Answer:
The rectangle's area is 48 square meters
Step-by-step explanation:
Recall that the perimeter of a rectangle of base b and height h is given by the formula:
Perimeter = 2 b + 2 h
we know that the perimeter is 28 meters, then we can create our first equation;
2 b + 2 h = 28
which means:
2 (b + h) = 28
b + h = 28/2
b + h = 14
the tell us that the diagonal is 10 meters, so we use the Pythagorean theorem to write a second equation using the rectangle's base, height, and diagonal (which form in between the three a right angle triangle where the hypotenuse is the rectangle's diagonal:
So, we can use the equation : b + h = 14 to write one variable in terms of the other one and use it as substitution in the second (quadratic) equation:
h = 14 - b
then:
which we have reduced at the end by dividing both sides by 2.
we can use factoring to solve these equation;
Se we find two possible solutions: b = 6 m or b = 8 m
If we call b = 8 m, then the height becomes h = 14 - (8) = 6 m
and viceversa.
So a rectangle with such dimensions will render an area that equals :
Area = b x h = 8 x 6 = 48 square meters.
Answer:
x = 5
Step-by-step explanation:
Given
= ( cross- multiply )
6x = 30 ( divide both sides by 6 )
x = 5
Answer:
And if we solve for a we got
And for this case the value would be 96.2 for the P40
Step-by-step explanation:
Let X the random variable that represent the IQ scores of a population, and for this case we know the distribution for X is given by:
Where and
We want to find the P40 ( a) so we need to satisfy the following condition:
(a)
(b)
For this case we can look for the critical value in the normal standar ddistirbution who accumulate 0.4 of the area in the left and 0.6 in the right and we got z=-0.253.
If we use condition (b) from previous we have this:
And we can set up the following equationL
And if we solve for a we got
And for this case the value would be 96.2 for the P40
Step-by-step explanation:
By 30°-60°-90° triangle theorem: