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2 years ago

What is the value of y?

Mathematics

1 answer:

horrorfan [7]2 years ago

5 0

Answer:

y = 25

Step-by-step explanation:

Hey There!

The angle labeled x is supplementary to the angle that is equal to 115 meaning that the sum of the two angles will add up to equal 180

so to find x we subtract 115 from 180

180-115=65 so x = 65

Now we can find y

remember the sum of the triangles angles add up to equal 180

so we subtract the given angles(90 and 65) from 180

180-90-65=25

so y = 25

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Step-by-step explanation:

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3 years ago

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Solve $16x+9=9y-2x$ for $y$ .

s344n2d4d5 [400]

Answer:

The solution for y is y = 2x + 1

Step-by-step explanation:

* <em>Lets explain how to solve an equation for one of the variables</em>

- We need to solve the equation 16x + 9 = 9y - 2 x for y

- That means we want to find y in terms of x and the numerical term

- the equation has two sides, one side contains x and numerical term

and the other side contains y and x

- We need to separate y in one side, and other term in the other side

* <em>Lets do that</em>

∵ 16x + 9 = 9y - 2x

- Add 2x to both sides to cancel -2x from the right side

∴ 16x + 2x + 9 = 9y - 2x + 2x

- Add like terms in each side

∴ 18x + 9 = 9y

- Divide each term by the coefficient of y ⇒ (÷9)

∴ (18 ÷ 9)x + (9 ÷ 9) = (9 ÷ 9)y

∴ 2x + 1 = y

- Switch the two sides

∴ y = 2x + 1

* The solution for y is y = 2x + 1

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2 years ago

Ben graphed a system of equations and stated that the solution is (4, 4). Check his solution algebraically.

Juliette [100K]

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3 years ago

Prove algebraically that the straight line with equation x=2y+5 is a tangent to the circle with equation x^2+y^2=5

zmey [24]

Differentiate both sides of the equation of the circle with respect to $x$ , treating $y=y(x)$ as a function of $x$ :

$x^2+y^2=5\implies2x+2y\dfrac{\mathrm dy}{\mathrm dx}=0\implies\dfrac{\mathrm dy}{\mathrm dx}=-\dfrac xy$

This gives the slope of any line tangent to the circle at the point $(x,y)$ .

Rewriting the given line in slope-intercept form tells us its slope is

$x=2y+5\implies y=\dfrac12x-\dfrac52\implies\mathrm{slope}=\dfrac12$

In order for this line to be tangent to the circle, it must intersect the circle at the point $(x,y)$ such that

$-\dfrac xy=\dfrac12\implies y=-2x$

In the equation of the circle, we have

$x^2+(-2x)^2=5x^2=5\implies x=\pm1\implies y=\mp2$

If $x=-1$ , then $-1=2y+5\implies y=-3\neq2$ , so we omit this case.

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3 years ago

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Kamila [148]

1) Parallel lines have equal slopes.

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Line 2 has slope 2/3.

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y = 2/5 x - 2

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