what is the 6th term in the geometric sequence described by this explicit formula ?

Work Shown:

y = (4/5)x + 3

5y = 4x + 15 ... multiply all terms by 5 to clear out the fraction

0 = 4x + 15 - 5y  ... subtract 5y from both sides

4x-5y+15 = 0 .... rearrange terms

The equation is in standard form Ax+By+C = 0 where A = 4, B = -5, C = 15.

Some books use Ax+By = C to represent standard form. It's effectively the same thing just with C on the other side.

Answer:

cos(theta/2) = sqrt((1+x)/2)

Step-by-step explanation:

From the double angle formula

cos^2(t)-sin^2(t) = cos(2t)  ...................(1)

cos^2(x)+sin^2(x) = cos(t-t) =1...............(2)

Add (1) and (2)

2cos^2(t) = 1+cos(2t)

cos^2(t) = (1+cos(2t))/2

cos(t) = sqrt((1+cos(2t))/2)

substitute t = theta/2

cos(theta/2) = sqrt((1+cos(theta))/2)

substitute cos(theta) = x

cos(theta/2) = sqrt((1+x)/2)

Answer:

Between all these pairs of numbers,a rational number can be found in all the 3 pairs

Step-by-step explanation:

PAIR1: -10 and -9

Rational numbers are: -10.5,-10.6,-10.1,etc (there are way more)

PAIR2: 5.91 and 5.92

Rational numbers:- 5.915,5.916,etc(there are way more)

PAIR3:2/3 and 4/5

LCM= 15

2/3=10/15

4/5=12/15 between these two (10/15 & 12/15)

Rational numbers: 11/15, 11.5/15(because it's result would be a recurring/repeating decimal),etc

Answer:

17.

Step-by-step explanation:

f(x) = 2x^2 - 1

f(-3) = 2(-3)^2 - 1

= 2 * 9 - 1

= 18 - 1

= 17

Hope this helps!

Hope it will help u....

Answer:

x intercept (10.5,0)

y intercept (0, -21)

Step-by-step explanation:

y=-2x-21

there are two intercept for a line

x intercept, the point of given equation of  line which lies on x axis.

For x intercept corodinate of y is o

Thus, value x intercept is form (x,0)

putting these value in y=-2x-21, we find x intercept

0=-2x-21

2x = 21

x = 21/2 = 10.5

Thus, x intercept (10.5,0)

Y intercept, the point of given equation of  line which lies on y axis.

For Y intercept coordinate of x is o

Thus, value y intercept is form (0,y)

putting these value in y=-2x-21, we find y intercept

y = -2*0 -21

y = -21

Thus, y intercept (0, -21)

Answer:

385 hamburgers.

Step-by-step explanation:

So the data they have given us is that there have been 2 home games, with 70 hamburgers sold. If we divide the number of hamburgers sold by the number of games (70/2), we come up with the average hamburgers sold per game, which is 35. We can use an equation to find the amount of hamburgers sold for every x amount of games. [tex]h = 35x[/tex], with x being the amount of games, and h being the total amount of hamburgers. If you plug in 11 for x, you will get 385.

Answer:

The distance between the plane and the observer is 16,659.18ft

Step-by-step explanation:

Complete question:

(An observer (O) spots a plane flying at a 42° angle to his horizontal line of sight. If the plane is flying at an altitude of 15,000 ft, what is the distance between the observer and the plane)

Hello,

The question above requires us to find the distance between an observer and a plane. This is very much easy because we are given the angle at which the observer makes with the plane. To solve this question correctly, we need a pictorial representation of the situation.

See attached document for better illustration

In the diagram, we need to find x.

Since the observer and the plane makes a right angled triangle with the distance apart them, we can use SOHCAHTOA

In this case, we have to use Tangent

Tanθ = opposite/ adjacent

θ = 42°

Opposite = 15,000

Adjacent = x

Tan42 = 15000 / x

x = 15000 / tan42

x = 15000 / 0.90

x = 16,659.18ft

The horizontal distance between the observer and the plane is 16,659.18ft

Answer:

I am not too sure but I know it is not 10,035, or 16,648, nor 20,188 because I put that and it wasn’t right so the last option would be.

22,417

Answer:

V=11*7*9=693

Step-by-step explanation:

V=Bh ( B is the base area ( base*height) , and h is the height of the prism)

find B=base*h

B=11*7=77 in²

V=B*h=77*9=693 in³

The volume of the triangular prism is 174.25 in³.

Volume is the measure of the capacity that an object holds.

Formula to find the volume of the object is Volume = Area of a base × Height.

Given that, the triangular base has a base of 11 inches and height of 7 inches.

The formula for finding the volume of a triangular prism is V = (base area x height) / 2.

In this case, the base area of the triangle can be calculated using the formula A = (1/2)bh, where b is the base length and h is the height.

In this case, b = 11 inches and h = 7 inches, so the base area is A = (1/2)(11)(7) = 38.5 inches squared.

Now that we have the base area, we can calculate the volume of the triangular prism: V = (38.5 inches² x 9 inches) / 2 = 174.25 in³.

Therefore, the volume of the triangular prism is 174.25 in³.

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Answer:

x ≤5

Step-by-step explanation:

Pointing to the left means less than or less than or equal to

x ≤5

Answer:

[tex]\boxed{x \leq 5}[/tex]

Step-by-step explanation:

[tex]\sf Arrow \ pointing \ to \ the \ left \ on \ a \ number \ line \ means \ that[/tex]

[tex]\sf \ the \ value \ is \ either \ less \ than \ or \ less \ than \ or \ equal \ to.[/tex]

[tex]\sf{Graph}[/tex] [tex]x\leq 5[/tex] [tex]\sf{on \ the \ number \ line.}[/tex]

Answer:

moves it up 6 units

Step-by-step explanation:

y = f(x) + C C > 0 moves it up

f(x) = f(x) + 6 moves it up 6 units

Answer:

Vertical shift, 6 up.

Step-by-step explanation:

The entire function f(x) has a value of six added to it. That means that regardless of where f(x) was plotted on the coordinate plane, after the translation f(x) + 6, every single point would increase its value by six. Since all points would increase their values by six, the entire function would shift 6 up.

Answer: C

Step-by-step explanation:

"w" represents the number of weeks. If she adds $10 per week, the equation will include 10w. Because she starts out with $60 already, the complete equation would be:

[tex]T=60+10w[/tex].

Hope this helps!

The equation that describes the amount she has after 'w' weeks is

C : T = 60 + 10w.

A function can be defined as the outputs for a given set of inputs.

The inputs of a function are known as the independent variable and the outputs of a function are known as the dependent variable.

Given, Sally wants to save for a new cell phone. She opens a bank account with $60 and adds $10 each week.

Assuming the total amount to be 'T' and no. of weeks to be 'w'.

∴ The equation that represents the amount of money she has is,

T = 60 + 10w.

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Answer:

[tex]\large \boxed{\sf \ \ \ p=-11 \ \ \ }[/tex]

Step-by-step explanation:

Hello,

[tex]\alpha \text{ and } \beta \text{ are the roots of the following equation}[/tex]

   [tex]2x^2+6x-7=p[/tex]

It means that

   [tex]2\alpha^2+6\alpha-7=p \\\\2\beta ^2+6\beta -7=p \\\\[/tex]

And we know that

[tex]\alpha= 2\cdot \beta[/tex]

So we got two equations

   [tex]2(2\beta)^2+6\cdot 2 \cdot \beta -7=p \\\\<=>8\beta^2+12\beta -7=p\\\\ and \ 2\beta ^2+6\beta -7=p \ So \\\\\\8\beta^2+12\beta -7 = 2\beta ^2+6\beta -7\\\\<=>6\beta^2+6\beta =0\\\\<=>\beta(\beta+1)=0\\\\<=> \beta =0 \ or \ \beta=-1[/tex]

For [tex]\beta =0, \ \ \alpha =0, \ \ p = -7[/tex]

For [tex]\beta =-1, \ \ \alpha =-2, \ \ p= 2-6-7=-11, \ p=2*4-12-7=-11[/tex]

I assume that we are after two different roots so the solution for p is p=-11

b) [tex]\alpha +2 =-2+2=0 \ and \ \beta+2=-1+2=1[/tex]

So a quadratic equation with the expected roots  is

[tex]x(x-1)=x^2-x[/tex]

Hope this helps.

Do not hesitate if you need further explanation.

Thank you

Answer:

Hey there!

To solve this problem, you want to divide 22 by 3, which is about 7.33 feet.

We can check this by seeing 7.33 times 3=22

Hope this helps :)

Answer:

0

Step-by-step explanation:

First let's solve for the value in the parentheses.

[tex]0.35 \cdot 100 = 35[/tex]

We know this is correct because if we multiply a value by 100, the decimal point is moved 2 places to the left.

35 - 35 = 0, so the value of this expression equals out to be 0.

Hope this helped!

Answer:

Step-by-step explanation:

[tex] \frac{26}{25} \times ( - \frac{16}{63} )[/tex]

Multiplying a positive and a negative equals a negative[tex]( + ) \times ( - ) = ( - )[/tex]

[tex] = - \frac{26}{25} \times \frac{16}{63} [/tex]

Multiply the fractions:

[tex] = - \frac{416}{1575} [/tex]

Hope this helps..

Best regards!!

Answer:

366 minutes

Step-by-step explanation:

divide 15000 by 41

Answer:

the inverse of the function f^-1(x)=(x-3)/(4+5x)

Step-by-step explanation:

( 3+4x)/(1-5x)

y=4x+3/1-5x swap the variables

x=4y+3/1-5y solve for y

y=x-3/4+5x

The inverse of a function is :y=x-3/4+5x

What is inverse of a function?

The inverse function returns the original value for which a function gave the output.

If you consider functions, f and g are inverse, f(g(x)) = g(f(x)) = x. A function that consists of its inverse fetches the original value.

Steps are:

for example:

Suppose, f(x) = 2x + 3 is a function.

Let f(x) = 2x+3 = y

y = 2x+3

x = (y-3)/2 = f-1(y)

This is the inverse of f(x).

Given function:

f(x)= ( 3+4x)/(1-5x)

now, swap the variables x and y.

y=4x+3/1-5x

Now solving for y

x=4y+3/1-5y

y=x-3/4+5x

Hence, the inverse of the function f^-1(x)=(x-3)/(4+5x).

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Answer:

50

Step-by-step explanation:

The value of P(A|B) = 0.50 which is correct option(B)

What is independent events?

Independent events is defined as an event that is not affected by other events.

A and B are independent events.

P(A) = 0.50

P(B) = 0.20

P(A|B) = P(A∩B)/P(B)

P(A|B) = P(A).P(B)/P(B)

P(A|B) = P(A)

Substitute the value of P(A) = 0.50,

P(A|B) = 0.50

Hence, the value of P(A|B) = 0.50

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Answer:

Colin is wrong

Step-by-step explanation:

The question is incomplete because the chart or the table which shows the data is not given. I have attached the full question at the bottom. Consult it for better understanding.

We can clearly see in the chart the number of lates in January is 30, while the number of lates in March is 20.

As the half of 30 is 15, not 20, we can say that the statement of Colin is wrong, because the number of lates in March should be 15 to prove his statement true

Answer:

First blank: 6a

Second blank: 2/3

Third blank: 21.6

Fourth blank: 3.9

Step-by-step explanation:

Basically, all you need to do is distribute the 2/3 to the stuff inside the parentheses. That means in the first blank, write 6a inside since you're multiplying 2/3 and 6a, and then in the second blank you write 2/3 since you're multiplying 2/3 and 9 together.

2/3*6a+2/3*9 = 21.6 is what you should have.

Now, just solve for a.

4a+6 = 21.6

4a=15.6

a=3.9

Answer:

2/3 * 6a+ 2/3 +9 = 21.6

a = 3.9

Step-by-step explanation:

2/3 ( 6a+9) = 21.6

Distribute

2/3 * 6a+ 2/3 +9 = 21.6

4a + 6 = 21.6

Subtract 6 from each side

4a = 15.6

Divide each side by 4

4a/4 = 15.6/4

a =3.9

Answer: In zhi's equation, the 18 is the initial amount of tickets, and the 3g means 3 times the amount of games.  

Diegos equation is the same, but write in factorised form. The 3 multiplies with the 6 to create 18, and the 3 multiple with the g to create 3g

Answer:

z = 44

Step-by-step explanation:

26/z = 13/22

Using cross products

26 * 22 = 13*z

Divide each side by 13

26/13 * 22 = 13z/13

2 *22 =z

44 =z

Answer:

Z=44

To solve this proportion, you have to isolate z. You have to do what you do on one side of the equal sign to the other as well.

Answer:

6x^3y^2+18x^4y^3+18x^2y^5

Step-by-step explanation:

Multiply each term:

6x^3y^2+18x^4y^3+18x^2y^5

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Answer:

The market price of the article is Rs. 978.72

Step-by-step explanation:

Let x represents the market price.

Let y represents the selling price.

Let z represents the cost price.

if an article is sold with 20% discount then there will be a profit of 15%.

SP = CP+Profit =z+0.15z=1.15z

ATQ

[tex]0.80x = 1.15z\\0.80x- 1.15z = 0[/tex]

If it is sold at 10% discount then there will be a profit of Rs.200

ATQ

[tex]0.9x - z = 200[/tex]

Now we are supposed to find the market price of an article.

[tex]0.9x - z= 200[/tex]

Multiplying 1.15 both sides

[tex]0.9x \times 1.15 - 1.15z = 200 \times 1.15\\1.035x - 1.15z = 230[/tex]

We know that[tex]1.15z = 0.80x[/tex]

[tex]1.035x - 0.80z = 230\\0.235x = 230\\x = \frac{230}{0.235}\\x= Rs. 978.72[/tex]

Hence The market price of the article is Rs. 978.72

Answer:

729 emails

Step-by-step explanation:

The pattern is to multiply by 3

3*3 = 9

9*3 = 27

27*3 = 81

81*3 = 243

If the pattern continues, Martin will sent on monday:

243*3 = 729

729 emails

Answer:

729

Step-by-step explanation:

Answer:

[tex]\large \boxed{\sf \ \ \ a\cdot b= 6 \ \ \ }[/tex]

Step-by-step explanation:

Hello,

[tex](a-bi)^2 = 13 - 12i\\\\<=> a^2+(bi)^2-2abi = 13-12i\\\\<=>a^2-b^2-2abi=13-12i[/tex]

Imaginary term must be the same so

-2ab=-12

2ab = 12

ab = 12/2 = 6

So the product of a and b is 6

Hope this helps.

Do not hesitate if you need further explanation.

Thank you

Let's solve the given equation step by step to find the product of a and b. Initially,

let's expand the left side of the equation: [tex](a - bi)^2 = (a - bi)(a - bi) = a^2 - abi - abi + b^2i^2 = a^2 - 2abi + b^2(-1) = a^2 - 2abi - b^2[/tex] We are given that this result is equal to[tex]13 - 12[/tex]i, so we can set up the following equation: [tex]a^2 - 2abi - b^2 = 13 - 12i[/tex] By comparing the real and imaginary parts of both sides, we can form two equations:

Equation [tex]1: a^2 - b^2 = 13[/tex]  (Equating real parts) Equation [tex]2: -2ab = -12[/tex](Equating imaginary parts) From Equation 2, we can deduce that ab = 6. To proceed further and find the product of a and b, we need more information. The current given equation has infinite possible solutions for a and b.

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Answer: 0.127 feet by 0.090 feet

Step-by-step explanation:

Given that :

The USA's flag dimension = 19feet by 10feet

Union's (blue rectangle in the top left corner) dimension = 7 5/8 feet by 5 3/8 feet.

Union dimension for the shoulder patch of the USA flag used by astronauts for the Apollo mission has a scale factor of 1/60

Therefore, dimension of the union patch ;

1/60 * ( 7 5/8 feet by 5 3/8 feet)

1/60 * (61 / 8 feet by 43/8 feet)

61/480 feet by 43/480 feet

0.127 feet by 0.0895 feet

0.127 feet by 0.090 feet

Answer:

The lenght of the tree sides of the triangle are:

first side: 21 inches

second side: 19 inches

third side: 33 inches

Step-by-step explanation:

a + b + c = 73

b = a - 2

c = a + 12

a = leght of the first side of the triangle

b = lenght of the second side of the triangle

c = lenght of the third side of the triangle

then:

a + (a-2) + (a+12) = 73

3a - 2 + 12 = 73

3a + 10 = 73

3a = 73 - 10

3a = 63

a = 63/3

a = 21 inches

b = a - 2

b = 21 - 2

b = 19 inches

c = a + 12

c = 21 + 12

c = 33 inches

Check:

21 + 19 + 33 = 73

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The length of the sides of the triangle are:

A branch of mathematics known as algebra deals with symbols and the mathematical operations performed on them.

Variables are the name given to these symbols because they lack set values. In order to determine the values, these symbols are also subjected to various addition, subtraction, multiplication, and division arithmetic operations.

Given:

let the sides of triangles be x, y, z.

As, perimeter of the triangle is 73 inches.

x+ y+ z= 73................(1)

and, length of the second side of a triangle is 2 inches less than the length of the first side.

y= x- 2

and,  length of the third side is 12 inches more than the length of the first side.

z= x + 12

Substitute the values of y  and z in equation (1)

x+ x-2 + x+ 12= 73

3x + 10 =73

3x= 63

x= 21

Then, First side= 21 inch

second side = 21 - 2 = 19 inch

third side= 21+ 12 = 33 inch

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