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3 years ago

A part-time job pays $237.50 for 25 hours of work how much money does it good job Pay per hour

Mathematics

2 answers:

Blababa [14]3 years ago

8 0

Divide 237.50 by 25. The answer is $9.50 per hour

Trava [24]3 years ago

3 0

Divide 25 by 237.50 which is...9.50 per hour

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Delvig [45]

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3 0

3 years ago

Find the product of all real values of r for which 1/2x=r-x/7

Dahasolnce [82]

Answer:

$r = \±\sqrt{14$

$Product = -14$

Step-by-step explanation:

Given

$\frac{1}{2x} = \frac{r - x}{7}$

Required

Find all product of real values that satisfy the equation

$\frac{1}{2x} = \frac{r - x}{7}$

Cross multiply:

$2x(r - x) = 7 * 1$

$2xr - 2x^2 = 7$

Subtract 7 from both sides

$2xr - 2x^2 -7= 7 -7$

$2xr - 2x^2 -7= 0$

Reorder

$- 2x^2+ 2xr -7= 0$

Multiply through by -1

$2x^2 - 2xr +7= 0$

The above represents a quadratic equation and as such could take either of the following conditions.

(1) No real roots:

This possibility does not apply in this case as such, would not be considered.

(2) One real root

This is true if

$b^2 - 4ac = 0$

For a quadratic equation

$ax^2 + bx + c = 0$

By comparison with $2x^2 - 2xr +7= 0$

$a = 2$

$b = -2r$

$c =7$

Substitute these values in $b^2 - 4ac = 0$

$(-2r)^2 - 4 * 2 * 7 = 0$

$4r^2 - 56 = 0$

Add 56 to both sides

$4r^2 - 56 + 56= 0 + 56$

$4r^2 = 56$

Divide through by 4

$r^2 = 14$

Take square roots

$\sqrt{r^2} = \±\sqrt{14$

$r = \±\sqrt{14$

Hence, the possible values of r are:

$\sqrt{14$ or $-\sqrt{14$

and the product is:

$Product = \sqrt{14} * -\sqrt{14}$

$Product = -14$

8 0

3 years ago

In Yellowstone National Park there are 300 species of birds that migrate. This accounts for 2/7 of all the species of birds sigh

Juli2301 [7.4K]

Answer:

$\frac{2}{7} x = 300$

Step-by-step explanation:

Let x = the number of all the species of birds sighted in the park

“300 species of birds that migrate. This accounts for 2/7 of all the species of birds sighted in the park”

the above sentence means “(2/7)x = 300”

now we can solve it :

(2/7)x = 300

⇔ 2x = 7×300

⇔ 2x = 2100

⇔ x = 2100/2

⇔ x = 1050

7 0

3 years ago

A dog runs 100 yards from one corner of a rectangular park to the opposite corner. If the length of the park is 28 yards, what i

kap26 [50]

9514 1404 393

Answer:

96 yards

Step-by-step explanation:

The diagonal through the park cuts the rectangle into two right triangles. The Pythagorean theorem tells you the relationship between the sides of a right triangle and its hypotenuse: the sum of the squares of the sides is equal to the square of the hypotenuse.

The diagonal is the hypotenuse, so we have ...

100² = 28² + w²

w = √(10000 -784) = 96

The width of the park is 96 yards.

_____

<em>Additional comment</em>

The integer side lengths of a right triangle form what is called a "Pythagorean triple." One of the most often seen of these is (3, 4, 5). Other commonly seen Pythagorean triples are (5, 12, 13), (7, 24, 25), (8, 15, 17).

You may notice that the numbers here are those of the (7, 24, 25) Pythagorean triple, multiplied by 4. If you recognize the given lengths as having the ratio 28:100 = 7:25, you have the clue you need to determine the answer simply from your knowledge of Pythagorean triples.

8 0

3 years ago

Two goals post are 8m apart. A footballer is 34m from one and 38m from the other. Within what angle must he kick the ball if he

dmitriy555 [2]

Answer:

11.06°

Step-by-step explanation:

The law of cosines can be used to find the angle. The sides adjacent to that angle are a=34, b=38, and the side opposite is c=8. Then the angle is found from ...

c² = a² +b² -2ab·cos(C)

cos(C) = (a² +b² -c²)/(2ab)

C = arccos((a² +b² -c²)/(2ab))

C = arccos((34² +38² -8²)/(2·34·38)) = arccos(317/323)

C ≈ 11.06°

From the footballer's viewpoint, the goal posts are 11.06° apart.

4 0

4 years ago