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Step2247 [10]
3 years ago
11

Christopher is analyzing a circle, y^2 + x^2 = 121, and a linear function g(x). Will they intersect?

Mathematics
1 answer:
Sav [38]3 years ago
7 0
Circle: x^2+y^2=121=11^2 => circle with radius 11 and centred on origin.
g(x)=-2x+12   (from given table, find slope and y-intercept)
We can see from the graphics that g(x) will be almost tangent to the circle at (0,11), and that both intersection points will be at x>=11.
To show that this is the case, 
substitute g(x) into the circle
x^2+(-2x+12)^2=121
x^2+4x^2-2*2*12x+144-121=0
5x^2-48x+23=0
Solve using the quadratic formula,
x=(48 ± √ (48^2-4*5*23) )/10
=0.5058 or 9.0942
So both solutions are real and both have positive x-values.

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4 - 5/2 * (1/10x) = 1 what is the value of x
Inga [223]

4 - 5 / 2 * (1/10x) = 1\\

The first step is to identify the order in which the equation must be solved, by following PEMDAS (you might know it as BEDMAS):

Parenthesis (or Brackets)

Exponents

Multiplication and Division

Addition and Subtraction

My advice would be to add parenthesis, following these rules, if you are not very good at finding them immediately by sight.

So:

4 - 5 / 2 * (\frac{1}{10x})  = 1\\\\4 - [(5/2)*(\frac{1}{10x})]=1\\\\4-(2.5*\frac{1}{10x})=1\\\\4-\frac{2.5}{10x}-1=0\\3-\frac{x}{4}=0\\\frac{x}{4}=3\\x=3*4\\x=12

We check our answer:

x=12\\4 - [(5 / 2) * (1/10)*(x)] = 1\\4 - [(5 / 2) * (\frac{1}{10}) * (12))] = 1\\4 - [2.5 * (\frac{1}{10})*12] = 1\\4 - [(\frac{2.5}{10})*12] = 1\\4 - [(\frac{1}{4})*12] = 1\\4 - 3 = 1\\1=1

We are right!

So, x=12.

6 0
3 years ago
SOMEONE PLEASEEEEE HELP .... GIVING BRAINILEST!!!
Vanyuwa [196]

Answer: Value of M: -49

Value of N: 24

Step-by-step explanation:

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3 0
2 years ago
Read 2 more answers
5. Mrs.Weed's puppy weighed o.236 kg when it was born. At the next check-up it weighed 0.37 kg. How much weight had it gained?
musickatia [10]

Answer:

5.) 0.134 kg.

6.) 6.15 km.

7.) 5.9 kg.

Step-by-step explanation:

5.) 0.37 - 0.236 = 0.134

6.) 9.71 - 3.56 = 6.15

7.) 1.7 + 4.2 = 5.9

5 0
3 years ago
Two architects bid for a small government project, both
blondinia [14]

Answer:

10 hours

Step-by-step explanation:

let x be the total number of hours

Amazing design total charge = 45x+250

super structures total charge = 60x+100

both companies charge the same amount when both equation equals

45x+250=60x+100

60x-45x=250-100

15x=150

x=10

therefore at 10 hours both companies will charge the same amount

4 0
2 years ago
Given that f(x) = 5x − 10 and g(x) = x + 3, solve for f(g(x)) when x = −1. (1 point)?
Viefleur [7K]
F(g(x)) means u solve g(x) first then you plug that value into f(x)
x = -1
g(-1) = -1 + 3 = 2
plug 2 into f(x)
f(2) = 5(2) - 10 = 0
4 0
2 years ago
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