64)259 dived with remainder

In isosceles right triangle ABC, point is on hypotenuse \overline{BC} such that \overline{AD} is an altitude of \triangle ABC an

Dmitriy789 [7]

Answer:

Area of triangle is 25.

Step-by-step explanation:

We have been given an isosceles right triangle

Isosceles triangle is the triangle having two sides equal.

Figure is shown in attachment

By Pythagoras theorem

$BC^2=AC^2+AB^2$

AD is altitude which divides the triangle into two parts

DC=5 implies BC =10 since D equally divides BC

Let AC=a implies AB=a being Isosceles

On substituting the values in the Pythagoras theorem:

$10^2=a^2+a^2$

$100=2a^2$

$\Rightarrow a^2=50$

$\Rightarrow a=\pm5\sqrt{2}$

WE can find area of right triangle by considering height AB and AD

Area of triangle ABC is:

$\frac{1}{2}\cdot BC\cdot AD$ (1)

$\Rightarrow \frac{1}{2}\cdot 10\cdot AD$

And other method of area of triangle is:

$\frac{1}{2}\cdot AB\cdot BC$ (2)

Equating (1) and (2) we get:

$\frac{1}{2}\cdot 10\cdot AD=\frac{1}{2}\cdot a\cdot a$

$\Rightarrow AD=\frac{a^2}{10}$

$\Rightarrow AD=\frac{50}{10}=5$

Using area of triangle is: $\frac{1}{2}\cdot BC\cdot AD$

Now, the area of triangle ABC= $\frac{1}{2}\cdot 5\cdot 10$

$\Rightarrow 25$

4 0

3 years ago

The table shows transactions from five different bank accounts. Fill in the missing numbers. ( THE IMAGE ATTACHED PLEASE)

velikii [3]

Answer:

Part 1) $A=80$

Part 2) $B=-25$

Part 3) $C=-40$

Step-by-step explanation:

we know that

The old account balance plus the transaction amount is equal to the new account balance

The transaction amount can be a positive number (example a deposit) or a negative number (example a withdrawal)

Part 1) Find the value of A

$432+A=512$

solve for A

subtract 432 both sides

$A=512-432=80$

Part 2) Find the value of B

$75-100=B$

solve for B

$-25=B$

Rewrite

$B=-25$

Part 3) Find the value of C

$C+52=12$

solve for C

subtract 52 both sides

$C=12-52$

$C=-40$

4 0

3 years ago

Solve the following equations by finding the value of x.

kozerog [31]

1.4 2.7 3. 12 4 6/7 5 8

4 0

3 years ago

Newton's law of cooling is:

Mnenie [13.5K]

Answer:

$t = \frac{ln(\frac{21}{59})}{-0.15}=6.887 hr$

So it would takes approximately 6.9 hours to reach 32 F.

Step-by-step explanation:

For this case we have the following differential equationÑ

$\frac{du}{dt}= -k (u-T)$

We can reorder the expression like this:

$\frac{du}{u-T} = -k dt$

We can use the substitution $w = u-T$ and $dw =du$ so then we have:

$\frac{dw}{w} =-k dt$

IF we integrate both sides we got:

$ln |w| = -kt +C$

If we apply exponential in both sides we got:

$w = e^{-kt} *e^c$

And if we replace w = u-T we got:

$u(t)= T + C_1 e^{-kt}$

We can also express the solution in the following terms:

$u(t) = (T_i -T_{amb}) e^{kt} +T_{amb}$

For this case we know that $k =-0.15 hr$ since w ehave a cooloing, $T_{i}= 70 F, T_{amb}=11F$ , we have this model:

$u(t) = (70-11) e^{-0.15t} +11$

And if we want that the temperature would be 32F we can solve for t like this:

$32 = 59 e^{-0.15 t} +11$

$21=59 e^{-0.15 t}$

$\frac{21}{59} = e^{-0.15 t}$

If we apply natural logs on both sides we got:

$ln (\frac{21}{59}) =-0.15 t$

$t = \frac{ln(\frac{21}{59})}{-0.15}=6.887 hr$

So it would takes approximately 6.9 hours to reach 32 F.

7 0

3 years ago

Please help me on these questions, Thanks

gogolik [260]

29). The 'six' is the same as (6 x 5) = 30 fifths.
So six and three fifths = (30 + 3) fifths = thirty-three fifths.

30). The 'eight' is the same as (8 x 6) = 48 sixths.
So eight and five sixths = (48 + 5) fifths= fifty-three sixths.

31). Twenty-seven of the thirds are the same as (27/9) = 3 .
That leaves a remainder of 2 thirds.
So twenty-nine thirds are the same as 3 and 2/3 .

32). Thirty-two of the fourths are the same as (32/4) = 8 .
That leaves a remainder of one fourth.
So thirty-three fourths are the same as 4 and 1/4 .

5 0

3 years ago