X^2+4x+4=12 find the solutions to the equation

Step-by-step explanation:

the sum of an infinite geriatric series with |r| < 1 is

s = a1/ (1 - r)

in our case we have

a1 = 8

12 = 8/(1 - r)

12(1 - r) = 8

1 - r = 8/12 = 2/3

-r = -1/3

r = 1/3

so, the first 4 terms (I added a5 too, just in case your teacher meant the NEXT 4 terms) are

a1 = 8

a2 = a1 × 1/3 = 8/3

a3 = a2 × 1/3 = 8/9

a4 = a3 × 1/3 = 8/27

a5 = a4 × 1/3 = 8/81

...

Answer:

[tex]8,\quad \dfrac{8}{3},\quad \dfrac{8}{9},\quad\dfrac{8}{27}[/tex]

Step-by-step explanation:

Sum to infinity of a geometric series:

[tex]S_\infty=\dfrac{a}{1-r} \quad \textsf{for }|r| < 1[/tex]

Given:

Substitute given values into the formula and solve for [tex]r[/tex]:

[tex]\implies 12=\dfrac{8}{1-r}[/tex]

[tex]\implies 1-r=\dfrac{8}{12}[/tex]

[tex]\implies r=1-\dfrac{8}{12}[/tex]

[tex]\implies r=\dfrac{1}{3}[/tex]

General form of a geometric sequence: [tex]a_n=ar^{n-1}[/tex]

(where a is the first term and r is the common ratio)

Substitute the found values of [tex]a[/tex] and [tex]r[/tex]:

[tex]\implies a_n=8\left(\dfrac{1}{3}\right)r^{n-1}[/tex]

The first 4 terms:

[tex]\implies a_1=8\left(\dfrac{1}{3}\right)r^0=8[/tex]

[tex]\implies a_2=8\left(\dfrac{1}{3}\right)r^1=\dfrac{8}{3}[/tex]

[tex]\implies a_3=8\left(\dfrac{1}{3}\right)r^2=\dfrac{8}{9}[/tex]

[tex]\implies a_4=8\left(\dfrac{1}{3}\right)r^3=\dfrac{8}{27}[/tex]

Answer: If you’re doing algebra, -3<x or x<_4.

Another answer is -3<x<_4

Answer:

-3 < x <_4

Step-by-step explanation:

-8 < 3x+1 <_13

First solve for the left side: -8 < 3x + 1

Subtract 1 from each side

-9 < 3x

Divide each side by 3

-3 < x

Solve for the right side: 3x+1 <_13

Subtract 1 from each side

3x <_ 12

Divide each side by 3

x<_4

Put it together for your answer

-3 < x <_4

A particle moves along line segments from the origin to the points, work done is mathematically given as

W=184.5units

Considering line segments from (0,0,0)origin to (2,0,0) , (2,5,1) and (0,5,1) under the infulence of force

Generally,  the equation for force is mathematically given as

F = z2i + 5xyj + 2y2k

Therefore, Considering u*v

[tex]u * v = (u_1j+u_2j+u_3k) * (v_1i+v_2j+v_3k)[/tex]

[tex]u* v = u_1v_1(i * i) + u_1v_2(i * j)+u_1v_3(i * k) + u_2v_1(j * i) + u_2v_2(j * j)+u_2_3(j* k) + u_3v_1(k * i) + u_3v_2(k * j)+u_3v_3(k * k)[/tex]

Where

[tex]i * i = j *j=k * k=0[/tex]

Hence

[tex]u* v = u_1v_2k-u_1v_3j-u_2v_1k+u_2v_3i +u_3v_1j - u_3v_2i[/tex]

[tex]u = (u_1,u_2,u_3) = (0,5,1)\\\\v = (v_1,v_2,v_3) = (-3,0,0)[/tex]

The normal equation formed

-2y + 15z = 0

z= (1/5)y

Considering the level surface and differential surface area

h(x,y,z) = -y + 5z =0

[tex]dS = |grad(h)| dA[/tex]

In terms of the x and y coordinates of (2,0,0) and (2,5,1) and (0,5,1), we can state that the ranges are 0 to 3 and 5 respectively we have

[tex]0 \leq x \leq 2 \ and \ 0 \leq y \leq 5[/tex]

Using strokes theorem to evaluate

[tex]F = z2i + 5xyj + 2y2k[/tex]

[tex]curl \ F = 4yi+2zj+5yk = (4y,2z,5y)[/tex]

[tex]curl \ F * nds= \frac{1}{5}(-2z + 25y)\ dy \ dx[/tex]

In conclusion, The work done is

[tex]W=\int _CF *dr[/tex]

[tex]\int _C F * dr = \int \int curl \ F * n ds[/tex]

[tex]\int _C F *dr = \frac{123}{2}\int_0^3 \ dx[/tex]

[tex]\int _C F * dr = \frac{123*3}{2}[/tex]

W= 184.5units

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Answer:

Median: 21

Eric took the longest

Ed took 18 minutes longer than Mike

Oscar took the shortest amount of time to solve the puzzle

Step-by-step explanation:

The median is the middle amount of the numbers, line them up from smallest to largest and find the number in the middle...the largest number is the person who took the longest...subtract Ed's score (25) from Mike's score (4) to get the answer...and the smallest number is the person who took the shortest amount of time

Answer: 538

Step-by-step explanation: en verdad no sé pero eso fuelo que me salio

Answer:

f(3) = 1

Step-by-step explanation:

substitute x = 3 into f(x) , that is

f(3) = 3² - 4(3) + 4 = 9 - 12 + 4 = 1

Answer:

1

Step-by-step explanation:

Substitute 3 for x in your equation leaving you with (3)^2-4(3)+4.

9-12+4

-3+4=1

Answer:

The line has no slope. I hope this helps

The slope of the linear equation is 15, so the correct option is B.

A linear equation can be written as:

y = a*x + b

Where a is the slope and b is the intercept.

For a line that passes through the points (x₁, y₁) and (x₂, y₂), the slope can be written as:

[tex]a = \frac{y_2 - y_1}{x_2 - x_1}[/tex]

Here we have the two points (0.2, 3) and (0.4, 6), so the slope is:

[tex]a = \frac{6 - 3}{0.4 - 0.2} = 15[/tex]

So the slope of the line is 15, which means that the correct option is B.

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Answer:

The answer is 7

Step-by-step explanation:

To find the volume you multiply the width, height, and the length.

Length= 7/3

width= 3/3

height= 9/3

When you multiply you then have to simplify which is 7/1 or 7.

Mark this correct to help me gain!!

Given the diameter of the surface of the clock, the area of the surface of the alarm clock is 3846.5cm².

Note that: Area of a circle is expressed as;

A = πr²

Where r is radius and π is constant pi ( π = 3.14 )

Given that;

A = πr²

A = 3.14 × ( 35cm )²

A = 3.14 × 1225cm²

A = 3846.5cm²

Therefore, given the diameter of the surface of the clock, the area of the surface of the alarm clock is 3846.5cm².

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a) T - Calories, 2000 - Minimum calories, 500 - Additional calories per exercise hour, b) We should consume 3500 calories to spend three hours exercising.

In this question we have a linear function where the independent variable is the exercise time (h), in hours, and the dependent variable is the calorie gain (T), in calories. The constant "2000" is the minimum calorie consumption and the constant "500" represents the amount of additional calories per each hour of exercise.

Now we proceed to respond the questions of the part a):

(i) T - Amount of calories needed, (ii) 2000 - Minimum calorie consumption, (iii) 500 - Amount of additional calories per hour of exercise.

b) And lastly we calculate the amount of calories by evaluating the function:

T = 2000 + 500 · 3

T = 2000 + 1500

T = 3500

We should consume 3500 calories to spend three hours exercising.

The statement is incomplete, the complete form is shown below:

You are trying to bulk up and gain muscle. Your trainer says that your daily calorie intake should increase based on the hours you spend exercising and can be represented by the following equation: T = 2000 +  500 · h

a) What does each part of this expression represent? (i) T = , (ii) 2000, (iii) 500, (iv) h

b) If you spend 3 hours exercising, how many calories should you consume?

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Answer:

$135.98

Step-by-step explanation:

15% of $159.98 = 0.15 × $159.98 = $24.00

$159.98 - $24.00 = $135.98

Answer: all integers

Step-by-step explanation:

[tex]A \cup B[/tex] denotes the union of the two sets, and is thus the set of all integers.

Answer: 363

Step-by-step explanation:

The common difference is 7, so the explicit formula is [tex]a_{n}=-92+7(n-1)[/tex].

Substituting in n=66,

[tex]a_{66}=-92+7(66-1)=\boxed{363}[/tex]

Answer:

2 Hours

Step-by-step explanation:

First you have to add up all the points which would be;

1 1/2 + 1 1/2+ 2 1/2+ 2 1/2= 8 hours

Then you have to divide by how many points to find the average;

8 hours divided by 4 points= 2 hours average

In total, she will practice 2 hours every day

Answer:

The angle is referred to as a ∠ZYX angle, or ∠XYZ angle, because of the overall positioning. Think of it this way, you have a triangle with 3 angles. You have point X the high point, point Y the farthest point out, and point Z which makes the triangle complete. Connect these, and your angle becomes ZYX / XYZ.

Hope this helps!

Answer:

wedg

Step-by-step explanation:

ed

Answer:

A1 5×3 = 15

A2 = 2×4= 8

an=I don't know that one

Answer:

All rectangles are parallelograms. Parallelograms have 2 pairs of parallel sides. Therefore, all rectangles have 2 pairs of parallel sides.

Step-by-step explanation:

Answer:

Equation: 2w + 2(2w) = 12

width = 2

length = 4

Step-by-step explanation:

Width is w

Length is 2 * width = 2w

Perimeter is 2w + 2l

Substitute 2w for L.

Perimeter is now 2w + 2(2w) = 12

Distribute the 2 to the parentheses.

2w + 4w = 12

Combine Like terms

6w = 12

Divide by 6 to solve for w.

w = 2

If w = 2, then the length = 4.

Answer:

6.28 ft

Step-by-step explanation:

using the formula [tex]\pi d[/tex] to find the circumference of the circle, you substitute the numbers. 3.14(2). 3.14 x 2 = 6.28 hence the answer

Answer:

2/3 or 0.66 repeated

Step-by-step explanation:

Since 2022 is only divisible by 1,2,4, and 5, the probability of getting a number that is a divisor of 2020 is 4/6, simplified to 2/3 or %0.66.

The theoretical probability of getting an odd number is 0.6, but the experimental probability was 0.5.

Probability of getting an odd number: 3/5 = 0.6 or 60%

The experimental probability is lower than the theoretical probability.

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Answer:

Answer in pic below

Step-by-step explanation:

Answer: 36.9

Step-by-step explanation:

The dividend that's represented by the synthetic division is 2x³ + 10x² + x + 5.

From the information, given that the vertical line and a horizontal lines combined to form the L shape.

Row 1 has entries 2, 10, 1, 5.

Row 2 has entries -10, 0, -5.

In this situation, entry -5 is outside to the let of the shape.

Here, the dividend that's represented by the synthetic division is 2x³ + 10x² + x + 5.

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Answer:

step 1: 2 Step 2: 1

Step-by-step explanation:

Step 3: 2, -1, -2

Complete the division. The remainder is 0. The quotient is x^2 - x - 12.

Answer:

y = 6x + [tex]\frac{-1}{2}[/tex]

Step-by-step explanation:

I think take this with a grain of salt

The slope of the line is 1/2 or one-half if the line that cuts through the points (1, 2) and (5, 4) option (c)  One-half is correct.

The ratio that y increase as x increases is the slope of a line. The slope of a line reflects how steep it is, but how much y increases as x increases. Anywhere on the line, the slope stays unchanged (the same).

[tex]\rm m =\dfrac{y_2-y_1}{x_2-x_1}[/tex]

We have a line that cuts through the points (1, 2) and (5, 4).

The slope of a line:

[tex]\rm m =\dfrac{4-2}{5-1}[/tex]

m = 2/4

m = 1/2

Thus, the slope of the line is 1/2 or one-half if the line that cuts through the points (1, 2) and (5, 4).

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Answer:

  y -6 = -5(x -3)

Step-by-step explanation:

The point-slope form of the equation for a line is ...

  y -k = m(x -h) . . . . . . line with slope m through point (h, k)

__

You have been given ...

  m = -5

  (h, k) = (3, 6)

Putting the given values into the point-slope form gives the equation you want:

  y -6 = -5(x -3)

To hold 1,000,000 inflated balloons,

38 classrooms are needed.

In three-dimensional space,

the amount of space taken by an object is the volume of that object.

The volume of the cubic,

= length x width x height

Given:

The dimensions of the normal classroom are 15 ft × 50 ft × 35 ft.

The volume of the classroom,

= 15 ft by 50 ft by 35 ft.

= 26250 cubic feet.

The number of classrooms,

= 1,000,000 / 26250

Simplifying the fraction,

we get,

= 38.09

≈ 38 to the nearest whole number.

Therefore, 38 classrooms are required.

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