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3 years ago

Find the value of the variable(s). If your answer is not an integer, leave it in simplest radical form.

Mathematics

1 answer:

Georgia [21]3 years ago

6 0

Answer:

Step-by-step explanation:

First, let's find x.

We know that one of the angles is 30. The side opposite to than angle is 11, and x is the adjacent side to it. Therefore, we can use the trig function tangent.

Recall that:

$\tan(x)=opp/adj\\$

Plug in 30 for the angle, 11 for the opposite, and x for the adjacent. Solve for x by cross-multiplying:

$\tan(30)=11/x\\x\tan(30)=11\\x=11/\tan(30)$

From the unit circle, recall that tan(30) is equal to one over the square root of 3. Thus:

$x=11/(1/\sqrt3)\\x=11\cdot\sqrt3\\x=11\sqrt3$

Now, we can use the Pythagorean Theorem to find y. y is the hypotenuse. Thus:

$c^2=a^2+b^2\\c^2=(11\sqrt3)^2+11^2\\c^2=121(3)+121\\c^2=4(121)\\c^2\sqrt{4(121}=2(11)=22$

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PLEASE HELP Show all Your work 25 points will give brainly

julsineya [31]

Answer:

x=9

Step-by-step explanation:

√117²=x²+6²

117=x²+36

x²=117-36

x²=81

x=9

6 0

4 years ago

Volume of prisms just 3 problems

Vladimir79 [104]

Answer:

2. 18 cubic cm.

3. 27 cubic cm

5. 90 cubic m

Step-by-step explanation:

2. Triangular prism

So, we have a triangular prism with a width of 3 cm, a height of 1.5 cm and a length of 4. We'll take the triangle shape as the base.

Like for any prism, the volume is the base multiplied by the height.

So, the area of the base is found with the regular formula: base x height:

so, 3 x 1.5 = 4.5 sq cm for the base.

Then we multiply the base by the length to get the volume: 4.5 x 4 = 18 cubic cm.

3. Trapezoidal prism

Again, first step is to calculate the area of the trapezoid shape, then multiply by its depth.

The area of a trapezoid is calculated with the formula:

A = h/2 * (a + b) where a and b represent the short and long sides respectively.

So, for our given trapezoid:

A = 1.5/2 * (2+4) = 0.75 * 6 = 4.5 sq cm.

Then we multiply the base area by the height to get the volume:

V = 4.5 * 6 = 27 cubic cm

5. Triangular prism 2

The best way to approach this one is to consider it's a triangle prism with a height of 3 cm, and use the triangle shape (with sides of 13 and 5) as the base.

But to calculate the area of that triangle we need to find out the missing length. Using Pythagore's theorem, we can easily find the length of the other side with the hypotenuse formula:

hypotenuse² = sideA² + sideB²

In our case, we have:

13² = x² + 5²

169 = x² + 25

x² = 144

x = 12

Now we can calculate the area of the triangle easily:

A = (b x h)/2 = (5 x 12)/2 = 30 sq m

Then multiply by the thickness of the prism....

V = 30 x 3 = 90 cubic m

4 0

3 years ago

I need help. this is the problem x^2/3+10=7x^1/3

Arlecino [84]

$\it x^{\frac{2}{3}}+10=7x^{\frac{1}{3}} \Leftrightarrow (x^{\frac{1}{3}})^2-7x^{\frac{1}
 {3}} +10=0 
\\\;\\
We\ note\ x^{\frac{1}{3}} =t \ \ and \ the \ equation \ will \ be:
\\\;\\
t^2-7t+10 = 0 \Leftrightarrow t^2 -2t-5t+10=0 \Leftrightarrow t(t-2) -5(t-2)=0$

$\it \Leftrightarrow (t-2)(t-5)=0 
\\\;\\
t-2=0 \Rightarrow t=2 \Rightarrow x^{\frac{1}{3}}=2 \Rightarrow (x^{\frac{1}{3}})^3 =2^3 \Rightarrow x = 8
\\\;\\
t-5=0 \Rightarrow t=5 \Rightarrow x^{\frac{1}{3}}= 5 \Rightarrow (x^{\frac{1}{3}})^3 = 5^3 \Rightarrow x = 125$

S = {8; 125}

7 0

4 years ago

How can you represent the system of inequalities with a matrix? 11x-12y=7 5x+12y=-7

Ahat [919]

$\left[\begin{array}{ccc}11&-12&7\\5&12&-7\end{array}\right]$

4 0

3 years ago

What is the radius of circle c

Oxana [17]

Answer:

radius = 13

Step-by-step explanation:

Look at the attached picture below. We can calculate radius with the help of the Pythagorean theorem. But first we have to find out the values of the two legs.

First let's find the shorter leg.

Equidistant Chords Theorem

Two chords are congruent if they are equidistant from the center.

Chords in the picture are congruent and that means that the distance from the center to each of them is the same!

Let's calculate the distance. But to get the distance we have to find x first.

Since the distances are the same:

$x + 3 = 2x + 1\\2 = x$

Therefore:

$\text{distance (short leg)} = 2x + 1 = 2\cdot2 + 1 = 5$

Let's focus on the longer leg. Since part of the radius is perpendicular to the chord, it actually bisects the chord! That means that the long leg is going to be a half of the length of the chord.

Therefore:

$\text{long leg} = \frac{\text{chord}}{2} = \frac{24}{2} = 12$

All that is left is the Pythagorean Theorem in the right triangle.

Pythagorean Theorem

$\text{hypotenuse}^2 = \text{leg}_1^2 + \text{leg}_2^2$

Hypotenuse in our case is the radius.

$\text{radius}^2 = 5^2 + 12^2\\\text{radius}^2 = 25 + 144\\\text{radius}^2 = 169\\\text{radius} = 13$

7 0

2 years ago