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2 years ago

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Preston and Joel are both solving the equation 2x=14. Preston is not sure what to do because he does not know a power of 2 that

equals 14. Joel uses his calculator to graph y=2x and y=14 and find the point of intersection. Will Joel's method work?

1 answer:

Murrr4er [49]2 years ago

7 0

Answer:

yes

Step-by-step explanation:

You can always separate an equation into two parts and see where those graphs intersect.

Joel's method works well.

_____

<em>Additional comments</em>

Preston should know that the invention of logarithms makes it easy to solve equations like this. x = log₂(14) = log(14)/log(2) ≈ 3.8073549.

As for Joel's method, I prefer to subtract the right side to get the equation ...

2^x -14 = 0

Then graphing y = 2^x -14, I look for the x-intercept. Most graphing calculators make it easy to find x- and y-intercepts. Not all make it easy to find points of intersection between different curves.

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NEED HELP WITH THIS PROBLEM!!!!!!

zzz [600]

Answer:

$\displaystyle\frac{\sqrt[4]{3x^2}}{2y}$

Step-by-step explanation:

It can work well to identify 4th powers under the radical, then remove them.

$\displaystyle\sqrt[4]{\frac{24x^6y}{128x^4y^5}}=\sqrt[4]{\frac{3x^2}{16y^4}}=\sqrt[4]{\frac{3x^2}{(2y)^4}}\\\\=\frac{\sqrt[4]{3x^2}}{2y}$

_____

The applicable rules of exponents are ...

1/a^b = a^-b

(a^b)(a^c) = a^(b+c)

The x-factors simplify as ...

x^6/x^4 = x^(6-4) = x^2

The y-factors simplify as ...

y/y^5 = 1/y^(5-1) = 1/y^4

The constant factors simplify in the usual way:

24/128 = (8·3)/(8·16) = 3/16

3 0

3 years ago

Please help me find the area of shaded region and step by step

Bumek [7]

Answer:

Part 1) $A=60\ ft^2$

Part 2) $A=80\ cm^2$

Part 3) $A=96\ m^2$

Part 4) $A=144\ cm^2$

Part 5) $A=9\ m^2$

Part 6) $A=(49\pi -33)\ in^2$

Step-by-step explanation:

Part 1) we know that

The shaded region is equal to the area of the complete rectangle minus the area of the interior rectangle

The area of rectangle is equal to

$A=bh$

where

b is the base of rectangle

h is the height of rectangle

so

$A=(12)(7)-(8)(3)$

$A=84-24$

$A=60\ ft^2$

Part 2) we know that

The shaded region is equal to the area of the complete rectangle minus the area of the interior square

The area of square is equal to

$A=b^2$

where

b is the length side of the square

so

$A=(12)(8)-(4^2)$

$A=96-16$

$A=80\ cm^2$

Part 3) we know that

The area of the shaded region is equal to the area of four rectangles plus the area of one square

so

$A=4(4)(5)+(4^2)$

$A=80+16$

$A=96\ m^2$

Part 4) we know that

The shaded region is equal to the area of the complete square minus the area of the interior square

so

$A=(15^2)-(9^2)$

$A=225-81$

$A=144\ cm^2$

Part 5) we know that

The area of the shaded region is equal to the area of triangle minus the area of rectangle

The area of triangle is equal to

$A=\frac{1}{2}(b)(h)$

where

b is the base of triangle

h is the height of triangle

so

$A=\frac{1}{2}(6)(7)-(6)(2)$

$A=21-12$

$A=9\ m^2$

Part 6) we know that

The area of the shaded region is equal to the area of the circle minus the area of rectangle

The area of the circle is equal to

$A=\pi r^{2}$

where

r is the radius of the circle

so

$A=\pi (7^2)-(3)(11)$

$A=(49\pi -33)\ in^2$

7 0

2 years ago

Please help ill give you BRAINLIEST. No links please

Nat2105 [25]

Answer:

m(arc FE) = 166°

Step-by-step explanation:

By theorem of intersecting chords and tangent of a circle,

Measure of the angle formed by a chord and tangent intersecting on the circle measure the half of the intercepted arc.

m(∠GFE) = $\frac{1}{2}\text{m (arc} FE)$

83° = $\frac{1}{2}\text{m (arc} FE)$

m(arc FE) = 166°

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3 years ago

Please help, I’m very confused

snow_tiger [21]

Answer:

1st picture: (0,4)

The lines intersect at point (0,4).

2nd picture: Graph D

2x ≥ y - 1

2x - 5y ≤ 10

Set these inequalities up in standard form.

y ≤ 2x + 1

-5y ≤ 10 - 2x → y ≥ -2 + 2/5x → y ≥ 2/5x - 2

When you divide by a negative number, you switch the inequality sign.

Now you have:

y ≤ 2x + 1

y ≥ 2/5x - 2

Looking at the graphs, you first want to find the lines that intersect the y-axis at (0, 1) and (0, -2).

In this case, it is all of them.

Next, you would look at the shaded regions.

The first inequality says the values are less than or equal to. So you look for a shaded region below a line. The second inequality says the values are greater than or equal to. So you look for a shaded region above a line.

That would mean Graph B or D.

Then you look at the specific lines. You can see that the lower line is y ≥ 2/5x - 2. You need a shaded region above this line. You can see the above line is y ≤ 2x + 1. You need a shaded region below this line. That is Graph D.

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2 years ago

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36 inches, 20 inches, and 24 inches. What type of triangle did Rosa draw?

Rama09 [41]

Answer:

Scalene triangle

Step-by-step explanation:

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3 years ago