Answer:
Step-by-step explanation:
If OA is perpendicular to OC, then <OAC = 90°
<OAC = <AOB + <BOC
Given
<AOB = 6x-12
<BOC = 3x+30
On substituting this values into the formula:
6x-12+3x+30 = 90
9x+18 = 90
Subtract 18 from both sides
9x+18-18 = 90-18
9x = 72
x = 72/9
x = 8°
Since <AOB = 6x-12
<AOB = 6(8)-12
<AOB = 48-12
<AOB = 36°
Also <BOC = 3x+30
<BOC = 3(8)+30
<BOC = 24+30
<BOC = 54°
V=x^3+5x^2-57x-189
Width: W=(x+3) in = 15 in →x+3=15
Solving for x:
x+3-3=15-3→x=12
With x=12 the Volume would be:
V=(12)^3+5(12)^2-57(12)-189
V=1,728+5(144)-684-189
V=1,728+720-684-189
V=1,575
V=W*D*H
Depth: D
Height: H
with H>D
V=1,575; W=15
Replacing in the equation above:
1,575=15*D*H
Dividing both sides by 15
1,575/15=(12*D*H)/15
105=D*H
3*5*7=D*H
D<H
If D=5→H=3*7→H=21
If D=7→H=3*5→H=15
Answer: Option <span>C. height: 21 in. depth: 5 in.
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Please, see the attached file for another form to solve the problem
Answer:
9a²b
Step-by-step explanation:
Hi there!
We need to find the greatest common factor out of 45a²b³ and 18
b
We can split apart the monomials to make it easier
45a²b³ is 45*a²b³
18
b is 18*
b
First, let's find the GCF out of 45 and 18 (the number coefficients)
we can find all of the multiples of the 2 numbers:
45 is made up of 9 and 5
9 is made up of 3 and 3
so 3*3*5 is 45
18 is made up of 2 and 9
9 is made up of 3 and 3
so 2*3*3 is 18
3*3 is in both 45 and 18, so 9 is the GCF out of 45 and 18
Now let's find the GCF out of a²b³ and
b
a²b³ made up of a² and b³
so a²b³ is a*a*b*b*b
b is made up of
and b
so
b is a*a*a*a*b
a*a*b is in both a²b³ and
b, so the GCF out of a²b³ and
b is a²b
Now multiply 9 and a²b together, as they are only the GCF of the parts of the monomials
9*a²b=<u>9a²b</u>
there's the greatest common factor of the 2 monomials
Hope this helps!
Answer:
10,000
Step-by-step explanation:
My last acount got deleted :,(