Answer:
Length of the rectangle is 18 ft when its width is 4ft
Step-by-step explanation:
Let us assume that the length is represented by l.
Let us assume that the width is represented by w.
As given
The length of the rectangle varies inversely with its width.
Thus
L x 1/w
l=k/w
Where k is the constant of proportionality .
As given
If the
length of the rectangle is 6 feet when the width is 12 feet,
l=6, w=12
putting the values in l = k/w
6 = k/12
k = 12 x 6
k=72
As given
width is 4ft
k= 72, w = 4
Putting the values in, L = k/w
L= 72/4
L=18 ft
Therefore the length of the rectangle is 18 ft when its width is 4ft
Hope this helps You
The volume of water in a rectangular, in-ground, swimming pool is given by V(x ) =x3 + 11x2 + 24x where V (x) is the volume in cubic feet when the water is x ft high
What is the dimension of the base of the pool? (a) x + 3 and x + 8 (b) x + 4 and x + 7 (c) x + 4 and x + 8(d) x + 3 and x + 7 What is the volume of the pool when x = 3 ft?
(a) 298 ft3 (b) 148 ft3 (c) 268 ft3 (d) 198 ft3
If the volume is 100 ft3 of water, what is the height x ? (a) 2 ft (b) 3 ft (c) 4 ft (d) 5 ft
If the maximum capacity of the pool is 520 ft3 what is the maximum depth? (a) 2 ft (b) 3 ft (c) 4 ft (d) 5 ft
1) The dimension of the base of the pool is; (x + 3) and (x + 8)
2) The volume of the pool when x = 3 ft is; 198 ft³
3) If the volume is 100 ft³ of water, the height x is; 2 ft
4) If the maximum capacity of the pool is 520 ft³, the maximum depth is; 5 ft
How to find the volume of a cuboid?We are given that the volume of water in a rectangular, in-ground, swimming pool is; V(x) = x³ + 11x² + 24x
where;
V(x) is the volume in cubic feet when the water is x ft high
1) V(x ) =x³ + 11x³ + 24x
V(x) is the volume in cubic feet when the water is x ft high
Factorizing the polynomial into its' factors gives;
V(x) = x(x² + 11x + 24)
V(x) = x(x + 8)(x + 3)
The water is x ft high and so the dimensions of the base of the pool are (x + 3) and (x + 8)
2) We want to find the volume of the pool when x = 3 ft. Thus;
V(3) = 3(3 + 8)(3 + 3)
V(3) = 3 (11)(6)
V(3) = 198 ft³
3) If the volume is 100 ft³ of water, the height x is calculated as;
x(x + 8)(x + 3) = 100
Solving for x gives us;
x = 2 ft
4) If maximum capacity of the pool is 520 ft³, then the maximum depth is;
x(x + 8)(x + 3) = 520
Solving for x gives us;
x = 5 ft
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(a) Write 7.97 x 10 ^-6 as an ordinary number.
Answer:
0.00000797
Step-by-step explanation:
Draw and label a coordinate plane so that the x-axis extends from -9 to 9 and the y-axis
extends from -6 to 6. Represent each of these points with a dot, and label the point using
its letter name.
The required given Co-ordinates are plotted in graph below.
What are Co-ordinates?The numbers on a direction lattice are utilized to find focuses. Each point can be recognized by an arranged sets of numbers; that is, a number on the x-axis called a x-coordinate, and a number on the y-hub called a y-coordinate. Requested matches are written in enclosures (x-coordinate, y-coordinate).
Explain graph.Graph is characterized as to make an outline that shows a connection between at least two things. An illustration of diagram is to make a progression of bars on charting paper
According to question:coordinates plane so that the x-axis extends from -9 to 9 and the y-axis
extends from -6 to 6
Plotted points on the graph are shown in image below.
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Find the measure of each acute angle in a right triangle where the measure of one acute angle is 8 times the measure of the other acute angle
The measure of the acute angles in the right triangle are 10 and 80 degrees.
How to find the angle of a right angle triangle?A right angle triangle is a triangle that has one of its angles as 90 degrees. The sides of a right angle triangle can be named base on the position of the angles. The sides includes hypotenuse side, opposite side and adjacent side.
The sum of angles in a right angle triangle is 180 degrees.
The other measures of the right triangle are acute angles.
Any angle that measures greater than 0° and less than 90° is called an acute angle.
Hence, let's find the measure of the acute angles
let
x = measure of one acute angle
Hence,
x + 8x + 90 = 180
9x = 180 - 90
9x = 90
x = 90 / 9
x = 10
Therefore, the measure of the acute angles are 10 and 80 degrees.
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I need help with number nine please
On #9:
Slope-intercept form is y = mx + b
Based on the graph, the slope is -4/3 and the y-intercept is (0,0).
The answer is y = –4/3 x.
You could add "+0" at the end to have y = –4/3 x +0, but since adding 0 doesn't change it, it's usually left off.
Answer:
y = -4/3x + 0 or just y = -4/3
Step-by-step explanation:
you just find the slope by doing rise over run, and find the y-intercept by looking at what number the line hits on the y-axis.
C is directly proportional to D, when C-125 and D=5. Work out the value of C when D = 6. Work out the value of D when C = 4725
Answer:
d=189 when c=4725
Step-by-step explanation:
c:d
125:5
divide by 5 to find the value of c when d=1
25:1
multiply by 6 to find the value of c when d=6
150:6
4725:?
4725/25=189
189*1=189
slope of (-3,-2) and (-1,-5)
Answer: Slope of [tex](-3, -2)[/tex] and [tex](-1, -5)[/tex] is [tex]-1.5[/tex].
Step-by-step explanation:
The slope of a line is given by, [tex]m=\frac{y_2-y_1{} }{x_2-x_1}[/tex]
Here we have,
[tex](x_{1}, y_{1}) = (-3, -2)[/tex] and [tex](x_{2}, y_{2}) = (-1, -5)[/tex]
Now put the known values in the slope formula we get,
[tex]m=\frac{(-5) -(-2) {} }{(-1) -(-3)}[/tex]
[tex]m=\frac{(-3) {} }{2}[/tex]
Slope (m) = 1.5
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Does this given information represent a function?
Write an equation of the line that passes through the point (1, 4) and has a slope of -2
WIth point- intercept form
The equation of the line that passes through the point (1, 4) and has a slope of -2 is y = -2x + 6
What is slope-intercept form of a line?
The equation of the line in slope-intercept form is given by:
y = mx + c
Here,
(x, y) = Every point on the line
m = Slope of the line
c = y-intercept of the line
According to the given question:
The given line has slope m = -2 and point (1, 4) passes through the line.
By slope-intercept form general equation of line is y = mx + b where b is
y-intercept.
Substituting values of m and point (1, 4) in this equation to get value of b
y = mx + b
4 = -2(1) + b
b = 6
Hence equation of the line is y = -2x + 6
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Determine if the triangles are similar by Angle-Angle similarity
The triangles are similar by Angle-Angle similarity since they are congruent.
What is Angle-Angle Similarity?According to the Angle-Angle Similarity Theorem, if two angles in one triangle are equal to two angles in another triangle, the triangles are similar. The triangles are similar if two pairs of corresponding angles in a pair of triangles are congruent. We know this because if two angle pairs are equal, then the third pair must be equal as well.
Two triangles with two angles, starting with Triangle 1, one measuring 47 degrees and the other measuring 53 degrees, are congruent to two angles in Triangle 2. Following the AA similarity theorem, it is assumed that Triangle 1 is similar to Triangle 2.
In this case, angle MNP = angle QPL (corresponding angles, //lines) (A)
angle QLP is common angle (A)
By AA, the 2 triangles are similar.
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i need answers now pls asap im going to fail I will pay someone on pay pal
The next day Patsy have t choose between cheerleading and play practice is 17th September
How to find the next day Patsy will choose between cheerleading and play practiceTo solve the problem of calculating the next day Patsy will have the events of cheerleading and school play same day, we find the lowest common multiple of the intervals of the occurrence of the two events
The interval of the events are:
cheerleading - 4th day
school play - 6th day
The Lowest common multiple of 4 and 6 is calculated to be 12
If the two events occurred on 5th September the next will on
= 5 + 12
= 17
The next time to choose between the two will be on 17th September
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which statement about the graph of y=3x+5 is correct?
The correct statement regarding the linear function y = 3x + 5 is given as follows:
The line passes through the ordered pair (0,5) and has a slope of 3.
What are the slope and the intercept of the linear function?The slope-intercept definition of a linear function is presented as follows:
y = mx + b.
The slope and the intercept are given as follows:
m is the slope, representing the rate of change of the linear function.The intercept is of b, representing the numeric value of the function when the input is of zero, hence the line passes through the ordered pair (0,b).In this problem, the function is defined as follows:
y = 3x + 5.
Hence the coefficients have the values given as follows:
m = 3, b = 5.
Missing InformationThe statements are given by the image shown at the end of the answer.
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Select the correct answer. about 1,500,000 bacteria are found in 1 milliliter of water of coastal ocean. how many bacteria will be there in 100 milliliters of water? a. 1.5 × 104 b. 1.5 × 105 c. 1.5 × 106 d. 1.5 × 107 e. 1.5 × 108
The amount of bacteria that will be there in 100 milliliters of water will be: 1.5 × 10⁸.
What is standard notation?A standard notation is a method of writing a given number, equation, or expression in a specific format that adheres to certain rules. 4.5 billion years, for example, is written as 4,500,000,000 years.
The main reason for converting numbers to scientific notation is to make calculations involving unusually large or small numbers easier.
Even though zeros are no longer always seemed to set the decimal point, all digits in a scientific notation number are significant.
Here, it is given that,
The number of bacteria found in 1 milliliter of water = 1,500,000.
So,
The number of bacteria in 100 milliliters of water = 1,500,000 x 100
The number of bacteria in 100 milliliters of water = 15,00,00,000
The number of bacteria in 100 milliliters of water = 1.5 × 10⁸.
Correct option: e
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NOT MANY POINTS BUT I NEED HELP ON MY FINAL
A linear pair's total angles are always equal to 180°. Hence ∠ HJL is 94°
What is a Linear Pair of Angles?When two lines cross at one point, a linear pair of angles is created. If the angles follow the intersection of the two lines in a straight line, they are said to be linear. A linear pair's total angles are always equal to 180°.Those two neighboring angles whose sum is 180° are referred to as a linear pair of angles. They are represented by a ray that serves as a common arm between the angles and is drawn on a straight line.The name "linear" comes from the standard illustration of a linear function in one dimension: a line drawn through the origingiven
∠HJL and ∠LJK are linear pair
∠ HJL = ?
∠HJL + ∠JLK =180
x + x -8 = 180
2x -8 =180
x = 188/ 2 = 94°
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Aubrey and Charlie are driving to a city that is 120 mi from their house. They have already traveled 15 mi, and they are driving at a constant rate of 65 mi/h. Complete the function that models the distance they drive as a function of time. Then complete a reasonable domain for this situation.
Therefore, the solution of this problem is the domain would be
0 < t ≤ 1.61.
What is domain?A function's domain is the set of possible values that can be entered. This set reflects the values of x in a function like f. (x). Its range refers to the set of possible values that a function can accept. These are the values that are returned by the function when we enter an x value.
Here,
The remaining distance that would result from multiplying the speed by the time t will be added to the 20 miles that make up the total distance. The formula for the equation would be as follows:
120 = 15 + 65t
It would be 0 hours at the very least. When the entire 120-mile distance has been accomplished, the time limit is reached.
t ≤ (120 - 15)/65
t ≤ 1.61 hours
Therefore, the solution is the domain would be 0 < t ≤ 1.61.
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slope of the line that passes through (10, 4) and (5, 13). as a integer
The slope of the line that connects (10,4) and (5,13) is -9/5.
What is a slope?The slope of a line indicates its steepness. Slope is calculated mathematically as "rise over run" (change in y divided by change in x).Here given,
The two points are (10,4) and (5,13).
We have to find the slope that passes through the given points,
The formula to find slope(m) is,
The slope of the line that passes through (x1 , y1) and (x2,y2) is,
Slope(m) = y2 - y1 / x2 - x1
By substituting the values in x and y
Slope = 13 - 4 / 5 - 10
= 9 / -5
Slope = -9/5
= -1.8
Therefore the slope of line that passes through (10,4) and (5,13) is -9/5.
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The length of a rectangular drainage pond is changing at a rate of 8 ft/hr and the perimeter of the pond is changing at a rate of 24 ft/hr. At what rate is the width changing?
The rate of width changing will be;
⇒ 4 feet/hour
What is mean by Rectangle?
A rectangle is a two dimension figure with 4 sides, 4 corners and 4 right angles. The opposite sides of the rectangle are equal and parallel to each other.
Given that;
The length of a rectangular drainage pond is changing at a rate of 8 ft/hr and the perimeter of the pond is changing at a rate of 24 ft/hr.
Now,
We know that;
⇒ Perimeter of rectangle = 2 (Length + Width)
Substitute al the values, we get;
⇒ 24 = 2 (8 + x)
⇒ 12 = 8 + x
⇒ x = 12 - 8
⇒ x = 4
Thus, The rate of width changing will be;
⇒ 4 feet/hour
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Solve for r in terms of q, s, and r. S=-qtr
To isolate a certain variable in an equation, we must perform inverse operations on both sides of the equal sign to cancel out values.
Solving the Question[tex]S=-qtr[/tex]
⇒ Right now, r is being multiplied by q and t. Divide both sides by qt to cancel these values out:
[tex]\dfrac{S}{qt}=\dfrac{-qtr}{qt}\\\\\dfrac{S}{qt}=-r[/tex]
⇒ Now, to remove the negative symbol, multiply both sides by -1:
[tex]r=-\dfrac{S}{qt}[/tex]
Answer[tex]r=-\dfrac{S}{qt}[/tex]
There were 234 roses growing in the back garden. If 50% of the roses were red. How many were not red?
Answer:117
Step-by-step explanation:
I’m good at math
Answer:
117 Roses
Step-by-step explanation:
234 *0.5 = 117
The number of students in attendance since 2000 at Lamar Community College can be represented by the equation below, where x equals the time in years after 2000. S(x) = (x - 50)² + 19 The college creates a graph to better view the decreases and increases in attendance. Which of the following describes the end behavior of their graph? O A. As x approaches positive infinity, S(x) remains constant. OB. As x approaches positive infinity, S(x) approaches positive infinity. OC. As x approaches positive infinity, S(x) approaches zero. OD. As x approaches positive infinity, S(x) approaches negative infinity.
As domain x approaches positive infinity, S(x) approaches positive infinity. Option B is correct.
What is a graph?The graph is a demonstration of curves that gives the relationship between the x and y-axis.
Given expression for the attendance of the student is,
S(x) = (x - 50)² + 19
The end behavior of their graph is given as after x = 50 the graph starts heigh increasing gradient and it keeps increasing, till x = infinity, as shown in the graph.
Thus, the curve of the given equation S(x) will increase from x = 50 to x = ∞ .
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Is 38 / 53 and simplest form explain? Why t? Or or why not
yes 38/53 is the simplest form
Step-by-step explanation:
The fraction is already reduced.
Five times a number increased by 5 is equal to 25, find the number.
Answer: the number is 4
Step-by-step explanation:
5x+5=25 is the equation
solve for x by isolating x
5x+5-5=25-5
5x=20
divide both sides by 5 to isolate x
x=4
Answer: 4
Step-by-step explanation:
5x + 5 = 25 this is what the equation is!
Then we subtract 5 on both side
5x = 20
Then divided by 5 on both side
x= 4
What is 2/9 to the 4th power?
Answer:
[tex]\frac{16}{6561}[/tex]
Step-by-step explanation:
[tex]\frac{2x2x2x2}{9x9x9x9}[/tex] = [tex]\frac{16}{6561}[/tex]
Sidney bought two magazines that
were each $4.95. If Sidney paid a total of
$10.59 for the two magazines with tax,
what percent tax did she pay for her s
purchase?
Answer:
Step-by-step explanation:
0.69
*URGENT* I need help with 5,6,7 please answer correctly and quickly
Answer:
Step-by-step explanation:
(5). ( [tex]x_{1}[/tex] , [tex]y_{1}[/tex] )
y - [tex]y_{1}[/tex] = m( x - [tex]x_{1}[/tex] )
~~~~~~~~~~~~~~~~~
( 4 , 8 )
y = [tex]\frac{1}{7}[/tex] x - 5 ; slope m = [tex]\frac{1}{7}[/tex]
Slope of line ⊥ to the given line is opposite reciprocal to [tex]\frac{1}{7}[/tex] and equal to ( - 7)
y - 8 = - 7( x - 4 )
(6).
( [tex]x_{1}[/tex] , [tex]y_{1}[/tex] )
( [tex]x_{2}[/tex] , [tex]y_{2}[/tex] )
m = [tex]\frac{ y_{2} -y_{1} }{ x_{2} -x_{1} }[/tex]
y = mx + b
~~~~~~~~~~~~
( 4 , 3 )
( 5 , 1 )
m = [tex]\frac{1-3}{5-4}[/tex] = - 2
y - 3 = - 2( x - 4 )
y = - 2x + 11
(7). y = - [tex]\frac{1}{2}[/tex] x + 2
............. i need help past due
The unit rate in acres of land planned by the workers per day is found is 16/35 acres.
What is meant by rate of doing work?Power refers to the rate of work completion. It is a measure of how much energy is used up each unit of time. The joule per second (J/s) is the unit of power in the SI system.Force applied across a distance is called work. Examples such work include dragging down a confined helium balloon, driving a vehicle up a steep hill, and lifting an article against the gravitational attraction of the Earth. Energy manifests mechanically as work.For the mentioned question-
Total acres of land planted = 2/5 acres.
Total time taken = 7/8 days.
Thus, unit rate in acres per day = Total acres of land planted / Total time taken
unit rate in acres per day = (2/5) / (7/8)
unit rate in acres per day = (2*8)/(5*7)
unit rate in acres per day = 16/35
Thus, unit rate in acres of land planned by the workers per day is found is 16/35 acres.
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Please answer fast lots of points!!!!
Answer:
Step-by-step explanation:
Solve 3+8X+6 = 5(X+2) + 3X-1
Answer: x= (−∞,∞)
Step-by-step explanation:
3+8x+6 = 5(x+2) + 3x-1
9+ 8x = 5x +10 + 3x -1
9 + 8x = 8x +9
Subtract nine on both sides
8x= 8x
x = Any number!
What will the dividend income be on W number of shares of XYZ stock if XYZ distributes a $Y per share dividend?
Answer:
In general, the dividend income on W number of shares of XYZ stock will be W * Y dollars if XYZ distributes a $Y per share dividend.
Step-by-step explanation:
The dividend income on W number of shares of XYZ stock will be W * Y dollars if XYZ distributes a $Y per share dividend. This is because the dividend income is calculated by multiplying the number of shares that an investor owns by the amount of the dividend per share.
For example, if an investor owns W = 100 shares of XYZ stock and XYZ distributes a $Y = 5 per share dividend, then the investor's dividend income will be 100 * 5 = 500 dollars.
In general, the dividend income on W number of shares of XYZ stock will be W * Y dollars if XYZ distributes a $Y per share dividend.
Given that the equation of line one (L1) is 2x-y=3 and equation of line two (L2) is kx+2y=3 where k is a constant.
(a) Find the value of k such that L1 and L2 are parallel.
(b) Find the value of k such that L1 and L2 are perpendicular.
This question is related to Linear functions, Answers: (a) k = -4, (b) k=1. Someone pls tell me how to get there though
Answer:
see explanation
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
(a)
given the equation of L1 is
2x - y = 3 ( subtract 2x from both sides )
- y = - 2x + 3 ( multiply through by - 1 )
y = 2x - 3 ← in slope- intercept form
with slope m = 2
• Parallel lines have equal slopes
then slope of L2 is m = 2
given the equation of L2 is
kx + 2y = 3 ( subtract kx from both sides )
2y = - kx + 3 ( divide through by 2 )
y = - [tex]\frac{k}{2}[/tex] + [tex]\frac{3}{2}[/tex] ← in slope- intercept form
with slope m = - [tex]\frac{k}{2}[/tex]
since slope of L1 and L2 are equal, both 2 , then
- [tex]\frac{k}{2}[/tex] = 2 ( multiply both sides by 2 to clear the fraction )
- k = 4 ( multiply both sides by - 1 )
k = - 4
----------------------------------------------
(b)
given the slope of a line is m then the slope of a line perpendicular to it is
[tex]m_{perpendicular}[/tex] = - [tex]\frac{1}{m}[/tex] = - [tex]\frac{1}{2}[/tex]
Then
for L2 to be perpendicular to L1
- [tex]\frac{k}{2}[/tex] = - [tex]\frac{1}{2}[/tex] ( multiply both sides by - 1 )
[tex]\frac{k}{2}[/tex] = [tex]\frac{1}{2}[/tex] , thus
k = 1