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3 years ago

Distributive property of 9*45

Mathematics

1 answer:

Mashutka [201]3 years ago

8 0

9*45
= 9(40 + 5)
= 360 + 45
= 405

answer
Distributive property of 9*45 = 9(40 + 5)

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Use a half-angle identity to find the exact value

Tatiana [17]

Given:

$\cos 15^{\circ}$

To find:

The exact value of cos 15°.

Solution:

$$\cos 15^{\circ}=\cos\frac{ 30^{\circ}}{2}$

Using half-angle identity:

$$\cos \left(\frac{x}{2}\right)=\sqrt{\frac{1+\cos (x)}{2}}$

$$\cos \frac{30^{\circ}}{2}=\sqrt{\frac{1+\cos \left(30^{\circ}\right)}{2}}$

Using the trigonometric identity: $\cos \left(30^{\circ}\right)=\frac{\sqrt{3}}{2}$

$$=\sqrt{\frac{1+\frac{\sqrt{3}}{2}}{2}}$

Let us first solve the fraction in the numerator.

$$=\sqrt{\frac{\frac{2+\sqrt{3}}{2}}{2}}$

Using fraction rule: $\frac{\frac{a}{b} }{c}=\frac{a}{b \cdot c}$

$$=\sqrt{\frac {2+\sqrt{3}}{4}}$

Apply radical rule: $\sqrt[n]{\frac{a}{b}}=\frac{\sqrt[n]{a}}{\sqrt[n]{b}}$

$$=\frac{\sqrt{2+\sqrt{3}}}{\sqrt{4}}$

Using $\sqrt{4} =2$ :

$$=\frac{\sqrt{2+\sqrt{3}}}{2}$

$$\cos 15^\circ=\frac{\sqrt{2+\sqrt{3}}}{2}$

5 0

3 years ago

You have 42 oz of egg noodles. You need 5 oz to make one serving of chicken noodle soup. How many servings can you

GenaCL600 [577]

Answer:

8 servings

Step-by-step explanation:

Take the total ounces and divide by the number of ounces per serving

42/5 =8.4

Round down since we don't want to short someone on their soup

4 0

3 years ago

Sean is employed as a truck driver. He drives x hours a week and is paid $21.60 per hour. Also he is paid $250 for food per week

allsm [11]

Answer:

Hours driven= 40 hours

Step-by-step explanation:

Giving the following information:

Variable income= $21.6 per hour

Fixed income= $250

Total income= $1,114

To calculate the number of hours driven, we need to use the following formula:

Total income= fixed income + hourly rate*number of hours

1,114 = 250 + 21.6*x

864 = 21.6x

864 / 21.6 = x

40=x

Hours driven= 40 hours

5 0

3 years ago

Pls help due in 10 minutes!!!

Luden [163]

Answer:

$\sf 500,000,000,000=5 \times 10^{11}$

$\sf 0.00000000005=5 \times 10^{-11}$

Step-by-step explanation:

Scientific notation

$\large\boxed{a \times 10^n}$

where:

$1\leq a < 10$

$n$ is any positive or negative whole number.

To convert a number into scientific notation, move the decimal point to the left or right until there is one digit to the left of the decimal point.

The number of times you have moved the decimal point is $n$ .

If the decimal point has moved to the left, $n$ is positive.
If the decimal point has moved to the right, $n$ is negative.

To convert 500,000,000,000 into scientific notation, move the decimal point 11 places to left, so a = 5. As we have moved the decimal point 11 places to the left, the exponent "n" is 11 and is positive.

$\implies \sf 500,000,000,000=5 \times 10^{11}$

To convert 0.00000000005 into scientific notation, move the decimal point 11 places to the right, so a = 5. As we have moved the decimal point 11 places to the right , the exponent "n" is 11 and is negative.

$\implies \sf 0.00000000005=5 \times 10^{-11}$