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2 years ago

23.49 is 27% of what number?

Mathematics

2 answers:

Digiron [165]2 years ago

5 0

Answer: 100

Step-by-step explanation: 100 divided by 27= 0.27, 23.49x0.27= 6.34.

Daniel [21]2 years ago

5 0

I believe the answer is 100

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Yasmin swims at a constant rate of 2 km/h for 2.5 h. How far does Yasmin swim? 4.5 km 5 km 6 km 6.5 km

Neporo4naja [7]

She swims for 2.5 hours at a rate of 2 km/hr
Multiply 2.5 * 2 = 5 km

3 0

3 years ago

I need help with #6 please.

Juliette [100K]

9514 1404 393

Answer:

6. (A, B, C) ≈ (112.4°, 29.5°, 38.0°)

7. (a, b, C) ≈ (180.5, 238.5, 145°)

Step-by-step explanation:

My "work" is to make use of a triangle solver calculator. The results are attached. Triangle solvers are available for phone or tablet and on web sites. Many graphing calculators have triangle solvers built in.

We suppose you're to make use of the Law of Sines and the Law of Cosines, as applicable.

6. When 3 sides are given, the Law of Cosines can be used to find the angles. For example, angle A can be found from ...

A = arccos((b² +c² -a²)/(2bc))

A = arccos((8² +10² -15²)/(2·8·10)) = arccos(-61/160) = 112.4°

The other angles can be found by permuting the variables appropriately.

B = arccos((225 +100 -64)/(2·15·10) = arccos(261/300) ≈ 29.5°

The third angle can be found as the supplement to the other two.

C = 180° -112.411° -29.541° = 38.048° ≈ 38.0°

The angles (A, B, C) are about (112.4°, 29.5°, 38.0°).

7. When insufficient information is given for the Law of Cosines, the Law of Sines can be useful. It tells us side lengths are proportional to the sine of the opposite angle. With two angles, we can find the third, and with any side length, we can then find the other side lengths.

C = 180° -A -B = 145°

a = c(sin(A)/sin(C)) = 400·sin(15°)/sin(145°) ≈ 180.49

b = c(sin(B)/sin(C)) = 400·sin(20°)/sin(145°) ≈ 238.52

The measures (a, b, C) are about (180.5, 238.5, 145°).

7 0

3 years ago

Need help ASAP

joja [24]

Part (1) : The solution is $729$

Part (2): The solution is $\frac{1}{16 x^{8}}$

Part (3): The solution is $\frac{2 x^{2}}{3 y z^{7}}$

Explanation:

Part (1): The expression is $3^{2} \cdot3^{4}$

Applying the exponent rule, $a^{b} \cdot a^{c}=a^{b+c}$ , we get,

$3^{2} \cdot 3^{4}=3^{2+4}$

Adding the exponent, we get,

$3^{2} \cdot3^{4}=3^6=729$

Thus, the simplified value of the expression is $729$

Part (2): The expression is $\left(2 x^{2}\right)^{-4}$

Applying the exponent rule, $a^{-b}=\frac{1}{a^{b}}$ , we have,

$\left(2 x^{2}\right)^{-4}=\frac{1}{\left(2 x^{2}\right)^{4}}$

Simplifying the expression, we have,

$\frac{1}{2^4x^8}$

Thus, we have,

$\frac{1}{16 x^{8}}$

Thus, the value of the expression is $\frac{1}{16 x^{8}}$

Part (3): The expression is $\frac{2 x^{4} y^{-4} z^{-3}}{3 x^{2} y^{-3} z^{4}}$

Applying the exponent rule, $\frac{x^{a}}{x^{b}}=x^{a-b}$ , we have,

$\frac{2x^{4-2}y^{-4+3}z^{-3-4}}{3}$

Adding the powers, we get,

$\frac{2x^{2}y^{-1}z^{-7}}{3}$

Applying the exponent rule, $a^{-b}=\frac{1}{a^{b}}$ , we have,

$\frac{2 x^{2}}{3 y z^{7}}$

Thus, the value of the expression is $\frac{2 x^{2}}{3 y z^{7}}$

8 0

4 years ago

Calculate the perimeter of a rectangle which is 11 metres long and 4 metres wide

mote1985 [20]

To calculate the perimeter of a rectangle what you would do is add the parallel sides together so 11+11=22 and then 4+4=8 so we would add 22+8=30

So your answer would be 30
(correct me if im wrong)

3 0

4 years ago

I need to simplify this

Korvikt [17]

Hi there!

$3 \sqrt{54} + 2 \sqrt{24} =$
First we split up the square root into two parts.

$3 \times \sqrt{9} \times \sqrt{6} + 2 \times \sqrt{4} \times \sqrt{6} =$
Now we calculate the value of the square roots which have an integer as a solution

$3 \times 3 \times \sqrt{6} + 2 \times 2 \times \sqrt{6} =$
Multiplying the integers gives us our next step.

$9 \sqrt{6} + 4 \sqrt{6} =$
And finally we add up the roots.

$13 \sqrt{6}$

3 0

3 years ago