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3 years ago

Show that (x+1) is a factor of f(x)=19x^42+18x-1

Mathematics

1 answer:

Dmitry_Shevchenko [17]3 years ago

6 0

Answer:

see explanation

Step-by-step explanation:

If (x + 1) is a factor then f(- 1) = 0

f(- 1) = 19 $(-1)^{42}$ + 18(- 1) - 1 = 19 - 18 - 1 = 0

Thus (x + 1) is a factor of f(x)

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What are the endpoint coordinates for the midsegment of △PQR that is parallel to PQ¯¯¯¯¯?

andriy [413]

Answer:

M(x₄ ,y₄) = (-3.5 , 0.5) and

N (x₅ ,y₅) = ( -1 , -0.5 )

Step-by-step explanation:

Let the endpoint coordinates for the mid segment of △PQR that is parallel to PQ be

M(x₄ ,y₄) and N(x₅ ,y₅) such that MN || PQ

point P( x₁ , y₁) ≡ ( -3 ,3 )

point Q( x₂ , y₂) ≡ (2 , 1 )

point R( x₂ , y₂) ≡ (-4 , -2)

To Find:

M(x₄ ,y₄) = ? and

N (x₅ ,y₅) = ?

Solution:

We have Mid Point Formula as

$Mid\ point(x,y)=(\frac{x_{1}+x_{2} }{2}, \frac{y_{1}+y_{2} }{2})$

As M is the mid point of PR and N is the mid point of RQ so we will have

$Mid\ pointM(x_{4} ,y_{4})=(\frac{x_{1}+x_{3} }{2}, \frac{y_{1}+y_{3} }{2})$

$Mid\ pointN(x_{5} ,y_{5})=(\frac{x_{2}+x_{3} }{2}, \frac{y_{2}+y_{3} }{2})$

Substituting the given value in above equation we get

$Mid\ pointM(x_{4} ,y_{4})=(\frac{-3+-4 }{2}, \frac{3+-2} }{2})$

∴ $Mid\ pointM(x_{4} ,y_{4})=(\frac{-7} }{2}, \frac{1}{2})$

∴ $Mid\ pointM(x_{4} ,y_{4})=(-3.5, 0.5)$

Similarly,

$Mid\ pointN(x_{5} ,y_{5})=(\frac{2+-4 }{2}, \frac{1+-2 }{2})$

∴ $Mid\ pointN(x_{5} ,y_{5})=(\frac{-2 }{2}, \frac{-1}{2})$

∴ $Mid\ pointN(x_{5} ,y_{5})=(-1, -0.5)$

∴ M(x₄ ,y₄) = (-3.5 , 0.5) and

N (x₅ ,y₅) = ( -1 , -0.5 )

3 0

3 years ago

Round to underline digit 3 in 32, 336

Charra [1.4K]

I dont know if you know this, but there are 3 different 3's. So how can we figure out the question if we don't know which one is underlined?

5 0

3 years ago

Solve. 90<img src="https://tex.z-dn.net/?f=x" id="TexFormula1" title="x" alt="x" align="absmiddle" class="latex-formula"> = 27.

Irina-Kira [14]

Answer: $x$ ≈ $0.732$

Step-by-step explanation:

You need to find the value of the variable "x".

To solve for "x" you need to apply the following property of logarithms:

$log(m)^n=nlog(m)$

Apply logarithm on both sides of the equation:

$90^x=27\\\\log(90)^x=log(27)$

Now, applying the property mentioned before, you can rewrite the equation in this form:

$xlog(90)=log(27)$

Finally, you can apply the Division property of equality, which states that:

$If\ a=b,\ then\ \frac{a}{c}=\frac{b}{c}$

Therefore, you need to divide both sides of the equation by $log(90)$ . Finally, you get:

$\frac{xlog(90)}{log(90)}=\frac{log(27)}{log(90)}\\\\x=\frac{log(27)}{log(90)}$

$x$ ≈ $0.732$

7 0

3 years ago

PLEASE HELP

notsponge [240]

Answer:

(a)

x cubed is

=x^3=x3

5 times the cube of x is

=5x^3=5x3

4 times x is

=4x=4x

the quotient of 4 times x and 3 is

=\frac{4x}{3}=34x

so,

the difference of 5 times the cube of x cubed and the quotient of 4 times x and 3 is

=5x^3-\frac{4x}{3}=5x3−34x ..........Answer

(b)

5 times cube of x is

=5x^3=5x3

5 times cube of x divided by 4 times x is

=\frac{5x^3}{4x}=4x5x3 ..........Answer

(c)

difference of 5 times x cube and 4 is

=5x^3 -4=5x3−4

so,

the quotient of the difference of 5 times x cube and 4 and x is

=\frac{5x^3-4}{x}=x5x3−4 ...........Answer

(d)

difference of 5 times x and 4 is

=5x-4=5x−4

so,

the cube of the difference of 5 times x and 4 is is

=(5x-4)^3=(5x−4)3 ............Answer

5 0

2 years ago

Explicit equation for 5,10,20,40

eduard

Answer:

see explanation

Step-by-step explanation:

These are the terms of a geometric sequence with n th term

$a_{n}$ = a $(r)^{n-1}$

Where a is the first term and r the common ratio

r = $\frac{10}{5}$ = $\frac{20}{10}$ = $\frac{40}{20}$ = 2

and a = 5, hence explicit equation is

$a_{n}$ = 5 $(2)^{n-1}$

3 0

3 years ago