The time taken by thunder to travel a distance of 5 miles is 25 seconds.
Which is the direct variation?A direct variation, as well known as a direct proportion, is a relationship that exists between two variables.Your distance from lightning differs directly with duration it takes you to hear thunder. If you hear thunder 10 seconds upon seeing lightning, you are approximately 2 miles away.Let d denote the distance and t the time.
Distance varies linearly with time, implying that distance is proportional to time.
Distance ∝ Time
d ∝ t
When the proportionality symbol is removed;
d = kt or k = d/t
Where k is the constant of proportionality.
In the equation, d = 2 and t = 10 are substituted.
k = 2/10 = 1/5
Therefore,
The following is a direct variation formula for the correlation between time and distance: d = (1/5)t
Now, for the distance of 5 miles, the time taken by the thunder is-
5 = (1/5)t
t = 5 × 5
t = 25 seconds.
Thus, the time taken by thunder to travel a distance of 5 miles is 25 seconds.
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explain which of the following is better to but
slope of p=
slope of q=
slope of r=
slope of m=
*PLEASE HELP*
verify that real number can be a complex number but a complex number can not be a real number. Also verify that the lengths of the complex number and its conjugate are equal but the converse is not necessarily true.
real number can be a complex number but a complex number can not be a real number, verified.
the lengths of the complex number and its conjugate are equal but the converse is not necessarily true., verified.
Not all complex numbers are real numbers, despite the fact that every complex number is a real number.
In fact, determining whether the complex number z = a + bi is real is one of the complex conjugate's most useful applications. If and only if z = a + 0i, a complex number is real. In other words, a complex number is real if it contains an imaginary part.
Mathematical proof:
Let z = a+bi, where a and b = real numbers.
Let z* =complex conjugate of z.
Then the magnitude (absolute value) of z is:
|z| = √(a²+b²).
And the value of z* is:
|z*| = √[a²+(-b)²] = √(a²+b²).
So |z| = |z*|.
This Completes the Proof.
what are real numbers?
its a quantity whose decimal expansion has an endless range. In contrast to the natural numbers 1, 2, 3,... that result from counting, real numbers are utilised in measurements of continuously altering quantities such as size and time.
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(1 - 3k) - 4(2 + 2.5k)
HELP!! Quick answer pls
The answer is -13k - 7
Answer:
1 - 3k - 8 + 10k
1 - 3k + 10k - 8
1 - 13k - 8
1 - 8 - 13k
-7 - 13k or -7 + (-13k)
how is g ( x ) = – | x + 2 | + is related to the graph of the parent function.
Answer: These linear functions can be represented by two lines y = 5x and y' = 5x' + 3
So when we shift line y = 5x by 3 units up on the y-axis then a new graph of
y = 5x + 3 will be formed.
Therefore, Option A is the answer.
Write the sentence as an equation.
341 is the same as the product of k and 273, minus 79
Answer:
341 = 273k - 79 or 273k - 79 = 341
100 points ANSWER ASAP
Answer: Question 1: 113 & Question 2: 27
Step-by-step explanation:
For question 1 you would add 35+32=67,then you subtract 180-67 to get 113 for your answer & question 2 you would subtract 155-128 to get 27 for the answer
Angles in a triangle add up to 180 degrees.
[tex]180-35-32=113[/tex]
Angles on a line add up to 180 degrees.
[tex]p=180-113=67[/tex]
Angles on a line add up to 180 degrees.
[tex]180-155=25[/tex]
Angles in a triangle add up to 180 degrees.
[tex]q=180-128-25=27[/tex]
A 25-foot ladder is leaning against the side of a house so that the bottom of the ladder is 15 feet from the base of the house. Will the ladder reach a window that is 21.5 feet above the ground?
The ladder will not reach a window that is 21.5 feet above the ground if the length of the ladder is 25 feet.
What is a right-angle triangle?It is a triangle in which one of the angles is 90 degrees and the other two are sharp angles. The sides of a right-angled triangle are known as the hypotenuse, perpendicular, and base.
From the data:
The right angle triangle can be drawn:
From the diagram:
Applying Pythagoras' theorem:
BC² = AB² + AC²
25² = 15² + AC²
After solving
AC = 20 feet
AC < 21.5 feet
Thus, the ladder will not reach a window that is 21.5 feet above the ground if the length of the ladder is 25 feet.
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Answer:
No, because the ladder will only reach 20 feet high
Step-by-step explanation:
I go it right on my quiz :]
For a given week, Tammy's Coffee House has available 1584 ounces of A grade coffee and 1536 ounces of B grade coffee. These are blended into 1-pound
packages as follows: an economy blend that contains 3 ounces of A grade coffee and 8 ounces of B grade coffee, and a superior blend that contains 9 ounces of
A grade coffee and 3 ounces of B grade coffee. (The remainder of each blend is made of filler ingredients.) There is a $3 profit on each economy blend package
sold and a $2 profit on each superior blend package sold. Assuming that the coffee house is able to sell as many blends as it makes, how many packages of
each blend should it make to maximize its profit for the week?
Note that the ALEKS graphing calculator can be used to make computations easier.
Economy blend:
Superior blend:
package(s)
package(s)
X
S
There is a requirement of 176 packets of economy blend and 96 packets of a superior blend to make maximum profit for the week.
Using the given data, calculate the x number of packages of the economy blend as well as the y number of packages of the superior mix.
3x + 11y =1584
6x + 4y = 1440
From the graph of these two equations, three extreme points are deduced: (240,0), (0,144), and (176,96).
The maximum (2x +4y) is the goal function.
Determine the aim function's value at all these extreme points,
The objective function value for (240,0) is 2 × 240 = 480
The objective function value for (0,144) is 4 × 144 = 576
The value of the objective function for (176,96) is 2 × 176 + 4 × 96 = 736
∴ The optimal point is (176,96) where x = 176 and y = 96.
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The school store has 2000 pencils in stock and sells an average of 50 pencils per day. The manager reorders when the the number of pencils in stock is 950 let d= the number of days
we make a equation depending of the days
[tex]T=2000-50d[/tex]Where T is the total of pencils
In this equation we are going to subtract 50 pencils for each day from the original 2000
to know the days where are 950 pencils we replace the total by 950 and solve d
[tex]\begin{gathered} 950=2000-50d \\ 50d=2000-950 \\ 50d=1050 \\ d=\frac{1050}{50} \\ \\ d=21 \end{gathered}[/tex]the number of days is 21
3) Speedy Car Rental charges a flat fee of 30$ plus $.15 for each mile
a) write an equation for the cost as a function of the number of miles driven.
b) how much would the cost be if you drove 80 miles?
Answer:
a) C(m) = flat rate + rate per mile
b) $42
Step-by-step explanation:
a) C(m) = flat rate + rate per mile*No. of miles => 30+.15x
b) 30+.15*80 = 42
Which best describes and corrects the error in finding the solution?
X
x+8 =
10
+8 +8
x = 18
The 10 should have been subtracted rather than added.
Correct answer: x = -2
The 8 should have been subtracted rather than added.
Correct answer: a = 2
The 8 should have been subtracted rather than added.
Correct answer: x = -2
The 10 should have been subtracted rather than added.
Correct answer: x = 2
Plssss help :(
Answer:
answer D is right. You need to substract,so that you can get x=2
A disco ball is shaped like a sphere with diameter of 60 inches to the nearest square inch what is the surface area of the disco ball
To calculate the surface area of a sphere, you have to use the following formula:
[tex]SA=4\pi r^2[/tex]Where "r" is the radius of the sphere.
We know that the diameter of the sphere is d = 60 inches and that the radius is half the diameter, then the radius can be determined as follows:
[tex]\begin{gathered} r=\frac{d}{2} \\ r=\frac{60}{2} \\ r=30in \end{gathered}[/tex]Once the radius is calculated, you can determine the surface area of the sphere:
[tex]\begin{gathered} SA=4\pi(30^2) \\ SA=4\pi\cdot900 \\ SA=3600\pi\approx11309.73in^2 \end{gathered}[/tex]The surface area of the sphere is 3600π in², expressed as a decimal value, the surface area is equal to 11309.73 in²
Use these two representations of reflection at the right to sort each each statement below as the or false
The statements that are true are:
Statement A: Figure A was reflected from the third quadrant to the second quadrant
Statement B: Triangle DEF was reflected over the x-axis
The False statements are:
Statement C: The image of DEF is in quadrant 3
Statement D: The reflection of A can be represented by (-x, y)
Statement E: The reflection of DEF can be represented by (-x, y)
Here is a linear equation: y = 2/3x + 1 Are (6, 5) and (9, 8) solutions to the equation? Explain or show your reasoning.
A linear equation is a mathematical form of a line segment the point (6,5) satisfies the equation y = 2/3x + 1 so it is the solution of the equation but (9,8) is not the solution.
What is a linear function?A straight line on the coordinate plane is represented by a linear function.
The formula for a linear function is f(x) = ax + b, where a and b are real values.
As per the given linear equation, y = 2/3x + 1
To be a point of its solution the point must satisfy the given equation.
Substitute (6,5)
5 = (2/3)6 + 1
5 = 2(2) + 1 = 5
Therefore, the (6,5) is the solution of the equation.
Substitute,(9,8)
(2/3)9 + 1 = 7
8 ≠ 7
So,(9,8) is not the solution of the equation.
Hence "A linear equation is a mathematical form of a line segment the point (6,5) satisfies the equation y = 2/3x + 1 so it is the solution of the equation but (9,8) is not the solution".
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using ordinary interest, calculate the missing information for the following simple discount
Face Value $50,000. Discount Rate (%) 13. Date of Note Apr. 5. Term (days) — Maturity Date, Aug. 14. Bank Discount — Proceeds —
The Bank discount and proceeds of the given information is:
$2365.27 and $47634.73 respectively.
Given the face value is $50,000
Discount rate = 13%
No.of term days = April 5 to August 14
= 131 days.
Bank discount = ?
Proceeds = ?
First calculate the bank discount using the formula:
Bank discount = face value × discount rate × time
Bank discount = $50,000 × 0.13 × 131/360
= 50,000×0.13×0.36388
= $2365.27
now calculate the proceeds using the formula :
Proceeds = face value - bank discount
= 50,000 - 2365.27
= $47634.73
Hence the bank discount and proceeds are $2365.27 and $47634.73 respectively.
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someone help me with the last two problems
Here is the completed table:
x /AM/
14 16
3 13
11 33
10 40
What are the values?/AM/ + /AC/ = /AC/
(x + 2) + (3x - 9) = 6x - 21
4x - 7 = 6x - 21
6x - 4x = 21 - 7
2x = 28
x = 28 / 2
x = 14
/AM/ = 14 + 2 = 16
/AM/ + /MW/ = /AW/
(2X + 7) + (3x - 4) = 18
5x + 3 = 18
5x = 18 - 3
5x = 15
x = 15/5
x = 3
/AM/ = (2 X 3) + 7 =
= 6 + 7 = 13
x + x + x + x = 44
4x = 44
x = 44 / 4
x = 11
/AM/ = 11 x 3 = 33
/AG/ + /GM/ = /AM/
2(x + 10) = 3x + 10
2x + 20 = 3x + 10
20 - 10 = 3x - 2x
10 = x
/AM/ = (3 x 10) + 10
= 30 + 10
= 40
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Mark says, '81 is a square number. Therefore, 810 is a square number.'
Is Mark correct? Explain your answer.
Answer:
mark is right
Step-by-step explanation:
3+5x5 =13
Answer:
Mark is not correct , becouse squared number Is number which can be after "=" when you times same numbers for example: 4*4=16 so 16 is squared number,is this make sense?
The table shows the linear relationship between the distance in feet below sea level and the time in seconds traveled by a submarine What is the rate of change of the distance in feet below sea level with respect to time that the submarine traveled? Record your answer
The rate of change of the distance in feet below the sea level over time is: 8 ft/sec.
What is the Rate of Change of a Linear Relationship?The rate of change of a linear relationship between variables x and y is calculated as:
Rate of change = change in y / change in x.
From the table given, we have:
x = time (in seconds)y = distance below sea level (in feet)Using any two points from the table, (0, 460) and (18, 604):
Rate of change of the linear relationship = change in y / change in x = (604 - 460)/(18 - 0)
Rate of change of the linear relationship = 144/18
Rate of change of the linear relationship = 8 ft/sec.
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5. Which of the following is a perfect square trinomial?
A. x^2 + 9x + 18
C. 3x²+ 10x +3
B. x²+ 6x +9
D. x²-4
Answer:
Step-by-step explanation:
B)
x² + 6*x + 9 = x² + 2*x*3 +3² = (x + 3)²
7. It has been estimated that Halley's comet has a mass of 1 X 10"' tons.
This comet is estimated to lose 1 X 108 tons of material each time its orbit brings it close to the sun. With an orbital period of 76 years, what is the maximum remaining life span of Halley's comet?
The maximum remaining life span of Halley's Comet is 76000 years.
The formula for calculating maximum remaining life span of Halley's Comet is [tex]L = \frac{M}{m} \times t[/tex]
M = mass of comet = [tex]1 X 10^{11}[/tex] tons
m = Mass of material lost =[tex]1 X 10^{8}[/tex] tons
t=orbital period = 76 years
Equating values in the equation
L = [tex]\frac{1 X 10^{11}}{1 X 10^{8}} \times76[/tex]
L = 76000 years
What is life span?life span, is the time between the birth and death of an organism. It is normal for all organisms to die. Some die after a short existence, like the nymph fly, which returns to adult life in a day, and others, like the wrinkled fly, which live for thousands of years. It seems that the lifespan limits of each species are ultimately determined by heredity. Locked in the code of the genetic material are instructions that determine the age at which a species cannot survive even under the most favourable conditions. And many environmental factors reduce this upper age limit.
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Find each sum:
1. 4j+k, -3k+7, 5-2j, and j+k-8
2. 5x^2-9x+3 and -2x^3+4x^2+7
1. The sum for the algebraic expression 4j+k, -3k+7, 5-2j, and j+k-8 is 3j-k+4
2.The sum for the algebraic expression 5x^2-9x+3 and -2x^3+4x^2+7 is -2x³+9x²-9x+10
What is algebraic addition?The addition of two or more numbers or quantities taken with regard to their signs according to the rules of addition in algebra.
First we will find the sum of 4j+k, -3k+7, 5-2j, and j+k-8
0i + 4j + k + 0
0i + 0j - 3k + 7
0i - 2j + 0k + 5
0i + j + k- 8
So the sum of 4j+k, -3k+7, 5-2j, and j+k-8 is 3j-k+4
First we will find the sum of 5x²-9x+3 and -2x³+4x^2+7
0x³ + 5x² - 9x + 3
-2x³ + 4x² + 0x+ 7
So the sum of 5x²-9x+3 and -2x³+4x²+7 is -2x³+9x²-9x+10
Therefore, the sum of the given algebraic expressions 4j+k, -3k+7, 5-2j, and j+k-8 is 3j-k+4 and 5x²-9x+3 and -2x³+4x²+7 is -2x³+9x²-9x+10.
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Write a quadratic equation to match the relationship given in the table
In order to find the quadratic equation, let's use the standard form of a quadratic equation:
[tex]y=ax^2+bx+c[/tex]Using the point (0, 2) from the table, we have:
[tex]\begin{gathered} 2=a\cdot0^2+b\cdot0+c \\ c=2 \end{gathered}[/tex]Now, using the points (-1, -2) and (1, 22):
[tex]\begin{gathered} -2=a(-1)^2+b(-1)+2 \\ a-b=-4 \\ 22=a(1)^2+b(1)+2 \\ a+b=20 \end{gathered}[/tex]Adding both equations, we can solve for a:
[tex]\begin{gathered} a-b+(a+b)=-4+(20) \\ 2a=16 \\ a=8 \\ a+b=20 \\ 8+b=20 \\ b=12 \end{gathered}[/tex]Therefore the equation is y = 8x² + 12x + 2
NEEED HELPPP ASAPPPPPP
The inverse of the function → f(x) = [tex]\sqrt{11x+12}[/tex] is
f⁻¹(x) = (x² - 12)/11
We have -
y = f(x) = [tex]\sqrt{11x+12}[/tex]
We have to find its inverse function.
What is the procedure to find inverse of function ?Inverse of a function can be calculated by following the steps mentioned below -
Step 1 - Replace 'y' with 'x' and vice - versa.
Step 2 - Rewrite the equation by solving for 'y'.
Step 3 - Replace 'y' with f⁻¹(x).
According to the question -
y = f(x) = [tex]\sqrt{11x+12}[/tex]
x = [tex]\sqrt{11y+12}[/tex]
x² = 11y + 12
x² - 12 = 11y
y = (x² - 12)/11
f⁻¹(x) = (x² - 12)/11
Therefore, the inverse of the function → f(x) = [tex]\sqrt{11x+12}[/tex] is
f⁻¹(x) = (x² - 12)/11
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The perimeter of a rectangular room is 60.5 feet. Let x be the width of the room (in feet) and let y be the length of the room (in feet). Select the equation that could model this situation.
A. y=−2x+60.5
B. y=−x+30.25
C. 2x+y=30.25
D. x+2y=60.5
The equation that could model the given situation is y = -x + 30.25. The correct option is B. y = -x + 30.25
Perimeter of a rectangle and equationsFrom the question, we are to determine the equation that could model the given situation
The perimeter, P, of a rectangle is given by the formula,
P = 2(l + w)
Where P is the perimeter
l is the length
and w is the width
From the given information,
The perimeter of a rectangular room is 60.5 feet.
∴ P = 60.5 feet
Also,
x is the width of the room and y is the length of the room
That is,
l = y
and
w = x
Thus,
The equation becomes
60.5 = 2(y + x)
2(y + x) = 60.5
Divide through by 2
y + x = 30.25
y = -x + 30.25
Hence,
y = -x + 30.25 is the equation that might be used to model the circumstance.
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X
x=-4y
The slope is -4, and
the y-intercept is O.
The description of the error in finding the slope and y-intercept, of the graph of the equation is given by the option:
To be in slope-intercept form, the equation needs to be solved for y, not x
The equation in slope-intercept form is, [tex]\displaystyle{y = -\frac{1}{4} \cdot x[/tex]
What is the slope-intercept form of a straight-line equation?The slope-intercept form of the equation of a straight line is an equation of the form, y = m·x + c
The slope-intercept form of a straight-line equation is of the form, y = m·x + c, where:
m = The slope of the equation
c = The y-intercept
The given equation is x = -4·y
The given equation is not in the slope and intercept form given that the subject of the equation is x, rather than y
The error is therefore, in making x, the subject of the equation rather than y, that is the equation needs to be solved for y, not x
The correction of the error is performed as follows:
x = -4·y
-4·y = x
[tex]\displaystyle{y = \frac{x}{-4} = -\frac{1}{4} \cdot x[/tex]
Which gives: [tex]\displaystyle{y = -\frac{1}{4} \cdot x[/tex]
The slope of the graph of the equation is [tex]-\frac{1}{4}[/tex], the y-intercept, c, is 0
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What is the equation of the line that is perpendicular to y = 3x + 3 and passes through the point (−6, 9)?
y equals negative one-third times x plus 3
y equals negative one-third times x plus 7
y = 3x − 33
y = 3x + 27
Answer:
y=-1/3x+7
Step-by-step explanation:
put it in y-y1=m(x-x1)
perpendicular means the slope is opposite
slope is -1/3
y-9=-1/3 (x+6)
y-9=-1/3x -2
+9 +9
y=-1/3x +7
I just want the answer :)
Answers ↓
angle 1 → 90°
angle 2→ 44°
angle 3 → 90°
angle 4 → 46°
I hope this helps u
4*10^8 -9*10^7 pls work it out
Answer:
Answer down below!
Step-by-step explanation:
Answer: 310000000
Step-by-step is provided in the picture below!
As the number of degrees of freedom for a t distribution increases, the difference between the t distribution and the standard normal distribution.
The standard normal distribution becomes smaller.
What is standard deviation?
Your dataset's average level of variability is represented by the standard deviation. It reveals the average deviation of each statistic from the mean. A low standard deviation denotes that values are grouped close to the mean, whereas a large standard deviation shows that values are often far from the mean.Think about the following data: 2, 1, 3, 2, 4. The average and the sum of squares representing the observations' variances from the mean will be 2.4 and 5.2, respectively. This means that (5.2/5) = 1.01 will be the standard deviation.As the number of degrees of freedom for a t distribution increases, the difference between the t distribution and the standard normal distribution
becomes smaller.
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