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SAT Math Prep - No Calculator Practice Test 1

Steve Crow・2 minutes read

Substitute K with 3 in the equation X - 1/3 = K to find X as 10, simplify expressions with i and numbers, solve for P in various equations, and determine the values of variables in different scenarios.

Insights

  • When K equals 3 in the equation X - 1/3 = K, substituting K with 3 results in X = 10, showcasing the process of solving for X with a specific value of K.
  • In the loan payment equation M = P(1 + r/n)^(nt), multiplying by the reciprocal yields P = M / (1 + r/n)^(nt), leading to option B as the solution, emphasizing the manipulation required to isolate the variable P.

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Recent questions

  • How can I simplify expressions with variables?

    To simplify expressions with variables, combine like terms by adding or subtracting coefficients of the same variables. Remember to follow the rules of arithmetic operations, such as distributing coefficients and simplifying terms with exponents. By applying these steps, you can simplify complex expressions into a more manageable form.

  • What is the significance of slope in mathematical models?

    The slope in mathematical models represents the rate of change or the steepness of a line. In the context of estimating a boy's height each year, a slope of 3 inches indicates that the height increases by 3 inches annually. Understanding the slope allows for predicting future values based on the established pattern of change, providing valuable insights into the relationship between variables in mathematical models.

  • How can I solve equations with multiple variables?

    To solve equations with multiple variables, use algebraic techniques such as substitution or elimination to isolate one variable and find its value. By systematically manipulating the equations and applying operations to eliminate one variable at a time, you can determine the values of all variables in the system. This approach allows for finding solutions that satisfy all equations simultaneously.

  • What is the formula for calculating loan payments?

    The formula for calculating loan payments is M = P(1 + r/n)^(nt), where M represents the monthly payment, P is the principal loan amount, r is the annual interest rate, n is the number of compounding periods per year, and t is the number of years. By substituting the known values into the formula and solving for the missing variable, you can determine the monthly payment amount for a given loan.

  • How can I determine the value of x in a triangle problem?

    In a triangle problem involving proportional calculations, the value of x can be determined by setting up ratios based on the given information. By establishing proportional relationships between the sides or angles of the triangle, you can use the properties of similar triangles to find the unknown value of x. Applying the concept of proportionality allows for solving geometric problems involving triangles and determining the missing measurements accurately.

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Summary

00:00

Mathematical Equations and Problem Solutions Summarized

  • To find the value of X when K equals 3 in the equation X - 1/3 = K, substitute K with 3, leading to X - 1 = 9, resulting in X = 10.
  • Combining like terms in the expression with i, 7 + (-8) = -1, and 3i + 9i = 12, simplifying the sum.
  • Arman sent M text messages per hour for 5 hours, while Tyrone sent P messages per hour for 4 hours, totaling 5M + 4P messages sent by both.
  • In a phone repair scenario, P = 108 - 23D, with P representing phones left and D days worked, indicating 108 as the initial number of phones.
  • Simplify the expression by changing subtraction to addition, leading to 2XY^2 + 2Y^2, and 5XY^2 - 3XY^2 = 2XY^2, determining the equivalent form.
  • The slope of a model estimating a boy's height in inches each year is 3, showcasing a 3-inch increase annually.
  • To solve for P in the loan payment equation M = P(1 + r/n)^(nt), multiply by the reciprocal to obtain P = M / (1 + r/n)^(nt), resulting in option B.
  • Given a/b = 2, determine 4B/a by recognizing B/a as 1/2, leading to 4 * 1/2 = 2, hence the solution is C.
  • Solving a system of equations, 3X + 4Y = -23 and -X + 2Y = -19, yields X = 3, providing the solution to the system.
  • Calculate G of -4 by first finding a = -1, leading to G of -4 = 8, as per the given function.

18:29

"Equation Solution Leads to Triangle Calculation"

  • The coefficient of x squared is 15, making B equal to 15.
  • Given that a + B equals 8, B can be expressed as 8 - a.
  • Solving the equation leads to a = 5 or a = 3.
  • By substituting a and B values, C is found to be either 41 or 31.
  • The value of x in a triangle problem is determined through proportional calculations.
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