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3 years ago

Factor the expression. 3x2 + 14x-5

Mathematics

1 answer:

Irina18 [472]3 years ago

8 0

Answer:

(3x-1)(x+5)

Step-by-step explanation:

Find two numbers that when they multiply, you get the third term,

which is -5 in this problem. And when they add up, you get the second term,

which is 14 in this problem.

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A mother is 26 years older than her daughter. The daughter is one-third her mother's age. How old is each now? When will the mot

marshall27 [118]

Answer:

now: daughter: 13, mother: 39
then: daughter: 26, mother: 52

Step-by-step explanation:

If the daughter's age is 1/3 the mother's age, the difference in their ages is ...

1-1/3 = 2/3

the mother's age. The daughter's age is half that (1/3 the mother's age), so the daughter's age is 26/2 = 13 years. The mother's age is 13+26 = 39 years, which is 3 times the daughter's age.

The daughter is 13 now; the mother is 39.

When the mother is twice as old, the daughter's age will be equal to their age difference: 26. The mother's age will be 26 +26 = 52

When the mother is twice as old, she will be 52, and the daughter will be 26.

_____

<em>Additional comment</em>

You can assign variables and write equations that will give you the same result. If you let d and m represent the daughter's age and the mother's age, respectively, you could write the system ...

m = d +26

d = m/3

Substituting for d, you get ...

m = m/3 +26

2/3m = 26 . . . . . . subtract m/3

Note that this is the relationship we came to in the discussion above.

When an age difference is given, you know it will remain the same throughout the problem. Everybody ages at the same rate, so the difference is constant. As we have done above, it is often useful to compare the age difference to the difference in ratio units. This tells you the size of a ratio unit.

3 0

2 years ago

Find the rectangular coordinates of the point (sqrt3,pi/6)

madreJ [45]

Answer:

$(x, y) = \left(\frac{3}{2}, \frac{\sqrt{3}}{2}\right)$

Step-by-step explanation:

The rectangular coordinates of the point are:

$(x,y) = \left(\sqrt{3}\cdot \cos\frac{\pi}{6}, \sqrt{3}\cdot \sin\frac{\pi}{6}\right)$

$(x, y) = \left(\frac{3}{2}, \frac{\sqrt{3}}{2}\right)$

5 0

2 years ago

Help pls and no links

aalyn [17]

Answer:

y > 4x - 2

Step-by-step explanation:

The basic format of a line in slope-intercept form is,

$y=mx+b$

This format undergoes no change when one implements it for the use of a two-variable inequality.

The parameter (m) represents the slope of a line, this can be found by using the formula ( $\frac{rise}{run}$ ). Traditionally, one would use a formula to find the slope of a line that is the following, ( $\frac{y_2-y_1}{x_2-x_1}$ ). However, in the given situation, one can simply count the number of boxes from one point with respect to the x-axis to another, and thus get (4).