Answer:
○ A. No, x = -6 is not a zero of the polynomial.
The quotient is x - 29, and the remainder is 234.
Step-by-step explanation:
[x - 3][x - 20] >> Factored Form
Obviously, this is not a zero. Now, to get the remainder, we have to plug in the vertical line of <em>x = -6</em> into its conjugate, meaning an expression with opposite signs, which is <em>x + 6</em>. This is the expression we divide the dividend by, so you will have this:
\frac{{x}^{2} - 23x - 60}{x + 6}
Since the divisor is in the form of <em>x - c</em>, using Synthetic Division, we get this:
x - 29 + \frac{234}{x + 6}
You see? You have <em>x - 29</em> in the quotient, and you have 234 as the numerator remainder.
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Answer:
18y+30y+14y+150°+142=540
62y+292=540
subtract 292 from both sides
62y= 248
divide 62
y=4°
Answer:
There is no solution because the slopes of the two lines are the same.
Step-by-step explanation:
3x + 5 = 3x - 7
-3x - 3x Subtract 3x from both sides
5 ≠ - 7 No solution
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Answer:
The support is 41 inches long.
Step-by-step explanation:
There's two ways we can do this: one with the diagonal formula and one without.
Since we know that Point C is halfway down leg A and that the table legs are 18 inches tall, Point C is 9 inches down leg A. The support, from Point C to Point D, will form a diagonal, the length of which we need to find. We know from the diagram that the width of the table is 24 inches and that its length is 32 inches. We have a height, length, and width for this problem, so let's imagine a rectangular prism, which has all three of those things, instead of a table. The formula for finding a rectangular prism's diagonal is 
. Let's put in those numbers:
Therefore, the support is 41 inches long.
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Another way you can do this is to use the Pythagorean Theorem twice: once to find the diagonal of the tabletop and another time for the support.
Now that we know the corner-to-corner distance for the tabletop, we'll use that and the 9 inch distance for Point C to find the distance between C and D:
Again, the support is 41 inches long.
Answer:
60 ships.
Step-by-step explanation:
Let the total number of ships in the naval fleet be represented by x
One-third of the fleet was captured = 1/3x
One-sixth was sunk = 1/6x
Two ships were destroyed by fire = 2
Let surviving ships be represented by y
One-seventh of the surviving ships were lost in a storm after the battle = 1/7y
Finally, the twenty-four remaining ships sailed home
The 24 remaining ships that sailed home =
y - 1/7y = 6/7y of the surviving fleet sailed home.
Hence
24 = 6/7y
24 = 6y/7
24 × 7/ 6
y = 168/6
y = 28
Therefore, total number of ships that survived is 28.
Surviving ships lost in the storm = 1/7y = 1/7 × 28 = 4
Total number of ships in the fleet(x) =
x = 1/3x + 1/6x + 2 + 28
Collect like terms
x - (1/3x + 1/6x) = 30
x - (1/2x) = 30
1/2x = 30
x = 30 ÷ 1/2
x = 30 × 2
x = 60
Therefore, ships that were in the fleet before the engagement were 60 ships.
