7, 9, 13 are the first three terms of a sequence with
nth term = an² + bn + c.
(i) By substituting n = 1, 2 and 3 set up three simultaneous equations in
a, b and c.
(ii) Solve your simultaneous equations and hence write down an
expression for the nth term.

Angle DAB will be equal to angle CAB

Trigonometry is the branch of mathematics which set up a relationship between the sides and angle of the right-angle triangles.

AC is a straight line and forms one of the sides of the triangle ABC. If point D is placed on line AC, angle DAB would remain equal to angle CAB since they are on the same line the angle formed with line AB remains the same.

To know more about Trigonometry follow

https://brainly.com/question/24349828

#SPJ1

Answer: The answer is x = +/- [tex]\sqrt{y+1}[/tex].

Step-by-step explanation: You can solve this by simply rearranging the equation to make x by itself.

-[tex]x^{2}[/tex] = -y - 1

Then cancel out the -1 by dividing it through to obtain.

[tex]x^{2} =y+1[/tex]

The final step is to square root both sides to get rid of the exponent.

x = [tex]\sqrt{y+1}[/tex]

This should be the answer since square roots have a +/-.

Answer:

  6/x²

Step-by-step explanation:

Rational expressions are added the same way numerical fractions are added. Their sum is the quotient of the sum of numerators, and the common denominator.

__

The given fractions already have the same denominator, so we simply add their numerators.

  [tex]\dfrac{2}{x^2}+\dfrac{4}{x^2}=\dfrac{2+4}{x^2}=\boxed{\dfrac{6}{x^2}}[/tex]

Answer:

[tex]\dfrac{1}{4}[/tex]

Step-by-step explanation:

Given information:

We can assume that 3 pupils play the flute only as we have also been told that 6 pupils play both instruments.

To calculate the probability that a randomly chosen pupil plays neither instrument, first determine how many pupils do not play an instrument by subtracting the number of pupils who do play an instrument from the total number of pupils:

⇒ total number of pupils - pupils who play instruments

⇒ 20 - (3 + 6 + 6)

⇒ 20 - 15

⇒ 5

Therefore, 5 pupils do not play the piano and/or flute.

To calculate probability:

[tex]\sf Probability\:of\:an\:event\:occurring = \dfrac{Number\:of\:ways\:it\:can\:occur}{Total\:number\:of\:possible\:outcomes}[/tex]

Therefore:

[tex]\implies \textsf{Probability of a pupil playing neither instrument} = \dfrac{5}{20}=\dfrac{1}{4}[/tex]

Answer:

The group that is most likely able to have a lower mean age of painting students is Group A

Step-by-step explanation:

mean = sum of all terms divided by total number of terms

Looking at the graph data you have provided you can see that group A's students are a younger than students in Group B.

Which means when you calculate the mean the group which would give you the lower ratio with the same denominator of K (let there is K number of students in the class) will have lower mean age

here group A students are younger therefore their ratio will be lower

hence lower mean age

more mean based questions at

https://brainly.com/question/26509052

#SPJ10

Answer: A stretch by a factor of 2 for the exponential growth function f(x)= a(9/4)^x occurs when a =✔ 2

A stretch by a factor of 11/3  for the exponential decay function f(x)= a(3/5)^x occurs when a =✔ 11/3

A shrink by a factor of 1/3 for the exponential growth function f(x)= a(7)^x occurs when a =✔ 1/3

A shrink by a factor of 2/5  for the exponential decay function f(x)= a(2/9)^x occurs when a =✔ 2/5

Step-by-step explanation:

The exponential growth equation is stretched and compressed by a scale factor k = 2 , 11/3 , 1/3 and 2/5

The exponential growth or decay formula is given by

x ( t ) = x₀ × ( 1 + r )ⁿ

x ( t ) is the value at time t

x₀ is the initial value at time t = 0.

r is the growth rate when r>0 or decay rate when r<0, in percent

t is the time in discrete intervals and selected time units

Given data ,

Let the exponential growth equation be represented as A

Now , the value of A is

For the exponential growth function f(x)= a(9/4)ˣ, a stretch by a factor of 2 occurs when a = 2

For the exponential decay function f(x)= a(3/5)ˣ, a stretch by a factor of 11/3 occurs when a = 11/3

For the exponential growth function f(x)= a(7)ˣ, a shrink by a factor of 1/3 occurs when a = 1/3

For the exponential decay function f(x)= a(2/9)ˣ, a shrink by a factor of 2/5 occurs when a = 2/5

Hence , the exponential equation is solved

To learn more about exponential growth factor click :

https://brainly.com/question/13674608

#SPJ5

Answer:

3/5

Step-by-step explanation:

scale factor of ab to A'B'

AB:A'B'

5 : 3

in fraction the scale

factor is 3

—

5

heance a reduction.

hope it helps thank me later

#galadohannadivine29

#carry on learning

Answer:

x^4 - 3x^2 - 4.

Step-by-step explanation:

Imaginary roots  occur as conjugate pairs  so a 4th roots is -i.

So in factor form we have:

f(x) = (x - 2)(x + 2)(x - i)x + i)

     = (x^2 + 1)(x - 2)(x + 2)

     = (x^2 + 1)(x^2 - 4)

      = x^4 - 3x^2 - 4.

Answer:b.f(x) = x^4 – 3x^2 – 4

Step-by-step explanation:

Answer:

8

Step-by-step explanation:

3 - -5 = 8

filling space here dont mind this

Answer:

[tex]\huge\boxed{2400}[/tex]

Useful Information:

The formula for compound interest is: [tex]initial.amount*interest.rate^{no.years}[/tex]

Step-by-step explanation:

To work this out, you would first have to convert the percentage into a decimal. You can do this by dividing the percentage of 5% by 100, which gives you 0.05. This is because percentages are out of 100.

The next step is to add 1 to 0.05, this gives you 1.05. This is because you are working out the percentage increase.

The next step is to substitute the values into the formula. This gives you[tex]initial.amount*1.05^{3}=2778.30[/tex]

To work out the initial value, you would divide the final amount of 2778.30 by [tex]1.05^3[/tex], which gives you 2400. This is because you are rearranging the formula to find the initial investment.

1) Divide 5 by 100.

[tex]\frac{5}{100}=0.05[/tex]

2) Add 1 to 0.05.

[tex]1+0.05=1.05[/tex]

3) Substitute the values into the formula.

[tex]initial.amount*1.05^{3}=2778.30[/tex]

4) Divide 2778.30 by [tex]1.05^3[/tex].

[tex]\frac{2778.30}{1.05^3}=2400[/tex]

Answer:

11.65

Step-by-step explanation:

45 cos 75 (in degrees not radians) =

11.6468570296

jiskha

raka

Answer:

See below

Step-by-step explanation:

4(x + 5) = 9x + 4x − 34

4x + 20 = 9x + 4x − 34   [Distributive]

4x + 20 =  13x − 34         {Combine Like Terms]

4x - 13x + 20 = 13x - 13x − 34  [Subtractive:  -13x both sides]

-5x + 20 = - 34            [Combine Like Terms]

-5x + 20 - 20 = -34 - 20     [Subtractive:  - 20 both sides]

-5x  = -54               [Combine Like Terms]

x = -54/-5             [Division Property:  divide both sides by -5]

x =  - 10 4/5            

The true statements about ∠MJK and ∠MJL are

The statement is given as:

∠MJK and ∠MJL are a linear pair of angles and the angles are also supplementary

As a general rule, linear pair angles are adjacent angles that add up to 180 degrees. This means that:

The above means that, the following options are true:

(e), (f) and (h)

Also, the converse of the statement is:

∠MJK and ∠MJL are supplementary angles and the angles are also  linear pair of angles

This is false because not all supplementary angles are  linear pair angles

Read more about linear pair angles at:

https://brainly.com/question/1511741

#SPJ1

The solution to the inequality, -2(8x – 4) < 2x + 5, is: B. x > 1/6.

To find the solution to an inequality, solve the inequality to isolate the variable.

Given the inequality, -2(8x – 4) < 2x + 5, open the bracket:

-16x + 8 < 2x + 5

Combine like terms

-16x - 2x < -8 + 5

-18x < -3

Divide both sides by -18 then reverse < to >

-18x/-18 > -3/-18

x > 1/6

The solution is: B. x > 1/6

Learn more about inequalities on:

https://brainly.com/question/11613554

#SPJ1

Answer:

x = -15

Step-by-step explanation:

Answer:

The value of K in free space is 9 × 109

Step-by-step explanation:

-243

Step-by-step explanation:

số dương nhân -3 thì đc số âm, số âm nhân với -3 để đc số dương.

vd: 1. -3 = -3 ;   -3 .-3= 9 ;..... 81 . -3= -243

Answer:

all once will product the term by mines 3

so the final will bt -3 *81 = -243

Answer:

pm = 4

M is the mid point of PQ which means that pm = mq

so MQ = 4

PQ = PM + MQ

= 4 + 4

= 8

Answer:

[tex]\displaystyle{y=-3x-1}[/tex]

Step-by-step explanation:

I have two methods: standard-learning which will explain overall mathematically - basically formula, etc. - while the other one trick-tips method will rely on choices rather mathematical calculations but with explanation on why and how.

First, let’s pick two points that are integers since they are easily to be found via graphs. We see that (-1,2) and (0,-1) is a part of the graph so now we finally have picked two points for our calculations.

When we have finally picked two points, we will be using them for slope calculation. This part is crucial for finding an equation of a line because a line has to contain slope in its equation.

To calculate the slope, we use rise over run formula which is:

[tex]\displaystyle{\dfrac{\Delta y}{\Delta x} = \dfrac{y_2-y_1}{x_2-x_1}}[/tex]

Note that [tex]\displaystyle{\Delta}[/tex] is delta - in both mathematic and physics, it means changes in.

So, we will be using those two points that we have picked to substitute in the slope formula. Let’s determine that [tex]\displaystyle{(x_2,y_2)=(-1,2)}[/tex] and [tex]\displaystyle{(x_1,y_1)=(0,-1)}[/tex].

Therefore, our slope will be:

[tex]\displaystyle{m=\dfrac{2-(-1)}{-1-0}}\\\\\displaystyle{m=\dfrac{2+1}{-1}}\\\\\displaystyle{m=-3}[/tex]

Next, find the y-intercept. From the graph, we see that the graph intercepts at (0,-1) which is y-intercept so we will only use y-value. Hence, b = -1.

From the slope-intercept form:

[tex]\displaystyle{y=mx+b}[/tex]

Substitute m (slope) = -3 and b (y-intercept) = -1. Hence, the equation of line is:

[tex]\displaystyle{y=-3x-1}[/tex]

Relying on choices and knowledge of graph, notice that there are slopes of 3 and -3.

Keep in mind that if slope is negative, it will decrease down and if slope is positive, it will increase up.

Therefore, cut off all choices with positive slopes which are 1 and 3. We are now left with 2 and 4.

Next, look at the graph and tell its y-intercept. It intercepts y at y = -1 so we take value of -1.

So choice 4 is cut off and now we have choice 2 as the answer.

Learn More:

https://brainly.com/question/27514958 - Find the line equation with given points

Answer:

2400

Step-by-step explanation:

Find the accumulated amount of an account if the principal amount was 5000 at 16% interest at the end of 3 years

Solution

The formula for simple interest

S.I = P *R* T/100

Where P = Principal = 5000

           R = Rate = 16%

           T = Time = 3 years

 5000 * 16 * 3/100

 50 * 16 * 3

  = 2400.

Answer:

The answer will be 9/25.

Please mark me as the brainliest.

The value of r is 6

Given start fraction and end fraction are 4/3,r/6 and 3 divided by 4 end fraction which is equal to start fraction 6 divided by r end fraction  

We need to calculate the value of r

Fractions are used to depict the components of a whole or group of items. Two components make up a fraction. The numerator is the number that appears at the top of the line.

It indicates how many equally sized pieces of the entire thing or collection were removed. The denominator is the quantity listed below the line. The total number of identical objects in a collection or the total number of equal sections that the whole is divided into are both displayed

According to the statement the equation formed

4/3*r/6*3/4 = 6/r

Solving the equation by 4/3*3/4 = 1

Hence 1*r/6 = 6/r

Therefore r^2 = 36

r = 6

Hence the value of r is 6

Learn more about fraction here

https://brainly.com/question/78672

#SPJ10

I think it's C but also not completely sure good luck

The quadratic equation is  3x² - 27.

A quadratic equation is a second-order polynomial equation in a single variable x ax²+bx+c=0. with a ≠ 0 .

Given:

The roots are 3 and -3

We have

α= 3   and β=-3

So,

α+β = -b/a  and αβ = c/a

α+β = 0 =-b/a and  αβ= -9 = c/a

Comparing from above

a=1, b= 0 and c=-9

Also, the leading coefficient is 3.

Then the quadratic equation is,

= 3(ax² + bx + c)

= 3( x² +0x- 9)

Hence, the quadratic equation is 3x² - 27.

Learn more about this concept here:

https://brainly.com/question/13771721

#SPJ1

Answer:

b. y= 4x-34.

Step-by-step explanation:

We can use the information in the problem to make an equation in slope-intercept form (y=mx+b).

Steepness typically means the slope of the graph, thus m=4.
This means we can automatically cross out "a" and "c", which leaves us with "b" and "d" as possible answers.

Next, I will plug in the given point (8, -2) into "b" and "d".
b. y=4x-34
-2=4(8)-34
-2=32-34

d. y=4x+34
-2=4(8)+34
-2 does not equal 66

Thus, the answer is b. y= 4x-34.

Answer:

[tex]\huge\boxed{\dfrac{1}{-1x}=-\dfrac{1}{1x}=-\dfrac{1}{x}=-x^{-1}}[/tex]

Answer:

[tex]x=\frac{15}{4}=3\frac{3}{4}[/tex]

Equation:

[tex]\frac{2}{3}x+\frac{5}{6} =\frac{10}{3}[/tex]

_____________________________________

1. Group all constants on the right side of the equation

[tex]\frac{2}{3}\cdot x+\frac{5}{6}=\frac{10}{3}[/tex]

Subtract [tex]5/6[/tex] from both sides:

[tex]\frac{2}{3}x+\frac{5}{6}-\frac{5}{6}=\frac{10}{3}-\frac{5}{6}[/tex]

Combine the fractions:

[tex]\frac{2}{3}\cdot x+\frac{5-5}{6}=\frac{10}{3}-\frac{5}{6}[/tex]

Combine the numerators:

[tex]\frac{2}{3}\cdot x+\frac{0}{6}=\frac{10}{3}-\frac{5}{6}[/tex]

Reduce the zero numerator:

[tex]\frac{2}{3}\cdot x+0=\frac{10}{3}-\frac{5}{6}[/tex]

Simplify the arithmetic:

[tex]\frac{2}{3}\cdot x=\frac{10}{3}-\frac{5}{6}[/tex]

Find the lowest common denominator:

[tex]\frac{2}{3}\cdot x=\frac{10\cdot 2}{3\cdot 2}+\frac{-5}{6}[/tex]

Multiply the denominators:

[tex]\frac{2}{3}\cdot x=\frac{10\cdot 2}{6}+\frac{-5}{6}[/tex]

Multiply the numerators:

[tex]\frac{2}{3}\cdot x=\frac{20}{6}+\frac{-5}{6}[/tex]

Combine the fractions:

[tex]\frac{2}{3}\cdot x=\frac{20-5}{6}[/tex]

Combine the numerators:

[tex]\frac{2}{3}\cdot x=\frac{15}{6}[/tex]

Find the greatest common factor of the numerator and denominator:

[tex]\frac{2}{3}\cdot x=\frac{5\cdot 3}{2\cdot 3}[/tex]

Factor out and cancel the greatest common factor:

[tex]\frac{2}{3}\cdot x=\frac{5}{2}[/tex]

2. Isolate the x

[tex]\frac{2}{3}\cdot x=\frac{5}{2}[/tex]

Multiply both sides by inverse fraction 3/2:

[tex]\frac{2}{3}x\cdot \frac{3}{2}=\frac{5}{2}\cdot \frac{3}{2}[/tex]

Group like terms:

[tex]\frac{2}{3}\cdot \frac{3}{2}x=\frac{5}{2}\cdot \frac{3}{2}[/tex]

Simplify the fraction:

[tex]x=\frac{5}{2}\cdot \frac{3}{2}[/tex]

Multiply the fractions:

[tex]x=\frac{5\cdot 3}{2\cdot 2}[/tex]

Simplify the arithmetic:

[tex]x=\frac{15}{2\cdot 2}[/tex]

Simplify the arithmetic:

[tex]x=\frac{15}{4}[/tex]

______________________

Why learn this

Linear equations cannot tell you the future, but they can give you a good idea of what to expect so you can plan ahead. How long will it take you to fill your swimming pool? How much money will you earn during summer break? What are the quantities you need for your favorite recipe to make enough for all your friends?

Linear equations explain some of the relationships between what we know and what we want to know and can help us solve a wide range of problems we might encounter in our everyday lives.

__________________________

Terms and topics

Answer:  3 3/4

Step-by-step explanation: i took the test (sorrry i cant tell why, im bad at explaining)