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nikdorinn [45]
3 years ago
6

in the xy-plane, the line x + y=k, where k is a constant, is tangent to the graph of y=x^2+3x+1. What is the value of k?

Mathematics
1 answer:
Sholpan [36]3 years ago
3 0
When a line and a curve are tangent to each other, they are joined together by 1 point (x,y). So, you equate both equations either in terms of x or y. For this problem, let's equate in terms of y.

y = k - x
y = x² + 3x + 1

k - x = x² + 3x + 1
k = x² + 3x + x + 1
k = x² + 4x + 1

This would be the value of k. Since we are not given the common point, it can only be expressed in terms of x or y.
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Distance between (-6, -2) and (0,-1)
s344n2d4d5 [400]

Hey there! I'm happy to help!

To find the distance between two points, you square the difference of the x-values and square the difference of the y-values, add them, and then you square root it!

First, we'll add our two x-values.

-6-0= -6

We square it, which means to multiply it by itself.

-6(-6)=36        (If you multiply an even number of negative numbers, your answer is positive. Since we have two negative numbers, we get positive 36)

Now, we do the same with the y-values.

-2-(-1)=-1           (two negatives make it a plus, as in minus minus 1 is plus one.)

We square it.

-1(-1)=1              

Now, we add these x and y value differences.

36+1=37

Now, we find the square root using a calculator.

√37≈6.08

Have a wonderful day!

5 0
2 years ago
Clodagh and Eva went school supply shopping together. Clodagh bought 3 packs of pencils and 5 notebooks for a total of $18. Eva
elena55 [62]

Answer:

each notebook costs $2.70

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Step-by-step explanation:

system of equations:

let p = pack of pencils

let n = notebook

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I used the elimination method by multiplying the first equation by 4 and the second equation by -3

4(3p + 5n = 18)  =  12p + 20n = 72

-3(4p + 4n = 16.8)  =  -12p -12n = -50.4

adding the new equations together you get:  8n = 21.6

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solve for 'p':

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2 years ago
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scZoUnD [109]

Answer:

Step-by-step explanation:

20/100 * 5,120 = 1024

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3 years ago
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3 0
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