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3 years ago

What is the equation of a line that is tangent to the circle (x + 1)2 + (y −2)2 = 10 at the point (0, 4)

Mathematics

2 answers:

KengaRu [80]3 years ago

6 0

Answer:

2x+-4y=10

Step-by-step explanation:

Stells [14]3 years ago

6 0

The answer would be 2x+(-4)=10

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Two sets of equatic expressions are shown below in various forms: Line 1: x2 + 3x + 2 (x + 1)(x + 2) (x + 1.5)2 − 0.25 Line 2: x

kherson [118]

Answer: The correct line is

$\textup{Line 1 :}x^2+3x+2=(x+1)(x+2)=(x+1.5)^2-0.25.$

Step-by-step explanation: We are given the following two sets of quadratic expressions in various forms:

$\textup{Line 1: }x^2+3x+2=(x+1)(x+2)=(x+1.5)^2-0.25,\\\\\textup{Line 2 :}x^2+5x+6=(x+2)(x+3)=(x+2.5)^2+6.25.$

We are to select one of the lines from above that represent three equivalent expressions.

We can see that there are three different forms of a quadratic expression in each of the lines:

First one is the simplified form, second is the factorised form and third one is the vertex form.

So, to check which line is correct, we need to calculate the factorised form and the vertex form from the simplified form.

We have

$\textup{Line 1: }\\\\x^2+3x+2\\\\=x^2+2x+x+2\\\\=x(x+2)+1(x+2)\\\\=(x+1)(x+2),$

and

$x^2+3x+2\\\\=x^2+2\times x\times 1.5+(1.5)^2-(1.5)^2+2\\\\=(x+1.5)^2-2.25+2\\\\=(x+1.5)^2-0.25.$

So,

$\textup{Line 1 :}x^2+3x+2=(x+1)(x+2)=(x+1.5)^2-0.25.$

Thus, Line 1 contains three equivalent expressions.

Now,

$\textup{Line 2: }\\\\x^2+5x+6\\\\=x^2+3x+2x+6\\\\=x(x+3)+2(x+3)\\\\=(x+2)(x+3),$

and

$x^2+5x+6\\\\=x^2+2\times x\times 2.5+(2.5)^2-(2.5)^2+6\\\\=(x+2.5)^2-6.25+6\\\\=(x+2.5)^2-0.25\neq (x+2.5)^2+6.25.$

So,

$\textup{Line 2 :}x^2+3x+2=(x+1)(x+2)=(x+1.5)^2+6.25.$

Thus, Line 2 does not contain three equivalent expressions.

Hence, Line 1 is correct.

7 0

3 years ago

The functions and g are defined as follows.

elena-s [515]

Answer:

- 27 and 7

Step-by-step explanation:

To obtain f(- 6) substitute x = - 6 into f(x), that is

f(- 6) = 4(- 6) - 3 = - 24 - 3 = - 27

To obtain g(- 3) substitute x = - 3 into g(x), that is

g(- 3) = - 3(- 3) - 2 = 9 - 2 = 7

6 0

3 years ago

Write this number in standard form 3 thousand 16 ten and 7 ones

Lady_Fox [76]

Its 3,167 hope this helped

5 0

3 years ago

Given the function f(x)=4x^8+7x^7+1x^6+1 What is the value of f(−2)?

qwelly [4]

f(x)=4x^8+7x^7+1x^6+
∴ f(-2)=4(-2)^8+7(-2)^7+1(-2)^6+1
∴ f(-2)=(4x256) + (7x-128) + (1x64) +1
∴ f(-2)=1024 - 896 + 64 +1
∴ f(-2)= 193

7 0

3 years ago

Write the number 0.5 in the form a/b using integers to show that it is a rational number

LekaFEV [45]

$0.5 = \frac{5}{10} = \frac{1}{2}$

5 0

3 years ago

Read 2 more answers