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2 years ago

Which two points on the number line represent numbers that can be combined to make zero?

Mathematics

1 answer:

Archy [21]2 years ago

8 0

Where is the number line

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Please help!! Find the value of x.

Ludmilka [50]

Answer:

x = 4

Step-by-step explanation:

2(8x) = 64

x = 4

4 0

3 years ago

B= R/E - T, solve for E

Cloud [144]

R(B+T)=E because you first have to add T to both sides then multiply R to cancel out the division sign

3 0

3 years ago

given two terms in a geometric sequence find the 8th term and the recursive formula . a4=-12 and a5=-6

Crazy boy [7]

A geometric sequence is defined by a starting point, $a$ , and a common ratio $r$

The first term is $a$ , and you get every next term by multiplying the previous one by r.

So, our terms are

$\left[\begin{array}{c|c}a_1&a\\a_2&ar\\a_3&ar^2\\a_4&ar^3=-12\\a_5&ar^4=-6\end{array}\right]$

We can see that when we pass from $a_4$ to $a_5$ the number gets halved ( $-12 \mapsto -6$ )

This implies that the common ratio is $r = \frac{1}{2}$

So, the table becomes

$\left[\begin{array}{c|c}a_1&a\\a_2&\frac{1}{2}a\\a_3&\frac{1}{4}a\\a_4&\frac{1}{8}a=-12\\a_5&\frac{1}{16}a=-6\end{array}\right]$

So, we can derive the starting point from either $a_4$ or $a_5$ :

$\dfrac{1}{8}a = -12 \iff a = -12\cdot 8 = -96$

The sequence is thus

$\left[\begin{array}{c|c}a_1&-96\\a_2&-48\\a_3&-24\\a_4&-12\\a_5&-6\\a_6&-3\\\vdots&\vdots\end{array}\right]$

And the recursive formula is

$a_n = -\dfrac{96}{2^{n-1}}$

7 0

4 years ago

What is the equation (4, 5) m=-1/4 solved in point slope form?

hammer [34]

Answer:

Step-by-step explanation:

The point-slope form of an equation of a line:

$y-y_1=m(x-x_1)$

We have m = -1/4 and the point (4, 5). Substitute:

$y-5=-\dfrac{1}{4}(x-4)$

8 0

3 years ago

Calc help pretty please

Gre4nikov [31]

Answer:

A. 77.4

Step-by-step explanation:

Linear approximation formula

$L(x)=f(a)+f'(a)(x-a)$

Given function:

$f(x)=(x+1)^2$

$\boxed{\begin{minipage}{5.4 cm}\underline{Chain Rule for Differentiation}\\\\If $y=f(u)$ and $u=g(x)$ then:\\\\$\dfrac{\text{d}y}{\text{d}x}=\dfrac{\text{d}y}{\text{d}u}\times \dfrac{\text{d}u}{\text{d}x}$\\\end{minipage}}$

$\boxed{\begin{minipage}{5 cm}\underline{Differentiating $x^n$}\\\\If $y=x^n$, then $\dfrac{\text{d}y}{\text{d}x}=xn^{n-1}$\\\end{minipage}}$

$\boxed{\begin{minipage}{4 cm}\underline{Differentiating $ax$}\\\\If $y=ax$, then $\dfrac{\text{d}y}{\text{d}x}=a$\\\end{minipage}}$

Use the chain rule to differentiate the function.

$\textsf{Let }\:y=u^2\:\textsf{ where }u=(x+1)$

Differentiate the two parts separately:

$y=u^2 \implies \dfrac{\text{d}y}{\text{d}u}=2u$

$u=x+1 \implies \dfrac{\text{d}u}{\text{d}x}=1$

Put everything back into the chain rule formula:

$\begin{aligned} \implies \dfrac{\text{d}y}{\text{d}x} & =2u \times 1\\ & = 2u \\ & = 2(x+1)\\ & = 2x+2 \end{aligned}$

$\textsf{Therefore, }\:f'(x)=2x+2.$ .

The linear approximation at a = 8 is:

$\begin{aligned}L(x) & =f(a)+f'(a)(x-a)\\\\\implies L(x) & = f(8)+f'(8)(x-8)\\& = (8+1)^2+(2(8)+2)(x-8)\\& = 81+18(x-8)\\& = 18x-63\end{aligned}$

Finally, substitute x = 7.8 into the linear approximation equation:

$\begin{aligned}\implies L(7.8) & =18(7.8)-63\\& = 140.4-63\\& = 77.4\end{aligned}$

4 0

2 years ago

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