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3 years ago

Which number has factors besides 1 and itself? A) 31 B) 33 C) 37 D) 41

Mathematics

2 answers:

ivann1987 [24]3 years ago

6 0

Answer:

B) 33

Step-by-step explanation:

A) 31 only has factors 1 and 31

B) 33 has factors 1, 3, 11, and 33

C) 37 only has factors 1 and 37

D) 41 only has factors 1 and 41

KiRa [710]3 years ago

5 0

Answer:

B. 33

Step-by-step explanation:

The number 33 can be factored by the number 11

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If a number is added yo the numerator of 12/43 and twice the number is added to the denominator of 12/43 the resuliting fraction

DaniilM [7]

Answer:

The number is 7.

Step-by-step explanation:

In this case we have an unkown variable that is a number. We will call this number by "x", this is what we want to calculate. In the first part it is said that the number or x is added to the numerator and in the second part it is said that twice the number is added to the denominator, and that this fraction is equal to 1/3. So we have:

1/3 = (12 + x)/(43 + 2*x)

43 + 2*x = 3*(12 + x)

43 + 2*x = 36 + 3*x

43 - 36 = 3*x - 2*x

x = 7

The number is 7.

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3 years ago

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Jack and Harry are waiters in a restaurant. They are both paid the same amount of money for each hour that they work. Jack worke

Alex787 [66]

Answer:

£48 because if they are paid the same amount, it will stay the same as jack's paycheck

Step-by-step explanation:

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2 years ago

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Looking at the top of tower A and base of tower B from points C and D, we find that ∠ACD = 60°, ∠ADC = 75° and ∠ADB = 30°. Let t

katrin2010 [14]

Answer:

$\text{Exact: }AB=25\sqrt{6},\\\text{Rounded: }AB\approx 61.24$

Step-by-step explanation:

We can use the Law of Sines to find segment AD, which happens to be a leg of $\triangle ACD$ and the hypotenuse of $\triangle ADB$ .

The Law of Sines states that the ratio of any angle of a triangle and its opposite side is maintained through the triangle:

$\frac{a}{\sin \alpha}=\frac{b}{\sin \beta}=\frac{c}{\sin \gamma}$

Since we're given the length of CD, we want to find the measure of the angle opposite to CD, which is $\angle CAD$ . The sum of the interior angles in a triangle is equal to 180 degrees. Thus, we have:

$\angle CAD+\angle ACD+\angle CDA=180^{\circ},\\\angle CAD+60^{\circ}+75^{\circ}=180^{\circ},\\\angle CAD=180^{\circ}-75^{\circ}-60^{\circ},\\\angle CAD=45^{\circ}$

Now use this value in the Law of Sines to find AD:

$\frac{AD}{\sin 60^{\circ}}=\frac{100}{\sin 45^{\circ}},\\\\AD=\sin 60^{\circ}\cdot \frac{100}{\sin 45^{\circ}}$

Recall that $\sin 45^{\circ}=\frac{\sqrt{2}}{2}$ and $\sin 60^{\circ}=\frac{\sqrt{3}}{2}$ :

$AD=\frac{\frac{\sqrt{3}}{2}\cdot 100}{\frac{\sqrt{2}}{2}},\\\\AD=\frac{50\sqrt{3}}{\frac{\sqrt{2}}{2}},\\\\AD=50\sqrt{3}\cdot \frac{2}{\sqrt{2}},\\\\AD=\frac{100\sqrt{3}}{\sqrt{2}}\cdot\frac{ \sqrt{2}}{\sqrt{2}}=\frac{100\sqrt{6}}{2}={50\sqrt{6}}$

Now that we have the length of AD, we can find the length of AB. The right triangle $\triangle ADB$ is a 30-60-90 triangle. In all 30-60-90 triangles, the side lengths are in the ratio $x:x\sqrt{3}:2x$ , where $x$ is the side opposite to the 30 degree angle and $2x$ is the length of the hypotenuse.

Since AD is the hypotenuse, it must represent $2x$ in this ratio and since AB is the side opposite to the 30 degree angle, it must represent $x$ in this ratio (Derive from basic trig for a right triangle and $\sin 30^{\circ}=\frac{1}{2}$ ).