Step-by-step explanation:
4x2=−9x−4
Step 1: Subtract -9x-4 from both sides.
4x2−(−9x−4)=−9x−4−(−9x−4)
4x2+9x+4=0
For this equation: a=4, b=9, c=4
4x2+9x+4=0
Step 2: Use quadratic formula with a=4, b=9, c=4.
x=
−b±√b2−4ac
2a
x=
−(9)±√(9)2−4(4)(4)
2(4)
x=
−9±√17
8
x=
−9
8
+
1
8
√17 or x=
−9
8
+
−1
8
√17
let's do 1, 5, 6, 10 and 13.
1)
well, the denominator is the same on each, so we simply have to look at the numerator, who is larger 3 or 5? 3 < 5, 3 is less than 5, so then........
5)
6)
we can make both denominators the same if we simply <u>multiply each fraction by the other's denominator</u>.
10)
we'll convert the mixed fractions to improper fractions first, then make their denominator the same just like we did in 6).
![\bf \stackrel{mixed}{4\frac{1}{7}}\implies \cfrac{4\cdot 7+1}{7}\implies \stackrel{improper}{\cfrac{29}{7}}~\hfill \stackrel{mixed}{3\frac{3}{18}}\implies \cfrac{3\cdot 18+3}{18}\implies \stackrel{improper}{\cfrac{57}{18}} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ \begin{cases} \cfrac{29}{7}\cdot \cfrac{18}{18}\implies \cfrac{522}{126} \\\\\\ \cfrac{57}{18}\cdot \cfrac{7}{7}\implies \cfrac{399}{126} \end{cases}\qquad \implies \cfrac{522}{126}>\cfrac{399}{126}\qquad therefore\qquad 4\frac{1}{7}>3\frac{3}{18}](https://tex.z-dn.net/?f=%5Cbf%20%5Cstackrel%7Bmixed%7D%7B4%5Cfrac%7B1%7D%7B7%7D%7D%5Cimplies%20%5Ccfrac%7B4%5Ccdot%207%2B1%7D%7B7%7D%5Cimplies%20%5Cstackrel%7Bimproper%7D%7B%5Ccfrac%7B29%7D%7B7%7D%7D~%5Chfill%20%5Cstackrel%7Bmixed%7D%7B3%5Cfrac%7B3%7D%7B18%7D%7D%5Cimplies%20%5Ccfrac%7B3%5Ccdot%2018%2B3%7D%7B18%7D%5Cimplies%20%5Cstackrel%7Bimproper%7D%7B%5Ccfrac%7B57%7D%7B18%7D%7D%20%5C%5C%5C%5C%5B-0.35em%5D%20%5Crule%7B34em%7D%7B0.25pt%7D%5C%5C%5C%5C%20%5Cbegin%7Bcases%7D%20%5Ccfrac%7B29%7D%7B7%7D%5Ccdot%20%5Ccfrac%7B18%7D%7B18%7D%5Cimplies%20%5Ccfrac%7B522%7D%7B126%7D%20%5C%5C%5C%5C%5C%5C%20%5Ccfrac%7B57%7D%7B18%7D%5Ccdot%20%5Ccfrac%7B7%7D%7B7%7D%5Cimplies%20%5Ccfrac%7B399%7D%7B126%7D%20%5Cend%7Bcases%7D%5Cqquad%20%5Cimplies%20%5Ccfrac%7B522%7D%7B126%7D%3E%5Ccfrac%7B399%7D%7B126%7D%5Cqquad%20therefore%5Cqquad%204%5Cfrac%7B1%7D%7B7%7D%3E3%5Cfrac%7B3%7D%7B18%7D)
13)
so both fractions are at a value from 9, so we can simply say, which is larger 2/6 or 4/12?
Answer:
e. R′
Step-by-step explanation:
Let the Sample Space be a universal set consisting of 3 red and 6 blue cards. Then the event of of getting 4 blue cards will be given
R complement = R` = Universal Set minus Red cards will give blue cards.
a. R OR O
It cannot be this option because we need 4 blue card
b. B AND O
It cannot be this choice as well because 4 is not odd.
c. R OR E
4 is even but we need blue
d. R AND O
Red and odd is again not required
e. R′ = It will give our required result.
f. E′= 4 is even if it is complemented it cannot be obtained and will be left out.
Answer:
m∠ABE = 27°
Step-by-step explanation:
* Lets look to the figure to solve the problem
- AC is a line
- Ray BF intersects the line AC at B
- Ray BF ⊥ line AC
∴ ∠ABF and ∠CBF are right angles
∴ m∠ABF = m∠CBF = 90°
- Rays BE and BD intersect the line AC at B
∵ m∠ABE = m∠DBE ⇒ have same symbol on the figure
∴ BE is the bisector of angle ABD
∵ m∠EBF = 117°
∵ m∠EBF = m∠ABE + m∠ABF
∵ m∠ABF = 90°
∴ 117° = m∠ABE + 90°
- Subtract 90 from both sides
∴ m∠ABE = 27°
