Simplify: squrt 18x⁷

Answer:

The area of the circle is 100 square units.

Step-by-step explanation:

We are given that the circumference of a circle is 20π, and we want to determine its area.

Recall that the circumference of a circle is given by the formula:

[tex]\displaystyle C = 2\pi r[/tex]

Substitute:

[tex]20 \pi = 2 \pi r[/tex]

Solve for the radius:

[tex]\displaystyle r = \frac{20\pi}{2\pi} = 10[/tex]

The area of a circle is given by:

[tex]\displaystyle A = \pi r^2[/tex]

Since the radius is 10 units:

[tex]\displaystyle A = \pi (10)^2[/tex]

Evaluate:

[tex]\displaystyle A = 100\pi\text{ units}^2[/tex]

In conclusion, the area of the circle is 100 square units.

Answer:

Step-by-step explanation:

Given,

n = 5

and, b = 4

Equation:

n + b × 5

= 5 + 4 × 5

= 5 + 20

= 25 (Ans)

Answer:

Let ABC = 73.6

Complement = ABD = 16.4

ABx = unknown angle

ABx + (ABx + 73.6) = 90

ABx = 16.4 / 2 = 8.2

The angles are 8.2 and (8.2 + 73.6) = 90

9514 1404 393

Answer:

Step-by-step explanation:

Substitute the expressions.

After the first translation, the value of x is (x+n). Put that as the value of x in the second translation.

  x ⇒ x +s . . . . . . . . . the definition of the second translation

  (x+n) ⇒ (x+n) +s . . . the result after both translations

The same thing goes for y. After the first translation, its new value is (y+1).

  y ⇒ y +m . . . . . . . . the definition of the second translation

  (y+1) ⇒ (y+1) +m . . . the result of both translations

Then the composition of A followed by B is (x, y) ⇒ (x +n +s, y +1 +m).

__

The same reasoning applies. After the B translation, the x-coordinate is (x+s) and the y-coordinate is (y+m). Then the A translation changes these to ...

  x ⇒ x +n . . . . . . . . . . definition of translation A

  (x+s) ⇒ (x+s) +n . . . . translation A operating on point translated by B

  y ⇒ y +1 . . . . . . . . . . . definition of translation A

  (y+m) ⇒ (y+m) +1 . . . . translation A operating on point translated by B

The composition of B followed by A is (x, y) ⇒ (x + s + n, y + m + 1).

__

You should recognize that the sums (x+n+s) and (x+s+n) are identical. The commutative and associative properties of addition let us rearrange the order of the terms with no effect on the outcome.

The two translations give the same result in either order.

Answer:

I found x for you, right there.

Answer:  x is 12 and y is 5

Step-by-step explanation:

Answer:

6.8 gallions i believe. im not quite sure

Answer:

A " (1,-2)

B " (4,0)

C " (6,-3)

Step-by-step explanation:

Hope it helped.

° ° °

[tex]\\ \sf\longmapsto Interest=Rate\times Time[/tex]

[tex]\\ \sf\longmapsto Interest=5.3(10)[/tex]

[tex]\\ \sf\longmapsto Interest =53[/tex]

It means that if your principal is $100 after 10years you will receive $53 as interest

Step-by-step explanation:

[tex]thank \: you[/tex]

Step-by-step explanation:

Hi there!

Please see the answer in the picture.

Hope it helps!

1. Approach

One is given a trigonometric equation with and one is asked to prove that it is true. Using the attached image, combined with the knowledge of trigonometry, one can evaluate each trigonometric function. Then one can simplify each ratio to solve. To yield the most accurate result, one has to each of the ratios in a fractional form, rather than simplifying it into a decimal form. Remember the right angle trigonometric ratios, these ratios describe the relationship between the sides and angles in a right triangle. Such ratios are as follows,

[tex]sin(\theta)=\frac{opposite}{hypotenuse}\\\\cos(\theta)=\frac{adjacent}{hypotenuse}\\\\tan(\theta)=\frac{opposite}{adjacent}\\\\csc(\theta)=\frac{hypotenuse}{opposite}\\\\sec(\theta)=\frac{hypotenuse}{adjacent}\\\\cot(\theta)=\frac{adjacent}{opposite}[/tex]

Please note that the terms (opposite) and (adjacent) are relative to the angle uses in the ratio, however the term (hypotenuse) refers to the side opposite the right angle, this side never changes its name. Use these ratios to evaluate the trigonometric functions. Then simplify to prove the identity.

2. Problem (9)

[tex]\frac{sin(60)+cos(30)}{1+sin(30)+cos(60)}=sin(60)[/tex]

As per the attached image, the following statements regarding the value of each ratio can be made:

[tex]sin(60)=\frac{\sqrt{3}}{2}\\\\cos(30)=\frac{\sqrt{3}}{2}\\\\sin(30)=\frac{1}{2}\\\\cos(60)=\frac{1}{2}[/tex]

Substitute,

[tex]\frac{sin(60)+cos(30)}{1+sin(30)+cos(60)}=sin(60)[/tex]

[tex]\frac{\frac{\sqrt{3}}{2}+\frac{\sqrt{3}}{2}}{1+\frac{1}{2}+\frac{1}{2}}=\frac{\sqrt{3}}{2}[/tex]

Simplify,

[tex]\frac{\frac{\sqrt{3}}{2}+\frac{\sqrt{3}}{2}}{1+\frac{1}{2}+\frac{1}{2}}=\frac{\sqrt{3}}{2}[/tex]

[tex]\frac{\frac{2\sqrt{3}}{2}}{1+\frac{1}{2}+\frac{1}{2}}=\frac{\sqrt{3}}{2}[/tex]

[tex]\frac{\frac{2\sqrt{3}}{2}}{1+1}=\frac{\sqrt{3}}{2}[/tex]

[tex]\frac{\sqrt{3}}{1+1}=\frac{\sqrt{3}}{2}[/tex]

[tex]\frac{\sqrt{3}}{2}=\frac{\sqrt{3}}{2}[/tex]

Thus, this equation is true.

2. Problem (10)

Use a similar strategy to evaluate this equation,

[tex]\frac{1-cos(30)}{sin(30)}=\frac{1-cot(60)}{1+cot(60)}[/tex]

Use the attached image to evaluate the ratios.

[tex]cos(30)=\frac{\sqrt{3}}{2}\\\\sin(30)=\frac{1}{2}\\\\cot(60)=\frac{1}{\sqrt{3}}[/tex]

Substitute,

[tex]\frac{1-cos(30)}{sin(30)}=\frac{1-cot(60)}{1+cot(60)}[/tex]

[tex]\frac{1-\frac{\sqrt{3}}{2}}{\frac{1}{2}}=\frac{1-\frac{1}{\sqrt{3}}}{1+\frac{1}{\sqrt{3}}}[/tex]

Simplify,

[tex]\frac{1-\frac{\sqrt{3}}{2}}{\frac{1}{2}}=\frac{1-\frac{1}{\sqrt{3}}}{1+\frac{1}{\sqrt{3}}}[/tex]

[tex]\frac{\frac{2-\sqrt{3}}{2}}{\frac{1}{2}}=\frac{1-\frac{1}{\sqrt{3}}}{1+\frac{1}{\sqrt{3}}}[/tex]

[tex]\frac{\frac{2-\sqrt{3}}{2}}{\frac{1}{2}}=\frac{\frac{\sqrt{3}-1}{\sqrt{3}}}{1+\frac{1}{\sqrt{3}}}[/tex]

[tex]\frac{\frac{2-\sqrt{3}}{2}}{\frac{1}{2}}=\frac{\frac{\sqrt{3}-1}{\sqrt{3}}}{\frac{\sqrt{3}+1}{\sqrt{3}}}[/tex]

[tex]2-\sqrt{3}=\frac{\frac{\sqrt{3}-1}{\sqrt{3}}}{\frac{\sqrt{3}+1}{\sqrt{3}}}[/tex]

[tex]2-\sqrt{3}=\frac{\sqrt{3}-1}{\sqrt{3}}*\frac{\sqrt{3}}{\sqrt{3}+1}}[/tex]

[tex]2-\sqrt{3}=\frac{\sqrt{3}-1}{\sqrt{3}+1}[/tex]

Rationalize the denominator,

[tex]2-\sqrt{3}=\frac{\sqrt{3}-1}{\sqrt{3}+1}[/tex]

[tex]2-\sqrt{3}=\frac{\sqrt{3}-1}{\sqrt{3}+1}*\frac{\sqrt{3}-1}{\sqrt{3}-1}[/tex]

[tex]2-\sqrt{3}=\frac{(\sqrt{3}-1)^2}{3-1}[/tex]

[tex]2-\sqrt{3}=\frac{3-2\sqrt{3}+1}{2}[/tex]

[tex]2-\sqrt{3}=\frac{4-2\sqrt{3}}{2}[/tex]

[tex]2-\sqrt{3}=2-\sqrt{3}[/tex]

Therefore, this equation is also true.

Answer:

33/14

Step-by-step explanation:

[tex] - 10 \frac{2}{7} + ( - 4 \frac{4}{11} )[/tex]

[tex] = - \frac{72}{7} \div - ( \frac{48}{11} )[/tex]

[tex] = \frac{72}{7} \times \frac{11}{48} [/tex]

[tex] = \frac{3}{7} \times \frac{11}{2} [/tex]

[tex] = \frac{33}{14} [/tex]

stan dreamcatcher

Answer:

k = 14

Step-by-step explanation:

Prime factorize 32

32 = 2 * 2 * 2 * 2 * 2  = 2⁵

[tex]\frac{2^{12}}{2^{\frac{k}{2}}}= 32\\\\\frac{2^{12}}{2^{\frac{k}{2}}}=2^{5}\\\\2^{12-\frac{k}{2}}=2^{5}[/tex]

Both sides base are same.So, compare exponents

[tex]12-\frac{k}{2}=5\\[/tex]

Subtract 12 from both side

[tex]-\frac{k}{2}=5-12\\\\-\frac{k}{2}=-7\\[/tex]

Multiply both sides by (-2),

[tex](-2)*(-\frac{k}{2})=-7*(-2)\\\\k = 14[/tex]

Answer:

{1, 0, 16}

Step-by-step explanation:

given..

j(x) = x^2-2x+1

put all given values of domain (1,0 and 5 ) in the equation..

the values you get are range of the function

Answer: 1

Step-by-step explanation

0(2)-2(0)+1=0+0+1= 1

1(1)-(2)(1)+1=1-2+1= 1

(5)(2)-(2)(5)+1=10-10+1= 1

Answer: [tex]w=\frac{33}{28}[/tex]

Step-by-step explanation:

To solve for w, we want to isolate w.

[tex]-\frac{9}{7}=-\frac{2}{3}w-\frac{1}{2}[/tex]            [add both sides by 1/2]

[tex]-\frac{11}{14}=-\frac{2}{3}w[/tex]                 [multiply both sides by -3/2]

[tex]w=\frac{33}{28}[/tex]

Now we know that [tex]w=\frac{33}{28}[/tex].

Answer:

[tex]\sf w=\dfrac{33}{28} \\[/tex]

Step-by-step explanation:

[tex]\sf -\dfrac{9}{7} =-\dfrac{2w}{3} -\dfrac{1}{2}[/tex]

First, take -2w/3 to the left side.

[tex]\sf -\dfrac{9}{7}+\dfrac{2w}{3} = -\dfrac{1}{2}[/tex]

Then, add 9/7 to both sides.

[tex]\sf \dfrac{2w}{3} = -\dfrac{1}{2}+\dfrac{9}{7}[/tex]

Make the denominators the same and add the fractions.

[tex]\sf \dfrac{2w}{3} = -\dfrac{1*7}{2*7}+\dfrac{9*2}{7*2}\\\\\sf \dfrac{2w}{3} = -\dfrac{7}{14}+\dfrac{18}{14}\\\\\sf \dfrac{2w}{3} = \dfrac{-7+18}{14}\\\\\sf \dfrac{2w}{3} = \dfrac{11}{14}[/tex]

Use cross multiplication.

[tex]\sf 2w*14=11*3\\\\28w=33[/tex]

Divide both sides by 28.

[tex]\sf w=\dfrac{33}{28} \\[/tex]

Answer:

Step-by-step explanation:

∠OST = 90° as ST ⊥ OS (tangent is perpendicular to radius at same point)

m∠OSP = 1/2(180° - m∠SOP) = 90° - 96°/2 = 42° (sum of interior angles of the triangle SOP)

m∠PST = 90° - m∠OSP = 90° - 42° = 48° (angle addition postulate)

Correct choice is B

Answer:

3rd graph

Step-by-step explanation:

Answer:

O D. 3x2 + 2x-3

Answer:

A.7x2-5x questions 2of 20

9514 1404 393

Answer:

  2. (only)

Step-by-step explanation:

The Pythagorean theorem tells you the sum of the squares of the two legs of a right triangle is equal to the square of the hypotenuse. To determine if these are right triangles, determine if that condition is met.

  1. 3^2 +5^2 = 9 + 25 = 34 ≠ (√35)^2 . . . . not a right triangle

  2. 5^2 +4^2 = 25 +16 = 41 = (√41)^2 . . . a right triangle

  3. 6^2 +8^2 = 36 +64 = 100 ≠ (√10)^2 . . . . not a right triangle

  4. 3^2 +3^2 = 9 +9 = 18 ≠ (3√3)^2 = 27 . . . . not a right triangle

Answer:

Step-by-step explanation:

This is the problem we need to solve:

[tex]z=\frac{x_i-\bar{x}}{\sigma}[/tex] and we have everything but the z-score (which we find from a table) with our main unknown being the standard deviation.

If the probability that a random variable that is less than 11 is .67, we first have to find the z-score from the table that is closest to .67, and there are 2:

P(z < .43) = .66640 and P(z < .44) = .67003

We'll use z = .44

[tex].44=\frac{11-10}{\sigma}[/tex] and

[tex].44=\frac{1}{\sigma}[/tex] and

[tex]\sigma=\frac{1}{.44}[/tex] so

σ = 2.27 (check it; it works!)

Answer:

The equation is true.

Step-by-step explanation:

In order to solve this problem, one must envision a right triangle. A diagram used to represent the imagined right triangle is included at the bottom of this explanation.  Please note that each side is named with respect to the angle is it across from.

Right angle trigonometry is composed of a sequence of ratios that relate the sides and angles of a right triangle. These ratios are as follows,

[tex]sin(\theta)=\frac{opposite}{hypotenuse}\\\\cos(\theta)=\frac{adjacent}{hypotenuse}\\\\tan(\theta)=\frac{opposite}{adjacent}[/tex]

One is given the following equation,

[tex]\frac{sin(A)+sin(B)}{cos(A) +cos(B)}+\frac{cos(A)-cos(B)}{sin(A)-sin(B)}=0[/tex]

As per the attached reference image, one can state the following, using the right angle trigonometric ratios,

[tex]sin(A)=\frac{a}{c}\\\\sin(B)=\frac{b}{c}\\\\cos(A)=\frac{b}{c}\\\\cos(B)=\frac{a}{c}[/tex]

Substitute these values into the given equation. Then simplify the equation to prove the idenity,

[tex]\frac{sin(A)+sin(B)}{cos(A) +cos(B)}+\frac{cos(A)-cos(B)}{sin(A)-sin(B)}=0[/tex]

[tex]\frac{\frac{a}{c}+\frac{b}{c}}{\frac{b}{c}+\frac{a}{c}}+\frac{\frac{b}{c}-\frac{a}{c}}{\frac{a}{c}-\frac{b}{c}}=0[/tex]

[tex]\frac{\frac{a+b}{c}}{\frac{a+b}{c}}+\frac{\frac{b-a}{c}}{\frac{a-b}{c}}[/tex]

Remember, any number over itself equals one, this holds true even for fractions with fractions in the numerator (value on top of the fraction bar) and denominator (value under the fraction bar).

[tex]\frac{\frac{a+b}{c}}{\frac{a+b}{c}}+\frac{\frac{b-a}{c}}{\frac{a-b}{c}}[/tex]

[tex]\frac{\frac{a+b}{c}}{\frac{a+b}{c}}+\frac{\frac{-(a-b)}{c}}{\frac{a-b}{c}}[/tex]

[tex]1+(-1)=0[/tex]

[tex]1-1=0[/tex]

[tex]0=0[/tex]