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4 years ago

Solve each exponential equation. 32^x = 81

Mathematics

1 answer:

vesna_86 [32]4 years ago

7 0

Answer:

The solution is $x = 1.268$ .

Step-by-step explanation:

The best way to solve this exponential equation is applying the logarithm of base 10 to each side of the equality.

It is also important to remember the following logarithm proprierty:

$\log{a^{b}} = b \log{a}$

$32^{x} = 81$

$\log{32^{x}} = \log{81}$

$x\log{32} = \log81$

$1.505x = 1.908$

$x = \frac{1.908}{1.505}$

$x = 1.268$

The solution is $x = 1.268$ .

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Compare the line passing through the points (-2, 9) and (4, 6) to the line given by the equation y= 2/5 x -4.

Licemer1 [7]

Answer:

No relation ( see bottom for detail )

I'm not sure if you want this explanation, but here you go.

Step-by-step explanation:

If you want to find out if the points are on this line, substitute in the values.

y = 2/5x - 4 y = 2/5x - 4

6 = 2/5 ( 4 ) - 4 9 = 2/5 ( -2 ) - 4

6 = 8/5 -4 9 = -4/5 - 4

6 = 8/5 - 20/5 9 = -4/5 - 20/5

6 ≠ -12/5 9 ≠ -24/5

After substituting in the values, I've come to the conclusion that these points don't pass through this line.

Solving to find if they are perpendicular, I use the rise/run equation-

y_2 - y_1 over x_2 - x_1

y_2 and x_2 is the second set of points, which then can help determine the slope of two points.

6 - 9

4 - ( negative 2 ) ( this is also equal to adding a positive 2 )

-3 / 6

= -1/2 is the slope of these two points

Comparing the slopes given, I can conclude that the equation and these two points have no relation.

4 0

3 years ago

Graph the polygon and its image after a dilation centered at C(1,1)

Grace [21]

Now we proceed to present the graphs of the polygon and its image with the help of a graphing tool. The original polygon is highlighted in red and the image is highlighted in blue.

DIlations are defined by the follwing operation:

$P'(x,y) = O(x,y) + k\cdot [P(x,y)-O(x,y)]$ (1)

Where:

$O(x,y)$ - Center of dilation.
$k$ - Dilation factor.
$P(x,y)$ - Original point of the polygon.
$P'(x,y)$ - Dilated point of the polygon.

If we know that $O(x,y) = (1,1)$ , $k = 0.5$ , $J(x,y) = (3,1)$ , $K(x,y) = (5, -3)$ , $L(x,y) = (5,5)$ and $M(x,y) = (3,7)$ , then the coordinates of the new polygon are:

$J'(x,y) = (1,1) + 0.5\cdot [(3,1)-(1,1)]$

$J'(x,y) = (1,1)+0.5\cdot (2,0)$

$J'(x,y) = (1,1) +(1,0)$

$J'(x,y) = (2,1)$

$K'(x,y) = (1,1) + 0.5\cdot [(5,-3)-(1,1)]$

$K'(x,y) = (1,1) +0.5\cdot (4,-4)$

$K'(x,y) = (1,1) +(2,-2)$

$K'(x,y) = (3,-1)$

$L'(x,y) = (1,1) + 0.5\cdot [(5,5)-(1,1)]$

$L'(x,y) = (1,1) + 0.5\cdot (4,4)$

$L'(x,y) = (1,1) + (2,2)$

$L'(x,y) = (3,3)$

$M'(x,y) = (1,1) + 0.5\cdot [(3,7)-(1,1)]$

$M'(x,y) = (1,1) +0.5\cdot (2,6)$

$M'(x,y) = (1,1) +(1,3)$

$M'(x,y) = (2,4)$

We kindly invite to check this question on dilations: brainly.com/question/13176891

6 0

3 years ago

Can someone please help, I'll give out 20 points !

ElenaW [278]

I believe it would be negative three (-4) since the lines are thinner however; there is a chance they are skip counting by 2. In that case the answer would be negative six (-6).

6 0

3 years ago

Read 2 more answers

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Oksi-84 [34.3K]

Answer:

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2 years ago

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PtichkaEL [24]

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3 years ago