How do I use the cosine rule for these problems?

Answer:

Option D:  - 6;  [tex]$ \textbf{-5}\frac{\textbf{5}}{\textbf{2}} $[/tex];   [tex]$ \textbf{-4}\frac{\textbf{1}}{\textbf{5}} $[/tex].

Step-by-step explanation:

The sequence is defined by:

[tex]$ A(n) = -6 + (n - 1)\bigg( \frac{1}{5} \bigg ) $[/tex]

To find the first term of the sequence simply substitute n = 1.

First term of the sequence:

[tex]$ A(1) = -6 + (1 - 1)\bigg( \frac{1}{5} \bigg ) $[/tex]

        [tex]$ = - 6 $[/tex]

Fourth term of the sequence:

[tex]$ A(2) = -6 + (4 - 1) \bigg ( \frac{1}{5} \bigg) $[/tex]

        [tex]$ = - 6 + 3\bigg( \frac{1}{5} \bigg) $[/tex]

        [tex]$ = \frac{- 30 + 3}{5} $[/tex]

        [tex]$ = \frac{-27}{5} $[/tex]

        [tex]$ = \frac{-25 - 2}{5} $[/tex]

        [tex]$ = - 5 - \frac{2}{5} $[/tex]

        [tex]$ = -5\frac{2}{5} $[/tex]   is the required answer.

Tenth term of the sequence:

[tex]$ A(10) = - 6 + (10 - 1) \bigg( \frac{1}{5} \bigg) $[/tex]

         [tex]$ = - 6 + 9\bigg( \frac{1}{5} \bigg) $[/tex]

         [tex]$ = \frac{-30 + 9}{5} $[/tex]

         [tex]$ = \frac{-21}{5} $[/tex]

         [tex]$ = \frac{-20 - 1}{5} $[/tex]

         [tex]$ = - 4 - \frac{1}{5} $[/tex]

         [tex]$ = -4\frac{1}{5} $[/tex]  is the required answer.

Answer:

x =3

Step-by-step explanation:

step 1:Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation :

                    3*x-5-(2*x-8)=0

step 2:solve x+3=0

subtract 3 from both sides

step 3:   x=-3

answer:x= -3

Answer:x=3

Step-by-step explanation:

Move variable to the left side and change its sign

3x-2+5=8

Move constant to the right side and change its sign

3x-2x=8-5

Combine like terms

X=3

Answer:

6.7

Step-by-step explanation:

the tenths place is one spot after the decimal

Answer: a) A'=(2, 3), B'=(-2,3), C'=(-2,-3) D'=(2,-3)

b) the measure of each angle is 90 degrees.

Step-by-step explanation:

a) To find the coordinates you need to know that (x,y) is changed to (-y,x). This means that they are flipped and changed from either negative to positive or positive to negative.

b) Each angle is 90 degrees because that shape is a rectangle with all equal right angles.  

The coordinates of the vertices of rectangle A'B'C'D' after rotating rectangle ABCD 90° about the origin are A'(-2,-3), B'(-2,3), C'(-2,-3), and D'(2,-3). All angles in rectangle A'B'C'D' measure 90°.

When a point is rotated 90° about the origin, the new coordinates can be found using the formula (y, -x). Therefore, applying this to each vertex of the rectangle, A'(3,-2) becomes A'(-2,-3), B'(3, 2) becomes B'(-2,3), C'(-3, 2) becomes C'(-2,-3) and D'(-3, -2) becomes D'(2,-3).

Since A'B'C'D' is a rectangle, all its angles are right angles. This means all the angles measure 90°.

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Answer:

y = - 8x + 9

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c

Given

8x + y = 9 ( subtract 8x from both sides )

y = - 8x + 9 ← in slope- intercept form

The required slope intercept of the given equation of the line is given as y = -8x + 9.

The slope of the line is a tangent angle made by line with horizontal. i.e. m =tanx where x in degrees.

The equation is the relationship between variables and represented as y = ax + b is an example of a polynomial equation.

Here,
Given the equation of the line,
8x + y = 9,

Rearrange the equation in slope intercept form,
y = -8x + 9

Thus, the required slope intercept of the given equation of the line is given as y = -8x + 9.

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To simulate the 20% probability of rain over three days, generate a random number between 1 and 100 for each day. Count the trials where all three numbers are between 21 to 100 as 'non-rainy' days. The experimental probability of no rain in three days is the ratio of 'non-rainy' trials to total trials.

Probability is a branch of mathematics that studies randomness and the chance of an event occurring. In this case, we can perform a simulation to experimentally determine the probability that it will not rain on the next 3 days even though there is a forecast of a 20% chance of rain.

One way to perform the said simulation is by using random numbers from 1 to 100. Why? Because probability can be expressed as a percentage, and the range from 1 to 100 encompasses all percentage possibilities (0% to 100%). So, for each day, we can generate a random number in this range. If the generated number falls in the range 1-20 (which represents the 20% predicted chance of rain), we consider that day as a 'rainy day'. If it falls in the range 21-100, we consider it a 'non-rainy day'.

We repeat this process for three days. The experimental probability of it not raining on all three days will be the ratio of favorable outcomes (all three numbers landing in the 'non-rainy day' range) to the total number of trials.

If we perform a large number of these three-day simulations, we'll have a good estimate of the experimental probability. The Law of Large Numbers ensures that as more trials are conducted, the experimental probability will approach the theoretical probability.

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To find out how long it took Juan to finish, we add the time differences to Jesse's time. Tim finished 12 seconds faster than Jesse and Juan finished 8 seconds faster than Tim.

To find out how long it took Juan to finish, we need to add the time differences to Jesse's time. First, we know that Tim finished 12 seconds faster than Jesse, so we can add 12 seconds to Jesse's time which becomes 2 minutes and 19 seconds. Next, we know that Juan finished 8 seconds faster than Tim, so we can add 8 seconds to Tim's time which becomes 2 minutes and 27 seconds. Therefore, it took Juan 2 minutes and 27 seconds to finish the race.

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Answer:

A(2,1) , B(-3,2) , C(-1,6)

Step-by-step explanation:

A translation of 2 units up means the y values will be shifted up 2 units

A (2,-1) -> A(2,1)

B (-3,0) -> B(-3,2)

C (-1,4) -> C(-1,6)

The vertices of the image of triangle ABC after a translation of 2 units up are A' (2, 1), B' (-3, 2), and C' (-1, 6), found by adding 2 to the y-coordinate of each original vertex.

The student has asked how to find the vertices of the image of triangle ABC after a translation of 2 units up. To do this, we simply add 2 to the y-coordinate of each vertex of the triangle. Here are the steps for the translation:

For vertex A (2, -1), the new position after translation is A' (2, -1 + 2) or A' (2, 1).

For vertex B (-3, 0), the new position after translation is B' (-3, 0 + 2) or B' (-3, 2).

For vertex C (-1, 4), the new position after translation is C' (-1, 4 + 2) or C' (-1, 6).

Therefore, the vertices of the image of triangle ABC after the translation are A' (2, 1), B' (-3, 2), and C' (-1, 6).

Answer:

n = 4

Step-by-step explanation:

Solve using the distributive property. This means you can multiply the number outside the brackets with each number inside the brackets. Then isolate "n" by moving all other numbers to the right side, leaving "n" alone on the left.

–2(5n + 7) + 8n = 2(1 – 3n)        Distribute

(5n)(-2) + (7)(-2) + 8n = (1)(2) – (3n)(2)  Multiply with each number in brackets

–10n + (–14) + 8n = 2 – 6n        Remove brackets around –14

–10n – 14 + 8n = 2 – 6n        Adding a negative is subtracting it's positive

–14 –2n = 2 – 6n        

–14 + 14 –2n = 2 + 14 – 6n        Add 14 to both sides

–2n = 16 – 6n        

–2n + 6n = 16 – 6n + 6n        Add 6n to both sides

4n = 16        

4n/4 = 16/4        Divide both sides by 4

n = 4        Solved for "n"

Check answer by substituting "4" whenever there is "n" in the original equation. Then solve each side.

–2(5n + 7) + 8n = 2(1 – 3n)

–2(5(4) + 7) + 8(4) = 2(1 – 3(4))         Solve inside brackets

–2(20 + 7) + 32 = 2(1 – 12)         Distribute

(20)(–2) + (7)(–2) + 32 = (1)(2) – (12) (2)        Multiply where necessary

–40 + (–14) + 32 = 2 – 24        Simplify

–22 = –22        Same answer

LS = RS        Left side equals right side

The answer we found is correct.

Total surface area of the square pyramid is 1476 cm².

Step-by-step explanation:

Total surface area of a pyramid = 12pl + B. Here p is perimeter of the base which is a square = 4 × side, l is the slant height and B is the area of the base = side²

Find perimeter of the base

⇒ p = 4 × side = 4 × 6 = 24 cm

Find the slant height of the prism. l² = height² + (side/2)² (Based on Pythagoras Theorem)

⇒ l² = 4² + (6/2)² = 16 + 9 = 25

⇒ l = √25 = 5 cm

Find the area of the base of the pyramid.

⇒ B = side² = 6² = 36 cm²

Calculate total surface area of the pyramid.

⇒ TSA = 12 × 24 × 5 + 36 = 1440 + 36 = 1476 cm²

Answer:

49 blue marbles

Step-by-step explanation:

From the question we are given;

We need to determine the number of blue marbles;

Assuming the number of red marbles is x

Then, blue marbles will be 5x + 4

Therefore;

x + 5x + 4 = 58

6x + 4 = 58

6x = 54

  x = 9

5x + 4 = 5(9) + 4 = 49

Therefore, the red marbles are 9 while the blue marbles are 49

Hence there are 49 blue marbles

Answer:

(3 , 2.5)

the trip would cost $12.5

12.5 = 3.5 (3)+2

12.5 = 3 (2.5)+5

Step-by-step explanation:

The distance at which the cost of each taxi is the same is 6 miles.

The trip would cost $23.

An equation is a mathematical statement that is made up of two expressions connected by an equal sign.

Example:

2x + 4 - 9 is an equation.

We have,

Taxi A:

c = 3.5d + 2

Taxi B:

c = 3d + 5

Where c is the cost of the taxi after d distance.

Now,

The cost of the taxi is the same.

3.5d + 2 = 3d + 5

3.5d - 3d = 5 - 2

0.5d = 3

d = 3/0.5

d = 30/5

d = 6

The cost of the taxi at d = 6.

c = 3.5d + 2 = 3.5 x 6 + 2 = 21 + 2 = 23

c = 3d + 5 = 3 x 6 + 5 = 18 + 5 = 23

Thus,

The cost of both taxis is the same after 5 miles.

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Answer:

A parabola with an x-intercept of (3, 0)  

Step-by-step explanation:

We can immediately rule out the first and third options, because the equation of a second degree function is a parabola.

Your equation is

ƒ(x) = x² - 6x + 9 = 0

We can factor this equation as

ƒ(x) = (x - 3)²

The parent parabola, y = x², has its x-intercept at (0,0).

Your function subtracts three from x, so the intercept is shifted three units to the right.

The graph of your function is a parabola with an x-intercept of (3, 0).

The figure below shows the graph of your function shifted three units by subtracting three from x.

Answer:

2 years

Step-by-step explanation:

K = 4D. K = D + 6

4D = D + 6

-D. -D

3D = 6

3. 3

D = 2

Answer:

d=2

Step-by-step explanation:

We can use the given information to write down two equations that describe the ages of Kevin and Daniel.

Let Kevin's current age be k and Daniel's current age be d.

k=4d

k=d+6

Now we have two independent equations, and we can solve for our two unknowns.

Since we are looking for d, and both of our equations have k alone on one side, this is a convenient time to use elimination.

Subtracting the second equation from the first equation, we get:

0=4d-(d+6)

which combines the information about d from both of our original equations.

Solving for d, we get: 3d = 6.

d=2

Answer:

The values of x and y in the diagonals of the parallelogram are x=0 and y=5

Step-by-step explanation:

Given that ABCD is a parallelogram

And segment AC=4x+10

From the figure we have the diagonals AC=3x+y and BD=2x+y

By the property of parallelogram the diagonals are congruent

∴ we can equate the diagonals AC=BD

That is 3x+y=2x+y

3x+y-(2x+y)=2x+y-(2x+y)

3x+y-2x-y=2x+y-2x-y

x+0=0 ( by adding the like terms )

∴ x=0

Given that segment AC=4x+10

Substitute x=0  we have AC=4(0)+10

=0+10

=10

∴ AC=10

Now (3x+y)+(2x+y)=10

5x+2y=10

Substitute x=0, 5(0)+2y=10

2y=10

[tex]y=\frac{10}{2}[/tex]

∴ y=5

∴ the values of x and y are x=0 and y=5

Answer:

  15/2

Step-by-step explanation:

Subtract 5x from both sides of the equation to find out.

  5x +3x -5x = 5x +15/2 -5x . . . . . . subtract 5x

  3x = 15/2 . . . . . . . . . . . . . . . . . . . . collect terms

The required value of 3x is 15/2.

Answer:

864 cards

Step-by-step explanation:

72 cards per set times 15 sets = 1080 cards - 216 cards he already has =864 cards

Step-by-step explanation:

[tex] \angle 1 [/tex] is the exterior angle of the given [tex] \triangle. [/tex]

Therefore, by remote exterior angle theorem.

[tex] \therefore \: m \angle \: 1 = 60 \degree + 63\degree \\ \\ \huge \red{ \boxed{\therefore \: m \angle \: 1 = 123 \degree }}[/tex]

Answer: 55 lbs of $0.40 and 45 lbs of $1.40

Step-by-step explanation:

Let's say that we have two buckets, one that weighs x pounds and the candies in it are $0.40 per pound and another that weighs 100-x pounds (because we know the two added together must be 100 pounds) and the candies in it are $1.40 per pound.

There is a third bucket that is made when you combine the two, it weighs 100 pounds and the candies in it are $0.85. Multiply the cents per pound by the pounds of the candy for each bucket and you get this equation:

0.4 * x + 1.4 (100-x) = 0.85 * 100

Solve!

0.4x + 140 - 1.4x = 85

-x + 140 = 85

-x = -55

x = 55

From this we get that 100 - x = 45.

So, the answer is 55 lbs of $0.40 and 45 lbs of $1.40

ANSWER: 55 lbs of $0.40 and 45 lbs of $1.40

Step-by-step explanation:

Let's say that we have two buckets, one that weighs x pounds and the candies in it are $0.40 per pound and another that weighs 100-x pounds (because we know the two added together must be 100 pounds) and the candies in it are $1.40 per pound.

There is a third bucket that is made when you combine the two, it weighs 100 pounds and the candies in it are $0.85. Multiply the cents per pound by the pounds of the candy for each bucket and you get this equation:

0.4 * x + 1.4 (100-x) = 0.85 * 100

Solve!

0.4x + 140 - 1.4x = 85

-x + 140 = 85 .

-x = -55

x = 55

From this we get that 100 - x = 45.

So, the answer is 55 lbs of $0.40 and 45 lbs of $1.40

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pronouns:she/they

Answer:  yes

Step-by-step explanation:

Answer:

10 degrees

Step-by-step explanation:

Divide 360 by however many sides or angles are within the polygon.

360/x

360/36

10

Answer:

I = 0.5[tex]t^{4}[/tex] + 6.5t³ + 16t² + 10t

Step-by-step explanation:

Given

V = [tex]\frac{I}{R}[/tex] ( multiply both sides by R )

I = VR

  = (0.5t³ + 6t² + 10t)(t + 1) ← distribute

  = 0.5[tex]t^{4}[/tex] + 6t³ + 10t² + 0.5t³ + 6t² + 10t ← collect like terms

  = 0.5[tex]t^{4}[/tex] + 6.5t³ + 16t² + 10t

Answer:

i have no clue

Step-by-step explanation:

ask someone else

Answer:6

Step-by-step explanation:

Dividing 750 by 125 you get 6

i dont know why i did thus

eeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee

Answer:

No

Step-by-step explanation:

A triangular prism has a uniform cross-section.A parallel cut of the solid will produce a cross section which is parallel to the triangular base.

A right prism contains uniform cross-sections, meaning the area of each cross-section is the same.

In this case, the position of the line indicating a cut will not produce polygons congruent to the base.

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

[tex]\bf{Which\ expressions\ are\ equivalent\ to\ \dfrac{2^5}{6^5}?}[/tex]

[tex]\bf{First:\ 2^5=2\times2\times2\times2\times2=4\times4\times2=16\times2\rightarrow32}[/tex]

[tex]\rightarrow\bf{2^5=32}[/tex]

[tex]\bf{Second: \ 6^5 = 6\times6\times6\times6\times6=36\times36\times2 = 1296\times6\rightarrow7,776}[/tex]

[tex]\rightarrow\bf{6^5=7,776}[/tex]

[tex]\bf{You\ can\ convert\ your\ new\ equation \ to (\text{ If this is helpful to you}):}\\\bf{\dfrac{32}{7,776}}[/tex]

[tex]\mathsf{\dfrac{32\div32}{7776\div32}}\\\\\mathsf{32\div32 = 1\leftarrow Your\ numerator}\\\\\mathsf{7,776\div32=243\leftarrow Your\ denominator}\\\\=\dfrac{1}{243}\\\\\boxed{\mathsf{Answer\#1: \dfrac{32}{7,776}}}\checkmark\\\\\boxed{\mathsf{Answer\#2:\dfrac{1}{243}}}\checkmark[/tex]

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

~[tex]\frak{LoveYourselfFirst:)}[/tex]

Answer:

Only B and C are correct

Step-by-step explanation:

Answer:

B edit: C is also correct and E isnt my bad

Step-by-step explanation:

The difference of d and 6 times 2

for the equation 2(d-6)

Answer:

$1910.1744

Step-by-step explanation:

To start we have to calculate how much the total will give us in one year,  for this we divide the number by 100 and multiply it by 102, so we will get that 2%  in one year

(1800 / 100) * (100 + 2) =

18 * 102

1836

Now we will repeat the procedure but instead of using the 1800 we will use the 1836 which will be what we will have when the first year ends.

(1836 / 100) * (100 + 2) =

18.36 * 102

1872.72

Finally we do the same with the new number

(1872.72 / 100) * (100 + 2) =

18.7272 * 102

1910.1744

So  in conclusion putting $1800 at the end of the 3 years we will get $1910.1744

$1910.1744 - $1800 = $110.1744

that is the exact amount of the profit that we will obtain.