y=2x+1 when x=7, substitute the x value=7 in the given rule. y=2*7+1 =14+1 =15 That is when the input is 7, the output is 15. To predict the output when input is 31/2, for that, you just put the value x=31/2 in the given rule that is, y = 2 * 31/2 +1 = 31 + 1= 32 That is when the inputis 31/2, the out put is 32Relation with monomials. Given a monomial equation =, taking the logarithm of the equation (with any base) yields: = + . Setting = and = , which corresponds to using a log-log graph, yields the equation: = + where m = k is the slope of the line and b = log a is the intercept on the (log y)-axis, meaning where log x = 0, so, reversing the logs, a is the y value corresponding(a) Show that the utility function v(x;y) = 10x + 10y represent the same preferences with u, that is, v and u are monotonic transformations of each other. Solution: Arbitrarily pick two bundles x = (x 1;x 2) and y = (y 1;y 2), and show that both u and v represent the same preference relation. Assume that x ˜y, then u(x 1;x 2) > u(y 1;y 2Q. Linear function y=x is graphed on a coordinate plane. The graph of a new line is formed by changing the slope of the original line to ½ and the y-intercept to 6. Which statement about the relationship between these two graphs is true?Which graph represents the same relation as the rule y = 2x, for all real numbers x? ch 6) A 5 4 3 2 1 2 3 4 5 x 1
Log-log plot - Wikipedia
A rule of thumb reminds us that when we have a positive symbol before x 2 we get a happy expression on the graph and a negative symbol renders a sad expression. The vertical line that passes through the vertex and divides the parabola in two is called the axis of symmetry.Which function represents the same relationship? answer choices . h(x) = -3x - 10.5 . h(x) = -x - 3.5 . h(x) = 3x - 10.5 . All real numbers greater than or equal to 0 and less than or equal to 28. Which graph represents a function with a domain of all real numbers greater than or equal to -7 and less than 2?Does the graph represent y as a function of x? A) C) B) D) 28) Yes, because for every x-value there is only one y-value. Yes, because for every y-value there is only one x-value. No, because there are two y-values for the same x-value. No, because there are two x-values for the same y-value. 17Example 4 Graph x . y. Solution First graph x = y. Next check a point not on the line. Notice that the graph of the line contains the point (0,0), so we cannot use it as a checkpoint. To determine which half-plane is the solution set use any point that is obviously not on the line x = y. The point ( - 2,3) is such a point.
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If the relation is not a function the graph contains at least two points with the same x-coordinate but with different y-coordinates. The relation portrayed in the graph to the left shows a function whereas the relation in the graph to the right is not a function since the vertical line is crossing the graph in two points.Now that we can find the inverse of a function, we will explore the graphs of functions and their inverses. Let us return to the quadratic function [latex]f\left(x\right)={x}^{2}[/latex] restricted to the domain [latex]\left[0,\infty \right)[/latex], on which this function is one-to-one, and graph it as in Figure 7.Which graph represents the same relation as the rule y = 2x, for all real numbers x? C. Given f(x)=10-2x find f(7).-4 3 7 56-4. Given b(x)=|x+4|, what is b(-10)? 6. Which table represents the same relation as the set {(-6,4),(-4,0).(-3,2).(-1,2)} B. Given h(f)=-2(t+5)^2+4, find h(-8)-334-14 45 445-14. Which graph represents the same relation asplease help.. j Graph h(x) = 2 sin (2x) - 3. Use 3.14 for it. Use the sine tool to graph the function. The first point must be on the midline and the … second point must be a maximum or minimum value on the graph closest to the first point.Graph y=2x. Use the slope-intercept form to find the slope and y-intercept. Tap for more steps... The slope-intercept form is , To find the x-intercept (s), substitute in for and solve for . Solve the equation. Tap for more steps... Rewrite the equation as . Divide each term by and simplify.
The formulation for the quantity of a sphere is V=3/4πr^3 What is the system solved for r?
C
When 10b=5(c+2) is solved for c, one equation is Which of the following is an identical equation to seek out c?
…
Which graph represents the same relation as the rule y = 2x, for all real numbers x?
C
Given f(x)=10-2x find f(7).-43756
-4
Given b(x)=|x+4|, what is b(-10)?
6
Which desk represents the same relation as the set (-6,4),(-4,0).(-3,2).(-1,2)
B
Given h(f)=-2(t+5)^2+4, in finding h(-8)-334-1445445
-14
Which graph represents the same relation as the set
(-3,2).(5,5).(3,3).(3-2)
Which relation underneath represents a one-to-one function?
D
Which graph represents the same relation as the desk under?
D
What is the vary of the serve as graphed below?
-3<y≤3
In which function is x = 2 mapped to 32?
B
The domain of f(x) is the set of all real values except for 7, and the domain of g(x) is the set of all real values excluding -3. Which of the following describes the domain of (G*f)(x)
D
If h(x) = x – 7 and g(x) = x2, which expression is identical to (g*h)(5)?(5 – 7)2(5)2 – 7(5)2(5 – 7)(5 – 7)x2
(5 – 7)^2
If s(x) = x – 7 and t(x) = 4×2 – x + 3, which expression is similar to (t*s)(x)?4(x – 7)2 – x – 7 + 34(x – 7)2 – (x – 7) + 3(4×2 – x + 3) – 7(4×2 – x + 3)(x – 7)
4(x – 7)^2 – (x – 7) + 3
If f(x) = x2 + 1 and g(x) = x – 4, which price is equivalent to (f*g)(10)?3797126606
37
If g(x)=x+1/x-2 and h(x) = 4 – x, what is the worth of (g*h)(-3)?
8/5
If m(x)=x+5/x-1 and n(x)=x-3, which function has the same domain as (m*n)(x)
h(x)=11/x-4
If g(x)=2x and (f*g)(x)=3/x, what's f(x)
f(x)=6/x
If (z*z)(x)=1/16x, what is z(x)
z(x)=x/4
If h(x) = 5 + x and ok(x)=1/x, which expression is similar to (okay*h)(x)?
1/(5+x)
If f(x)=x-3/x and g(x)=5x-4, what is the area of (f*g)(x)?
x≠4/5
Which observation could be used to give an explanation for why the serve as h(x) = x3 has an inverse relation that is also a function?The graph of h(x) passes the vertical line test.The graph of the inverse of h(x) is a vertical line.The graph of the inverse of h(x) passes the horizontal line test.The graph of h(x) passes the horizontal line take a look at.
The graph of h(x) passes the horizontal line take a look at.
If f(x) and g(x) are inverse functions of one another, which of the following shows the graph of f(g(x))?
B.
If f(x) = 5x, what is f-1(x)?
C.
If f(x) = 3x and g(x)=1/3x which expression might be used to make sure that g(x) is the inverse of f(x)?
C. 1/3(3x)
Which graph presentations a function whose inverse could also be a serve as?
A.
Which serve as is the inverse of f(x) = 2x + 3?
B.
Which function has an inverse that also is a serve as?(-1, -2), (0, 4), (1, 3), (5, 14), (7, 4)(-1, 2), (0, 4), (1, 5), (5, 4), (7, 2)(-1, 3), (0, 4), (1, 14), (5, 6), (7, 2)(-1, 4), (0, 4), (1, 2), (5, 3), (7, 1)
C. (-1, 3), (0, 4), (1, 14), (5, 6), (7, 2)
Which commentary could be used to provide an explanation for why f(x) = 2x – Three has an inverse relation that is a serve as?The graph of f(x) passes the vertical line check.f(x) is a one-to-one serve as.The graph of the inverse of f(x) passes the horizontal line take a look at.f(x) isn't a serve as.
B. f(x) is a one-to-one serve as.
If f(x) and f-1(x) are inverse purposes of each other and f(x)=2x+5 what's f-1(8)?
B. 3/2
If f(x)=5x-25 and g(x)=1/5x+5
C.
The axis of symmetry of a quadratic equation is x = -3. If considered one of the zeroes of the equation is 4, what's the different zero?-10-7-6-4
-10
What is the vertex and the equation of the axis of symmetry of the graph of Y=x^2-6x-7?vertex: (-16, 3)a.o.s: x = -16vertex: (-3, 20)a.o.s: x = -3vertex: (3,-16)a.o.s: x = 3vertex: (20, -3)a.o.s: x = 20
vertex: (3,-16) a.o.s: x = 3
What is the equation of the axis of symmetry of the graph of y=ax^2+bx+c
x=-b/2a
What is the vertex of the graph of y = x2 + 4x?(-2, -12)(-2, -8)(-2, -6)(-2, -4)
(-2, -4)
Which serve as is a quadratic function?h(t) = 12 – 8t + 6t3g(t) = 7t2 + 3t3 + 2tk(t) = 3t4 + 3t2 + 4h(t) = 12 – t + 6t2
h(t) = 12 – t + 6t2
What is the axis of symmetry for the graph of y – 4x = 7 – x2 ?x = 2y = 2x = 11y = 11
x = 2
The path of a football kicked by a field purpose kicker can be modeled via the equation y = -0.04×2 + 1.56x, where x is the horizontal distance in yards and y is the corresponding height in yards. What is the approximate maximum peak of the soccer?15.21 yd19.5 yd38.ninety four yd45.sixty three yd
15.21 yd
The peak of a baseball hit from a bat is modeled by a quadratic function of time, h(t). What does the 2nd coordinate of the vertex of the quadratic serve as constitute?the minimum peak of the baseballthe time at which the baseball hits the groundthe time at which the baseball hits the maximum heightthe most height of the baseball
the most top of the baseball
The function C(x) = 400x – 0.2×2 represents the general prices for a company to supply a product, where C is the overall price in dollars and x is the choice of gadgets bought. Which remark is true?One thousand gadgets have the minimal cost of 0,000.One thousand devices have the maximum price of 0,000.Two thousand devices have the minimum value of 0,000.Two thousand gadgets have the most cost of 0,000.
One thousand gadgets have the most cost of 0,000.
The value, C, to supply b baseball bats in step with day is modeled via the function C(b) = 0.06b2 – 7.2b + 390. What selection of bats must be produced to stay prices at a minimum?27 bats60 bats174 bats390 bats
60 bats
A rectangular patio is Nine toes by 6 ft. When the length and width are greater via the same amount, the house turns into 88 squareft. Ginger is using the zero product belongings to solve the equation (6 + x)(9 + x) = 88. What do her solutions constitute?one imaginable duration and one conceivable widthtwo possible quantities for the widthstwo possible quantities for the lengthstwo conceivable amounts via which the dimensions were higher
two conceivable quantities by which the dimensions have been higher
The benefit an organization makes from generating x tabletops is modeled by means of the equation P(x) = 480x – 2×2. For what choice of tabletops does the company make a benefit of [scrape_url:1]
{title}
{content}
[/scrape_url]?100 tabletops120 tabletops240 tabletops480 tabletops240 tabletops
The sq. of Nine not up to a number is 3 less than the quantity. What is the quantity?-12 or 7-12 or -7-7 or 127 or 12
7 or 12
The square of a number is 12 less than 7 times the number. What is the number?-Four or -3-Four or 3-Three or forty three or 4
Three or 4
What are the answers to the equation (x – 6)(x + 8) = 0?x = -6 or x = 8x = -6 or x = -8x = 6 or x = -8x = 6 or x = 8
x = 6 or x = -8
Lisa is using the equation x2 + (x – 5)2 = 157 to seek out two numbers that vary by means of 5 and that experience squares that sum to 157. When Lisa solves the problem the usage of the zero product belongings, what do the two solutions represent?two numbers that vary by way of 5 and squares that have a sum of 157one conceivable quantity is 5 less than the different numberone conceivable quantity that can be used to search out numbers that range by Five and squares that experience a sum of 157two possible numbers that can be used to search out numbers that differ by 5 and squares that have a sum of 157
two conceivable numbers that can be used to seek out numbers that vary by Five and squares that experience a sum of 157
What are the answers to the equation 3(x – 4)(x + 5) = 0?x = -Four or x = 5x = 3, x = 4, or x = -5x = 3, x = -4, or x = 5x = 4 or x = -5
x = Four or x = -5
A rectangular deck is 12 ft by way of 14 ft. When the period and width are increased through the same amount, the house turns into 288 sq. toes. By how much were the dimensions increased?2 ft4 ft8 ft10 ft
Four ft
The solutions to a quadratic equation are x = 2 and x = 7. If ok is a nonzero constant, which of the following must be equivalent to the quadratic equation?
ok(x-2)(x-7)=0
The solutions to the equation 2x^2+x-1=2 are x=-3/2 or
x=1
What is the answer set of the quadratic inequality 6x^2+1≤0?
slashed out 0
What are the answers to the inequality (x-3)(x+5)≤0
-5≤x≤3
What is the solution set to the inequality (4x-3)(2x-1)≥0?
x
An acorn falls from the branch of a tree to the ground 25 toes beneath. The distance, S, that the acorn is from the flooring as it falls is represented by the equation S(t) = -16t2 + 25, where t is the number of seconds. For which interval of time is the acorn transferring thru the air?
0<t≤5/4
What is the answer set of the quadratic inequality 4(x + 2)2≤0
x=-2
What is the resolution set of the quadratic inequality f(x)≥0?
xER
The graph below represents the solution set of which inequality?-4 to 2
x2 + 2x – 8 < 0
Greg is in a automobile at the top of a roller-coaster experience. The distance, d, of the automotive from the flooring as the car descends is determined by means of the equation d = 144 – 16t2, where t is the choice of seconds it takes the automotive to travel all the way down to each point on the ride. For which period of time is Greg's automotive moving in the air?
0<t<3
Reyna runs a textile corporate that manufactures T-shirts. The profit, p, made by means of the corporate is modeled via the serve as p=s2+9s-142, the place s is the choice of T-shirts offered. How many T-shirts must be sold to earn a benefit of more than
{title}
{content}
,000?s > 42
If f(x) = x3 – 2×2, which expression is an identical to f(i)?-2 + i-2 – i2 + i2 – i
2 – i
Which complex quantity is represented by means of the point graphed on the advanced aircraft beneath?
3 – 4i
In which quadrant is the number -14 – 5i located on the complicated aircraft?IIIIIIIV
III
If f(x) = 1 – x, which worth is identical to |f(i)|?
sqr2
if i=sq.-1 what's the value of i3
-i
If the complicated quantity x = 3 + bi and |x|2 = 13, which is a possible worth of b?
2
Which of the following is identical to 18-sq.-25
18-5i
Which complicated quantity has a distance of sqr17 from the foundation on the complicated aircraft?
4 – i
What is the sq. root of -1?-ii-11
i
Which complex number has an absolute value of 5?-3 + 4i2 + 3i7 – 2i9 + 4i
-3 + 4i
equation
x2 – 2x – 4 = 0
Using the quadratic method to unravel 7×2 – x = 7, what are the values of x?
B
What is the discriminant of 9×2 + 2 = 10x?-356-1722872
28
Equation
3×2 – 10x – 1 = 0
What is the discriminant of 3x^2-10x=-2?
76
If x = -3 is the simplest x-intercept of the graph of a quadratic equation, which statement perfect describes the discriminant of the equation?
The discriminant is 0.
If the discriminant of a quadratic equation is equal to mc027-1.jpg, which remark describes the roots?There are two complex roots.There are two real roots.There is one real root.There is one advanced root.
There are two complicated roots.
Which equation shows the quadratic formula used accurately to resolve 5×2 + 3x – 4 = 0 for x?
A
If x=6 is the best x-intercept of the graph of a quadratic equation, which commentary highest describes the discriminant of the equation?
The discriminant is 0.
What is the discriminant of 3×2 + 6x = 2?12184260
60
Which pair of equations generates graphs with the same vertex?y = -(x + 4)2 and y = (x – 4)2y = -4×2 and y = 4×2y = -x2 – 4 and y = x2 + 4y = (x – 4)2 and y = x2 + 4
y = -4×2 and y = 4×2
Which equation is y = 6×2 + 12x – 10 rewritten in vertex shape?y = 6(x + 1)2 – 11y = 6(x + 1)2 – 10y = 6(x + 1)2 – 4y = 6(x + 1)2 – 16
y = 6(x + 1)2 – 16
Which word perfect describes the translation from the graph y = 6×2 to the graph of y = 6(x + 1)2?6 unit left6 unit right1 unit left1 unit proper
1 unit left
Which word highest describes the translation from the graph y = 2(x – 15)2 + 3 to the graph of y = 2(x – 11)2 + 3?Four devices to the left4 units to the right8 gadgets to the left8 gadgets to the proper
Four gadgets to the left
Which equation has a graph that could be a parabola with a vertex at (-2, 0)?y = -2×2y = (x + 2)2y = (x – 2)2y = x2 – 2
y = (x + 2)2
Which equation has a graph that is a parabola with a vertex at (5, 3)?y = (x – 5)2 + 3y = (x + 5)2 + 3y = (x – 3)2 + 5y = (x + 3)2 + 5
y = (x – 5)2 + 3
Which equation has a graph that may be a parabola with a vertex at (-1, -1)?y = (x – 1)2 + 1y = (x – 1)2 – 1y = (x + 1)2 + 1y = (x + 1)2 – 1
y = (x + 1)2 – 1
What is the first step when rewriting y = -4×2 + 2x – 7 in the form y = a(x – h)2 + ok?2 must be factored from 2x – 7-Four must be factored from -4×2 + 2xx will have to be factored from -4×2 + 2x-Four will have to be factored from -4×2 – 7
-Four should be factored from -4×2 + 2x
What is the first step when rewriting y = 3×2 + 9x – 18 in the shape y = a(x – h)2 + okay?Three will have to be factored from 3×2 + 9xx should be factored from 3×2 + 9x9 must be factored from 9x – 183 should be factored from 3×2 – 18
3 must be factored from 3×2 + 9x
What is the first step when rewriting y = 6×2 + 18x + 14 in the shape y = a(x – h)2 + k?Sixteen must be factored from 18x + 14x should be factored from 6×2 + 18x6 must be factored from 6×2 + 146 will have to be factored from 6×2 + 18x
6 should be factored from 6×2 + 18x
Which equation is the inverse of y = 2×2 – 8?
A
Which equation is the inverse of two(x – 2)2 = 8(7 + y)?
D
If the domain of the square root serve as f(x) is mc024-1.jpg, which remark must be true?7 is subtracted from the x-term inside of the radical.The radical is multiplied through a destructive quantity.7 is added to the radical time period.The x-term inside of the radical has a unfavourable coefficient.
The x-term inside of the radical has a adverse coefficient.
What is the domain of the sq. root function graphed below?
D
Which equation is the inverse of y = 100 – x2?
A
Which could be the function graphed beneath?
f(x)=sq. x -2
if f(x)=sq. x-3, which inequality can be used to find the domain of f(x)?
B
What is the domain of the serve as y=sq. x+6-7
B
Which equation will also be simplified to seek out the inverse of y = 5×2 + 10?
A
Which equation will also be simplified to search out the inverse of y = 2×2?
D
Which equation is the inverse of y = 16×2 + 1?
D
Which equation will also be simplified to seek out the inverse of y = x2 – 7?
C
Which equation is the inverse of 5y+4=(x+362+1/2
D
What is the area of the serve as y=sq. x+4
C
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