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3 years ago

9

How do you write 1.8 × 10^1 in standard form?

1 answer:

gayaneshka [121]3 years ago

7 0

Answer:that would be 18

Step-by-step explanation:

You might be interested in

Find the set of values of k for which the line y=kx-4 intersects the curve y=x²-2x at 2 distinct points?

Sonbull [250]

Answer:

$-6 < k < 2$

Step-by-step explanation:

Given

$y = x^2 - 2x$

$y =kx -4$

Required

Possible values of k

The general quadratic equation is:

$ax^2 + bx + c = 0$

Subtract $y = x^2 - 2x$ and $y =kx -4$

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

$0 = x^2 - 2x - kx +4$

Factorize:

$0 = x^2 +x(-2 - k) +4$

Rewrite as:

$x^2 +x(-2 - k) +4=0$

Compare the above equation to: $ax^2 + bx + c = 0$

$a = 1$

$b= -2-k$

$c =4$

For the equation to have two distinct solution, the following must be true:

$b^2 - 4ac > 0$

So, we have:

$(-2-k)^2 -4*1*4>0$

$(-2-k)^2 -16>0$

Expand

$4 +4k+k^2-16>0$

Rewrite as:

$k^2 + 4k - 16 + 4 >0$

$k^2 + 4k - 12 >0$

Expand

$k^2 + 6k-2k - 12 >0$

Factorize

$k(k + 6)-2(k + 6) >0$

Factor out k + 6

$(k -2)(k + 6) >0$

Split:

$k -2 > 0$ or $k + 6> 0$

So:

$k > 2$ or k $> -6$

To make the above inequality true, we set:

$k < 2$ or $k >-6$

So, the set of values of k is:

$-6 < k < 2$

3 0

3 years ago

Albie's total income is $695.25 in a week

ikadub [295]

Answer:

Step-by-step explanation:

7.5/100= .075

$580000 x .075 = $43,500 commission

5 0

3 years ago

A freshly inoculated bacterial culture of Streptococcus contains 100 cells. When the culture is checked 60 minutes later, it is

Luba_88 [7]

Answer:

$P(t) = 100e^{0.0251t}$

The doubling time is of 27.65 minutes.

Step-by-step explanation:

Exponential equation of growth:

The exponential equation for population growth is given by:

$P(t) = P(0)e^{kt}$

In which P(0) is the initial value and k is the growth rate.

A freshly inoculated bacterial culture of Streptococcus contains 100 cells.

This means that $P(0) = 100$ . So

$P(t) = 100e^{kt}$

When the culture is checked 60 minutes later, it is determined that there are 450 cells present.

This means that $P(60) = 450$ , and we use this to find k. So

$450 = 100e^{60k}$

$e^{60k} = 4.5$

$\ln{e^{60k}} = \ln{4.5}$

$60k = \ln{4.5}$

$k = \frac{\ln{4.5}}{60}$

$k = 0.0251$

So

$P(t) = 100e^{0.0251t}$

Doubling time:

This is t for which P(t) = 2P(0) = 200. So

$200 = 100e^{0.0251t}$

$e^{0.0251t} = 2$

$\ln{e^{0.0251t}} = \ln{2}$

$0.0251t = \ln{2}$

$t = \frac{\ln{2}}{0.0251}$

$t = 27.65$

The doubling time is of 27.65 minutes.

7 0

3 years ago

This is the graph of f(x). What is the value of f(3)?

Paul [167]

Answer:

The value of f(3) is 8 ⇒ D

Step-by-step explanation:

In the function f(x) = y, y is the corresponding value of x

Ex: If f(a) = b, then the value of y = b at x = a

Let us solve the question

∵ The given figure represents the function f(x)

→ That means every point on the graph represents f(x) = y

∴ f(x) = y

∵ We need to find f(3)

→ That means we need the value of y at x = 3

∴ x = 3

Look at the graph and find the y-coordinate of the point that lies on the curve and has x-coordinate = 3

→ Each small square on the x-axis represents 1 unit, and on the y-axis

represents 2 units

∵ There is a point on the graph that has x-coordinate = 3

∵ The y-coordinate of this point is 8

∴ The point (3, 8) lies on the graph of f(x)

∴ x = 3 and y = 8

∴ f(3) = 8

∴ The value of f(3) is 8

7 0

3 years ago

Determine whether each pair of segments is congruent

Dafna1 [17]

They are both labeled as 3 feet, so both must be equal, unless you doubt the labeling. Unless that is so, then both segments are equal.

6 0

4 years ago