For the function G defined by G(x)=5x+3, find G(r+5)

Compute the quotient and remainder,

[tex]\dfrac{2x^4+x^3-14x^2+5x+6}{x^2+2x+k} \\\\ = 2x^2 - 3x - (8+2k) + \dfrac{(21+7k)x+(6+8k+2k^2)}{x^2+2x+k}[/tex]

The remainder upon dividing [tex]2x^4+x^3-14x^2+5x+6[/tex] by [tex]x^2+2x+k[/tex] should leave no remainder, which means

[tex]21+7k = 0 \implies 21 = -7k \implies k=-3[/tex]

and

[tex]6+8k+2k^2 = 0 \implies 2(k+3)(k+1)=0 \implies k=-3\text{ or }k=-1[/tex]

Only k = -3 makes both remainder terms vanish.

Then the previous result reduces to

[tex]\dfrac{2x^4+x^3-14x^2+5x+6}{x^2+2x-3} = 2x^2 - 3x - 2[/tex]

so that

[tex]2x^4+x^3-14x^2+5x+6 = (x^2+2x-3) (2x^2 - 3x - 2) \\\\ 2x^4+x^3-14x^2+5x+6 = (x+3)(x-1)(2x + 1)(x-2)[/tex]

and so the zeroes of the quartic polynomial are x = -3, x = 1, x = -1/2, and x = 2.

Answer:

Square both sides

√(2x+1)=2+√(x-3)

or, 2x+1=(2+√(x-3))²

solving it you'll get two values of x, which are,

x = 4 and x = 12

Answer:

Hello,

x=4 or x=12

Step-by-step explanation:

[tex]\sqrt{2x+1} =2+\sqrt{x-3} \\\\2x+1=4+4\sqrt{x-3} +(x-3)\\\\2x+1-x+3-4=4\sqrt{x-3} \\\\x=4\sqrt{x-3} \\\\ x^2-16x+48=0\\\\\Delta=16^2-4*48=64=8^2\\\\x=\dfrac{16-8}{2} \ or x=\dfrac{16+8}{2}\\\\x=4 \ or\ x=12\\\\Since \ we\ have \ squared \ we\ must\ verify\ the \ solutions\ found:\\\\x=4 \Longrightarrow \sqrt{2*4+1} =? 2+\sqrt{4-3} \Longrightarrow 3 =? 2+1 \\\\x=12 \Longrightarrow \sqrt{2*12+1} =? 2+\sqrt{12-3} \Longrightarrow 5 =? 2+3 \\\\[/tex]

Answer:

F(5;4)

Step-by-step explanation:

Call F(x;y)

cuz E is the midpoint so we have a formula:

(-3+x)/2=1 -> x=5

(-8+y)/2=-2 -> y= 4

so F(5;4)

We know at centroid medians bisect each other in the ratio 2:1.

[tex]\\ \sf\longmapsto TY=2x[/tex]

[tex]\\ \sf\longmapsto 2x=30[/tex]

[tex]\\ \sf\longmapsto x=\dfrac{30}{2}[/tex]

[tex]\\ \sf\longmapsto x=15[/tex]

Answer:

A

Step-by-step explanation:

On the median TW the distance from the vertex to the centroid is twice the distance from the centroid to the midpoint , then

YW = [tex]\frac{1}{2}[/tex] × TY = [tex]\frac{1}{2}[/tex] × 30 = 15

225125₆/101₆ = 2225₆

One way to arrive at this is to convert both given numbers to base 10, compute the quotient in base 10, then convert back to base 6.

101₆ = 1×6² + 0×6¹ + 1×6⁰ = 37

225125₆ = 2×6⁵ + 2×6⁴ + 5×6³ + 1×6² + 2×6¹ + 5×6⁰ = 19,277

So we have

225125₆/101₆ = 19,277/37 = 521

Next,

521 = 2×216 + 89 = 2×6³ + 89

89 = 2×36 + 17 = 2×6² + 17

17 = 2×12 + 5 = 2×6¹ + 5×6⁰

and so

521 = 2×6³ + 2×6² + 2×6¹ + 5×6⁰ = 2225₆

Or you can use the long division algorithm. Division in base 6 is the same as in base 10, except numerals range from 0 to 5 instead of 0 to 9. See if you can follow this diagram (replaced with an attachment)

Answer: x>12

so i think x is 16.

Answer:

B

Step-by-step explanation:

The two angles are alternate interior angles. The have to be equal.

7x + 15 = 148                     Subtract 15 from both sides

7x = 148 - 15

7x = 133                             Divide by 7

x = 133/7

x = 19

B

Both the angles will be 105°

Just add up the given angles, subtract the result by 360, and divide by 2.

Answer:

(x-3)(5x+4)

x=3 x=-4/5

Answer:

(5x + 4)(x - 3)

Step-by-step explanation:

Hello!

Factor:

Think: What two numbers add up to -11 but multiply to (5)(-12)?

Answer: -15 and 4

Continue:

The factored expression is (5x + 4)(x - 3)

Answer:

y - 7 = -4 (x + 2)

Step-by-step explanation:

y - 7 = -4 (x + 2)

Answer:

a) -8x³+x²+6x

d) 16x²-9

Step-by-step explanation:

a) -2x(x+4x²)+3(x²+2x)

Expand each bracket:

-2x(x+4x²)

As the -2x is on the outside of the bracket, you have to times everything inside the bracket by -2x.

-2x times x equals -2x²

-2x times 4x² equals -8x³

Then we expand the other bracket:

3(x²+2x)

3 times x² equals 3x²

3 times 2x equals 6x

We then put all of it together:

-2x²-8x³+3x²+6x

Collect like terms:

-8x³+x²+6x

b) (4x-3)(4x+3)

We will use the FOIL method:

F-First

O-outer

I-Inner

L-Last

Times the first two terms in each bracket:

4x times 4x equals 16x²

Times the outer terms in the bracket:

4x times 3 equals 12x

Times the inside terms in the bracket:

-3 times 4x equals -12x

Times the last terms in the bracket:

-3 times 3 equals -9

Put it together:

16x²+12x-12x-9

The 12x and -12x cancel out to leave 16x²-9

Hope this helps :)

Answer:

18.9

Step-by-step explanation:

if 200miles = 9gallons

then 420miles = ?

note:if more less divide and if less more divide.

so it is 420/200×9=18.9

Answer:

hello,

answer A c=n+2

Step-by-step explanation:

if n=0 then c=2

if n=2 then c=4

slope=m=(4-2)/(2-0) =2/2=1

c-2=1*(n-0)

c=n+2

Answer:

Solution given:

Sin[tex]\theta_{1}=\frac{-24}{25}[/tex]

[tex]\frac{opposite}{hypotenuse}=\frac{-24}{25}[/tex]

equating corresponding value

opposite=-24

hypoyenuse=25

adjacent=x

By using Pythagoras law

hypotenuse²=opposite²+adjacent²

25²=(-24)²+x²

625=576+x²

x²=625-576

x=49

x=[tex]\sqrt{49}=7[/tex]

In IV quadrant

Cos angle is positive

Cos[tex]\theta_{1}=\frac{adjacent}{hypotenuse}[/tex]

Answer:

cos theta = 7/25

Step-by-step explanation:

sin theta = opp / hyp

We can find the adj side by using the pythagorean theorem

adj ^2 + opp ^2 = hyp^2

adj^2 + (-24)^2 = 25^2

adj^2 +576 = 625

adj^2 =625 -576

adj^2 = 49

Taking the square root of each side

adj = 7

Since we are in the 4th quadrant, adj is positive

cos theta = adj / hyp

cos theta = 7/25

Answer:

-2.45

Step-by-step explanation:

I used a calculator to find this so I hope it helps :)

Answer:

the equivalent equation of

[tex]5^{-3}[/tex]=[tex]\frac{1}{5^{3}}=\frac{1}{125}[/tex]

Answer:

use the information provided to write the standard form equation of the circle

1. ends of a diameter: (11,-6) and (1,14)

use the information provided to write the genral conic form equation of each circle.

1. three points of the circle:

( 7,-4)(-3,-4) and ( 6,-7)

identify the centere and radius. then sketch the graph

1. x^2+y^2-4x-14=0

Answer:

(x + y - 2xy)*(x + y + 2xy)

Step-by-step explanation:

x^2-4x^2y^2+y^2+2*x*y

=x^2 + 2xy + y^2 - (2xy)^2

=(x + y)^2 - (2xy)^2

=(x + y - 2xy)*(x + y + 2xy)

Answer:

[tex](x^{-3})^2[/tex]

Step-by-step explanation:

applying the exponent rule to the inside of the bracket, x^3 x x^-6 = x^-3 since you add the exponents

Answer:

8r+8pg-pq

Step-by-step explanation:

The subtractable pg cancels out one of the 9 pg's. So 9 pg-1 pg= 8 pg

Hope this helps!

Hi there!

[tex]\large\boxed{\text{9 quarters}}[/tex]

We can let x = dimes and y = quarters.

We know that one dime = $0.10 and a quarter = $0.25, so:

$3.05 = $0.10x + $0.25y

And:

17 = x + y

Solve the system of equations. We can rearrange the bottom equation to create an expression equal to y:

17 - x = y

Substitute this into the top equation for y:

3.05 = 0.10x + 0.25(17 - x)

Distribute and simplify:

3.05 = 0.10x + 4.25 - 0.25x

3.05 = 4.25 - 0.15x

Solve for x:

-1.2 = -0.15x

x = 8

Find y using the above expression:

17 - 8 = y

y = 9

Answer:

216

Step-by-step explanation:

Volume of prism = BH

B -> Base area

Area of base:

b = 10 mi

h = 3.6mi

Area of the triangular base = [tex]\dfrac{1}{2}*b*h[/tex]

                        [tex]=\dfrac{1}{2}*10*3.6\\\\= 18 \ mi^{2}[/tex]

H = 12 mi

Volume of prism = 18 * 12 = 216  cubic mi

Answer:

Final answer is  ---> -4

Step-by-step explanation:

Answer:

gmvlɛpuyhgn

gteeyolpp

jwjvy

Step-by-step explanation:

y+80+70=180

y+150=180

y=30

Now you can, easily find x

Answer:

72

Step-by-step explanation:

The interior angles of a 6 sided figure add to (n-2) * 180

where n is the number of sides

(6-2) *180

4*180

720

2x+4x+4x+4x+4x+2x = 720

20x = 720

Divide by 20

20x/20 = 720/20

x =36

We want <F

<F = 2x = 2*36 = 72

Answer:

80°

Step-by-step explanation:

m<COB = 80°, it's the central angle for arc CB,

so mCB = 80°

Answer:

c  a = 2.4b

Step-by-step explanation:

y = kx is the form of the equation where k is the constant of proportionality

y and x can be any letters

Replacing y and x with a and b  and k with 2.4

a = 2.4b

9514 1404 393

Answer:

  b, c

Step-by-step explanation:

The factor (x+7) is common to both numerator and denominator. The function can be simplified by cancelling that factor.

  y = (x -3)/(x -9) . . . . . . x ≠ -7

The restriction x ≠ -7 is put on the simplified function because the original function is undefined there. The denominator factor x+7 makes the denominator 0 at that point.

The point at x=-7 is called "hole" in the graph. A properly drawn graph will show the function is undefined there (has a hole).

__

The denominator of the simplified function is zero when x=9. This means there is a vertical asymptote at x=9.

__

The ratio of the highest-degree terms of the numerator and denominator will tell you the end behavior of the function — its value when x is large. Here, that ratio is y = x/x = 1. This represents a horizontal asymptote at y=1. The function approaches this line as x gets large, but never reaches it.

The appropriate descriptors are ...