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2 years ago

The equation f(x)=x−5 translated 4 units to the left is g(x)=

Mathematics

1 answer:

elixir [45]2 years ago

3 0

The equation of the function g(x) is g(x) = x - 1

<h3>How to determine the equation of the function g(x)?</h3>

The given parameters are:

f(x) = x - 5

The above function f(x) is translated left by 4 units

So, we have

g(x) = f(x + 4)

This gives

f(x + 4) = x + 4- 5

Evaluate the sum

f(x + 4) = x - 1

So, we have:

g(x) = x - 1

Hence, the equation of the function g(x) is g(x) = x - 1

Read more about function transformation at:

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Factor:

nekit [7.7K]

Answer:

a) $(7\cdot m^{6}+4)\cdot (7\cdot m^{6}-4)$

b) $(7\cdot a\cdot b^{8}+1)\cdot (7\cdot a\cdot b^{8}-1)$

c) $a = 0.7\cdot t^{9}$

d) There are two possible answers only considering real coefficients:

(i) $16\cdot x^{2}-81 = (4\cdot x +9)\cdot (4\cdot x - 9)$

(ii) $14\cdot x^{2}-81 =(\sqrt{14}\cdot x+9)\cdot (\sqrt{14}\cdot x - 9)$

e) $(a^{3}+4)\cdot (a^{3}-4)$

Step-by-step explanation:

Now we proceed to solve each algebraic equation:

a) Factor $49\cdot m^{12}-16$

This binomial is of the form $a^{2}-b^{2} = (a+b)\cdot (a-b)$ . In this case, we can rewrite and factor the equation below:

$49\cdot m ^{12}-16$

$(7\cdot m^{6})^ 2-4^{2}$

$(7\cdot m^{6}+4)\cdot (7\cdot m^{6}-4)$

b) Factor $49\cdot a^{2}\cdot b^{16}-1$

This binomial is of the form $a^{2}-b^{2} = (a+b)\cdot (a-b)$ . In this case, we can rewrite and factor the equation below:

$49\cdot a^{2}\cdot b^{16}-1$

$(7\cdot a\cdot b^{8})^{2}-1^{2}$

$(7\cdot a\cdot b^{8}+1)\cdot (7\cdot a\cdot b^{8}-1)$

c) Nicole is factoring $0.49\cdot t^{18}-25$ by using the rule $a^{2}-b^{2} = (a+b)\cdot (a-b)$ . What will she use for the value of $a$ ?

From this rule we find that $a^{2} = 0.49\cdot t^{18}$ , that is:

$a^{2} = 0.49\cdot t^{18}$

$a^{2} = \frac{49}{100}\cdot t^{18}$

$a = \frac{7}{10}\cdot t^{9}$

$a = 0.7\cdot t^{9}$

d) Which binomial is a difference of squares?

A binomial is a difference of square if and only if $a^{2}-b^{2} = (a+b)\cdot (a-b)$ . There are two possible answers only considering real coefficients:

(i) $16\cdot x^{2}-81 = (4\cdot x +9)\cdot (4\cdot x - 9)$

(ii) $14\cdot x^{2}-81 =(\sqrt{14}\cdot x+9)\cdot (\sqrt{14}\cdot x - 9)$

e) Factor $a^{6}-16$

This binomial is of the form $a^{2}-b^{2} = (a+b)\cdot (a-b)$ . In this case, we can rewrite and factor the equation below:

$a^{6}-16$

$(a^{3})^{2}-4^{2}$

$(a^{3}+4)\cdot (a^{3}-4)$

6 0

2 years ago

10. What is the value of x in the figure at the right? (Examples 3 and 4

Montano1993 [528]

Answer:

x = 37

Step-by-step explanation:

Vertically opposite angles are equal

Therefore, 2x + 6 = 80

Subtract 6 from both sides: 2x = 74

Divide both sides by 2: x = 37

8 0

2 years ago

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Pre algebra problem help solve it<br><br> b( a + b )+ a; use a=9, and b = 4

Tomtit [17]

The answer to the following question is 61

5 0

3 years ago

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The owner of a bookstore ordered 75 copies of a book and paid $1,350. The owner of another bookstore also ordered the same book

kherson [118]

Answer:

$18

Step-by-step explanation:

I did the following expressions:

1,350 / 75 = 18

1,080 / 60 = 18

4 0

2 years ago

Rearrange b + 4 = a to b=

mojhsa [17]

$b+4=a\\
b=a-4$

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2 years ago

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