The third and the sixth term of a geometric progression are 24 and 64/9 respectively. Find

a) the first term and common ratio
b) the sum of the first five terms​

Step-by-step explanation:

a) 13=$7

x=$1

(do cross multiplication)

13=7x

x=1.86 pounds

9514 1404 393

Answer:

  18.8 cubic inches

Step-by-step explanation:

The formula for the volume of a cone is useful:

  V = 1/3πr²h

Where r is half the diameter, we can use r=d/2 to write this in terms of diameter:

  V = 1/3π(d/2)²h = (π/12)d²h

For the given dimensions, the volumes are ...

  large cone: v = (π/12)(4.5 in)²(5.1 in) ≈ 27.04 in³

  small cone: v = (π/12)(3 in)²(3.5 in) ≈ 8.25 in³

Then the difference in volume is ...

  (27.04 -8.25) in³ ≈ 18.8 in³

The larger cone has about 18.8 cubic inches more volume.

Answer:

Area of ΔXYZ = 10 square units

Step-by-step explanation:

Area of the triangle XYZ = [tex]\frac{1}{2}(\text{Height})(\text{Base})[/tex]

Height of the triangle = AY

Base of the triangle = XZ

To get the length of any segment we will use the formula,

d = [tex]\sqrt{(y_2-y_1)^2+(x_2-x_1)^2)}[/tex]

Here [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex] are the endpoints of the segment.

Length of AY = Distance between (-1, 4) and (3, 6)

                      = [tex]\sqrt{(6-4)^2+(3+1)^2}[/tex]

                      = [tex]\sqrt{20}[/tex]

Length of XZ = [tex]\sqrt{(6-2)^2+(-2-0)^2}[/tex]

                      = [tex]\sqrt{20}[/tex]

Area of ΔXYZ = [tex]\frac{1}{2}(\sqrt{20})(\sqrt{20})[/tex]

                       = 10 square units                      

Answer:

the range is 8-1=7

Step-by-step explanation:

There are 16 ounces in one pound.

Set up a proportion and solve for x.

3/x = 16/1.7

16x = 3(1.7)

16x = 5.1

x = 5.1 ÷ 16

x = 0.31875

Rounding to the nearest cent, we get 30 cents.

Answer:

49050

Step-by-step explanation:

(5 x 109)x (9 x 10)

545×90

49050

So the answer is 49050

Answer:5.78

Step-by-step explanation: It is 5.78 bc do 40.50 divided by 7 and you will get your answer

Brainliest please???

Answer:

Each tube costs about $5.79.

Step-by-step explanation:

To find the cost of each tube, divide the total cost by the total number of toothpaste tubes.

40.50/7 = 5.785714286 which approximates to 5.79

Answer:

Step-by-step explanation:

The third angle measures:

Angles and opposite sides are:

The greater the angle, the greater the opposite side, therefore the sides in increasing order will be:

x ≤ -2    OR  x ≥ 4

__________________________________________________________

We are given the inequality:

|2x - 2| ≥ 6

Getting rid of the Modulus:

Since 2x-2 is in modulus:

|2x-2| =  -(2x-2)    OR   2x-2

(since the modulus of both these values is 2x-2)

Hence, our inequality can be written in 2 different ways:

__________________________________________________________

Solving these 2 inequalities:

Solving inequality 1:

2x - 2 ≥ 6                

2x ≥ 8                     [adding 2 on both sides]

x ≥ 4                       [dividing both the sides by 2]

This is the solution of the inequality if: 2x-2 ≥ 0

Solving Inequality 2:

-(2x-2) ≥ 6

It can be rewritten as:

2 - 2x ≥ 6                

2 ≥ 6 + 2x                [adding 2x on both the sides]  

-4 ≥ 2x                     [Subtracting 6 from both sides]

x ≤ -2                       [Dividing both sides by 2]

This is the solution of the given inequality if: 2x-2 < 0

__________________________________________________________

Solution of the given Inequality:

Therefore, the solution of the given inequality |2x-2| ≥ 6 are:

x ≥ 4   (if 2x-2 ≥ 0)

x ≤ -2  (if 2x-2 < 0)

Hence, option C is correct!

Answer:

0.83

Step-by-step explanation:

add the hot, cold, and both sections together

The probability of people liking hot or iced coffee is 0.61. Therefore, option C is the correct answer.

Probability can be defined as the ratio of the number of favourable outcomes to the total number of outcomes of an event.

We know that, probability of an event = Number of favourable outcomes/Total number of outcomes

Given that, according to sales records at a local coffee shop, 75% of all customers like hot coffee, 30% like cold coffee and 22% like both hot and iced coffee.

People like only hot coffee = 0.53

People like only iced coffee = 0.08

Customers like hot or iced coffee =0.53+0.08

= 0.61

Therefore, option C is the correct answer.

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Answer:

0.75meters

Step-by-step explanation:

25% of 3 is 0.75

Plz mark me brainliest

Answer:

B

Step-by-step explanation:

Answer:

b

Step-by-step explanation:

i did flvs

Answer:

Explanation below

Step-by-step explanation:

First Degree Equations

A first-degree equation can have one, none, or infinitely many solutions.

An equation like

2x + 3 = -x + 6

Has one solution: x=1

An equation like:

4x + 2 = 4x + 1

Has no solutions because when trying to solve for x we get:

2 = 1

This equality is false and no value of x can make it true

Finally, the equation:

3x + 2 = x + 2x + 2

Has infiniteyl many solutions, because when trying to solve it, we get:

2 = 2

Which is true regardless of the value of x

3x + 9 + 4x + x = ??

can be simplified as:

8x + 9 = ??

For this equation not having solutions, we should have 8x plus any number but 9 on the right side of the equation:

8x + 9 = 8x -3, or

8x + 9 = 8x + 4

3x + 9 + 4x + x = ??

can be simplified as:

8x + 9 = ??

If the equation has one solution, the only condition is that we should not have 8x on the right side. Thus any of those will do:

8x + 9 = 3x + 9

8x + 9 = -x + 5

8x + 9 = 0

3x + 9 + 4x + x = ??

can be simplified as:

8x + 9 = ??

For this equation to have infinitely many solutions, the right side must be exactly equal to the left side:

8x + 9 = 8x + 9

Answer:

x = 60°

General Formulas and Concepts:

Pre-Algebra

Geometry

Step-by-step explanation:

Step 1: Set up equation

x° + 90° + 30° = 180°

Step 2: Solve for x

Answer: 17%

Step-by-step explanation: 83+17 = 100, 17/100 = 0.17 = 17%

9514 1404 393

Answer:

  12 units

Step-by-step explanation:

Reflection over two lines x units apart is equivalent to a translation of 2x units. Since the given lines are 6 units apart, ...

  the equivalent translation is of 12 units.

___

Example:

Lines at x=0 and x=6. Point (x, 0). After reflection over x=0, the point is located at (2·0 -(x), 0) = (-x, 0). After reflection of that over x=6, the point is located at (2·6 -(-x), 0) = (12 +x, 0). That is, 12 has been added to the x-coordinate, meaning the point was translated 12 units. (The translation is in the direction the second line is from the first.)

Answer:

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

General Formulas and Concepts:

Pre-Algebra

Algebra I

Step-by-step explanation:

Step 1: Define

Find points from graph.

Point (-3, 1)

Point (2, -3)

Step 2: Find slope m

Answer:

The answer should be b: x=-9

Answer:

b. -9

Step-by-step explanation:

-8x+10=82

     -10   -10

-8x=72

divide both side by -8

x=-9

Answer:

=38

Step-by-step explanation:

Answer:

It's C [-2 0]

Step-by-step explanation:

If you multiply the product [-1 0] both by 2 you get [-2 0]

Answer:

The domain of the graph must be [tex]x\ge \:-4[/tex].

Therefore,

[tex]x\ge \:-4\quad :\quad \begin{bmatrix}\mathrm{Solution:}\:&\:x\ge \:-4\:\\ \:\mathrm{Interval\:Notation:}&\:[-4,\:\infty \:)\end{bmatrix}[/tex]

Hence, option a is true.

Step-by-step explanation:

From the graph, it is clear that the graph is heading towards positive infinity from x=-4.

The point x=-4 is included in the graph as the starting point of the graph i.e. x=4 is showing a closed circle on x=4, and heading towards positive infinity onward.

i.e. [-4, ∞)

Hence, the domain of the graph must be [tex]x\ge \:-4[/tex].

Therefore,

[tex]x\ge \:-4\quad :\quad \begin{bmatrix}\mathrm{Solution:}\:&\:x\ge \:-4\:\\ \:\mathrm{Interval\:Notation:}&\:[-4,\:\infty \:)\end{bmatrix}[/tex]

Hence, option a is true.

Answer:

4 hour

Step-by-step explanation:

The time it takes to fly from Los Angeles to New York varies inversely as the speed of the plane i.e.

[tex]t\propto v^2[/tex]

Here, t₁ = 5 h, v₁ = 950 km/h, v₂ = 850 km/h, t₂=?

[tex]\dfrac{t_1}{t_2}=\dfrac{v_1^2}{v_2^2}\\\\t_2=\dfrac{t_1v_2^2}{v_1^2}\\\\t_2=\dfrac{5\times (850)^2}{(950)^2}\\\\t_2=4\ h[/tex]

If the speed is 850 km/h then the time is 4 h.

Answer: x= 13/3

Step-by-step explanation: solve x

by simplifying both sides of the equation, then isolating the variable.

Answer:

[tex]x=\frac{13}{3}[/tex]

Step-by-step explanation:

The explanation on how to solve it is from the attached picture.

Hope this helps! :)

Answer:

give me 1hour

Step-by-step explanation:

Answer:.

Step-by-step explanation:

Answer:

The correct answer is A

Step-by-step explanation:

I think you are trying to find corresponding sides. In the answer that you think it is, it says BC = DF. Well, is you look triangle ABC you see that BC is at the bottom. However, this differs from triangle DEF because EF is the bottom line. So if you look at the answer A, you see that it has the correct corresponding sides. I hope that helps :))

Answer:

[tex]\frac{dL}{dt}=30 \frac{ft}{s}[/tex]

Step-by-step explanation:

In order to solve this it is always a good idea to start by drawing a diagram of the situation (See attached picture).

From the diagram we can see that we are dealing with similar triangles. We can use similar triangles to build an equation that relates the length of the shadow with the height of the lamp, so we get:

[tex]\frac{L}{6}=\frac{10+L}{h}[/tex]

the height of the lamp can be found by subtracting the [tex]16t^{2}[/tex] distance the lamp falls in a given time t from the original 30ft the lamp was located at.

So the equation will now lok like this:

[tex]\frac{L}{6}=\frac{10+L}{30-16t^{2}}[/tex]

So now we can solve the equation for L, we can start by multiplying by the LCD SO WE GET:

[tex]L(30-16t^{2})=6(10+L)[/tex]

next, we can distribute the right side of the equation so we get:

[tex]L(30-16t^{2})=60+6L[/tex]

and subtract 6L from both sides so we get:

[tex]L(30-16t^{2})-6L=60[/tex]

and factor L, so we get:

[tex]L(30-16t^{2}-6)=60[/tex]

and solve for L:

[tex]L=\frac{60}{24-16t^{2}}[/tex]

now, we can differentiate this equation by using the chain rule, so we get:

[tex]dL=-\frac{60}{(24-16t^{2})^{2}}(-32t)dt[/tex]

which can be simplified to:

[tex]\frac{dL}{dt}=\frac{1920t}{(24-16t^{2})^{2}}[/tex]

and now we can substitute t for 1s so we get:

[tex]\frac{dL}{dt}=\frac{1920(1)}{(24-16(1)^{2})^{2}}[/tex]

[tex]\frac{dL}{dt}=30 \frac{ft}{s}[/tex]

Answer: 61

Step-by-step explanation:

[tex]\sqrt{x+20}=9\\\\x+20=81\\\\x=\boxed{61}[/tex]

The value of x will be 61.

What is mathematical expression?

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

The mathematical expression is,

⇒ √x + 20 = 9

Now,

Solve the expression for the value of x as;

The mathematical expression is,

⇒ √x + 20 = 9

Take square on both side, we get;

⇒ (√x + 20 )² = 9²

⇒ x + 20 = 81

Subtract 20 both side, we get;

⇒ x + 20 - 20 = 81 - 20

⇒ x = 61

Therefore, The value of x will be 61.

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Answer:

5/8 quart

Step-by-step explanation:

Answer:  y = -7

graph attached.

Step-by-step explanation:

This is a horizontal line passing through -7 in the y-axis. It passes through all x-values

Answer:

2

Step-by-step explanation:

Answer:

Fourth Option

Step-by-step explanation:

In order to find the answer to this question you need to change the mixed number into a improper fraction and then add by finding the least common denominator (LCD).

[tex]-\frac{3}{4} +2\frac{3}{4}[/tex]

Convert into improper fraction:

[tex]2\frac{3}{4} =4\times2=8+3=11[/tex]

[tex]-\frac{3}{4} +\frac{11}{4}[/tex]

Since how the denominators are the same you can just add numerators:

[tex]-3+11=8[/tex]

[tex]=\frac{8}{4}[/tex]

Reduce:

[tex]8\div4=2[/tex]

[tex]4\div4=1[/tex]

[tex]=\frac{2}{1}[/tex]

[tex]\frac{2}{1} =2[/tex]

Hope this helps.

Answer:

200 ft

Step-by-step explanation:

Answer:

220

Step-by-step explanation:

60 times 2 equals 120

50 times 2 equals 100

120 plus 100 equals 220