sum of first nth term of the seris 2^2+4^2+6^2+8^2+.........n terms is​

Answer:

= 70 Meters

Step-by-step explanation:

We can use the sine rule as follows:

Angle ABC=180-(70.5+38.833)

=70.667°

Using the sine rule and sides AB, AC and angles ABC and ACB:

b/Sin B=c/Sin C

Replacing with the values above we get:

AC/Sin ABC= AB/Sin ACB

105.6/Sin 70.667=AB/Sin 38.833

AB=(105.6 Sin 38.833)/Sin 70.667

=70.17 meters

The distance between the two points to the nearest meter is 70 meters

Answer:

70 m

Step-by-step explanation:

I got it correct on founders edtell

Answer:

500.5

Step-by-step explanation:

The average of a set of numbers is the sum of the numbers divided by the number of numbers.

The sum of all whole number form 1 to n is n(n + 1)/2.

The sum of all whole numbers from 1 to 1000 is

1000(1000 + 1)/2 = 1000(1001)/2 = 500,500

The average is the sum of the numbers divided by the number of numbers.

average = 500,500/1000 = 500.5

Answer:

(A.)A computer randomly generates 6 put of 100 numbers.

Step-by-step explanation:

This is an actual probability.

Answer:

[tex]\large\boxed{y+5=\dfrac{2}{3}(x-4)}[/tex]

Step-by-step explanation:

The point-slope form of an equation of a line:

[tex]y-y_1=m(x-x_1)[/tex]

m - slope

Parallel lines have the same slope.

We have the equation in the slope-intercept form (y = mx + b)

[tex]y=-\dfrac{2}{3}x+8\to m=\dfrac{2}{3}[/tex]

Put to the point-slope equation value of the slope and the coordinates of the point (4, -5):

[tex]y-(-5)=\dfrac{2}{3}(x-4)\\\\y+5=\dfrac{2}{3}(x-4)[/tex]

The equation in point-slope form for the line parallel to y = (-2/3)x + 8 that passes through (4, -5) is y - (-5) = (-2/3)(x - 4), which is option C.

The equation is the relationship between variables and represented as y = ax + b is an example of a polynomial equation.

Here,
The equation of a line in point-slope form is given by:

y - y₁ = m(x - x₁)

where m is the slope of the line, and (x₁, y₁) is a point on the line.

We are given that the line we want to find is parallel to y = (-2/3)x + 8, which means it has the same slope of -2/3.

We are also given that the line passes through the point (4, -5).

Substituting the values into the point-slope form equation, we get:

y - (-5) = (-2/3)(x - 4)

Therefore, the equation in point-slope form for the line parallel to y = (-2/3)x + 8 that passes through (4, -5) is y - (-5) = (-2/3)(x - 4), which is option C.

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Answer:

Step-by-step explanation:

The slope-intercept form of an equation of a line:

[tex]y=mx+b[/tex]

m - slope

b - y-intercept.

Put the given y-intercept b = 2 and the coordinates of the point (1, 1) to the equation:

[tex]1=1m+2[/tex]            subtract 2 from both sides

[tex]-1=m\to m=-1[/tex]

The equation of a line:

[tex]y=-1x+2\to y=-x+2[/tex]

The general form of an equation of a line:

[tex]Ax+By+C=0[/tex]

Convert:

[tex]y=-x+2[/tex]          add x to both sides

[tex]x+y=2[/tex]         subtract 2 from both sides

[tex]x+y-2=0[/tex]

Chapter : Linear equations

Lesson : Math of Junior High School

2x - 3 + 3x = -28

= 5x - 3 = -28

= 5x = -28 + 3

= 5x = -25

= x = -25 / 5

= x = 5

For this case we must find the value of "x" of the following expression:

[tex]2x-3 + 3x = -28[/tex]

We add similar terms:

[tex]5x-3 = -28[/tex]

We add 3 to both sides of the equation:

[tex]5x = -28 + 3[/tex]

Different signs are subtracted and the sign of the major is placed:

[tex]5x = -25[/tex]

We divide between 5 on both sides of the equation:

[tex]x = \frac {-25} {5}\\x = -5[/tex]

ANswer:

[tex]x = -5[/tex]

Answer:

Sweater =400 grams

Hat =80 grams

Scarf =75 grams

Step-by-step explanation:

The amount of wool used to make a sweater, a hat and a scarf=555 grams

Let the amount of wool used to make a sweater be = x

The amount of wool for the sweater =x/5

The amount of wool used for the scarf=x/5 -5

Total amount of wool used = x+(x/5)+(x/5-5)

x+x/5 +x/5-5=555

Multiply all through by the LCM 5

5x+x+x-25=2775

7x=2800

x=400

Sweater =400 grams

Hat=400/5=80 grams

Scarf =400/5 -5=75 grams

Answer:

B: (2, -1)

Step-by-step explanation:

1) First isolate the y in both equations

2) Set the equations equal to each other

3) Solve for x (you should get 2 and 5)

4) Insert the x values back in to get your y values

5) You should have gotten (2, -1) and (5, 2)

These are your two answers, but the question is only asking for one solution and (5,2) isn't one of the options, so it has to be (2,-1).

Answer:

65x^2 – 26x

Step-by-step explanation:

To determine the total number of seats, take the number of rows and multiply by the number of seats per row

f(x) * g(x)

13x * (5x-2)

65x^2 -26x

Answer:d

Step-by-step explanation:A wedding planner is organizing the seating for a wedding. He can represent the number of rows by the function f(x) = 13x and the number of seats in each row by the function g(x) = 5x – 2.Which function represents the total number of seats?65x + 2665x – 2665x2 + 26x65x2 – 26x

Answer:

$1x + $3y = c

Step-by-step explanation:

To write an expression you need to pick a variable to represent the cups of orange juice and lemonade.

x = cups of lemonade sold

y = cups of orange juice sold

Now you have the variables to represent the amount of cups sold, so now you need a variable to represent the total cost.

c = amount of money earned from selling drinks

Now you have all the variables, so you need to write how much is cost for that drink.

$1 for one cup of lemonade so $1x

$3 for one cup of orange juice so $3x

Now put the expression together:

$1x + $3y = c

The expression that represents the amount of money that Alice selling drinks​ is $ (a+ 3b)

An expression obtained by a finite number of the fundamental operations of algebra upon symbols representing numbers.

According to the problem,

Let the number of cups of lemonade sold are a and the cups of orange juice sold are b.

Cost of 1 cup of lemonade is $ 1

∴Cost of a cups of lemonade = $ a

Similarly we can say,

Cost of 1 cup of orange juice is $ 3

∴ Cost of b cups of orange juice is $ 3b

So the total cost is represented by the expression : $(a + 3b)

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Answer:

[tex]z=\frac{63}{4}[/tex]

Step-by-step explanation:

When two variables vary in a directly proportional way, it means that when one variable grows, the other also grows.

This is represented by the following equation

[tex]y = kx[/tex]

Where k is the constant of proportionality

When two variables vary in an inversely proportional way, it means that when one variable grows, the other decreases.

This is represented by the following equation

[tex]y = \frac{k}{x}[/tex]

In this case we know that:

z varies directly with [tex]x^4[/tex] and inversely with y.

We write this as:

[tex]z = k\frac{x ^ 4}{y}[/tex]

We know that When [tex]x = 2[/tex] and [tex]y = 4,\ z = 3[/tex].

So we use this information to find the constant k

[tex]3 = k\frac{2 ^ 4}{4}[/tex]

[tex]3 = k\frac{16}{4}[/tex]

[tex]3 = 4k[/tex]

[tex]k = \frac{3}{4}[/tex]

So the equation is:

[tex]z = \frac{3}{4}\frac{x ^ 4}{y}[/tex]

Finally when x = 4 and y = 9 then:

[tex]z = \frac{3}{4}\frac{4 ^ 4}{9}[/tex]

[tex]z = \frac{3}{4}\frac{4 ^ 4}{9}[/tex]

[tex]z=\frac{63}{4}[/tex]

Answer:

slope is

Step-by-step explanation:

slope of line is -3

Answer:

The answer is -3.

Step-by-step explanation:

I just got it correct.

Answer:

C

Step-by-step explanation:

c is the answer to your question

Answer:

C

Step-by-step explanation:

Answer:

She has seven 3 cents stamps and six 8 cents stamps.

Step-by-step explanation:

7*3 = 21

6*8 = 48

48 + 21 = 69

Answer: She has SEVEN 3 cent stamps and SIX 8 cent stamps.

Step-by-step explanation:

Let be "x" the number of  8 cent stamps and "y" the number of  3 cent stamps.

Set up the following system of equations:

[tex]\left \{ {{x=y-1} \atop {8x+3y=69}} \right.[/tex]

Substitute the first equation into the second one and the solve for "y":

[tex]8(y-1)+3y=69\\\\8y-8+3y=69\\\\11y=77\\\\y=7[/tex]

Substitute the value of "y" into the first equation:

[tex]x=7-1\\\\x=6[/tex]

Answer:

C) 360pi in2

Step-by-step explanation:

Given:

radius, r= 10in

height, h=26in

surface area of the cone, T.S.A= ?

T.S.A=πrl +πr^2

         =π(10)(26) +π(10)^2

         =260π+100π

         =360π^2 !

[tex]\bf \cfrac{p^{-4}~~\begin{matrix} q^3 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~ r^{-7}}{p^{-2}~~\begin{matrix} q^3 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~ p^{-2}}\implies \cfrac{1}{p^{4}p^{-2}p^{-2}r^7}\implies \cfrac{1}{p^{4-2-2}r^7}\implies \cfrac{1}{p^0r^7}\implies \cfrac{1}{r^7}[/tex]

Answer:

[tex]\large\boxed{r^{-7}=\dfrac{1}{r^7}}[/tex]

Step-by-step explanation:

[tex]\dfrac{p^{-4}q^3r^{-7}}{p^{-2}q^3p^{-2}}\qquad\text{use}\ \dfrac{a^n}{a^m}=a^{n-m}\\\\=p^{-4-(-2)-(-2)}q^{3-3}r^{-7}\\\\=p^{-4+2+2}q^0r^{-7}\\\\=p^0q^0r^{-7}\\\\=r^{-7}\qquad\text{use}\ a^{-n}=\dfrac{1}{a^n}\\\\=\dfrac{1}{r^7}[/tex]

Answer:

Radius of the cone's base is 3x ....

Step-by-step explanation:

We have given that the volume of a cone is 3πx³

Height = x units.

The volume of a cone of radius r and height h units is given by:

V= 1/3 π r² *h

Simply plug the values given in the question into the above mentioned equation:

1/3πr²*x = 3*π*x³

1/3r²*x= 3x³

r² = 3*3*x³/x

r²=9x²

Taking square root at both sides we get:

√r² =√9x²

r = 3x

Thus the radius of the cone's base is 3x.

Answer: The volume given is 3Pi(x^3) and the radius is x. The formula for the volume of a cone is V= [1/3]Pi(r^2)*height => [1/3]Pi (r^2) x = 3Pi(x^3) => (r^2)x = 3*3(x^3) => (r^2)x = 9(x^3) => (r^2) = 9x^2 => r = sqrt[9x^2] = 3x. So THE CORRECT Answer is: A) r = 3x

Step-by-step explanation: I just paid for this answer

Answer:

It is the second statement.

Step-by-step explanation:

y = 25(3)^(n - 1)   where y = the number of fleas and n = the number of days.

On day 1,  y = 25 3^0 = 25

On day 2, y = 25(3^1 = 75

On day 3, y = 25(3) ^2 = 225  and so on.

Exponential growth.

Answer: Second Option

Step-by-step explanation:

Initially there are 25 fleas, and each day triples the amount.

So:

Day 1: 25

Day 2: [tex]25 * 3 = 75[/tex]

Day 3: [tex]25 * (3) ^ 2 = 225[/tex]

Day 4: [tex]25 * (3) ^ 3 = 675[/tex]

Day n: [tex]25 * (3) ^ {n-1}[/tex]

Note that the function that models the number of fleas for day n is an exponential growth function with an increase factor of 3 and an initial quantity of 25. Therefore, the answer is the second option.

Answer:

the Answer is: D

Step-by-step explanation:

so that means he makes 11 dollars an hour so at most he can make that because he can work really work however long which means he can't really have less than 11 dollars an hour therefore its D

Answer: (-5,8)

Step-by-step explanation: since the radius of a circle square root of 14 so

x² + y² + 10x − 16y + 75 = 0

x² +10x + y² − 16y = -75

x² +10x + 25 + y² − 16y + 64 = -75 + 25 + 64

(x + 5)² + (y − 8)² = 14

ANSWER

The center is

[tex](-5,8)[/tex]

EXPLANATION

The given circle has equation

[tex] {x}^{2} + {y}^{2} + 10x - 16y + 75= 0[/tex]

An easy way to find the center is by comparing to the general equation of the circle

[tex] {x}^{2} + {y}^{2} + 2gx + 2fy + c = 0[/tex]

where (-g,-f) is the center.

By comparing, we have

[tex]2gx = 10x[/tex]

[tex] \implies \: 2g = 10[/tex]

Divide both sides by 2.

[tex]g = 5[/tex]

Also,

[tex]2fy = - 16y[/tex]

[tex]2f = - 16[/tex]

Divide both sides by 2

[tex]f = - 8[/tex]

Therefore the center is

[tex](-5,- - 8) = (-5,8)[/tex]

Answer:

Answer in picture.

Step-by-step explanation:

First step: You must plot the point (-3,5).

To graph this point, start at the origin.  

The point says move left 3 and up 5 and put your dot (your point).

Second step: Use your slope to find a second point to plot.  The slope is [tex]\frac{-1}{2}[/tex].

Slope is rise/run.  So it says down 1 and right 2.

So starting at the first point you plotted and you count down 1 and then go right 2 and put your second point.

Third step: Connect the two points with a straight-edge. Extend in both directions.

The two points I used to graph my line is (-3,5) and (-1,4).

Step-by-step explanation:

[tex]slope=\dfrac{rise}{run}=\dfrac{\Delta y}{\Delta x}\\\\\Delta y-\text{run up (+) or down (-)}\\\\\Delta x-\text{run to the right (+) or to the left (-) }\\\\\text{We have}\ slope=-\dfrac{1}{2}=\dfrac{1}{-2}\to\Delta y=1\ (\text{1 unit up}),\ \Delta x=-2\ (\text{2 units to the left})\\\\\text{Mark the point (-3, 5) in the coordinates system. Go 1 unit up}\\\text{and 2 units to the left. Mark next point.}\\\text{Draw a line passing through the given points.}\\\\\bold{Look\ at\ the\ picture.}[/tex]

Step-by-step explanation:

(f+g)(x) means f(x) + g(x).

(f−g)(x) means f(x) − g(x).

So all you have to do is add them and subtract them.

1. (f+g)(x) = f(x) + g(x)

(f+g)(x) = (3x − 7) + (2x − 4)

(f+g)(x) = 5x − 11

2. (f−g)(x) = f(x) − g(x)

(f−g)(x) = (3x − 7) − (2x − 4)

(f−g)(x) = 3x − 7 − 2x + 4

(f−g)(x) = x − 3

3. (f+g)(x) = f(x) + g(x)

(f+g)(x) = (2x + 3) + (x² + ½ x − 7)

(f+g)(x) = x² + 2½ x − 4

4. (f−g)(x) = f(x) − g(x)

(f−g)(x) = (2x + 3) − (x² + ½ x − 7)

(f−g)(x) = 2x + 3 − x² − ½ x + 7

(f−g)(x) = -x² + 1½ x + 10

Answer:

x=9

Step-by-step explanation:

90-30= 60

now set 60 = 5x + 15

solve for x

45= 5x

divide by 5

x = 5

Answer:

Some polyhedrons are both prisms and pyramids.- False

The provided statement "Some polyhedrons are both prisms and pyramids" is false.

It is defined as the branch of mathematics that is concerned with the size, shape, and orientation of two-dimensional and three-dimensional figures.

We have a statement:

Some polyhedrons are both prisms and pyramids.

As we know,

A polygon-based solid figure is known as a polyhedron, for instance, a soccer ball, a cuboid, etc.

A strong figure with two equal bases is a prism for instance: Cube. Cylinder, Cuboid, etc.

A polyhedron with a base and an top at the top is called a pyramid, cone, a pyramid with triangles as its base, etc.

Thus, the provided statement "Some polyhedrons are both prisms and pyramids" is false.

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Answer:

[tex]\large\boxed{\dfrac{5}{-7x}\cdot\dfrac{-9y}{8}=\dfrac{45y}{56x}}[/tex]

Step-by-step explanation:

[tex]\dfrac{5}{-7x}\cdot\dfrac{-9y}{8}=\dfrac{(5)(-9y)}{(-7x)(8)}=\dfrac{-45y}{-56x}=\dfrac{45y}{56x}[/tex]

Answer:

[tex]24x -{6x}^{2} = 0 \: matches \: with \: 6x(4 - x) \: and \: the \: solution \: x = 0 \ \: or \: \: x = 4[/tex]

[tex]2 {x}^{2} + 6x = 0 \: matches \: with \: 2x(x + 3) = 0 \: and \: the \: solution \: x = 0 \: or \: x = - 3[/tex]

[tex]4x - {x}^{2} = 0 \: matches \: with \: x(4 - x) = 0 \: and \: the \: solution \: x = 0 \: or \: x = 4[/tex]

[tex]14x - {7x}^{2} = 0 \: matches \: with \: 7x(2 - x) = 0 \: and \: the \: solution \: x = 0 \: or \: x = 2

[/tex]

Answer:

B.

Step-by-step explanation:

Quarterly interest rate is 4.5 / 4 = 1.125%.

Monthly rate is 4.5 / 12 = 0.375%.

Answer:

B 1.25%-0.375%

Step-by-step explanation:

Compounded quarterly means there are 4 interest periods in 1 year, so divide the annual interest rate by 4.

4.5% ÷ 4 = 1.125%

Compounded monthly means there are 12 interest periods in 1 year, so divide the annual interest rate by 12.

4.5% ÷ 12 = 0.375%

Answer:

The correct answer for question A is x=2i or x= -2i

The correct answer for question B is (x+2i)(x-2i)

Step-by-step explanation:

Solution of question A:

x²+4=0

Subtract 4 from both sides.

x²+4-4=0-4

x²=-4

Take square root of both sides

√x²=+/-√-4

We know that i=√-1

So,

x=+/-(√4)(√-1)

x=+/-2i

Therefore x= 2i, x= -2i

Solution of question B:

x²+4

It cannot be factored using real number coefficient. You have to use complex numbers.

As we know -4 =(2i)², so we can write as:

x²+4=x² - (-4)= x²-(2i)²

Now factor using the difference of squares:

x²+4=(x+2i) (x-2i)....

[tex]\bf a^{-4}+b^2\implies \cfrac{1}{a^4}+b^2\qquad \begin{cases} a=2\\ b=\frac{3}{4} \end{cases}\implies \cfrac{1}{2^4}+\left( \cfrac{3}{4} \right)^2\implies \cfrac{1}{16}+\cfrac{3^2}{4^2} \\\\\\ \cfrac{1}{16}+\cfrac{9}{16}\implies \cfrac{1+9}{16}\implies \cfrac{10}{16}\implies \cfrac{5}{8}[/tex]

Answer:

The correct answer is option C. 75 m³

Step-by-step explanation:

Points to remember

Volume of rectangular prism = Base area * Height

To find the volume of given prism

Here Base area = 15 m² and

Height = 5 m

Volume = base area * height

 = 15 * 5

 = 75 m³

Volume of prism = 75 m³

Therefore the correct answer is option C. 75 m³

Answer:

Rectangular Prism Volume =  length x width x height

Rectangular Prism Volume =  15 x 5

Rectangular Prism Volume =  75 cubic meters

Step-by-step explanation: