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ten/two/20

THE CORRECT ANSWER IS A.

The question asks for a pair of equations to correspond the situation. Translate each statement, slice by piece. The commencement part tells us that "the product of x and y is 76." Since production ways multiplication, the first equation must exist xy = 76, so you tin can eliminate (C). The 2d part says that "x is twice the square of y," which translates to x = twoy 2, so eliminate (B) and (D), and (A) is the simply pick left. Notice that only the y needs to exist squared, which is why (B) is wrong. The second equation for (B) would be written equally "the square of twice y," which is non what the problem states. The correct answer is (A).

9/28/xx

THE CORRECT ANSWER IS D.

The question asks for the to the lowest degree possible value of ivr + 3. Notice that this question is asking for an expression instead of a variable, so manipulate the inequality so that yous become 4r + 3 in the inequality. Treat each side of the inequality separately to avoid confusion. Starting with the –half dozen < –ivr + 10 part, multiply both sides of the inequality by –ane, remembering to switch the sign, to go half dozen > ivr – 10. Add 13 to each side to go 19 > 4r + three. Then solve the correct side of the inequality. Again, multiply both sides of the inequality by –1, switching the sign to get 4r – 10 ≥ –2. Now add xiii to each side of the equation: 4r + three ≥ 11. Finally, combine the equations to get the range for ivr + three. The least possible value of the expression is 11. If you see the respond before the concluding stride above, you don't need to combine the equations. The right answer is (D).

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nine/25/20

THE Correct ANSWER IS B.

The question asks for the value of a in an equation with fractions. The lowest number that both 8 and 10 are factors of is forty. Convert the fractions to a denominator of xl: 5/40 + iv/40 = 9/40. There is no factor that nine and 40 have in common, so the fraction cannot be reduced. The number in identify ofa ina/b is 9. Be careful not to cull (D), which contains the value ofb. The correct answer is (B).

9/21/20

THE Correct ANSWER IS C.

The question asks for the value of x in an equation with exponents. Negative exponents mean to take the reciprocal and apply the positive exponent. And then 9–ii= (1/nine)2 = 1/81. Now find what ability of ane/iii equals 1/81. Considering threeiv = 81, (1/three)iv  = one/81 , andx must be iv. The correct answer is (C).

9/18/20

THE CORRECT ANSWER IS D.

The question asks for the value of an expression for a certain value of the variable. Plug in the number given for a in the expression to find the value: –2 + (–2)2 – (–2)three + (–2)4 – (–two)five. Recollect PEMDAS, the order of operations: The kickoff thing to practice here is deal with the Exponents, then we tin can have care of the Addition and Subtraction: –two + 4 – (–8) + 16 – (–32), which simplifies to –2 + 4 + eight + 16 + 32 = 58. The correct answer is (D).

9/14/20

THE CORRECT ANSWER IS B.

The question asks for the value ofn. First, simplify the equation 4 x  •n 2 = 4 x + one •north to 4x •northward = 4 x + 1, and then try an like shooting fish in a barrel number forx. Ifx = 2, then iv2 •n = ivii + 1. Since 16n = 43, so 16n = 64 andnorth = 4. The correct answer is (B).

9/11/20

THE CORRECT ANSWER IS D.

The question asks for the value oft. To figure out how much you demand to add together to two.74 to get to iv.22, take 4.22 – ii.74 on your calculator. The difference between the ii numbers is one.48. This increase reflects the same number,t, added to each of the four numbers on the list. Divide 1.48 by 4 to discover thatt = 0.37. The correct respond is (D).

nine/7/20

THE CORRECT ANSWER IS D.

The question asks for the value of 24/10 . Outset, solve forx. Carve up both sides of the equation past iii, and you getx = four. So dissever 24 by four, which gives you lot six. The correct answer is (D).

9/4/20

THE CORRECT Respond IS C.

The nothing ofchiliadis the value of the variable, in this casex, when the equation is set to 0. This is also chosen the root or solution of an equation. Set the equation to 0 to go 0 = ii10 2 –dx– 6. Plug six in forxto get 0 = 2(62) –d(vi) – 6. Simplify the equation to go 0 = 72 – half dozend– six, or 0 = 66 – 6d. Solve fordto become –66 = –6d, and so 11 =d. Plug 11 in fordand set the quadratic to 0 to get 0 = 2x 2 – 11x– 6. Factor the equation to get 0 = (10– 6)(2ten+ one). The other nada of the equation is when ii10 + ane = 0. Solve for10 to get twox = –1, orx = –1/2. The correct answer is (C).

8/31/2020

THE CORRECT Reply IS B.

The question asks for the value off(3) +f(5), so observe the values off(3) and f(5) separately:f(3) = 2(3)ii + iv = 22 and f(5) = 2(5)2 + four = 54. And thenf(3) +f(5) = 76. Now evaluate the answers to see which one will requite a upshot of 76. Y'all can tell thatf(four) volition be between 22 and 54, so you can cross out (A). If you lot Ballpark (C) and (D), putting 10 or xv in the function will give you lot a number bigger than 100, and you lot're looking for 76, so (C) and (D) are too large. The correct reply is (B).

8/28/xx

THE CORRECT ANSWER IS C.

The question asks for the equation that best models the ball'due south acceleration. Figure out the points that volition be on the graph from the information given: (0, 0), (1, 5), (two, 10), (three, 15), (four, 20). Draw a line through or close to these points to get an idea of what the graph will look like. Then use POE. The line is linear, not quadratic, and then you can eliminate (D). Information technology is also clear that the line begins at the origin, so the y-intercept will be 0. This will eliminate (A). A slope of 25 is far also big—Ballpark—so you lot can eliminate (B). The correct answer is (C).

8/24/2020

THE Correct ANSWER IS B.

The question asks for the value ofc. Start by plugging in what y'all know into the given role. Iff(ten) =10 2–c, andf(–2) = half-dozen, so plug in –2 forxin the role:f(–two) = (–2)2–c. Solve and replacef(–2) with 6: 6 = 4 –c; 2 = –c; andc= –ii. If you picked (A), you forgot that (–two)2is positive 4. The correct reply is (B).

8/21/20

THE CORRECT ANSWER IS D.

The question asks for the departure in minutes betwixt Steve's fourth dimension and Adam'south fourth dimension. Employ a Rate Pie to calculate the time for each runner. To detect Steve's time, dissever his distance past his charge per unit, which means that he runs for 1 1/2 hours (or 1.five if you're using your calculator). Adam runs the same 12 miles at six miles per hr. This means that Adam runs for two hours. Adam takes half an hour longer to complete the race, and half an hr is xxx minutes. The right answer is (D).

viii/17/2020

THE Correct ANSWER IS C.

The question asks for an expression that is equivalent to the given one. There are variables in the respond choices, which means this is a perfect Plug In trouble. Since yous can't use a reckoner, make upward an easy value forx, such every bit 2. Therefore, 9 x + 3 10 + 1 so becomes 9 2  + three 2 + ane = 81 + 27 = 108. Use the number you plugged in for 10 to try to findy:y= 3 x , soy= iii ii = 9. At present plug iny= 9 to each respond choice to see which one gives you 108. Choice (C) isy (y+ three), which is 9(12) = 108 and the only respond that matches the target. The right answer is (C).

viii/14/xx

THE Correct Answer IS D.

The question asks for the ratio ofa toc and defines both in terms ofx. Since y'all are never told whatx is, and there is no style to find it, plug in forten. Say thatten = 100. Then, 63% of 100 is 63, and 3/8 of 100 is 37.5. The ratio ofa toc isa / c. So, 63/37.five = 1.68. To salve time, you can Ballpark the respond, sincea >c and (D) is the just choice greater than i. The correct answer is (D).

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