Daily Digest Exam 1-1 Algebra I

1) What is 35% of 20?

To find 35% of 20, you can multiply 20 by 0.35. This will give you the result of 7, which represents 35% of 20. Alternatively, you can express the answer as 7.0, which is the same value but with a decimal point.

Explanation

To find 35% of 20, you can multiply 20 by 0.35. This will give you the result of 7, which represents 35% of 20. Alternatively, you can express the answer as 7.0, which is the same value but with a decimal point.

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2) If the perimeter of a square is 28, what is the measure of its length?

The perimeter of a square is the sum of all its sides. Since a square has all sides equal in length, we can divide the perimeter by 4 to find the length of each side. In this case, the perimeter is given as 28, so dividing it by 4 gives us a length of 7 for each side of the square.

Explanation

The perimeter of a square is the sum of all its sides. Since a square has all sides equal in length, we can divide the perimeter by 4 to find the length of each side. In this case, the perimeter is given as 28, so dividing it by 4 gives us a length of 7 for each side of the square.

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4) Using the figure, compute the perimeter if x = 6, y = 8, and z =10.

The perimeter of a shape is the sum of the lengths of all its sides. In this figure, there are four sides: two sides with length x, one side with length y, and one side with length z. Given that x = 6, y = 8, and z = 10, we can calculate the perimeter by adding the lengths of all the sides: 6 + 6 + 8 + 10 = 30. Therefore, the answer of 24 is incorrect.

Explanation

The perimeter of a shape is the sum of the lengths of all its sides. In this figure, there are four sides: two sides with length x, one side with length y, and one side with length z. Given that x = 6, y = 8, and z = 10, we can calculate the perimeter by adding the lengths of all the sides: 6 + 6 + 8 + 10 = 30. Therefore, the answer of 24 is incorrect.

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6) If the perimeter of a square is 28, what is the measure of its length?

The perimeter of a square is the sum of all its sides. In this case, the perimeter is given as 28. Since all sides of a square are equal in length, we can divide the perimeter by 4 to find the length of each side. 28 divided by 4 is equal to 7, so the measure of the length of each side of the square is 7.

Explanation

The perimeter of a square is the sum of all its sides. In this case, the perimeter is given as 28. Since all sides of a square are equal in length, we can divide the perimeter by 4 to find the length of each side. 28 divided by 4 is equal to 7, so the measure of the length of each side of the square is 7.

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7) Given the equation y = x + 4. What is the y value when x = - 4?

When x = -4, we can substitute this value into the equation y = x + 4. Thus, y = -4 + 4 = 0. Therefore, the y value when x = -4 is 0.

Explanation

When x = -4, we can substitute this value into the equation y = x + 4. Thus, y = -4 + 4 = 0. Therefore, the y value when x = -4 is 0.

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8) Which point on the graph represents the following coordinate: ( 8, 1) ?

A

B

C

D

Point C on the graph represents the coordinate (8, 1) because it is the only point that is located at x = 8 and y = 1.

Explanation

Point C on the graph represents the coordinate (8, 1) because it is the only point that is located at x = 8 and y = 1.

9) If the area of a cirlce is 49pi, what is the measure of its radius?

The formula to calculate the area of a circle is A = πr^2, where A is the area and r is the radius. In this case, the area is given as 49π. By substituting this value into the formula, we get 49π = πr^2. Simplifying the equation, we can cancel out the π on both sides, leaving us with 49 = r^2. Taking the square root of both sides, we find that the radius, r, is equal to 7.

Explanation

The formula to calculate the area of a circle is A = πr^2, where A is the area and r is the radius. In this case, the area is given as 49π. By substituting this value into the formula, we get 49π = πr^2. Simplifying the equation, we can cancel out the π on both sides, leaving us with 49 = r^2. Taking the square root of both sides, we find that the radius, r, is equal to 7.

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10) Find the absolute value of x in: x = -13 + 13

The absolute value of a number is the distance of that number from zero on the number line. In this case, x is equal to -13 + 13 which simplifies to 0. Therefore, the absolute value of x is 0, as it is exactly 0 units away from zero on the number line.

Explanation

The absolute value of a number is the distance of that number from zero on the number line. In this case, x is equal to -13 + 13 which simplifies to 0. Therefore, the absolute value of x is 0, as it is exactly 0 units away from zero on the number line.

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11) A bag contains 2 orange marbles, 4 purple marbles, and 6 green marble. What is the probability of pulling out an orange marble on the first pick? Express your answer as a simplified fraction.

The probability of pulling out an orange marble on the first pick can be found by dividing the number of orange marbles (2) by the total number of marbles (12). Simplifying this fraction gives us 1/6.

Explanation

The probability of pulling out an orange marble on the first pick can be found by dividing the number of orange marbles (2) by the total number of marbles (12). Simplifying this fraction gives us 1/6.

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12) A bag contains 2 orange marbles, 4 purple marbles, and 6 green marble. What is the probability of pulling out a purple marble on the first pick? Express your answer as a simplified fraction.

The probability of pulling out a purple marble on the first pick can be calculated by dividing the number of purple marbles by the total number of marbles in the bag. In this case, there are 4 purple marbles and a total of 12 marbles in the bag. Simplifying the fraction 4/12 gives us 1/3, so the probability of pulling out a purple marble on the first pick is 1/3.

Explanation

The probability of pulling out a purple marble on the first pick can be calculated by dividing the number of purple marbles by the total number of marbles in the bag. In this case, there are 4 purple marbles and a total of 12 marbles in the bag. Simplifying the fraction 4/12 gives us 1/3, so the probability of pulling out a purple marble on the first pick is 1/3.

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13) A bag contains 2 orange marbles, 4 purple marbles, and 6 green marble. What is the probability of pulling out a green marble on the first pick? Express your answer as a simplified fraction.

The probability of pulling out a green marble on the first pick can be determined by dividing the number of green marbles (6) by the total number of marbles (12). Simplifying the fraction 6/12 gives 1/2, which represents the probability of pulling out a green marble on the first pick.

Explanation

The probability of pulling out a green marble on the first pick can be determined by dividing the number of green marbles (6) by the total number of marbles (12). Simplifying the fraction 6/12 gives 1/2, which represents the probability of pulling out a green marble on the first pick.

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15) What is 2/5 of 25?

To find 2/5 of 25, we can multiply 25 by 2/5. This can be done by multiplying 25 by the numerator (2) and then dividing the result by the denominator (5). So, 25 multiplied by 2 equals 50, and when we divide 50 by 5, we get the answer of 10. Therefore, 2/5 of 25 is 10.

Explanation

To find 2/5 of 25, we can multiply 25 by 2/5. This can be done by multiplying 25 by the numerator (2) and then dividing the result by the denominator (5). So, 25 multiplied by 2 equals 50, and when we divide 50 by 5, we get the answer of 10. Therefore, 2/5 of 25 is 10.

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16) Given the equation y = 2x + 4. What is the y value when x = 3?

When the equation y = 2x + 4 is given, it means that the value of y is equal to 2 times the value of x, plus 4. In this case, when x = 3, we can substitute this value into the equation to find the value of y. Therefore, y = 2(3) + 4 = 6 + 4 = 10. So, the y value when x = 3 is 10.

Explanation

When the equation y = 2x + 4 is given, it means that the value of y is equal to 2 times the value of x, plus 4. In this case, when x = 3, we can substitute this value into the equation to find the value of y. Therefore, y = 2(3) + 4 = 6 + 4 = 10. So, the y value when x = 3 is 10.

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18) Using the figure, compute the area if x = 7 and y =10.

The formula to calculate the area of a rectangle is length multiplied by width. In this case, x is the length and y is the width. Substituting the given values, x = 7 and y = 10, into the formula, we get 7 * 10 = 70. Therefore, the area of the rectangle is 70.

Explanation

The formula to calculate the area of a rectangle is length multiplied by width. In this case, x is the length and y is the width. Substituting the given values, x = 7 and y = 10, into the formula, we get 7 * 10 = 70. Therefore, the area of the rectangle is 70.

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19) Find the absolute value of x in: x = - 4 - 4

The absolute value of a number is its distance from zero on the number line. In this case, the given equation x = -4 - 4 / 8 can be simplified to x = -8 / 8, which further simplifies to x = -1. Therefore, the absolute value of x is 1.

Explanation

The absolute value of a number is its distance from zero on the number line. In this case, the given equation x = -4 - 4 / 8 can be simplified to x = -8 / 8, which further simplifies to x = -1. Therefore, the absolute value of x is 1.

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20) Using the figure, compute the circumference if x = 7.

The circumference of a circle can be calculated using the formula C = 2πr, where π is a constant equal to approximately 3.14 and r is the radius of the circle. In this question, the value of x is given as 7, which represents the radius of the circle. By substituting this value into the formula, we can calculate the circumference as 2π(7) = 14π. Therefore, the correct answer is 14π or 14 pi.

Explanation

The circumference of a circle can be calculated using the formula C = 2πr, where π is a constant equal to approximately 3.14 and r is the radius of the circle. In this question, the value of x is given as 7, which represents the radius of the circle. By substituting this value into the formula, we can calculate the circumference as 2π(7) = 14π. Therefore, the correct answer is 14π or 14 pi.

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21) Using the figure, compute the circumference if x = 12.

The circumference of a circle is calculated using the formula C = 2πr, where r is the radius of the circle. In this case, the value of x is given as 12, which represents the radius of the circle. Therefore, substituting x = 12 into the formula, we get C = 2π(12) = 24π, which simplifies to 24π or 24 pi.

Explanation

The circumference of a circle is calculated using the formula C = 2πr, where r is the radius of the circle. In this case, the value of x is given as 12, which represents the radius of the circle. Therefore, substituting x = 12 into the formula, we get C = 2π(12) = 24π, which simplifies to 24π or 24 pi.

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22) Factor the following: x^2 + 11x +10

The given expression can be factored as (x+10)(x+1) or (x+1)(x+10). Both of these expressions are equivalent and represent the factored form of x^2 + 11x + 10.

Explanation

The given expression can be factored as (x+10)(x+1) or (x+1)(x+10). Both of these expressions are equivalent and represent the factored form of x^2 + 11x + 10.

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23) Given the equation y = 3x + 4. What is the slope of the line?

The slope of a line is the coefficient of the x term in the equation of the line. In this case, the equation is y = 3x + 4, so the coefficient of the x term is 3. Therefore, the slope of the line is 3.

Explanation

The slope of a line is the coefficient of the x term in the equation of the line. In this case, the equation is y = 3x + 4, so the coefficient of the x term is 3. Therefore, the slope of the line is 3.

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24) Given the equation y = 2x + 5. At what y value does the line cross the y-axis?

The line crosses the y-axis at the point (0, 5) because the y-intercept is the value of y when x is equal to 0. In the equation y = 2x + 5, when x is 0, the equation becomes y = 2(0) + 5, which simplifies to y = 5. Therefore, the line crosses the y-axis at y = 5.

Explanation

The line crosses the y-axis at the point (0, 5) because the y-intercept is the value of y when x is equal to 0. In the equation y = 2x + 5, when x is 0, the equation becomes y = 2(0) + 5, which simplifies to y = 5. Therefore, the line crosses the y-axis at y = 5.

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26) Using the figure, compute the area if x = 3.

The area can be calculated using the formula A = πr^2, where r is the radius of the circle. In this case, the radius is given as x = 3. Plugging this value into the formula, we get A = π(3)^2 = 9π. Therefore, the area is 9π.

Explanation

The area can be calculated using the formula A = πr^2, where r is the radius of the circle. In this case, the radius is given as x = 3. Plugging this value into the formula, we get A = π(3)^2 = 9π. Therefore, the area is 9π.

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27) Simplify: 4x + 4xy + 8xy + 4y

The given expression is a sum of terms that contain variables x and y. To simplify the expression, we can combine like terms by adding the coefficients of the same variables. In this case, the terms 4xy and 8xy have the same variables, so we can add their coefficients to get 12xy. The terms 4x and 4y do not have any other terms with the same variables, so they remain unchanged. Therefore, the simplified expression is 4x + 12xy + 4y. The other two answer choices are just different ways of writing the same simplified expression.

Explanation

The given expression is a sum of terms that contain variables x and y. To simplify the expression, we can combine like terms by adding the coefficients of the same variables. In this case, the terms 4xy and 8xy have the same variables, so we can add their coefficients to get 12xy. The terms 4x and 4y do not have any other terms with the same variables, so they remain unchanged. Therefore, the simplified expression is 4x + 12xy + 4y. The other two answer choices are just different ways of writing the same simplified expression.

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30) Factor the following: x^2 - 2x - 24

The correct answer is (x-6)(x+4) or (x+4)(x-6). This is the factored form of the given quadratic expression x^2 - 2x - 24. The factoring was done by finding two numbers that multiply to -24 and add up to -2, which are -6 and 4. Therefore, the factors are (x-6) and (x+4). The order of the factors can be reversed, resulting in (x+4)(x-6).

Explanation

The correct answer is (x-6)(x+4) or (x+4)(x-6). This is the factored form of the given quadratic expression x^2 - 2x - 24. The factoring was done by finding two numbers that multiply to -24 and add up to -2, which are -6 and 4. Therefore, the factors are (x-6) and (x+4). The order of the factors can be reversed, resulting in (x+4)(x-6).

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31) Which point on the graph represents the following coordinate: ( -1, -8) ?

A

B

C

D

The point on the graph that represents the coordinate (-1, -8) is point B.

Explanation

The point on the graph that represents the coordinate (-1, -8) is point B.

32) Which point on the graph represents the following coordinate: ( 8, -1) ?

A

B

C

D

The point (8, -1) on the graph is represented by point D.

Explanation

The point (8, -1) on the graph is represented by point D.

33) Find the absolute value of x in: x = -5 - ( -5)

The absolute value of a number is the distance of that number from zero on the number line. In this case, the expression -5 - (-5) simplifies to -5 + 5, which equals 0. Therefore, the absolute value of 0 is 0.

Explanation

The absolute value of a number is the distance of that number from zero on the number line. In this case, the expression -5 - (-5) simplifies to -5 + 5, which equals 0. Therefore, the absolute value of 0 is 0.

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34) Using the figure, compute the perimeter if x = 4 and y =8

The perimeter of a shape is the sum of the lengths of all its sides. In this figure, there are two sides with length x and two sides with length y. Given that x = 4 and y = 8, we can calculate the perimeter by adding the lengths of all the sides: 4 + 4 + 8 + 8 = 24.

Explanation

The perimeter of a shape is the sum of the lengths of all its sides. In this figure, there are two sides with length x and two sides with length y. Given that x = 4 and y = 8, we can calculate the perimeter by adding the lengths of all the sides: 4 + 4 + 8 + 8 = 24.

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37) Factor the following: x^2 - 9x +20

The given expression can be factored as (x-5)(x-4) or (x-4)(x-5). Both of these factorizations are equivalent and correct.

Explanation

The given expression can be factored as (x-5)(x-4) or (x-4)(x-5). Both of these factorizations are equivalent and correct.

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38) Factor the following: x^2 + 9x - 36

The given expression can be factored as (x+12)(x-3) or (x-3)(x+12). Both of these factorizations are correct and equivalent.

Explanation

The given expression can be factored as (x+12)(x-3) or (x-3)(x+12). Both of these factorizations are correct and equivalent.

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39) Find the slope (m) of the line that contains the following points. P1 = ( -1, 9) P2 = ( 1, 5)

The slope of a line can be found using the formula (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are the coordinates of two points on the line. Plugging in the values from the given points, we get (5 - 9) / (1 - (-1)) = -4 / 2 = -2. Therefore, the slope of the line is -2.

Explanation

The slope of a line can be found using the formula (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are the coordinates of two points on the line. Plugging in the values from the given points, we get (5 - 9) / (1 - (-1)) = -4 / 2 = -2. Therefore, the slope of the line is -2.

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40) Simplify: 5x - 10y + 8x + 15y

The given expression involves adding and subtracting variables with coefficients. By combining like terms, we can simplify the expression to 13x + 5y. The order of the terms does not affect the result, so 5y + 13x is also a valid simplified form.

Explanation

The given expression involves adding and subtracting variables with coefficients. By combining like terms, we can simplify the expression to 13x + 5y. The order of the terms does not affect the result, so 5y + 13x is also a valid simplified form.

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41) What is the area of a triangle that has a hypoetnuse of 20 and a base of 16?

The area of a triangle can be calculated using the formula A = 1/2 * base * height. In this case, the base of the triangle is given as 16. However, the height is not provided in the question. Without the height, it is not possible to calculate the area of the triangle accurately. Therefore, an explanation for the given answer of 96 is not available.

Explanation

The area of a triangle can be calculated using the formula A = 1/2 * base * height. In this case, the base of the triangle is given as 16. However, the height is not provided in the question. Without the height, it is not possible to calculate the area of the triangle accurately. Therefore, an explanation for the given answer of 96 is not available.

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42) Which point on the graph represents the following coordinate: ( -1, 8) ?

A

B

C

D

Point A represents the coordinate (-1, 8) on the graph.

Explanation

Point A represents the coordinate (-1, 8) on the graph.

43) Which of the following represents the equation of the graph below?

Y = -2x - 3

Y = -2x + 3

Y = -3x - 2

Y = 3x - 3

The equation of the graph can be determined by observing the slope and y-intercept. In this case, the slope is -2 and the y-intercept is -3. Therefore, the equation that represents the graph is y = -2x - 3.

Explanation

The equation of the graph can be determined by observing the slope and y-intercept. In this case, the slope is -2 and the y-intercept is -3. Therefore, the equation that represents the graph is y = -2x - 3.

44) Which of the following represents the equation of the graph below?

Y = -2x - 2

Y = -2x + 2

Y = 2x - 2

Y = 2x + 2

The equation of the graph can be determined by analyzing the slope and y-intercept. In this case, the slope is positive 2 and the y-intercept is positive 2. The equation y = 2x + 2 represents a line with a slope of 2 and a y-intercept of 2, which matches the given graph.

Explanation

The equation of the graph can be determined by analyzing the slope and y-intercept. In this case, the slope is positive 2 and the y-intercept is positive 2. The equation y = 2x + 2 represents a line with a slope of 2 and a y-intercept of 2, which matches the given graph.

45) Which of the following represents the equation of the graph below?

Y = -1x - 1

Y = -1x + 1

Y = 1x - 1

Y = 1x + 1

The equation y = 1x - 1 represents the graph below because it has a slope of 1, meaning that for every increase of 1 in the x-coordinate, there is a corresponding increase of 1 in the y-coordinate. Additionally, the equation has a y-intercept of -1, which is where the graph intersects the y-axis.

Explanation

The equation y = 1x - 1 represents the graph below because it has a slope of 1, meaning that for every increase of 1 in the x-coordinate, there is a corresponding increase of 1 in the y-coordinate. Additionally, the equation has a y-intercept of -1, which is where the graph intersects the y-axis.