Verify each trigonometric identity

Answer:

B

Step-by-step explanation:

the domain of a graph consists of all the input values shown on the x-axis.

so because the only parts shown on the x axis are 6 and -6 that is the answer!

hope this helps!

Answer:

23.33

Step-by-step explanation:

The sum of the internal angles of a triangle is 180°, which is given by The Angle Sum Property of Triangles.

⇒ 3x - 17 + 2x + 5 + x + 52 = 180

⇒ 6x + 40 = 180

⇒ 6x = 140

⇒ x = 140/6

⇒ x = 70/3

⇒ x = 23.33

Answer: x = 23.333

In any triangle, all the three angles will ALWAYS add up to 180°. According to that:

▪ 180° = <a + <b + <c

(2x + 5) + (3x - 17) + (x + 52) = 180

2x + 5 + 3x - 17 + x + 52 = 180

Rearrange according to like terms

2x + 3x + x + 52 - 17 + 5 = 180

6x + 40 = 180

Now we'll find the value of x

6x = 180 - 40

x = 140/6

By cross cancellation we get

x = 70/3

You could change it into decimal as well

x = 23.333 answer

therefore, the third option that says 23.33 is correct.

Hope that helps...

Answer:

d

Step-by-step explanation:

Answer:

13.125 inches wide

Step-by-step explanation:

5% more than 12.5 which is 12 1/2 as a decimal, equals 13.125 inches.

Multiply your needed fabric  width (12.5 or 12 1/2) by (1 + %/percent you're increasing it by) to equal the width you cut instead:

[tex]12.5(1+5) = 12.5(1.05) = 13.125[/tex]

The equivalent expression on expanding -1/4 (-8x + 12y) is 2x - 3y

Expansion of expression can be carried out using the distributive rule a shown:

A(B + C) = AB + AC

Note that A is distributed over B and C
Given the expression

-1/4 (-8x + 12y)

-1/4(-8x) - 1/4(12y)

2x - 3y

Hence the equivalent expression on expanding -1/4 (-8x + 12y) is 2x - 3y

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Answer:

slope m = - [tex]\frac{7}{3}[/tex]

Step-by-step explanation:

ANSWER:

The polynomial with 6 roots is the one of degree 6, so the correct option is:

[tex]f(x) = 7x^6 + 3x^2 + 12[/tex]

You need to remember that if p(x) is a polynomial of degree N, then it has N roots (such that some of these N roots may be equal or not).

Then we just need to find the polynomial of degree 6. (Remember that the degree represents the maximum exponent of the polynomial).

In this case, the only one of degree 6 is:

[tex]f(x) = 7x^6 + 3x^2 + 12[/tex]

Which is the last option.

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Answer:

The answer is D

Step-by-step explanation:

I took the test

Answer:

AC = [tex]3\sqrt{3}[/tex]
BC = [tex]6\sqrt{3}[/tex]

Step-by-step explanation:

AC is [tex]x\sqrt{3}[/tex] and x = 3 so [tex]3\sqrt{3}[/tex] and it [tex]=3\sqrt{3}[/tex]

BC is [tex]2x[/tex] and x = 3 so [tex]2(3\sqrt{3}) = 6\sqrt{3}[/tex]

Hopefully this was what you wanted, and is correct!

Answer:

[tex]x=3.18[/tex] [tex]cm[/tex]

Explanation:

[tex]x=3.18[/tex] [tex]cm[/tex]

Substitute [tex]y=6 cm[/tex] into  [tex]\frac{}{AC} =y:\frac{}{AC} =6cm[/tex]

Substitute [tex]0=32[/tex] into ∠[tex]CAB=0:[/tex] ∠[tex]CAB=32^o[/tex]

sinA=leg opposite ∠A/hypotenuse : [tex]sin(CAB)=\frac{\frac{}{BC} }{\frac{}{AC} }[/tex]

Substitute [tex]\frac{}{BC} =x,\frac{}{AC}=6cm,[/tex] ∠[tex]CAB=32^o[/tex]

into sin(∠[tex]CAB[/tex]) [tex]=\frac{\frac{}{BC} }{\frac{}{AC} }:sin(32^o)=\frac{x}{6}[/tex]

Calculate [tex]sin(32^o)=\frac{x}{6} :x=3.18cm[/tex]

The BTU required by the air conditioner/hour to cool the following structures is given as:

It is to be noted that the BTU required to cool per cubic foot of space is 4BTUs.

Since we are not given the dimensions of the structures, the required constant is thus, multiplied by the volume of the structures whose equations have been given above.

Note that:

Volume translates to enclosed space; and

BTU means British Thermal Unit.

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Answer:

=24

Step-by-step explanation:

Correct Q:

-b•2a

Ans:

=+3*2•4

=24

Answer:

2

Step-by-step explanation:

The scale factor shows the proportion of a number to another one

The side lengths for triangle ABC: 12-4-2

The side lengths for triangle LMN: 6-2-1

if we write them as fractions

12/6 = 2

4/2 = 2

2/1 = 2 so the answer is in third option.

Answer:

7x - 30

Step-by-step explanation:

5x -2(15-x)

Distribute -2 to the parenthesis

= 5x -30 +2x

Combine like terms

7x-30

Answer:

Step-by-step explanation:

{x,y}={5,-5}

Answer:

42 units ^2

Step-by-step explanation:

Break in to a top triangle   a middle rectangle and a bottom triangle

area =   1/2 7 *2      +    4 * 7        1/2 * 2 * 7 = 42 units ^2

Step-by-step explanation:

there are just some big words trying to confuse you.

it just means that there is a right-angled triangle :

there is the point on the ground, where the surveyor is standing.

then there is the elevated point up there, where the surveyor was measuring the angle to.

and then there is the point on the ground directly under this elevated point. at this point in the ground we have the right angle (90°).

this height of the elevated point above this ground point is what we are looking for, and it is one leg of the right-angled triangle.

the ground distance from the surveyor to the ground point under the elevated point is 5 miles and the second leg.

the direct line of sight from the surveyor to the elevated point is inclined up by 20°, and is the Hypotenuse (baseline opposite of the 90° angle) of the triangle.

remembering that the sum of all angles in a triangle is always 180°, we also know the angle at the elevated point :

180 - 90 - 20 = 70°

now we are using the law of sine :

a/sin(A) = b/sin(B) = c/sin(C)

where the sides are always opposite to their associated angles.

so, we have in our triangle

height/sin(20) = 5/sin(70)

height = 5×sin(20)/sin(70) = 1.819851171... miles

so, the elevated point is 1.819851171... miles above the elevation of the surveyor.

Explanation:

The term "right angle" is another way of saying "90 degree angle".

Such angles are marked as squares. Usually there are tiny square symbols inside the angle to be very clear that we have 90 degree angles. Some diagrams may not do this, and simply imply that anything that looks like a square 90 degree angle actually is one.

With this in mind, the angles that fit the description are angles J and M at the bottom of the figure. Therefore, there are 2 right angles in this shape.

Side note: This figure is a trapezoid because it has exactly one set of parallel sides KJ and LM.

The polygon abcdef in the coordinate plane shown with area of 18 square units.

A polygon is a geometric figure with a finite number of sides in two dimensions. On the sides or edges of a polygon, straight-line segments are joined end to end to form a closed shape. The vertices, also known as corners, are the points where two line segments meet and form an angle.

We have vertices for the polygon:

a=(-2,-3), b=(0,-3), c=(0,1), d=(3,1), e=(3,3), f=(-2,3)

After marking the coordinates on the coordinate plane and connecting the lines, we will get a polygon.

We can find the area of the shape:

Area of the shape = 18 square units

Thus, the polygon abcdef in the coordinate plane shown with area of 18 square units.

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Using the normal distribution, it is found that the probability that a data value is between 28 and 35 is given by:

A. 29.6%.

The z-score of a measure X of a normally distributed variable with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

Researching the problem on the internet, the mean and the standard deviation are given by:

[tex]\mu = 26, \sigma = 4[/tex].

As a proportion, the probability that a data value is between 28 and 35 is the p-value of Z when X = 35 subtracted by the p-value of Z when X = 28, hence:

X = 35:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{35 - 26}{4}[/tex]

Z = 2.25

Z = 2.25 has a p-value of 0.988.

X = 28:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{28 - 26}{4}[/tex]

Z = 0.5

Z = 0.5 has a p-value of 0.692.

0.988 - 0.692 = 0.296 = 29.6%, which means that option A is correct.

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Step-by-step explanation:

[tex] = {(3 \sqrt{ {x}^{2} } )}^{6} [/tex]

[tex] = {(3 {x}^{ \frac{2}{2} } )}^{6} [/tex]

[tex] = {(3x)}^{6} [/tex]

[tex] = {3}^{6} {x}^{6} [/tex]

[tex] = 729 {x}^{6} [/tex]

====================================

[tex]\large \sf \underline{Problem:}[/tex]

Which expression is equivalent to (3√x^2)^6

====================================

[tex]\large \sf \underline{Answer:}[/tex]

The answer is x⁴

====================================

[tex]\large \sf \underline{Explanation:}[/tex]

[tex]( \sqrt[3] {x}^{2} )⁶ \: {The \: cube \: root \: of \: x² \: is \: x^(2/3)} (x^(2/3))⁶ {Now, \: simply \: multiply \: 2/3 \: by \: 6 \: to \: get \: 4.}[/tex]

x⁴

[tex]( \sqrt[3] {x}^{2} )⁶ \: is \: equivalent \: to \: x⁴[/tex]

====================================

Answer:

Because of the order of operations, we start the equation backwards because exponents are what we prioritize here.

[tex]3^2 = 9\\\\9 * 5 = 45\\\\\sqrt{-125} = -11.1803399\\\\45 - -11.1803399 = 56.1803399\\\\56.1803399 * 3 = \boxed{168.54}[/tex]                                      Result rounded to 2 DP

Answer:

Jorge needs 1/2 apple to make the snack.

As it's already graphed their inetresection point is solution for both functions

The solution is (1,5)

Answer:

(1, 5)

Step-by-step explanation:

The solution to the system of equations would be where the lines of the two intersect. The point of intersection (based on the graph) is :

Answer:

D. 31/40

Step-by-step explanation:

3/8 + 2/5 =

15/40 + 16/40 =

31/40

Total balls=sample space=9

Multiples of 2

Total multiples=4

Probability

Option C

Hello, the answer should be [tex]\frac{4}{9}[/tex], C option.

First, let's define the numbers that are a multiple of 2 from the balls we have.

Then, we will calculate our probability. To do this correctly, we must divide the amount of expected states into the amount of all the states.

Expected numbers: 2-4-6-8

All numbers: 1-2-3-4-5-6-7-8-9

[tex]P=\frac{{2,4,6,8}}{1,2,3,4,5,6,7,8,9} =\frac{4}{9}[/tex]

Good luck! If you have any questions, then feel free to ask in comments!

The extension cord is an illustration of unit rates, and the price per foot is $0.47 per foot

The given parameters are:

Length = 6 yards

Cost = $8.46

Convert the length from yard to feet.

So, we have:

Length = 6 feet * 3

This gives

Length= 18 feet

The price per foot is then calculated using:

Rate = Cost/Length

This gives

Rate = 8.46/18

Evaluate

Rate = 0.47

Hence, the price per foot is $0.47 per foot

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Answer: 18a4 - 6a3b - 5a2b4 - 45a2b2 + 36ab2 - 12ab + 3b

———————————————————————————————-

3

Step-by-step explanation:

Answer:

[tex]x=\frac{1}{2}\left(\tan^{-1}{4}+\pi k\right)[/tex], where k is any integer

Step-by-step explanation:

Let's start by getting all the trig functions on one side and all the constants on the other. We can do this by dividing both sides by [tex]\cos{2x}[/tex]:

[tex]\dfrac{\sin{2x}}{\cos{2x}}=4[/tex]

This ratio looks familiar! It just so happens that the tangent function is defined as the ratio of sine to cosine. In our case:

[tex]\dfrac{\sin{2x}}{\cos{2x}}=\tan{2x}[/tex]

Substituting this back into our equation, we have [tex]\tan{2x}=4[/tex]. We can unwrap the 2x by applying the inverse tangent function to both sides, giving us [tex]2x=\tan^{-1}{4[/tex]. Note, this specific solution only accounts for values of 2x between 0 and 2π radians. To make it general, we can add the term πk to the end of the right side, where k is any integer. We use π as a coefficient because the tangent function has a period of π radians, and it repeats its values every period.

Finally, we divide both sides of the equation by 2 to isolate x, giving us

[tex]2x=\tan^{-1}{4}+\pi k\\x=\frac{1}{2}\left(\tan^{-1}{4}+\pi k\right)[/tex]