-5[/tex]
SHOW YOUR WORK. Algebra question. 100 POINTS. Easy
Answer:
x = 3/2Step-by-step explanation:
Add up the given equations t eliminate y and solve for x:
3x + 2y + 3x - 2y = 4 + 56x = 9x = 9/6x = 3/2Your choice is correct
Which table represents exponential growth?
Answer:
B.
Step-by-step explanation:
Exponential graphs means that it starts to go up slowly but then goes up faster. A is going down, so that's wrong since the graph needs to go up. The correct answer is B.
Write a quadratic function whose zeros are -12 and -2.
Answer:
(x+12) (x+2)
x(x+12)+2(x+12)
x^2+12x+2x+24
x^2+14x+24
Step-by-step explanation:
Answer:
f(x) = x² + 14x + 24
Step-by-step explanation:
Given the zeros of -12 and -2, then it means that:
x + 12 = 0 and x + 2 = 0
As a proof, if you isolate x, you'll end up with the given values:
x + 12 - 12 = 0 - 12
x = -12
x + 2 - 2 = 0 - 2
x = -2
In terms of using these values into the quadratic function:
(x + 12) (x + 2)
Perform the FOIL method in order to find the quadratic function:
(x + 12) (x + 2)
f(x) = x² + 2x + 12x + 24
f(x) = x² + 14x + 24 ⇒ This is the quadratic function, given the zeros as x = -12, and x = -2.
Question
Jackson's backpack weighed 15 kg. Convert the weight to pounds. Round to the nearest pound.
Answer:
[tex]15 \times 2.205 = 33.0693 \: lb[/tex]
Unit conversion is a way of converting some common units into another without changing their real value. The Weight of Jackson's backpack is 33.075 pounds.
What is unit conversion?Unit conversion is a way of converting some common units into another without changing their real value. for, example, 1 centimetre is equal to 10 mm, though the real measurement is still the same the units and numerical values have been changed.
Since 1 kg is equal to 2.205 pounds. Therefore, the Weight of Jackson's backpack is,
15 kg = 2.205 × 15 kg = 33.075 pounds
Hence, the Weight of Jackson's backpack is 33.075 pounds.
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Subtract.
3−(−5)−(−2)
Plot the solution on the number line.
Answer:
10
Step-by-step explanation:
Answer: Its 10, so plot it on 10 in the number line
Step-by-step explanation: Since the subtraction signs cancel out, they make a addition sign. Henceforth its " 3+5+2" which would mean the sum is 10.
Jenny's test grades are 88, 95, 97, and 100.
What is her average?
Answer:
95
Step-by-step explanation:
For average you just add all the numbers together and divide by how many numbers there are.
88+95+97+100=380
380÷4=95
The average of the given data is 95.
What is an average?Average is defined as the ratio of the sum of the number of the data sets to the total number of the data. The average actually determines the middle value of the data.
Given that Jenny's test grades are 88, 95, 97, and 100. The average of the numbers will be calculated by adding all the numbers and dividing it by the total count of the numbers.
For average you just add all the numbers together and divide by how many numbers there are.
Average = ( 88+95+97+100 ) / 4
Average = 380 / 4
Average = 95
Therefore, the average of the given data is 95.
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Complete the equation _,287x6=25,_ 2_
Answer:
4,287 x 6 = 25,722
.......
Hey may someone please help me<4! I’ll greatly appreciate it
Answer:
1st figure out how many feet in 1 yard
Then you can take that number <x>
X x 5
Step-by-step explanation:
Answer:
1.67 yards or 5/3
Step-by-step explanation:
I just looked it up
A constant head permeability test is performed on a soil that is 2 cm x 2 cm square and 2.5 cm long. The head difference applied during the test is 18 cm, and 5 cm3is collected over a time of 100 sec. a) Compute the permeability based on these test conditions and results b) A falling head test is to be done on the same soil specimen in teh same time (t1 - t2
Answer:A
Step-by-step explanation:por que se calcula correctamente