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2 years ago

Round 40.2 to the next number

Mathematics

1 answer:

Aleksandr-060686 [28]2 years ago

4 0

Answer:

Step-by-step explanation:

2 is less than 5 round down

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Question 4 (1 point)

mrs_skeptik [129]

Answer:

(C)y=0

Step-by-step explanation:

An exponential function of the form $f(x) = a (b^x) + c$ always has a horizontal asymptote at y = c.

Given our function $y=4^x$

Comparing with the form, $f(x) = a (b^x) + c$ , we observe that c=0.

Therefore, the exponential function has an <u>asymptote at y=0.</u>

The correct option is C.

7 0

3 years ago

Element X decays radioactively with a half-life of eight minutes. If there are 800 g of element X, how long, to the nearest 10th

Harman [31]

Answer: 41.5 min

Step-by-step explanation:

This problem can be solved with the Radioactive Half Life Formula:

$A=A_{o}.2^{\frac{-t}{h}}$ (1)

Where:

$A=22 g$ is the final amount of the radioactive element

$A_{o}=800 g$ is the initial amount of the radioactive element

$t$ is the time elapsed

$h=8 min$ is the half life of the radioactive element

So, we need to substitute the given values and find $t$ from (1):

$22 g=(800 g) 2^{\frac{-t}{8 min}}$ (2)

$\frac{22 g}{800 g}=2^{\frac{-t}{8 min}}$ (3)

$\frac{11}{400}=2^{\frac{-t}{8 min}}$ (4)

Applying natural logarithm in both sides:

$ln(\frac{11}{400})=ln(2^{\frac{-t}{8 min}})$ (5)

$-3.593=-\frac{t}{8 min}ln(2)$ (6)

Clearing $t$ :

$t=41.46 min \approx 41.5 min$ This is the time elapsed

7 0

2 years ago

Use lengths |OQ| = 9.4 units and |OQ’| = 17.1 units to determine the scale factor r of dilation D (round to the nearest hundredt

NNADVOKAT [17]

Answer:

Scale factor = 1.82 units.

Step-by-step explanation:

We have been given that side length OQ of our prei-mage is 9.4 units and side length OQ' after dilation is 17.1 units. Since our pre-image (original image) is smaller than our new image, so our scale factor (r) will be greater than 1.

Since we know that in a dilation, the sides of the pre-image and the corresponding sides of the image are proportional, so we will use proportion to find a scale factor our given side lengths as:

$\frac{OQ'}{OQ}=\frac{17.1}{9.4}$