Can someone help me with the middle question?

What is the sum of 3 consecutive integers of 87

Leviafan [203]

Hey there! Hello!

So, to set this problem up, all you need to do is imagine that the smallest number of these consecutive integers is x. The next two numbers will be x+1, then x+2, and that, altogether, will equal 87. In a problem, this will look like this:

$x+x+1+x+2=87$

All we need to do is solve for x! We can simplify the problem by combining like terms:

$x+x+x+1+2=3x+3=87$
$3x+3-3=87-3$
$3x/3=84/3$
$x=28$

Now that we know what x is, we can plug it into our original problem:

$x+x+1+x+2 = 28+29+30=87$

Hope this helped you out! Feel free to ask me any additional questions if you need further clarification. :-)

3 0

3 years ago

2) A girl starts from a point A and walks 285m to B on a bearing of 078°. She then walks due south to a point C which is 307m fr

adelina 88 [10]

Answer:

bearing of A from C is - 65.24°

the distance |BC| is 187.84 m

Step-by-step explanation:

given data

girl walks AB = 285 m (side c)

bearing angle B = 78°

girl walks AC = 307 m (side a)

solution

we use here the Cosine Law for getting side b that is

ac² = ab² + bc² - 2 × ab × cos(B) ...............1

307² = 285² + x² - 2 × 285 cos(78)

x = 187.84 m

and

now we get here angle θ , the bearing from A to C get by law of sines

sin (θ) = $\frac{187.84}{307} \times sin(78)$

sin (θ) = 0.5985

θ = 36.76°

and as we get here angle BAC that is

angle BCA = 180 - ( 36.76° + 78° )

angle BCA = 65.24°

and here negative bearing of A from C so - 65.24°

7 0

3 years ago

I don’t understand this.. <br> will someone please help? Will mark Brainliest along with 20 points.

inn [45]

To say two quantities $a$ and $b$ "vary directly" with one another means that a change in one of the quantities results in a proportional change in the other quantity. For example, if $a=2b$ , then $b$ is proportional to $a$ by a factor of 2, or $a$ is proportional to $b$ by a factor of 1/2. In other words, if you change $b$ by some fixed amount, then $a$ changes by double that amount.

Mathematically this means there is some constant scaling factor $k$ such that $a=kb$ . In question 4, we're told $f(x)$ varies directly with $x^2$ , which means there's some $k$ such that

$f(x)=kx^2$

We're given that $f(x)=40$ when $x=2$ , so

$40=k\cdot2^2\implies40=4k\implies k=10$

Then when $x=5$ , we get

$f(5)=10\cdot5^2=10\cdot25=250$

- - -

For $a,b$ to "vary inversely" with one another means that a change in one quantity results in an "opposite" change in the other. In other words, if $a$ increases, then $b$ decreases, and vice versa.

Mathematically, this is the same as saying there is some fixed number $k$ such that $ab=k$ .

For example, if $k=1$ and we start with $a=1$ , then $b=1$ also. If we change to $a=2$ , then $b=\dfrac12$ ; if $a=10$ , then $b=\dfrac1{10}$ , and so on.