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2 years ago

What is the equation of g(x)?

Mathematics

1 answer:

Ksenya-84 [330]2 years ago

4 0

Answer:

$g(x)=10^{x-3}$

Step-by-step explanation:

Notice that function $g(x)$ has the exat shape of function $f(x)$ , and it has just be translated to the right by 3 whole units.

Recall that horizontal translations to the right involve subtracting the number of units moved in the translation from the variable "x". therefore, in our case this means:

$f(x)=10^x\\g(x)=10^{x-3}$

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A sample of radium has a weight of 1.5 mg and a half-life of approximately 6 years.

pogonyaev

Answer:

0.75 mg

Step-by-step explanation:

From the question given above the following data were obtained:

Original amount (N₀) = 1.5 mg

Half-life (t₁/₂) = 6 years

Time (t) = 6 years

Amount remaining (N) =.?

Next, we shall determine the number of half-lives that has elapse. This can be obtained as follow:

Half-life (t₁/₂) = 6 years

Time (t) = 6 years

Number of half-lives (n) =?

n = t / t₁/₂

n = 6/6

n = 1

Finally, we shall determine the amount of the sample remaining after 6 years (i.e 1 half-life) as follow:

Original amount (N₀) = 1.5 mg

Half-life (t₁/₂) = 6 years

Number of half-lives (n) = 1

Amount remaining (N) =.?

N = 1/2ⁿ × N₀

N = 1/2¹ × 1.5

N = 1/2 × 1.5

N = 0.5 × 1.5

N = 0.75 mg

Thus, 0.75 mg of the sample is remaining.

5 0

2 years ago

Which of the following is a proportion?

poizon [28]

Answer:

Option C, 14/21=9/21 is the proportion.

Step-by-step explanation:

Given:

a.5/7 = 10/12

b.9/15 = 12/18

c.4/6 = 8/12

d.14/21 = 9/12

We have to find the proportions.

In proportion two ratios are equal, as it has an equality sign in between so both side must be of same ratio in its simplest form.

Let's work with option C

⇒ $\frac{4}{6}=\frac{8}{12}$

To find the simplest form we have to divide the numerator and denominator with same digit (or its factor).

Simplest form of $\frac{8/2}{12/2}$ = $\frac{4}{6}$ , $\frac{4/2}{6/2}$ = $\frac{2}{3}$

Simplest form of $\frac{4}{6}$ = $\frac{2}{3}$

Both sides in option C have equal ratios of 2/3.

So 4/6=8/12 is in proportion.

6 0

2 years ago

Find the selling price of a $7.50 agenda book with a 15% discount.

tatuchka [14]

The answer is $6.38 hope this helps

7 0

2 years ago

Read 2 more answers

What is the vertex form of y=-2x2+4x + 3?

sukhopar [10]

Answer:

$y=-2(x-1)^2+5$

Step-by-step explanation:

we have

$y=-2x^2+4x+3$

This is the equation of a vertical parabola open downward

The vertex represent a maximum

Convert the quadratic equation into vertex form

step 1

Factor -2

$y=-2(x^2-2x)+3$

step 2

Complete the square

$y=-2(x^2-2x+1)+3+2$

$y=-2(x^2-2x+1)+5$

step 3

Rewrite as perfect squares

$y=-2(x-1)^2+5$ ----> equation in vertex form

The vertex is the point (1,5)

3 0

2 years ago

Calculate the sales tax:<br> 10% of 25.75

ivanzaharov [21]

Answer: 103/40, or 2 23/40 or, 2.575

Step-by-step explanation:

5 0

2 years ago