All categories

3 years ago

PLEASE HELP ME ASAP!

Mathematics

1 answer:

TEA [102]3 years ago

4 0

Answer:

x=5, y=2

Step-by-step explanation:

You simply write down what you see:

3x - 4y + 4x - 5y = 17

2x - 3y + 3x - 5y = 9

Then you simplify by grouping the x and the y terms:

7x - 9y = 17

5x - 8y = 9

Now you want to get equal amounts of x or y. Let's go for x. If we multiply the top eq with 5 and the bottom one with -7, we get:

35x - 45y = 85

-35x + 56y = -63

-------------------------+ now we can add them:

11y = 22 divide by -11

y = 2

So 7x - 18 = 17, x =5

Finally, it makes sense to double check by filling in these answers in the original equations, just to see if no mistakes were made:

3*5 - 4*2 = 7

4*5 - 5*2 = 10

7+10 = 17: ok!

2*5 - 3*2 = 4

3*5 - 5*2 = 5

4+5 = 9: ok!

You might be interested in

3. A utility pole is 38 ft tall. The pole creates a 53 ft shadow. What is the angle of elevation of the sun? Round your answer t

dybincka [34]

Answer:

The angle of elevation of the sun is $36\degree$ .

Step-by-step explanation:

Let $x$ be the angle of elevation of the sun as shown in the diagram.

Then the side length which is $38$ feet is opposite to $x$ and the side length which is $53$ feet is adjacent to $x$ .

Therefore we use the trigonometric ratio that involves the opposite and adjacent sides, which is the tangent ratio.

$\tan x=\frac{38}{53}$

$\Rightarrow \tan x=0.71698$

We solve for $x$ to get,

$x=\arctan (0.71698)$

$\Rightarrow x=35.63981$

To the nearest degree, the angle of elevation is $36\degree$

4 0

3 years ago

What is 354,605 rounded to the nearest thousand

Assoli18 [71]

354,605 rounded to the nearest thousand would be 355,000
because the 6 in the hundreds place is greater than 5 so it rounds up the 4 in the thousands place

Hope this helps!! :D

6 0

4 years ago

How do i find the antiderivative of sin^2(x, cos^2(x and tan^2(x? i know how to antidifferentiate sinx, cosx, and tanx, but thes

Lena [83]

For $\sin^2x$ and $\cos^2x$ , it's helpful to remember the half-angle identities:

$\sin^2x=\dfrac{1-\cos2x}2$
$\cos^2x=\dfrac{1+\cos2x}2$

So

$\displaystyle\int\sin^2x\,\mathrm dx=\frac12\int(1-\cos2x)\,\mathrm dx=\frac x2-\frac{\sin2x}4=C$
$\displaystyle\int\cos^2x\,\mathrm dx=\frac12\int(1+\cos2x)\,\mathrm dx=\frac x2+\frac{\sin2x}4=C$

For $\tan^2x$ , the Pythagorean identity suffices:

$\sin^2x+\cos^2x=1\implies \tan^2x+1=\sec^2x$

which means

$\displaystyle\int\tan^2x\,\mathrm dx=\int(\sec^2x-1)\,\mathrm dx=\tan x-x+C$

since $\dfrac{\mathrm d}{\mathrm dx}\tan x=\sec^2x$ .