In mathematical modelling, we take a real-world problem and write it as an equivalent mathematical problem.
We then solve the mathematical problem, and interpret its solution in terms of the real-world problem.
After this we see to what extent the solution is valid in the context of the real-world problem.
Mathematical modeling is one of the bases of mathematics education. Mathematical modeling is described as conversion activity of a real problem in a mathematical form. Modeling involves to formulate the real-life situations or to convert the problems in mathematical explanations to a real or believable situation.
It's extremely precise, since it's math-based, which allows you to develop accurate ideas and assumptions. It's concise, with clear and established rules. It gives you direction when trying to solve a problem.
characters of modeling;
In mathematical models parameters are most often represented by variables. Changes in the numbers assigned to the variables change the model. 3) Simplification/Idealization.It should necessarily be incomplete.It may be changed or manipulated with relative ease.
It is simplification/Idealization. Mathematical modeling has many benefits related to real-world problems, but the main disadvantages are process simplification, specific rules of the model, and lack of information or data monitoring.
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solve for x 34=-2x need help asap
34 = -2x
Divide through by -2
x = -17
Fill in the blank.
In words, the logarithm of x is
the logarithm of x ells us the value of the exponent y of 10 such that 10^y is equal to x.
What is the logarithm of x?
First, let's define the natural logarithm.
We know that the natural logarithm is the inverse of the exponential function, then:
[tex]e^{ln(x)} = x\\ln(e^x) = x[/tex]
So the natural logarithm of x tells us the value of the exponent y of e such that e^y is equal to x.
And the logarithmic function is a logarithm on base 10, which is written as:
log(x) = log₁₀(x) = ln(x)/ln(10)
If we say that this is equal to e^y for some value of y, we get:
ln(x) = ln(10)*y
If now we apply the exponential function in both sides, we get:
expo(ln(x)) = exp(ln(10)*y) = 10^y
x = 10^y
So, the logarithm of x ells us the value of the exponent y of 10 such that 10^y is equal to x.
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What is the equation, in point-slope form, of the line that
is parallel to the given line and passes through the point
(-3, 1)?
Oy-1=-(x+3)
Oy-1=-(x+3)
Oy-1= (x+3)
Oy-1= (x+3)
The equation, in point-slope form, of the line that is parallel to the given line and passes through the point (−3, 1) is y - 1 = 3/2(x+3)
What is point slope form?One of the most popular ways to represent a linear equation is in point-slope form, which has the following structure:
y - y1 = m(x - x1) (x - x1),
where (x1, y1) is a point on the line, m is the slope, and x and y are variables that denote further points along the line. When one point on the line and the slope are known, the point-slope form can be employed. Given that at least one point and the slope of the line are known, it is helpful for locating further points on a line.
According to the given values;
Equation of a line in point-slope form
The equation of a line in point-slope form is expressed as:
y-y0 = m(x-x0)
where:
m is the slope
(x0,y0) is the point on the line
The slope of the given line is as shown:
Slope = 2-(-4)/2-(-2)
Slope = 2+4/2+2
Slope = 6/4 = 3/2
Substitute the slope and the point
y - 1 = 3/2(x-(-3))
y - 1 = 3/2(x+3)
Hence the equation, in point-slope form, of the line that is parallel to the given line and passes through the point (−3, 1) is y - 1 = 3/2(x+3)
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g(a)=3a-2 find g(1),g(-2)
Answer:
1 and -8
Step-by-step explanation:
g(1) = 3*1-2
= 3-2
= 1
g(-2) = 3*-2-2
= -6-2
= -8
The required value of the function at g(1) and g(-2) are 1 and -8 respectively.
Given that,
g(a) = 3a - 2
To determine the value function at a = 1 and a = -2
Functions is the relationship between sets of values. e g y=f(x), for every value of x there is its exists in a set of y. x is the independent variable while Y is the dependent variable.
Here,
Given function is,
g(a) = 3a-2
at a = 1
g(1) = 3 * 1 - 2
g(1) = 3 - 2
g(1) = 1
Now,
at = -2
G(-2) = 3 * -2 - 2
G(-2) = -6 - 2
g(-2) = -8
Thus, the required value of the function at g(1) and g(-2) are 1 and -8 respectively.
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A baseball is hit from an initial height of 3 feet. The baseball reaches its maximum height of 81 feet when it is 156 feet from home plate. Write a quadratic function to represent the height of the baseball as a function of its distance from the home plate.
The quadratic function to represent the given situation is y=-(1/312)x²+x+3
A quadratic function is of the form y=g(x) where g(x) is a polynomial in x with degree 2.
The baseball is hit at a initial height of 3 feet. The baseball follows a path of a parabola.
Maximum height=81 feet
Distance from home plate =156 feet
So, (156,81) is the vertex of the parabolic path.
We know that when vertex is at (h,k) then the vertex form of the parabola is y=a(x-h)²+k
So the quadratic equation is of the form
y=a(x-156)²+81
Now the initial height is given as 3 feet.
So at x=0, y=3
Putting the values in the equation we get:
3=a(0-156)²+81
or, -78=a×156²
or, a=-(78÷156²)
or, a=-(1/312)
So the quadratic equation can be written as
y=-(1/312)(x-156)²+81
Simplifying we get : y=-(1/312)x²+x+3
The quadratic function to represent the path of the baseball is given by y=-(1/312)x²+x+3
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Write in slope - intercept form
14x -7y = 21
Answer: y = 2x - 3
Step-by-step explanation:
y = mx + b
y + 2x - 3
Zane has 5 2/5 of soil for his garden. Each bag of soil will cover 20 square feet. How many square feet will zane be able to cover if he uses all these bags of soil?
100 points help me and answer ALL the questions right trolls get banned
Using translation concepts, it is found that:
The coordinates of P' are (-5,3).The coordinates of the new triangle are P'(5,3), K'(3,1) and Y'(1,4).The new coordinates of the dilated triangle are: A'(2,2), B'(10,4) and C'(6,10).The new coordinates of C' are (-1,-5).The bottom-right image(the one that is already marked) represents a translation.What is a translation?A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction either in it’s definition or in it’s domain. Examples are shift left/right or bottom/up. Other types of transformations are rotations or dilation.
For the first question, the rule for a reflection over the x-axis is given by:
(x,y) -> (x,-y).
Then:
P': (-5,-3) -> (-5,3).
The coordinates of P' are (-5,3).
For the second question, the rule for a 180º clockwise rotation about the origin is given by:
(x,y) -> (-x,-y).
Hence:
P': (-5,-3) -> (5,3).K': (-3,-1) -> (3,1).Y': (-1,-4) -> (1,4).Hence:
The coordinates of the new triangle are P'(5,3), K'(3,1) and Y'(1,4).
For a dilation by a scale factor of 2, every coordinate is multiplied by 2, hence:
A': (1,1) -> (2,2).B': (5,2) -> (10, 4).C': (3,5) -> (6, 10).The new coordinates of the dilated triangle are: A'(2,2), B'(10,4) and C'(6,10).
The rule for a translation 5 units down is:
(x,y) -> (x, y - 5).
Hence:
(-1,4) -> (-1,-5).
The new coordinates of C' are (-1,-5).
For the final question, a translation is when just the position of the image changes up/down, having no changes in size or orientation, hence:
The bottom-right image(the one that is already marked) represents a translation.
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Sandra has 4³ jars of honey and each one sells for 42 dollars. How much money
will she make if she sells them all?
o Exponent Expression Model:
o Simplify and tell how much money she will earn.
1) Write the expression to model the situation (should see exponents still).
2) Show work to answer the question.
Show Your Work
Sandra has 4³ jars of honey and each one sells for 42 dollars, then if she sells total money = 2.688 * 10³ dollars.
Y = 42x is Sandra's equation.
To find her hourly rate, we need to find how much she earns in "1" hour. Since x is hours, we plug in x = 1 and find y (which is her pay).
Y = 42x
Y = 42(1)
Y = 42
Therefore, $42 is Sandra's hourly rate.
Based on the condition,
Sandra has 4³ jars of honey and each one sells for 42 dollars.
= 4³ * 42$
The expression to exponent expression model is equal to = 4³ * 42
Simplify the expression,
= 4³ * 42$
4³ means 4*4*4 = 64
We can write 64 is in this equation,
= 64 * 42$
= 2688$
= $2.688 * 10³
Hence,
The expression to model the situation is equal to = $2.688 * 10³
Therefore,
Sandra has 4³ jars of honey and each one sells for 42 dollars, then if she sells total money = 2.688 * 10³ dollars.
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H(x)=x^2-3x find h(-7)
Answer: h(-7)=70
Step-by-step explanation:
h(x)=x^2-3x
h(-7)=(-7)^2-3(-7)
h(-7)=49-(-21)
h(-7)=49+21
h(-7)=70
PLEASE HELP✨ 7th grade math 10 points
A twelve inch candle and an 18 inch candle are lit at 6pm. The 12-in. candle burns 0.5 inches every hour. The 18 inch candle burns two inches every hour. At what time will the two candles be the same height? Let h represent the number of hours.
Answer: alright, here we go
Step-by-step explanation:
best way to represent this is linear equations, so:
y=-0.5x+12
y=-2x+18
-2x+18=-0.5+12
+0.5x +0.5x
-1.5x+18=12
-18 -18
-1.5x=-6
-x=-4
x=4
y=-2(4)+18
y=-8+18
y=10
answer: (4,10)
answer: h=4
bonus: the candles will each be ten inches tall after four hours
Find the slope of the line passing through the points 2, 5 and −8, 4.
Answer:
10.
Step-by-step explanation:
1) formula of the required slope is:
[tex]slpoe=\frac{y_2-y_1}{x_2-x_1};[/tex]
2) according to the formula above:
[tex]slope=\frac{2+8}{5-4}=10.[/tex]
P.S. x₁=2; x₂=-8; y₁=5; y₂=4.
2) [8 points] Benjamin wishes to strengthen a mixture that is 10% alcohol to
one that is 30% alcohol. How much pure alcohol should they add to 12L of
the 10% mixture?
you need to add 3.43 liters of pure alcohol to reach a concentration of 30%.
How much pure alcohol should they add to 12L of the 10% mixture?Let's define the variable x as the number of liters of the 30% that you need to use.
The concentration of the mixture then will be:
1*x + 0.1*12
Where the concentration for the x liters is 100%, because this is pure alcohol, and for the 12 liters we use a concentration of 10%.
Now, that must be equal to a mixture with a concentration of the 30%, then we can write:
x + 0.1*12 = (x + 12)*0.3
Now we just need to solve this linear equation for x.
x + 1.2 = x*0.3 + 12*0.3
x - x*0.3 = 12*0.3 - 1.2
x*0.7 = 12*0.3 - 1.2
x = (12*0.3 - 1.2)/0.7 = 3.43
This means that you need to add 3.43 liters of pure alcohol to reach a concentration of 30%.
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If a is -3 then what is a squared
Answer:
a = -3
(-3)² = -9
Answer: -9
Step-by-step explanation:
-3 x -3 = -9
(I think)
What is the slope of the line passing through the points (-3, 4) and (2, - 1)?
A.-1
B.3/5
C.-5/3
D.1
Answer:
A) -1
Step-by-step explanation:
If B2 is changed from 7 to 9, what value will appear in C3 if C3 contains the formula =B2*2?
The value of C3 will increase with a factor of 4 because the value of B2 increased with a factor of 2 and C3 is multiplying B2 by 2.
How to find how C3 will change if it has the formula =B2*2 and B2 increased from 7 to 9Given data
B2 is changed from 7 to 9
C3 contains the formula =B2*2
Finding the increment in B2
= 9 - 7
= 2
The effect on C3
C3 = B2 * 2
C3 = 2 * 2
C3 = 4
We can therefore say that The value of C3 will increase with a factor of 4 because the value of B2 increased with a factor of 2 and C3 is multiplying B2 by 2.
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write the equation of the line that passes through the points (1, 7) and (-3, -1)
Answer:
y = 2x + 5
Step-by-step explanation:
The slope is
[tex]\frac{-1-7}{-3-1}=2[/tex]
Substituting into point-slope form, we get the equation to be
[tex]y-7=2(x-1)[/tex]
which rearranges into slope-intercept form as:
[tex]y-7=2x-2 \\ \\ y=2x+5[/tex]
A list of facts from which a c conclusion can be drawn
Answer:
fjfj dhfj dh. hfhc hfh hfh hfh hfh hcdh
PLS HELP ME I ONLY HAVE 2 MINS!!!
Complete the following sentence with the correct symbol. Select all that apply
|-1| ___ 1
≥
≤
≠
<
>
=
Match the polynomial on the left with the appropriately factored expression on the right.
4x² + 18x
2x(2x + 1)
4x² + 2x + 18x +9
2x(2x + 9)
(2x + 1)(2x +9)
(2x + 3)(2x + 3)
The polynomials that match with other equivalent expressions are :
(a) → (iii), (b) → (ii), (c) → (iv), (d) → (i)
Consider the polynomials,
(a) 4x² + 18x (i) 2x(2x + 1)
(b) 4x² + 2x + 18x +9 (ii) (2x + 1)(2x +9)
(c) (2x + 3)(2x + 3) (iii) 2x(2x + 9)
(d) 4x² + 2x (iv) 4x² + 12x + 9
Now,
Consider the polynomial 2x(2x + 1),
2x(2x + 1) = 2x(2x) + 2x(1)
2x(2x + 1) = 4x² + 2
Therefore, (d) is equal to (i).
Consider the polynomial 2x(2x + 9),
2x(2x + 9) = 2x(2x) + 2x(9)
2x(2x + 9) = 4x² + 18x
Therefore, (a) is equal to (iii).
Consider the polynomial (2x + 1)(2x +9) ,
(2x + 1)(2x +9) = (2x)(2x) + (2x)(9) + (2x)(1) + 9
(2x + 1)(2x +9) = 4x² + 18x + 2x + 9
Therefore, (b) is equal to (ii).
Consider the polynomial (2x + 3)(2x + 3),
(2x + 3)(2x + 3) = (2x)(2x) + (2x)(3) + (3)(2x) + 9
(2x + 3)(2x + 3) = 4x² + 12x + 9
Therefore, (c) is equal to (iv).
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The complete question is mentioned below:
Match the polynomial on the left with the appropriately factored expression on the right.
(a) 4x² + 18x (i) 2x(2x + 1)
(b) 4x² + 2x + 18x +9 (ii) (2x + 1)(2x +9)
(c) (2x + 3)(2x + 3) (iii) 2x(2x + 9)
(d) 4x² + 2x (iv) 4x² + 12x + 9
Give the slope and the
y
intercept of the line
8
x
−
9
y
=
−
4
.
The slope of the line, m = 8/9.
The y-intercept of the line, b = 4/9.
How to Find the Slope and Y-intercept of a Line?An equation that represents a line can be expressed in slope-intercept form as, y = mx + b, where we have the following:
Slope = m
Y-intercept = b.
Given that a line is represented by the equation, 8x - 9y = -4, rewrite the equation in slope-intercept form:
8x - 9y = -4
8x - 9y - 8x = -8x - 4 [subtraction property of equality]
-9y = -8x - 4
-9y/-9 = -8x/-9 - 4/-9 [division property of equality]
y = 8/9x + 4/9
Therefore:
The slope of the line, m = 8/9.
The y-intercept of the line, b = 4/9.
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Find the area of the figure. RIGHT ANSWERS ONLY
Answer:
56 yd²
Step-by-step explanation:
You cut up the figure into 2 distinctive rectangles where it looks like one small rectangle is intersecting a larger one.
So you would do
4(4 + 4 + 4) = 4(12) = 48 yd²
2(4) = 8 yd²
Add
8 + 48 = 56
56 yd²
Hope this helps! :)
Which point is a solution to the system of inequalities below?
3x + 2y < 15
7x - 4y > 9
O (4,4)
O (3, 3)
O (2, 1)
O (1, 0)
The ordered pair which is a solution to the given inequality is: C. (2, 1).
What is an inequality?An inequality can be defined as a mathematical relation that compares two (2) or more integers and variables in an equation based on any of the following arguments:
Less than (<).Greater than (>).Less than or equal to (≤).Greater than or equal to (≥).Next, we would test the ordered pair with the given inequality to determine a solution as follows:
For ordered pair (4, 4), we have:
3x + 2y < 15
3(4) + 2(4) < 15
12 + 8 < 15
20 < 15 (False).
For ordered pair (3, 3), we have:
3x + 2y < 15
3(3) + 2(3) < 15
9 + 6 < 15
15 < 15 (False).
7x - 4y > 9
7(3) - 4(3) > 9
21 - 12 > 9
9 > 9 (False)
For ordered pair (2, 1), we have:
3x + 2y < 15
3(2) + 2(1) < 15
6 + 2 < 15
8 < 15 (True).
7x - 4y > 9
7(2) - 4(1) > 9
14 - 4 > 9
10 > 9 (True)
For ordered pair (1, 0), we have:
3x + 2y < 15
3(1) + 2(0) < 15
3 + 0 < 15
3 < 15 (True).
7x - 4y > 9
7(1) - 4(0) > 9
7 - 4 > 9
3 > 9 (False)
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Can you solve the question please…..
Answer:
the answer is 0.888
Which is 8÷9
Answer: The answer is B: 0.88888888888
Step-by-step explanation:
Macmillan Learning
The table contains information on the price per month and the monthly demand and supply of online music streaming
subscriptions.
Price Quantity demanded (thousands)
$9.80
270
$10.00
230
$10.20
180
$10.40
100
What is the quantity demanded at $10.20?
What is the quantity supplied at $10.20?
At what price
the quantity supplied equal to 200,000?
Using linear functions and the given table, it is found that:
The quantity demanded at $10.20 is of 170,000 of subscriptions.The quantity supplied at $10.20 is of 290,000 of subscriptions.The quantity supplied will be equal to 200,000 at a price of $9.87.What is a linear function?A linear function is modeled by:
y = mx + b
In which:
m is the slope, which is the rate of change, that is, by how much y changes when x changes by 1.b is the y-intercept, which is the value of y when x = 0, and can also be interpreted as the initial value of the function.From the table, we have that:
The quantity demanded at $10.20 is of 170,000 of subscriptions.The quantity supplied at $10.20 is of 290,000 of subscriptions.For the supply equation, we have two points:
(9.8, 190), (10, 220).
Hence the slope is given by:
m = (220 - 190)/(10 - 9.8) = 150.
Hence:
y = 150x + b.
When x = 9.8, y = 190, hence:
190 = 150(9.8) + b
b = -1280.
Hence:
y = 150x - 1280.
We want to find x when y = 200, hence:
200 = 150x - 1280
x = 1480/150
x = $9.87.
The quantity supplied will be equal to 200,000 at a price of $9.87.
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HELP ME SOLVE THIS!!!!! GETS BRAINLIST AND 100 POINTS
Scale Factor: A measure for similar figures.
Similar Figures: Two figures which are same in shape. these shapes do not have the same size as shapes with the same shape and size are congruent.
Finding the scale Factor: The scale factor can be found by dividing the dimension of the new shape by the dimension of the old shape.
21 ÷ 6 = 3.5
The scale factor would be 3.5
Now we can use this scale factor to find the dimension of the smaller rectangle.
52.5 cm ÷ 3.5 = 15 cm
The dimension of the smaller rectangle is 15 cm
We can check the answer by multiplying the new found dimension by the scale factor:
15 cm x 3.5 = 52.5 cm
∴ The scale factor is 3.5
∴ The dimension of the smaller rectangle is 15 cm
A shipping company charges based on calculations of the volume of a rectangular box and the sum of the dimensions of the box. A square rectangular prism has a side length represented by the linear function f(x), and a height represented by the linear function g(x). Which statement describes the combined functions V(x) and S(x)? The volume function is linear but the sum function is not. The sum function is linear but the volume function is not. Both the volume function and the sum function are linear. Neither the volume function nor the sum function is linear.
The statement that describes the combined functions V(x) and S(x) is B. The sum function is linear but the volume function is not.
How to illustrate the information?It should be noted that we are given that f(x) and g(x) are linear. Due to this, the sum function S(x) is linear.
And we know the shape of our figure, so we just need to multiply the dimensions for V(x) but the product of three linear functions results in a cubic function, and we conclude V(x) is not linear.
Therefore, the statement that describes the combined functions V(x) and S(x) is that the sum function is linear but the volume function is not.
In conclusion, the correct option is B.
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I need help with this stat
Answer:
2,835
Step-by-step explanation:
63 x 5 = 315
63 x 4 = 252
315
+2520
2835
Use roster method to write set A’
The set A’ using the roster method is A' = {5, 6, 8}
How to use roster method to write set A’?The sets are given as
Universal set, U = {5, 6, 7, 8, 9, 10, 11}
Set A, A = {7, 9, 10, 11}
The elements of the set A’ are the elements that are in the universal set but not in set A
Using the above as a guide, we have the following values
A' = {5, 6, 8}
The above is in roster method or form
Hence, the set A’ using the roster method is A' = {5, 6, 8}
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Solve the literal equation for y y+x=11
Answer: y = 11-x
This is the same as y = -x+11
To get either result, we subtract x from both sides of the original equation. This is to undo the plus x.