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How do you solve x2-3x-28 equals 0?
You can use the quadratic formula for an equation of the form a*x^2 + b*x + c = 0. x = (-b +/- sqrt(b^2-4*a*c))/(2*a) In this case: a = 1 b = -3 c = -28 x = (3 +/- sqrt(9 - 4*(-28)))/2 x = (3 +/- sqrt(121))/2 x = (3 +/- 11)/2 x = 7 or -4 Another option is to attempt to simplify the equation into the form (x-a)(x-b) = 0. Sometimes you can do this by observation. For example: 28 = 4*7 7-4 = 3 Thus: (x-7)(x+4)=0 In this case, a and b are known as the "roots" of the equation, with a = 7 and b = -4.
What are factors in an expression?
Factors aremultiplicativeterms (i.e., they multiply into all the terms). The easiest way to see this is by example.Example 1:a(b+cd)a is a factor and (b+cd) is a factorExample 2:x2 - 9 = (x-3)(x+3)(x-3) is a factor and (x+3) is a factorHopefully you are beginning to notice you can always wrap parenthesis around a factor without altering the order of operations.Example 3:2a(b)(9n-x)+8This is a trick one, but you can factor out a 2:2a(b)(9n-x)+8 = (1)(2)a(b)(9n-x)+(4)(2) = (2)(ab(9n-x)+4)The factors are: 2 and (ab(9n-x)+4)Example 4:If that +8 wasn't on example 3, what would the factors be?2a(b)(9n-x)They would be:2, a, b, and (9n-x)
Which equation describes the line with a slope of 2 and contains the point (4-3)?
The equation of a line with slope m through a point (x0, y0) has equation: y - y0 = m(x - x0) Thus the equation of the line with slope 2 through the point (4, -3) has equation: y - (-3) = 2(x - 4) → y + 3 = 2x - 8 → y = 2x - 11
How do you write the equation of the line in standard form through 4 and 0 and 0 and 3?
In y=mx + b form, y = (-3/4)x - 3 - Found the slope (m) to be -3/4 - Substituted slope and a point into y = mx + b to find y-intercept (b). - b = - 3 , Substitute b and m into y=mx+b
In chest A there are three times as many coins as in chest b altogether there are 120 coins how many coins are there in chest B?
there are 30 coins in chest B...3/4 of the total are in A and 1/4 of the total are in B. So you divide 120 by 4 and get 30. So 30 x 3 = 90 = A, and 30 x 1 = 30 = B
Is 3 over 4 x b the same as 3xb qver 4?
It is difficult to answer the question because it is still ambiguous. Putting brackets in helps. So: (3 over 4) x b = 3/4*b = 3*b / 4 YES but 3 over (4 x b) = 3/(4*b) is not 3/4*b
What is 4 x b x b x b?
The expression 4 x b x b x b simplifies to 4b^3. This is because when you multiply the coefficients 4 and 1, you get 4. When you multiply the variables b, b, and b, you add the exponents, resulting in b^3. Therefore, 4 x b x b x b equals 4b^3.
How do you solve x2-3x-28 equals 0?
You can use the quadratic formula for an equation of the form a*x^2 + b*x + c = 0. x = (-b +/- sqrt(b^2-4*a*c))/(2*a) In this case: a = 1 b = -3 c = -28 x = (3 +/- sqrt(9 - 4*(-28)))/2 x = (3 +/- sqrt(121))/2 x = (3 +/- 11)/2 x = 7 or -4 Another option is to attempt to simplify the equation into the form (x-a)(x-b) = 0. Sometimes you can do this by observation. For example: 28 = 4*7 7-4 = 3 Thus: (x-7)(x+4)=0 In this case, a and b are known as the "roots" of the equation, with a = 7 and b = -4.
How do you divide two numbers that are in scientific notation?
For example, (4.1076 x 10^3)/(2.8 x 10^4) = (4.1076/2.8) x [10 ^(3 - 4)] = 1.467 x 10^-1 or (4.1076 x 10^3)/(2.8 x 10^-4) = (4.1076/2.8) x [10 ^(3 - -4)] = 1.467 x 10^7
What is the sum of the prime factors of 81?
As a product of its prime factors: 3*3*3*3 = 81 and 4*3 = 12
What is 3 x a x a x 4 x b?
The result would be 12a2b.
How to solve x to the third times x to the fourth?
Use x^a * x^b = x^(a+b). x^3 * x^4 = x^7
What property is (4 3) 12 12 (4 3)?
a(b + c) = ab + ac 4 x 53 = 4(50 + 3) = (4 x 50) + (4 x 3) = 200 + 12 = 212
What is the exponent form for 2x2x2x2?
A number a multiplied b times (so a x a is b=2, a x a x a is b=3, a x a x a x a is b = 4, and so on) is written as ab. Since 2 is multiplied 4 times, you have 24.
What is the value of B minus a If the function f is defined by f x X2 plus ax plus b where a and b are constants In the xy plane thr graph of f intersects the x-axis of the two points 1 0 and 3 0?
Since the function ( f(x) = x^2 + ax + b ) intersects the x-axis at the points (1, 0) and (3, 0), these points are the roots of the equation. Thus, we can express the function as ( f(x) = (x - 1)(x - 3) = x^2 - 4x + 3 ). Comparing coefficients, we find ( a = -4 ) and ( b = 3 ). Therefore, ( B - a = 3 - (-4) = 3 + 4 = 7 ).
A florist has 6 banksias 5 wattles and 4 waratahs all the flowers of each kind are different. In how many ways can she make a bunch of 10 flowers if she has to use at least 3 of each kind. 1200?
Must split 4-3-3. Banksia: 3 from 6 = 20, 4 from 6 = 15 Wattles: 3 from 5 = 10, 4 from 5 = 5 Waratahs: 3 from 4 = 4, 4 from 4 = 1 Possible combinations: 4 x B, 3 x each W: 15 x 10 x 4 = 600 4 x Wat, 3 each B & War: 5 x 20 x 4 = 400 4 x War, 3 each B & Wat: 1 x 20 x 10 = 200 Your 1200 is correct.
What are factors in an expression?
Factors aremultiplicativeterms (i.e., they multiply into all the terms). The easiest way to see this is by example.Example 1:a(b+cd)a is a factor and (b+cd) is a factorExample 2:x2 - 9 = (x-3)(x+3)(x-3) is a factor and (x+3) is a factorHopefully you are beginning to notice you can always wrap parenthesis around a factor without altering the order of operations.Example 3:2a(b)(9n-x)+8This is a trick one, but you can factor out a 2:2a(b)(9n-x)+8 = (1)(2)a(b)(9n-x)+(4)(2) = (2)(ab(9n-x)+4)The factors are: 2 and (ab(9n-x)+4)Example 4:If that +8 wasn't on example 3, what would the factors be?2a(b)(9n-x)They would be:2, a, b, and (9n-x)
