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3 years ago

-8x - 8y = 0 and -5x - 4y = 5. Solve the system of equations

Mathematics

2 answers:

Gre4nikov [31]3 years ago

6 0

Answer:

x=-5 and y=5

Step-by-step explanation:

You can change both of the equations by:

-1(-8x-8y)=-1(0)

2(-5x-4y)=2(5)

Then they become:

8x+8y=0

-10x-8y=10

Add both equations onto one another and you get:

-2x=10 with x=-5

Plug back x=-5 into either equation (original or changed)

-8(-5)-8y=0

40-8y=0

40=8y

y=5

Rashid [163]3 years ago

4 0

Answer:

x=-5, y=5 or (-5,5)

Step-by-step explanation:

We can do elimination with this

this means we should first multiply -5x-4y=5 by 2

this would make it -10x-8y=10

we can now subtract this from the original equation

-8x-8y=0 - (-10x-8y=10)

the ys would cancel out

so this would equal

2x=-10

x=-5

now we can plug this back into the equation to find y

-8(-5)-8y=0

40-8y=0

-8y=-40

y=5

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Find the value of x. Picture below

Wittaler [7]

Here a right angled triangle given. We know that one angle of a right angled triangle is 90°.

As the sum of three angles of a triangle is 180°, so we can say the sum of other two angles of a right angled triangle is (180-90)° = 90°.

Here in the figure the other two angles given $(2x)^o$ and $(x+15)^o$ . Sum of these two angles is 90°.

So we can write the equation as,

$(2x)+(x+15) = 90$

We have to remove the parenthesis now.

$2x+x+15 = 90$

Now we will add the like terms. Here x and 2x are like terms. By adding them we will get,

$3x+15 = 90$

To solve it for x, now we have to move 15 to the other side by subtracting it from both sides.

$3x+15-15 = 90-15$

$3x= 90-15$

$3x= 75$

Now to get x, we have to move 3 to the other side, by dividing it to both sides.

$(3x)/3 = (75)/3$

$x = (75)/3$

$x = 25$

We have got the required value of x.

The solution is x= 25.

3 0

4 years ago

Is anyone able to figure this out, I can't do this

katrin [286]

Answer:

C. √2 - 1

Step-by-step explanation:

If we draw a square from the center of the large circle to the center of one of the small circles, we can see that the sides of the square are equal to the radius of the small circle (see attached diagram)

Let r = the radius of the small circle

Using Pythagoras' Theorem $a^2+b^2=c^2$

(where a and b are the legs, and c is the hypotenuse, of a right triangle)

to find the diagonal of the square:

$\implies r^2 + r^2 = c^2$

$\implies 2r^2 = c^2$

$\implies c=\sqrt{2r^2}$

So the diagonal of the square = $\sqrt{2r^2}$

We are told that the radius of the large circle is 1:

⇒ Diagonal of square + r = 1

$\implies \sqrt{2r^2}+r=1$

$\implies \sqrt{2r^2}=1-r$

$\implies 2r^2=(1-r)^2$

$\implies 2r^2=1-2r+r^2$

$\implies r^2+2r-1=0$

Using the quadratic formula to calculate r:

$\implies r=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}$

$\implies r=\dfrac{-2\pm\sqrt{2^2-4(1)(-1)}}{2(1)}$

$\implies r=\dfrac{-2\pm\sqrt{8}}{2}$

$\implies r=-1\pm\sqrt{2}$

As distance is positive, $r=-1+\sqrt{2}=\sqrt{2}-1$ only

5 0

3 years ago

Read 2 more answers

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faltersainse [42]

X+y<10x+y<10 and x>4x4

8 0

3 years ago

Read 2 more answers

17 + x =31 <br> i need help

Gelneren [198K]

Answer:

x= 14

Step-by-step explanation:

First (and only) we subtract 17 from both sides :

17 + x - 17 = 31 - 17

x = 31 - 17

x = 14

Hope this helped and have a good day

4 0

2 years ago

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The Louvre is an art museum in Paris. A glass square base pyramid sits in front of the entrance to the museum. If the pyramid is

Sveta_85 [38]

Answer:

lateral area = 2320 m²

Step-by-step explanation:

The question wants us to calculate the lateral area of a square base pyramid. The square base pyramid has a side of 40 meters.The height is 21 meters.

Half of the square base is 40/2 = 20 meters . With the height it forms a right angle triangle. The hypotenuse side is the slant height of the pyramid.

Using Pythagoras's theorem

c² = a² + b²

c² = 20² + 21²

c² = 400 + 441

c² = 841

square root both sides

c = √841

c = 29 meters

The slant height of the pyramid is 29 meters.

The pyramid has four sided triangle. The lateral area is 4 multiply by the area of one triangle.

area of triangle = 1/2 × base × height

base = 40 meters

height = 29 meters

area = 1/2 × 40 × 29

area = 580

area of one triangle = 580 m²

Lateral area = 4(580)

lateral area = 2320 m²

5 0

3 years ago