Math

z^2 + 10z - 24 = 0 What is one of the solutions to the given equation?

Two answers: 2 or -12 (z+12)(z-2)=0 (Rewrite by factoring. Two factors that multiply to -24 is 2 and -12.) The rewritten equation makes two equations z+12=0 & z-2=0 Subtract 12 from 12 and 0 in first equation to get -12 Subtract 2 from 2 and 0 in 2nd equation to get 2

Data value Frequency 6 3 7 3 8 8 9 8 10 9 11 11 12 9 13 0 14 6 The frequency table summarizes the 57 data values in a data set. What is the maximum data value in the data set?

14 14 is the greatest number in the data value data set

An event planner is planning a party. It costs the event planner a onetime fee of $35 to rent the venue and $10.25 per attendee. The event planner has a budget of $200. What is the greatest number of attendees possible without exceeding the budget?

16 35 + 10.25x (equal to or less than sign) 200 10.25x (equal to or less than sign) 165 (Subtract 35 from 35 and 200) Divide by 10.25 and round down for answer

The function f is defined by the equation f(x)= 7x + 2. What is the value of f(x) when x = 4 ?

30 f(x)= 7x+2 f(4)= 7(4)+2 (Substitute x with 4) 7x4=28 28+2=30

A circle in the xy-plane has a diameter with endpoints (2,4) and (2,14) . An equation of this circle is (x-2)^2 + (y-9)^2 =r^2, where r is a positive constant. What is the value of r ?

5 (x-x)^2+(y-y)^2 (whole equation in division sign) 1 2 1 2 (2-2)^2+(9-4)^2

(Another graph one. It is a parabola all positive. There are two points: (6,3) and (8,3). The bottom ends on (7,0). Graph looks like: | 0 0 | 0 0 | 0 0 |_____0________ The x-intercept of the graph shown is (x , 0). What is the value of x ?

7 The graph ends/goes through 7

What is 10 % of 470? A)37 B)47 C)423 D)460

B) 47 10/100(470)=47

The function f is defined by f(x) = 1/10x - 2. What is the y-intercept of the graph of y = f(x) in the xy -plane? A)(−2, 0) B)(0, −2) C){0, 1/10} D){1/10 , 0}

B)(0, −2) The y-intercept of a graph on the xy-plane is x=0 Substitute x with 0. f(0) = 1/10(0) - 2. y = -2 when x = 0

g(x) = x^2 = 55 What is the minimum value of the given function? A)0 B)55 C)110 D)3,025

B)55 It is given that the equation is equal to 55, the only possible choice

s = 40 + 3t The equation gives the speed s, in miles per hour, of a certain car t seconds after it began to accelerate. What is the speed, in miles per hour, of the car 5 seconds after it began to accelerate? A)40 B)43 C)45 D)55

D)55 Substitute t with 5 since t is speed and 5 is time given s = 40 + 3(5)

Bacteria are growing in a liquid growth medium. There were 300,000 cells per milliliter during an initial observation. The number of cells per milliliter doubles every 3 hours. How many cells per milliliter will there be 15 hours after the initial observation? A)1,500,000 B)2,400,000 C)4,500,000 D)9,600,000

D)9,600,000 y=a(b)^x/k = 300,000(2)^15/3 300,000(2)^5 600000^5 a=cells per mil b=how much increase (double=2) x=how much time k=time per hours

The function f is defined by f(x) = 7x^3. In the xy -plane, the graph of y = g(x) is the result of shifting the graph of y = f(x) down 2 units. Which equation defines function g ? A)g(x)) = 7/2x^3 B)g(x) = 7x^ 3/2 C)g(x)) = 7x^3 + 2 D)g(x) = 7x^3 − 2

D)g(x) = 7x^3 − 2 Since you move down 2, the equation is 2 less than it was

For a training program, Juan rides his bike at an average rate of 5.7 minutes per mile. Which function m models the number of minutes it will take Juan to ride x miles at this rate? A)m(x) = x/5.7 B)m(x) = x + 5.7 C)m(x)= x - 5.7 D)m(x) = 5.7x

D)m(x) = 5.7x Multiply his average rate by number of miles (x).

A list of 10 data values is shown. 6, 8, 16, 4, 17, 26, 8, 5, 5, 5 What is the mean of these data?

10 Add all numbers and divide by how many numbers your adding (in this case, youd divide the total number by 10)

The perimeter of an equilateral triangle is 624 centimeters. The height of this triangle is k 3(3 is inside a square root sign) centimeters, where k is a constant. What is the value of k?

104 Equilateral triangle=all 3 same side lengths and all angles=60 degrees The triangle=2 right triangles Each hypotenuse=2k in length Perimeter is the sum of the lengths 2k+2k=2k+624 or 6k=624 3 square root rounds up to 2 so each side would be 2k

A printer produces posters at a constant rate of 42 posters per minute. At what rate, in posters per hour, does the printer produce the posters?

2,520 60 minutes =1 hour (42 posters divided by 1 minute)(60 minutes divided by 1 hour)

If |4x − 4| = 112, what is the positive value of x − 1 ?

28 Rewrite: 4x - 4 = 112 and 4x - 4 = -112 Solve first equation 4x = 116 (Add 4 to 4 and 112) x = 29 (Divide 4 and 116 by 4) Solve second equation 4x = -108 (Add 4 to 4 ands -112) x = -27 (Divide 4 and -108 by 4 Choose positive x and plug into given equation

x^2 − 34x + c = 0 In the given equation, c is a constant. The equation has no real solutions if c > n. What is the least possible value of n?

289 ax^2 + bx + c = 0 a=1; b=-34 (-34)^2 - 4 (1) (c) 1,156 - 4c 1,156 - 4c *less than sign* 0 (add 4c to both sides) 1,156 *less than sign* 4c (Divide 4 to both sides) 289 *less than sign* c or c *greater than sign* 289

4x + 5 = 165 What is the solution to the given equation?

40 4x + 5 = 165 4x = 160 (subtract 5 from 5 and 165) Then divide 4 by 4 and 160

Vivian bought party hats and cupcakes for $71 . Each package of party hats cost $3 , and each cupcake cost $1 . If Vivian bought 10 packages of party hats, how many cupcakes did she buy?

41 10 x 3 =30 (Find how much she spent on hats) 71 - 30 =41 (Subtract hat cost by the total cost) Usually would divide the cost of cupcakes but 1 divided by anything gives you the other number so you already have your answer.

(A picture is given. Two parallel lines that are horizontal and a diagonal line going fromright to left through them. Kind of like this: _____________________/x______ _______________110/________ / In the figure shown, line c intersects parallel lines s and t. What is the value of x ?

70 Straight lines= 180 degrees x + 110 = 180 Subtract 110 from 180

x + 7 = 10 (x+7)^2 = y Which ordered pair (x,y) is a solution to the given system of equations? A)(3,100) B)(3,3) C)(3,10) D)(3,70)

A)(3,100) Solve each equation x + 7 = 10 x= 3 (Subtract 7 from 7 and 10) (x+7)^2 = y (3+7)^2=y (plug in x) (10)^2=y (square 10)

Each face of a fair 14-sided die is labeled with a number from 1 through 14, with a different number appearing on each face. If the die is rolled one time, what is the probability of rolling a 2? A)1/14 B)2/14 C)12/14 D)13/14

A)1/14 Total possible=14 Possible times rolling a 2=1

A cube has an edge length of 68 inches. A solid sphere with a radius of 34 inches is inside the cube, such that the sphere touches the center of each face of the cube. To the nearest cubic inch, what is the volume of the space in the cube not taken up by the sphere? A)149,796 B)164,500 C)190,955 D)310,800

A)149,796 Find volume of cube V = s^3 (V=vol.; s=edge length) V= 314, 432 Find volume of sphere V = 4/3 pi r^3 (V= vol.; r=radius) V= 164,636 Subtract both volumes for answer

The function p is defined by p(n) = 7n^3. What is the value of n when p(n) is equal to 56? A)2 B)8/3 C)7 D)8

A)2 56 = 7n^3 8 = n^3 (divide 7 and 56 by 7) Cube root 8

Tilly earns p dollars for every w hours of work. Which expression represents the amount of money, in dollars, Tilly earns for 39w hours of work? A)39 p B)p/39 C)p + 39 D)p-39

A)39 p Tilly earns p dollars for every w hours of work (given) This looks like p/w The amount of money is x The equation can be set up as p/w=x/39w Or you can rewrite it as 39pw=xw and divide both sides by w

The function g is defined by g(x) =x^2 +9. For which value of x is g(x) = 25 ? A)4 B)5 C)9 D)13

A)4 25= x^2 +9 (substitute g(x) with 25) 16= x^2 (Substract 9 from 9 and 25) x=4 (slash through = sign but can't put it) (Square root of both) This makes the answer either +4 or -4. +4 is the only option

A neighborhood consists of a 2-hectare park and a 35-hectare residential area. The total number of trees in the neighborhood is 3,934. The equation 2x + 35y = 3,934 represents this situation. Which of the following is the best interpretation of x in this context? A)The average number of trees per hectare in the park B)The average number of trees per hectare in the residential area C)The total number of trees in the park D)The total number of trees in the residential area

A)The average number of trees per hectare in the park There 2-hectare park (given) There 3-hectare residential (given) "Per" means divide a.k.a. find average of so the last 2 options are out.

The equation E(t) = 5(1.8)^t gives the estimated number of employees at a restaurant, where t is the number of years since the restaurant opened. Which of the following is the best interpretation of the number 5 in this context? A)The estimated number of employees when the restaurant opened B)The increase in the estimated number of employees each year C)The number of years the restaurant has been open D)The percent increase in the estimated number of employees each year

A)The estimated number of employees when the restaurant opened Since the function E(t) = 5(1.8)^t gives the estimated number of employees at a restaurant and t is the number of years since the restaurant opened, the best interpretation of the number 5 in this context is the estimated number of employees when t =0, or when the restaurant opened.

Which expression is equivalent to (7x^3 + 7x) - (6x^3 - 3x) ? A)x^3 + 10x B)-13x^3 + 10x C)-13x^3 = 4x D)x^3 = 4x

A)x^3 + 10x Distribute and rewrite: 7x^3 + 7x - 6x^3 + 3x Group like terms: (7x^3 - 6x^3) + (7x + 3x)

5x + 7y = 1 ax + by = 1 In the given pair of equations, a and b are constants. The graph of this pair of equations in the xy -plane is a pair of perpendicular lines. Which of the following pairs of equations also represents a pair of perpendicular lines? A)10x + 7y = 1 ax − 2by = 1 B)10x + 7y = 1 ax + 2by = 1 C)10x + 7y = 1 2ax + by = 1 D)5x − 7y = 1 ax + by = 1

B)10x + 7y = 1 ax + 2by = 1 y = mx + b Solve first equation 5x + 7y = 1 (Subtract -5 from 5 and transfer -5 over = ) 7y = -5x +1 (Divide everything by 7) y = -5/7x + 1/7 Slope= -5/7 Solve second equation ax + by = 1 (Subtract ax from ax and transfer ax over the = ) by = -ax +1 (Divide b and put it to the 1, making it 1/b) y = -a/b(x) + 1/b Slope= -5/7 Rewrite each choice option given until it matches this pattern

Which expression is equivalent to a^11/12, where a > 0 ? A)12 *square root sign* a^132 (12 outside) (a^132 inside) B)144 *square root sign* a^132 (114 outside) (a^132 inside) C)121 *square root sigh* a^132 (121 outside) (a^132 inside) D)11 *square root sign* a^132 (11 outside) (a^132 inside)

B)144 *square root sign* a^132 12/12 = 1 a(11/12)(12/12) (Multiple 1 (or 12/12) by equation) a^132/144 Rewrite for answer

Right triangles LMN and PQR are similar, where L and M correspond to P and Q, respectively. Angle M has a measure of 53°. What is the measure of angle Q ? A)37° B)53° C)127° D)143°

B)53° LMN and PQR are similar (or congruent) (given info) That means L=P, M=Q, N=R Since measure of M was given, you were given the answer

3x = 12 -3x + y = -6 The solution to the given system of equations is (x, y). What is the value of y ? A)−3 B)6 C)18 D)30

B)6 Add the given to make both equations one: 3x + (-3x + y) = 12 + (-6)

What is the diameter of the circle in the xy-plane with equation (x - 5)^2 + (y - 3)^2 = 16 ? A)4 B)8 C)16 D)32

B)8 Find length of radius: 16^2 = 4 Diameter is twice of radius: answer

Another graph. All points shown are positive by it is decreasing. Roughly looks like: 0 0 0 0 The graph shows the relationship between the number of shares of stock from Company A, x, and the number of shares of stock from Company B, y, that Simone can purchase. Which equation could represent this relationship? A)y= 8x + 12 B)8x + 12y = 480 C)y= 12x + 8 D)12x + 8y = 480

B)8x + 12y = 480 The x-intercept is 60 The y-intercept is 40 60 x 8 =480 40 x 12 =480 This leaves B and D Not sure how to decide from here but you have 50% chance

A model estimates that at the end of each year from 2015 to 2020, the number of squirrels in a population was 150 percent sign 150% more than the number of squirrels in the population at the end of the previous year. The model estimates that at the end of 2016, there were 180 squirrels in the population. Which of the following equations represents this model, where n is the estimated number of squirrels in the population t years after the end of 2015 and t ≤ 5 ? A)n = 72(1.5)^t B)n = 72(2.5)^t C)n = 180(1.5)^t D)n = 180(2.5)^t

B)n = 72(2.5)^t n = a(1 + p/100)^t (For when there's specific number given) p = 150 (the percent from year before) n = a(1 + 150/100)^t (can be rewritten as:) n = a(2.5)^t n = 180 (the percent from 2016) 180 = a(2.5)^1 or 180 = 2.5a Divide 2.5 and 180 by 2.5 to get answer

(Theres a scatter plot that goes with this but I can't include it but all of the dots are positive on the x axis and positive on y axis) What they look like: 0 0 0 0 Which of the following equations is the most appropriate linear model for the data shown in the scatterplot? A)y= -1.9x - 10.1 B)y= -1.9x + 10.1 C)y= 1.9x - 10.1 D)y= 1.9x + 10.1

B)y= -1.9x + 10.1 The form is y=a+bx or y=bx+a (b=slope and a=y-intercept) Points on x-axis decrease Points on y-axis increase/are positive

2x + 3y = 7 10x + 15y = 35 For each real number r, which of the following points lies on the graph of each equation in the xy-plane for the given system? A){r/5 + 7, -r/5 +35} B){-3r/2 + 7/2, r} C){r, 2r/3 + 7/3} D){r, -3r/2 +7/2}

B){-3r/2 + 7/2, r} -3r/2 + 7/2 2(-3r/2 + 7/2) + 3r =7 which is equivalent to: -3r +7 +3r =7 or 7=7 which represents the first equation provided

The population of Greenville increased by 7% from 2015 to 2016. If the 2016 population is k times the 2015 population, what is the value of k ? A)0.07 B)0.7 C)1.07 D)1.7

C)1.07 7% = 0.07 Add that number by the 2016 population (x) x + (0.07)x Rewrite it as: 1.07

y = -3x 4x + y = 15 The solution to the given system of equations is (x, y). What is the value of x ? A)1 B)5 C)15 D)45

C)15 4x + y = 15 4x + (-3x) = 15 (Substitute the x for -3) This can also be viewed as x = 15

The measure of angle R is 2π/3 radians. The measure of angle T is 5π/12 radians greater than the measure of angle R. What is the measure of angle T, in degrees? A)75 B)120 C)195 D)390

C)195 T=2π/3 + 5π/12 Get a common dominator by multiplying by 4/4 T=8π/12+5π/12 T=13n/12 (Add) 180 is the whole circle so T=13π/12 x 180/π

4x + 6 = 18 Which equation has the same solution as the given equation? A)4x = 108 B)4x = 24 C)4x = 12 D)4x = 3

C)4x = 12 4x + 6 =18 (subtract 6 from 6 and 18) 4x=12

Which expression is equivalent to 6x^8y^2 + 12x^2y^2 ? A)6x^2y^2(2x^6) B)6x^2y^2(x^4) C)6x^2y^2(x^6+2) D)6x^2y^2(x^4+2)

C)6x^2y^2(x^6+2) Since each option has the common 6x^2y^2, rewrite to: 6x^2y^2(x^6)+6x^2y^2(2) or 6x^2y^2(x^6+12)

Each year, the value of an investment increases by 0.49% of its value the previous year. Which of the following functions best models how the value of the investment changes over time? A)Decreasing exponential B)Decreasing linear C)Increasing exponential D)Increasing linear

C)Increasing exponential Since the value of the investment changes by a fixed percentage each year, the function that best models how the value of the investment changes over time is an exponential function.

(Another graph. This time the line decreases then increases slightly and the decrease again) Roughly looks like (dots are axis's and read left to right) Probably won't get this right but you will get the feel of it) 0 I 0 I 0 I 0 --------------- 0 I 0 0 The graph of y= f(x) is shown, where the function f is defined by f(x) =ax^3+bx^2+cx+d and a, b, c, and d are constants. For how many values of x does f (x) =0 ? A)One B)Two C)Three D)Four

C)Three 3 points when the graph touches the x-axis

For the exponential function f, the value of f (1) is k, where k is a constant. Which of the following equivalent forms of the function f shows the value of k as the coefficient or the base? A)f(x) = 50(1.6)^x + 1 B)f(x) = 80(1.6)^x C)f(x) = 128(1.6)^x − 1 D)f (x) = 204.8(1.6)^x−2

C)f(x) = 128(1.6)^x − 1 Value of 128(1.6)^x - 1 can be seen as 128(1.6)^1 - 1 Or 128(1.6)^0 Multiple 128 by 1.6 for first number of answer

In the xy-plane, the graph of the equation y=-x^2 + 9x - 100 intersects the line y=c at exactly one point. What is the value of c? A)− 481/4 B)−100 C)− 319/4 D)− 9/2

C)− 319/4 The equation is a parabola and y=c is a horizontal line This means a parabolas can only intersect a horizontal line once at it's vertex. The value of c is equal to y-coordinate of the vertex. The equation can be rewritten as: y={x^2-2(9/2)x + (9/2)^2} + (9/2)^2 - 100

Circle A has a radius of 3n and circle B has a radius of 129n, where n is a positive constant. The area of circle B is how many times the area of circle A? A)43 B)86 C)129 D)1,849

D)1,849 Area=pi times radius squared Radius of Circle A is 3n (given) A=(pi)(3n)^2 Radius of Circle B is 129n (given) A=(pi)(129n)^2 Divide the two answers for the answer to the question

A certain town has an area of 4.36 square miles. What is the area, in square yards, of this town? (1 mile = 1,760 yards) A)404 B)7,674 C)710,459 D)13,505,536

D)13,505,536 1,760^2 =3,097,600 4.36(3,097,600

The total cost, in dollars, to rent a surfboard consists of a $25 service fee and a $10 per hour rental fee. A person rents a surfboard for t hours and intends to spend a maximum of $ 75 to rent the surfboard. Which inequality represents this situation? A)t10 ≤ 75 B)10 + 25t ≤ 75 C)25t ≤ 75 D)25 + 10t ≤ 75

D)25 + 10t ≤ 75 10t=rental fee 25=additional service fee 75=max of what they want to spend

(There is a picture of a right triangle. Labeled like:) |\ a I \ c I_____\ b For the right triangle shown, a = 4 and b = 5. Which expression represents the value of c ? A)4 + 5 B)(4)(5) (both are inside a square root symbol) C)4 + 5 (both are inside a square root symbol) D)4^2 + 5 ^2 (both are inside a square root symbol)

D)4^2 + 5 ^2 (both are inside a square root symbol) c^2 = a^2 + b^2 c^2 = 4^2 + 5^2

A teacher is creating an assignment worth 70 points. The assignment will consist of questions worth 1 point and questions worth 3 points. Which equation represents this situation, where x represents the number of 1-point questions and y represents the number of 3-point questions? A)4xy= 70 B)4(x +y ) = 70 C)3x+y = 70 D)x+3y = 70

D)x+3y = 70 x=number 1-point questions y=number of 3-point questions The assignment is worth a total of 1*x+3*y or x+3y points The assignment is worth 70 points (given info) So it would be x+3y= 70

x y 18 130 23 160 26 178 For line h, the table shows three values of x and their corresponding values of y. Line k is the result of translating line h down 5 units in the xy-plane. What is the x-intercept of line k? A){- 26/3, 0} B) {- 9/2, 0} C){-11/3, 0} D){-17/6, 0}

D){-17/6, 0} y=mx+b m=slope b=y-intercept m=160-130/23-18 y=6x+b 130=6(18)+b (substitute m for 130 and x for 18) b=22 Since this is the result of moving 5 units down, use another eq. y=6x+22-5 0=6x+22-5 (substitute y for 0) The result of this is 0=6x+17 which x equals -17/6