a
2a
3a
5a
The sum of the first five terms of this sequence is 228
Work out the value of a,

Answer:

1. 96

2. 84

Step-by-step explanation:

I used the Circle theorems:

For 1 you use the alternate segment theory

For 2 you use the theory that opposite angles in a cyclic quadrilateral add up to 180.

I can't be asked to explain it properly I'm sorry but if no one else does it properly you can give me brainliest?

The equation represents the general form a circle with a center at

(–2, –3) and a diameter of 8 units is,

[tex]x^{2} +4x+y^{2} +6y-3=0[/tex]

Given that,circle with a center at (–2, –3)

diameter of circle is  8 units

To find

the equation of the circle that represents the general form of a circle with a center at (–2, –3) and a diameter of 8 units.

Radius of the Circle is,

The diameter of the circle is 8 units. therefore,

[tex]radius=\frac{d}{2}=\frac{8}{2} =4[/tex]

Equation of a circle

The equation of the circle that represents the general form of a circle with a center at (–2, –3) and a radius of 4 units.

[tex](x-h)^{2} +(y-k)^{2} =R^{2}[/tex]

Substituting the values,

[tex](x-(-2))^{2} + (y-(-3))^{2} =4^{2}[/tex]

[tex](x+2)^{2} + (y+3)^{2} =4^{2}\\[/tex]

[tex]x^{2} +4x+4+y^{2} +6y+9=0[/tex]

[tex]x^{2} +4x+y^{2} +6y-3=0[/tex]

Therefore, the option C is correct.

The equation represents the general form a circle with a center at

(–2, –3) and a diameter of 8 units is

[tex]x^{2} +4x+y^{2} +6y-3=0[/tex]

To learn more about the general form of circle visit:

https://brainly.com/question/3612143

Answer:

9%

Step-by-step explanation:

67 + 24 = 91%

100- 91 = 9%

This means they lost 9% of their games.

The requried football team lost 9% of their matches.

The percentage is the ratio of the composition of matter to the overall composition of matter multiplied by 100.

Since the football team won 67% of their matches and drew 24% of them, the percentage of matches they lost can be found by subtracting the percentage of matches they won and the percentage of matches they drew from 100%:

Percentage of matches lost = 100% - 67% - 24%

Percentage of matches lost = 9%

Therefore, the football team lost 9% of their matches.

Learn more about percentages here:

brainly.com/question/13450942

#SPJ3

average speed= total distance/total time taken

60+45= 105miles

1 mile= 1.609

105×1.609= 168.945km

168.945/4

Hence answer = 33.79 km/hr

Answer:

To find Alex's average speed for the whole journey, we can use the formula:

Average Speed = Total Distance / Total Time

Let's calculate the total distance traveled first:

Distance1 = 60 miles/hour * 3 hours = 180 miles

Distance2 = 45 miles/hour * 2 hours = 90 miles

Total Distance = Distance1 + Distance2 = 180 miles + 90 miles = 270 miles

Next, let's calculate the total time taken for the whole journey:

Total Time = 3 hours + 2 hours = 5 hours

Now, we can find the average speed:

Average Speed = 270 miles / 5 hours = 54 miles per hour

So, Alex's average speed for the whole journey is 54 miles per hour.

Please mark as Brainliest

Answer:

The answer is D : (10,9)

Step-by-step explanation:

As you can see... the cordinate (10,9) is far away from the other points, therefore it is clearly the outlier of the data set

Answer:

Explicit rule, because you can find the 40th term directly using the explicit rule. You would need to find the first 39 terms before finding the 40th terms using recursive rule.

hope this helps...

Answer:

8 1/2

or 8.5

Step-by-step explanation:

Answer:

The second one, √4^9

Sorry lol i posted the answer in the questions section by accident

Answer:

True

Step-by-step explanation:

The equation 2x² - 3x + 1 = 0 is in quadratic form.

Answer:

True.

Step-by-step explanation:

The equation [tex]2x^{2} - 3x + 1 = 0[/tex] is in quadratic form because it meets the quadratic formula: [tex]Ax^{2} + Bx + C = 0[/tex].

Answer:

2a+6

I'm sure of it!!

trust me

Answer:

The zoo was open 362 days and had an average of 272 visitors a day.

Step-by-step explanation:

365-3=362

98,464÷362=272

Answer: $1.08

Step-by-step explanation:

30cent x 4 = 120 cents. 1 dollar and 20 cents, $3 - $1.20 = $1.08

Answer:

Billy has 1.8 dollars left.

Step-by-step explanation:

So, .30 x 4 is 1.2. I subtracted 1.2 from 3 and got 1.8. I hope it's the right answer and wish you luck on the rest of your work!

Correct Question :-

If sec[tex]\theta[/tex] + tan[tex]\theta[/tex]= x , then prove that ,

[tex]\implies\sf sin\theta =\dfrac{x^2-1}{x^2+1}[/tex]

Proof :-

Here we are given that ,

[tex]\longrightarrow \sec\theta + tan\theta = x[/tex]

Firstly write everything in terms of sine and cosine .

[tex]\longrightarrow \dfrac{1}{\cos\theta}+\dfrac{\sin\theta}{\cos\theta}=x [/tex]

Add ,

[tex]\longrightarrow \dfrac{1+\sin\theta}{\cos\theta}=x [/tex]

On squaring both sides , we have ;

[tex]\longrightarrow \dfrac{(\sin\theta+1)^2}{(\cos\theta)^2}=x^2[/tex]

Simplify using identity sin²x + cos²x = 1 ,

[tex]\longrightarrow \dfrac{(1+\sin\theta)^2}{1-\sin^2\theta}=x^2 [/tex]

Simplify using identity (a+b)(a-b)=a²-b² ,

[tex]\longrightarrow \dfrac{(1+\sin\theta)^2}{(1+\sin\theta)(1-\sin\theta)}=x^2 [/tex]

Simplify,

[tex]\longrightarrow \dfrac{1+\sin\theta}{1-\sin\theta}=x^2 [/tex]

On using Componendo and Dividendo , we have ;

[tex]\longrightarrow \dfrac{1+\sin\theta+1-\sin\theta}{1+\sin\theta-1+\sin\theta}=\dfrac{x^2+1}{x^2-1}[/tex]

[tex]\longrightarrow \dfrac{2}{2\sin\theta}=\dfrac{x^2+1}{x^2-1}[/tex]

Simplify,

[tex]\longrightarrow \dfrac{1}{\sin\theta}=\dfrac{x^2+1}{x^2-1}\\[/tex]

Divide both the sides by 1 ,

[tex]\longrightarrow \underline{\underline{\sin\theta =\dfrac{x^2-1}{x^2+1}}} [/tex]

Hence proved .

And we are done !

[tex]\rule{200}4[/tex]

1) Trigonometric table :-

[tex]\small{ \begin{tabular}{|c|c|c|c|c|c|} \cline{1-6} \theta & \sf 0^{\circ} & \sf 30^{\circ} & \sf 45^{\circ} & \sf 60^{\circ} & \sf 90^{\circ} \\ \cline{1-6} $ \sin $ & 0 & $\dfrac{1}{2 }$ & $\dfrac{1}{ \sqrt{2} }$ & $\dfrac{ \sqrt{3}}{2}$ & 1 \\ \cline{1-6} $ \cos $ & 1 & $ \dfrac{ \sqrt{ 3 }}{2} } $ & $ \dfrac{1}{ \sqrt{2} } $ & $ \dfrac{ 1 }{ 2 } $ & 0 \\ \cline{1-6} $ \tan $ & 0 & $ \dfrac{1}{ \sqrt{3} } $ & 1 & $ \sqrt{3} $ & $ \infty $ \\ \cline{1-6} \cot & $ \infty $ &$ \sqrt{3} $ & 1 & $ \dfrac{1}{ \sqrt{3} } $ &0 \\ \cline{1 - 6} \sec & 1 & $ \dfrac{2}{ \sqrt{3}} $ & $ \sqrt{2} $ & 2 & $ \infty $ \\ \cline{1-6} \csc & $ \infty $ & 2 & $ \sqrt{2 } $ & $ \dfrac{ 2 }{ \sqrt{ 3 } } $ & 1 \\ \cline{1 - 6}\end{tabular}}[/tex]

[tex]\rule{200}4[/tex]

2) Important identities :-

[tex]\boxed{\begin{minipage}{6cm} Important Trigonometric identities :- \\ \\ $\: \: 1)\:\sin^2\theta+\cos^2\theta=1 \\ \\ 2)\:\sin^2\theta= 1-\cos^2\theta \\ \\ 3)\:\cos^2\theta=1-\sin^2\theta \\ \\ 4)\:1+\cot^2\theta=\text{cosec}^2 \, \theta \\ \\5)\: \text{cosec}^2 \, \theta-\cot^2\theta =1 \\ \\ 6)\:\text{cosec}^2 \, \theta= 1+\cot^2\theta \\\ \\ 7)\:\sec^2\theta=1+\tan^2\theta \\ \\ 8)\:\sec^2\theta-\tan^2\theta=1 \\ \\ 9)\:\tan^2\theta=\sec^2\theta-1$\end{minipage}}[/tex]

[tex]\rule{200}4[/tex]

If sec theta + tan theta equals to x then prove that:-

[tex]\longrightarrow \: sin \theta = \frac{ {x}^{2} - { \bold{1}} }{ {x}^{2} + 1 } [/tex]

Given that:

[tex]\longrightarrow \: sec \: \theta + tan \: \theta =x \: \: ..(i) [/tex]

We have to prove:

[tex]\longrightarrow \: sin \: \theta = \frac{ {x}^{2} - 1 }{ {x}^{2} + 1} [/tex]

We know that:

[tex]\longrightarrow \: { \sec}^{2} \theta \: - \: { \tan}^{2} \theta = 1[/tex]

[tex] \longrightarrow ( \sec \: \theta \: + \: \tan \: \theta)( \sec \: \theta - \tan \: \theta )[/tex]

[tex] \longrightarrow x( \sec \: \theta - \tan \: \theta) \: = 1[/tex]

[tex] \longrightarrow \: \sec \theta - \tan \: \theta = \frac{1}{x} \ ..(ii)[/tex]

Adding equation (i) and (ii), we get:

[tex] \longrightarrow \: 2\sec \theta = x + \frac{1}{x} [/tex]

[tex] \longrightarrow \: 2 \sec \: \theta = \frac{ {x}^{2} + 1}{x} [/tex]

[tex] \longrightarrow \: \sec \: \theta = \frac{ {x}^{2} + 1}{2x} [/tex]

[tex] \longrightarrow \: \cos \: \theta = \frac{2x}{ {x}^{2} + 1 } [/tex]

Now, we know that:

[tex] \longrightarrow \: { \sin}^{2} \theta + { \cos }^{2} \: \theta = 1[/tex]

Therefore,

[tex] \longrightarrow \: \sin \theta \: = \sqrt{1 - { \cos }^{2} } \: \theta[/tex]

[tex] \longrightarrow \: \sin \: \theta = {\sqrt{1 - ( \frac{2x}{ {x}^{2} + 1} } )}^{2} [/tex]

[tex] \longrightarrow \: \sin \: \theta = \sqrt{ \frac{ {({x}^{2} + 1)}^{2} - {(2x)}^{2} }{( {x}^{2} + 1)} } [/tex]

[tex] \longrightarrow \: \sin \: \theta = \sqrt{ \frac{ {x}^{4} \: + 2 {x}^{2} + 1 - \: 4 {x}^{2} }{( {x}^{2} { + 1)}^{2} } } [/tex]

[tex] \longrightarrow \: \sin \: \theta = \sqrt{ \frac{ {x}^{4} - {2x}^{2} + 1 }{( {x}^{2} { + 1)}^{2} } } [/tex]

[tex] \longrightarrow \: \sin \: \theta = \sqrt{ \frac{( {x}^{2} { - 1)}^{2} }{ {(x}^{2} + {1)}^{2} } } [/tex]

[tex] \longrightarrow \: \sin \: \theta = \frac{ {x}^{2} - 1 }{ {x}^{2} + 1} [/tex]

[tex] \: [/tex]

Answer:

a

Step-by-step explanation:

Answer:

r = 3

Step-by-step explanation:

[tex]\dfrac{r}{2} - 3 = 3(4 - \dfrac{3r}{2} )[/tex]

The first step to solve for "r" is to simplify the distributive property on the RHS. To simplify the distributive property, we need to multiply the term outside the parenthesis with the terms inside the parenthesis.

[tex]\rightarrow \dfrac{r}{2} - 3 = 12 - \dfrac{9r}{2}[/tex]

Now, add 9r/2 and 3 both sides to isolate the constants and variables.

[tex]\rightarrow \dfrac{r}{2} + \dfrac{9r}{2} = 12 + 3[/tex]

Simplify both sides.

[tex]\rightarrow \dfrac{10r}{2}= 12 + 3[/tex]

[tex]\rightarrow 5r = 15[/tex]

Divide 5 both sides.

[tex]\rightarrow \boxed{r = \frac{15}{5} = 3}[/tex]

Answer:

10

Step-by-step explanation:

Given;

a = 2

b = 3

c =4

ab+c

Solve;

Since a = 2, b = 3, and c = 4

Substitute

(2)(3)+4

6 +4

= 10

Answer = 10

~Learn with lenvy~

Answer:

10

Step-by-step explanation:

Given the following question:

[tex]a=2[/tex]
[tex]b=3[/tex]
[tex]c=4[/tex]
[tex]ab+c[/tex]

To find the answer we need to substitute the values in for the variables and then solve using PEMDAS.

[tex]ab+c[/tex]
[tex]2\times3+4[/tex]
[tex]2\times3=6[/tex]
[tex]6+4[/tex]
[tex]6+4=10[/tex]
[tex]=10[/tex]

Your answer is "10."

Hope this helps.

Answer:

9m

Step-by-step explanation:

A parallelogram you have listed has the following side lengths:
1.8m and 5m.

First, we need to understand the formula and simply comprehend it.
In this case, we're dealing with an area of a quadrilateral which is a four-sided shape.

The area is base times height.

You will simply need to do 1.8 x 5 = m

That is pretty simple. You need to setup a question like this:

1.8

x 5

____

 9.0

Remember you need to move the decimal point when you're done mulitplying. This case 9.0 is simply 9 by itself.

Answer:

(-2, -9)

explanation:

original coordinates of B: (7, 9)

use the formula: (x, y) ---> (x, -y)

If horizontally shifted there will be change in x axis,

Answer:

see down

Step-by-step explanation:

10. a one to one function means only one  input goes to the same output,

this one is not a one to one function, because there is 2 out put for each input except vertx

Answer:

1.x,y is the answer to first question

2.y=2x+5

Answer:

16: 28 is the answer for the above question

Using the definition of the floor function, it is found that the correct statement is:

Because 2 is the greatest integer not greater than 2.4, and –3 is the greatest integer not greater than –2.4.

Modeled by [x], it is the value of the greatest integer that is not greater than x.

Hence, in this problem:

Hence, the correct statement is:

Because 2 is the greatest integer not greater than 2.4, and –3 is the greatest integer not greater than –2.4.

More can be learned about the floor function at https://brainly.com/question/15457745

Answer:

a

Step-by-step explanation:

on edge

Answer:

-6x - 2y = 10 and -24x - 8y = 40
-4x + 3y = 20 and 12x - 9y = -60
2x + 5y = 18 and 4x + 10y = 36

Step-by-step explanation:

first equation with second row second equation
third equation with second row first equation

second equation with second row third equation

for the line that goes up - it cuts the y-axis at - 5  (p = -5)

when we take 2 points we go from one to the other by going to the right of 1 unit and going up of 3 units (slope m : 3/1)

=> y = 3x - 5

and

for the line which goes down - it cuts the y-axis in +2 (p=2)

when we take 2 points we go from one to the other by going to the right of 2 units and going down of 1 unit (slope m : -1/2)

=> y = -1/2x + 2

=> y + 1/2x = 2

2x + 4y = 8

=> B

Answer:

6

Step-by-step explanation:

There are 6 faces on a die so on average, one has to roll a fair die 6 times in order to get number 6 to show.

On average it's 6 as 6 sides a die has

But

i.e

There is 1/6 chances getting any number

Answer:

Penta Trinomial

Step-by-step explanation:

Highest power is 5 (penta)

Highest number of term is 3 (tri)

Answer:

Step-by-step explanation:

Given polynomial

It has 3 terms so is trinomial

It has degrees as

As the greatest degree is 6, this expression is 6th degree trinomial

Answer:

No biscuits.

Step-by-step explanation:

We know that there is a total of 100 biscuits.
Let's assign variables.

X=Icing
Y=Hundreds and Thousands

Z=Cherries

X appears every 5 biscuits, y appears every 8 biscuits, and z appears every 9 biscuits. Let's start solving by finding their multiples that are less than or equal to 100.

X: 5,10,15,20,25,30,35,40,45,50,55,60,65,70,75,80,85,90,95,100

Y: 8,16,24,32,40,48,56,64,72,80,88,96

Z: 9,18,27,36,45,54,63,72,81,90,99

The multiples need to be a multiple of 5,8, and 9.

The numbers that have both x and y are: 40 and 80

The numbers that have both x and z are: 45 and 90.

Seeing as the numbers never overlap, there are no biscuits that have x,y, and z.

Note: If you like my answer, please rate it a 5 and click thanks! (It helps with my leveling. If you want to be extra nice, you can also give me brainliest if you want!) If you think there is something wrong with my answer or that there is something I should improve on, please leave it in the comments.

Answer:

its 11:09 pm......

Step-by-step explanation:

are u on pc?