The equation which is best representing the height above ground, y, of the model rocket and x seconds after it reaches the maximum height is 75x + y = 2000.
The height above ground, y, of the model rocket, x seconds after it reaches its maximum height can be represent by a linear equation,
The maximum height is 2000 feet, after this the rocket starts to descend with a rate of 75 feet per second.
Let us say that when the rocket starts descending, our time is started from zero,
So, on plotting these points of graph, we can one point, (0,2000).
The rate of descend is the slope m of the graph,
m = -75 ft/s
We are taking it negative because height is decreasing with time,
We can use the point slope form of equation of line,
It says, if a line passes through (a,b) and has slope m. Then the equation of line is,
(y-b) = m(x-a)
So, our line is passing through (0,2000) and has slope -75 ft/s.
So, equation of the line is,
(y-2000) = -75(x-0)
75x + y = 2000.
This above equation of line is representing the relation between the height above ground and time of the model rocket.
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What would be the Area in square inches of a rectangle with a length of radial 279 in and a width of radial 31 in
(You do not have put the units in your answer)
The area of rectangle in square inches is 8649 inches .
What is mensuration ?The subject of mathematics known as mensuration is concerned with measuring geometric shapes and their various characteristics, such as length, volume, shape, surface area, lateral surface area, etc. In fundamental mathematics, learn about mensuration.
Mensuration is the name given to the area, volume, and length of various geometric shapes in mathematics. These shapes can be found in either two or three dimensions.
Mensuration is the process of calculating various shape parameters, such as the perimeter, area, and volume, whereas geometry is the study of the characteristics and relationships between the points and lines that make up different shapes.
Calculationthe area of rectangle will be = length * width
therefore just substituting the values given in the question
thus ,
area will be = 279 * 31
= 8649 square inches
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please simplify this:(5x^4)^3
[tex](5x^{4} )^{3} \\=5x^{4*3} \\=5x^{12}[/tex]
I used the law of exponents as indicated below:
[tex](x^{n} )^{m} \\=x^{n*m} \\=x^{nm}[/tex]
Line g has an equation of y = 1/3x - 1. Parallel to line g is line h, which passes throush the point (10, 2). What is the equation of line h?
The equation reads: y = 1/3x - 4/3.
Describe Line.The points that make up a line can be extended endlessly in opposite directions. Two points along the same line are referred to as collinear points.
The slopes are the same if two lines are parallel to one another.
Consequently, line h's slope would be equal to line g's 1/3.
All that is left to do is plug the points into the formula to determine the y-intercept.
2 = 1/3(10) + b
2 = 10/3 + b
2 - 10/3 = b
2-10/3 = b
-4/3 = b
Hence, the equation for h is y = 1/3x - 4/3.
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Please help me get a 100%!
Answer: D) there are no solutions.
Step-by-step explanation:
Convert the standard form equation into slope-intercept form. 5x - 4y = -20
Answer: y=5/4x+5 is the equation in slope-intercept form.
Tea that sells for $2.00 a pound is mixed with a different tea that sells for
$5.00 a pound to produce 40 pounds of a custom blended tea that will
sell for $4.25 a pound. How many pounds of the less expensive tea
should be used in the mixture?
(1) 10
(2) 15
(3) 25
(4) 30
Pls show work
The pounds of the less expensive tea used in the mixture is 10 pounds.
The correct option is Option(1) 10.
Given:
Price of less expensive tea = $2.00
Price of expensive tea = $5.00
Price of custom-blended tea = $4.25
The total price of 40 pounds of custom blended tea = 40 × $4.25
= $170
Let the pounds of the less expensive tea used in the mixture be x pounds.
So, the pounds of expensive tea = 40-x
Now, the equation is
2x + 5(40 - x) = 170
2x + 200 - 5x = 170
3x = 30
x = 10 pounds
Therefore, there are 10 pounds of less expensive tea.
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4
Royce deposits $1200 into a savings account. After nine year, he made $3472.32.
What is the annual simple interest rate of the loan?
The interest rate needed to make $3,472.32 from simple interest on a principal of $1,200.00 over 9 years is 21.04% per year.
How to determine simple interest rate?Simple interest is expressed mathematically as;
A = P( 1 + rt )
Where A is accrued amount, P is principal, r is rate and t is the time period.
Given the data in the question;
Principal P = $1200 Accrued amount A = $3472.3Time period t = 9 yearsInterest rate r = ?Plug the given values into the simple interest formula and solve for r
A = P( 1 + rt )
r = (1/t)(A/P - 1)
r = ( 1/9 )( $3472.3/$1200 - 1)
r = ( 1/9 )( 2.8936 - 1)
r = ( 1/9 )( 1.8936)
r = 0.2104
Convert to percentage
r = 0.2104 × 100%
Rate r = 21.04%
Therefore, the interest rate of the loan is 21.04%.
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PLease help me with this!!
The linear equation is:
y = -6*x + 59
The slope is -6, and means that each hour the distance decreases by 6 miles.
The y-intercept is 59, and it is the initial distance to the waterfall.
How to get the linear equation?A general linear equation in the slope-intercept form is:
y = a*x + b
Where a is the slope (also called the rate of change) and b is the y-intercept.
We know that if the line passes through two points (x₁, y₁) and (x₂, y₂) then the slope is:
a = (y₂ - y₁)/(x₂ - x₁).
Here we can define the variables:
y = distance
x = hours.
Then we have two points (8, 11) and (9, 5).
So the slope is:
a = (5 - 11)/(9 - 8) = -6
This means that the distance to the waterfall decreases by 6 miles each hour.
Then the linear equation is like:
y = -6*x + b
To find the value of b we can use any of the given points, I will use (9, 5), this means that:
5 = -6*9 + b
5 = -54 + b
54 + 5 = b
59 = b
This is the y-intercept, and gives the initial distance to the waterfall.
The equation is:
y = -6*x + 59
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Expand and simplify (x -6)(x + 2)
Answer: X^2 - 4x -12
1. Distribute :
(x−6)(x+2)
x(x+2)-6(x+2)
2. Distribute:
x(x+20-6(x+2)
X^2 +2x-6(x+2)
3. Distribute:
X^2+2x-6(x+2)
X^2+2x-6x-12
4. Combine like terms:
x^2+2x-6x-12
solution:X^2-4x-12
Find the midpoint between (31, 7) and (–17, 19).
(7, 13)
(14, 26)
(19, 1)
(24, –6)
Answer:
It's (7, 13) not sure how to explain that
Find k such that f(x) = x^4+ kx³ + 2 has the factor x + 1.
K = 1 is the value when x = - 1 is Factor of equation .
Why do we use the term factors?
A factor is a number that completely divides another number. In other words, if multiplying two whole numbers results in a product, the numbers we are multiplying are factors of the product since the product is divisible by them. Factors can be found using either division or multiplication.As an illustration, 3 and 6 are factors of 12 because 12 3 = 4 and 12 6 = 2, respectively. 1, 2, 4, and 12 are the other components that make up 12.f(x) = x^4+ kx³ + 2
x + 1 = 0
x = -1 put in equation
(-1)⁴ + k( -1)³ + 2 = 0
1 - k + 2 =0
k = 1
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Need help on this question ASAP On a sunny day, a 3-foot red kangaroo casts a
shadow that is 5 feet long. The shadow of a nearby
eucalyptus tree is 7 feet long. Find the height of the
tree.
Answer:
i think it is 5 feet
Step-by-step explanation:
i hope this helps
Mikki used 18 tea bags to make 4 quarts of
iced tea. How many tea bags did Mikki use for
each quart of iced tea?
Answer:
[tex] \frac{18}{4} [/tex]
Step-by-step
4.5
Consider the following word problem: Twenty more than four times a number is equal to the difference between 2 and twice the number. Find the number.
Given:
The objective is to find the number.
Explanation:
Consider the unknown number as x,
First, four times the number can be written as 4x.
Twenty more than 4 time the number will be,
[tex]4x+20\ldots\ldots.\text{ (1)}[/tex]Then, twice the number can be represented as 2x.
And the difference between 2 and twice the number will be,
[tex]2-2x\ldots\ldots..(2)[/tex]Now, equate both the equations (1) and (2).
[tex]\begin{gathered} 4x+20=2-2x \\ 4x+2x=2-20 \\ 6x=-18 \\ x=\frac{-18}{6} \\ x=-3 \end{gathered}[/tex]Hence, the unknown number is -3.
(-2)^-3 how would i do this
Answer:
[tex]\frac{-1}{8}[/tex]
Step-by-step explanation:
To make the -3 positive, you put the power under 1.
[tex]\frac{1}{(-2)^{3} }[/tex] This means [tex]\frac{1}{-2}[/tex] x [tex]\frac{1}{-2}[/tex] x [tex]\frac{1}{-2}[/tex] = [tex]\frac{1}{-8}[/tex] Which means the same as[tex]\frac{-1}{8}[/tex]
1. Kai teaches music lessons as an independent contractor. Last month, he taught 41
music lessons at $65 each. Determine the amount of Kai's self-employment taxes for
last month, using the tax rate of 15.3%.
The amount for Kai's self employment taxes for the last month is $407.745 .
In the question ,
it is given that
number of music lessons that Kai taught = 41
per music lesson charge = $65 .
the tax rate for self employment = 15.3%
So, the total amount earned is = (number of classes)*(per class charge)
= 41*65 = $2665
According to the question .
Kai's self employment tax = 15.3% of total amount earned
On substituting the values , we get
Kai's self employment tax = 15.3% of 2665
= 0.153*2665
= 407.745
Therefore , The amount for Kai's self employment taxes for the last month is $407.745 .
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Use the product rule to find the derivative of the following. (Hint: Write the quantity as a product.)k(t) = (t² − 2) ²k' (t) =
I NEED ANSWER REALLY FAST IN GEOMETRY 40 POINTS
The diagram shows a certain construction technique. If
mABF = x + 10x - 1, mCBF = 12x + 7,
what is mLCBF?
Error Analysis A classmate finds the area of a circle with radius 30 in. to be s 900 in.2. What error did your classmate make? Your answer
radius = 30 in
Area = 900 in^2
To calculate the area of a circle, use the equation A = pi r^2
His mistake was that he did not multiplicate by pi (3.1416)
The actual area = (3.1416)(30)^2
A = 2827.44 in^2
through(−1,−5),slope=9
Answer:
y = 9x+4
Step-by-step explanation:
Using the slope-intercept formula
y = mx+b where m is the slope and b is the y-intercept
y = 9x+b since we are given the slope is 9
Using the point is (-1,-5)
-5 = 9(-1) +b
-5 =-9 +b
Solving for b
-5+9 =b
4 = b
y = 9x+4
Which of the following macromolecule provides quick energy to cells?
O lipid
O protein
O carbohydrate
O nucleic acid
Answer:
c
Step-by-step explanation:
I definitely didn't searched it
8 grade, help please!!!
Answer:
Yes the triangles are congruent.
Step-by-step explanation:
You are going to move all the points 2 units to the left and 4 units up.
Look at the vertices of the triangle. The points are (0,1) and (-5,0) and (2,-5). If we moved all three of these points to places to the left and 4 up, they would be at (-2,4), (-7,4) and (0,-1) This would make a image that is a congruent triangle. You have just translated the original triangle 2 places to the left and 4 places up.
60 - 18 / 2 + 4 + 10 / 2 = 12
Answer:60 =12
Step-by-step explanation:
A car has 6 gallons of gasoline remaining in the tank. This is 60% of the total amount of gasoline the tank will hold. How many gallons of gasoline does the car’s tank hold?
the car's tank hold 10 gallons of gasoline.
Step-by-step explanation:
if 6 is 60% of total amount of gasoline so what is the 100% of the gasoline so when we solve the 100% of the gasoline will be 10.
solve: ? 100%
6 60%
it first we write the thing that we want to find
9 = 3/4v solve for v simplify your answer as much as possible
Answer:
v = 12
Step-by-step explanation:
to solve this equation you must first multiply 4 to both sides
9 * 4 = 3/4v * 4
36 = 3v
now divide 3 to both sides
36 / 3 = 3v / 3
12 = v
flip it
v = 12
that is your answer
I need help with this please someone help its due today
Answer:8
Step-by-step explanation:
2+6=8
Answer:
8 ghdhlhskgslhdlhskgz
A dice is rolled 2 times. What is the probability of showing a 4 on every roll?
Since we are rolling a die twice
The possible out come of rolling a die is
[tex]\mleft\lbrace1,2,3,4,5,6\mright\rbrace[/tex]Therefore, the probability of getting a 4 on every roll is
[tex]P(\text{getting a 4 on every roll) }=P(1st\text{ 4) and P(2nd 4)}[/tex]From the sample outcome above
P(of 4) = 1/6
Therefore
[tex]\begin{gathered} P(\text{getting a 4 on every roll)}=\frac{1}{6}\times\frac{1}{6} \\ P(\text{getting a 4 on every roll)}=\frac{1}{36} \\ P(\text{getting a 4 on every roll)}=0.0278 \end{gathered}[/tex]Therefore, thr porbability is 0.0278
Using the Pythagorean Theorem find the missing length and then round the result to the nearest tenth.
a = 7, b = 4, c =
Answer:11
Step-by-step explanation: because 7+4=11
Help! What is f(4) for the function F(x) =5x+7?
f(4)=
Answer:
27
Step-by-step explanation:
f(x) = 5x + 7
f(4) = 5(4) + 7
= 20 + 7
f(4) = 27
The perimeter of a kite can be found using the formula P = 2S + 2L. Which
equation expresses S in terms of P and L?
Answer:
S = ( P - 2L) / 2
Step-by-step explanation:
P = 2S + 2L
P - 2L = 2S
(P - 2L) / 2 = S
Hope this helps :D