She started with 32 pieces.
Explanation: If she had 5 children and each child received 5 pieces, you can determine that she gave her children a total of 25 pieces because 5 x 5 = 25. If she took 7 pieces for herself before giving the rest away, you can determine that she had 32 pieces of candy to start with because 25 + 7 = 32.
Step-by-step explanation:
A=base length × height
if base is 6cm, and h 4 cm, multiply
6×4=24cm2
Given:
The polynomial function is
![F(x)=4x^3-6x^2+9x+10](https://tex.z-dn.net/?f=F%28x%29%3D4x%5E3-6x%5E2%2B9x%2B10)
To find:
The possible roots of the given polynomial using rational root theorem.
Solution:
According to the rational root theorem, all the rational roots and in the form of
, where, p is a factor of constant and q is the factor of leading coefficient.
We have,
![F(x)=4x^3-6x^2+9x+10](https://tex.z-dn.net/?f=F%28x%29%3D4x%5E3-6x%5E2%2B9x%2B10)
Here, the constant term is 10 and the leading coefficient is 4.
Factors of constant term 10 are ±1, ±2, ±5, ±10.
Factors of leading term 4 are ±1, ±2, ±4.
Using rational root theorem, the possible rational roots are
![x=\pm 1+,\pm 2, \pm 5, \pm 10,\pm \dfrac{1}{2}, \pm \dfrac{5}{2}, \dfrac{1}{4}, \pm \dfrac{5}{4}](https://tex.z-dn.net/?f=x%3D%5Cpm%201%2B%2C%5Cpm%202%2C%20%5Cpm%205%2C%20%5Cpm%2010%2C%5Cpm%20%5Cdfrac%7B1%7D%7B2%7D%2C%20%5Cpm%20%5Cdfrac%7B5%7D%7B2%7D%2C%20%5Cdfrac%7B1%7D%7B4%7D%2C%20%5Cpm%20%5Cdfrac%7B5%7D%7B4%7D)
Therefore, the correct options are A, C, D, F.
Answer:
2x-3y=2
x=6y-5
2(6y-5)-3y=2
use the distributive property.
2*6y=12y
2*-5=-10
12y-10-3y=2
combine like terms
12y-3y=9y
9y-10=2
add 10 to both sides.
9y-10+10=9y
2+10=12
9y=12
divide both sides by 9
9y/9=y
y=about 1.33
plug in the value of y in the expression equal to the value of x.
x=6(1.33)-5
solve
6*1.33=7.98
x=7.98-5
7.98-5=2.98
Step-by-step explanation:
x=2.98
y=1.33