Find the sum of the first 10 terms of the following series, to the nearest integer.
40, 32, 128/5,...
​
,...

5^-2 * 5x = 1

Simplify:

5^-2 = 1/25

Now you have 1/25 * 5x = 1

1/25 x 5 = 1/5

1/5x = 1

Divide both sides by 1/5 ( when dividing by a fraction, flip the fraction over an multiply)

x - 1 x 5/1 = 5

X = 5

Answer:

x = 5

Step-by-step explanation:

This statement translates into 5^(-2)*5x = 1, which by rules of exponents simplifies to:

  5x                           x

--------- = 1,  or          ----- = 1

  5^2                          5

Cross-multiplying, we get x = 5

Answer:

the 48

Step-by-step explanation:

fairly obvious

Answer:

The slope represents the cost per gallon for heating oil while the y-intercept represents the fee for heating oil.

Answer:

$31728

Step-by-step explanation:

sorry if I'm wrong

Answer:

Part A

The estimated solution of the graph is (37/29, -30/29)

Part B

The equation of the blue line is y = 0.6·x - 1.8

The equation of the red line is y = (-4/3)·x + 2/3

Step-by-step explanation:

Part A

From the given graph, we have two lines, one red and one blue line, intersecting in Quadrant IV

Given that the equation of the lines are also required, we find the solution of the graph, through the equation of the lines as follows;

The points through which the blue line passes are (-2, -3), and (3, 0)

The slope of the blue line, [tex]m_b[/tex] = (0 - (-3))/(3 - (-2)) = 0.6

Therefore, we have;

y - 0 = 0.6·(x - 3)

∴ The equation of the blue line is y = 0.6·x - 1.8

The approximate points through which the red line passes are (-1, 2) and (-2.5, 4)

The slope of the red line, [tex]m_r[/tex] = (4 - 2)/((-2.5) - (-1)) = -4/3

Therefore, we have;

y - 2 = (-4/3)·(x - (-1)) = (-4/3)·x - 4/3

∴ The equation of the red line is y = (-4/3)·x - 4/3 + 2 = (-4/3)·x + 2/3

y = (-4/3)·x + 2/3

The solution for the graph is the point where the y-values are equal

Therefore, wat the solution point, y = y, and 0.6·x - 1.8 = (-4/3)·x + 2/3

0.6·x + 4/3·x  = 1.8 + 2/3

x = (1.8 + 2/3)/(0.6 + (4/3)) = 37/29 ≈ 1.28

At the solution of the graph, y = 0.6 × (37/29) - 1.8 = -30/29

Therefore, the estimated solution of the graph is (37/29, -30/29)

Part B

From the above solution of the graph, we have;

The equation of the blue line: y = 0.6·x - 1.8

The equation of the red line: y = (-4/3)·x + 2/3

Answer:

$5.76

Step-by-step explanation:

We solve using the formula of the area of a rectangular prism

A = 2(LW + LH + WH)

The dimensions of the package are given as: 10 inches horizontally, 4 inches vertically, and 4 inches on the side

=2 × (4 × 10 + 4 × 10 + 4 ×4)

=192 square inches

If the cost of packaging is $0.03 per square inch, the total cost of the package is calculated as:

1 square inch = $0.03

192 square inches = x

Cross Multiply

= 192 × $0.03

= $5.76

Answer:

Area of the rectangle = x² - 3x - 10

2019

Step-by-step explanation:

Length of the rectangle = x + 2

Width of the rectangle = x - 5

Area of the rectangle = length × width

= (x + 2) (x - 5)

= x² + 2x - 5x - 10

= x² - 3x - 10

Area of the rectangle = x² - 3x - 10

C = 20t² + 135t + 3050

Where

C = the number of new cars

t = year the number of new cars was purchased

t = 0 corresponds to 1998

Find the when c = 15,000

C = 20t² + 135t + 3050

15,000 = 20t² + 135t + 3050

20t² + 135t + 3050 - 15,000 = 0

20t² + 135t - 11,950 = 0

4t² + 27t - 2390 = 0

Solve using quadratic equation

t = -b ± √b² - 4ac / 2a

= -27 ± √27² - 4(4)(-2390) / 2(4)

= -27 ± √729 -(-38240) / 8

= -27 ± √729 + 38240 / 8

= -27 ± √38969 / 8

= -27/8 + √38969/8 or 27/8 - √38969/8

= -3.375 + 197.41/8 or -3.375 - 197.41/8

= -3.375 + 24.67625 or -3.375 - 24.67625

t = 21.30125 or - 28.05125

t cannot be negative

Therefore,

t = 21.30125

To the nearest whole number

t = 21

Recall,

t = 0 corresponds to 1998

Therefore

1998 + 21 = 2019

c = 15,000 in the year 2019

Answer:

x^2 - 2x - 8.

Step-by-step explanation:

Using long division:

x - 2)x^3 - 4x^2 - 4x + 16( x^2 - 2x - 8 <------ Quotient

       x^3 - 2x^2

              -2x^2 - 4x

              -2x^2 + 4x

                         - 8x + 16

                          -8x + 16

                            ............

Answer:

false it can be in any order but must be according to the set of data

Answer:

Holly would have 20 1/10 sized ribbons.

Step-by-step explanation:

One whole ribbon would equal out to 10, this number multiplied by 2 would be 20. Therefore meaning she should have 20 1/10 sized pieces of ribbon.

Answer:

semi-regular tessellations

Step-by-step explanation:

Answer:

1:3. That's the answer to this question.

Answer:

y=2x+1

Step-by-step explanation:

Hi there!

We are given the slope (m), which is 2, as well as the point (5,11).

We need to find the equation of the line.

There are 3 ways to write the equation of the line, but the most common type is slope-intercept form, or y=mx+b, where m is the slope and b is the y intercept

We're already given the slope (2), so we can substitute it into the equation right away

here's the equation so far:

y=2x+b

now we need to find b.

We can do this by plugging (5,11) into the equation, as the line passes through that point.

Substitute x as 5 and 11 as y

11=2(5)+b

multiply

11=10+b

subtract 10 from both sides

1=b

substitute 1 as b into the equation

y=2x+1

Hope this helps! :)

Answer:

B y = x² +9

Step-by-step explanation:

A quadratic function must have the highest power of x being x^2 and must have an x^2 term

A y = X-9  - linear

B y = x² +9 quadratic

C y = x + 2x -9 - linear

Answer:

273 - 153.94 = 119.1 [tex]in^{2}[/tex]

Step-by-step explanation:

area of a trapezoid - area of a circle = shaded area

Answer:

7 gallons

Step-by-step explanation:

Montraie is driving on a long road trip

He currentlyhase 13 gallons of fuel in his car

Each hour that he drives, he uses up 1 gallon of fuel

Therefore the amount of gas that would be left after 6 hours can be calculated as follows

= 13-6

= 7

Hence there will be 7 gallons of fuel left

=

Answer: If the diagonals of a parallelogram are perpendicular, then the parallelogram is a rhombus. If one diagonal of a parallelogram bisects a pair of opposite angles, then the parallelogram is a rhombus. To prove a square, you must prove it is both a rectangle and a rhombus.

Answer:

Step-by-step explana

multiply it by 2 or sdd itself to it

The  account will have $1536.007 after 9 years.

Part A:

To express the total amount of money A(t) in the account after 7 years, we can use the formula:

A(t) = P[tex](2^t)[/tex]

where:

A(t) is the total amount in the account after t years,

P is the initial amount in the account (starting with $3.00 in this case),

t is the number of years.

Substituting the values into the formula, we get:

A(t) = 3 ([tex]2^7[/tex])

A(t) = 3 x 128

A(t) = 384

Therefore, the total amount of money in the account after 7 years is $384.

B) To find out after how many years the account will have $1536.007, we need to solve the equation:

1536.007 = 3 [tex](2^t)[/tex]

Dividing both sides of the equation by 3, we get:

512.0023333333 = [tex]2^t[/tex]

Taking the logarithm (base 2) of both sides, we have:

log2(512.0023333333) = t

t = 9.000317.

Therefore, the account will have $1536.007 after 9 years.

Learn more about Equation here:

https://brainly.com/question/29538993

#SPJ2

Answer:

D

Step-by-step explanation:

Answer:

first blank- 2 second blank- 3 1/2 or 4 may be 3 too

Step-by-step explanation:

well when you look at the shape you can go from a to b and count the blocks which it would be 2

and you would want to do the same thing with C,D

Answer:

1331 m^2

Step-by-step explanation:

To find the volume of the cube, we should first find the length of one side's edge. The square root of 121 (the face area) gives us our edge length, 11.

Now, to find the volume of the whole cube, we use the equation V=11^3, and our result is 1331.

Answer:

33 ft

Step-by-step explanation:

C = 2 r [tex]\pi[/tex]

The length of the arc is [tex]\frac{18\pi }{360}[/tex] × 210 ≈ [tex]\frac{18*22*210}{360*7}[/tex] = 33 ft .

Answer:

6>x=4

hope that helps!

please mark brainiest<3

Answer: I'm not smart or nun but u tryna find the graph? It's (3, -36)

Step-by-step explanation:

Kinda did it-

Answer:

x=28

Step-by-step explanation:

Hi there!

SSS similarity theorem is a theorem that can determine similar triangles; the criteria for SSS~ is that the corresponding sides of the triangles create proportions which is the same as the ratio of similitude (k)

First, we need to find the ratio of similitude.

We need to assume that the triangles are similar.

15 corresponds with 20 (if you turn both triangles until they're titled the same way, you will see that 15 and 20 are the measures of the same sides on the triangles)

so that means 15/20 must make the ratio of similitude

15/20 is equal to 3/4

therefore k=3/4

as the triangle is already assumed similar, that means that 21/x will also give us a ratio that is equal to 3/4 (ratio of similitude)

therefore, 21/x=k

Since both ratios are equal to k, set 3/4 and 21/x equal to each other. This is possible via a property called transitivity (if a=b and b=c, then a=c)

3/4=21/x

cross multiply

3x=84

divide both sides by 3

x=28

So that means that 28 will make the triangles similar by SSS similarity

*you double check by doing 21/28 and see that it's also equal to 3/4

Hope this helps!

Answer:

yehshjdjejrdjjej3u Rudd ixjje

Answer:

1: 16.7%

prime number: 50%

Step-by-step explanation:

divide the numbers

Answer:

2/3

Step-by-step explanation:

There are 6 possible numbers

all of the prime numbers from 1 to 6 are

2, 3, 5 ( plus 1 because this problem is counting 1 along with the prime numbers)

That is 4 numbers

4 out of 6 numbers

so there is a 4/6 or 2/3 chance that George will roll a 1 or a prme number

Hi there!  

»»————-　★　————-««

I believe your answer is:

A vertical shift down one unit.

»»————-　★　————-««  

Here’s why:

»»————-　★　————-««  

Hope this helps you. I apologize if it’s incorrect.  

Answer:

A

Step-by-step explanation:

-15(-8)

=+(15*8)

=120

So, the ans is A