A triangle has a base of (2 - x) cm and a height of (2x + 6) cm. What is the maximum area of the triangle? What value of x will produce the maximum area? (Hind: find an expression for the area first.)

Q: A playground is (x+7) units long and (x+3) Units way. If a square of side x is sectioned off from…

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Q: Use the graph of fAx) = -x +3x-4 to identify the values of x for which (x) = 0 and to factor Ax) %3!

A: In this question given that a function f(x) and we find its factor and also find value of x.  Here i…

Q: State the number of solutions for the polynomial. f (2) = 26 - a4- 25x? +24

A: The polynomial is given by f(x) = x6-x4-25x2+24 To evaluate : The number of solutions for the…

Q: Find the number in (-5≤x≤1) such that the sum of thrice the number and its square is a maximum.…

A: let the x be the number in the  interval [-5,1]

Q: 3. Find the quotient and the remainder for (x4 + 8x² − 6x − 3 ) ÷ (x+2).

A: 3. A polynomial p(x) can be written as p(x)=q(x)d(x)+r(x)⇒p(x)d(x)=q(x)+r(x)d(x) Where, d(x) is…

Q: Find the maximum and minimum value of the expression x² - x + 7 = 0.

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Q: List the zeros of y (x + 7)(5x + 6). If you have more than one solution, separate them with commas,…

A: The zero product property states that if a·b=0, then either a=0 or b=0.

Q: A soft-drink vendor at a popular beach analyzes his sales records and finds that if he sells x cans…

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Q: i have a question about the step by step of 0= -x2+4x-5 using the quadratic formula

A: Consider the quadratic equation, -x2+4x-5=0 To solve the given equation,…

Q: A soft-drink vendor at a popular beach analyzes their sales records and finds that if they sell x…

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Q: . The polynomial 3x3 + mx2 - nx – 10 has a factor of x - 1. When divided by  x + 2, the remainder is…

A: given that x-1 is factor

Q: What is the value of the discriminant for this quadratic: + 4 = y 4 O 16 O-4 August

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Q: 2. Is the expression 4x³ – 3.6x? – V2 a polynomial? If so, what is its degree?

A: Let p(x)=4x3-3.6x2-2. The general form of a 3 degree polynomial with real coefficients is given by…

Q: Suppose a rectangle has a perimeter of 60 cm. If the rectangle as a length of 16 cm, what is its…

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Q: A rectangular prism has a volume of 8x3+14x2+x-2 and a height of 2x+1.Find the expression which…

A: We know that volume = base*height So, base= volume / height=(8x3+14x2+x-2)/(2x+1)

Q: A cubed - shaped box has a volume of 27in^3.If the size of the box is increased, the volume, in…

A: The volume of cube = 27 in3 New volume = x+27 where x = 30 New volume = 30+27 = 57 in3

Q: Marcus states that the polynomial expression 3x3 – 4x2y + y3 + 2 is in standard form. Ariel states…

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Q: find the vertex for ƒ (x) = æ² – 6x + 13.

A: We have to find

Q: Find zeros for :  x^3-12x^2+36x

A: First we factor gcf x.

Q: A rectangular poster has dimensions (2x-1) by (3x+2). Two congruent squares are cut out of the…

A: Let length of one side of rectangle be (2x-1) and length of other side be (3x+2). Two congruent…

Q: 9) Is x-2 a factor of x3 – 13x + 12?

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Q: Simplify the polynomial. 3x² – 2x² + 4x – x² + x - -3x2 + 5x 6х? - 5х 5x

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Q: What is the value of n to show that (x - 7) is a factor of 2x3 - 13x2 - 10x + n?

A: Given- 2x3-13x2-10x+n To find-  The value of n as x-7 is a factor of the above expression. Concept…

Q: find the constant term of (2x² + 1/x)⁹

A: find the constant term of (2x² + 1/x)⁹

Q: find all the zeroes x^4-6x^2-7x-6=0

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Q: A soft-drink vendor at a popular beach analyzes his sales records and finds that if he sells x cans…

A:

Q: A rectangle has its two lower corners on the x-axis and its two upper corners on the curve y = 64 –…

A: Given that: y=64-x2

Q: Show the proper algebraic steps to 2x+4 = 4x. %3D

A: According to the question, we have to solve the algebraic expression 2x+4=4x and find the value of…

Q: If f(x) = 3x2 + βx + 4 and f(−1) = 12, what is the value of β? Show that If 2 is a root of  kx4 -…

A: Given  f(x) = 3x2 +βx + 4 f(-1) = 12 β = ? f(-1) = 3(-1)2 + β(-1) +4 = 12            3(1) -β +4 = 12…

Q: One of the zeroes of the polynomial 2x2+7x-4 is

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Q: Solve the polynomial inequality: 4(x+4)(x+6)(x−5)≥0  What do I do with the beginning number 4? do i…

A: This is the question of inequality and we solve it for the variable x. But we get x in interval.

Q: Is 5 a root of x* 5x' + 8x– 40? Is (x + 1) a factor of x- 1?

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Q: The volume of a rectangular box is x^3+16x^2+83x+140cm^3. The box is (x+5) cm long and (x+7) cm…

A: Solution: Volume of rectangular box = L*W*H  where L=Length of rectangular box W= Width of…

Q: Solve the inequality for real x:  3x – 7 > 5x – 1

A: Given inequality:

Q: When a ball is tossed into the air, the height h is feet of the ball t seconds from the time that…

A: ht=-16t2+80t+4 Comparing with ht=at2+bt+c, we get a=-16, b=80 & c=4 Now maximum value occurs at,…

Q: The profit function, in dollars for a product is given by π(x)=-x3 +76x2-380x-2800 where x is the…

A: Breakeven occurs at 10 means x=10 is a factor of pi(x)

Q: 10) If x = -2 is a zero, what are the other zeros for 3x3 + 10x2 + 4x - 8 = 0? %3D

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Q: Find the factor of x^2-7x+10

A: We have to find the factor of  x2 - 7x + 10  = x2 - 5x - 2x + 10

Q: The height of a ball (in feet) after t seconds is given by the quadratic: h= -16t^2 +64t+ 60 a) When…

A: topic - quadratic equations a) t=2 seconds b) 124 feet

Q: What is the largest possible value of the quadratic form 5x} + 8x} if x = (x1,x2) and x"x = 1, that…

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Q: 5. If the remainder dividing the polynomial P(x) = 2x³ + kx? + 7x +6 by x- 4 is 114, find the…

A: Quotient Remainder theorem  The answer after we divide one number by another. dividend ÷ divisor =…

Q: A student attempted to solve the inequality x+4/x-3< 0 by multiplying both sides of the inequality…

A: Given, a The inequality   x+4x-3≤0   ⇒x+4x-3×x-3≤0×x-3  ⇒x+4≤0  ⇒x≤-4  We have to find the…

Q: Find the second derívate of x Fx=-8/square root of 3x+6

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Q: List the zeros of y = (x + 5)(4x + 7). If you have more than one solution, separate them with…

A: We have to find zeros of the given function or polynomial: y=x+54x+7 To find the zeros of any…

Q: the area of a rectangle is (4x^4-4x^3+15x^2-3x+9) square centimeters its length is (x^2-x+3)cm find…

A: Solve the following

Q: The quadratic expression 4x – 7x – 2 represents the area of a rectangular garden. What expression…

A: The expression which represents the area of the rectangular garden is given by 4x2-7x-2 To evaluate…

Q: Use the graph of the polynomial function to solve the inequality. 2x3 + 11x2 &lt; 7x + 6

A: Combine all the terms on the left hand side of the inequality: 2x3+11x2&lt;7x+6               The…

Q: The number of tickets sold each day for an upcoming performance of Handel's Messiah is given by N(x)…

A: We use second derivative test to find out number of days where tickets sell at peak

Equations and Inequations

Equations and inequalities describe the relationship between two mathematical expressions.

Linear Functions

A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.