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3 years ago

The diagram shows a triangle. 108° 42° 15c What is the value of c?

1 answer:

8 0

Assuming these are the angles for the inside of the triangle:

c=2

Step-by-step:

108+42+15c=180
150+15c=180
15c=30
c=2

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Is table A liner or nonlinear

Kipish [7]

I think table A is liner

7 0

2 years ago

I need help I don't know how to do this

Sidana [21]

Answer:

$x\geq 23$

Step-by-step explanation:

This equation can simply be solved by adding 15 to both sides.

To graph, draw a closed point at the center of the line and darken the area to the right of it.

5 0

2 years ago

Find the solution of the initial value problem dy/dx=(-2x+y)^2-7 ,y(0)=0

Leokris [45]

Substitute $v(x)=-2x+y(x)$ , so that $\dfrac{\mathrm dv}{\mathrm dx}=-2+\dfrac{\mathrm dy}{\mathrm dx}$ . Then the ODE is equivalent to

$\dfrac{\mathrm dv}{\mathrm dx}+2=v^2-7$

which is separable as

$\dfrac{\mathrm dv}{v^2-9}=\mathrm dx$

Split the left side into partial fractions,

$\dfrac1{v^2-9}=\dfrac16\left(\dfrac1{v-3}-\dfrac1{v+3}\right)$

so that integrating both sides is trivial and we get

$\dfrac{\ln|v-3|-\ln|v+3|}6=x+C$

$\ln\left|\dfrac{v-3}{v+3}\right|=6x+C$

$\dfrac{v-3}{v+3}=Ce^{6x}$

$\dfrac{v+3-6}{v+3}=1-\dfrac6{v+3}=Ce^{6x}$

$\dfrac6{v+3}=1-Ce^{6x}$

$v=\dfrac6{1-Ce^{6x}}-3$

$-2x+y=\dfrac6{1-Ce^{6x}}-3$

$y=2x+\dfrac6{1-Ce^{6x}}-3$

Given the initial condition $y(0)=0$ , we find

$0=\dfrac6{1-C}-3\implies C=-1$

so that the ODE has the particular solution,

$\boxed{y=2x+\dfrac6{1+e^{6x}}-3}$

5 0

2 years ago

Three roots of the polynomial equation x4 - 4x3 - 2x2 + 12x + 9 = 0 are 3, -1 and -1. Explain why the fourth root must be a real

LiRa [457]

Descares Theorem says that the number of roots of a polynomial is equal to its highest exponent, and the roots could be real and/or imaginary (complex).

However is their is one complex root (a + i.b), it's conjugate is also
a root (a-i.b).

In the equation x⁴ - 4x³ - 2x² + 12x + 9 = 0, we have already 3 roots, then the 4rth cannot be a complex one since we don't have a fifth for its conjugate.

3 0

2 years ago

Simplify 8 over negative 3 divided by negative 4 over 9 . (5 points) -8 -6 6 8

denpristay [2]

Answer:

Step-by-step explanation:

(8/3) / (-4/9)

when dividing fractions you use the acronym k.c.f (keep change flip)

keep the first fraction

change the operation (divide to multiply)

flip the other fraction

(8/-3) x (9/4)

after re-writing your expression, you want to solve

do this by multiplying both numerators by each other and same with the denominators

(-8x9) / (3x-4)

then you get a new fraction,

-72/-12

simplify,

-72/-12 = 6 (multiplying/dividing 2 negatives will always give you a positive)

3 0

2 years ago