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3 years ago

The straight line P has the equation y= 2x-5

Mathematics

1 answer:

Sunny_sXe [5.5K]3 years ago

4 0

Answer:

y=−x/2+2.

Step-by-step explanation:

The equation of the line in the slope-intercept form is y=2x−5.

The slope of the perpendicular line is negative inverse: m=−12.

So, the equation of the perpendicular line is y=−x/2+a.

To find a, we use the fact that the line should pass through the given point: 3=(−12)⋅(−2)+a.

Thus, a=2.

Therefore, the equation of the line is y=−x/2+2.

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The equation $a^7xy-a^6y-a^5x=a^4(b^4-1)$ is equivalent to the equation $(a^mx-a^n)(a^py-a^2)=a^4b^4$ for some integers $m$, $n$

Ksivusya [100]

Let <span>simplify the equations $a^7xy-a^6y-a^5x=a^4(b^4-1)$ and $(a^mx-a^n)(a^py-a^2)=a^4b^4$ :
</span>
<span>1) $a^7xy-a^6y-a^5x+a^4=a^4b^4$
</span>
<span>and
</span>
<span>2) $a^{m+p}xy-a^{n+p}y-a^{m+2}x+a^{n+2}=a^4b^4$ .
</span>
<span>Equate the coefficients:
</span><span>
</span><span> $xy: m+p=7 \\ y: n+p=6 \\ x: m+2=5 \\ 1: n+2=4$ .</span>
Then $n=2 \\ p=4 \\ m=3$ and mnp=24.
<span />

3 0

3 years ago

Suppose the true proportion of voters in the county who support a restaurant tax is 0.54. Consider the sampling distribution for

Eva8 [605]

Answer:

The correct answer is:

(a) 0.54

(b) 0.0385

Step-by-step explanation:

Given:

Restaurant tax,

p = 0.54

Sample size,

n = 168

Now,

(a)

The mean will be:

⇒ μ $\hat{p}= p$

$=0.54$

(b)

The standard error will be:

$\sigma \hat{p}$ = $\sqrt{[\frac{p(1-p)}{n} ]}$

= $\sqrt{[\frac{(0.54\times 0.46)}{168} ]}$

= $\sqrt{[\frac{(0.2484)}{168} ]}$

= $0.0385$

6 0

3 years ago

Create a 5th degree trinomial that has a constant term of 3.

erastovalidia [21]

Answer:

$4x^5\:+\:9x^2\:+\:3$ is a trinomial having three terms, with degree 5 and the constant term '3'.

Step-by-step explanation:

Considering the trinomial

$4x^5\:+\:9x^2\:+\:3$

As the polynomial contains 3 terms, so it is a trinomial.

As the highest power of the variable 'x' is 5, so the degree of this polynomial is 5.

Any term with no variable is called a constant term. so, 3 is a term with no variable. Therefore, the constant term is 3.

Therefore, $4x^5\:+\:9x^2\:+\:3$ is a trinomial having three terms, with degree 5 and the constant term '3'.

8 0

3 years ago

Help me please: answer as an improper fraction

rewona [7]

1) $\frac{7}{24}$
2) $\frac{2}{7}$
3) $\frac{1}{5}$
4) $\frac{3}{14}$
5) $\frac{1}{3}$
6) $\frac{7}{20}$
7) $\frac{6}{10}$
8) $\frac{1}{12}$
9) $\frac{1}{3}$
10) $\frac{1}{90}$
11) $\frac{1}{40}$
12) $\frac{1}{50}$
13) $\frac{20}{21}$
14) $\frac{1}{4}$
15) $\frac{5}{6}$
16) $\frac{9}{35}$
17) $\frac{35}{12}$ ( $2 \frac{11}{12}$ )
18) $\frac{9}{1}$ (9)

7 0

3 years ago

(01.03. 106, 1.08 HC)

zlopas [31]

Answer:

A) see attached for a graph. Range: (-∞, 7]

B) asymptotes: x = 1, y = -2, y = -1

C) (x → -∞, y → -2), (x → ∞, y → -1)

Step-by-step explanation:

A graphing calculator is useful for graphing the function. We note that the part for x > 1 can be simplified:

$\dfrac{-x^2+x+2}{x^2-3x+2}=-\dfrac{(x-2)(x+1)}{(x-2)(x-1)}=-\dfrac{x+1}{x-1}\quad x\ne 2$

This has a vertical asymptote at x=1, and a hole at x=2.

The function for x ≤ 1 is an ordinary exponential function, shifted left 1 unit and down 2 units. Its maximum value of 3^-2 = 7 is found at x=1.

The graph is attached.

The range of the function is (-∞, 7].

As we mentioned in Part A, there is a vertical asymptote at x = 1. This is where the denominator (x-1) is zero.

The exponential function has a horizontal asymptote of y = -2; the rational function has a horizontal asymptote of y = (-x/x) = -1. The horizontal asymptote of the exponential would ordinarily be y=0, but this function has been translated down 2 units.

The end behavior is defined by the horizontal asymptotes:

for x → -∞, y → -2

for x → ∞, y → -1

7 0

2 years ago