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2 years ago

Condense log 2 4 + log 2 5

Mathematics

2 answers:

choli [55]2 years ago

7 0

Log 2 4 + log 2 5= log 2 4x5= log 2 20
This exercises the log rule log a + log b= log ab

dimulka [17.4K]2 years ago

3 0

Answer:

$log_{2}$ 20

Step-by-step explanation:

using the rule of logarithms

loga + logb = logab

then

$log_{2}$ 4 + $log_{2}$ 5

= $log_{2}$ (4 × 5)

= $log_{2}$ 20

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A bean plant grows at a constant rate for a month. After 10 days, the plant is 25 centimeters tall. After 20 days, the plant is

wariber [46]

Y = 2x + 5

If you take the height at 10 days, 25 centimeters, after 10 more days the height is 45 centimeters, meaning for those 10 extra days the been plant grown 20 centimeters. Since we're told the plant is growing at a constant rate, this shows the bean plant is growing 2 centimeters per day. We can represent this with y = 2x. (After 10 days, the bean plant will be 20 centimeters, after 20 days, the bean plant will be 40 centimeters, etc.)

However, this is not completely true yet. As you can see, after the first 10 days the plant is not 20 centimeter, it's 25 centimeters. We already know the rate in which the plant is changing, but now we need to find the height that the plant was originally, before it started growing.

After the first 10 days, the plant is 25 centimeters tall. Since we know that the plant is growing 2 centimeters per day, we can subtract 20 from 25 to find the original height of the bean plant.

25 - 20 = 5
The bean plant was originally 5 centimeters.

This makes our final equation y = 2x + 5.
2x is the slope, and 5 is the y intercept.

Hope this helps1!

5 0

3 years ago

Five times the sum of a number and 3 is 15

lara [203]

Answer:

the answer is 30 ok my friend your welcome

Step-by-step explanation:

3 0

3 years ago

Answer the question in the picture

nekit [7.7K]

Recall the angle sum identities:

$\sin(x+y)=\sin x\cos y+\cos x\sin y$

$\cos(x+y)=\cos x\cos y-\sin x\sin y$

Now,

$\tan(x+y)=\dfrac{\sin(x+y)}{\cos(x+y)}=\dfrac{\sin x\cos y+\cos x\sin y}{\cos x\cos y-\sin x\sin y}$

Divide through numerator and denominator by $\cos x\cos y$ to get

$\tan(x+y)=\dfrac{\tan x+\tan y}{1-\tan x\tan y}$

Next, we use the fact that $x,y$ lie in the first quadrant to determine that

$\sin x=\dfrac12\implies\cos x=\sqrt{1-\sin^2x}=\dfrac{\sqrt3}2$

$\cos y=\dfrac{\sqrt2}2\implies\sin x=\sqrt{1-\cos^2x}=\dfrac1{\sqrt2}$

So we then have

$\tan x=\dfrac{\sin x}{\cos x}=\dfrac{\frac12}{\frac{\sqrt3}2}=\dfrac1{\sqrt3}$

$\tan y=\dfrac{\sin y}{\cos y}=\dfrac{\frac1{\sqrt2}}{\frac{\sqrt2}2}=1$

Finally,

$\tan(x+y)=\dfrac{\frac1{\sqrt3}+1}{1-\frac1{\sqrt3}}=\dfrac{1+\sqrt3}{\sqrt3-1}=2+\sqrt3\approx3.73$

4 0

3 years ago

A total of 722 tickets were sold for the school play. they were either adult tickets or student tickets. there were 72 more stud

ololo11 [35]

S + a = 722
s = 72 + a

(72 + a) + a = 722
2a + 72 = 722
2a = 722 - 72
2a = 650
a = 650/2
a = 325 <== adults

s = 72 + a
s = 72 + 325
s = 397 <== students

5 0

4 years ago

Please answer this in two minutes

alisha [4.7K]

Answer:

WX = 7.9

Step-by-step explanation:

By applying tangent rule (law of tan) in the given right triangle WXY.

tan(W) = $\frac{\text{Opposite side}}{\text{Adjacent side}}$