All categories

2 years ago

A rectangle has a length of 16 inches and the length of the diagonal is 20 inches. What is the width of the rectangle

Mathematics

1 answer:

prohojiy [21]2 years ago

8 0

Answer:

12 inches

Step-by-step explanation:

1. The diagonal is the hypotenuse of the right triangle. so since we know one side length, we can figure out the other side length

You might be interested in

I can't figure this out

andriy [413]

Suppose that equation of parabola is
y =ax² + bx + c

Since parabola passes through the point (2,−15) then
−15 = 4a + 2b + c

Since parabola passes through the point (-5,-29), then
−29 = 25a − 5b + c

Since parabola passes through the point (−3,−5), then
−5 = 9a − 3b + c

Thus, we obtained following system:
4a + 2b + c = −15
25a − 5b + c = −29
9a − 3b + c = −5

Solving it we get that
a = −2, b = −4, c = 1

Thus, equation of parabola is
y = −2x²− 4x + 1

____________________

Rewriting in the form of
(x - h)² = 4p(y - k)

i) -2x² - 4x + 1 = y

ii) -3x² - 7x = y - 11
(-3x² and -7x are isolated)

iii) -3x² - 7x - 49/36 = y - 1 - 49/36
(Adding -49/36 to both sides to get perfect square on LHS)

iv) -3(x² + 7/3x + 49/36) = y - 3
(Taking out -3 common from LHS)

v) -3(x + 7/6)² = y - 445/36

vi) (x + 7/6)² = -⅓(y - 445/36)
(Shifting -⅓ to RHS)

vii) (x + 1)² = 4(-1/12)(y - 445/36)
(Rewriting in the form of 4(-1/12) ; This is 4p)

So, after rewriting the equation would be -

(x + 7/6)² = 4(-⅛)(y - 445/36)

__________________

I hope this is what you wanted.

Regards,
Divyanka♪
__________________

6 0

3 years ago

Read 2 more answers

A lighthouse keeper has a 10 degrees angle of depression between the horizontal light beam and the line of sight from the ship.

Andrei [34K]

107.75m
This is a trigonometric ratio problem. the angle of depression (10) is opposite the height (19m) and the distance is adjacent to the distance (x). opposite ad adjacent sides to the angle is a tangent problem.
$tan \theta = \frac{opp}{adj}$
plus in values, we know.
$tan (10) = \frac{19}{x}$
switch tan(10) and x using the products property.
$x = \frac{19}{tan (10)}$
plug in to calulator to get answer
x=107.75

4 0

3 years ago

Create a set of coordinates to model a relation that is linear function.

weqwewe [10]

Answer:

Step-by-step explanation:

The following points (coordinates) lie on a straight line with slope 3:

(1, 0), (2, 3), (3, 6), (4, 9) ... and so on

So the linear function is y = 3x + b, where b is the y-intercept.

3 0

3 years ago

A book sold 35400 copies in its first month of release. Suppose this represent 9.7 % of the number of copies sold to date. How m

Nata [24]

Answer:

ADDDDDDDD

Step-by-step explanation:

7 0

2 years ago

The drama club is selling T-shirts and caps to raise money for a spring trip. The caps sell for $5.00 each, and the T-shirts sel

Zinaida [17]

The required inequality is $5x+10y\geq 500$

<em><u>Solution:</u></em>

Given that,

Cost of 1 cap = $ 5

Cost of 1 t-shirt = $ 10

Let "x" be the number of caps sold

Let "y" be the number of t-shirts sold

The drama club needs to raise at least $500.00 for the trip

Based on this information, we can frame a inequality as:

number of caps sold x cost of 1 cap + number of shirts sold x cost of 1 shirt $\geq$ 500

Which means,

$x \times 5 + y \times 10\geq 500\\\\5x + 10y\geq 500$

Here we used "greater than or equal to" symbol , because club needs to raise at least $ 500

They can raise 500 or more than $ 500 also

Thus the required inequality is $5x+10y\geq 500$

8 0

3 years ago