Can the sine rule relationship in trigonometry be used with non right angled triangle

Answer:

The brainliest!

Step-by-step explanation:

c= 7/6k- 17(7/6)

6/7c = k - 17

k = 6/7c+17

Answer:

The next number going up or down?

Step-by-step explanation:

Down

20

5

Up

180

Answer:

60

Step-by-step explanation:

The sequence is to first add 20 and then divide by 2. To find the next number in the sequence, add 20. This means the next number in the sequence is 40+20=60.

Answer:

60

Step-by-step explanation:

The exterior angle is the sum of the opposite interior angles.

120 = x + the other angle next to x but not the one next to 120

Since it is an isosceles triangle

120 = x + x

120 = 2x

60 = x

Hope that helped!!! k

Answer:

13 and 14.

Step-by-step explanation:

So we have two consecutive integers.

Let's call the first integer a.

Since the integers are consecutive, the other integer must be (a+1) (one more than the last one).

We know that the sum of the greatest integer (or a+1) and twice the lesser integer (a) is 40. Therefore, we can write the following equation:

[tex](a+1)+2(a)=40[/tex]

The first term represents the greatest integer. The second term represents 2 times the lesser integer. And together, they equal 40.

Solve for a. Combine like terms:

[tex]a+1+2a=40\\3a+1=40[/tex]

Subtract 1 from both sides. The 1s on the left cancel:

[tex](3a+1)-1=(40)-1\\3a=39[/tex]

Divide both sides by 3:

[tex]\frac{3a}{3}=\frac{39}{3}\\a=13[/tex]

Therefore, a or the first integer is 13.

And the second integer is 14.

And we can check:

14+2(13)=14+26=40

Let the two consecutive integers be x and x + 1.

According to the question,

★ Greatest integer = x + 1

★ Lesser integer = x

The sum of the greatest integer and twice the lesser integer is 40. [ Given ]

⇒ ( x + 1 ) + 2 ( x ) = 40

⇒ x + 1 + 2x = 40

⇒ 3x + 1 = 40

⇒ 3x = 40 - 1

⇒ 3x = 39

⇒ x = 39/3

⇒ x = 13

★ x + 1 = 13 + 1 = 14

Hello, when x tends to [tex]\infty[/tex] the term with the highest degree will lead the behaviour.

In other words.

[tex]\displaystyle \lim_{x\rightarrow+\infty} {x^4+3x^3-2x+7}\\\\=\lim_{x\rightarrow+\infty} {x^4}\\\\=+\infty\\\\\\\displaystyle \lim_{x\rightarrow-\infty} {x^4+3x^3-2x+7}\\\\=\lim_{x\rightarrow-\infty} {x^4}\\\\=+\infty[/tex]

So, the answer B is correct.

Thank you.

As x → - ∞, then y → ∞ and x → ∞, then y → ∞. Then the correct option is B.

A statement, principle, or policy that creates the link between two variables is known as a function. Functions are found all across mathematics and are required for the creation of complex relationships.

The function is given below.

f(x) = x⁴ + 3x³ - 2x + 7

If the value of x approaches the negative infinity, then the value of the function will be

f(x) = x⁴ + 3x³ - 2x + 7

We know that the value of (x⁴ - 2x) is greater than the value of 3x³. Then the value of the function will approach the positive infinity.

If the value of x approaches the positive infinity, then the value of the function will be

f(x) = x⁴ + 3x³ - 2x + 7

We know that the value of (x⁴ + 3x³) is greater than the value of 2x. Then the value of the function will approach the positive infinity.

Thus, As x → - ∞, then y → ∞ and x → ∞, then y → ∞.

Then the correct option is B.

More about the function link is given below.

https://brainly.com/question/5245372

#SPJ2

Answer:

Number = 14

Step-by-step explanation:

It is given that,

Twice the sum of a number and seven is three times the number

Let the number be x. Twice of the number is 2x. Three times of the number is 3x.

So,

2(x+7)=3x is the equation that models the given scenario

Opening brackets on LHS,

2x+14=3x

Subtracting 2x on both the sides

2x-2x+14=3x-2x

14=x

So, the number is 14.

The number is 14.

The calculation is as follows:

Based on the above information, the calculation is as follows:

2(x+7)=3x  

2x+14=3x

x = 14

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Answer:

A

Step-by-step explanation:

So we have the quadratic equation and it's written in three equivalent forms:

[tex]f(x)=0.5x^2+x-1.5\\f(x)=0.5(x+1)^2-2\\f(x)=(0.5x+1.5)(x-1)[/tex]

Let's determine the characteristics of the quadratic equation with the given equations.

From the first equation, since the leading coefficient (0.5) is positive, we can be certain that the graph opens upwards.

Also, the constant term is -1.5, so the y-intercept is (0,-1.5).

The second equation is the vertex form. Vertex form has the format:

[tex]f(x)=a(x-h)^2-k[/tex]

Where (h,k) is the vertex. From the second equation we know that h is -1 (because (x+1) is the same as (x-(-1))) and k is -2. Therefore, the vertex is (-1,-2).

And since the graph points upwards, this means that (-1,-2) is the minimum point of the function. In other words, the range of the function is greater than or equal to -2. In interval notation, this is:

[tex][-2,\infty)[/tex]

This also means that the end behavior of the graph as a x approaches negative and positive infinity is positive infinity because the graph will always go straight up.

Also, the third form is the factored form. With that, we can solve for the zeros of the quadratic. The zeros are:

[tex]0.5x+1.5=0\text{ and } x-1=0\\0.5x=-1.5 \text{ and }x=1\\x=-3\text{ and }x=1[/tex]

Therefore, the graph crosses the x-axis at x=-3 and x=1.

So, from the three equations, we gathered the following information:

1) The graph curves upwards.

2) The roots of zeros of the function is (-3,0) and (1,0).

3) The y-intercept is (0,-1.5).

4) The vertex is (-1,-2). This is also the minimum point.

5) Therefore, the range of the graph is all values greater than or equal to -2.

6) The end behavior of the graph on both directions go towards positive infinity.

Therefore, our correct answer is A.

B is not correct because the line of symmetry (or the x-coordinate of the vertex) here is -1 and not 1/2.

C is not correct because the graph goes towards positive infinity since it shoots straight up.

And D is not correct because the y-intercept is (0,-1.5).

Step-by-step explanation:

So we have the quadratic equation and it's written in three equivalent forms:

\begin{gathered}f(x)=0.5x^2+x-1.5\\f(x)=0.5(x+1)^2-2\\f(x)=(0.5x+1.5)(x-1)\end{gathered}

f(x)=0.5x

2

+x−1.5

f(x)=0.5(x+1)

2

−2

f(x)=(0.5x+1.5)(x−1)

Let's determine the characteristics of the quadratic equation with the given equations.

From the first equation, since the leading coefficient (0.5) is positive, we can be certain that the graph opens upwards.

Also, the constant term is -1.5, so the y-intercept is (0,-1.5).

The second equation is the vertex form. Vertex form has the format:

f(x)=a(x-h)^2-kf(x)=a(x−h)

2

−k

Where (h,k) is the vertex. From the second equation we know that h is -1 (because (x+1) is the same as (x-(-1))) and k is -2. Therefore, the vertex is (-1,-2).

And since the graph points upwards, this means that (-1,-2) is the minimum point of the function. In other words, the range of the function is greater than or equal to -2. In interval notation, this is:

Answer: 2000

Step-by-step explanation:

Answer:

The density is 3.8 g

Step-by-step explanation:

D=M/V (Density= Mass divided by Volume)

5.7 divided by 1.5 is 3.8

equation is y = 8x

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

Explanation:

Divide each x and y pair like so: y/x

If we get the same result each time, then we have a direct proportion.

y/x = 32/4 = 8

y/x = 56/7 = 8

y/x = 96/12 = 8

Each time we get the same result 8, which is the constant of proportionality. The table does show a direct proportional relationship. The equation is y = 8x which is in the form y = kx. The k value is the constant of proportionality. So k = y/x.

Answer:

a. Probability is simply how likely something is to happen. Whenever we're unsure about the outcome of an event, we can talk about the probabilities of certain outcomes—how likely they are

b. Theoretical Probability. Experimental Probability.

Use theoretical probability by counting the favorable outcomes and put that in a fraction above all possible outcomes.

Use experimental probability by comparing the number of times the event occurs to the total number of trials.

Step-by-step explanation:

I don't really know what to explain.  :v

Answer:

1. 1435

2. 4235

3. WEAR

4. 6512

5. 3265

6. TERM

Step-by-step explanation:

In the first 3 questions, the number codes are:

1 = D

2 = E

3 = A

4 = R

5 = M

6 = W

In the last 3 questions, the number codes are:

1 = T

2 = E

3 = S

4 = R

5 = I

6 = M

Answer:

$0.14

Step-by-step explanation:

Hello!

To find the price per ounce you divide the total cost by the number of ounces

11.99/84 = 0.1427

Round to nearest hundredth

0.14

The answer is $0.14

Hope this helps!

Hello, let's note A the matrix, we need to find [tex]\lambda[/tex] such that A[tex]\lambda[/tex]=[tex]\lambda[/tex] I, where I is the identity matrix, so the determinant is 0, giving us the characteristic equation as

[tex]\left|\begin{array}{cc}1-\lambda&3\\-3&1-\lambda\end{array}\right|\\\\=(1-\lambda)^2+9\\\\=\lambda^2-2\lambda+10\\\\=0[/tex]

We just need to solve this equation using the discriminant.

[tex]\Delta=b^2-4ac=2^2-40=-36=(6i)^2[/tex]

And then the eigenvalues are.

[tex]\lambda_1=\dfrac{2-6i}{2}=\boxed{1-3i}\\\\\lambda_2=\boxed{1+3i}[/tex]

To find the basis, we have to solve the system of equations.

[tex]A\lambda_1-\lambda_1 I=\left[\begin{array}{cc}3i&3\\-3&3i\end{array}\right] \\\\=3\left[\begin{array}{cc}i&1\\-1&i\end{array}\right] \\\\\text{For a vector (a,b), we need to find a and b such that.}\\\\\begin{cases}ai+b=0\\-a+bi=0\end{cases}\\\\\text{(1,-i) is a base of this space, as i-i=0 and -1-}i^2\text{=-1+1=0.}[/tex]

[tex]A\lambda_2-\lambda_2 I=\left[\begin{array}{cc}-3i&3\\-3&-3i\end{array}\right] \\\\=3\left[\begin{array}{cc}-i&1\\-1&-i\end{array}\right]\\\\\text{For a vector (a,b), we need to find a and b such that.}\\\\\begin{cases}-ai+b=0\\-a-bi=0\end{cases}\\\\\text{(1,i) is a base of this space as -i+i=0 and -1-i*i=0.}[/tex]

Thank you

Answer:

2,267.9g

Step-by-step explanation:

2,267.9g is more precise than 2,268 g becasue it is providng the actual number, with decimals.  It is providind the most accurate weight, showing that it's just a tiny bit less than 2,268 g, but still has the exact weight.  2,268g on the other hand, is rounded up which is also good in some scenarios, but it's not as accuracte/precise as the exact amount of something.

Answer:

21 feet

Step-by-step explanation:

The pool has dimension 15 feet by 17 feet, which is in the form of a rectangle.

The area of the pool = length × width

                                   =  17 × 15

                                   = 255 square feet

Area of the pool and cement walkway = 483 square feet

Area of walkway = area of pool and walkway - Area of pool

                            = 483 - 255

                            = 228 square feet

Let's assume that the cement walkway has equal thickness across its perimeter, so that;

the dimension of the pool and the cement walkway = 23 feet × 21 feet

The width of the cement walkway is 21 feet.

Answer:

5 seconds

1220 ft

Step-by-step explanation:

Step 1: Know when the stone reaches the maximum height

We know the maximum or minimum height of a parabola is at the vertex so we need to find the vertex

Step 2: Calculate the vertex

The t coordinate of the vertex can be calculated with [tex]\frac{-b}{2a}[/tex]

b = 160

a = 16

[tex]t=\frac{-(160)}{2(-16)}\\t=\frac{-160}{-32}\\t=5[/tex]

Step 3: We know the t coordinate we can find the height at that time

[tex]h_{(t)} =-16(5)^{2} +160(5)+20\\h_{(t)}=16(25)+ (800)+20\\h_{(t)}=400+ 800+20\\h_{(t)}=1220[/tex]

Therefore the stone reaches its maximum height of 1220 ft in 5 secs

Answer:

The maximum height of 420 feet is reached after 5 seconds.

Step-by-step explanation:

Answer:

[see below]

Step-by-step explanation:

Reflection across the x-axis is: [tex](x,y)\rightarrow(x,-y)[/tex]

Apply that to the point: [tex](4,-6.5)\rightarrow(4,6.5)[/tex].

Reflection across the y axis: [tex](x,y)\rightarrow(-x,y)[/tex]

Apply that to the point: [tex](4,-6.5)\rightarrow(-4,-6.5)[/tex]

Hope this helps.

Answer:

(27+x)/6

Step-by-step explanation:

(2x)/3 + (9-x)/2

Get a common denominator of 6

(2x)/3 *2/2 + (9-x)/2*3/3

4x/6  +3(9-x)/6

Distribute

4x/6 + (27-3x)/6

Combine like terms

(27+4x-3x)/6

(27+x)/6

Answer:

Option (4)

Step-by-step explanation:

From the given circle O,

AC and BD are the diameters intersecting at point O.

∠AOB ≅ ∠COD [Vertical angles]

Therefore, length of intercepted arcs by these central angles will be same.

[tex]m(\widehat{AB})=m(\widehat{CD})[/tex]

(3x - 70) = (x + 10)

3x - x = 70 + 10

2x = 80

x = 40

Since, [tex]m(\widehat{AB})+m(\widehat{BC})=180[/tex] [Since AC is a diameter]

(3x - 70) + [tex]m(\widehat{BC})[/tex] = 180°

3(40) - 70 + [tex]m(\widehat{BC})[/tex] = 180°

[tex]m(\widehat{BC})[/tex] = 180° - 50°

           = 130°

Therefore, Option (4) will be the correct option.

Answer:

130 degrees

Step-by-step explanation:

Answer:

This is  called a mid segment theorem in which the al ine segment (DE) joining the midpoints of two sides of a triangle is parallel to the third side.

Step-by-step explanation:

Suppose we have a triangle ABC. Then the midpoints can be located as D, E and F. If we join D , E and F another triangle is formed.

From the figure we can see that

AE≅ CE

AD≅DB

BF≅CF  

BECAUSE  all the given points are the midpoints which divide the lines into two equal halves.

If we increase the line DE to a point L we find out that DL is parallel to BC i.e. it does not meet at any point with BC. ( the two lines do not meet)

(1)

If we join C with L we find out that the the line DE is half in length to the line BC.

AS

AE= CE  (midpoints dividing into equal line segements.)

LE= DE

Triangle CEL= Triangle DEF

so

DL= BC

But DE = 1/2 DL

therefore

DE= 1/2 BC (2)

Therefore from 1 and 2 we find that a line segment (DE) joining the midpoints of two sides of a triangle is parallel to the third side

Answer:

according to circle theorem the angle in the center is twice of the angle of the angle form by the cords of the circle.

Since, the center circle is 90 theta is 45 degrees

Step-by-step explanation:

*Another approach

Answer:

Hey again! Just remember about the number lines. If it's easier, you can use a calculator to divide the fractions to make them easier to visualize in decimal form.

The answer to this one is:

-2.4

-2.25

-11/5 (which is -2.2)

-15/10 (1.5)

-1.6

Derrick's value = 0

Ari's value = 0.5

Wesley's value = 2.1

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

Explanation:

Derrick doesn't shade anything, so his value is 0.

Ari shades half of one model, so 1/2 = 0.5 is his value

Wesley shades 2 full models, plus 1/10 = 0.1 of another one, leading to 2+0.1 = 2.1 as his value.

The fractional amount of the model shaded by each of the boys are :

The size of each model cut out = 1/100 = 0.01

DERRICK :

ARI :

WESLEY

Therefore, the amount shaded by each of the boys represented as a decimal are :

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Answer:

The answer is

Step-by-step explanation:

Equation of a line is y = mx + c

where

m is the slope

c is the y intercept

To find the equation of the line parallel to 3x - y = 14 we must first find the slope of 3x - y = 14.

So we have

y = 3x - 14

Comparing with the general equation above

Slope / m = 3

Since the lines are parallel their slope are also the same

So slope of parallel line = 3

Equation of the line using point ( - 4 , -7) and slope 3 is

We have the final answer as

Hope this helps you

Answer:

(-53)/80

Step-by-step explanation:

Simplify the following:

-23/30 + 5/48

Put -23/30 + 5/48 over the common denominator 240. -23/30 + 5/48 = (8 (-23))/240 + (5×5)/240:

(8 (-23))/240 + (5×5)/240

8 (-23) = -184:

(-184)/240 + (5×5)/240

5×5 = 25:

(-184)/240 + 25/240

-184/240 + 25/240 = (-184 + 25)/240:

(-184 + 25)/240

-184 + 25 = -159:

(-159)/240

The gcd of -159 and 240 is 3, so (-159)/240 = (3 (-53))/(3×80) = 3/3×(-53)/80 = (-53)/80:

Answer: (-53)/80

Answer:

29 years

Step-by-step explanation:

The population of the Chinese people is 1.3 bn, and they grow at a rate of 0.49% per year. To get the number of years it requires to reach 1.5 bn, we use this method

after x years, the population will be

1.3 * 1.0049^x

so you just need to solve

1.3 * 1.0049^x = 1.5

1.0049^x = 1.5/1.3

x log 1.0049 = log(1.5/1.3)

x = log(1.5/1.3)/log(1.0049)

x = 0.062 / 0.002122

x = 29.25 years

Therefore, at the rate of 0.49%, the Chinese population of 1.3bn needs 29 years to clock 1.5 bn

Answer:

B) -4 and E) 4

Step-by-step explanation:

Answer:

68.5

Step-by-step explanation:

Subtract 4 from 73.

You get 69.

Then, subtract 0.5 more.

Your answer is 68.5.

Hope it helps!