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3 years ago

Which two values of x are roots of the polynomial below x^2-11x+17

Mathematics

1 answer:

svetlana [45]3 years ago

3 0

Answer

9.14 and 1.86

Explanation

x²-11x+17

The first thing is to equate it to zero.

x²-11x+17 = 0

x²-11x = -17

x² - 11x + (11/2)² = -17 + (11/2)²

(x² - 11/2)² = -17 + 121/4

(x - 11/2)² = 13.25

x -11/2 = √13.25 or x - 11/2 = -√13.25

x = √13.25 + 11/2 x = -√13.25 + 11/2

= 3.64 + 5.5 = -3.64 + 5.5

= 9.14 = 1.86

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Solve using substitution. 7x-4y=-12 9x-4y=-20

MrRissso [65]

Answer:y= -4

Step-by-step explanation:

1 Solve for xx in 7x-4y=-127x−4y=−12.

x=\frac{4(y-3)}{7}

4(y−3)

2 Substitute x=\frac{4(y-3)}{7}x=

4(y−3)

into 9x-4y=-209x−4y=−20.

\frac{36(y-3)}{7}-4y=-20

36(y−3)

−4y=−20

3 Solve for yy in \frac{36(y-3)}{7}-4y=-20

36(y−3)

−4y=−20.

y=-4

y=−4

4 Substitute y=-4y=−4 into x=\frac{4(y-3)}{7}x=

4(y−3)

x=-4

x=−4

5 Therefore,

\begin{aligned}&x=-4\\&y=-4\end{aligned}

x=−4

y=−4

3 0

2 years ago

Patrick is keeping track of how far he jogs each morning.

katrin2010 [14]

Answer:

21:50

Step-by-step explanation:

We need to find the ratio of 420 m to 1 km.

We know that,

1 km = 1000 m

So,

The ratio becomes,

$\dfrac{420\ m}{1\ km}=\dfrac{420\ m}{1000\ m}\\\\=\dfrac{42\ m}{100\ m}\\\\=\dfrac{21}{50}$

So, the required ratio is 21:50.

5 0

3 years ago

20 minute deadline. right answers only.

emmainna [20.7K]

The answer has to be 1

4 0

3 years ago

Marymount Township secured the construction of a power plant, which opened in 1990. Once the power plant opened

Aleksandr [31]

Answer:

92087,14873

Step-by-step explanation:

Given that Marymount Township secured the construction of a power plant, which opened in 1990. Once the power plant opened in 1990, the population of Marymount increased by about 20% each year for the first ten years and then increased by 5% each year after that

Let P0 be the population in 1990

Then we have in 2000 the population is

$P(2000) = P_0(1.2)^{10}$

with this initial population for next growth we have in 2010 the population would be

$P(1.05)^{10}$ , where P = population is 2000

a) Given that $P(1.05)^{10) = 150000\\P = 150000(1.05)^{-10} =92.086.99\\=92087$

b) we use the exponential equation and solve for initial population in 2000.

c) we have

$P_0(1.2)^{10} =92087\\P_0 = 92087((1.2)^{-10})\\=14872.56\\=14873$

6 0

3 years ago

Find the vertex and length of the latus rectum for the parabola. y=-1/2(x-2)^2+8

victus00 [196]

Y = -(1/2)(x-2)² +8
Re write it in standard form:
(y-8) = -1/2(x-2)² ↔ (y-k) = a(x-h)²

This parabola open downward (a = -1/2 <0), with a maximum shown in vertex
The vertex is (h , k) → Vertex(2 , 8)
focus(h, k +c )
a = 1/4c → -1/2 = 1/4c → c = -1/2, hence focus(2, 8-1/2) →focus(2,15/2)

Latus rectum: y-value = 15/2

Replace in the equation y with 15/2→→15/2 = -1/2(x-2)² + 8
Or -1/2(x-2)² +8 -15/2 = 0
Solving this quadratic equation gives x' = 3 and x" = 2, then
Latus rectum = 5

4 0

3 years ago