Consider [tex]$\triangle ABC$ such that $BC = 3AC$ and $\angle A = \pi/6$[/tex]
What are [tex]\[12 \sin(\angle B), 12 \sin(\angle C)\][/tex] in that order?

Answer: Option (1)

Step-by-step explanation:

The domain and range of all linear functions is the set of real numbers.

The domain and range of the function is

Domain = (-∞, ∞) and Range = (-∞, ∞)

The domain of a function is the set of values that we are allowed to plug into our function. This set is the x values in a function such as f(x). The range of a function is the set of values that the function assumes. This set is the values that the function shoots out after we plug an x value in.

The range is the set of outputs of a relation or function. In other words, it's the set of possible y values. Recall that ordered pairs are of the form (x,y) so the y coordinate is listed after the x. The output is listed after the input.

Given data ,

Let the function be represented as f ( x )

Now , the value of f ( x ) is

f ( x ) = ( 3/4 )x + 5

The domain of the function is the set of all possible input values for x, which in this case is all real numbers, since there are no restrictions on the value of x that can be plugged into the function. Therefore, the domain of the function is:

Domain = (-∞, ∞)

The range of the function is the set of all possible output values that the function can produce. Since the function is a linear function of the form y = mx + b, where m is the slope and b is the y-intercept, we know that the range of the function is all real numbers, since a line can take on any y-value.

Range = (-∞, ∞)

Hence , the domain and range are set of all real numbers

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Answer: 192

Step-by-step explanation:

2×8=16

2×6=12

17×12=192

So, the answer is 192.

Answer:

115

Step-by-step explanation:

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The formula to convert degrees Fahrenheit to Celsius is:

[tex]\bf{^{\circ}C=\dfrac{5}{9}(^{\circ}F-32) \ \ \to \ \ \ Formula }[/tex]

Convert 59°F to degrees Celsius.

Add the number 59 in the formula, and solve.

        [tex]\bf{=\dfrac{5}{9}(59-32) }[/tex]

Subtract 32 from 59.

         [tex]\bf{=\dfrac{5}{9}(27) }[/tex]

Multiply 5 x 9 = 135, then divide 135/9 = 15.

         [tex]\bf{=15 \ ^{\circ}C}[/tex]

Therefore 59 °F = 15 °C. The correct option is "D".

a. The equation of the ellipse is x²/900 + y²/400 = 1

b. the foci of the ellipse are at (±10√5,0)

c. Find the graph in the attachment

Since the ellipse is made from a block of wood and centered at the origin, and x- axis major axis.

So, the equation of an ellipse with center at origin and x - axis major axis is

x²/a² + y²/b² = 1 where

Since the rectangular piece of wood  has a length of 60 inches and a width of 40 inches.

The length of the rectangle equals the length of the major axis

So, 2a = 60

a = 60/2

= 30

Also, the width of the rectangle equals the length of the minor axis

So, 2b = 40

b = 40/2

= 20

So, substituting a and b into the equation of the ellipse, we have

x²/a² + y²/b² = 1

x²/30² + y²/20² = 1

x²/900 + y²/400 = 1

So, the equation of the ellipse is x²/900 + y²/400 = 1

The foci of the ellipse are at (±c,0) where c² = a² - b²

= 30² - 20²

= 900 - 400

= 500

c = ±√500

c = ±10√5

So, the foci of the ellipse are at (±10√5,0)

c. Find the graph in the attachment

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Answer:

30 or 120 /4

Step-by-step explanation:

a^p/q here p denotes power raised and q denotes inverse power or root. So, 60^1/2 denotes square root of 60 raised to power 1.

Step-by-step explanation:

[tex] = ( {x}^{3} ) { ({x}^{7} )}^{2} [/tex]

[tex] = {x}^{3} \times {x}^{7 \times 2} [/tex]

[tex] = {x}^{3} \times {x}^{14} [/tex]

[tex] = {x}^{3 + 14} [/tex]

[tex] = {x}^{17} [/tex]

The solutions for the given quadratic equation are:

[tex]x = 8 \pm i[/tex]

Here we have the quadratic equation:

[tex]x^2 = 16x - 65[/tex]

We can rewrite it as:

[tex]x^2 - 16x + 65 = 0[/tex]

Using Bhaskara's formulas, we get:

[tex]x = \frac{-(-16) \pm \sqrt{(-16)^2 - 4*65} }{2} \\\\x = \frac{16 \pm \sqrt{(-4)} }{2}[/tex]

Now, remember that:

[tex]\sqrt{-1} = i[/tex]

Then we can rewrite:

[tex]x = \frac{16 \pm \sqrt{-1} *\sqrt{4} }{2}\\\\x = 8 \pm i[/tex]

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Answer:

H (3x,3y)

Step-by-step explanation:

Dilation is a transformation when figure is enlarged or reduced by scale factor. During dilation, every point of preimage is dilated by scale factor, so it means each coordinate of that point must be multiplied by scale factor.

Hence, H(3x,3y) can be the result of dilation with scale factor of 3.

Answer:

obtuse because 6^2+10^2<10^2

Step-by-step explanation:

The given triangle whoe sides are 6cm, 10cm, and 12cm is an obtuse triangle and it can be determine by using pythagorian theorem, i.e. 6^2 + 10^2 < 12^2.

Pythagorean theorem, the well-known geometric theorem that the sum of the squares on the legs of a right triangle is equal to the square on the hypotenuse (the side opposite the right angle)—or, in familiar algebraic notation, a^2 + b^2 = c^2.

here, we have,

Given :

The side lengths of a triangle are: 6cm, 10cm, and 12cm.

Pythagorian theorem can be used to find out that the triangles are acute or obtuse. According to pythagorian theorem, the sum of square of shorter side is equal to the square of the third side of the right angle triangle.

According to pythagorian theorem:.

That is, H^2 = P^2 + B^2.

There are some rules to find the triangle is obtuse or acute:

If  H^2 > P^2 + B^2, than the triangle is obtuse.

If H^2 < P^2 + B^2, than the triangle is acute.

Now, applying pythagorian theorem:

we get,

6^2 + 10^2 = 12^2

136 = 144

Here, it is clearly observe that 136 <  144, i.e. 6^2 + 10^2 < 12^2 therefore, the triangle is obtuse.

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The fourth proportional is found by applying the formula

The product of extremes = The product of means.

The fourth proportional is equal to bc/a and st/r

Let the fourth proportional be x then this can be written as

a:b::c:x

Applying the formula of product of extremes

ax= bc

or

x= bc/a

The fourth proportional can be obtained by multiplying the variables bc and dividing by a

Similarly

Let the fourth proportional be y then this can be written as

r:s::t:y

Applying the formula of product of extremes

ry= st

or

y= st/r

The fourth proportional can be obtained by multiplying the variables st and dividing by r

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The attached graph represents the location of the pH values 0 and 1

The given parameters are:

pH value 0 = (1, 0)

pH value 1 = (0.1, 1)

This means that we plot a point at the coordinate (1, 0) and another point at the coordinate (0.1, 1).

See attachment for the graph

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Complete question

The pH value is 0 at (1, 0) and 1 at (0.1, 1).

Using desmos

A. Locate, plot, and label on your graph where the pH value is 0.1

B. Locate, plot, and label on your graph where the pH value is 1.

A triangle undergoes a sequence of transformations.

First, the triangle is dilated by a scale factor of 1/3 about the origin. Then the triangle is reflected over the x-axis. Finally, the triangle is translated left 3 units and up 2 units.

The amount of the temperature decrease will be 332 °C.

The analysis of mathematical representations is algebra, and the handling of those symbols is logic.

The oven temperature was at 325 degrees because my mom just finished baking a pie.

I increased the temperature, 75 degrees, so I could bake a pizza.

Then the temperature will be

⇒ 325 °C + 75 °C

⇒ 400 °C

After the pizza was cooked, I turned off the oven.

The oven cooled to the room temperature of 68 degrees.

Then the amount of the temperature decrease will be

⇒ 400 °C – 68 °C

⇒ 332 °C

The remaining question is given below.

How much did the temperature decrease?

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The perimeter of the entire figure is 62.8 cm.

Given, that the diameter of the inner semicircles is 9 cm and the width between the outer and inner semicircles is 2 cm.

The radius of the inner semicircle =4.5 cm and the radius of outer semicircle =5.5 cm (∵Diameter=9+2=11 cm)

We need to find the perimeter of the entire figure.

A perimeter is a closed path that encompasses, surrounds, or outlines either a two-dimensional shape or a one-dimensional length. The perimeter of a circle or an ellipse is called its circumference.

We know that, the circumference of a semicircle=πr and the circumference of two semicircles=2πr

Thus, the circumference of inner semicircles=2×3.14×4.5=28.26 cm

The circumference of outer semicircles=2×3.14×5.5=34.54 cm

The perimeter of the entire figure=28.26+34.54=62.8 cm

Therefore, the perimeter of the entire figure is 62.8 cm.

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The perimeter of whole path is 12.56 cm

Perimeter is the distance around the edge of a shape.

r1= 4.5cm, r2= 6.5cm

Perimeter of semicircle 1,

=πr1

= 3. 14 * 4.5

= 14.13 cm

Perimeter of semicircle 2

=πr2

= 3. 14 * 6.5

= 20.41 cm

Perimeter of path = 20.41 - 14.13 =6.28 cm

Perimeter of whole path = 2 * 6.28 =12.56

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[tex]y = 3x + 6 \\ switch \: y \: and \: x[/tex]

[tex]x = 3y + 6 \\ solve \: for \: y \\ x - 6 = 3y \\ y = \frac{x - 6}{3} [/tex]

Answer:

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Step-by-step explanaon

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The complement of y is 110 - 8x degrees.

Complementary angles are angles that add up to 90 degrees.

Therefore,

y = 8x - 20

The complement of y can be found as follows;

complement of y = 90 - (8x - 20)

complement of y = 90 - 8x + 20

complement of y = 110 - 8x

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The area of the playground of dimensions 18 and 240is 432 [tex]m^{2}[/tex].

Given  If the dimensions of the playground in the layout are given by 180 cm x 240 cm.

The area of rectangle is length *breadth.

The given playground is in the shape of rectangle because there are two sides given and both the sides are different. In a rectangle length of opposite side found to be equal and each side form an angle of 90 degree.

Area=length*breadth

=180*240

=43200 [tex]cm^{2}[/tex]

We have to convert in meters so we have to divide by 100.

Area=43200 [tex]cm^{2}[/tex]

=43200/100

=432 [tex]m^{2}[/tex]

Hence the area of playground having dimensions 180 cm and 240 cm is 432[tex]m^{2}[/tex].

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Answer:

3

Step-by-step explanation:

V=⅓b²h

16=⅓*16*h

16=16h/3

h=3cm

Answer:

9 students

Step-by-step explanation:

First find the amount of cross-country team students, 4% * 1125 = 45

Then 20% * 45 = 9, so 9 students in the team weigh between 60 and 70 kilos.

Answer:

SOLUTION :-

There is theorem/proof that tells that in these types of figure the other angle is double of the previous one

Means , the required angle will be ( 36 x 2 ) i.e. 72°.

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Answer:

78 m²

Step-by-step explanation:

V = bh

V = 13 m × 6 m

V = 78 m²

The correct option is (A). The solution of the equation is x=48.125.

Given an equation [tex]x+\frac{x}{7}+\frac{1}{11}\left(x+\frac{x}{7}\right)=60[/tex].

A statement that uses the equal sign to show that two expressions have the same value is called an equation. The equation is represented as ax+by=c.

Firstly, we will apply the distributive property to the given equation a×(b+c)=ab+ac, we get

[tex]x+\frac{x}{7}+\frac{x}{11}+\frac{x}{77}=60[/tex]

Now, we will simplify the right-hand side equation by taking LCM, we get

[tex]\begin{aligned}\frac{77x+11x+7x+x}{77}&=60\\ \frac{96x}{77}&=60\end[/tex]

Further, we will multiply both sides with 77, we get

77×(96x/77)=77×60

96x=4620

Then, we will divide both sides with 96, we get

96x/96=4620/96

x=48.125

Hence, the solution of the given equation [tex]x+\frac{x}{7}+\frac{x}{11}+\frac{x}{77}=60[/tex] is x=48.125.

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Answer:

The correct option is (A). The solution of the equation is x=48.125.

Given an equation .

A statement that uses the equal sign to show that two expressions have the same value is called an equation. The equation is represented as ax+by=c.

Firstly, we will apply the distributive property to the given equation a×(b+c)=ab+ac, we get

Now, we will simplify the right-hand side equation by taking LCM, we get

Further, we will multiply both sides with 77, we get

77×(96x/77)=77×60

96x=4620

Then, we will divide both sides with 96, we get

96x/96=4620/96

x=48.125

Hence, the solution of the given equation is x=48.125.

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Step-by-step explanation:

Answer:

Step-by-step explanation:

Answer:

x+10

Step-by-step explanation:

x is any number and sum means addition, so x(number) +(sum) 10(10)