The ratio of the lengths of the sides of a right triangle is 1: √3:2. What is the sine of the triangle's
smallest angle?

The solution to the following functions are 1) 6x5-3x4, 3x4+1, 6x5-3x4, 3x4 / (2x-1),  2)(x-1)/x3, (x-1)/x2 - 1/x,  (x-1)/x3, x-1

The relationship between two sets of numbers is described mathematically by a function. It is a mathematical equation that assigns a unique output value to each input value inside a specific domain. Functions are frequently expressed by a letter, such as  F(x) = 3x+ 4 or g(x), where the letter indicates the function and the input value is represented by the variable x.

Functions can be either linear or nonlinear, and they can have a single or numerous outputs for each value of the input. They are frequently employed to simulate real-world situations and generate predictions based on available information. Functions can be graphed on a coordinate plane to visualise their behavior, and they can be combined or transformed using various mathematical operations.

How to solve?

1)a. (fg)(x) = (3x4)(2x-1) = 6x5-3x4

b. (f-g)(x) = (3x4) - (2x-1) = 3x4+1

c. (f *g )(x) = (3x4) * (2x-1) = 6x5-3x4

d. (f/g) (x) = (3x4) / (2x-1) = 3x4 / (2x-1)

2)a. (fg)(x) = (x-1/x2) * (1/x) = (x-1)/x3

b. (f-g)(x) = (x-1/x2) - (1/x) = (x-1)/x2 - 1/x

c. (f *g )(x) = (x-1/x2) * (1/x) = (x-1)/x3

d. (f/g) (x) = (x-1/x2) / (1/x) = (x-1)/x2 / (1/x) = (x-1)/x2 * x = x-1

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[tex]\frac{7}{30}[/tex] of water is left in the pitcher

Least Common Multiple is a mathematical term. The smallest number that is a multiple of both of two numbers is called the least common multiple.

According to the given information

Total water in container = [tex]\frac{5}{6}[/tex]

Total water used to water the plants = [tex]\frac{3}{5}[/tex]

Water left in pitcher = [tex]\frac{5}{6} - \frac{3}{5}[/tex]

Taking LCM we will get

= [tex]\frac{25-18}{30}[/tex]

= [tex]\frac{7}{30}[/tex]

[tex]\frac{7}{30}[/tex] of water is left in the pitcher

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Answer:

c=65

Step-by-step explanation:

a=115

180-115=b

b=65

b=c

c=65

The theorem or principle that helps to solve the above is the properties of a parallelogram. On the basis of the same, we can state that the proof that Triangle ABC is congruent to Triangle ADC is the property that indicates that each diagonal of a parallelogram separates it into two congruent triangles. Hence, ΔABC ≅ Δ ADC.

There are six crucial parallelogram qualities to understand:

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Answer:

-12.5 -10.5n

Step-by-step explanation:

Use distributive property to solve:

1. -2.5 x -3 = 7.5

2. -2.5 x 4.2n = -10.5n

3. -2.5 x 8 = -20

Simplify:

7.5-20= -12.5

-12.5 -10.5n

By using the functions we have found the value of x and it is found out to be as x = -20/3.

What is a function?

In mathematics, a function from a set X to a set Y assigns to each element of X exactly one element of Y. The set X is called the domain of the function and the set Y is called the codomain of the function.

Given data:

f(x) = -4x + 1, g(x) = x2 - 8x + 21, and h(x) = 19 - 3x and h(x) = 39.

By using the h(x) function, we can write

               h(x) = 19 - 3x

                39 = 19 - 3x

                3x = 19 - 39

                3x = -20

                  x = -20/3

Hence, by using the functions we have found the value of x and it is found out to be as x = -20/3.

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Answer:

b=-2

Step-by-step explanation:

I dont have the steps srry :(

Answer:

b = -2

Step-by-step explanation:

7b + 3-4b= 3 - 3 (b +4)

Answer:

21

Step-by-step explanation:

The formula to find the common difference of an arithmetic sequence is: d = a(n) - a(n - 1), where a(n) is a term in the sequence, and a(n - 1) is its previous term in the sequence

What is arithmetic sequence?

A series of numbers called an arithmetic progression or arithmetic sequence has a constant difference between the terms. For instance, the number sequence 5, 7, 9, 11, 13, and 15 has a common difference of 2 in arithmetic.

Sequences can in fact begin at any number that we choose. A sequence with the general word an is commonly notated as ann=1 a n n = 1.

or d = (an + 1 - an) (an – an-1). AP reduces if the common difference is negative. For instance, the AP drops in these numbers: -4, -6, -8.

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Answer: -9/50

Step-by-step explanation: It's asking you to give the answer of A (5/12) - B (3/5), how you do it is simple, you subtract 5/12 and 3/5 like so: 5/12 3/5 = -0.18 and -0.18 as a fraction is -9/50

So there is your answer :)

Answer:

  12

Step-by-step explanation:

You want a 2-digit number that rounds to 10 and has 2 as one of its digits.

The integers that round to 10 are in the rangle 5–14. The only one of these that has a digit of 2 is 12.

The 2-digit number is 12.

One of the factors is present in all of the items mentioned. The order of the value of the other factor will match the order of the value of the product.

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Answer: 8.8 (-8.8'F)

Step-by-step explanation:

What we know:

Temperature started as 7.2

Temperature ended as -1.6

We need to find the difference

How to solve:

By doing simple subtraction, we can solve this.

Process:

Write equation                                                   7.2 - (-1.6) = ?

Simplify                                                               7.2 + 1.6 = ?

Solve                                                                                 = 8.8

Solution:  {8.8 (-8.8'F)}

The temperature decreased by 8.8'F, but it increased/changed by -8.8'F.

Answer:

---------------------------

Convert the statement into equation, considering the number as x, and solve:

Correct choice is B.

the time between high and low tide i 7. 8 hour. At high tide the depth of water i 19. 2 feet, while at low tide the depth i 5. 1 feet. So roughly 2 hours and 15 minutes, the depth will be 12 feet

What is depth?

a measurement made through an object or body of material, typically horizontally inward from an outer surface, upward from an upper surface, or upward from the top of something considered to be one of multiple layers. deepness, the property of being deep.

(0,6)

(8,20)

(16,6)

y = C*sin( k*pi*x) + 6 since (0,6) is given

C(sin(k*pi*8) + 6 = 20

C(sin(k*pi*8) = 14 <--- label this equation ALPHA

Also,

C(sin(k*pi*16) + 6 = 6

C(sin(k*pi*16) = 0

since C cannot be zero,  k*pi*16 must be 180 = pi

                                          k*16 = 1

 k = 1/.16

C(sin( (1/16)*pi*8) = 14

C ( sin (pi/2) ) = 14

C = 14

D(t) = 14 sin( (pi/16) t ) + 6 where D is the depth and t is time

12 = 14 sin((pi/16)t) + 6

6/14 = sin((pi/16)t)

arcsin(3/7)*16/pi = t

t = 2.25572...

So roughly 2 hours and 15 minutes, the depth will be 12 feet

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Answer: answer is b 12$.

Step-by-step explanation:

The number of fests of light that Mr Green needs 140 feet of lights

The perimeter is the distance around the object. For example, your house has a fenced yard. The perimeter is the length of the fence.

From the formula for perimeter L x W which will give us.L being 5 and W being 3.5

The equation is 5 × 3.5 = 17.5.

With that being said I just need to multiply that answer by 8 which gives us 140. This means that he will need 140 feet of light in order to put light around each window.

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Answer:

Step-by-step explanation:

can you send a much clear image its to blurry I can not read it.

Answer:

(4,12) Quadrant l

(-5,2) Quadrant ll

(-9,-4) Quadrant lV

(3,-3) Quadrant lll

Step-by-step explanation:

hope this helps!

[tex]\huge\text{Hey there!}[/tex]

[tex]\mathsf{6\%\ of\ 33.00}[/tex]

[tex]\mathsf{= \dfrac{6}{100}\ of\ 33.00}[/tex]

[tex]\mathsf{= \dfrac{6}{100}\times33.00}[/tex]

[tex]\mathsf{= \dfrac{6}{100}\times 33}[/tex]

[tex]\mathsf{= \dfrac{6}{100}\times \dfrac{33}{1}}[/tex]

[tex]\mathsf{= \dfrac{6\div2}{100\div2}\times \dfrac{33}{1}}[/tex]

[tex]\mathsf{= \dfrac{3}{50}\times\dfrac{33}{1}}[/tex]

[tex]\mathsf{= \dfrac{3\times 33}{50 \times1}}[/tex]

[tex]\mathsf{= \dfrac{99}{50}} \mathsf{\rightarrow 1 \dfrac{49}{50}}[/tex]

[tex]\huge\text{Answer: }[/tex]

[tex]\huge\boxed{\mathsf{\dfrac{99}{50} \ or\ 1\dfrac{49}{50}}}\huge\checkmark[/tex]

[tex]\uparrow\large\text{Either those should work because they are equivalent to (equal to)}\\\large\text{each other}\uparrow[/tex]

[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]

The solutions are that Two comparable triangles have proportional corresponding sides. And Two comparable triangles matching angles

Two triangles are said to be congruent if the length of the sides is equal, a measure of the angles are equal and they can be superimposed.

A triangle is a polygon that has three sides and three vertices. It is one of the basic figures in geometry.

For a regular polygon of any number of sides, therefore the sum of its exterior angle is 360°.

Given statements that the corresponding sides might be altered, they must still be proportionate.

The triangles will be congruent also, if they are.

But the angles must always line up otherwise the triangle's overall shape will change and it won't look the same.

Two comparable triangles must have proportional corresponding sides.

Two comparable triangles must matching angles match up.

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Answer:

z = 7

Step-by-step explanation:

We know that, sum of the exterior angles of a quadrilateral is added up to 360°.

Accordingly,

115 + 7z + 12z + 16z = 360

Combine like terms.

115 + 35z = 360

Subtract 115 from both sides.

35z = 360 - 115

35z = 245

Divide both sides by 35.

z = 7

Answer:

the answer is 306.25 feet and b is 8 sec

Step-by-step explanation:

Explanation

The height of the ball as a function of the time is given by the following formula:

A. Maximum height of the ball

To find the value of the maximum height, we maximum the function h(t) computing its first derivative and equalling the result to zero:

Solving the last equation for t, we get time t when the height is maximum:

So the maximum height is given by the value of h(t) when t = 2.5:

The maximum height is 196ft.

B. Time until the ball hits the ground

The ball will hit the ground when h(t) = 0. So we must find the value of t such that:

Solving this equation is equivalent to finding the roots of a second-order polynomial:

Where:

• a = -16,

,

• b = 80,

,

• c = 96.

The roots of this polynomial are given by the following formula:

s

Answer

A. The maximum height of the ball is 196 ft.

Answer: 2/8

Step-by-step explanation: 2/16 can be simplified to 1/8, 1/8 + 5/8 = 6/8, since a whole bone is 8/8, or 1. 8/8 - 6/8 = 2/8

so, once more, the answer is 2/8.

Answer:

Step-by-step explanation:

The slopes of the segments can be the same as long as the change in y divided by the change in x of both segments is the same. This means that the two segments are parallel.

The slope of a linear function represents the rate of change of the output variable y relative to the input variable x.

Hence, given two points on a line, the slope is calculated by the division of the change in y divided by the change in x.

As long as the changes are the same, two different segments can have the same slope, which is the case when they are parallel, meaning that they meet only at infinity.

One possible example of two parallel segments is given as follows:

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The resulting perfect square using the given trinomial is found as (4y + 9)².

a²-2ab+b² or a²+2ab+b²

since:

a²-2ab+b²  = (a-b)²

and

a²+2ab+b² = (a+b)²

A trinomial is written as the square of the a binomial in the equations above.

Knowing that the aforementioned equations are correct, we may use the binomial that has been provided and proceed backwards from there:

= (4y)² +__+ (9)² ....eq 1

a = 4y and b = 9.

Thus, 2ab = 2(4y)(9) = 72y

Put in eq 1;

=  (4y)² + 72y + (9)²

The resulting perfect square:

= (4y + 9)²

Thus, resulting perfect square using the given trinomial is found as (4y + 9)².

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Answer: asa

Step-by-step explanation: I just did this

Answer:

582.1

Step-by-step explanation: