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Sergeu [11.5K]
3 years ago
13

Find all values of k so that the following system has no solutions x²+(y-k)²=36 ; y=5x+k.Illustrate with a graph.

Mathematics
1 answer:
musickatia [10]3 years ago
5 0

Step-by-step explanation:

x^2+(y-k)^2=36

y=5x+k

Substituting y in the first equation

x^2+(5x+k-k)^2=36\\\Rightarrow x^2+25x^2=36\\\Rightarrow 26x^2=36\\\Rightarrow x^2=\frac{36}{26}\\\Rightarrow x=\sqrt{\frac{36}{26}}\\\Rightarrow x=\pm 1.17

At x = 1.17

y=5\times 1.17+k\\\Rightarrow y=5.85+k

At x = -1.17

y=5\times -1.17+k\\\Rightarrow y=-5.85+k

The intersection points are (1.17, 5.85k) and (-1.17, -5.85k)

The graph would intersect regardless of what value k is.

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Ibuki factored 12x^7as (4x^3)(3x^4)
Marina86 [1]

Answer:

Both are correct.

Step-by-step explanation:

The key understanding here is that you can factor a monomial in many different ways!

To check if any of the factorizations is correct, we can multiply the factors and see if their product is really 12x^712x

7

12, x, start superscript, 7, end superscript.

Hint #22 / 4

\begin{aligned} (\blueD{4}\maroonD{x^3})(\blueD{3}\maroonD{x^4})&=(\blueD{4})(\blueD{3})(\maroonD{x^3})(\maroonD{x^4}) \\\\ &=\blueD{12}\maroonD{x^7} \end{aligned}

(4x

3

)(3x

4

)

​

 

=(4)(3)(x

3

)(x

4

)

=12x

7

​

So Ibuki is correct!

Hint #33 / 4

\begin{aligned} (\blueD{2}\maroonD{x^6})(\blueD{6}\maroonD{x})&=(\blueD{2})(\blueD{6})(\maroonD{x^6})(\maroonD{x}) \\\\ &=\blueD{12}\maroonD{x^7} \end{aligned}

(2x

6

)(6x)

​

 

=(2)(6)(x

6

)(x)

=12x

7

​

So Melodie is also correct!

Both Ibuki and Melodie are correct.

8 0
3 years ago
BRAINLIEST FOR THE FIGHT ANSWER!!!
Gemiola [76]
= .91(.85)(.82) = .63427 
<span>or 63.427% of the original price 

so your answer is B</span>
3 0
3 years ago
Will give brainliest!!!!<br>Explain how solving -7y &gt; 161 is different from solving 7y &gt; -161.
Jlenok [28]

To solve -7y > 161, we divide both sides by -7 and we get y < -23. The inequality sign flipped because we divided both sides by a negative number.

To solve 7y > -161, we divide both sides by 7 and it leads to y > -23. The inequality sign does not flip in this case, because we are not dividing both sides by a negative number.

The similarities is that we end up with -23 on the right side, but the inequality signs are different.

5 0
2 years ago
Miah has a fish tank were she keeps her fish! Find the volume of the fish tank
Luden [163]
To do this, you’ll have to utilize the formula for volume.

Volume = length•width•height
V = 12•6•4
V = 12•24
V = 288 cm^3

** Remember that volume is always cubed.
8 0
3 years ago
. He rowed 3 1/2 miles in 1/2 hour.What is the average speed in miles per hour.
Rudiy27

Answer:

7 miles per hour

Step-by-step explanation:

3 1/2 miles = 7/2 miles

1/2 hours= 30 minutes

So,

In 30 mins, travelled 7/2 miles

In 1 min, travelled 7/2 ÷ 30= 7/2× 1/30 = (7×1)/(2×30) = 7/60 miles

In 60 mins, travelled (7×60)/60 miles = 420/60 miles = 7 miles.

Hence, the speed is 7 miles per hour.

Hope this helps :)

7 0
2 years ago
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