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3 years ago

Factor this expression: 2x + 12 PLEASE EXPLAIN

Mathematics

2 answers:

Fudgin [204]3 years ago

5 0

Well you would 12 12 because you double the number twice ad you would do 12 in 12 and you get 24

Elenna [48]3 years ago

5 0

2(x+6)

What you do is find the greatest common factor between the two terms.
Then you put that number outside the parenthesis and divide the terms inside by that number.
Here's my work:
2x+12
2x/2=x
12/2=6
2(x+6)

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Anybody know how to do this ?

Morgarella [4.7K]

Answer: Part a: x=sqrt(104) in; Part b: x=sqrt(5) in

Step-by-step explanation:

Part a:

Because the figure has a right angle (signified by the square), it is a right triangle. Therefore, the Pythagorean Theorem, a²+b²=c² where c is the hypotenuse (longest side) and a and b are the legs (shorter sides), applies. Thus:

a²+b²=c²

The 15 in side is opposite the right angle, so it is the hypotenuse.

The 11 in side and x in side are not opposite the right angle, so they are legs.

11²+x²=15²

121+x²=225

(121+x²)-121=225-121

x²=104

sqrt(x²)=sqrt(104)

x=±sqrt(104)

Reject x=-sqrt(104) because a negative side length in a triangle is impossible. Therefore,

x=sqrt(104) in

Part b:

The figure is a right triangle. Therefore, the Pythagorean Theorem (a²+b²=c²) applies. Hence,

5²+(2x)²=(3x)²

25+4x²=9x²

(25+4x²)-4x²=9x²-4x²

25=5x²

5=x²

sqrt(5)=sqrt(x²)

x=±sqrt(5)

Reject x=-sqrt(5) because a negative side length is impossible.

The answer must be x=sqrt(5) in.

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3 years ago

Convert 3(3.14)/8 radians to degrees

wolverine [178]

67.5 degrees

3pi/8 * 180/pi = 67.5

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4 years ago

You buy $2.75$ pounds of pistachios and $2$ pounds of cashews. Do you pay more for the pistachios or for the cashews?

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Answer:

what's the rate? ........

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3 years ago

Find the area! NEED HELP ASAP!!!!!!!!

allochka39001 [22]

seperate it into a square and right triangle

area of square: 2*2=4m^2

area of traignle: (1*2)/2= 1m^2

add them

5m^2

5 0

4 years ago

Read 2 more answers

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 $\sin 30^{\circ}=\frac{1}{2}$ ).

Therefore, AB must be exactly half of AD:

$AB=\frac{1}{2}AD,\\AB=\frac{1}{2}\cdot 50\sqrt{6},\\AB=\frac{50\sqrt{6}}{2}=\boxed{25\sqrt{6}}\approx 61.24$

3 0

3 years ago

Read 2 more answers