How many prime numbers less than 100 have a units digit of 7?
2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97
I count five of them.
.
Find the sum of all solutions to the equation 4x(x-3) = 23 + 3x^2 + 10x.
4x(x – 3) = 23 + 3x2 + 10x
4x2 – 12x = 23 + 3x2 + 10x
x2 – 22x – 23 = 0
(x + 1)(x – 23) = 0
x = +23
x = – 1
their sum: +22
What real value of t produces the smallest value of the quadratic t^2 -9t - 36 + t^2 - t + 14?
t2 – 9t – 36 + t2 – t + 14
This is a parabola that opens upward
so the smallest value is at the vertex. 2t2 – 10t – 22
Set the first derivitive equal to zero. 4t – 10 = 0
4t = 10
t = 2.5
The question doesn't ask for it, but at t = 2.5 the value of the quadratic is –34.5.
What is the largest number c such that 2x^2 + 5x + c = x^2 - 4x has at least one real solution? Express your answer as a common fraction.
2x2 + 5x + c = x2 – 4x
x2 + 9x + c = 0
For there to be any real solutions,
the discriminant must be positive. b2 – 4ac > 0
92 – (4)(1)c > 0
81 – 4c > 0
4c < 81
c < 81/4
what is the factored form of this polynomial
x^3 + 3x^2 - 13x -15
x3 + 3x2 – 13x – 15
(x + 1) • (x + 5) • (x – 3)
Levans writes a positive fraction in which the numerator and denominator are integers, and the numerator is 1 greater than the denominator. He then writes several more fractions. To make each new fraction, he increases both the numerator and the denominator of the previous fraction by 1. He then multiplies all his fractions together. He has 20 fractions, and their product equals 3. What is the value of the first fraction he wrote?
x+1 x+2 x+3 x+4 x+17 x+18 x+19 x+20 3
––– • ––– • ––– • ––– • • • • –––– • –––– • –––– • –––– = ––
x x+1 x+2 x+3 x+16 x+17 x+18 x+19 1
Now, cancellation . . . .
(x + 20) / (x) = 3
x + 20 = 3x
2x = 20
x = 10
11
so the first fraction was –––
10
Emanuel was charged $32 for a 14 2/9 taxi ride. The kilometer is constant. What was the cost per kilometer?
32.00 / 128/9 = 32.00 x 9/128 = 0.25 x 9 = 2.25
Which expression is equivalent to 2/7(14x + 3)? 2x + 6/7 4x + 2/21 4x + 6/7 4x + 3
2 14x + 3 28x + 6 28x 6
––– • ––––––– = ––––––– = –––– + ––– = 4x + 6/7
7 1 7 7 7
Shelly has a beaker that contains 5 and two-thirds fluid ounces of water. She pours out 3 and one-third fluid ounces of water. Which expression can be used to find the number of fluid ounces of water that remain in the beaker? 5 and two-thirds minus 3 and one-third 5 and two-thirds + 3 and one-third 3 and one-third minus 5 and two-thirds 5 and two-thirds minus (negative 3 and one-third)
No wonder you have trouble solving it. I can't even read that. Let's do it this way:
Shelly has a beaker that contains 5 and two-thirds fluid ounces of water.
She pours out 3 and one-third fluid ounces of water.
Which expression can be used to find the number of fluid ounces of water that remain in the beaker?
i) 5 and two-thirds minus 3 and one-third <<—— It's this one.
ii) 5 and two-thirds + 3 and one-third
iii) 3 and one-third minus 5 and two-thirds
iv) 5 and two-thirds minus (negative 3 and one-third)
