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mathematics
basic technical mathematics

Questions and Answers of Basic Technical Mathematics

Solve the given quadratic equations by completing the square.3y2 = 3y + 2
Use a calculator to solve the given equations. Round solutions to the nearest hundredth. If there are no real roots, state this.4R2 = 12 − 7R
Solve the given quadratic equations by using the quadratic formula.6x2 = 28 − 2x
Solve the given quadratic equations using the quadratic formula. If there are no real roots, state this as the answer.20r2 = 20r + 1
Solve the given quadratic equations by factoring.9 = a2x2
Solve the given quadratic equations by completing the square.8x2 + 2x = 6
Use a calculator to solve the given equations. Round solutions to the nearest hundredth. If there are no real roots, state this.6w − 15 = 3w2
Solve the given quadratic equations by using the quadratic formula.2x2 − x = 36
Solve the given quadratic equations using the quadratic formula. If there are no real roots, state this as the answer.s2 = 9 + s(1 − 2s)
Solve the given quadratic equations by factoring.12m2 = 3
Use a calculator to solve the given equations. Round solutions to the nearest hundredth. If there are no real roots, state this.x(2x − 1) = −3
Solve the given quadratic equations by completing the square.2s2 + 5s = 3
Solve the given quadratic equations by using the quadratic formula.1 + 7D = D2
Solve the given quadratic equations using the quadratic formula. If there are no real roots, state this as the answer.2d(d − 2) = −7
Solve the given quadratic equations by factoring.15L = 20L2
Use a calculator to solve the given equations. Round solutions to the nearest hundredth. If there are no real roots, state this.2t2 = 7t + 4
Solve the given quadratic equations by completing the square.12 = 8Z − Z2
Solve the given quadratic equations by using the quadratic formula.m2 + 2m = 6
Solve the given quadratic equations using the quadratic formula. If there are no real roots, state this as the answer.5t2 + 3 = 7t
Solve the given quadratic equations by factoring.40x − 16x2 = 0
Use a calculator to solve the given equations. Round solutions to the nearest hundredth. If there are no real roots, state this.−3x2 + 9x − 5 = 0
Solve the given quadratic equations by using the quadratic formula.x2 + 3x − 18 = 0
Solve the given quadratic equations using the quadratic formula. If there are no real roots, state this as the answer.62x + 63 = 40x2
Solve the given quadratic equations by completing the square.v(v + 4) = 6
Solve the given quadratic equations by factoring.x2 + 30 = 11x
Use a calculator to solve the given equations. Round solutions to the nearest hundredth. If there are no real roots, state this.5 − x2 = 0
Solve the given quadratic equations by completing the square.(R + 9)(R + 1) = 13
Solve the given quadratic equations by using the quadratic formula.x2 − 4x − 96 = 0
Solve the given quadratic equations using the quadratic formula. If there are no real roots, state this as the answer.30y2 + 23y − 40 = 0
Solve the given quadratic equations by factoring.R2 + 12 = 7R
Use a calculator to solve the given equations. Round solutions to the nearest hundredth. If there are no real roots, state this.2x2 − 7 = 0
Solve the given quadratic equations by completing the square.n2 = 6n − 4
Solve the given quadratic equations by factoring.6π2x2 = 8 − 47πx
Solve the given quadratic equations using the quadratic formula. If there are no real roots, state this as the answer.2 + 6v = 9v2
Solve the given quadratic equations by factoring.x2 + x − 6 = 0
Sketch the graph of each parabola by using the vertex, the y-intercept, and two other points, not including the x-intercepts. Check the graph using a calculator.y = −3x2 − x
Solve the given quadratic equations by completing the square.t2 + 5t − 6 = 0
Solve the given quadratic equations by factoring.4B2 = 8B + 21
Solve the given quadratic equations by factoring.x2 − 5x − 14 = 0
Solve the given quadratic equations using the quadratic formula. If there are no real roots, state this as the answer.z + 2 = 2z2
Sketch the graph of each parabola by using the vertex, the y-intercept, and two other points, not including the x-intercepts. Check the graph using a calculator.y = −2x2 − 2x − 6
Solve the given quadratic equations by completing the square.D2 + 3D + 2 = 0
Solve the given quadratic equations by factoring.23n + 35 = 6n2
Solve the given quadratic equations using the quadratic formula. If there are no real roots, state this as the answer.3x2 = 3 − 4x
Solve the given quadratic equations by factoring.2x2 = 0.32
Sketch the graph of each parabola by using the vertex, the y-intercept, and two other points, not including the x-intercepts. Check the graph using a calculator.s = t2 + 2t + 2
Solve the given quadratic equations by completing the square.x2 − 8x − 20 = 0
Solve the given quadratic equations by factoring.4s2 = 18s
Solve the given quadratic equations using the quadratic formula. If there are no real roots, state this as the answer.3y2 = 3y + 2
Solve the given quadratic equations by factoring.4y2 = 9
Sketch the graph of each parabola by using the vertex, the y-intercept, and two other points, not including the x-intercepts. Check the graph using a calculator.y = 2x2 + 3
Solve the given quadratic equations by completing the square.x2 + 2x − 15 = 0
Solve the given quadratic equations by factoring.3x2 + 5x + 2 = 0
Solve the given quadratic equations using the quadratic formula. If there are no real roots, state this as the answer.4x2 + x = 3
Solve the given quadratic equations by factoring.B2 − 400 = 0
Solve the given quadratic equations by factoring.6t2 = 13t − 5
Solve the given quadratic equations using the quadratic formula. If there are no real roots, state this as the answer.8s2 + 20s = 12
Solve the given quadratic equations by factoring.x2 − 25 = 0
Sketch the graph of each parabola by using the vertex, the y-intercept, and the x-intercepts. Check the graph using a calculator.y = −2x2 − 6x + 8
Solve the given quadratic equations by using the square root property.(y + 3)2 = 7
Solve the given quadratic equations by factoring.11y = 6y2 + 3
Solve the given quadratic equations using the quadratic formula. If there are no real roots, state this as the answer.16V − 24 = 2V2
If y = x2 − 8x + 8, sketch the graph using the vertex and any other useful points and find graphically the values of x for which y = 0.
Determine whether or not the given equations are quadratic. If the resulting form is quadratic, identify a, b, and c, with a > 0. Otherwise, explain why the resulting form is not quadratic.z(z +
Sketch the graph of each parabola by using the vertex, the y-intercept, and the x-intercepts. Check the graph using a calculator.y = x2 + 3x
Solve the given quadratic equations by using the square root property.(x + 2)2 = 10
Solve the given quadratic equations by factoring.3x2 + 11x = 4
Solve the given quadratic equations using the quadratic formula. If there are no real roots, state this as the answer.v2 = 15 − 2v
The perimeter of a rectangular window is 8.4 m, and its area is 3.8 m2. Find its dimensions.
Determine whether or not the given equations are quadratic. If the resulting form is quadratic, identify a, b, and c, with a > 0. Otherwise, explain why the resulting form is not quadratic.y2(y
Sketch the graph of each parabola by using the vertex, the y-intercept, and the x-intercepts. Check the graph using a calculator.y = x2 − 4
Solve the given quadratic equations by using the square root property.(x − 2)2 = 25
Solve the given quadratic equations by factoring.P2 − 27 = 6P
Solve the given quadratic equations using the quadratic formula. If there are no real roots, state this as the answer.x2 + 10x − 4 = 0
Solve by completing the square: x2 = 6x + 9
Determine whether or not the given equations are quadratic. If the resulting form is quadratic, identify a, b, and c, with a > 0. Otherwise, explain why the resulting form is not quadratic.(T −
Sketch the graph of each parabola by using only the vertex and the y-intercept. Check the graph using a calculator.y = −2x2 − 5x
Solve the given quadratic equations by using the square root property.4x2 − 7 = 2
Solve the given quadratic equations by factoring.x2 − 10x + 21 = 0
Solve the given quadratic equations using the quadratic formula. If there are no real roots, state this as the answer.x2 − 5x + 3 = 0
In electricity, the formula P = EI − RI2 is used. Solve for I in terms of E, P, and R.
Determine whether or not the given equations are quadratic. If the resulting form is quadratic, identify a, b, and c, with a > 0. Otherwise, explain why the resulting form is not quadratic.n(n2 +
Sketch the graph of each parabola by using only the vertex and the y-intercept. Check the graph using a calculator.R = v2 − 4v
Solve the given quadratic equations by using the square root property.2y2 − 5 = 1
Solve algebraically: 2x(3 − x) 3 X 2 x + 2 = 1
Solve the given quadratic equations by factoring.x2 + 3x − 10 = 0
Solve the given quadratic equations using the quadratic formula. If there are no real roots, state this as the answer.t2 + 5t − 6 = 0
Sketch the graph of y = 2x2 + 8x + 5 using the extreme point and the y-intercept.
Determine whether or not the given equations are quadratic. If the resulting form is quadratic, identify a, b, and c, with a > 0. Otherwise, explain why the resulting form is not quadratic.x(2x2 +
Sketch the graph of each parabola by using only the vertex and the y-intercept. Check the graph using a calculator.s = 2t2 + 8t − 5
Solve the given quadratic equations by using the square root property.s2 = 15
Solve the given quadratic equations by factoring.x2 + 3x − 4 = 0
Solve the given quadratic equations using the quadratic formula. If there are no real roots, state this as the answer.D2 + 3D + 2 = 0
Determine whether or not the given equations are quadratic. If the resulting form is quadratic, identify a, b, and c, with a > 0. Otherwise, explain why the resulting form is not quadratic.x2 = (x
Determine each of the following as being either true or false. If it is false, explain why.The quadratic formula is -b ± √b². 2a 4ac
Sketch the graph of each parabola by using only the vertex and the y-intercept. Check the graph using a calculator.y = −3x2 + 10x − 4
Solve the given quadratic equations by using the square root property.x2 = 7
Determine each of the following as being either true or false. If it is false, explain why.The graph of y = ax2 + bx + c has a minimum point if a > 0.
Solve the given quadratic equations using the quadratic formula. If there are no real roots, state this as the answer.x2 − 8x − 20 = 0
Make the given changes in the indicated examples of this section and then solve the resulting quadratic equations by completing the square.In Example 3, change the coefficient of the second term from

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