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2 years ago

Solve for y please I have no clue I am so lost thank you

Mathematics

1 answer:

Inga [223]2 years ago

3 0

In the Triangle ABD, Using Pythagoras theorem we can write

$AB^2=BD^2+AD^2\\ \\ AB^2=9^2+y^2\\ \\ AB^2=81+y^2\\ \\$

In the Triangle ACD using Pythagoras Theorem

$AC^2=AD^2+CD^2\\ \\ AC^2=y^2+7^2\\ \\ AC^2=y^2+49\\$

Now in the larger Triangle ABC, we can write

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

Now substitute the values from the above equations we get

$81+y^2+49+y^2=(9+7)^2\\ \\ 130+2y^2=16^2\\ \\ 130+2y^2=256\\ \\ 65+y^2=128\\ \\ y^2=128-65=63\\ \\ y=\sqrt{63} =3\sqrt{7} \\$

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A rectangular piece of plywood has a diagonal which measures two feet more than the width. The length of the plywood is twice th

icang [17]

Answer:

The length of the plywood's diagonal(to the nearest tenth) is, 3.6 and 1.4

Step-by-step explanation:

let l be the length and w be the width of the rectangle respectively;

Diagonal(D) of a rectangle is given by:

$D = \sqrt{l^2+w^2}$ ......[1]

As per the given statement we have;

Diagonal(D) = width + 2

and

$l = 2 \times w$ = 2w

Now, substitute these in [1] we have;

$\sqrt{(2w)^2+w^2} = w+5$

Squaring both the sides we get;

$4w^2+w^2 = (w+2)^2$

$5w^2 = w^2 + 4 + 4w$

$5w^2 -w^2 = 4w + 4$ or

$4w^2= 4w + 4$

Simplify:

$w^2-w-1 =0$ ......[2]

The quadratic equation is in the form of $ax^2+bx+c = 0$

the solution is given by: $x = \frac{-b \pm\sqrt{b^2-4ac}}{2a}$

On comparing with [1] we get

a= 1 , b = -1 and c = -1

Then the solution is:

$w= \frac{-(-1) \pm\sqrt{(-1)^2-4(1)(-1)}}{2(1)}$

$w =\frac{1 \pm\sqrt{1+4}}{2} = \frac{1 \pm\sqrt{5}}{2}$

Simplify:

$w \approx 1.62$ and $w \approx -0.62$

Then, the diagonal D = w+2

For $w \approx 1.62$

$D = 1.62 +2 \approx 3.62$

For $w \approx -0.62$

$D =-0.62 +2 \approx 1.38$

therefore, the length of the plywood's diagonal(to the nearest tenth) is, 3.6 and 1.4

5 0

3 years ago

Help me please asap!

Dmitriy789 [7]

So sorry I can’t good luck

8 0

3 years ago

Yall PLEASE HELP!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

Pavlova-9 [17]

Y=-9x+5 is your answer

5 0

3 years ago

What is the inverse function for f(x)= square root of 1/2x+4

Zepler [3.9K]

The inverse of f(x) would be f(x) = 2 $x^{2}$ - 8.

We can find this by taking the original equation and switching the x and f(x). Once we do this, we solve for the f(x) in its new place and that is the inverse equation. It is taken step by step for you below.

Take the original.

f(x) = $\sqrt{\frac{1}{2}x + 4}$

Now switch the x and f(x)

x = $\sqrt{\frac{1}{2}f(x) + 4}$

Now square both sides.

$x^{2}$ = $\frac{1}{2}$ f(x) + 4

Now subtract 4 from both sides.

$x^{2}$ - 4 = $\frac{1}{2}$ f(x)

Now multiply both sides by 2.

2 $x^{2}$ - 8 = f(x)

And once you've returned to f(x) =, then you have your inverse.

6 0

2 years ago

Read 2 more answers

Can anyone please solve this for me right now?

MrRa [10]

The population of the country by an exponential function which is used to describe the population of a country in millions t years after the 2003 is, 645.4.

<h3>What is an exponential function?</h3>

Exponential function is the function in which the function growth or decay with the power of the independent variable. The curve of the exponential function depends on the value of its variable.

The population model, which describes the population of a country in millions t years after the 2003 is,

$A=645.4 e^{0.001t}$

For the year 2003 the value of t will be 0 as no year is passed after 20036. Thus,

$A=645.4 e^{0.001\times0}\\A=645.4 e^{0}\\A=645.4(1)\\A=645.4$

Thus, the population of the country by an exponential function which is used to describe the population of a country in millions t years after the 2003 is, 645.4.

Learn more about the exponential function here;

brainly.com/question/15602982

#SPJ1

5 0

1 year ago