Draw a quadrilateral with one pair of parallel sides and two right angles. Explain why this figure is a trapezoid.

A rectangle is removed from the middle of a larger rectangular shaped board. What is the area of the remaining board?

jeyben [28]

Answer:

The area of the remaining board is [(L × B) - (l × b)].

Step-by-step explanation:

Suppose the bigger rectangle is labelled as ABCD and the smaller rectangle is labelled as PQRS.

Consider that the length and breadth of the bigger rectangle are L and B respectively. And the length and breadth of the bigger rectangle are l and b respectively.

The area of any rectangle is:

Area = Length × Breadth

The area of the bigger rectangle is:

Area of ABCD = L × B

The area of the smaller rectangle is:

Area of PQRS = l × b

Then the area of the remaining board will be:

Area of remaining board = Area of ABCD - Area of PQRS

= (L × B) - (l × b)

Thus, the area of the remaining board is [(L × B) - (l × b)].

8 0

2 years ago

What is shaded in here?

Lady_Fox [76]

Answer:

4/100 is the fraction

Step-by-step explanation:

there are four blue blocks shaded out of the 100

7 0

3 years ago

Read 2 more answers

A quadratic relation has zeros at 3 and –5. The parabola goes through the point (2, –14). What is the equation of the parabola i

olasank [31]

Answer:

$\displaystyle 2 {x}^{2} + 4x - 30 = 0$

Step-by-step explanation:

we are given the zeros and a point where it goes through of a quadratic equation

remember that when the roots are given then the function should be

$\displaystyle \: y = a(x - x_{1})(x - x_{2})$

where a is the leading coefficient and x1 and x2 are the roots

substitute:

$\displaystyle y = a(x - (3))(x - ( - 5))$

simplify:

$\displaystyle y = a(x - 3)(x + 5)$

now the given point tells us that when x is 2 y is -14 therefore by using the point we can figure out a

substitute:

$\displaystyle a(2 - 3)(2 + 5) = - 14$

simplify parentheses:

$\displaystyle a( - 1)(7) = - 14$

simplify multiplication:

$\displaystyle - 7a = - 14$

divide both sides by -7:

$\displaystyle a = 2$

altogether substitute:

$\displaystyle y = 2(x - 3)(x + 5)$

since it want the equation y should be

$\displaystyle 2(x - 3)(x + 5) = 0$

recall quadratic equation standard form:

$\displaystyle {ax}^{2} + bx + c = 0$

so simplify parentheses:

$\displaystyle 2( {x}^{2} + 2x - 15 ) = 0$

distribute:

$\displaystyle 2 {x}^{2} + 4x - 30 = 0$

hence,

the equation of the parabola in standard form is 2x²+4x-30=0

8 0

3 years ago

Find a polar equation for the curve represented by the given cartesian equation. x2 + y2 = 10cx

RoseWind [281]

The usual rectangular to polar substitutions can be used:
x = r·cos(θ)
y = r·sin(θ)

These give
r² = 10c·r·cos(θ)
or
r = 10c·cos(θ)

6 0

3 years ago

Read 2 more answers

Christopher weighs 211 pounds and has a BMI of 28.5. How many whole ponds must be gain or lose to get into the healthy BMI range

eduard

BMI = (pounds * 703) / (height^2)

so in the information you are missing the height
let's find it :)
first plug in what you know:
28.5 = (211 * 703) / (height)^2 then solve for (height)
28.5 (height)^2 = (211 * 703) multiplied both sides by (height)^2
(height)^2 = (211 * 703) / 28.5 divided both sides by 28.5
(height) = square root [(211 * 703) / 28.5] square rooted both sides
(height) = 72.143 inches

The healthy BMI is about 25
so 25 = (pounds)(703) / (72.143^2)
25(72.143^2) / (703) = (pounds) divide by 703, multiply by (72.143^2)
pounds = 185

211 - 185 = 26
Therefore Christopher would have to lose 26 pounds.

*Note: If the BMI you wanted to use was not 25, then just replace it like this
(pounds) = (BMI)(72.143^2) / (703) = goal weight

5 0

3 years ago