Math 1 exam review

Daniel rents a bicycle at the beach for and spends $16 for 4 hours. If the rate per hour is $1.50, write the equation that BEST models this situation.

(y − 16) = 1.5(x − 4)

Write the point- slope form through (-1, 3), slope: -5/4

(y-3) = -5/4 (x +3)

What would the coordinate points be given the function: f(-1) = 1

-1 = x, 1=y SO: (-1, 1)

Evaluate the function given g(10): g(x)= -3x +1

-29

how to find standard deviation

1. Work out the Mean (the simple average of the numbers) 2. Then for each number: subtract the Mean and square the result. 3. Then work out the mean of those squared differences. 4. Take the square root of that and we are done!

solve: (8x+8y)(2x^2-6xy+5y^2)

16x^3-32x^2y-8xy^2+40y^3

Find product: 4x(6x+2y)

24x^2+8xy

Convert to Standard form (remember a cannot be negative): y= -3/7x -1

3x + 7y= -7

At a school play, children's tickets cost $3 each and adult tickets cost $7 each. The total amount of money earned from ticket sales equals $210. Write a linear model that BEST relates the number of children's tickets sold to the number of adult tickets sold.

3x + 7y= 210

Solve: (6x+6y)(8x+4y)

48x^2+72xy+24y^2

Solve: (2x^4+7x+x^2-4x^3) +(4x^4-4-x+5x^3)

6x^4+x^3+x^2+6x-4

Give the factors of AC that yield B: A. 3a^2-11a+8=0 B. 3b^2 +7b+1=-3

A. -8,-3 B. 4,3

Solve by square root method: A. 4(x+8)^2+3= 67 B. 4m^2=16 C. 10(n-1)^2+5= 365

A. x= -4, x=-12 B. m=+- 2 C. n=7, n=-5

Solve: A. 6x^2-6x-72=0 B. 11x^2-1=-x+4x^2+7

A. x=4, x=-3 B. x= -8/7, x=1

how to find residual

ACTUAL VALUE - PREDICTED VALUE actual value is y in point predicted value is found by putting x into regression equation - also called line of best fit (which may have to be found)

Find the: mean, five-number summary, IQR, and outlier of the data set 43, 69, 49, 78, 88, 54, 73, 194, 54, 59, 70

Mean: 75.55, Min: 43, Q1: 54, med: 69, Q3: 78, max: 94, IQR: 24, Outlier: 194

2) Find mean, median, mode, Q3-Q1 18, 16, 19, 15, 17

Median (Q2): 17 Mode: none Q3-Q1: 2 mean: 17

Write an equation through (-3, -2) perpendicular to y= -3/7x -4

Point: (-3, -2) Slope: 7/3 y+2 = 7/3 (x +3)

Write the Standard form through the points (3, -4), (1,-5)

Slope: 1/2 Point: ( 1, -5) y= 1/2x -11/2

Is this quadratic in standard, factored or vertex form? y= x^2+6x+10

Standard form, and its y-intercept is 10 It opens up because a is positive

how to tell if an equation is the line of best fit:

To tell if the regression equation is the line of best fit add all of the residuals, if they equal zero than the equation is the line of best fit if it doesn't equal zero its not

Is this quadratic in standard, factored or vertex form? y= 1/2(x+4)^2+3

Vertex form, its vertex is (-4,3) We can also tell that the parabola opens up because a is positive

solve each equation: a. 3/4(x-5)-2 = 1/3(x+1) b. -1+x/15=0 c. 3k-7(8-7k)= -4k

a. 14.6 b. 15 c. -1

A. Solve for b: A= 1/2bh B. Solve for w: a/w = lw/w C. Solve for b: y=mx +b

a. 2A/h = b b. a/w= l c. y-mx = b

a. Find the common difference: -15, -7, 1, 9.. b. Find a1: c. Then find the explicit formula:

a. 8 b. -15 c. an= -23+ 8n

Name the polynomial by degree and terms a. 8v^3- 7v^2+v b. 8m^6

a. Cubic (degree of 3) Trinomial (3 terms) b. 6th degree Monomial (1 term)

Solve: a. 2k^2-5k+4=4 b. x^2+12x-6=5x-6

a. k=0, k=5/2 b. x= 0, x=-7

Find the slope, type of form, and point on the line based on the equation given: a. 3x-4y= 8 b. (y-2) = 6 (x-5) c. y= x-1

a. standard form, slope: 3/4 b. Point-Slope form, Slope: 6, Point: (5, 2) c. Slope-Intercept form, Slope: 1, Y-intercept: -1

solve each inequality: a. 6(1-3x) > -102 b. 6(1+5x)+8x _> 310 c. - (1/2m+1/2) +1/2 < -7/4 (2m+1/4)+9/5m

a. x < 6 and graph will be an open circle at 6 going left since x is LESS than 6 b. x _> 8 and graph will have a CLOSED circle at 8 going right because x is GREATER than 8 c. m < -35/96 and graph will be an open circle going left at -35/96

A. Solve for y: -3 (x+y) = 8+3x B. solve for y: Ax+By = c

a. y= -2x - 8/3 b. y= -A/Bx + C/B

Find the standard deviation. Round to the nearest tenth as needed. 86​,23​,76​,37

about 26.2

equation: y= .49x Points: (5,3), (10,4), (15,9), (20,7), (25,13), (30,15) Find predicted value for (5,3), and residual value:

actual: 3 predicted: .49(5)= 2.45 So: 3 - 2.45= .55 Residual is .55

Given a term in an arithmetic sequence and the common difference find the explicit formula: (explicit formula: an= a1 + (n-1)d) A14= -371 d= -30

an = 49- 30n

standard form of a quadratic equation

ax² + bx + c = 0

Is this quadratic in standard, factored or vertex form? (4p-7)(5p+1)=0

factored form, the x-intercepts are (0,0), (4,0)

Is this skewed left or skewed right or symmetric?

skewed left

How to find the regression equation using points in desmos

type in y1 ~ mx1 +b graph: data points then look at m and b

Solve for x : -8(x-5) = 22/7x -64/5

x= 308/65

A machine salesperson earns a base salary of $40,000 plus a commission of $300 for every machine he sells. Write an equation that BEST shows the total amount of income the salesperson earns, if he sells x machines in a year.

y = 300x + 40,000

How to find slope given 2 points

y-y/x-x

Convert to Slope-Intercept form: 3x-5y = 12

y= 3/5x - 12/5

vertex form of a quadratic function

y=a(x-h)^2+k

factored form of a quadratic equation

y=a(x-p)(x-q)