To find the maxima and minima of the function, we need to calculate the derivative of the function. Note, before the denominator is a perfect square trinomial, so the function can be simplified as
[tex]\large\displaystyle\text{$\begin{gathered}\sf \bf{\displaystyle f(x) = \frac{x^2 - x - 2}{(x - 3)^2}} \end{gathered}$}[/tex]
So the derivative is:
[tex]\large\displaystyle\text{$\begin{gathered}\sf \bf{\displaystyle f'(x) = \frac{(2x - 1)(x - 3)^2 - 2(x - 3)(x^2 - x - 2)}{(x - 3)^4} } \end{gathered}$}[/tex]
Simplifying the numerator, we get:
[tex]\large\displaystyle\text{$\begin{gathered}\sf \bf{\displaystyle f'(x) = \frac{(x - 3)(-5x + 7)}{(x - 3)^4} = \frac{-5x + 7}{(x - 3)^3} } \end{gathered}$}[/tex]
The function will have a maximum or minimum when f'(x) = 0, that is,
[tex]\large\displaystyle\text{$\begin{gathered}\sf \bf{\displaystyle f'(x) = \frac{-5x + 7}{(x - 3)^3} = 0 } \end{gathered}$}[/tex]
which is true if -5x + 7 = 0. Then x = 7/5.
To determine whether x = 7/5 is a maximum, we can use the second derivative test or the first derivative test. In this case, it is easier to use the first derivative test to avoid calculating the second derivative. For this, we evaluate f'(x) at a point to the left of x = 7/5 and at a point to the right of it (as long as it is not greater than 3). Since 1 is to the left of 7/5, we evaluate:
[tex]\large\displaystyle\text{$\begin{gathered}\sf \bf{\displaystyle f(1) = \frac{-5 + 7}{(1 - 3)^3} = \frac{2}{-8} < 0} \end{gathered}$}[/tex]
Likewise, since 2 is to the right of 7/5, then we evaluate:
[tex]\large\displaystyle\text{$\begin{gathered}\sf \displaystyle \bf{\frac{-10 + 7}{(2 - 3)^3} = \frac{-3}{-1} > 0} \end{gathered}$}[/tex]
Note that to the left of 7/5 the derivative is negative (the function decreases) and to the right of 7/5 the derivative is positive (the function increases).
The value of f(x) at 7/5 is:
[tex]\large\displaystyle\text{$\begin{gathered}\sf \bf{\displaystyle f\left(\tfrac{7}{5}\right) = \frac{\tfrac{49}{25} - \tfrac{7}{5} - 2}{\tfrac{49}{25} - 6 \cdot \tfrac{7}{5} + 9} = -\frac{9}{16} } \end{gathered}$}[/tex]
This means that [tex]\bf{\left( \frac{7}{5}, -\frac{9}{16} \right)}[/tex] is a minimum (and the only extreme value of f(x)).
[tex]\huge \red{\boxed{\green{\boxed{\boldsymbol{\purple{Pisces04}}}}}}[/tex]
Answer:
[tex]\text{Minimum at }\left(\dfrac{7}{5},-\dfrac{9}{16}\right)[/tex]
Step-by-step explanation:
The local maximum and minimum points of a function are stationary points (turning points). Stationary points occur when the gradient of the function is zero. Differentiation is an algebraic process that finds the gradient of a curve.
To find the stationary points of a function:
Differentiate f(x)Set f'(x) = 0Solve f'(x) = 0 to find the x-valuesPut the x-values back into the original equation to find the y-values.[tex]\boxed{\begin{minipage}{5.5 cm}\underline{Quotient Rule for Differentiation}\\\\If $y=\dfrac{u}{v}$ then:\\\\$\dfrac{\text{d}y}{\text{d}x}=\dfrac{v \dfrac{\text{d}u}{\text{d}x}-u\dfrac{\text{d}v}{\text{d}x}}{v^2}$\\\end{minipage}}[/tex]
[tex]\text{Given function}: \quad \text{f}(x)=\dfrac{x^2-x-2}{x^2-6x+9}[/tex]
Differentiate the function using the Quotient Rule:
[tex]\text{Let }u=x^2-x-2 \implies \dfrac{\text{d}u}{\text{d}x}=2x-1[/tex]
[tex]\text{Let }v=x^2-6x+9 \implies \dfrac{\text{d}v}{\text{d}x}=2x-6[/tex]
[tex]\begin{aligned}\implies \dfrac{\text{d}y}{\text{d}x} & =\dfrac{(x^2-6x+9)(2x-1)-(x^2-x-2)(2x-6)}{(x^2-6x+9)^2}\\\\& =\dfrac{(2x^3-13x^2+24x-9)-(2x^3-8x^2+2x+12)}{(x^2-6x+9)^2}\\\\\implies \text{f}\:'(x)& =\dfrac{-5x^2+22x-21}{(x^2-6x+9)^2}\\\\\end{aligned}[/tex]
Set the differentiated function to zero and solve for x:
[tex]\begin{aligned}\implies \text{f}\:'(x)& =0\\\\\implies \dfrac{-5x^2+22x-21}{(x^2-6x+9)^2} & = 0\\\\-5x^2+22x-21 & = 0\\\\-(5x-7)(x-3) & = 0\\\\\implies 5x-7 & = 0 \implies x=\dfrac{7}{5}\\\\\implies x-3 & = 0 \implies x=3\end{aligned}[/tex]
Put the x-values back into the original equation to find the y-values:
[tex]\implies \text{f}\left(\frac{7}{5}\right)=\dfrac{\left(\frac{7}{5}\right)^2-\left(\frac{7}{5}\right)-2}{\left(\frac{7}{5}\right)^2-6\left(\frac{7}{5}\right)+9}=-\dfrac{9}{16}[/tex]
[tex]\implies \text{f}(3)=\dfrac{\left(3\right)^2-\left(3\right)-2}{\left(3\right)^2-6\left(3\right)+9}=\dfrac{4}{0} \implies \text{unde}\text{fined}[/tex]
Therefore, there is a stationary point at:
[tex]\left(\dfrac{7}{5},-\dfrac{9}{16}\right)\:\text{only}[/tex]
To determine if it's a minimum or a maximum, find the second derivative of the function then input the x-value of the stationary point.
If f''(x) > 0 then its a minimum.If f''(x) < 0 then its a maximum.Differentiate f'(x) using the Quotient Rule:
Simplify f'(x) before differentiating:
[tex]\begin{aligned}\text{f}\:'(x) & =\dfrac{-5x^2+22x-21}{(x^2-6x+9)^2}\\\\& = \dfrac{-(5x-7)(x-3)}{\left((x-3)^2\right)^2}\\\\& = \dfrac{-(5x-7)(x-3)}{(x-3)^4}\\\\& = -\dfrac{(5x-7)}{(x-3)^3}\\\\\end{aligned}[/tex]
[tex]\text{Let }u=-(5x-7) \implies \dfrac{\text{d}u}{\text{d}x}=-5[/tex]
[tex]\text{Let }v=(x-3)^3 \implies \dfrac{\text{d}v}{\text{d}x}=3(x-3)^2[/tex]
[tex]\begin{aligned}\implies \dfrac{\text{d}^2y}{\text{d}x^2} & =\dfrac{-5(x-3)^3+3(5x-7)(x-3)^2}{(x-3)^6}\\\\& =\dfrac{-5(x-3)+3(5x-7)}{(x-3)^4}\\\\\implies \text{f}\:''(x)& =\dfrac{10x-6}{(x-3)^4}\end{aligned}[/tex]
Therefore:
[tex]\text{f}\:''\left(\dfrac{7}{5}\right)=\dfrac{625}{512} > 0 \implies \text{minimum}[/tex]
in an isosceles triangle, the perimeter is 75 cm and one of the sides is 25 cm. Find all its sides. can you find all angles of the triangles?
Answer:
all angles of the triangles is 60
Step-by-step explanation:
the perimeter = 2*side of an isosceles triangle + bottom edge
----> bottom edge = the perimeter - 2*side of an isosceles triangle =25
----> This is an equilateral triangle ----> all angles of the triangles is 60
How do you use the additive inverse to evaluate an expression that uses subtraction ?
To use the additive inverse to evaluate an expression that uses subtraction, change the sign of the number to positive
What is additive inverse?Additive inverse is simply changing the sign of a number and then adding it to the original number to get an answer that is equal to 0.
The additive inverse of a number is another number
The additive inverse of number 3 is - 3
For an expression that uses subtraction, to use the additive inverse, change the sign of the number to positive
Thus, to use the additive inverse to evaluate an expression that uses subtraction, change the sign of the number to positive
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Please help asap thanks so much!
Answer:
see the attachment photo!
please place the dot for me(20 points will give brainliest!!!)
Answer:
Domain & Range are both all real numbers.
Step-by-step explanation:
i
If this was a traditional parabola, the range would be y<=4. However, the arrow on the left going back up means eventually y will go to both positive & negative infinity.
What is the range of the function y=-x² +1?
A) y≤ -1
B) y²-1
C) y≤ 1
D) y≥ 1
Answer:
Option (C)
Step-by-step explanation:
The minimum value of x² is 0, and the maximum value is unbounded, so therefore, the maximum value of -x² is 0, and the minimum value is unbounded.
So, this means that adding 1 to this, the range matches with option C.
what is the answer in system form
y=-2x
5x-7y=-38
Answer:
x = -2
y = 4
Step-by-step explanation:
To solve the system of equations, you want to plug one equation into the other and then simplify. You can do this by setting one equation equal to a variable (like in the first equation), and then substituting the function into the variable into the second equation.
First Equation: y = -2x
Second Equation: 5x - 7y = -38
5x - 7y = -38 <----- Second equation
5x - 7(-2x) = -38 <----- Plug first equation into "y"
5x + 14x = -38 <----- Multiply -7 and -2x
19x = -38 <----- Add 5x and 14x
x = -2 <----- Divide both sides by 19
Now that you know the value of one variable, you can use it to find the value of the second variable. This can be done by plugging x = -2 in to one of the equations.
y = -2x <----- First equation
y = -2(-2) <----- Plug -2 in "x"
y = 4 <----- Multiply -2 and -2
This table represents a quadratic function with a vertex at (1, 1). What is the
average rate of change for the interval from x = 5 to x = 6?
OA. 26
OB. 13
O C. 7
OD. 9
1
2
3
4
5
X
1
2
LO
5
10
17
y
The average rate of change on the interval (5, 6) is 9. So the correct option is D.
How to find the average rate of change on the interval?
Here we want to find the average rate of change of f(x), the function on the table, on the interval (5, 6).
This is just:
[tex]r = \frac{f(6) - f(5)}{6 - 5}[/tex]
[tex]f(x) = a*x^2 + b*x + c[/tex]
I we look at the table we see that:
[tex]f(1) = 1 = a + b + c[/tex]
[tex]f(2) =2 = 4a + 2b + c[/tex]
[tex]f(3) = 5 = 9a + 3b + c[/tex]
This is a system of equations.
If we subtract the second and first functions, we get:
[tex]2 - 1 = (4a + 2b +c) - (a + b + c)\\1 = 3a + b = a + b + c[/tex]
From that we take two relations:
[tex]1 - 3a = b\\2a = c[/tex]
Now we can replace these two in the last equations so we get:
[tex]5 = 9a + 3b + c\\\\5 = 9a + 3*(1 - 3a) + 2a\\\\5 = 9a + 3 - 9a + 2a\\\\5 = 3 + 2a\\\\5 - 3 = 2a\\\\2 = 2a\\\\a = 1[/tex]
Now that we know the value of a:
[tex]c = 2a = 2*1 = 2\\\\b = 1 - 3a = 1 - 3 = -2[/tex]
The quadratic equation is:
[tex]f(x) = x^2 - 2x + 2[/tex]
Evaluating this in x = 6 we get:
[tex]f(6) = 6^2 - 2*6 + 2 = 26[/tex]
And from the table we know that f(5) = 17, then the average rate of change is:
[tex]r = \frac{f(6) - f(5)}{6 - 5} = \frac{26-17}{1} = 9[/tex]
The correct option is D.
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Triangle ABC is shown on the graph. What are the coordinates of the image of point B after the triangle is rotated 270° about the origin?
(4, 2)
(2, 4)
(–4, –2)
(–2, –4)
The coordinates of the image of point B after the triangle is rotated 270° about the origin is (4, 2)
How to determine the image of point B?The complete question is added as an attachment
From the attached image, we have the following coordinate
B = (-2, 4)
When the triangle is rotated by 270 degrees, the rule of rotation is:
(x, y) ⇒ (y, -x)
For point B, we have:
B' = (4, 2)
Hence, the coordinates of the image of point B after the triangle is rotated 270° about the origin is (4, 2)
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Round 2
5. A Cadillac Escalade gasoline tank has a capacity of 24
gallons. The car uses approximately 1 gallon for every 25
miles it drives. If the tank starts full, write an equation that
describes the amount of gas, g, left in the tank after it has
been driven for m miles.
Answer:
g = 24 - 1/25m
Step-by-step explanation:
Since the Cadillac Escalade can travel 25 miles per gallon, each mile the Escalade travels is 1/25th of a gallon of gas.
This means that every mile the Escalade travels, 1/25th of a gallon is subtracted from the gas tank. Since the gas tank has a capacity of 24 gallons, the value of the gas tank is 24.
This leads us to the equation:
g = 24 - 1/25m
where g is the amount of gas left, and m is the number of miles driven.
When planning road development, the road commission estimates the future population using the function represented in the table, where x is the time in years and f(x) is the total population.
What is the significance of 160,000 in the function?
the maximum population of the city
the expected population in 5 years
the initial population at the time of the estimation
the amount of increase in the popu
Considering that 160,000 is the y-intercept of the function, it's significance is given by:
the initial population at the time of the estimation.
What is the y-intercept of a function f(x)?The y-intercept is f(0), that is, the value of y when x = 0, which is interpreted as the initial value of the function.
Researching this problem on the internet, it is found that f(0) = 160,000, hence the significance of 160,000 in the function is given by:
the initial population at the time of the estimation.
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Domain of y=5x+2 help!!!!
Triangle A C D is shown. A line is drawn from point D to point B on side A C to form a right angle. Line A D is labeled s. The length of A B is 8, the length of B C is 5, and the length of B D is 15.
What is the value of s in units?
Answer:
s = 17units
Step-by-step explanation:
For this problem, we are trying to find a specific unknown side length.
We're actually given some extraneous information (information that is not needed to solve the problem): It isn't necessary to know that BC is 5.
If the side AD with the unknown length is part of a right triangle (the triangle in red in the attached diagram), we can use the Pythagorean Theorem to solve for AD.
It isn't clear if the diagram you were provided gives ∠ABD as a right angle, if it only gives ∠CBD as a right angle, or if it gives both as a right angle. Below, we prove that it doesn't matter, because regardless, both must be right angles.
Is Triangle ABD a "right triangle"?
Since B is between A and C, then the two angles ∠ABD & ∠CBD form a linear pair, and by the linear pair postulate are supplementary. Since they are supplementary, their measures add to 180°. Using the fact that all right angles are 90°, substitution, the subtraction property of equality, arithmetic, the measure of ∠ABD is also 90°, and thus must be a right angle. Thus, based on the given information, both ∠ABD & ∠CBD must be right angles.
Consequently, triangle ABD is a right triangle, by definition (it is a triangle that has a right angle).
Pythagorean Theorem
Since triangle ABD is a right triangle, the Pythagorean Theorem can be applied.
The Pythagorean Theorem states that [tex]a^{2} +b^{2} =c^{2}[/tex] where "c" is the hypotenuse (the side across from the right angle) and "a" and "b" the the lengths of the two other sides (called legs) of the right triangle. (Aside: Because of the commutative property of addition, it doesn't matter which of the two legs' lengths is used for a, and which is used for b. The only thing that is required is that "c" be the length of the hypotenuse)
In our triangle, side AD, with unknown length "s" is the length of our hypotenuse, and sides AB and BD are the two legs. Substituting values into the Pythagorean Theorem equation, we can solve for the unknown "s":
[tex]a^{2} +b^{2} =c^{2}[/tex]
[tex](8)^{2} +(15)^{2} =(s)^{2}[/tex]
[tex]64 +225 =s^{2}[/tex]
[tex]289 =s^{2}[/tex]
Applying the square root property...
[tex]\pm \sqrt{289} =\sqrt{s^{2}}[/tex]
[tex]s=17 \text{ or } s=-17[/tex]
Final Solution
We discard the negative solution we obtained, since s represents the length of the side of a triangle.
s = 17units
Answer:
17
Step-by-step explanation:
Find the perimeter of the triangle.
23.
7 in.
(x + 4) in.
(4x + 1) in.
Answer:
17 in.
Step-by-step explanation:
There are two same angles shown, so two sides are equal. We can form an equation x+4=4x+1. Solution is x=1, then both unknown sides are 5 in. long. Given all side lengths we add them 7+5+5+15 getting the perimeter.
Step 1: We know that Angle A B C Is-congruent-to Angle F G H because all right angles are congruent. Step 2: We know that Angle B A C Is-congruent-to Angle G F H because corresponding angles of parallel lines are congruent. Step 3: We know that Line segment B C is-congruent-to line segment G H because it is given. Step 4: Triangle A B C Is-congruent-to Triangle F G H because of the
Triangles FGH and ABC are congruent because of the: AAS congruence theorem.
What is the AAS Congruence Theorem?
The AAS congruence theorem states that when two angles and one non-included side in one triangle are congruent to corresponding two angles and one non-included side in another triangle, then both triangles are congruent.
In the proof given, it is established that both triangles have two corresponding congruent angles, and also, BC ≅ GH which are non-included sides.
Therefore, both triangles are congruent because of the AAS congruence theorem.
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please help and answer it in a sentence :)
Answer:
x = $1 & y = $2.
Each doughnut cost $1 and hot chocolate cost $2.
All of the details to the question are in the picture that is attached in this question, please help
Answer: 10
The arc length of the semicircle is
a+(a+1)+(a+2)+(a+3)+(a+4)=5a+10
As x = 42, this means a+4 is 42/180 of the arc length of the circle, 5a+10.
So,
(42/180)(5a+10)=a+4
42(5a+10)=180(a+4) [multiply both sides by 180]
210a+420=180a+720 [distributive property]
30a+420=720 [subtract 180a from both sides]
30a=300 [subtract 420 from both sides]
a=10 [divide both sides by 30]
4
12 + 17 < -18 *
True
False
Select all the correct answers.
Which expressions are equivalent to this exponential expression? Please help
An expression is defined as a set of numbers, variables, and mathematical operations. The correct options are A and C.
What is an Expression?In mathematics, an expression is defined as a set of numbers, variables, and mathematical operations formed according to rules dependent on the context.
The given exponential (6⁻¹⁰/6⁻⁴) function can be simplified as shown below,
(6⁻¹⁰/6⁻⁴)
= 6⁻¹⁰ × 6⁴
= 6⁽⁻¹⁰⁺⁴⁾
= 6⁻⁶
= 1/6⁶
Hence, the correct options are A and C.
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Type the correct answer in each box. Use numerals instead of words. If necessary, use / for the fraction bar(s).
Answer:
3 days, 27
Step-by-step explanation:
After 3 days :
3³ = 27 belts4(3) + 15 = 12 + 15 = 27 beltsAfter 3 days, the number of belts and wallets sold will be the same, equal to 27.
After 3 days, the number of belts and wallets sold will be the same, equal to 27.
It is given that the number of belt sold s, x days after its online lunch s=3^x
and s=4x+15.
To find correct answer in each box.
What is arithmetic?The branch of mathematics dealing with the properties and manipulation of numbers.
After 3 days :
3³ = 27 belts
4(3) + 15 = 12 + 15 = 27 belts
So, after 3 days, the number of belts and wallets sold will be the same, equal to 27.
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(-3 +6 i )(-3 - 6 i )
Answer:
45
Step-by-step explanation:
Zippy company manufactured 10,000 units in december with a total product cost of $22,900 they had zero finished goods inventory at the start of december. in december zippy sold 7,796 units at a unit price of $5.54. period expenses were $4,723. what is the amount of zippy's gross profit (otherwise know as gross margin).? round any intermediate calculations to four decimal places
The amount of zippy's gross profit (otherwise know as gross margin) is: $25,337.
Gross profitSales revenue $43,189.84
(7,796 units × $5.54)
Less Cost of goods sold $17,852.84
[($22,900/10,000)×7,796]
Gross profit $25,337
( $43,189.84-$17,852.84)
Therefore the amount of zippy's gross profit (otherwise know as gross margin) is: $25,337.
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Emily works at a local restaurant. She made $200 in tips last night. She shared 15 percent of her tips with the crew that cleans the tables. How much did she give to the clean-up crew?
$
A percentage is a way to describe a part of a whole. The amount Emily shared is $30.
What are percentages?A percentage is a way to describe a part of a whole. such as the fraction ¼ can be described as 0.25 which is equal to 25%.
To convert a fraction to a percentage, convert the fraction to decimal form and then multiply by 100 with the '%' symbol.
Emily works at a local restaurant. She made $200 in tips last night. She shared 15% of her tips with the crew that cleans the tables. The amount Emily shared is,
15% of $200
= 0.15 × $200
= $30
The amount Emily shared is $30.
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Select the correct answer. A linear function on a coordinate plane passes through (minus 3, 2), (0, 4), and (3, 6) Which equation describes the line graphed above? A. B. C. D.
Answer:
I don't see the equation options. See below for a predicted equation.
y= (2/3)x + 4
Step-by-step explanation:
The points are (-3,2), (0,4), and (3,6). I will assume they lie in a straight line.
Find an equation of the form y=mx+b, where m is the slope and b is the y-intercept (the value of y when x=0).
m, the slope, is also known as the "Rise/Run."
Pick any two points. I'll use (0,4) and 3,6)
Rise = (6-4) = 2
Run = (3-0) = 3
Slope = 2/3
The equation becomes y = (2/3)x + b
B is easy in this case. Point (0,4) tells us that y = 4 when x = 0 (the definition of b).
The equation is y= (2/3)x + 4
See the attached graph.
Janet solves this equation
log(x-3)+logx=1
She finds the two solutions; x=5 and x=-2
Of Janet’s two solutions, ____ correct because _____
A. Neither x=5 nor x=-2 is
B. Only x=5 is
C. Only x=-2 is
D. Both x=5 and x=-2 are
1. x=5 is an extraneous solution
2. Both x=-2 and x=5 are valid solutions
3. Both x=-2 and x=5 are extraneous solutions
4. x=-2 is an extraneous solution
(TWO DIFFERENT ANSWERS FILL IN THE BLANK)
Of Janet’s two solutions, both x=5 and x=-2 are correct because both x=-2 and x=5 are extraneous solutions
Logarithmic functionGiven the log function expressed as:
log(x-3) + logx=1
According to the law of logarithm, addition becomes product to have:
log x(x -3) = log₁₀10
x² - 3x = 10
x² - 3x -10 = 0
x² - 5x + 2x - 10 = 0
x(x-5) + 2(x-5) = 0
(x+2)(x-5)=0
x = -2 and 5
Of Janet’s two solutions, both x=5 and x=-2 are correct because both x=-2 and x=5 are extraneous solutions
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Determine the linear function for a graph that is a line with a slope of 1/7
and contains the point
(−4, 1).
The linear equation is y = (1/7)*x + 11/7.
How to get the linear equation?
The general linear equation is:
y = a*x + b
Where a is the slope.
Here we know that a = (1/7), then the line is:
y = (1/7)*x + b
We also know that the line contains the point (-4, 1), this means that when x = -4, we must have y = 1.
Replacing that, we get:
1 = (1/7)*(-4) + b
1 + 4/7 = b
7/7 + 4/7 = b
11/7 = b
So the linear equation is:
y = (1/7)*x + 11/7.
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The equation of the linear function of the line is: y = 1/7x + 11/7.
What is a Linear Function Equation?A linear function equation is modelled as, y = mx + b, where m is the slope and b is the y-intercept.
Slope (m) = 1/7, and the line passes through (-4, 1), therefore, substitute (x, y) = (-4, 1) and m = 1/7 into y = mx + b:
1 = 1/7(-4) + b
1 = -4/7 + b
1 + 4/7 = b
11/7 = b
b = 11/7
Plug in the values of m and b into y = mx + b:
y = 1/7x + 11/7
The equation of the linear function is: y = 1/7x + 11/7
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Help me show your work
The value of x should be greater than or equal to -2. The number line from -2 to the entire right till ∞ of the number line will satisfy this condition.
What is a number line?A number line is just that – a straight, horizontal line with numbers placed at even increments along the length. It’s not a ruler, so the space between each number doesn’t matter, but the numbers included on the line determine how it’s meant to be used.
The value of x that will satisfy this condition can be found by simplifying the given inequality. Therefore, The given inequality can be simplified as,
4x + 1 - 1 ≥ -8
4x ≥ -8
x ≥ -2
Hence, the value of x should be greater than or equal to -2. The number line from -2 to the entire right till ∞ of the number line will satisfy this condition.
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Brandon is a running back for his local high school football team. In the last game, he carried the ball 8 times. In the first 5 carries, he gained 6 yards, 12 yards, and 4 yards before losing 2 yards and then losing additional yards. His last 7 carries combined for yards. What was his total net yardage for the game?
Using it's concept, it is found that Brandon's net yardage for the game was of 26.
How to find the net yardage?The total net yardage is the sum of all the yardage they gain, that is, the positive gains are added with a plus signal, while the negative gains are added with a negative signal.
Hence, his net yardage, considering that he gained 20 yards on his last 7 carries, is given by:
6 + 20 = 26.
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Match each pair of equivalent values.
1 .
1
square root of 16
2 .
12
square of 8
3 .
4
4 2
4 .
64
1 2
5 .
16
6 .
2
Answer:
1 - [tex]1^{2}[/tex]
12 - ?
4 - square root of 16
64 - [tex]8^{2}[/tex]
16 - [tex]4^{2}[/tex]
2.828 - square root of 8
Step-by-step explanation:
I need more terms to match
Square root of 16 is 4, square root of 8 is 2, but for an answer it would be , 4² is 16, 1² is 2, number 5 would be 64 and number 6 would be 12.
What are mathematical values?A mathematical value can generally be any specific mathematical object. This is most frequently a number in elementary mathematics, such as a real number like or an integer like 42. Every integer or even other mathematical object set to a variable or constant is that object's value.
A mathematical expression's value is the outcome of a computation it describes when its variables and constants are given values. The amount that the function assumes for these argument numbers is the result of a function, assuming the value(s) provided to its argument(s).
Square root of 16 is 4, square root of 8 is 2, but for an answer it would be , 4² is 16, 1² is 2, number 5 would be 64 and number 6 would be 12.
Therefore, Square root of 16 is 4, square root of 8 is 2, but for an answer it would be , 4² is 16, 1² is 2, number 5 would be 64 and number 6 would be 12.
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Separating variable in the equation gives you the following equation:
Answer:
[tex]\textsf{E.} \quad y\:dy=xe^x\:dx[/tex]
Step-by-step explanation:
Given equation:
[tex]ye^{-x}\dfrac{dy}{dx}=x[/tex]
Divide both sides by [tex]e^{-x}[/tex]:
[tex]\implies \dfrac{ye^{-x}}{e^{-x}}\:\dfrac{dy}{dx}=\dfrac{x}{e^{-x}}[/tex]
[tex]\implies y\:\dfrac{dy}{dx}=\dfrac{x}{e^{-x}}[/tex]
Multiply both sides by [tex]dx[/tex] :
[tex]\implies y\:\dfrac{dy}{dx}\cdot dx=\dfrac{x}{e^{-x}}\cdot dx[/tex]
[tex]\implies y\:dy=\dfrac{x}{e^{-x}}\:dx[/tex]
[tex]\textsf{Apply exponent rule} \quad \dfrac{1}{a^{-n}}=a^n:[/tex]
[tex]\implies y\:dy=xe^x\:dx[/tex]
Answer: E
Step-by-step explanation:
[tex]ye^{-x} \frac{dy}{dx}=x\\\\y \frac{dy}{dx}=xe^{x} \\ \\ \boxed{y dy=xe^{x} dx}[/tex]
√2/√2+√3-√5 rationalise the denominator
