19. Solve for the angle x.
sin²(2x) = 1

Answer:

D. 31/40

Step-by-step explanation:

3/8 + 2/5 =

15/40 + 16/40 =

31/40

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:

d

Step-by-step explanation:

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:

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.

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!

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

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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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:

Jorge needs 1/2 apple to make the snack.

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:

The volume of the soup can is 602. 88 cubic centimeters

Step-by-step explanation:

Volume of a cylinder = π {r} ^{2} h

Where π = 3.14

r = diameter ÷ 2

r= 8 ÷ 2

r= 4 cm

h= 12 cm

Volume of the soup can= 3.14 × 4 × 4 × 12

= 602. 88 cubic centimeters

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: (1,2)

Step-by-step explanation:

The center of the circle is the midpoint of the diameter, so using the midpoint formula, we get the answer to be [tex]\left(\frac{-1+3}{2}, \frac{5-1}{2} \right)=\boxed{(1,2)}[/tex]

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 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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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:

Step-by-step explanation:

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

Answer:

the answer is b you have it right

Step-by-step explanation:

your welcome

Answer:

=24

Step-by-step explanation:

Correct Q:

-b•2a

Ans:

=+3*2•4

=24

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

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]

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

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=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]

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.

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:

Step-by-step explanation:

Dimensions of the room

Find the surface area of the 4 walls

Convert the area to ft²

Find the amount of paint required

Covert the volume to liters

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]