A geometric series has a sum of 1365. Each item increases by a factor of 4. If there
are 6 terms in the series, find the value of the first term.

The difference of two squares expression is (c) (5x + 3y)(5x - 3y)

The difference of two squares expression is represented as:

a^2 - b^2 = (a + b)(a - b)

Using the above as a guide, we have the following expression in option (c)

(5x + 3y)(5x - 3y)

Hence, the difference of two squares expression is (c) (5x + 3y)(5x - 3y)

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Answer:

See below

Step-by-step explanation:

density = mass/volume

   re-arrange to    density * volume = mass

                                 20 * 64 = 1280 gm

Density = mass/volume    

   re-arrange to      volume = mass / density

                                                 560 / 14 = 40 cm^3

The largest possible area of the forest is 2500 km^2

The perimeter is given as:

P = 200 km

The shape that will give the largest possible area for the forest is a square, and the area is calculated as:

A = (P/4)^2

This gives

A = (200/4)^2

Evaluate

A = 2500 km^2

Hence, the largest possible area of the forest is 2500 km^2

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The equation for h = f(t) will be, ⁣[tex]\rm h(t)=7.5sin({\pi}t-\frac{\pi}{2})+12.5[/tex].

A connection between independent variables and the dependent variable is defined by the function. Functions help to represent graphs and equations.

The given data in the problem is;

Ferris wheel diameter,d= 15 meters

The platform is 5 m above the ground.

The Ferris wheel function is;

h(t) = A sin(Bt + C) + D

Here,

A is Amplitude

D is the midline

B is period

C is a phase shift

t is the time

The amplitude of the function is half of the diameter;

A = d/2

A=15 m /2

A = 7.5 m

The value of the mid-line is found as;

Mid-line =  amplitude  + distance from the mid-line;

D= 7.5 + 5

D = 12.5

From the given data, the wheel completes 1 full revolution in 2 minutes

The period of the wheel is T.

B = 2

The phase shift is found as;

[tex]\rm \frac{C}{\pi}=\frac{-1}{2}\\\\ {C}=\frac{-\pi}{2}[/tex]

The Ferris wheel function is;

h(t) = A sin(Bt + C) + D

Substitute the obtained values we get;

[tex]\rm h(t)=7.5sin({\pi}t-\frac{\pi}{2})+12.5[/tex]

Hence, the equation for h = f(t) will be, ⁣[tex]\rm h(t)=7.5sin({\pi}t-\frac{\pi}{2})+12.5[/tex].

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The value of a and b are 5.5 and 11.0.

The sides a and b of the triangle can be found as follows:

∠B = 29°

c = 11

∠C = 75°

∠A = 180 - 75 - 29 = 76°

Using sine ratio,

b / sin 29° = 11 / sin 75

b sin 75 = 11 sin 29

b =  11 sin 29 / sin 75

b = 5.33290582271 / 0.96592582628

b = 5.51816958277

b = 5.5

Let's find a,

a / sin 76 = 11 / sin 75

a sin 75 = 11 sin 76

a = 11 sin 76 / sin 75

a = 10.673252989 / 0.96592582628

a = 11.0466922042

a = 11.0

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Answer:

[tex]y=-\frac{3}{2}x-3[/tex]

Step-by-step explanation:

The slope-intercept form is written as y= mx +c, where m is the slope and c is the y-intercept.

For the equation to be in the slope-intercept form, first leave the y term on the left-hand side of the equation and bring the rest to the right-hand side.

2y= -3x -6

Ensure that the coefficient of y is 1. In this question, we can divide both sides of the equation by 2 to achieve the slope-intercept form.

[tex]y=\frac{-3x}{2}-\frac{6}{2}[/tex]

Simplify:

[tex]\bf{y=-\frac{3}{2}x-3 }[/tex]

Additional:

For more questions on slope-intercept form, do check out the following!

Answer:

The speed of aeroplane =875 miles/hr and the speed of wind =125 miles/hr.

Step-by-step explanation:

Let’s assume the speed of the plane =x miles/hr

And let the speed of wind =y miles/hr

So, the speed of the aeroplane in the direction of wind =(x+y) miles/hr

Speed of the aeroplane in the opposite direction of wind =(x–y) miles/hr

We know that, distance=speed×time

Then according to the given conditions, we have

3300=(x+y)×(3+(18/60))

here convert 18mins to hour by dividing by 60 and add to 3hrs.

⇒x+y= 3300/3.3

⇒x+y=1000 … (i)

And,

3300=(x-y)×(4+(24/60))

here convert 24mins to hour by dividing by 60 and add to 4hrs.

⇒x-y= 3300/4.4

⇒x-y=750 … (ii)

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

2x=1750

⇒x= 1750/2

=875

Substituting the value of x in equation (ii), we get

875−y=750

⇒y=875-750

⇒y=125

Therefore, the speed of aeroplane =875 miles/hr and the speed of wind =125 miles/hr.

Answer:

a=30,b=60,c=105

Step-by-step explanation:

a = 30 vertical angle therom

b = 180-120 = 60 using triangle sum therom

c = 180-75 = 105 because a line is always 180 degrees

The solution is about a distance-time graph. The interpretation of the graph is that it took the family 6 hours to travel a distance of 360 miles. Note that the distance is plotted on y-axis and time on the x-axis.

A distance time graph is a simple graph that shows the relationship between the time travelled the distance covered while doing do.

The slope-intercept form is

y= mx+b−⋯(1)

The y-intercept is 360

⇒b = 360; and m = −60

Substituting the value of m = −60

and b = 360

in (1) above,

⇒y = −60x  +360

The x-intercept is

y = 0,

⇒0= −60x+360

hence, x=6

The y-intercept is

x=0

⇒y=−60(0)+360

⇒y=360

In conclusion, the x - intercept is the time in hours between Cincinnati and St. Loui: and

The  y - intercept is the distance between Cincinnati and St. Louis.

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Answer:

  62,400 J

Step-by-step explanation:

As the problem statement tells you, the work done to lift the mass is the product of the force applied and the distance the mass is lifted. Here, the force decreases as the height of the mass increases.

For x meters of exposed cable, the force required to lift it is 3x newtons. The force required to lift the object is 1500 newtons, so the total force required to lift the masses an incremental distance (dx) is (3x +1500) newtons.

The work done lifting the mass that distance is the product of force and distance. The total work done is the integral of the incremental work over the total of distance lifted:

  [tex]\displaystyle W = \int_0^{40}(3x+1500)\,dx[/tex]

The value of the integral is ...

  [tex]\displaystyle W=\left.\left(\dfrac{3}{2}x^2+1500x\right)\right|_{x=0}^{x=40}=40\left(\dfrac{1}{2}(3\cdot40)+1500\right)=62\,400\qquad\text{joules}[/tex]

The work done to lift the cable and weight is 62,400 joules.

__

Additional comment

One reason for writing the integral evaluation this way is to demonstrate that the total of work done is that required to lift the weight (1500 N, 40 m) and that required to lift the center of mass of the cable (120 N, 20 m).

This will generally be the case for "disappearing mass" or "increasing distance" problems. Pumping from a pool is a similar kind of problem with a similar kind of solution.

Effectively, you're doing work on the center of mass of the system, moving it from its initial position to the top of the building.

The y-intercept of the function is  -9,25

The function is given as:

[tex]y = -5(.8)^{x - 1} - 3[/tex]

See attachment for the graph of the function

From the graph, we have the following highlights:

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The value of m and n to show the solution of the equation x² + 6x - 5 = 0 is m = -3 and n = ± √14

An equation is an expression that shows the relationship between two or more variables and numbers.

Given the equation:

x² + 6x - 5 = 0

x² + 6x = 5

x² + 6x + 9 = 5 + 9

(x + 3)² = 14

x + 3 = ±√14

x = -3 ± √14

The value of m and n to show the solution of the equation x² + 6x - 5 = 0 is m = -3 and n = ± √14

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The area of the figure is 11. 27 cm²

The figure given is a parallelogram

The formula for the area of a parallelogram is given thus;

Area = base × height

From the figure, we have that

base = 2. 3 cm

height = 4. 9 cm

Substitute into the formula

Area = 2. 3 × 4. 9

Area = 11. 27 cm²

Thus, the area of the figure is 11. 27 cm²

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The shaded region shown in the graph of the normal distribution corresponds to P(x < 92.5).

An equation is an expression that shows the relationship between two or more numbers and variables.

The z score shows by how many standard deviations the raw score is above or below the mean. It is given by:

z = (raw score - mean)/standard deviation

The diagram represents z < 1.5 mean = 100, standard dev = 5 hence:

-1.5 = (x - 100)/5

x = 92.5

The shaded region shown in the graph of the normal distribution corresponds to P(x < 92.5).

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The values of the functions are f(4) = 47, f(k) = 2(k)^2 + 4(k) - 1 and f(x + h) = 2x^2 + 4hx + 2h^2 + 4x + 4h - 4

The function is given as:

f(x) = 2x^2 + 4x - 1

To calculate f(4), we have:

f(4) = 2(4)^2 + 4(4) - 1

Evaluate the expression

f(4) = 47

To calculate f(k), we have:

f(k) = 2(k)^2 + 4(k) - 1

To calculate f(x + h), we have:

f(x + h) = 2(x + h)^2 + 4(x + h) - 1

Expand

f(x + h) = 2(x^2 + 2hx + h^2) + 4x + 4h - 4

Expand

f(x + h) = 2x^2 + 4hx + 2h^2 + 4x + 4h - 4

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Answer:

I can help you, just tell me what it is.

Step-by-step explanation:

Step 1: Tell me the problem

Step 2: Wait for a response.

Answer:

yes it can help in some ways I think

Answer:

Step-by-step explanation:

The interest based on the information given is $2564.

From the information given, the following can be deduced:

Principal = $36900

Time = 178 days

Rate = 14.25%

The simple interest will be:

= (PRT)/100

= (36900 × 14.25 × 178/365)/100

= $2564

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Answer:yes

15x times 2=30x

15x times 3= 45x

3y tines 2 =6y

3y times 3=9y

Step-by-step explanation:

Answer:

D

Step-by-step explanation:

If you substitute the radius, 10, and the center of the circle, the origin (also known as (0,0) into the equation of a circle, you should get: [tex](x - 0)^{2} + (y - 0)^{2} = 10 ^{2} [/tex]

Multiplying this out should leave you with D as your answer.

Answer:

gradient: 1.5

Explanation:

Take two points from the graph: (2, 0), (0, -3)

[tex]\sf gradient : \dfrac{y_2 - y_1}{x_2- x_1} = \dfrac{\triangle y}{\triangle x} \ \ where \ (x_1 , \ y_1), ( x_2 , \ y_2) \ are \ points[/tex]

So here given:

Inserting values

[tex]\rightarrow \sf gradient : \dfrac{-3-0}{0-2} = \dfrac{-3}{-2} = 1.5[/tex]

4 pounds of fertilizer is mixed to make a mix of 80 pounds of soil.

The relationship between two things is called Ratio. It is written in p:q form.

It is given that

For 10 pounds of soil , farmer mixes 8 ounces of fertilizer.

=8/16 = 0.5 pounds of fertiliser

The ratio is 10 : 0.5

Suppose he mixes x pounds of fertilizer for 80 pounds of soil

to determine x

The ratio is 80 : x

As they are in Proportion

10 / 0.5 = 80 /x

x = 80 * 0.5 /10

x = 4 pounds

Therefore 4 pounds of fertilizer is mixed to make a mix of 80 pounds of soil.

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The numerator for the following rational expression is 13

The rational expression is given as:

6/t + 7/t

Take the LCM of the denominator;

The LCM of t and t is t

So, we have:

6/t + 7/t = (6 + 7)/t

Evaluate the sum

6/t + 7/t = 13/t

13 is the numerator, while t is the denominator

Hence, the numerator for the following rational expression is 13

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Answer:

14x^7-56x^6=9

Step-by-step explanation:

distribute

(7x^2)(2x^3 +6)(x^2 -4 * 9=x)

(2x^3+6)(x^2 -4 * 9=x)=2x^5-8x^4=9

(7x^2)(2x^5-8x^4=9)

14x^7-56x^6=9

Answer:

The money multiplier is the ratio of money supply to the money base. The money base is the sum of currency in circulation and reserves held by commercial banks.

The reserve rate is the percentage of deposits that commercial banks must hold in reserve.

If the reserve rate is 4%, the money multiplier is 10.

Step-by-step explanation:

25

The angle sum theory says that the sum of all the interior angles in a triangle is 180 degrees.

Finding X

To solve for y, we must first find x. This way we know 2 of the interior angles. Luckily, angle x is a part of a linear pair.

Angle x and the angle with a measurement of 115 form a linear pair. Thus, we can create an equation to find x.

By subtracting 115 from both sides we know that x = 65.

Solving for Y

Now that we know x, we can find y. We know that one of the interior angles is 65 and that the other is 90 degrees. The square marking the bottom angles in the middle show that they are right angles.

Lastly, we can create a formula to find y with the angle sum theory.

Combine like terms

Subtract 155 from both sides

This means that the angle y is 25 degrees.

Answer:

47/14 is a mixed number i think

The value of the probability P(S or T) is 39%

The probability values are given as:

P(S) = 12% P(T) =27%

For mutually exclusive events,

P(S or T) = P(S) + P(T)

This gives

P(S or T) = 12% + 27%

Evaluate the sum

P(S or T) = 39%

Hence, the value of the probability P(S or T) is 39%

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The original dimensions of the metal sheet are 22 inches by 52 inch

The volume is defined as the space occupied by any object in three dimensions. For a rectangular box, the volume will be calculated by multiplying the length, width, and height of the object.

If the Width of the metal = x

The length is 30 inches longer than its width= x+30

If Squares with sides 6 in long are cut from the four corners and the flaps are folded.

The length of the pre-folded box =x+30-12=(x+18)inch

The width of the pre-folded box = (x-6-6)inch = (x-12) inch

The height of the flap= 6 inch

The volume of the box = 2400-inch cubed

Volume of a Cuboid = LWH

6(x-12)(x+18)=2400

6x²+36x-1296=2400

6x²+36x-1296-2400=0

6x²+36x-3696=0

6(x-22)(28+x)=0

x-22=0 or x+28=0

Therefore the original dimensions of the metal sheet are 22 inches by 52 inch

The complete question with correct data is given below:-

A rectangular piece of metal is 30 in longer than it is wide. Squares with sides 6 in long are cut from the four corners and the flaps are folded upward to form an open box. If the volume of the box is 2400 incubated​what were the original dimensions of the piece of​ metal?

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