PLEASE HELP ASAP!!

Find the area of the composite figure.
First, find the area of the triangle.
Triangle
Area = [?] cm2
4 cm
Rectangle
Area = [] cm
7 cm
Total Area of Composite
Figure = [ ] cm
12 cm
Enter

Answer:

[tex]\cot 330^{\circ} = -\sqrt{3}[/tex]

Step-by-step explanation:

The cotangent function can be rewritten by trigonometric relations, that is:

[tex]\cot 330^{\circ} = \frac{1}{\tan 330^{\circ}} = \frac{\cos 330^{\circ}}{\sin 330^{\circ}}[/tex] (1)

By taking approach the periodicity properties of the cosine and sine function (both functions have a period of 360°), we use the following equivalencies:

[tex]\sin 330^{\circ} = \sin (-30^{\circ}) = -\sin 30^{\circ}[/tex] (2)

[tex]\cos 330^{\circ} = \cos (-30^{\circ}) = \cos 30^{\circ}[/tex] (3)

By (2) and (3) in (1), we have following expression:

[tex]\cot 330^{\circ} = -\frac{\cos 30^{\circ}}{\sin 30^{\circ}}[/tex]

If we know that [tex]\sin 30^{\circ} = \frac{1}{2}[/tex] and [tex]\cos 30^{\circ} = \frac{\sqrt{3}}{2}[/tex], then the result of the trigonometric expression is:

[tex]\cot 330^{\circ} = -\frac{\frac{\sqrt{3}}{2} }{\frac{1}{2} }[/tex]

[tex]\cot 330^{\circ} = -\sqrt{3}[/tex]

The exact value of cot 330° with a rational denominator is √3.

To find the exact value of cot 330°, we can first determine the reference angle. The reference angle for 330° is 30°, as it is the angle between the terminal side of 330° and the x-axis.

Cotangent (cot) is the reciprocal of the tangent function, so we need to find the tangent of the reference angle, which is tan 30°. The tangent of 30° is √3/3.

Since cot is the reciprocal of tan, the cotangent of 330° is the reciprocal of √3/3, which is 3/√3.

To rationalize the denominator, we multiply the numerator and denominator by the conjugate of the denominator, which is √3.

(3/√3) x (√3/√3) = 3√3/3

Simplifying further, we can cancel out the common factor of 3:

(3√3/3) = √3

Therefore, the exact value of cot 330° with a rational denominator is √3.

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Answer: 88 gallons

Step-by-step explanation:

Every 2 vanillas = 11 chocolates

so 16 vanillas = 88 chocolates

i did this by multiplying both numbers by 8

sorry if this is wrong

Step-by-step explanation:

(I) A number which can be expressed in the form m/n, where m and n are integers and n is not equal to zero, is called a Rational Number .

(ii) If the integers m and n have no common divisor other than 1 and n is positive, then the rational number m/n is said to be in the Simplest form .

(iii) Two rational numbers are said to be equal, if they have the same Simplest form .

(iv) If m is a common divisor of x and y, then x/y = (x ÷ k)/( y ÷ k) .

(v) The standard form of -1 is -1/1

(vi) If m/n is a rational number, then n cannot be 0

(vii) Two rational numbers with different numerators are equal, if their numerators are in the same ratio as their denominators.

Answer:

16

Step-by-step explanation:

The area of a triangle is

A =1/2 bh  where b is the base length  and h is the height

Substitute the values in

69.6 = 1/2 ( 8.7) * p

69.6 = 4.35p

Divide each side by 4.35

69.6/4.35 = p

16 = p

The formula for the area of a triangle is: A = 1/2 * base * height.

Using this formula, let's plug in what we know.

69.6 = 1/2 * 8.7 * height

Next, we'll go ahead and get rid of that 1/2 by multiplying everything by its reciprocal, 2.

139.2 = 8.7 * height

Then, all that's left is to divide both sides by 8.7.

Height = 16 yards

Hope this helps!! :)

Given:

The figure of an algebraic tiles model of an inequality.

To find:

The inequality for the given model.

Solution:

On the left hand side of the inequality sign in the model we have 8 tiles of x and 12 tiles of 1. So,

[tex]LHS=8(x)+12(1)[/tex]

[tex]LHS=8x+12[/tex]

On the right hand side of the inequality sign in the model we have 12 tiles of -1. So,

[tex]RHS=12(-1)[/tex]

[tex]RHS=-12[/tex]

Now, the inequality for the given model is:

[tex]8x+12\geq -12[/tex]

Therefore, the required inequality for the given model is [tex]8x+12\geq -12[/tex].

Answer:

10

Step-by-step explanation:

5x2

Answer:

In order of increasing angle measure, the fourth roots of -3 + 3√3·i are presented as follows;

[tex]\sqrt[4]{6} \cdot \left[cos\left({-\dfrac{\pi}{12} } \right) + i \cdot sin\left(-\dfrac{\pi}{12} } \right) \right][/tex]

[tex]\sqrt[4]{6} \cdot \left[cos\left({\dfrac{5 \cdot \pi}{12} } \right) + i \cdot sin\left(\dfrac{5 \cdot\pi}{12} } \right) \right][/tex]

[tex]\sqrt[4]{6} \cdot \left[cos\left({\dfrac{11 \cdot \pi}{12} } \right) + i \cdot sin\left(\dfrac{11 \cdot\pi}{12} } \right) \right][/tex]

[tex]\sqrt[4]{6} \cdot \left[cos\left({\dfrac{17 \cdot \pi}{12} } \right) + i \cdot sin\left(\dfrac{17 \cdot\pi}{12} } \right) \right][/tex]

Step-by-step explanation:

The root of a complex number a + b·i is given as follows;

r = √(a² + b²)

θ = arctan(b/a)

The roots are;

[tex]\sqrt[n]{r}[/tex]·[cos((θ + 2·k·π)/n) + i·sin((θ + 2·k·π)/n)]

Where;

k = 0, 1, 2,..., n -2, n - 1

For z = -3 + 3√3·i, we have;

r = √((-3)² + (3·√3)²) = 6

θ = arctan((3·√3)/(-3)) = -π/3 (-60°)

Therefore, we have;

[tex]\sqrt[4]{-3 + 3 \cdot \sqrt{3} \cdot i \right)} = \sqrt[4]{6} \cdot \left[cos\left(\dfrac{-60 + 2\cdot k \cdot \pi}{4} \right) + i \cdot sin\left(\dfrac{-60 + 2\cdot k \cdot \pi}{4} \right) \right][/tex]

When k = 0, the fourth root is presented as follows;

[tex]\sqrt[4]{6} \cdot \left[cos\left(\dfrac{-\dfrac{\pi}{3} + 2\cdot 0 \cdot \pi}{4} \right) + i \cdot sin\left(\dfrac{-\dfrac{\pi}{3} + 2\cdot 0 \cdot \pi}{4} \right) \right] \\= \sqrt[4]{6} \cdot \left[cos\left({-\dfrac{\pi}{12} } \right) + i \cdot sin\left(-\dfrac{\pi}{12} } \right) \right][/tex]

When k = 1 the fourth root is presented as follows;

[tex]\sqrt[4]{6} \cdot \left[cos\left(\dfrac{-\dfrac{\pi}{3} + 2\cdot 1 \cdot \pi}{4} \right) + i \cdot sin\left(\dfrac{-\dfrac{\pi}{3} + 2\cdot 1 \cdot \pi}{4} \right) \right] \\= \sqrt[4]{6} \cdot \left[cos\left({\dfrac{5 \cdot \pi}{12} } \right) + i \cdot sin\left(\dfrac{5 \cdot\pi}{12} } \right) \right][/tex]

When k = 2, the fourth root is presented as follows;

[tex]\sqrt[4]{6} \cdot \left[cos\left(\dfrac{-\dfrac{\pi}{3} + 2\cdot 2 \cdot \pi}{4} \right) + i \cdot sin\left(\dfrac{-\dfrac{\pi}{3} + 2\cdot 2 \cdot \pi}{4} \right) \right] \\= \sqrt[4]{6} \cdot \left[cos\left({\dfrac{11 \cdot \pi}{12} } \right) + i \cdot sin\left(\dfrac{11 \cdot\pi}{12} } \right) \right][/tex]

When k = 3, the fourth root is presented as follows;

[tex]\sqrt[4]{6} \cdot \left[cos\left(\dfrac{-\dfrac{\pi}{3} + 2\cdot 3 \cdot \pi}{4} \right) + i \cdot sin\left(\dfrac{-\dfrac{\pi}{3} + 2\cdot 3 \cdot \pi}{4} \right) \right] \\= \sqrt[4]{6} \cdot \left[cos\left({\dfrac{17 \cdot \pi}{12} } \right) + i \cdot sin\left(\dfrac{17 \cdot\pi}{12} } \right) \right][/tex]

Answer:

Step-by-step explanation:

Just took the test.

1) 4sqrt6 cis(pie/6)

2) 4sqrt6 cis (2pie/3)

3) 4sqrt6 cis(7pie/6)

4) 4sqrt6 cis (5pie/3)

Answer:

Eat them. )llllllllllllllllllllllllll)

Answer:

Observational Study

Step-by-step explanation:

Because she stands by the front door and records each student

The data gathering technique used to know the number of students that wore their uniform is Observational study

Data gathering technique is the process of gathering, measuring, and analysing accurate data from a variety of relevant sources.

There are several procedure of acquiring this data, which includes the following:

The data gathering technique used to know the number of students that wore their uniform is Observational study.

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Answer:

6761/320

Step-by-step explanation:

[(51/2)÷32/3]+14/5

=6761/320

Answer:

1250 Meters

Step-by-step explanation:

75 kilometers divided by 60 minutes is 1.25 kilometers per minute.

1 kilometer = 1000 meters

Answer:

75km/hr =75000

60 sec =1min,60 min=1hr

75000÷60=1250m

Answer:

8,

4 and 8

3,4,8,9

6

Step-by-step explanation:

Answer: AE & AC

Step-by-step explanation:

:)

Answer:

0.166

Step-by-step explanation:

Answer:

38.46

Step-by-step explanation:

Percentage Calculator: 20 is what percent of 52? = 38.46.

Answer: 25

Step-by-step explanation:

Given

Kay found 4 frogs on Monday

and 9 frogs on Tuesday by her house

each frog has 5 warts

So, total warts on Monday and Tuesday

[tex]\Rightarrow \text{Monday=}4\times 5\\\Rightarrow 20\\\\\Rightarrow \text{Tuesday =}9\times 5\\\Rightarrow 45[/tex]

The difference of warts is

[tex]\Rightarrow 45-20\\\Rightarrow 25[/tex]

Thus, there are25 more warts on frogs from Tuesday than from Monday  

Frogs On Monday:

4 frogs x 5 = 20 warts

Frogs On Tuesday:

9 frogs x 5 warts = 45

Last Step:

45 (9 frogs each with 5 warts) - 20 (4 frogs each with 5 warts) =

Answer: 25

            ~Hope this helps!

      ~Hocus Pocus

Answer:

345

Step-by-step explanation:

Answer:

x = 82°

y = 8°

Step-by-step explanation:

x + 98° = 180°

x = 180° - 98°

x = 82°

x + y = 90°

82° + y = 90°

y = 90° - 82°

y = 8°

Answer:

value of discriminant=73

Answer:

1 17/18 and 2 4/15

Step-by-step explanation:

5 5/6 x 1 /3 = 1 17/18

1/3 x 6 4/6 = 2 4/15

Answer: 1 17/18 and 2 4/15

Step-by-step explanation:

In this number line, we marked -7/6 to the left of -1, and 4/3 to the right of 1.

To plot the numbers -1 1/6 and 4/3 on a number line, we need to find their relative positions and mark them accordingly.

Let's start with -1 1/6:

-1 1/6 can be written as a mixed number or an improper fraction. To simplify the plotting process, let's convert it to an improper fraction.

-1 1/6 = -(6/6 + 1/6) = -7/6

On the number line, we start from zero and move to the left because it is a negative number. Since -7/6 is less than -1, we will place it closer to zero but to the left of -1.

Next, let's plot 4/3:

4/3 is already in the form of an improper fraction. To plot it, we start from zero and move to the right since it is a positive number. 4/3 is greater than 1, so we will place it to the right of 1.

On this number line, we marked -7/6 to the left of -1, and 4/3 to the right of 1.

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Answer:

Pythagoras theorem is is a mathematical law that states that the sum of squares of the lengths of the two short sides of the right triangle is equal to the square of the length of the hypotenuse.

Step-by-step explanation:

The hypotenuse is the side opposite to the right angle and so the equation for finding the hypotenuse would be:

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

Answer:

I think it is 62.4 km.

Step-by-step explanation:

Consider that,

x^2+4x+4 = (x+2)(x+2)

x^2+7x+10 = (x+2)(x+5)

Dividing those expressions leads to

(x^2+4x+4)/(x^2+7x+10) = (x+2)/(x+5)

The intermediate step that happened is that we have (x+2)(x+2) all over (x+2)(x+5), then we have a pair of (x+2) terms cancel as the diagram indicates (see below). This is where the removable discontinuity happens. Specifically when x = -2. Plugging x = -2 into (x+2)/(x+5) produces an output, but it doesn't do the same for the original ratio of quadratics. So we must remove x = -2 from the domain.

Answer: 37

8(4)+11-3(2)

32+11-6

43-6

37

i think this is correct

Answer:

the oldest is Ty and his age is 24

Step-by-step explanation:

Let us assume the billy age be x

Noah age be y

And, Ty age be z

Now according to the question

y + x = 25 ..........(1)

y + z = 20..........(2)

x + z  = 31..............(3)

z = 31 - x

since

y + z = 20

y + 31 - x = 20

y - x = -11 .............(4)

Now solve (1) and (4) equation

So,

y + x = 25

y - x = -11

2y = 36

y = 18

x = 25 - 18

= 7

z = 31-7

= 24

Hence, the oldest is Ty and his age is 24