Given f(x)=x^2, after performing the following transformations: shift upward 66 units and shift 19 units to the right, the new function g(x)=

Answer:

4x²=2(x-4)

2x²=x-4

2x²-x+4=0​

x=1+√31​/ 4, 1-√31​/4

Step-by-step explanation:

1. Cancel log on both sides

2. Divide both sides by 2

3. Move all terms to one side

4. Use the quadratic formula

Let [tex]x[/tex] be the number of pounds of Nigerian coffee and [tex]y[/tex] be the number of pounds of Bolivian coffee.

We can set up a system of equations to represent the given information:

So we have the following system of equations:

[tex]\qquad\quad\begin{aligned} 17x + 18y &= 437.50 \\ x + y &= 50 \end{aligned}[/tex]

Solving this system of equations, we get:

[tex]\qquad\qquad\quad\begin{aligned} x &= 12.5 \\ y &= 37.5 \end{aligned}[/tex]

[tex]\therefore[/tex] We need 12.5 pounds of Nigerian coffee and 37.5 pounds of Bolivian coffee for the mixture.

[tex]\blue{\overline{\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad}}[/tex]

(ノ^_^)ノ [tex]\large\qquad\qquad\qquad\rm 06/21/2023[/tex]

Answer:

y = -2x+10

Step-by-step explanation:

Slope-intercept form of the equation for a line is

y = mx+b  where m is the slope and b is the y intercept

We know the slope is -2

y = -2x+b

Substituting the point in for x and y and solving for b.

8 = -2(1) + b

8 = -2+b

10 =b

Now

y = -2x+10

Answer:

y = - 2x + 10

Step-by-step explanation:

The equation of a line in slope-intercept form is given by:

y = m x + c

Here,

m → slope of the line

c →  y-intercept

Using the point-slope form of a line, we have:

( y - y₁ ) = m ( x - x₁ )

Substituting the coordinates ( x₁, y₁ ) = ( 1, 8 ), and the slope m = -2:

( y - 8 ) = - 2 ( x - 1 )

Expanding and rearranging the equation:

y - 8 = - 2x + 2

Adding 8 to both sides:

y = - 2x + 10

Let's start by using variables to represent the salaries of Saima and Atika. Let S be Saima's salary, and A be Atika's salary. Then, we can write:

We know that their total salary is Rs. 35,000, so we can write an equation:

S + 3S + 9S = 35,000

Simplifying the left side, we get:

13S = 35,000

Dividing both sides by 13, we get:

S = 2,692.31 (rounded to two decimal places)

Now that we know Saima's salary, we can find Farheen's salary:

Farheen's salary = 3S = 3 × 2,692.31 ≈ Rs. 8,076.92

Therefore, the closest answer choice is A. 10,000, which is not the exact value but is the closest option to the calculated value.

In this math problem, using the given ratios and total salary, we find Saima's salary is Rs. 5000. As Farheen's salary is three times Saima's, Farheen earns Rs.15,000.

According to the problem, Farheen's salary is three times Saima's salary, and Saima's is one-third of Atika's. Let's denote Saima's salary as 'x'. Hence, Farheen's salary is '3x' and Atika's salary is '3x'. All their salaries add up to Rs.35,000 as per the question. Therefore, the equation becomes as follows:

x + 3x + 3x = 35000. This reduces to 7x = 35000 after adding the like terms on the left hand side of the equation. Dividing each side by 7, we find 'x = 5000', which is Saima's salary.

Therefore, Farheen's salary is three times Saima's, so it equals '3 * 5000 = 15000', which matches with option C from the list. So, Farheen's salary is Rs. 15,000.

https://brainly.com/question/31606357

#SPJ2

The median cost of a home in 2014 is $480

First, we need to know that the median of a given set of data is expressed as the middle number determined with the data set is arranged in an order from least to greatest or in an ascending order.

Also, note that the median is one of the measures of central tendency.

From the information given, we have that;

The median cost of a home in 2014 traced from the point year to the cost on the graph is;

$480

Learn more about median at: https://brainly.com/question/26177250

#SPJ1

The domain and the range of the function are (-∝, ∝) and (-∝, -1), respectively

From the question, we have the following parameters that can be used in our computation:

The graph

The above graph is an quadratic function

The rule of an function is that

The domain is the set of all real values

In this case, the domain is (-∝, ∝)

For the range, we have

Range = (-∝, -1)

Read more about domain and range at

brainly.com/question/27910766

#SPJ1

Answer:

[tex]37in^2[/tex]

Step-by-step explanation:

We can break up this figure into two bits, the longer rectangle at the top, and the smaller square at the bottom.

To find area if a rectangle, you do length x width. You can do this with the square, too. For the area of the square, you would do:

[tex]3 * 3=9in^2[/tex]

For the area of the bigger rectangle, we know the length of it (7 at the top), so we now have to find the width. The only width number that is available to us is the 7 at the right, and the 3 at the left side of the square.

We can subtract these two numbers to get 4 for the width. We just have to multiply our length (7) by our width (4):

[tex]7*4=28in^2[/tex]

Now that we have our areas of our smaller figures, we just need to add them together:

[tex]9in^2 + 28in^2 = 37in^2[/tex]

The area of the figure is [tex]37in^2[/tex]

Answer:

A:(-1,0)

B:(0,5)

C:(2,9)

D:(5,0)

Step-by-step explanation:

count the x axis to get x and y axis to get y

(x,y)

Answer:

See below

Step-by-step explanation:

A is located at (-1,0) which is an x-intercept

B is located at (0,5) which is the y-intercept

C is located at (2,9) which is the vertex

D is located at (5,0) which is an x-intercept

Answer:5 drops

Step-by-step explanation:

Every 100 nanograms is 0.1 microgram so 500 nanograms + 0.5 micrograms so 5 drops because everydrop is 100 nanograms

The distance between points C and D is given as follows:

5 units.

Suppose that we have two points of the coordinate plane, and the ordered pairs have coordinates [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex].

The shortest distance between them is given by the equation presented as follows, derived from the Pythagorean Theorem:

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

The coordinates for this problem are given as follows:

(-4, -6) and (1, -6).

Hence the distance is given as follows:

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

D = 5 units.

More can be learned about the distance between two points at https://brainly.com/question/7243416

#SPJ1

Answer:

$71.95

Step-by-step explanation:

$29.95- 200 copies

$14- 100 copies

$14- 100 copies

$14- 25 copies

so 14[3] + 29.95 = $71.95

You would expect to pay $90 each month for electricity based on an average usage of 120 KWHs per month.

To calculate the monthly cost of electricity, you can multiply the average number of kilowatt-hours (KWH) used per month by the cost per KWH.

Given:

Cost per KWH: $0.75

Average monthly usage: 120 KWHs

To find the monthly cost, you can multiply the cost per KWH by the average monthly usage:

Monthly Cost = Cost per KWH * Average monthly usage

Plugging in the values, we have:

Monthly Cost = $0.75/KWH * 120 KWHs

Calculating the result:

Monthly Cost = $90

Learn more about Monthly Cost  at

https://brainly.com/question/24093839

#SPJ1

The division between the functions f(x) = ∛(4 · x) and g(x) = 2 · x + 3 is equal to (f / g) (x) = ∛(4 · x) / (2 · x + 3), x ≠ - 3 / 2. (Correct choice: D)

In this problem we find two functions, with which we must perform a division between two functions, whose definition is shown below:

(f / g) (x) = f(x) / g(x)

If we know that f(x) = ∛(4 · x) and g(x) = 2 · x + 3, then the division between the two functions is:

(f / g) (x) = ∛(4 · x) / (2 · x + 3)

The restrictions on the domain is represented by every x when 2 · x + 3 = 0:

2 · x + 3 = 0

2 · x = - 3

x = - 3 / 2

To learn more on operations with functions: https://brainly.com/question/31207478

#SPJ1

Answer:

2.4 yd

Step-by-step explanation:

Let the width of the walkway = x.

total length = x + 7.5

total width = x + 4.5

total area = (x + 7.5)(x + 4.5)

total area = 68.31 yd²

(x + 7.5)(x + 4.5) = 68.31

x² + 4.5x + 7.5x + 33.75 - 68.31 = 0

x² + 12x - 34.56 = 0

x = [-12 ± √(12² - 4(1)(-34.56)]/(2 × 1)

x = [-12 ± √(144 + 138.24)]/(2 × 1)

x = [-12 ± 16.8]/2

x = 2.4 or x = -14.4

Answer: 2.4 yd

135 as a product of its prime factors is written as  3 × 3 x 3 x 5

The prime factors are those prime digits that can divide a particular digit evenly and without leaving any remainder. To put it differently, these are the main digits that, when multiplied with one another, result in the initial number.

In mathematics and number theory, prime factors hold significant value as they enhance comprehension of number properties and interconnections. In addition, they are utilized in a range of mathematical calculations and algorithms.

From the information given, we have the value as;

135

The prime factors are  3 × 3 x 3 x 5

Learn more about prime factors at: https://brainly.com/question/1081523

#SPJ1

Reason:

0.5% = 0.5/100 = 5/1000

or you could say

5/100 = 0.05 = 5%

Answer:

∠ MON = 51°

Step-by-step explanation:

∠ LON is composed of the 2 angles LOM and MON , that is

∠ LOM + ∠ MON = ∠ LON

42° + ∠ MON = 93° ( subtract 42° from both sides )

∠ MON = 51°

Answer:

<MON= 51°

Step-by-step explanation:

Look at the diagram and locate LON. You can see that LON is the angle of the complete line. Now LOM is given which is the angle of a part of the lines. So that means that to find MON we can minus LON with LOM.

<MON= <LON - <LOM

= 93-42

<MON= 51°

Feel free to ask any doubt you have!

The expression (sinx + cosx)^2 + (sinx - cosx)^2 simplifies to

To simplify the expression (sinx + cosx)^2 + (sinx - cosx)^2 using trigonometric identities, we can expand and simplify the expression.

Expanding the squared terms

(sin^2x + 2sinxcosx + cos^2x) + (sin^2x - 2sinxcosx + cos^2x)

Using the trigonometric identity sin^2x + cos^2x = 1, we can simplify further:

(1 + 2sinxcosx + 1) + (1 - 2sinxcosx + 1)

Simplifying the expression, we have:

2 + 2sinxcosx + 2

Combining like terms, we get:

4 + 2sinxcosx

Learn more about identities at

https://brainly.com/question/7331447

#SPJ1

The cost of the labor per hour is $105. the equation can be used to determine x. The cost of labor per hour is $105. the total amount paid by Casho was $627 - $102 (the cost of the parts) = $525. The technician charged her $105 per hour for his labor.

Given, The technician at the store worked on the computer for 5 hours and charged her 102$ for parts a total 627.

Since Casho needed to get her computer fixed, she took it to the repair store. Therefore, the cost of labor per hour can be calculated.

To find the cost of labor per hour, we can use the following formula; Total Cost = Cost of Parts + Labor Cost * Hours Worked Given, Total Cost = 627Cost of Parts = $102 Labor Cost = x (unknown)Hours Worked = 5Thus, the equation can be written as;

Total Cost = Cost of Parts + Labor Cost * Hours Worked$627 = $102 + x * 5Solving the above equation for x; Let's first subtract $102 from both sides,$627 - $102 = x * 5$525 = x * 5Then, divide both sides by 5 to isolate x,$\frac{525}{5} = x$105 =

For more such questions on equation

https://brainly.com/question/29174899

#SPJ8

The best description of the graph is option B) It is a line which intersects the y-axis at (2, 2). This is because the line has a y-intercept of 2 and intersects the y-axis at the point (0, 2). Option B

To determine the best description of the graph of the equation x + y = 2, we can rearrange the equation into slope-intercept form, which is y = mx + b, where m is the slope and b is the y-intercept.

Rearranging the equation, we have:

y = -x + 2

From this equation, we can see that the slope is -1, meaning that for every unit increase in x, y decreases by 1. The y-intercept is 2, indicating that the line intersects the y-axis at the point (0, 2).

Therefore, the best description of the graph is option B) It is a line which intersects the y-axis at (2, 2). This is because the line has a y-intercept of 2 and intersects the y-axis at the point (0, 2).

Option A) It is a line which intersects the x-axis at (2, 2) is incorrect because the line intersects the x-axis at the point (2, 0), not (2, 2).

Option C) It is a line joining the points whose x- and y-coordinates add up to 2 is incorrect because the equation represents a line and not a set of points.

Option D) It is a line joining the points whose x- and y-coordinates add up to 4 is incorrect because the equation represents a line where the x- and y-coordinates add up to 2, not 4.

Option B

For more such question on graph visit:

https://brainly.com/question/19040584

#SPJ8

The inequality shown by the graph is m ≤ 1. This means that the values of m are less than or equal to 1. Any value of m that is equal to or smaller than 1 satisfies the inequality. However, any value of m that is greater than 1 does not satisfy the inequality.

Inequalities can be represented graphically using number lines.

The inequality m ≤ 1 means that all values of m that are less than or equal to 1 are solutions to the inequality.

The solution set is represented by a closed circle on the number line at the point where m = 1, and a line segment extending to the left of this point.
If we choose a value of m from the shaded region on the graph, such as m = 0, the inequality m ≤ 1 is satisfied because 0 is less than 1.

If we choose a value of m from the unshaded region, such as m = 2, the inequality is not satisfied because 2 is greater than 1. Therefore, the inequality shown by the graph is m ≤ 1.

for such more questions on

https://brainly.com/question/843074

#SPJ8

that is physics ...

but yes, applied math. we need to know the formulas though.

(1)

in general, since there are 2 cables supporting in an equal way.

that means each cable is responsible for 600/2 = 300 pounds to bring and hold up.

a cable or rope at an angle has to handle a combined tension force : horizontally (Fx) and vertically (Fy).

the tension force (Ftens) on the rope is a combination of both.

we know

Fx = Ftens × cos(theta)

Fy = Ftens × sin(theta)

from the problem we do know Fy (the vertical = up/down force), as this is the force needed to lift and keep the 300 pound weight up there.

and that is Fgravity, the force needed to counteract gravity.

Fgravity = mass × g

g being the constant gravitational acceleration of Earth = 9.8 m/s²

forces are described in Newton.

1 N ≈ 0.225 pounds (lifting on Earth)

so, to lift 1 pound requires 1/0.225 ≈ 4.44822 N

to lift 300 pounds requires

4.44822 × 300 ≈ 1334.47 N

that is what Fy is for one of the 2 cables.

the tension on one of the cables is then given by

Fy = Ftens × sin(60)

Ftens = Fy / sin(60) = 1334.47 / sin(60) =

= 1,540.913227... N = 346.41107515867... pounds

≈ 346 pounds per cable.

(2)

3cos(t) + 4 = 2

3cos(t) = -2

cos(t) = -2/3

cosine is negative in the 2nd and 3rd quadrant.

so, for t > pi/2 and t < 3pi/2.

because the given interval is [0, pi), we are only looking at the 2nd quadrant (pi/2, pi).

t = 131.8103149...° = 2.300523983... rad

(3)

well, that are the numbers

1/2

sqrt(2)/2 = 1/sqrt(2)

sqrt(3)/2

1

they are getting bigger and bigger, all positive, so they indicate larger and larger angles

1/2 is :

sin(30° or pi/6 or 150° or 5pi/6)

cos(60° or pi/3 or 300° or 5pi/3)

1/sqrt(2) is :

sin(45° or pi/4 or 135° or 5pi/4)

cos(45° or pi/4 or 315° or 7pi/4)

sqrt(3)/2 is :

sin(60° or pi/3 or 120° or 2pi/3)

cos(30° or pi/6 or 330° or 11pi/6)

1 is :

sin and csc(90° or pi/2)

cos and sec(0° or 0pi or 360° or 2pi)

tan and cot(45° or pi/4 or 225° or 5pi/4)

(4)

the height moves between 4 meters and 70 meters in a circle.

the circumference of the circle is 2pi×r or pi×d, so in our case : 66pi meters.

it takes 5 minutes to move along these 66pi meters.

let's say, when the height is 4 meters (starting position), the angle is 0 and the arc is 0.

after a quarter trip the angle is 90° or 66pi/4, and the height is 4 + 66/2 = 37 meters

and at 70 meters the angle is 180° or 66pi/2.

the function of the height based on the current angle is then for the first half-circle

height(theta) = 4 + (theta/360)×2×66

or

height(theta) = 4 + (theta/(2pi))×2×66

now we need to find the angle theta for which we reach the height of 47 meters :

47 = 4 + (theta/360)×132

43 = (theta/360)×132

theta/360 = 43/132

theta = 360×43/132 = 117.2727272...°

= 2.046795214... rad

so, after starting at the lowest position at 4 meters we reach the height of 47 meters at an angle of about 117°.

then we get and stay above 47 meters until we get to

360 - theta = 242.7272727...°

= 4.236390093... rad

when going down again on the second half-circle of the trip.

that means we are at and above 47 meters for

(360 - theta) - theta = 360 - 2×theta = 125.4545455...°

= 2.18959488... rad

of the whole trip of 360° or 2pi. which takes 5 minutes.

the time we spend there is then

5 × (360 - 2×theta)/360 = 1.742424242... minutes

= 1 minute 44.54545454... seconds

hmmm let's reword it

what is the Decay equation for sunlight, decaying at 69% at every interval of 10 mm of thickness for "t"?

[tex]\textit{Periodic/Cyclical Exponential Decay} \\\\ A=(1 - r)^{\frac{t}{c}}\qquad \begin{cases} A=\textit{current amount}\\ r=rate\to 69\%\to \frac{69}{100}\dotfill &0.69\\ t=thickness\\ c=period\dotfill &10 \end{cases} \\\\\\ A=(1 - 0.69)^{\frac{t}{10}}\implies A=0.31^{\frac{t}{10}}\hspace{5em}\boxed{S=0.31^{\frac{t}{10}}}[/tex]

The probability that both events B and C will occur is:

P(B and C) = 9/20

Probability is the likelihood of an event to occur. It is expressed as a number in the range from 0 to 1.

The probability of an impossible event is 0, that of an event that is certain to occur is 1.

We have:

The probability that event B will occur, P(B) = 3/4

The probability that event C will occur, P(C) = 3/5

The probability that both events B and C will occur is:

P(B and C) = P(B) × P(C)

P(B and C) = 3/4 × 3/5

P(B and C) = 9/20

Learn more about probability on:

brainly.com/question/251701

#SPJ1

We can conclude that the function f(x) = x² is increasing when x > 1.The given function is f(x) = x². You need to determine whether this function is increasing or decreasing when x > 1.

To do this, we can find the derivative of the function and evaluate it for x > 1.If the derivative is positive, then the function is increasing, and if it is negative, then the function is decreasing.

The derivative of the function f(x) = x² is given by:f '(x) = 2x

We can see that the derivative is always positive when x > 1, as 2x is always positive for x > 0.Therefore, we can conclude that the function f(x) = x² is increasing when x > 1.

For more question on function

https://brainly.com/question/11624077

#SPJ8

Answer: the correct answer would option (C).

Step-by-step explanation:7x²+16x+25  is corresponds to the equivalent expression of (x²+15x+65) + (2x - 5) (3x +8).

7x²-3x+8 is corresponds to the equivalent expression of (4x + 1)(3x - 4) - (5x²-10x-12)

11x²+6x-6 is corresponds to the equivalent expression of (8x²+19x+4) + (3x + 2)(x - 5).

11x²-5x+13 is corresponds to the equivalent expression of (6x + 1)(3x - 7) - (7x²-34x-20)

What is expression?

Expressions is the defined as mathematical statements that have a minimum of two terms containing variables or numbers.

Given expression no. 1 as :

⇒ (x²+15x+65) + (2x - 5) (3x +8).

⇒ x²+15x+65 + 6x²-15x+16x-40

⇒ 7x²+16x+25

Hence, the correct answer would be option (B).

Given expression no. 2 as :

⇒ (4x + 1)(3x - 4) - (5x²-10x-12)

⇒ 12x²+3x-16x-4 - 5x²+10x+12

⇒ 12x²-13x-4 - 5x²+10x+12

⇒ 7x²-3x+8

Hence, the correct answer would be option (D).

Given expression no. 3 as :

⇒ (8x²+19x+4) + (3x + 2)(x - 5).

⇒ (8x²+19x+4) + 3x²+2x-15x-10

⇒ 8x²+19x+4 + 3x²-13x-10

⇒ 11x²+6x-6

Hence, the correct answer would be option (A).

Given expression no. 4 as :

⇒ (6x + 1)(3x - 7) - (7x²-34x-20)

⇒ 18x²+3x-42x-7- 7x²+34x+20)

⇒ 11x²-5x+13

Hence, the correct answer would be option (C).

Since the probability of success is 0.74, the probability of failure is 1 - 0.74 = 0.26. This means that there is a 26% chance of failure in the given binomial trial. Option C

In a binomial trial, the probability of success, denoted by "p," represents the likelihood of the desired outcome occurring. The probability of failure, denoted by "q," represents the complement of the probability of success, i.e., the likelihood of the desired outcome not occurring.

In this case, the probability of success is given as 0.74. To find the probability of failure, we subtract the probability of success from 1, since the sum of the probabilities of success and failure must equal 1.

Probability of failure = 1 - Probability of success

Therefore, the probability of failure = 1 - 0.74 = 0.26.

Hence, the correct answer is C. 0.26.

It's important to understand that in a binomial distribution, there are only two possible outcomes: success and failure. The probabilities of these outcomes must add up to 1. Therefore, if the probability of success is known, the probability of failure can be obtained by subtracting the probability of success from 1.

Option C

For more such questions on probability visit:

https://brainly.com/question/251701

#SPJ8

The ratio of the length of the shortest diagonal to the length of the longest diagonal in a regular hexagon is [tex]$\sqrt{3}/2$[/tex]. This can also be written as [tex]$\frac{\sqrt{3}}{2}$[/tex].

A hexagon is a six-sided polygon with all angles equal to 120 degrees. In a regular hexagon, all sides are equal in length and all angles are equal. The diagonals of a hexagon are line segments that connect non-adjacent vertices of the hexagon.

A regular hexagon has nine diagonals. The shortest diagonal of a regular hexagon is the one that connects opposite vertices and is equal to the length of a side of the hexagon. The longest diagonal of a regular hexagon is the one that connects opposite vertices and passes through the center of the hexagon.

To find the ratio of the length of the shortest diagonal to the length of the longest diagonal, we need to find the length of the longest diagonal in terms of the length of the shortest diagonal. We know that the length of the shortest diagonal is equal to the length of a side of the hexagon.

We can draw the longest diagonal and form an equilateral triangle by connecting the center of the hexagon to the two endpoints of the longest diagonal. The length of the side of this equilateral triangle is equal to the length of the longest diagonal of the hexagon.

The ratio of the length of the shortest diagonal to the length of the longest diagonal is then equal to the ratio of the side length of this equilateral triangle to the length of the side of the hexagon, which is [tex]$\frac{\sqrt{3}}{2}$[/tex].
Therefore, the ratio of the length of the shortest diagonal to the length of the longest diagonal in a regular hexagon is $\sqrt{3}/2$. This can also be written as [tex]$\frac{\sqrt{3}}{2}$[/tex].

for such more questions on length

https://brainly.com/question/28322552

#SPJ8

[tex]~~~~~~~~~~~~\textit{quadratic formula} \\\\ \stackrel{\stackrel{a}{\downarrow }}{1}x^2\stackrel{\stackrel{b}{\downarrow }}{+5}x\stackrel{\stackrel{c}{\downarrow }}{+6}=0 \qquad \qquad x= \cfrac{ - b \pm \sqrt { b^2 -4 a c}}{2 a} \\\\\\ x= \cfrac{ - (5) \pm \sqrt { (5)^2 -4(1)(6)}}{2(1)} \implies x = \cfrac{ -5 \pm \sqrt { 25 -24}}{ 2 } \\\\\\ x= \cfrac{ -5 \pm \sqrt { 1 }}{ 2 }\implies x=\cfrac{-5\pm 1}{2}\implies x= \begin{cases} -2\\ -3 \end{cases} \\\\[-0.35em] ~\dotfill[/tex]

[tex]~~~~~~~~~~~~\textit{quadratic formula} \\\\ \stackrel{\stackrel{a}{\downarrow }}{2}x^2\stackrel{\stackrel{b}{\downarrow }}{-3}x\stackrel{\stackrel{c}{\downarrow }}{-2}=0 \qquad \qquad x= \cfrac{ - b \pm \sqrt { b^2 -4 a c}}{2 a} \\\\\\ x= \cfrac{ - (-3) \pm \sqrt { (-3)^2 -4(2)(-2)}}{2(2)} \implies x = \cfrac{ 3 \pm \sqrt { 9 +16}}{ 4 } \\\\\\ x= \cfrac{ 3 \pm \sqrt { 25 }}{ 4 }\implies x=\cfrac{3\pm 5}{4}\implies x= \begin{cases} 2\\ -\frac{1}{2} \end{cases}[/tex]

The sum  in scientific notation is  2.88 × 10⁰

To add numbers in scientific notation, we need to make sure the exponents are the same. Let's add 5.8 × 10⁴ and 2.3 × 10⁵.

First, we need to adjust the numbers so that they have the same exponent. We can do this by moving the decimal point.

5.8 × 10⁴ can be written as 0.58 × 10⁵ (moving the decimal point one place to the right).

Now, we have 0.58 × 10⁵ + 2.3 × 10⁵. Since the exponents are the same, we can add the coefficients:

0.58 + 2.3 = 2.88

The sum of the coefficients is 2.88. To express this in scientific notation, we need to adjust the decimal point and exponent.

Since we moved the decimal point one place to the right in 0.58 × 10⁵, we need to move it one place to the left in 2.88.

2.88 can be written as 0.288 × 10¹.

Therefore, the sum of 5.8 × 10⁴ and 2.3 × 10⁵ is 0.288 × 10¹.

In scientific notation, this can also be expressed as 2.88 × 10⁰ or simply 2.88.

So, the sum of 5.8 × 10⁴ and 2.3 × 10⁵ is 2.88.

For more question on sum  visit:

https://brainly.com/question/24205483

#SPJ8