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Mashcka [7]
3 years ago
15

Factor the trinomial: x2 - x - 56

Mathematics
1 answer:
MrMuchimi3 years ago
6 0
Hello : 
x² -x -56 = <span>(x + 7)(x - 8)
because : </span><span>(x + 7)(x - 8) = x² - 8x +7x - 56
                                      = x² -x -56</span>
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Mr. Walker, a runner, asked students to find the unit rate of the winner of the first Boston Marathon in 1897. John J. McDermott
EleoNora [17]

Answer: 8.4 miles per hour

Step-by-step explanation:

Since, total distance = 24.5 miles,

Time taken =  175 \text{ minutes} = \frac{175}{60} \text{ hours} =\frac{35}{12} \text{ hours}

Thus,

\text{ The unit rate} = \frac{\text{ Total distance}}{\text{ Time taken}}

=\frac{24.5}{35/12}

=\frac{294}{35}

=8.4\text{ miles per hour}

6 0
3 years ago
The length of a rectangle is 6 more than twice the width. if the area is 40 cm^2, find the length and breadth of the rectangle
ra1l [238]

Answer: 3.217 & 12.434

Step-by-step explanation:

If we use <em>w</em> to represent the width, the length will be 6 more than 2 times w.

Hence, the length is 2w+6.

The area of a rectangle would be its length times its width, so let's make an equation to represent it's area.

A=w(2w+6)

We can also substitute 40 in for A as it's given in the question.

40 = w(2w+6)

Distributing <em>w</em> by multiplying it by both terms in the parentheses, we get

40 = 2w^2+6w

We can make the equation simpler by dividing both sides by 2.

20 = w^2+3w

Subtracting both sides by 20 will make the left-hand side 0.

0=w^2+3w-20

Now that we have put this <em>quadratic equation</em> into standard form (ax²+bx+c), we can find its solutions using the quadratic formula.

For reference, the quadratic formula is

x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}

In this case, a is 1, b is 3, and c is -20.

Substituting, we get

w=\frac{-3\pm\sqrt{3^2-4(1)(-20)}}{2(1)}

w= \frac{-3\pm\sqrt{9+80}}{2}

w=\frac{-3+\sqrt{89}}{2}\hspace{0.1cm}or\hspace{0.1cm}\frac{-3-\sqrt{89}}{2}

Since the second solution results in a negative number, it cannot be the length of w.

w=\frac{-3+\sqrt{89}}{2}\approx3.217

The width/breadth of the rectangle is 3.217 cm.

To calculate the length, let's substitute the width into the expression for the length:

l=2(3.217)+6

l=12.434

The length of this rectangle is 12.434 cm.

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2 years ago
How many different combinations of shirts and ties are possible if you have 4 shirts and 5 ties?
Fittoniya [83]
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G(x) = –(x + 3)2 – 4?
professor190 [17]

Answer:

g(x)=-x-5

Step-by-step explanation:

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Finalize since no more simplification:

g(x)=-x-5

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Answer:

Step-by-step explanation:

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