Answer: There are 192 horses in the ranch
Step-by-step explanation:
The combined number of cattle and horses = 960.
Ratio of cattle to horses =12 :3
Total ratio =12+3=15
Number of horses on the ranch = ratio of horse / Total ratio x total number of horses and cattle
3/15 x 960 = 192
Therefore there are 192 horses in the ranch
Answer:
B. ∆LMN ≅ ∆OPQ because of ASA
Step-by-step explanation:
Two triangles are congruent if two angles and an included side of one triangle are congruent to two corresponding angles and a corresponding included side of the other.
From the information given, we have:
Two angles (<L and <M) in ∆LMN that are congruent to two corresponding angles (<O and <P) in ∆OPQ.
Also, included side in both triangles are congruent (ML ≅ PO).
Therefore, ∆LMN ≅ ∆OPQ by the ASA Theorem.
<em>Answer:</em>
<u>Tony</u> has 45 dollars
<u>Milan</u> has 15 dollars
<u>Lucy</u> has 25 dollars
<em>Explanation:</em>
<u>Let </u><u><em>x</em></u><u> represent the amount of money Milan has in his wallet.</u>
TONY: 3x
MILAN: x
LUCY: x+10
<u>Lucy, Milan, and Tony have a total of $85 in their wallets. Hence, the following equation.</u>
<u />
3x+x+x+10=85
5x+10=85
5x=75
x=75/5
x=15
Tony has 45 dollars (3*15=45)
Milan has 15 dollars (x=15)
Lucy has 25 dollars (10+15=25)
Answer:
non of these choices I guess
Answer: i) 1 - 9x² - 12x
ii) 17 - 3x²
iii) - 20 + 10x² - x⁴
<u>Step-by-step explanation:</u>
g(x) = 3x + 2 h(x) = 5 - x²
i) h(g(x))
h(3x + 2) = 5 - (3x + 2)²
= 5 - (9x² + 12x + 4)
= 5 - 9x² - 12x - 4
= 1 - 9x² - 12x
ii) g(h(x))
g(5 - x²) = 3(5 - x²) + 2
= 15 - 3x² + 2
= 17 - 3x²
iii) h(h(x))
h(5 - x²) = 5 - (5 - x²)²
= 5 - (25 - 10x² + x⁴)
= 5 - 25 + 10x² - x⁴
= -20 + 10x² - x⁴
