Kyote Practice Problems

Solve 8x−4 / 3 = x / 7 for x.

28/53

The rectangle below has vertices P, Q, and R. If P = (4,3) and R = (6,7) then Q =?

Q shares an x value with R and a Y value with P.

Simplify. 42 / 6−42

Simple math, plug into calculator (use parenthesis on denominator) -7 / 6

Which of the following is an equation of the line parallel to y=5x+3 that passes through the point (5,−4)?

Since they are parallel lines, they must have the same slope (5x) y=5x+b Plug in your coordinates to x and y and solve y=5x-29

Assuming that a car gets 20 miles per gallon of gas, how many gallons of gas are required for the car to go 175 miles?

$8.75 175/20

Which decimal number is smallest (left of the others on the number line)? A) -0.843 B) −0.834 C) −0.348 D) −0.438 E) −0.483

-0.843 It's just the smallest. That's it. Higher the number, lower it is.

A couple has two bank accounts. The second account contains 13 percent more than the first. Which expression represents the amount, in dollars, contained in both accounts if the first account contains x dollars?

2x+0.13x

Simplify. (−6x^3)^2

36x^6 take the square root of negative six and then multiply exponents

What is 7 percent of 400?

400 x 0.007

What is the price, in dollars, of an Iphone that has been marked down 11 percent from its original price of 440 dollars?

440 x 0.11 Subtract answer from original total.

Simplify. 6−2(3^3)

6-2(27) 6-54 -48

Simplify. (−3x^4)^2

9x^8 Square -3 and then multiply exponents

What is the area of a square, in square feet, whose perimeter is 36 feet?

All sides are equal, there are four sides. To get 36, you have to have 9 on each side. So you take 9x9 to get 81.

Combine like terms and simplify. (2x^2−5x+2)−(x^2−7x−9)

Combine like terms from both inequalities then simplify from this state.

Multiply. 3x^2(x^4 + 4x^3 − 9)

Distribute 3x^2 to all numbers inside the parenthesis. Add exponents if needed.

Multiply. (x^2−y^2)(x^5+y^5)

F.O.I.L. x^2 + x^5= x^7 combine terms x^2y^5 combine terms -y^2x^5 y^2 + y^5= y^7 Combine all terms in an inequality

Subtract 4r / x − 3s / y

Find a common denominator and multiply.

What is the least common denominator used to add the fractions 5 / 24 and 3 / 16?

Find a common denominator between the two denominators by finding their multiples and comparing.

A rectangle has length 36 inches and its perimeter is 6 times its width. What is its width in inches?

P=2w+2l 6w=2w+2l 4w=2l l=2w So 32=2w Simplify and solve.

The solutions of 2x^2−x−10=0 are...?

Plug into Quadratic Program on calculator. 5 / 2 and −2

Subtract. 3 / 8 − 2 / 3

Plug it into the calculator. Or to solve by hand... Set the two denominators equal to one another by finding a common denominator. Subtract the two.

Solve the system {x+y=9 −x+3y=3 What is the x-coordinate of this solution?

Solve x+y=9 for y. Take your solution and plug it into the y value in the other inequality and solve for x. 6

Find the value of 4+10x when x=−3.

Substitute the given value of x in the equation and solve.

What is the greatest common factor of the two terms in the expression x^3y^4z+x^4y^3

Take the lower exponent of each variable. (ex: x^3, y^3)

A boy has only dimes and quarters in his piggy bank. If he has 60 coins worth 12 dollars and 45 cents altogether, how many quarters does he have in his bank?

q+d=60 0.25q+0.10d=12.45 q+d=60-d q=60-d 0.25(60-d)+0.10d=12.45 solve for d then substitute answer in original inequality.

Simplify, assuming x is a positive number. √x^12+49x^6

x3√x6+49 Find a common factor in exponents and move it outside

Solve 3x+6 > 10x−10 for x.

x< 16 / 7 Flip the sign 16<7x x<16/7

There are 480 paper napkins in a package. Each napkin is either white or red. If there are 6 more than twice as many white napkins as red napkins in the package, how many white napkins are in the package?

x=white napkins y=red napkins 480= 2x+6 474=2x x=237

Simplify. x^14 + 3x^12 / x^3 + 3x^2

x^10(x^2 + 3) / x + 3 Factor the GCF The resulting term is a product of the GCF and the original expression divided by the GCF. x^12. Reduce fraction

What is the equation of the line whose graph is shown below...

y=3/2x-6 Find y-intercept on y-axis count your rise and then run