Simple Math SAT

Factor 147x²-192

3(7x-8)(7x+8)

What does √5² will equal to?

5 Why? √5*√5=√25=5

Factor 6x²+7x-3

6x²+7x-3 6*-3 = -18 + 9 - 2 6x + 9x -2x - 3 3x ( 2x + 3) -1(2x+3) (3x-1) (2x+3)

8 * ⁴√x³ - 15 = 49 Then √x - 4 = ? Answer choices: - 4, - 2, 0, 4, 8

8 * ⁴√x³ - 15 = 49 8 * ⁴√x³= 64 ⁴√x³= 8 x∧¾ = 8 x¹= (x∧¾)∧(4/3)‖ you are raising it to a reciprocal power x = 8∧(4/3) = ³√8⁴ = 2⁴= 16 The final answer is 0

Renting an air freshener from a rental car company costs $0.50 per hour. Which of the following equations represents the total cost c, in dollars, of renting an air freshener for d days? A c=0.50(24d) B c=0.50d+24 C c=24d/0.50 D c=0.50d/24

A

At the department store, Marianne and Alicia each bought a pair of pants. Marianne's pants cost n dollars, and Alicia's pants cost $5 more than Marianne's pants. They decided to split the cost of the pants evenly, and each paid 30% percent sales tax on top of the cost of the pants. Which of the following expressions represents the amount, in dollars, each of them paid? a 0.3n+0.75 B 2.5n+0.1 C 1.3n+3.25 D 2.6n+6.5

c⊕

5+ 2/x = 1 What is x - ?

Multiply by X to get rid of the fraction. 5x+2 = x 4x = -2 x = -½

If c= 4ⁿ where n and c are both integers, which is equivalent to 16ⁿ+4^(ⁿ+²) Answer choices c(c+16) c(c+4) 4(c+4) c² c²+16

Play with the base → 16ⁿ = (4²)ⁿ = 4²ⁿ 4^(ⁿ+²) = 4ⁿ×4² 4²ⁿ+16(4ⁿ) c = 4ⁿ c² + 16c = c(c+16)

What are real numbers?

Real Numbers is: any point anywhere on the number line (not just the whole numbers)

What are some Elements of a Linear Function?

Slope, y-intercept

if ƒ(x) = 2x + 5 g(x) = |3-x| + 2 What is g(f(1)) - ? 0 3 6 8 11

It's a Compound Function ƒ(1) = 2×1 + 5 ƒ(1) = 7 g(7)= |3-7|+2 g(7) = 4+2 = 6

If 4x - 5y = 6 What is the value 16x² - 40 xy + 25y²? Answer choices: - 12, -4, 9, 24, 36

(A+B)² = A² + 2 AB + B² (A-B)² = A² - 2 AB + B² A = 4x B = 5 y (4x - 5y)² = 6² = 36

Factor x² + 8x+15=0 and x²+11x+28=0

(X+3)(x+5); (x+4)(x+7)

What is 8⁻⁵ ?

1/8⁵

Factor 98q²-224q+128

2(7q-8)²

Factor 196w²-168w+36

4(7w-3)²

factor 6x²+84z+294

6(x+7)²

A car rental agency charges a $150 processing fee for each car rental, plus $75 for each day the car is rented. Which of the following represents the total cost, c, of renting a car for d days? A c=75d+150 B c =150d+75 C d=75c+150 D d=150c+75

A

discrete vs. discreet

Discreet implies the showing of reserve and prudence in one's behavior or speech. Discrete means something quite different: "distinct, separate, unrelated."

If 4c + (b-a)/7 = a, what is b in terms of a and c? 4(2a-7c) 2(14c-3a) 2a-4c+7 4(c+2a)

Solve for B GEt rid of the fraction 28C + b - a = 7a b = 7a + a -28C b= 8a - 28C Factor b=4(2a-7c)

X⁷÷X⁵= ?

when we divide two exponents with the same base, we SUBTRACT them. X²

X³ × X⁶= ?

when we multiply two exponent with the same base, we ADD the exponents X ⁹

|x+1|= 3 What is the value of x?

x+1 = 3 and - x - 1=3 x = 2 x = - 4

y=0.78x+30.6 The average number of apples grown per tree in an apple orchard from 1985 to 1995 is given by the equation above, where x represents the number of years since 1985, and y represents the average number of apples per apple tree. Which of the following is the best interpretation of the value 0.78 in the problem?

A The estimated increase in the average number of apples grown per tree each year B The average number of apples grown per tree in 1985 C The estimated difference between the average number of apples grown per tree in 1995 and in 1985 D The total number of apples grown in the orchard in 1985 a

What's a Function?

A function is like a vending machine for numbers. Each input has exactly one, predictable output.

adverse vs. averse

Adverse and averse are both turn-offs, but adverse is something harmful, and averse is a strong feeling of dislike. Rainstorms can cause adverse conditions, and many people are averse to rain. Adverse describes something that works against you, like a tornado or a computer crash, and is usually applied to things.

Roylan is throwing a huge party. A group of his closest friends will definitely come to the party no matter what, but the number of other people who attend will depend on the number of invitations he sends out. The following equation gives the number of total people who will attend his party, p, based on the number of invitations he sends, v: p(v)=5v+20 If Roylan sends out 34 invitations, how many people will attend his party?

All you have to do to solve a finding values problem is carefully plug the given value into the function. In this case, the problem gives us the value 34 and says that it is the number of invitations. The problem also says that v represents the number of invitations, so we plug in 34 for v and solve: p(v) = 5v+20 p(34) = 5(34)+20 = 170+20 = 190 190 people will attend Roylan's party if he sends out 34 invitations.

amiable vs. amicable

Amicable refers to a friendliness or goodwill between people or groups. Amiable refers to one person's friendly disposition. A group might have an amicable meeting, because the people there are amiable. Amicable refers to the connections between people or things, like a friendly situation with a crowd.

Assent vs ascent

Ascent is a noun that denotes "the act of rising or mounting upward" or "an advance in social status or reputation". Its verb form is ascend. Meanwhile, assent has two uses. It can be used as a noun which means "the expression of approval or agreement

R²-2RS+S²=49 What is R-S - ?

A²+ 2AB + B² = (A+B)² A²- 2AB + B² = (A-B)² R²-2RS+S²=49 (R-S)² R-S = √49 = 7

x+y=5 What is x²+2xy+y²=?

A²+ 2AB + B² = (A+B)² x+y=5 (x+y)²=5²=25

x²-25, what is x?

A²-B²=(A+B)(A-B) (x-5)(x+5) X=±5

oylan is throwing a huge party. A group of his closest friends will definitely come to the party no matter what, but the number of other people who attend will depend on the number of invitations he sends out. The following equation gives the number of total people who will attend his party, p, based on the number of invitations he sends, v: p(v)=5v+20 What is the meaning of the value 20 in this equation? A 20 people will attend the party B 20 people will attend the party if Roylan doesn't send out any invitations C 20 more people will attend for every invitation Roylan sends out D Roylan will send out 20 invitations

B

M(T)=T+215 W(T)=65−2/3T The number of morel mushrooms and the number of wood ear mushrooms in a certain habitat are function of the average temperature of the habitat. The functions for the estimated number of morel mushrooms and the estimated number of wood ear mushrooms are displayed above. The function M(T) gives the number of morel mushrooms in the habitat when the temperature is T degrees Fahrenheit. The function W(T) gives the number of wood ear mushrooms in the habitat when the temperature is T degrees Fahrenheit. If the temperature of the habitat is increased by 15 degrees Fahrenheit, how will the number of wood ear mushrooms in the habitat change? A The number of wood ear mushrooms will increase by 10. B The number of wood ear mushrooms will decrease by 10. C The number of wood ear mushrooms will decrease by 15. D The number of wood ear mushrooms will decrease by 80.

B Question: Please choose the answer that best matches the question asked. M(T)=T+215 W(T)=65− 2 3 T The number of morel mushrooms and the number of wood ear mushrooms in a certain habitat are function of the average temperature of the habitat. The functions for the estimated number of morel mushrooms and the estimated number of wood ear mushrooms are displayed above. The function M(T) gives the number of morel mushrooms in the habitat when the temperature is T degrees Fahrenheit. The function W(T) gives the number of wood ear mushrooms in the habitat when the temperature is T degrees Fahrenheit. If the temperature of the habitat is increased by 15 degrees Fahrenheit, how will the number of wood ear mushrooms in the habitat change? A The number of wood ear mushrooms will increase by 10. B The number of wood ear mushrooms will decrease by 10. C The number of wood ear mushrooms will decrease by 15. D The number of wood ear mushrooms will decrease by 80. Explanation SAT instructor Joshua The question asks us to find how the number of wood ear mushrooms changes when the temperature is increased by 15.We are only asked about wood ear mushrooms, so we can ignore the morel mushroom equation altogether; we only care about the equation W(T)=65− 2 3 T. There are two ways to do this problem. The first is use our understanding of linear equations, and the second is to plug in values. The second is way is great if our understanding of linear equations is fuzzy. Otherwise, the first way is quicker. Method 1 - Understanding linear equations: The equation W(T)=65− 2 3 T is a linear equation. We can see that by switching out W(T) for y and x for T, giving us y=5− 2 3 x, which is the characteristic y=mx+b form (except b and mx have been switched around). With linear relationships in y=mx+b form, there are two values that have very specific meanings: m and b. m is the slope of the graph y=mx+b, and is referred to as the "rate of change." More specifically, if x is increased by 1, then y is increased by m. If m=2 and x is increased by 1, y is increased by 2. If m=2 and x is decreased by 1, y is decreased by 2. If m=3 and x is increased by 2, y is increased by 6. If m=−2 and x is increased by 5, y is decreased by 10. b is the y-intercept of the graph y=mx+b, and is referred to as the "initial value". More specifically, b is the value of y when x=0. If b=4, then when x=0, y=4. If b=−2, then when x=0, y=−2. If you have trouble remembering which value is m and which value is b, use this mnemonic: m is multiplied by x, and b is the one that is added or subtracted. Since the question asks us how number of wood ear mushrooms changes as temperature changes, we know the question is asking us to use m. Since m is multiplied by x, in the equation W(T)=65− 2 3 T, m=− 2 3 . Specifically, the question asks us what happens if the temperature increases by 15 degrees Fahrenheit. Well, since m=− 2 3 , if temperature increased by 1 degree, the number of wood ears would decrease by 2 3 (remember that this is just a model, and that decreasing by a fraction of a wood ear is fine). So if temperature increased by 15 degrees, the number of wood ears would decrease by 15× 2 3 =10. This is what answer B says, so B is the correct answer. Method 2 - Plugging in values: The idea is to pick two temperatures, 15 degrees apart, at which we can find the number of wood ears. If we compare those two numbers together, it should match up with one of the answers. When using this strategy, we always want to use values that are easy to work with. For example, in this case, it's best to pick small temperatures so that our computations become a little easier. For our purposes, let's compare the number of wood ears at the temperatures 0 degrees Fahrenheit and 15 degrees Fahrenheit, since those two are small numbers and having 0 as one of our temperatures will make some of our calculations easier. We can find the number of wood ears at 0 degrees Fahrenheit by plugging 0 in for T in the equation W(T)=65− 2 3 T: W(T) = 65− 2 3 T →W(0) = 65− 2 3 (0) = 65 Since W(0)=65, the number of wood ear mushrooms at 0 degrees Fahrenheit is 65. Similarly, we can find the number of wood ears at 15 degrees Fahrenheit by plugging 15 in for T: W(T) = 65-2/3 T →W(15) = 65−2/3(15) = 65−10 = 55 Now we know there are 55 wood ears at 15 degrees Fahrenheit. Compare that to the 65 wood ears at 0 degrees Fahrenheit. When we increased the temperature by 15 degrees, the number of wood ears went from 65 to 55. That is, they decreased by 10. That is exactly what B says, so the answer is B

climatic vs climactic

Climactic describes the high point, the most intense part of a movie, play, song, or, well, anything. Climatic refers to the climate, like the climatic changes that turned Santa's workshop into a sauna for elves. ... But climatic is just air.

Roylan is throwing a huge party. A group of his closest friends will definitely come to the party no matter what, but the number of other people who attend will depend on the number of invitations he sends out. The following equation gives the number of total people who will attend his party, p, based on the number of invitations he sends, v: p(v)=5v+20 What is the meaning of the value 5 in this equation? A) Roylan will send out 5 invitations. B) 5 people will attend the party. C) Another person will attend the party for every 5 invitations Roylan sends out. D) 5 more people will attend the party for every invitation Roylan sends out.

D

The number of people who attend a concert is directly proportional to the number of advertisements that were run before the concert. If 240 people attend a concert for which 60 advertisements were run, how many people would attend a concert for which 100 advertisements were run?

DIrect proportion problem: y=kx where k is the constant value. 240=k60 y=k100 k = 4 y=4*100 y = 400

What is the y - intersect h(x)=2((x−4)/3)

Distribute the 2 and 1/3 2/3x-8/3 - 8/3

What is the slope f(x)=3((x-1)/5)

Distribute the 3 and 1/5 f(x)=3/5x-3/5 Slope is 3/5

What is the slope h(x)=x/2−3

Dividing by 2 is like multiplying by 1/2 h(x)= 1/2x−3 Slope is 1/2

immigrate vs emigrate

Emigrate means to leave one's country to live in another. Immigrate is to come into another country to live permanently. Migrate is to move, like birds in the winter. The choice between emigrate,immigrate, and migrate depends on the sentence's point of view.

(X² - 2x - 24)÷(x²+ 7x + 12)= 12/(x²+x-6) what is the value of X - ? Answer choices: -4, -2, 1, 5, 8

Factor Each expression and then multiply both sides by (x+3) The correct answer should be x = 0 AND x = 8, but you want to chose 8 as your answer

Factor 25t²-40t+16

Factoring perfect-square quadratics: a²+2ab+b²=(a+b)² a²-2ab+b²=(a-b)² (5t-4)² (5t-4)(5t-4) Expand 25t²-20t-20t+16 Apply the distributive property (FOIL) 25t²-40t+16 Yes, 25t²-40t+16=(5t-4)²

Factor. 98k²-242

First factor out 2, the greatest common factor of 98k²-242. 98k²-242=2(49k²-121) Next look at the quadratic inside the parentheses, 49k²-121. It is a difference of squares, because it can be written in the form a²-b², where a is 7k and b is 11. a²-b² (7k)²-112 49k²-121 Now use the formula for factoring a difference of squares. a²-b² = (a+b)(a-b) (7k)²-112 = (7k+11)(7k-11) 49k²-121 = (7k+11)(7k-11) Next go back and factor 2(49k²-121). 2(49k²-121) 2(7k+11)(7k-11) The factored form of 98k²-242 is 2(7k+11)(7k-11). Finally, check your work. 2(7k+11)(7k-11) 2(49k²+77k-77k-121) Apply the distributive property (FOIL) 2(49k²-121) 98k²-242 Yes, 98k²-242=2(7k+11)(7k-11).

Well vs. Good

Good describes job, which is a noun, so good is an adjective. Well is an adverb describing how the job was performed. Rule: With the four senses—look, smell, taste, feel—discern if these words are being used actively to decide whether to follow them with good or well.

6 = 3*|c-7| What is c?

Let's call the absolute value |c-7| →x The equation becomes 6 = 3x x = 2 c - 7 = 2 and - c + 7 = 2 c = 9 c = 5

A chemist is mixing liquids in two test tubes. The volume of liquid in test tube A is v milliliters, and the volume in test tube B is 3 millimeters more than the volume in test tube A. The chemist pours some of the liquid in test tube B into test tube A so that the volumes in the two test tubes are split evenly. She then increases the volume in each test tube by 10 percent. Which of the following expressions represents the volume, in milliliters, inside each of the test tubes? A 2.2v+3.3 B 1.1v+1.65 C 0.5v+0.15 D 0.1v+0.3

SAT instructor Joshua We want to figure out the volume inside one of the test tubes after all the steps outlined in the problem are done. We know: Test tube A has volume v, and Test tube B has 3 more than that. The chemist splits the volume in the two tubes evenly. The chemist then adds 10 percent to each test tube. We can approach this problem two ways: we could plug in values, or we could directly build the expression we want. The first way is useful if we're uncomfortable with setting up algebraic expressions, and is quicker for about 90% of students. The second way ought to be tried only if we're very comfortable with setting up algebraic expressions quickly. Method 1: Choosing values The easiest way to solve this problem is to plug in a value for v. Our plan of action is to follow each of the steps the chemist took to find out the volume of one test tube, and then compare that against the answers. For our purposes, let's choose v=10, since it's an easy number to multiply by, and all of the answers have us multiply by v. Finding the volumes of the two test tubes We know the volume of test tube A is v=10. We're told the volume of test tube B is 3 more than that, so its volume must be v+3=10+3=13. Splitting the volumes evenly The chemist's first step is to split the volumes between the test tubes evenly; each test tube should have an equal share of the total volume. The combined volume of the two test tubes is 10+13=23. To "split" the volume equally, we simply divide by 2. 23/2=11.5 Each test tube has a volume of 11.5 now. Adding 10 percent to each test tube The chemist's last step is to add 10 percent to each test tube. So to find the volume of each test tube, we'll have to add 10 percent of 11.5, TO 11.5. How do we do this? 11.5+[10percentof11.5]=11.5+1.15=12.65 The volume of each test tube is 12.65. We can now compare against the answers. Comparing against answers Now we just plug v=10 into each of the answers. The one that gives us 12.65 is the answer (though we'll try all of them just in case of false positives: answers that are only correct for the value we chose). 2.2v+3.3 → 2.2(10)+3.3 = 22+3.3 = 25.3❌ 1.1v+1.65 → 1.1(10)+1.65 = 11+1.65 = 12.65✅ 0.5v+0.15 → 0.5(10)+0.15 = 5+0.15 = 5.15❌ 0.1v+0.3 → 0.1(10)+0.3 = 1+0.3 = 1.3❌ B is correct by process of elimination. Method 2: Building the expression We can also try building the expression we need directly without plugging in values. We'll follow the same basic steps as before: finding the volumes of each test tube, splitting evenly the volume between them, then adding 10 percent. We'll just be using v instead of a concrete amount. Finding the volumes of the two test tubes We know the volume of test tube A is v. We're told the volume of test tube B is 3 more than that, so its volume must be v+3. Splitting the volumes evenly The chemist's first step is to split the volumes between the test tubes evenly; each test tube should have an equal share of the total volume. The combined volume of the two test tubes is v+(v+3)=2v+3. To "split" the volume equally, we simply divide by 2. (2v+3)/2=v+1.5 Each test tube has a volume of v+1.5 now. Adding 10 percent to each test tube The chemist's last step is to add 10 percent to each test tube. So to find the volume of each test tube, we'll have to add 10 percent of v+1.5, TO v+1.5 . How do we do this? e discussion above: 10percentof(v+1.5) = 10/100×(v+1.5) = 0.1(v+1.5) = 0.1v+0.15 Therefore, to add 10 percent of v+1.5, TO v+1.5 (and thus find the volume of each test tube),, we take: v+1.5+[10percentof(v+1.5)] = v+1.5+0.1v+0.15 = (v+0.1v)+(1.5+0.15) = 1.1v+1.65 The final volume of each test tube is 1.1v+1.65. So the answer is B.

What is the slope of this liune? f(x)=2x+1

Slope The slope of a function, algebraically, is the coefficient (value multiplied with) x: f(x)=2x+1 The slope of the function above is 2. If a function seems to be linear but does not have a clear number multiplied with x, try to change it into the form f(x)=mx+b, where m and b are numbers.

stationary vs. stationery

Stationary with an a is the older of these two terms, and it means "fixed in one place and not moving," like a stationary bicycle at the gym. Stationery with an e stems from the term stationer, which refers to "a person who sells the materials used in writing, such as paper, pens, pencils, and ink.

every day vs. everyday

The one-word adjective everyday means "commonplace, daily, or routine." Everyday as a noun refers to the mundane or the routine. Every day as two words means "each day."

persecute vs. prosecute

The side carrying out the legal claim is also referred to as the prosecution. An attorney representing the accuser (usually the government) is a prosecutor. Persecute means "to harrass, or pursue in order to injure or afflict." The act of persecuting is persecution.

What is a y-intersect?

The y-intercept of a function is where its graph -- surprise, surprise -- intersects the y-axis. So in the graph of y=2x+1 above, the y-intercept is 1. Algebraically, it is the number in the function that is not multiplied with x: in the form f(x)=mx+b, it is the number b.

What is the y - intersect f(x)=9

There are zero x's here! f(x)=0x+9 9

What is the slope of f(x)=9

There are zero x's here! f(x)=0x+9 Slope is 0

What is the slope g(x)=x+5

There's one x here! g(x)=1x+5 1

What is the y - intersect g(x)=x

There's zero added to x here! g(x)=x+0 0

affect vs. effect

Think of Edgar Allen Poe and his RAVEN: Remember Affect Verb Effect Noun. ... Most of the time, you'll want affect as a verb meaning to influence something and effect for the something that was influenced. The difference between affect and effect is so slippery that people have started using "impact" as a verb instead.

A bodybuilder begins his workout by lifting 150,000 grams of weight; the record weight he has lifted in the past is 275,000 grams. Every minute after the start of his workout, he adds an additional 2,500 grams to the weight he lifts. If x represents the time after the beginning of his workout in minutes, which of the following inequalities describes the set of minutes where he is lifting at or above his record weight? A 275,000−2,500≤x B 275,000≤2,500x C 125,000≥2,500x D150,000+2,500x≥275,000

This problem asks us to set up an inequality describing "the set of minutes where he is lifting at or above his record weight." We're given how much he begins by lifting, his record weight lifted, and how many grams he adds to his weights per minute. Since the question says "at or above his record weight," we know that the inequality will look like: [something]≥[recordweight] What should be on the left side of the inequality? Since he has to lift over his record weight, the [something] should be an expression for the amount of weight he lifts after x minutes. That way, we'd have: [amountofweightafterxminutes]≥[recordweight] ...which describes the minutes where the weight he is lifting is greater than or equal to his record weight, which is what we want. What is his [record weight]? We are told in the prompt that it is 275,000 grams, so our inequality is now: [amountofweightafterxminutes]≥275000 How much weight is he lifting after x minutes? Well, we know he starts off with 150,000 grams, and then adds 2,500 grams every x minutes. So after x minutes, he must be lifting 150000+x×2500=150000+2500x grams. Now our inequality is: 150000+2500x≥275000 This is the inequality found in answer D, so D is the correct answer.

Jet pilots calculate their average velocity V, given in miles per minute, over a time period t, given in minutes, using the equation V=tA, where A is their average acceleration in miles per minute squared. This equation is taken from a field of physics called kinematics, and is sometimes called Jackson's Law. Monica, a jet pilot, estimates that over a 2 minute period, her average acceleration was 6 miles per minute squared. Monica uses Jackson's Law to estimate that her average velocity is 12 miles per minute. Monica is given a chance to fly a new jet. She is told that, over the 2 hour period that it was tested, its average acceleration was 0.3 miles per minute squared. What was the average velocity of the jet during its testing period in miles per minute? GRID IN

This question has a LOT of words in it. Let's cut it down to what we need the most. We know that V=tA, where V is velocity in miles per minute, t is time in minutes, and A is acceleration in miles per minute squared. We know that the jet plane was flown for 2 hours, we know it's acceleration was 0.3 miles per minute squared, and we want to find its velocity. That's all we need; everything else is just fluff. Using V=tA, we can plug in the acceleration (0.3 miles per minute squared) and the time (2 hours) we're given to find V, the velocity of the jet during its test flight in miles per minute squared. However, there is one conundrum. In order to plug in our time for t, our time has to be in units of minutes, but we're told that testing time was 2 hours. So we should convert time to minutes. Since 1 hour is 60 minutes, 2 hours is 2×60=120 minutes. Now we have that the time t is 120 minutes, and we know that acceleration A is 0.3 miles per minute squared, so we can plug values into our equation V=tA and solve for V, which is the velocity we want. V = tA = (120)(0.3) = 36 Since V=36, the answer is 36.

What does 8, raised to the fractional exponent (5/3) and 16, raised to the fractional exponent (5/4) equal to?

To simplify the exponent, think of 5/3 as 1/3 * 5. 8 raised to 1/3 is ³√8 ( which is 2). Then Raise 2⁵ and you get = 32. Similarly, workout 16 to the 5/4th power.

Evaluate : X³+ X⁴+X⁷=?

We do NOT touch exponents when we add or subtract them.

If each mile has 5280 feet, and each foot has 12 inches, how many inches is 0.65 miles?

We set up the conversion, making sure the units can cancel out: 0.65miles×(5280feet/ 1miles) ×(12inches/1foot) =41184inches If you flipped any of the conversion terms, you would end up with a meaningless unit that didn't cancel out properly, and the wrong answer.

3/(x+2) = 5/4 What is x - ?

When two fractions are separated by an equal sign - you can cross - multiply 5(x+2)=3*4 5x+10 = 12 5x = 2 x = 2/5

(x⁵)⁴ =?

X²⁰

³√X⁴ is equivalent to ?

X¾ where 3/4 is a fractional exponent

What is another way of thinking about a slope?

You should think of the slope of a linear function as its rate of change: it is how much the output goes up or down for each increase of 1 in the input.

What is another way to think about y - intersects?

You should think of the y-intercept of a linear function as its starting point for outputs: it is the value of the output before the input starts to increase from zero.

Factor 25u²-16

a²-b²=(a+b)(a-b) Notice that 25u²-16 is a difference of squares, because it can be written in the form a²-b², where a is 5u and b is 4. a²-b² (5u)²-4² 25u²-16 Now use the formula for factoring a difference of squares. a²-b² = (a+b)(a-b) (5u)²-4² = (5u+4)(5u-4) 25u²-16 = (5u+4)(5u-4) The factored form of 25u²-16 is (5u+4)(5u-4).

In a laboratory experiment for Physics class, a toy car was rolled at a constant velocity along a flat table top. Every 6 seconds, Anita wrote down the car's distance, x, in inches, from the edge of the table, and the time, t, that had passed since the start of the experiment. She recorded these values in the following chart: LOOK in the back of the card Which of the following equations represents the relationship between the amount of time that has passed in the experiment and the distance the car has traveled? A x=t+12 B x=3t+12 C x=12t+3 D x=15t

b

Selecting BEST mathematical model Roylan is throwing a huge party. A group of 18 of his closest friends will definitely come to the party no matter what, and 9 more people will show up for every invitation he sends. Which of the following represents the total number of people, p, who will attend his party if he sends out v invitations? A) p=18v+9 B) p=9v+18 C) v=18p+9 D) v=9p+18

b

C(n)=675−80n M(n)=210+5.5n The number of CD players and MP3 players sold per month by a certain electronics store are functions of time. The functions above give the estimated number of CD players and MP3 sold by the electronics store. The function C(n) gives the quantity of CD players sold during the nth month after January 2001, and the function M(n) gives the quantity of MP3 players sold during the nth month after January 2001. How will the number of MP3 players sold per month change 4 months after January 2001? A The number sold will increase by 4. B The number sold will decrease by 22. C The number sold will increase by 22. DThe number sold will increase by 90.

c∵

Leslie and Ernest play a guessing game together at the candy shop. Leslie puts a grams of jelly beans into a bag, where a≤250. Ernest then picks a number b as a guess of how many grams of jelly beans are in the bag. If Ernest is within 5 grams of the actual weight of the jelly beans, Ernest wins the game. If they play this game and Ernest wins, which of the following inequalities represents the relationship between the actual weight of the jellybeans and Ernest's guess? A a+b<5 B b>a+5 C b<a−5 D−5<b−a<5

d

Shayla has $20. She sells carrots from her garden for $3 per pound. What is the slope of the function?

f(x)= 3x ....

What is the y - intersect here? Shayla has $20. She sells carrots from her garden for $3 per pound

f(x)=3x+20 20

At a party, the number of slices of pizza each person can have is inversely proportional to the number of people attending. If 64 people attend, each one can have 3 slices of pizza. How many slices can everyone have if 96 people attend?

it's an inverse ratio problem y = k/x where K is a constant 3=k/64 k = 3*64=192 y = 192/96 = 2

if ƒ(x)=(7x+5)/3 - (4x-7)/3 What is the value of ƒ(x) - x ? Grid in question.

ƒ(x) - x = (7x+5)/3 - (4x-7)/3 - x 7x/3 + 5/3 + 4x/3 + 7/3 - x = 3x/3 + 12/3- x = x+4-x=4

If ƒ(x,y) = 2x + y - 3 what is the value of ƒ(ƒ(3,4),5) -?

ƒ(x,y) = 2x + y - 3 ƒ(3,4) = 2×3 + 4 - 3 = 7 ƒ(7,5) = 14 + 5 -3 = 16

Let ƒ(x,y) = y²-5x If ƒ(x,3) = -21 What is the value of x - ?

ƒ(x,y) = y²-5x ƒ(x,3) = -21 → y = 3 y²-5x = - 21 9 - 5x = -21 -5x = -30 x = 6