All categories

2 years ago

X + 2

Mathematics

1 answer:

Alla [95]2 years ago

6 0

Answer:

see explanation

Step-by-step explanation:

The area (A) of a trapezium is calculated as

A = $\frac{1}{2}$ h (a + b)

where a, b are the measures of the parallel sides and h the perpendicular distance between them.

here h = x - 5, a = x + 6 and b = x + 2, thus

A = $\frac{1}{2}$ (x - 5)(x + 6 + x + 2) = 36

Multiply both sides by 2 to clear the fraction

(x - 5)(2x + 8) = 72 ← expand left side

2x² - 2x - 40 = 72 ← divide through by 2

x² - x - 20 = 36 ( subtract 36 from both sides )

x² - x - 56 = 0 ← as required

You might be interested in

Help me with just 27

tankabanditka [31]

Answer:

16/13

Step-by-step explanation:

the error is when it was divided, one of the fractions should be reversed to be multiplied

4 ÷ 13

7. 28

4 × 28 ,like this

7. 13

= 112 ,divide both by 7

= 16

7 0

2 years ago

The GCF of an odd number and an even number will always be even

Gelneren [198K]

This is false for example, the GCF of 13 and 26 is 13, an odd number.

8 0

2 years ago

Determine the values of the constants b and c so that the function given below is differentiable. f(x)={2xbx2+cxx≤1x>1

Lera25 [3.4K]

Assuming the function is

$f(x)=\begin{cases}2x&\text{for }x\le1\\bx^2+cx&\text{for }x>1\end{cases}$

For $f(x)$ to be differentiable, it necessarily has to be continuous. For this condition to be met, we need

$\displaystyle\lim_{x\to1^-}f(x)=\lim_{x\to1^+}f(x)=f(1)$
$\iff\displaystyle\lim_{x\to1}2x=\lim_{x\to1}(bx^2+cx)$
$\iff2=b+c$

For the derivative to exist, the one-sided limits of the derivative must also exist and be equal. We have

$f'(x)=\begin{cases}2&\text{for }x1\end{cases}$

$\displaystyle\lim_{x\to1^-}2=\lim_{x\to1^+}(2bx+c)$
$\iff2=2b+c$

Now we solve for $b$ and $c$ :

$\begin{cases}b+c=2\\2b+c=2\end{cases}\implies b=0,c=2$

5 0

3 years ago

At the gas station, each liter of gas costs $ 3 $3dollar sign, 3, but there's a promotion that for every beverage you purchase y

IgorC [24]

Answer:

Yes! Our total savings on gas proportional to the number of beverages you purchase.

Step-by-step explanation:

Here, each liter of gas costs $3.

Every beverage you purchase you save $0.20.

So, if you purchase for $9, you will save 3*$0.20 = $0.60

So, this is proportional because when increase in purchase, there is proportional increase in savings.

6 0

3 years ago

Evil lives to go swimming at 4:05 and returns at 4:57 how long has she been gone?

blsea [12.9K]

She has been gone 52 min.

57 - 5 = 52

7 0

3 years ago