Math Test #7

solve. Ia-4I=3

(aI 1 and 7)

find f(-6) +4 if f(x) = 2x+5

-3

Chris's wages vary directly as the time she works. If her wages for 20 hours are $150, what is her wages for 38 hours?

$285

simplify using 2 column method (15*1/15+8*0)*12

(15*1/15+8*0)*12 given (1+8*0)*12 mult. inverse (1+0)*12 zero prop. 1*12 add. identity 12 mult. identity

3d-2(8d-9)>3-(2d+7)

(d/d<2)

solve and graph: t-45≤-13

(t/t≤32), solid circle on 32, arrow pointing left

f+8≤3 and f+9≥-4

(x/-13≤x≤-5) closed circle on -13 and on -5 with arrows connecting them

Solve and graph: -6 <3x+9≤12

(x/-5<x≤1) open circle on -5 with an arrow connecting to a closed circle on 1

Write a compound inequality for the graph. closed circle on -3 with an arrow pointing to the left and a closed circle on 3 with an arrow pointing to the right

(x/x ≤ -3 or x ≥3)

solve and graph. I 2x+8I ≥6

(x/x≥-1 or x≤-7) closed circles on -7 and -1. arrow going left on -7 and going right on -1

integer. Ex.

..., -3, -2, -1, 0, 1, 2, 3, ...

whole. ex.

0, 1, 2, 3, ...

natural. ex.

1, 2, 3, 4, ...

Steps to writing an absolute value equation (2 steps)

1. find middle number 2. find the distance to the middle number

ways to represent a relation: (4)

1. set of ordered pairs 2. graph 3. table of values 4. mapping

How many points does a trend/regression line have to go through?

2

Abby has 3 more dimes than quarters. If the total value is $7.30, how many of each coin are there?

20 quarters 23 dimes

2m+5=5(m-7)-3m given

2m+5=5(m-7)-3m given 2m+5=5(m)-5(7)-3m dist. 2m+5=5m-35-3m subs. 2m+5=5m-3m-35 comm. 2m+5=2m-35 subs. 2m-2m+5=2m-2m-35 subt. 5=-35 subs. NO SOLUTION

3(r+1)-5=3r-2 given

3(r+1)-5=3r-2 given 3(r)+3(1)-5=3r-2 dist. 3r+3-5=3r-2 subs 3r+-2=3r-2 subs. 3r-3r+(-2)=3r-3r+(-2) subt. -2=-2 subs IMS [all real solutions, identity]

4(2r-8)=1/7(49r+70)

4(2r-8)=1/7(49r+70) given 4(2r)-(8)=1/7(49r)+(70) dist 8r-32=7r+10 subs 8r-32+32=7r+10+32 add 8r=7r+42 subs 8r-7r=7r-7r+42 subt r=42 subs

Solve. a^2-(b^3-4c) a=7, b=3, c=5

42

find the slope (1, -2) (1,3)

5/0 m= undefined

Solve. (7(2)-4) + (9+8(4))

51

simplify using 2 column method. 5y(-3y)-4y^2

5y(-3y)-4y^2 given 5(-3)(y)(y) -4y^2 comm. prop. -15y^2-4y^2 subs. -19y^2 subs.

In Mrs. Sullivans math class, a test is worth 3 times more than a quiz. If Katie has test grades of 88 and 93, and quiz grades of 80, 78, and 98, what is Katies average grade?

89%

which sign is it? is fewer than

<

which sign is it? is more than

>

formula for standard form

Ax+By=C

Mixtures problems chart

Columns: # of ___, price/lb. , total Rows: A, B, mixture

Investment problem charts

Columns: principle, rate(dec.), interest Rows: %, %, total

Uniform motion chart

Columns: rate, time, distance Rows: A, B, total

rate formula

D/t

Write an absolute value equation. <--3----9-->

I x-6I=3

Interest formula

I=prt

Or: If a graph looks like this, ----> <----, what is it and how would you graph it?

IMS, <-------->

solve and graph. I 3x+2 I >-7

IMS, <-------> above number line

Solve and graph. 1/2n > -2 or 2n-2<6+n

IMS, Arrow going along the entire thing

|3𝑓 + 10| ≤ 4

IMS, arrow over entire thing

n-7≤5 or n-7≥1

IMS, no circles just an arrowed line going left and right

Or can have what and is represented by what?

IMS/All real numbers <----->

In orders of operation you solve from ____ to _____.

Left to right

How to find weighted averages

Multiply the weighted item by how much it is more. Then add all items divided by all weights

Percent of change formula

New-original/original=%/100

And can have what and is represented by what?

No solution nothing on the graph

Or will never be an No solution so if it looks like this, <--- --->, then what is the number and how would you graph?

Number is what it is, <--- --->

And will never be an IMS so if it looks like this, ---><---, then what is the number and how would you graph?

Number is what it is, I----I

Distance formula

Rate•time

Average speed formula

Total distance/total time Distance 1+ distance 2 ÷ time one plus time two

A lamp costs $120 but is on sale for 20% off with 6% sales tax find the final price define variable and write an equation

X=new cost X-120/120=-20/100 Sale price=$96 Y=final price Y-96/96=6/100 $101.70=final price

function:

a relation in which each element of the domain is paired with exactly one element of the range

If there is a correlation what do you draw?

a trend/regression line

suppose you have already saved $50 toward the cost of a new t.v. set. You plan to save $5 more each week for the next several weeks. a) Write an equation for the total amount, T, you will have week, w, from now. b) find the total amount saved after 7 weeks.

a) T=5w+50 b) $85

rational. Define and ex.s

can be put into fraction form 1.6666, 1/2

How do you verbally say {x|x is 4,5}

for all values of x such that x is 4 and 5

Is these inequalities an and or or? >, ≥

greatOR

Is these inequalities an and or or? <, ≤

less thAND

slope = WAYS TO SOLVE AND FORMULA

m = rise / run y2 - y1 / x2 - x1

find the slope passing through (-1,2) and (3,4)

m=1/2

formula for slope of a line

m=y2-y1/x2-x1

What is the means and extremes of this proportion? 4/5=24/30

means: 24, 5 extreme: 30, 4

Define your variable, write an equations, then solve. twice the greater of the two consecutive odd integers is 13 less than 3 times the lesser number

n+2: 2nd odd, greater n: 1st integer, lesser 2(n+2)=3n-13 n=17 17,19

.486868686

n=.48686, 10n=.48686(10), 10n=4.8686, 1000n=1000(.48686), 1000n=486.86-10n=4.86=990n=482, 990n/990=483/990 n=241/495

8(t+2)-3(t-4)<5(t-7)-8

no solution

solve. I 2x +1 I <-6

no solution

solve. I 5x-2I=-8

no solution

2𝑐 − 4 < −6 𝑎𝑛𝑑 3𝑐 + 1 > 13

no solution, no arrow

Solve and graph. 3t-7>5 and 2t +6<12

no solution, no arrow at all

3t-7≥5 and 2t+6≤12

no solution, no circles and no arrows just a number line with no numbers just ticks

And: If a graph looks like this, <---- ---->, what is it and how would you graph it?

no solution, nothing graphed

perpendicular lines

opposite reciprocal slopes

find the value of r given (6,-2) (r, -6) M=4

r=5

What are the real numbers?

rational-integers-whole-natural, irrational

Rate of change:

real world slope

Parallel lines

slope is the same

Irrational. ex.

square root of 37, pi, 1.2345

When writing algebraic expression and you are subtracting, when do you change the order of the verbal expression

when you see THAN

If AND has 2 arrows pointing in the same direction what is the answer/where do you graph

where the 2 arrows intersect

If OR has 2 arrows pointing in the same direction what is the answer/where do you graph

where the inequality represents the whole thing

The price a used bookstore pays to buy book is five dollars the store sells the book for 28% about the price of paid. What is the selling price define variable and create an equation

x=new selling price X-5/5=28/100 $6.40

___ depends on _____

y, x

formula for point slope form

y2-y2=m(x2-21)

Formula of direct variation:

y=kx

formula for slope-intercept form

y=mx+b

3(𝑧 + 1) + 11 < −2(𝑧 + 13)

z<-8, open circle on -8 arrow pointing to the left

find the solution set for y=2x+3 given {(-2,-1), (-1,3),(0,4),(3,9)}

{(-2,-1), (3,9)}

If and, then write the inequality _ for both

≤

which sign is it? is no more than, at most

≤

which sign is it? at least, is no less than

≥