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3 years ago

What is the slope of a line perpendicular to y = -7/4x?

1 answer:

6 0

A line is perpendiculat to another which has a slope of m if the perpendicular line has a slope of -1/m.
That means that if the product of slopes of two lines is -1, the two lines are perpendicular.

Here, y1=-7/4x, or m=-7/4
The perpendicular should have a slope of -1/m=-1/(-7/4)=4/7

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What term is 1/1024 in the geometric sequence,-1,1/4,-1/6..?

Trava [24]

Answer:

$\large\boxed{\text{sixth term is equal to}\ \dfrac{1}{1024}}$

Step-by-step explanation:

The explicit formula for a geometric sequence:

$a_n=a_1r^{n-1}$

$a_n$ - n-th term

$a_1$ - first term

$r$ - common ratio

$r=\dfrac{a_2}{a_1}=\dfrac{a_3}{a_2}=...=\dfrac{a_n}{a_{n-1}}$

We have

$a_1=-1,\ a_2=\dfrac{1}{4},\ a_3=-\dfrac{1}{6},\ ...$

The common ratio:

$r=\dfrac{\frac{1}{4}}{-1}=-\dfrac{1}{4}\\\\r=\dfrac{-\frac{1}{6}}{\frac{1}{4}}=-\dfrac{1}{6}\cdot\dfrac{4}{1}=-\dfrac{2}{3}\neq-\dfrac{1}{4}$

<h2>It's not a geometric sequence.</h2>

If $a_3=-\dfrac{1}{16}$ then the common ratio is $r=\dfrac{-\frac{1}{16}}{\frac{1}{4}}=-\dfrac{1}{16}\cdot\dfrac{4}{1}=-\dfrac{1}{4}$

Put to the explicit formula:

$a_n=-1\left(-\dfrac{1}{4}\right)^{n-1}$

Put $a_n=\dfrac{1}{1024}$ and solve for <em>n </em>:

$-1\left(-\dfrac{1}{4}\right)^{n-1}=\dfrac{1}{1024}\qquad\text{use}\ a^n:a^m=a^{n-m}\\\\-\left(-\dfrac{1}{4}\right)^n:\left(-\dfrac{1}{4}\right)^1=\dfrac{1}{1024}\\\\-\left(-\dfrac{1}{4}\right)^n\cdot(-4)=\dfrac{1}{1024}\\\\(4)\left(-\dfrac{1}{4}\right)^n=\dfrac{1}{1024}\qquad\text{divide both sides by 4}\ \text{/multiply both sides by}\ \dfrac{1}{4}/\\\\\left(-\dfrac{1}{4}\right)^n=\dfrac{1}{4096}\\\\\dfrac{(-1)^n}{4^n}=\dfrac{1}{4^6}\qquad n\ \text{must be even number. Therefore}\ (-1)^n=1$

$\dfrac{1}{4^n}=\dfrac{1}{4^6}\iff n=6$

5 0

3 years ago

A geologist visits 40 volcanoes in Alaska and California.15% of volcanoes are in California.how many volcanoes does the geologis

ziro4ka [17]

Answer:

The answer is 34

4 0

3 years ago

What is the sum or difference?

dlinn [17]

1. Ans: Option (B) $-6x^4$

Explanation:
Given: $2x^4 - 8x^4$
Take the common out:
=> $x^4(2 - 8)$

Hence: => $[tex]-6x^4$ [/tex] (Option B)

2. Ans: Option (D) $-3y^5$

Explanation:
Given: $6y^5 - 9y^5$
Take the common term(s) out:
=> $y^5(6-9)$

Hence: => $-3y^5$ (Option D)

3. Ans: Option (B) $9x^2 - 12x + 6$ <span> quadratic trinomial

Explanation:
</span>Given: $6 - 12x + 13x^2 - 4x^2$

The standard form of polynomial function must have the highest powered value at the start, then the second highest and so on.

=> $13x^2 - 4x^2 - 12x + 6$
=> $9x^2 - 12x + 6$ (Option B)

4. Ans: Option (C) $7.3x^2 + 0.8x + 1.3$

Explanation:
In order to find the total number of C<span>ommon and Endler's guppies, you need to add both Common and Endler's guppies' polynomials, as follows:

</span>Common guppies: $3.1x^2 +6.0x + 0.3$ <span>
Endler's guppies: </span> $4.2x^2 - 5.2x + 1.0$
(add both)
-----------------------------------------------------------------
Total number: $7.3x^2 +0.8x + 1.3$
-----------------------------------------------------------------
Hence the ans is Option(C) $7.3x^2 + 0.8x + 1.3$

5. Ans: Option (D) $2x^2(133 - 18 \pi )$

Explanation:
First let's find the total area of the yard:
Total Area of the Yard = 14x * 19x = $266x^2$

Now the area of the circular fountain:
Area of the Circular Fountain = $\pi r^2$
Since, r=6x
Therefore,
Area of the Circular Fountain = $\pi (6x)^2 = 36 \pi x^2$

Now the final Area of the yard would be:
Final area of the Yard = Total Area of the Yard - Area of the Circular Fountain
Final area of the Yard = $266x^2$ - $36 \pi x^2$
=> Final area of the Yard = $2x^2(133 - 18 \pi)$ (Option D)

6. Ans: Option (A) $56x^2$

Explanation:
First let's find the total area of the lot:
Total Area of the lot= 6x * 10x = $60x^2$

Now the area of the stadium:
Area of the stadium = 1x * 4x = $4x^2$

Now the final Area of the lot would be:
Final area of the lot= Total Area of the lot - Area of the stadium
Final area of the lot= $60x^2$ - $4x^2$
=> Final area of the lot = $56x^2$ (Option A)

-i

4 0

3 years ago

Read 2 more answers

Why is 1/2 the same as 0.5

Basile [38]

Answer:

it’s because 0.50 is half of 100 and 1/2 is a reduced fraction of 50/100.

Step-by-step explanation:

5 0

2 years ago

Please help please please please

kap26 [50]