Factor the trinomial below 24x^2-49x-40

Someone please help me thank you

german

Answer:

4

Step-by-step explanation:

7x = x² - 8

=> x² - 7x - 8 = 0

use quadratic formula:

a = 1, b = -7, c = -8

x = $\frac{-(1)±\sqrt{(-7)^{2} - 4(1)(-8) } }{2(1)}$ <em>(pls ignore the "A" I don't know why it's showing up)</em>

=> x = $\frac{-1±\sqrt{49 + 32} }{2}$

=> x = $\frac{-1±9 }{2}$

=> x = $\frac{-1 +9}{2}$ = 4 or $\frac{-1-9}{2}$ = -5 <em>(the answer is only 4 since it's asking for the positive solution)</em>

6 0

3 years ago

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What is the Lcm of 2 and 7

wel

Answer:

14

Step-by-step explanation:

The least common multiple is a number that both numbers can multiply something to get to, and the smallest possible common one.

Let's try listing out the multiples of 2:

2, 4, 6, 8, 10, 12, 14, 16, 18, 20

And the multiples of 7:

7, 14, 21, 28, 35, 42, 49, 56, 63, 70

Notice that both have the number 14 in common, and it is the first number that they do so. There are lots of other multiples that they have in common too, but 14 is the least.

5 0

3 years ago

Can someone help me

erik [133]

Answer:

6 < x < 23.206

Step-by-step explanation:

To properly answer this question, we need to make the assumption that angle DAC is non-negative and that angle BCA is acute.

The maximum value of the angle DAC can be shown to occur when points B, C, and D are on a circle centered at A*. When that is the case, the sine of half of angle DAC is equal to 16/22 times the sine of half of angle BAC. That is, ...

(2x -12)/2 = arcsin(16/22×sin(24°))

x ≈ 23.206°

Of course, the minimum value of angle DAC is 0°, so the minimum value of x is ...

2x -12 = 0

x -6 = 0 . . . . . divide by 2

x = 6 . . . . . . . add 6

Then the range of values of x will be ...

6 < x < 23.206

_____

* One way to do this is to make use of the law of cosines:

22² = AB² + AC² -2·AB·AC·cos(48°)

16² = AD² + AC² -2·AD·AC·cos(2x-12)

The trick is to maximize x while satisfying the constraints that all of the lengths are positive. This will happen when AB=AC=AD, in which case the equations be come ...

22² = 2·AB²·(1-cos(48°))

16² = 2·AB²·(1 -cos(2x-12))

The value of AB drops out of the ratio of these equations, and the result for x is as above.

4 0

3 years ago

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Mary crocheted a rectangular blanket whose diagonal measures approximately 7.21 feet. What are the most likely length and width

mote1985 [20]

Answer:

If both sides are integers, one side will be 4 feet and the other will be 6 feet. The other solution is the symmetrical solution (4 feet instead of 6 feet, and 6 feet instead of 4 feet).

Step-by-step explanation:

We have a rectangular blanket, that has a diagonal that measures h=7.21 feet.

The two sides of the rectangle a and b can be related to the diagonal h by the Pithagorean theorem:

$a^2+b^2=h^2$