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3 years ago

The sum of two numbers is 30. one number is 12 more than the second number. what are the two numbers

Mathematics

2 answers:

masha68 [24]3 years ago

8 0

The 2 numbers are 9 and 21 I think

astraxan [27]3 years ago

4 0

Answer:

18 and 12

Step-by-step explanation:

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You had a collection of insects what ways might you classify them

Wittaler [7]

By the size , color, or if they have wings or no wings, etc. just think of what might be different on each one or group.

6 0

3 years ago

Can someone please help me

Shkiper50 [21]

Answer: B. 41 3/5 ounces of icing per cake

Step-by-step explanation:

52/5 divided by 1/4. Keep 52/5, change the division sign into a multiplication sign, and flip 1/4 to 4.
The new equation should be 52/5 * 4. The answer to this is 208/5, which simplified is 41 3/5.

5 0

3 years ago

Which of the following could be the ratio of the length of the longer leg of a 30-60-90 to the length of its hypotenuse? CHECK A

8_murik_8 [283]

Answer:

A. √3 : 2

D. 3√3 : 6

Step-by-step explanation:

In a triangle described as 30°-60°-90° triangle, the base angles are 90° and 60°

The side with angles 90° and 60° is the shortest leg and can be represented by 1 unit

The hypotenuse side is assigned a value twice the shorter leg value, which is 2 units

From Pythagorean relationship; the square of the hypotenuse side subtract the square of the shorter leg gives the square of the longer side

This is to say if;

The given the shorter leg = 1 unit

The hypotenuse is twice the shorter leg= 2 units

The longer leg is square-root of the difference between the square of the hypotenuse and that of the shorter leg

$=2^2-1^2\\\\=4-1=3\\\\\\b^2=3\\\\\\b=\sqrt{3}$

where the longer leg is represented by side b in the Pythagorean theorem, the hypotenuse by c and the shorter leg by a to make;

$a^2+b^2=c^2$

<u>Hence the summary is</u>

a=shorter leg= 1 unit

b=longer leg = √3 units

c=hypotenuse=2 units

The ratio of longer leg to its hypotenuse is

=√3:2⇒ answer option A

This is the same as 3√3:6 ⇒answer option D because you can divide both sides of the ratio expression by 3 and get option A

$=3\sqrt{3} :6\\\\\\\frac{3\sqrt{3} }{3} :\frac{6}{3} \\\\\\=\sqrt{3} :2$

Answers are :option A and D

4 0

3 years ago

Convert,the complex number into polar form: 4+4i

kow [346]

Z = a + bi
z = 4 + 4i

r² = a² + b²
r² = (4)² + (4)²
r² = 16 + 16
r² = 32
r = 4√(2)
r = 4(1.414)
r = 5.656

$cos\theta = \frac{a}{r}$
$cos\theta = \frac{4}{4\sqrt{2}}$
$cos\theta = \frac{4}{4\sqrt{2}} * \frac{\sqrt{2}}{\sqrt{2}}$
$cos\theta = \frac{4\sqrt{2}}{4\sqrt{4}}$
$cos\theta = \frac{4\sqrt{2}}{4(2)}$
$cos\theta = \frac{4\sqrt{2}}{8}$
$cos\theta = \frac{\sqrt{2}}{2}$
$2(cos\theta) = 2(\frac{\sqrt{2}}{2})$
$2cos\theta = \sqrt{2}$
$2cos\theta = 1.414$

$sin\theta = \frac{b}{r}$
$sin\theta = \frac{4}{4\sqrt{2}}$
$sin\theta = \frac{4}{4\sqrt{2}} * \frac{\sqrt{2}}{\sqrt{2}}$
$sin\theta = \frac{4\sqrt{2}}{4\sqrt{4}}$
$sin\theta = \frac{4\sqrt{2}}{4(2)}$
$sin\theta = \frac{4\sqrt{2}}{8}$
$sin\theta = \frac{\sqrt{2}}{2}$
$2(sin\theta) = 2(\frac{\sqrt{2}}{2})$
$2sin\theta = \sqrt{2}$
$2sin\theta = 1.414$

z = a + bi
z = rcosθ + (rsinθ)i
z = r(cosθ + i sinθ)

z = 4 + 4i
z = 5.656cosθ + (5.656sinθ)i
z = 5.656(cosθ + i sinθ)
z = 5.656(cos45 + i sin45)

$\theta = tan^{-1}\frac{b}{a}$
$\theta = tan^{-1}\frac{4}{4}$
$\theta = tan^{-1}(1)$
$\theta = 45$

The polar form of 4 + 4i is approximately equal to 5.656(cos45 + i sin45).

5 0

3 years ago

There is a photo attached

natulia [17]

You can use the sum of angles identities, then rearrange to put the result in the form of tangents.

$\displaystyle\frac{\sin{(x+y)}}{\sin{(x-y)}}=\frac{\sin{(x)}\cos{(y)}+\cos{(x)}\sin{(y)}}{\sin{(x)}\cos{(y)}-\cos{(x)}\sin{(y)}}\\\\=\frac{\left(\frac{\sin{(x)}\cos{(y)}+\cos{(x)}\sin{(y)}}{\cos{(x)}\cos{(y)}}\right)}{\left(\frac{\sin{(x)}\cos{(y)}-\cos{(x)}\sin{(y)}}{\cos{(x)}\cos{(y)}}\right)}\\\\=\frac{\tan{(x)}+\tan{(y)}}{\tan{(x)}-\tan{(y)}}$

6 0

3 years ago