SAT Randomized Questions - 1 Full Math Practice Test - Answers and Detailed Explanations at the END

To find \( a \), set \( q(x) = 0 \): \( -7x + 21 = 0 Rightarrow x = 3 \), so \( a = 3 \). For \( b \), evaluate \( q(0) = 21 \). Thus, \( a + b = 3 + 21 = 24 \).

The change in degrees Fahrenheit is determined by multiplying the temperature increase in kelvins by \( \frac{9}{5} \), since the \( x \) term in the function is being multiplied by this factor. Therefore, the increase in Fahrenheit temperature is \( \frac{9}{5} \times 5.00 = 9.00 \).

To find the surface area of the cube, we need to determine its side length. The formula for the volume of a cube is \( V = s^3 \). Given \( V = 474552 \), solve for \( s \): \( s = \sqrt[3]{474552} \approx 78 \). The formula for surface area is \( 6s^2 \). Thus, the surface area is \( 6(78)^2 = 36,504 \) square units.

Rewrite \(f(x)\) in vertex form as \(2(x + 2)^2 - 2\). The minimum of \(f(x)\) is at \(x = -2\), so \(g(x) = f(x + 1)\) shifts this to \(x = -3\).

To have no real solution, the discriminant of \(x(q x - 64) + 20 = 0\) must be negative. Solving gives \(\)q^2 < 16[/latex], so the smallest integer for [latex]q[/latex] is 4.

The decay factor is 0.75 per half-year, which means it decays by 25% every six months. Over a year, this represents a 25% drop, so \(q = 25\).

To find \( p \): \( 75 = \frac{p}{100} \times 150 \implies p = \frac{75 \times 100}{150} = 50 \). Calculate \( 50 \% \) of \( 75 \): \( \frac{50}{100} \times 75 = 37.5 \).

Since the triangles are congruent, angle \( Z \) is equal to angle \( C \), so the measure of angle \( C \) is 70°.

The percentage can be calculated using the formula: \( \frac{\text{Part}}{\text{Whole}} \times 100 \). Here, \( \frac{50}{200} \times 100 = 25\% \).

The percentage can be calculated using the formula: \( \frac{62.5}{250} \times 100 = 25\% \).

The lines have different slopes, indicating that they will intersect at exactly one point.

Using the slope \( \frac{1}{3} \) and point \( (-3, 5) \) in the point-slope formula, the resulting equation is \( y = \frac{1}{3}x + 6 \).

Since the triangles are similar, corresponding angles have equal trigonometric ratios, so \( \sin(U) = \sin(R) = \frac{40}{41} \).

The sum of the solutions is calculated separately for each factor. Using the given total sum of \( \frac{25}{2} \), solve for the value of \( p \).

The sum of the solutions of a polynomial equation can be determined using the relationship between the coefficients and the sum of the roots. For each factor, find the solutions and sum them. The given information specifies that the total sum of solutions is \( \frac{20}{3} \), which leads to solving for \( p \).

The rate of leakage is 7 milliliters per minute. Over one hour (60 minutes), the volume leaked is 7 * 60 = 420 milliliters. Converting to liters (1 liter = 1000 mL), the answer is 0.42 liters.

Both sides simplify to \( 3y - 9 \), which are identical. Therefore, the equation is true for all values of y, leading to infinitely many solutions.

To find \( a \), set \( p(x) = 0 \): \( 3x + 9 = 0 Rightarrow x = -3 \). Thus, \( a = -3 \). For \( b \), evaluate \( p(0) = 9 \). Therefore, \( a + b = -3 + 9 = 6 \).

To find \( a \), set \( r(x) = 0 \): \( 8x - 16 = 0 Rightarrow x = 2 \). Thus, \( a = 2 \). For \( b \), evaluate \( r(0) = -16 \). Therefore, \( a + b = 2 - 16 = -14 \).

Using the quadratic formula, \(x = \frac{12 \pm \sqrt{144 - 44}}{2} = 6 \pm \sqrt{25}\). So, the solution can be written as \(6 + \sqrt{25}\) and the correct value of \(k\) is 25.

We use the Pythagorean theorem: \( c^2 = 5^2 + 12^2 = 25 + 144 = 169 \). Therefore, \( c = \sqrt{169} = 13 \). Since the length is already in the form \( \sqrt{169} [/latex}, the value of [latex] d \) is 169.

Start with the slope \( -\frac{5}{6} \) and point \( (-6, 4) \). Using the point-slope formula, the equation is \( y = -\frac{5}{6}x + 4 \).

The change in degrees Fahrenheit is determined by multiplying the temperature increase in kelvins by \( \frac{9}{5} \), since the \( x \) term in the function is being multiplied by this factor. Therefore, the increase in Fahrenheit temperature is \( \frac{9}{5} \times 3.00 = 5.40 \).

Since \(g(x) = f(x+1) = 6(10)^{x+1} = 6 \cdot 10 \cdot (10)^x = 60(10)^x\), the correct answer is g(x) = 60(10)^x.

Since \(g(x) = f(x+4) = 7(2)^{x+4} = 7 \cdot 16 \cdot (2)^x = 112(2)^x\), the correct answer is g(x) = 112(2)^x.

The vertex of the function \( f(x) = \frac{1}{16}(x - 5)^2 + 2 \) occurs at \( (5, 2) \). This represents the minimum height of the roller coaster car. The vertex form of a quadratic function, \( a(x - h)^2 + k \), indicates the vertex as \( (h, k) \). Since \( h = 5 \) and \( k = 2 \), the minimum height is 2 feet above the ground.

To find \( f(0) \), substitute \( 0 \) for \( x \): \( f(0) = 250(0.4)^0 \). Since \( (0.4)^0 = 1 \), the expression becomes \( 250 imes 1 = 250 \).

Expanding the left side gives \( 5x + 15 \), which matches the right side. Therefore, the equation is true for all values of x, leading to infinitely many solutions.

To ensure no solution, we set the slopes equal, indicating b = 48 based on intercept calculations.

The function \(g(x) = 1.5x\) represents a proportional increase with respect to \(x\). As \(x\) increases, \(g(x)\) also increases linearly. Therefore, the correct answer is 'Increasing Linear.'

Factor out the greatest common factor, \(3x\), from the expression: \(3x(x^2 + 9x + 18)\). Then factor \(x^2 + 9x + 18\) as \((x + 3)(x + 6)\). The smallest possible value of \(b\) is 3.

To find the area in square miles, divide by \(1760^2\): \(8,673,280 / 3,097,600 = 2.8\) square miles.

To find \( p \): \( 45 = \frac{p}{100} \times 90 \implies p = \frac{45 \times 100}{90} = 50 \). Calculate \( 50 \% \) of \( 45 \): \( \frac{50}{100} \times 45 = 22.5 \).

The second equation is just a multiple of the first. Dividing the second equation by -2 yields \( 5x + 4y = 16 \). Thus, the two lines are the same and intersect at infinitely many points.

Using \( P = 40,000 \) and \( C = 5,000 \), set up the equation \( 40,000 = 5,000(2)^{5r} \). Dividing both sides by 5,000 gives \( 8 = (2)^{5r} \). Taking the logarithm base 2 of both sides yields \( 3 = 5r \). Therefore, \( r = \frac{3}{5} \).

Rewrite both equations in slope-intercept form. To have no solution, the slopes must be equal but the y-intercepts must differ. Solving, we find m = -6.

Substitute \( y = 24 \) into the equation: \( 3.5x + 7(24) = 140 \Rightarrow 3.5x + 168 = 140 \Rightarrow 3.5x = -28 \). Since \( x \) cannot be negative, the shelter cannot care for any cats, making this question tricky.

Let the number of people who voted against the proposal be x. According to the problem, 3 times as many people voted in favor, so the number in favor is 3x. The social media post states that 15,000 more people voted in favor, so the equation is 3x = x + 15,000. Solving for x gives 7,500.

In the equation 3𝑠 + 50𝑡 = 8,000, the coefficient 3 corresponds to the trail, meaning 𝑠 represents the total number of streetlights per kilometer along the trail.

The decay factor is 0.68 every half-year, which means it decays by 32% each six months. This translates to approximately a 55% annual decay rate, so \(p = 55\).

Start by setting up the equation with the given values: \( 64,000 = 8,000(2)^{6r} \). Divide both sides by 8,000 to get \( 8 = (2)^{6r} \). Taking the logarithm base 2 of both sides gives \( 3 = 6r \). Therefore, \( r = \frac{1}{2} \).

Using the quadratic formula, \(x = \frac{6 \pm \sqrt{36 - 12}}{2} = 3 \pm \sqrt{6}\). So, the solution can be written as \(3 + \sqrt{6}\) and the correct value of \(k\) is 6.

Expanding the right side results in \( 10a - 3 \), which is identical to the left side. Therefore, the equation holds for all values of a, implying infinitely many solutions.

Dividing the equation by 4, completing the square, and simplifying gives n = 4.