Answer:
(0, -2)
Step-by-step explanation:
The equation of y axis is x = 0. So, the y intercept is located at point (0, b). Therefore we can substitute 0 into x in the given equation to find b and hence the coordinates of the y intercept.
3x - 7y = 14
3*0 - 7y = 14
-7y = 14
y = -2
Please help me with this question <3
[tex] \qquad \qquad \bf \huge\star \: \: \large{ \underline{Answer} } \huge \: \: \star[/tex]
For two lines to be parallel, there should be angles that follow some specific properties that is usually observed with parallel lines.
We can clearly see that :
[tex] \qquad❖ \: \sf \: \angle7 \cong \angle16[/tex]
( by Alternate interior angle pair )
[tex] \qquad \large \sf {Conclusion} : [/tex]
Lines l and m are parallel to each other.
– A BOX CONTAINS 9 RED AND 2 BLUE MARBLES. IF YOU SELECT
ONE MARBLE AT RANDOM FROM THE BOX, DETERMINE THE ODDS AGAINST
SELECTING A RED MARBLE.
The odds against selecting a red marble is =2/11
Calculation of probabilityThe number of marbles which were red = 9
The number of marbles which were blue = 2
The total amount of marbles in the Box = 11
When one marble is picked at random from the box, the odds against selecting a red marble can be gotten through the blue marble.
That is, the number of blue marble/ total marble
= 2/11
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If a 90ml drink has 2 parts milk and 1 part chocolate topping, how many mls of milk and chocolate topping is that?
Answer:
The milk would be 60 ml and the topping would be 30 ml
Step-by-step explanation:
If there are 2 parts milk and 1 part toppings that would be a total of 3 (2+1 =3) So we are looking for 2/3 of 90 and 1/3 of 90.
Which statement correctly compares functions f and g? function f function g An exponential function passes through (minus 1, 5), and (2, minus 1.5) intercepts axis at (1, 0), and (0, 2) Function g is a decreasing exponential function with a y-intercept of 5 and no x-intercept. A. They have different end behavior as x approaches -∞ and different end behavior as x approaches ∞. B. They have different end behavior as x approaches -∞ but the same end behavior as x approaches ∞. C. They have the same end behavior as x approaches -∞ but different end behavior as x approaches ∞. D. They have the same end behavior as x approaches -∞ and the same end behavior as x approaches ∞.
A statement correctly compares functions f and g is that: C. they have the same end behavior as x approaches -∞ but different end behavior as x approaches ∞.
What is a function?A function can be defined as a mathematical expression that defines and represents the relationship between two or more variable, which is typically modelled as input (x-values) and output (y-values).
The types of function.In Mathematics, there are different types of functions and these include the following;
Periodic functionInverse functionModulus functionSignum functionPiece-wise defined function.Function g is represented by the following table and a line representing these data is plotted in the graph that is shown in the image attached below.
x -1 0 1 2 3 4
g(x) 24 6 0 -2
Based on the line, we can logically deduce the following points:
y-intercept approaches -2.43 to 24.86.x-intercept approaches negative infinity (-∞) to infinity (∞).This ultimately implies that, a statement correctly compares functions f and g is that both functions have the same end behavior as x approaches -∞ but different end behavior as x approaches ∞.
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If m = 4 and n = -7, what is the value of m + n?
The answer is -3.
If m = 4 and n = -7, we can evaluate the expression by substitution.
m + n
4 + (-7)
-3
❄ H there,
evaluate this expression by substituting the provided parameters –
[tex]\sf{m+n} \ | \ m=4 \ \& \ n=-7 \ | 4+(-7)=4-7=-3}[/tex]
That's it!
❄
The function f(x)=58(1.6)x represents the possible bird population in a park x years from now. Each year, the expected number of birds is ____the number the year before.
Answer:
1.6 times or 60% more than
Step-by-step explanation:
The question seems to be asking about the growth factor in the given exponential function.
Exponential functionA generic exponential function will have the form ...
quantity = (initial value) × (growth factor)^(number of intervals)
Comparing this form to the given formula ...
f(x) = 58 × 1.6^x
we see the "growth factor" is 1.6. This is the multiplier from one interval (year) to the next.
Each year the expected number of birds is 1.6 times the number the year before.
__
Additional comment
A growth factor is sometimes expressed in terms of a growth rate, usually a percentage.
growth factor = 1 + growth rate
1.6 = 1 + 0.60 = 1 + 60%
The growth rate of this bird population is 60% per year. Each year, the population is 60% more than the year before.
Answer: 1.6
Step-by-step explanation:
A small motorboat travels 12mph in still water. It takes 2 hours longer to travel 46 miles going upstream than it does going downstream. Find the rate of the current
Using the relation between velocity, distance and time, it is found that the rate of the current is of 3.33 mph.
What is the relation between velocity, distance and time?Velocity is distance divided by time, hence:
v = d/t
A small motorboat travels 12mph in still water. With the current, upstream, 46 miles are traveled in t hours, hence:
12 + r = 46/t
r = 46/t - 12
Downstream, the time is of t + 2 hours, hence:
12 - r = 46/(t + 2)
r = 12 - 46/(t + 2)
Hence, equaling the values for r:
46/t - 12 = 12 - 46/(t + 2)
46/t + 46/(t + 2) = 24
[tex]\frac{46t + 92 + 46t}{t(t + 2)} = 24[/tex]
92t + 92 = 24t² + 48t
24t² - 44t - 92 = 0
Using a quadratic equation calculator, the solution is t = 3. Hence the rate is found as follows:
r = 46/t - 12 = 46/3 - 12 = 3.33 mph.
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Use matrices to solve the system of equations if possible. Use Gaussian elimination with back substitution or gauss Jordan elimination. -x+y-z=-20,2x-y+z=29, 3x+2y+z=29
In matrix form, the system is given by
[tex]\begin{bmatrix} -1 & 1 & -1 \\ 2 & -1 & 1 \\ 3 & 2 & 1 \end{bmatrix} \begin{bmatrix} x \\ y \\ z \end{bmatrix} = \begin{bmatrix} -20 \\ 29 \\ 29 \end{bmatrix}[/tex]
I'll use G-J elimination. Consider the augmented matrix
[tex]\left[ \begin{array}{ccc|c} -1 & 1 & -1 & -20 \\ 2 & -1 & 1 & 29 \\ 3 & 2 & 1 & 29 \end{array} \right][/tex]
• Multiply through row 1 by -1.
[tex]\left[ \begin{array}{ccc|c} 1 & -1 & 1 & 20 \\ 2 & -1 & 1 & 29 \\ 3 & 2 & 1 & 29 \end{array} \right][/tex]
• Eliminate the entries in the first column of the second and third rows. Combine -2 (row 1) with row 2, and -3 (row 1) with row 3.
[tex]\left[ \begin{array}{ccc|c} 1 & -1 & 1 & 20 \\ 0 & 1 & -1 & -11 \\ 0 & 5 & -2 & -31 \end{array} \right][/tex]
• Eliminate the entry in the second column of the third row. Combine -5 (row 2) with row 3.
[tex]\left[ \begin{array}{ccc|c} 1 & -1 & 1 & 20 \\ 0 & 1 & -1 & -11 \\ 0 & 0 & 3 & 24 \end{array} \right][/tex]
• Multiply row 3 by 1/3.
[tex]\left[ \begin{array}{ccc|c} 1 & -1 & 1 & 20 \\ 0 & 1 & -1 & -11 \\ 0 & 0 & 1 & 8 \end{array} \right][/tex]
• Eliminate the entry in the third column of the second row. Combine row 2 with row 3.
[tex]\left[ \begin{array}{ccc|c} 1 & -1 & 1 & 20 \\ 0 & 1 & 0 & -3 \\ 0 & 0 & 1 & 8 \end{array} \right][/tex]
• Eliminate the entries in the second and third columns of the first row. Combine row 1 with row 2 and -1 (row 3).
[tex]\left[ \begin{array}{ccc|c} 1 & 0 & 0 & 9 \\ 0 & 1 & 0 & -3 \\ 0 & 0 & 1 & 8 \end{array} \right][/tex]
Then the solution to the system is
[tex]\boxed{x=9, y=-3, z=8}[/tex]
If you want to use G elimination and substitution, you'd stop at the step with the augmented matrix
[tex]\left[ \begin{array}{ccc|c} 1 & -1 & 1 & 20 \\ 0 & 1 & -1 & -11 \\ 0 & 0 & 1 & 8 \end{array} \right][/tex]
The third row tells us that [tex]z=8[/tex]. Then in the second row,
[tex]y-z = -11 \implies y=-11 + 8 = -3[/tex]
and in the first row,
[tex]x-y+z=20 \implies x=20 + (-3) - 8 = 9[/tex]
Write an equation that expresses the following relationship.
varies directly with the square of and inversely with
In your equation, use as the constant of proportionality.
The equation become u = k p^2 / d.
According to the statement
we have given that some conditions for the equations and we have t make the equation from the given equations.
So, For this purpose, we have given that
The equation in which u is varies directly with the square of p and inversely with d and use the k as the constant of proportionality.
So, From all these above the equation will become is
u = k p^2 / d
In latex form the equation write as :
[tex]u = \frac{kp^{2}}{d}[/tex]
In this equation all the given conditions are applicable.
So, The equation become u = k p^2 / d
Disclaimer: This question was incomplete. Please find the full content below.
Question:
Write an equation that expresses the following relationship. u varies directly with the square of p and inversely with d In your equation, use k as the constant of proportionality.
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NO LINKS!! Please help me with this problem
Answer:
[tex]x^2+y^2=64[/tex]
Step-by-step explanation:
So the first important thing in solving this problem, is identifying what the major and minor axis are. The major axis is the bigger one, and we want to find on which axis it is.
So by simply looking at the eclipse, you can see that it's larger on the horizontal axis, so the major axis is on the horizontal axis, and the minor axis is on the vertical axis.
This means the equation will be expressed as:
[tex]\frac{(x-h)^2}{a^2} + \frac{(y-k)^2}{b^2} = 1[/tex]
In this equation the major axis, has a length of 2a, and the minor axis has a length of 2b. It's also important to note that (h, k) is the middle of the eclipse, but in the equation you provided, there is no subtraction, so it's just 0, meaning the center is at the origin (0, 0)
So now let's solve for a, and b. I'll look at each individual fraction separately.
[tex]\frac{x^2}{64}[/tex]
The denominator is equal to the value of a^2, so we simply take the square root of this to get the equation: a=8
[tex]\frac{y^2}{36}[/tex]
The denominator is equal to the value of b^2, so we simply take the square root of this to get the equation: b=6
So by just looking at the graph the larger circle appears to have a denominator that is equal to the length of the major axis. The major axis is equal to 2a, and since we know the value of a (8), we simply multiply this by 2 to get a length of 16. This was a bit redundant to do, since in the equation of a circle we need the radius, and the radius is just half the diameter, so now we divide this 16 by 2 to get a radius of 8.
The circle also appears to be centered at the origin so the equation will have (x-0)^2 and (y-0)^2 which is just x^2 and y^2
Plugging in all the values we get the equation:
[tex]x^2+y^2=64[/tex]
[tex] {\qquad\qquad\huge\underline{{\sf Answer}}} [/tex]
Here we go ~
The ellipse shown here is a horizontal ellipse that has major axis parallel to x - axis and minor axis parallel to y - axis. Length of major axis = 2a, and that of minor axis = 2b.
And it has it's centre on origin, it's equation can be written as :
[tex]\qquad \sf \dashrightarrow \: \cfrac{ {x}^{2} }{ {a}^{2} } + \cfrac{ {y}^{2} }{ {b}^{2} } = 1[/tex]
so, let's equate given equation with the standard equation ~
[tex]\qquad \sf \dashrightarrow \: \cfrac{ {x}^{2} }{64} + \cfrac{ {y}^{2} }{36} = 1[/tex]
so we get :
a² = 64 ; a = 8b² = 36 ; b = 6As we know, length of major axis is : 2a = 2 × 8 = 16 units
and, the larger circle has diameter = 2a = 16 units
so, it's radius = 8 units ~
Now, let's write the equation of circle with origin as centre and radius = 8 units
[tex]\qquad \sf \dashrightarrow \: {(x - h)}^{2} + (y - k) {}^{2} = {r}^{2} [/tex]
[ h = 0, k = 0, since circle has centre at origin ]
[tex]\qquad \sf \dashrightarrow \: {x}^{2} + {y}^{2} = 64[/tex]
What is the length of S?
please help me with these calculus bc questions
4. Compute the derivative.
[tex]y = 2x^2 - x - 1 \implies \dfrac{dy}{dx} = 4x - 1[/tex]
Find when the gradient is 7.
[tex]4x - 1 = 7 \implies 4x = 8 \implies x = 2[/tex]
Evaluate [tex]y[/tex] at this point.
[tex]y = 2\cdot2^2-2-1 = 5[/tex]
The point we want is then (2, 5).
5. The curve crosses the [tex]x[/tex]-axis when [tex]y=0[/tex]. We have
[tex]y = \dfrac{x - 4}x = 1 - \dfrac4x = 0 \implies \dfrac4x = 1 \implies x = 4[/tex]
Compute the derivative.
[tex]y = 1 - \dfrac4x \implies \dfrac{dy}{dx} = -\dfrac4{x^2}[/tex]
At the point we want, the gradient is
[tex]\dfrac{dy}{dx}\bigg|_{x=4} = -\dfrac4{4^2} = \boxed{-\dfrac14}[/tex]
6. The curve crosses the [tex]y[/tex]-axis when [tex]x=0[/tex]. Compute the derivative.
[tex]\dfrac{dy}{dx} = 3x^2 - 4x + 5[/tex]
When [tex]x=0[/tex], the gradient is
[tex]\dfrac{dy}{dx}\bigg|_{x=0} = 3\cdot0^2 - 4\cdot0 + 5 = \boxed{5}[/tex]
7. Set [tex]y=5[/tex] and solve for [tex]x[/tex]. The curve and line meet when
[tex]5 = 2x^2 + 7x - 4 \implies 2x^2 + 7x - 9 = (x - 1)(2x+9) = 0 \implies x=1 \text{ or } x = -\dfrac92[/tex]
Compute the derivative (for the curve) and evaluate it at these [tex]x[/tex] values.
[tex]\dfrac{dy}{dx} = 4x + 7[/tex]
[tex]\dfrac{dy}{dx}\bigg|_{x=1} = 4\cdot1+7 = \boxed{11}[/tex]
[tex]\dfrac{dy}{dx}\bigg|_{x=-9/2} = 4\cdot\left(-\dfrac92\right)+7=\boxed{-11}[/tex]
8. Compute the derivative.
[tex]y = ax^2 + bx \implies \dfrac{dy}{dx} = 2ax + b[/tex]
The gradient is 8 when [tex]x=2[/tex], so
[tex]2a\cdot2 + b = 8 \implies 4a + b = 8[/tex]
and the gradient is -10 when [tex]x=-1[/tex], so
[tex]2a\cdot(-1) + b = -10 \implies -2a + b = -10[/tex]
Solve for [tex]a[/tex] and [tex]b[/tex]. Eliminating [tex]b[/tex], we have
[tex](4a + b) - (-2a + b) = 8 - (-10) \implies 6a = 18 \implies \boxed{a=3}[/tex]
so that
[tex]4\cdot3+b = 8 \implies 12 + b = 8 \implies \boxed{b = -4}[/tex].
Please solve this question step by step explanation
The value of ∠B is 60 degrees
How to solve for B?The given parameters are
2∠A = 3∠B = 6∠C
Let the angles in a triangle ABC be ∠A, ∠B and ∠C.
The sum of these angles in the triangle ABC is
∠A + ∠B + ∠C = 180
Multiply the above equation by 2
2 * (∠A + ∠B + ∠C) = 2 * 180
Evaluate the product
2∠A + 2∠B + 2∠C = 360
Recall that 2∠A = 3∠B.
Substitute the above in the equation 2∠A + 2∠B + 2∠C = 360
3∠B + 2∠B + 2∠C = 360
This gives
5∠B + 2∠C = 360
Multiply the above equation by 3
3 * (5∠B + 2∠C) = 3 * 360
Evaluate the product
15∠B + 6∠C = 1080
Recall that 3∠B = 6∠C.
Substitute the above in the equation
So, we have:
15∠B + 3∠B = 1080
Evaluate the like terms
18∠B = 1080
Divide both sides by 18
∠B = 60
Hence, the value of ∠B is 60 degrees
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PLEASE HELP ASAP WITH EXPLANATION: If f(x) = 2f(x − 1) for all integers x, and f(n) = 3 for some integer n, find the value of
[f(n − 5)][f(n + 5)].
Answer:F to the power of 2,N to the power of 2,—25,f to the power of 2
Step-by-step explanation: i really hope under stand
ASAP Please help me with this questions ASAP
Answer:
an angle bisector
Step-by-step explanation:
This is showing the construction of the bisector of ∠LNM
How to make 3 dimensional object become 4 dimensional object
Using Hinton's method;
Draw two ordinary 3D cubes in 2D space, one encompassing the other, separated by an "unseen" distanceThen draw lines between their equivalent vertices.The eight lines connecting the vertices of the two cubes in this case represent a single direction in the "unseen" fourth dimension.What is a 4 dimensional shape?A four-dimensional shape (4D) is a mathematical extension of a three-dimensional or 3D space.
Three-dimensional space is the simplest possible abstraction of the observation that one only needs three numbers, called dimensions, to describe the sizes or locations of objects.
Using Hinton's method;
Draw two ordinary 3D cubes in 2D space, one encompassing the other, separated by an "unseen" distanceThen draw lines between their equivalent vertices.The eight lines connecting the vertices of the two cubes in this case represent a single direction in the "unseen" fourth dimension.Learn more about dimensional shapes here:
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Which of the following is the equation of the line that passes through the point (-5,-7) and has a slope of 2/5?
No multiple choice
The equation of the line passing through the point (-5, -7) with a slope of 2/5 is y = (2/5)x - 5.
How did we get the values?To find the equation of a line, we can use the point-slope form of a linear equation:
y - y₁ = m(x - x₁),
where (x₁, y₁) is the given point on the line and m is the slope.
In this case, the given point is (-5, -7) and the slope is 2/5. Substituting these values into the equation, we have:
y - (-7) = (2/5)(x - (-5)).
Simplifying further:
y + 7 = (2/5)(x + 5).
Distributing the 2/5:
y + 7 = (2/5)x + 2.
Subtracting 7 from both sides:
y = (2/5)x - 5.
Therefore, the equation of the line passing through the point (-5, -7) with a slope of 2/5 is y = (2/5)x - 5.
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PLEASE HELP ME SOLVE THIS
he polynomial of degree 5, P ( x ) has leading coefficient 1, has roots of multiplicity 2 at x = 3 and x = 0 , and a root of multiplicity 1 at x = − 1 Find a possible formula for P ( x ) .
f]
The possible formula for the polynomial in discuss whose roots are described as; having roots of multiplicity 2 at x = 3 and x = 0 , and a root of multiplicity 1 at x = − 1 is; P(x) = x^5 -5x⁴-6x³+18x².
What is the polynomial in discuss whose roots and leading coefficient are as discussed?The polynomial which is as described in the task content whose roots are as given can be written in its factorised form as follows;
P(x) = (x-3) (x-3) (x) (x) (x+1)
The expanded form is therefore;
P(x) = x^5 - 5x⁴- 6x³+ 18x².
Therefore, the polynomial having roots of multiplicity 2 at x = 3 and x = 0 , and a root of multiplicity 1 at x = − 1 is P(x) = x^5 - 5x⁴- 6x³+ 18x².
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When a disease is rare in the general population, doctors are not likely to test everyone. Instead, they only test people that have specific risk factors or show symptoms of the disease. Even if resources are available, why do you think doctors would avoid giving a test for a rare disease to everyone in the general population? Explain using ideas from probability that were explored in this project
divide the sum of 36 and the product of 18 and 6 by 12
Answer:
12
Step-by-step explanation:
Here is what you have defined:
(36+ (18 x 6) ÷ 12
(36 + 108) / 12
144/12
12
HELP ASAP WITH EXPLANATION: If f(x) + f(2 − x) = 4 for all x, find f(y − 2) + f(4 − y)
Answer:
f(y-2)+f(4-y)=4
Step-by-step explanation:
Assume (let) x=y-2
So: y=x+2
f(y-2)+f(4-y)=f(x)+f(-x+2)=f(x)+f(2-x)
The value of that expression is 4 from the given.
Compare your response to the sample response. Which of these did your response include? Check all of the boxes that apply.
The real number is on the number line, but the complex number is in the complex plane.
Both are distances.
Both are positive values.
The distance formula or the Pythagorean theorem is used to calculate the absolute value of a complex number.
The responses include:
The real number is on the number line, but the complex number is in the complex plane.Both are distances.Both are positive values.How to illustrate the information?In mathematics, a real number simply means a value of a continuous quantity which can represent a distance along a line.
In this case, real numbers are the numbers that include both rational and irrational numbers. Here, Rmrational numbers such as integers (-2, 0, 1), fractions(1/2, 2.5) and the irrational numbers such as √3, π(22/7), etc., are all real numbers.
In conclusion, the correct options are A, B, and C.
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Write the equation y=-3x+3 in function notation using f(x) to denote the function.
The function notation form of the given equation; y = -3x +3 as in the task content is; f(x) = -3(x) +3.
What is the function notation form of the equation?According to the task content, the equation given; y = -3x +3 is to be written in function notation.
Consequently, since the function expression given is linear in variable X, it follows that the required function notation is;
f(x) = -3x +3.
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Your family borrowed $400,000 from the bank to purchase a new home. If the bank charges 3.8%
interest per year, compounded weekly, it will take 25 years to pay off the loan. How much will each
weekly payment be?
Answer:
472.19
Step-by-step explanation:
$472.19 weekly
Thus the required weekly installment is $402.30 for 25 years.
Given,
The family borrowed $400,000 from the bank to purchase a new home.
the bank charges 3.8% interest per year, compounded weekly, it will take 25 years to pay off the loan. How much will each weekly payment to be determined?
Statistics is the study of mathematics that deals with relations between comprehensive data.
The principle amount to refund = 400,000
Let the principle amount for weekly = P
Rate per year = 3.8%
Tenure = 25 year
For weekly installments,
52 Weeks in a year
Tenure = 25/52
Now,
[tex]Amount = P(1-(1+r)^{-tn})/i\\400000 = P (1-(1+0.038/52)^{-25*52}) / (0.038/52)\\400000 * 0.038/52 = P(1-(52.038)^{-25*52})\\292.30 = P(1-(1.001)^{-1300})\\292.30 = P(1-0.273)\\292.30=P * 0.727\\P = 402.30[/tex]
Thus the required weekly installment is $402.30 for 25 years.
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f(t) = 0.25t2 − 0.5t + 3.5
The resulting value of the function when the values of t is 2 and 6 are 3.5 and 6.5 respectively
Function and valuesFunctions are expressions in form of variables. Given the following quadratic equation expressed as:
f(t) = 0.25t^2 − 0.5t + 3.5
We can find the equivalent value of the function when the value of t a re 2 and 6.
If the value of t is 2. hence;
f(2) = 0.25(2)^2 − 0.5(2) + 3.5
f(2) = 1 - 1 + 3.5
f(2) = 3.5
If the value of t is 6, hence;
f(6) = 0.25(6)^2 − 0.5(6) + 3.5
f(6) = 9 - 3 + 3.5
f(6) = 6.5
Hence the resulting value of the function when the values of t is 2 and 6 are 3.5 and 6.5 respectively
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What is the solution to x2 – 9x < –8? x < 1 or x > 8 x < –8 or x > 1 1 < x < 8 –8 < x < 1
In mathematics a linear inequality is an inequality involving a linear function. A linear inequality contains one of the inequality symbols.< is less than > is greater than ≤ is less than or equal to ≥ is greater than or equal to ≠ is not equal to.
x²− 9x < − 8Let's find the critical points of the inequality.
x² − 9x = − 8x² − 9x −(−8) = − 8 −(−8) (Subtract -8 from both sides)
x² − 9x + 8 = 0(x − 1)(x − 8) = 0 (Factor left side of equation)
x − 1 = 0 or x − 8 = 0 (Set factors equal to 0)
x=1 or x=8Check intervals in between critical points. (Test values in the intervals to see if they work.)x < 1 (Doesn't work in original inequality)
1 < x < 8 (Works in original inequality)
x > 8 (Doesn't work in original inequality)
Answer:1 < x < 8
The third option is the correct one.
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Equivalent fraction statement
Answer:
x=18
Step-by-step explanation:
[tex]\frac{4}{12} =\frac{6}{x} \\[/tex]
[tex]\frac{4}{12}[/tex] ÷ [tex]\frac{2}{2}[/tex] = [tex]\frac{2}{6}[/tex] = [tex]\frac{6}{x}[/tex]
[tex]\frac{2}{6} = \frac{6}{x}[/tex]
2×3 =6
6×3=18
x=18
Describe the translation.
y=(x−5)2+5 → y=(x−0)2+0
A. T<−5,5>
B. T<5,−5>
C. T<−5,−5>
D. T<5,5>
Answer:
C
Step-by-step explanation:
This is a translation 5 units left and 5 units dowh.
Here, the translation is [tex]T < 5,-5 >[/tex].
What is translation?The translation is a coordinate transformation operation in which a point or a figure moves left/right/up or down in a coordinate system or a set of axes. After applying translation, the size of the figure remains unchanged, just the position changes. For example, consider a function [tex]y=f(x)[/tex]. If we translate it to the new function [tex]y'=f(x+a)+b[/tex], then the graph of [tex]y[/tex] moves [tex]a[/tex] units to the right and [tex]b[/tex] units to the up and in this case the translation is denoted by [tex]T < a,b >[/tex]Here, the translation is given as: [tex]y=2(x-5)+5\longrightarrow y=2(x-0)+0[/tex].
i.e. [tex]y=2(x-5)+5\longrightarrow y=2(x-5+5)+(5-5)[/tex].
So, the graph of [tex]y[/tex] moves 5 units to the right and (-5) units to the up i.e., 5 units to the down.
Therefore, here, the translation is [tex]T < 5,-5 >[/tex].
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Which function best fits the following points?
A.=-12.84032+0.0225x
O B. y=65.0778-772.9605*
O C. y=-197.0571x2+ 245.6243x + 6.0321
O D. None of the above
The function that best fits the graph points is; B: y = 65.0778 * 772.9605ˣ
How to Interpret Function Graphs?
From the given graph, we can see that is parabolic form and as such we can say it is an exponential function.
Looking at the options, only option B is in exponential form and as such, we will take one point on the graph to check if this is the right function.
Let us use the coordinate (0.9, 26000)
y = 65.0778 * 772.9605ˣ
y = 65.0778 * 772.9605^(0.9)
y = 25837.76
This is very close and as such is the correct option.
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