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3 years ago

Consider a graph of the equation y = x + 6. What is the y-intercept?

1 answer:

7 0

In y = mx + b form, which is what ur equation is in, the y int can be found in the b position

y = mx + b
y = x + 6

as u can see, the number in the b position, ur y int, is 6 <==

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an electronics store is selling a new tv for $640.00 if there is an 8% sales tax what is the actual cost of the tv

damaskus [11]

Answer:

$691.20

Step-by-step explanation:

640 * 1.08 = 691.2

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3 years ago

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2y=-8 which set of steps shows the solution to the equation

Rainbow [258]

2y=-8
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3 years ago

What is the approximate radius of a sphere with a volume of 34 cm3?

xz_007 [3.2K]

Answer:

Step-by-step explanation:

The formula of a volume of a sphere:

$V=\dfrac{4}{3}\pi R^3$

R - radius

We have

$V=34\ cm^3$

Substitute:

$\dfrac{4}{3}\pi R^3=34$ multiply both sides by 3

$3\!\!\!\!\diagup^1\cdot\dfrac{4}{3\!\!\!\!\diagup_1}\pi R^3=(3)(34)$

$4\pi R^3=102$ divide both sides by 4

$\dfrac{4\pi R^3}{4}=\dfrac{102}{4}$

$\pi R^3=\dfrac{51}{2}$ divide both sides by π

$\dfrac{\pi R^3}{\pi}=\dfrac{\frac{51}{2}}{\pi}$

$R^3=\dfrac{51}{2\pi}$ use π ≈ 3.14

$\R^3\approx\dfrac{51}{(2)(3.14)}$

$R^3\approx\dfrac{51}{6.28}\\\\R^3\approx8.121\to R\approx\sqrt[3]{8.121}\\\\R\approx2.01\ cm$

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4 years ago

use the definition of countinuity to find the value of k so that the function is continuous for all real numbers

liubo4ka [24]

First of all, recall the definition of absolute value:

$|x| = \begin{cases}x&\text{if }x\ge0\\-x&\text{if }x$

So if x < 4, then x - 4 < 0, so |x - 4| = -(x - 4), and the first case in h(x) reduces to

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

Next, in order for h(x) to be continuous at x = 4, the limits from either side of x = 4 must be equal and have the same value as h(x) at x = 4. From the given definition of h(x), we have

$h(4) = 5k-4\cdot4 = 5k-16$

Compute the one-sided limits:

• From the left:

$\displaystyle \lim_{x\to4^-}h(x) = \lim_{x\to4}\frac{|x-4|}{x-4} = \lim_{x\to4}(-1) = -1$

• From the right:

$\displaystyle \lim_{x\to4^+}h(x) = \lim_{x\to4}(5k-4x) = 5k-16$

If the limits are to be equal, then

-1 = 5k - 16

Solve for k :

-1 = 5k - 16

15 = 5k

k = 3

3 0

3 years ago