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Vanyuwa [196]
3 years ago
6

Let $x$ be a value such that $8x^2 + 7x - 1 = 0$ and $24x^2+53x-7 = 0.$ What is the value of $x$? Express your answer as a simpl

ified common fraction.
Mathematics
1 answer:
Fittoniya [83]3 years ago
6 0

8x^2+7x-1=0\ \wedge\ 24x^2+53x-7=0\\\\\text{The equation:}\\\\24x^2+53x-7=8x^2+7x-1\qquad\text{subtract}\ 8x^2\ \text{and}\ 7x\ \text{from both sides}\\\\16x^2+46x-7=-1\qquad\text{add 1 to both sides}\\\\16x^2+46x-6=0\qquad\text{divide both sides by 2}\\\\8x^2+23x-3=0\\\\8x^2+24x-x-3=0\\\\8x(x+3)-1(x+3)=0\\\\(x+3)(8x-1)=0\iff x+3=0\ \vee\ 8x-1=0\\\\x+3=0\qquad\text{subtract 3 from both sides}\\\boxed{x=-3}\\\\8x-1=0\qquad\text{add 1 to both sides}\\8x=1\qquad\text{divide both sides by 8}\\\boxed{x=\dfrac{1}{8}}

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What are the coordinates of R' after a dilation by a scale factor of 3, centered at the origin, followed by the translation (x,
emmainna [20.7K]

9514 1404 393

Answer:

  C.  (9, 18)

Step-by-step explanation:

Given R(3, 5), a dilation by a factor of 3 will multiply each coordinate to give ...

  (9, 15)

Then the translation up by 3 will give you the image coordinates ...

  (x, y) ⇒ (x, y+3)

  (9, 15) ⇒ (9, 15 +3) = (9, 18)

The coordinates of R' are (9, 18), matching choice C.

_____

<em>Comment on multiple choice answers</em>

As it often does, here it works to "guess" the answer that has the coordinates that are most-repeated. An x-coordinate of 9 is part of 3 answer choices; a y-coordinate of 18 is the only repeated value in the answer choices. If you were to guess, an appropriate guess would be (9, 18). That happens to be correct in this case.

8 0
3 years ago
Choose the correct choice?!? I think it's A but not sure??
SpyIntel [72]
Your answer is right
3x^2 + 13x + 4
5 0
3 years ago
PLZ HELP SCALE FACTOR TRIANGLE<br><br> A. 10.5 cm<br> B. 31.5 cm<br> C. 63 cm<br> D. 189 cm
Anarel [89]

If two similar triangles have sides in the ratio a : b, then their areas are in the ratio a² : b².

We have the ratio:

54:18=\dfrac{54}{18}=3:1

Area of the smaler triangle = x

Area of the larger triangle = 567 cm²

Therefore we have the equation:

567:x=3^2:1^2\\\\\dfrac{567}{x}=\dfrac{9}{1}\qquad|\text{cross multiply}\\\\9x=567\qquad|\text{divide both sides by 9}\\\\x=63

<h3>Answer: C. 63 cm²</h3>
3 0
3 years ago
66,681 rounded to the nearest ten thousand??
grandymaker [24]

Hey there! I'm happy to help!

This number is sixty six thousand six hundred eighty one. This means that our ten thousandths place is the first 6.

We look to the right place to see if it is 5 or bigger. It is also six.

Therefore we bump the ten thousands place up 1 to 7 and we make everything else 0, giving us 70,000.

Have a wonderful day! :D

7 0
3 years ago
Solve for (x, y) elimination method. show your work <br><br> 2x + y = 5 <br> x - y = 1
mr Goodwill [35]

Answer:

x=2

y=1

(i guess)

hope it helps

3 0
2 years ago
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