|a+x|/2 − |a−x|/2 , if a=−2; x=−6

PLZ HELP!!!

Answer:

90 euros more

Step-by-step explanation:

Let the number be x

Then,let Ivan's share be 4x and Tanya's share be x

From the given scenario, the equation to represent this would be

4x+x=150 euros

Combine the like terms so that

5x=150 euros

Divide both sides by 5 and simplify

5x/5 and 150/5

so x=30

Ivan's share is 4 times the amount of Tanya's so

4*30=120 euros

So Tanya's share is x=30 euros

Therefore, Ivan gets 90 euros more than Tanya

Answer:

Option B.

Step-by-step explanation:

Consider the given geometric series is

[tex]S=20-5+\dfrac{5}{4}-\dfrac{5}{16}+...[/tex]

We need to find the sum of given series.

Here, first term is a=20 and common ratio is

[tex]r=\dfrac{-5}{20}=-\dfrac{1}{4}[/tex]

The sum of infinite GP is

[tex]S=\dfrac{a}{1-r}[/tex]

Substitute [tex]a=20\text{ and }r=\dfrac{-5}{20}=-\dfrac{1}{4}[/tex].

[tex]S=\dfrac{20}{1-(-\dfrac{1}{4})}[/tex]

[tex]S=\dfrac{20}{\dfrac{5}{4}}[/tex]

[tex]S=\dfrac{20\times 4}{5}[/tex]

[tex]S=16[/tex]

Therefore, the correct option is B.

Answer:

B edge

Step-by-step explanation:

Answer:

15

Step-by-step explanation:

Answer:

78.  t=8.66yrs

79.  r=23.10%

80. r=11.0975%

Step-by-step explanation:

78. Given the initial deposit is $1,000 and the 8% compounded continuously. The doubling time can be calculated using the formula;

[tex]A=Pe^{it}[/tex]

Given that A=2P, we substitute in the equation to solve for t:

[tex]A=Pe^{rt}\\\\2P=Pe^{rt}\\\\2=e^{0.08t}\\\\0.08t=\ In 2\\\\t=8.66\ years[/tex]

Hence, it takes 8.66 years  for $1,000 to double in value.

79.

Given the initial deposit is $1,000 and the r% compounded continuously.

-The doubling rate can be calculated using the formula;

[tex]A=Pe^{rt}[/tex]

#We substitute our values in the equation to solve for r:

[tex]A=Pe^{rt}\\\\A=2P, t=3\\\\\therefore\\\\2P=Pe^{3r}\\\\2=e^{3r}\\\\r=\frac{In \ 2}{3}\\\\=0.23105\approx 23.10\%[/tex]

Hence, the deposit will double in 3 years at a rate of 23.10%

80.

Given the initial deposit is $30,000 and the future value is $2,540,689.

-Also, given t=40yrs, the rate of growth for continuous compounding is calculated as:

[tex]A=Pe^{rt}, \ \ \ r=r, t=40yrs\\\\2540689=30000e^{40r}\\\\\frac{2540689}{30000}=e^{40r}\\\\r=\frac{In \ (2540689/30000)}{40}\\\\\\=0.110975=11.0975\%[/tex]

Hence, the deposit will grow at a rate of approximately 11.0975%

d.

A full warranty will cover any repairs or replacement that the product needs, while a limited warranty will only pay for certain repairs.

A full warranty will cover all necessary repairs or replacements, whereas a limited warranty will only cover specific services. Option D is correct.

A full warranty guarantees the replacement of a damaged product. A comprehensive warranty will cover repairs no matter how many times the product breaks.

The difference between a full warranty and a limited warranty is that a full warranty will cover any repairs or replacements required by the product, but a limited warranty would only cover specified repairs.

Hence, option D is correct.

To learn more about the full warranty refer:

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Answer:

C

Step-by-step explanation:

Answer:

1 3/4 cups

Step-by-step explanation:

In order to be able to equally divide the stew into 5 containers we need to turn everything into the same format, in this case it would be by multiplying the whole number and the denominator and then adding the numerator like so

(8 * 4) + 3 =  [tex]\frac{35}{4}[/tex]

Now we can divide the numerator by 5 (container) in order to calculate how much stew each container will get.

[tex]\frac{35}{4} / 5 = \frac{7}{4}[/tex]

So each container will get 7/4 of the Stew or 1 3/4 cups

Answer:

Each container = 1 3/4 cups

Step-by-step explanation:

*** There are 8 3/4 cups of stew that MUST be put into five containers EQUALLY.

*** We are basically required to calculate the number of cups of stew that must be in each container.

Since 8 3/4 cups of stew needs to be equally distributed and placed in just about five containers, we will need to first convert 8 3/4 cups which is in mixed fraction into improper fraction in order to enable us to calculate successfully.

8 3/4 = [(4×8)+3]/4

= 35/4

We will now use a little bit of the principle of proportion to get through this:

If 8 3/4 cups must be equal in five containers, then one container will have ? number of cups:-

5 containers --------- 35/4 cups

1 container ---------- ? cups.

1/5 × 35/4

= 7/4 cups.

We will now convert it back to mixed fractions and we will have 1 3/4 cups.

Therefore, each container we will contain 1 3/4 cups

The probability that Sasha's first delay due to traffic will occur after the fifth day of travel to work is approximately 0.67232 or 67.232%.

The probability that Sasha will not experience a delay on any given day is 1 − 0.2 = 0.8, as the complement of the probability of experiencing a delay is the probability of not experiencing a delay.

Since each day is independent, the probability that Sasha will not experience a delay on the first day, second day, third day, fourth day, and fifth day is given by multiplying the probabilities for each day:

P(no delay on day 1 to day 5) = 0.8×0.8×0.8×0.8×0.8

Now, since we are looking for the probability that Sasha's first delay occurs after the fifth day, it means she did not experience a delay on the first five days. Therefore, the probability of the first delay occurring after the fifth day is the complement of the probability mentioned above:

P(first delay after the fifth day) = [tex]1 - 0.8^5[/tex]

Now, you can calculate this value:

P(first delay after the fifth day) = [tex]1 - 0.8^5[/tex]

P(first delay after the fifth day) = 1 − 0.32768

P(first delay after the fifth day) ≈ 0.67232

Answer:

Step-by-step explanation:

hello :

the distance between (3,5.25 and (3,-8.75) is :

√((3-3)²+(5.25+8.75)²) ......continu

Final answer:

To find the volume of a cylinder with a diameter of 10 inches and height of 8 inches, calculate the radius, then apply the volume formula V = πr²h. In this case, the volume is 628.32 cubic inches.

Explanation:

The volume of a cylinder is calculated using the formula V = πr²h, where r is the radius and h is the height of the cylinder.

First, find the radius by dividing the diameter by 2: radius = diameter / 2 = 10 inches / 2 = 5 inches.

Next, substitute the values into the formula:  V = 3.142 × (5 inches)² × 8 inches = 628.32 cubic inches.

Answer:

P(4)= 1/6

Step-by-step explanation:

Lots of Love!! <3

Stay Safe! Stay at Home!! =)

Answer:

Step-by-step explanation:

no of sample space, n(s) = 6

no of favorable cases , n(e) = 1

Probability of getting 4,

P(e) = n(e) / n(s)

       = 1 / 6

Answer:

979, 717

Step-by-step explanation:

Answer:

The are of the spotlight is 14.4m

Step-by-step explanation:

Step one :

To find the area of the spotlight

First let us understand that the shape is a circle since it's a spotlight

Hence we will use the formula for area of a circle which is

A=πr²

Step two :

Given r= 7feet - - - >metre =2.14m

i.e

1foot =0.305m

7feet =xm

Crosss multiplying we have

X=7*0.305=2.14m

π= 3.142

Step three :

Substituting into the formula we have

A=3.412*2.14²

A=3.142*4.58

A=14.4m

Answer:

154 square feet

Step-by-step explanation:

Extracting the key information from the question:-

*** At school play, there's spotlight above centre of floor.

*** This covers a light end area with radius 7 feet.

*** We are required to calculate the area covered by the spotlight.

In other words, we are basically required to calculate the area of a circle because it is almost certain that the area it covers will be a perfect circle. So all we need to do is to put down the formula for calculating the area of a circle.

We already know that the radius here is 7 feet. We will now simply draft this into the formula and we are good to go.

Formula for area of a circle = πr^2. π = 22/7, r = radius = 7 feet.

Then 22/7 × 7 × 7

= 154 feet^2. The area that is covered by the spotlight which is a perfect circle = 154ft^2

Answer:

-5

Step-by-step explanation:

Answer:

-5

Step-by-step explanation:

wHy aM i hErE?!?!

Answer:

C is the correct answer

Step-by-step explanation:

In this question, we are tasked with calculating the angle at standard position which has a cosine value of 1/2

With reference to the cartesian coordinates, there are only two quadrants which has positive valued for Cosine. These are the first quadrant and the last or 4th quadrant. While the first quadrant has angles in the range of 0-90 the fourth quadrant has an angle range from 270-360

Now back to the angle. In the first quadrant, the angle that has cosine value equal to 30 is cos 60. This is same as pi/3 radians

Now the general form of the angle on the fourth quadrant is 360-theta

Thus, since our theta is pi/3, which is 60, that angle on the fourth quadrant having same value as 1/2 is 360-60 = 300

This is same as 5pi/3 radians

So our answers are pi/3 radians and 5pi/3 radians where pi radians is same as 180 degrees

Answer:

8 and 40

Step-by-step explanation:

Both area multiples of 8:

8, 16, 24, 32, 40

40 = 8 × 5

Since 5 is prime, it can only be:

8 and 40

Answer:

Step-by-step explanation:

Purplemath

To simplify with exponents, don't feel like you have to work only with, or straight from, the rules for exponents. It is often simpler to work directly from the definition and meaning of exponents. For instance:

Simplify a6 × a5

The rules tell me to add the exponents. But I when I started algebra, I had trouble keeping the rules straight, so I just thought about what exponents mean. The " a6 " means "six copies of a multiplied together", and the " a5 " means "five copies of a multiplied together". So if I multiply those two expressions together, I will get eleven copies of a multiplied together. That is:

MathHelp.com

Simplifying Expressions on MathHelp.com

Simplifying Expressions

a6 × a5 = (a6)(a5)

= (aaaaaa)(aaaaa)

= aaaaaaaaaaa

= a11

Thus:

a6 × a5 = a11

Simplify the following expression:

\mathbf{\color{green}{\dfrac{6^8}{6^5}}}

6

5

6

8

​

The exponent rules tell me to subtract the exponents. But let's suppose that I've forgotten the rules again. The " 68 " means I have eight copies of 6 on top; the " 65 " means I have five copies of 6 underneath.

\dfrac{6 \cdot 6 \cdot 6 \cdot 6 \cdot 6 \cdot 6}{6 \cdot 6 \cdot 6 \cdot 6 \cdot 6}

6⋅6⋅6⋅6⋅6

6⋅6⋅6⋅6⋅6⋅6

​

How many extra 6's do I have, and where are they? I have three extra 6's, and they're on top. Then:

= \dfrac{6 \cdot 6 \cdot 6}{1} = \mathbf{\color{purple}{6^3}}=

1

6⋅6⋅6

​

=6

3

Unless the instructions also tell you to "evaluate", you're probably expected to leave numerical exponent problems like this in exponent form. If you're not sure, though, feel free to add "= 216", just to be on the safe side.

Simplify the following expression:

\mathbf{\color{green}{\dfrac{\mathit{t}^{10}}{\mathit{t}^8}}}

t

8

t

10

​

How many extra copies of t do I have, and where are they? I have two extra copies, on top:

\dfrac{t^{10}}{t^8} = \dfrac{t \cdot t \cdot t \cdot t \cdot t \cdot t \cdot t \cdot t \cdot t \cdot t}{t \cdot t \cdot t \cdot t \cdot t \cdot t \cdot t \cdot t}

t

8

t

10

​

=

t⋅t⋅t⋅t⋅t⋅t⋅t⋅t

t⋅t⋅t⋅t⋅t⋅t⋅t⋅t⋅t⋅t

​

= \dfrac{t \cdot t}{1} = \mathbf{\color{purple}{\mathit{t}^2}}=

1

t⋅t

​

=t

2

Once you become comfortable with the "how many extras do I have, and where are they?" reasoning, you'll find yourself not needing to write things out and cancel off the duplicate factors. The answers will start feeling fairly obvious to you.

Content Continues Below

Simplify the following expression:

\mathbf{\color{green}{\dfrac{5^3}{5^9}}}

5

9

5

3

​

This question is a bit different, because the larger exponent is on the term in the denominator. But the basic reasoning is the same.

How many extra copies of 5 do I have, and where are they? I have six extra copies, and they're underneath:

\dfrac{5^3}{5^9} = \dfrac{5 \cdot 5 \cdot 5}{5 \cdot 5 \cdot 5 \cdot 5 \cdot 5 \cdot 5 \cdot 5 \cdot 5 \cdot 5}

5

9

5

3

​

=

5⋅5⋅5⋅5⋅5⋅5⋅5⋅5⋅5

5⋅5⋅5

​

= \dfrac{1}{5 \cdot 5 \cdot 5 \cdot 5 \cdot 5 \cdot 5} = \mathbf{\color{purple}{\dfrac{1}{5^6}}}=

5⋅5⋅5⋅5⋅5⋅5

1

​

=

5

6

1

​

Note: If you apply the subtraction rule, you'll end up with 53–9 = 5–6, which is mathematically correct, but is almost certainly not the answer they're looking for.

Whether or not you've been taught about negative exponents, when they say "simplify", they mean "simplify the expression so it doesn't have any negative or zero powers". Some students will try to get around this minus-sign problem by arbitrarily switching the sign to magically get " 56 " on top (rather than below a "1"), but this is incorrect.

Let's move on to expressions that are a bit more complex.

Simplify the following expression:

\mathbf{\color{green}{\dfrac{5\mathit{x}^5}{3\mathit{x}^3}}}

3x

3

5x

5

​

I mustn't forget that the "5" and the "3" are just numbers. Since 3 doesn't go evenly into 5, I can't cancel the numbers.

And I mustn't try to subtract the numbers, because the 5 and the 3 in the fraction "\frac{5}{3}

3

5

​

" are not at all the same as the 5 and the 3 in rational expression "\frac{x^5}{x^3}

x

3

x

5

​

". The numerical portion \frac{5}{3}

3

5

​

 stays as it is.

For the variables, I have two extra copies of x on top, so the answer is:

\dfrac{5x^5}{3x^3} = \dfrac{5 \cdot x \cdot x \cdot x \cdot x \cdot x}{3 \cdot x \cdot x \cdot x}

3x

3

5x

5

​

=

3⋅x⋅x⋅x

5⋅x⋅x⋅x⋅x⋅x

​

= \dfrac{5 \cdot x \cdot x}{3}=

3

5⋅x⋅x

​

= \mathbf{\color{purple}{\dfrac{5\mathit{x}^2}{3} = \dfrac{5}{3}\mathit{x}^2}}=

3

5x

2

​

=

3

5

​

x

2

Either of the purple highlighted answers should be acceptable: the only difference is in the formatting; they mean the same thing.

Simplify (–46x2y3z)0

This is simple enough: anything to the zero power is just 1.

(–46x2y3z)0 = 1

Simplify –(46x2y3z)0

The parenthetical portion still simplifies to 1, but this time the "minus" is out in front of the parentheses; that is, it's out from under the power, so the exponent doesn't touch it. So the answer in this case is:

–(46x2y3z)0 = –1

Final answer:

The expression using only positive exponents is [tex]1/k^3[/tex].

Explanation:

To simplify the expression [tex]k^0 * k^-3[/tex] and write it using , we need to apply the laws of exponents.

The expression can be broken down into two parts.

Therefore,

[tex]k^0 = 1[/tex] (anything raised to the power of 0 is 1).

[tex]k^-3 = 1/k^3[/tex] (negative exponent indicates reciprocal).

Therefore,

[tex]k^0 * k^-3[/tex] [tex]= 1 * 1/k^3[/tex]

[tex]= 1/k^3.[/tex]

The man's age is 57 years old.

To find this answer follow the steps below:

1. Subtract 29 from 200 to get 171.

2. Divide 171 by 3 to get 57.

To check this, use the equation 200 - (57 x 3) = 29.

1. 57 x 3 = 171. 200 - 171 = 29

2. 200 - 171 = 29. 29 = 29.

Thus meaning the man is 57 years old. I hope this helps!

Answer:

57

Step-by-step explanation:

x=age

200-3x=29

x=57

Answer:

6.3 cm by 6.3 cm by 12.6cm

Step-by-step explanation:

Volume of the box=[tex]500 cm^3[/tex]

The minimal dimensions of a box always occur when the base is a square.

[tex]L^2H=[/tex][tex]500 cm^3[/tex]

[tex]H=\frac{500}{L^2}[/tex]

Surface Area of a cylinder=[tex]2(L^2+LH+LH)[/tex]

Surface Area of the sides and bottom= [tex]L^2+2(LH+LH)[/tex]

Surface Area for the top = [tex]L^2[/tex]

The material for the sides and bottom costs $0.05 per [tex]cm^2[/tex]

The material for the top costs $0.15 per [tex]cm^2[/tex]

Therefore Cost of the box

[tex]C=0.15L^2+0.05[L^2+4LH]\\C=0.2L^2+0.2LH[/tex]

Recall:[tex]H=\frac{500}{L^2}[/tex]

[tex]C=0.2L^2+0.2L(\frac{500}{L^2})\\=0.2L^2+\frac{100}{L}\\C=\frac{0.2L^3+100}{L}[/tex]

The minimum value of C is at the point where the derivative is zero.

[tex]C^{'}=\frac{2(L^3-250)}{5L^2}\\\frac{2(L^3-250)}{5L^2}=0\\2(L^3-250)=0\\L^3=250\\L=6.3cm[/tex]

[tex]H=\frac{500}{L^2}=\frac{500}{6.3^2}=12.6cm[/tex]

The dimensions that would minimize the cost are 6.3 cm by 6.3 cm by 12.6cm

Given:

The length of arc TS = 40 in

To find:

The length of arc RS.

Solution:

Length of TS = 40 in

θ = 80°

Using arc length formula:

[tex]$\text { Arc length }=2 \pi {r}\left(\frac{\theta}{360}\right)[/tex]

[tex]$40=2 \times 3.14 \times {r}\left(\frac{80}{360}\right)[/tex]

[tex]$40=6.28 \times {r}\left(\frac{2}{9}\right)[/tex]

[tex]$40=1.39\times r[/tex]

Divide by 1.39 on both sides, we get

[tex]28.7=r[/tex]

Radius = 28.7

Complete angle of circle = 360°

Angle measure of RS = 360° - 60° - 120° - 80°

Angle measure of RS = 100°

Arc length of RS:

[tex]$\text { Arc length }=2 \pi {r}\left(\frac{\theta}{360}\right)[/tex]

Substitute θ = 100° and r = 28.7

                 [tex]$=2 \times 3.14 \times 28.7 \left(\frac{100}{360}\right)[/tex]

                 = 50 inch

The length of arc Rs is 50 inches.

To find out how many different possible ways the coach can choose 5 players from a team of 10, we calculate the combinations using the formula C(10, 5) which results in 252 different possible ways.

To find out how many different possible ways the coach can choose a team of 5 from 10 players, we use combinations. In mathematics, a combination is a selection of items from a larger set, where the order of selection does not matter. This is often denoted as C(n, k) or sometimes nCk, where n represents the total number of items to choose from, in this case, 10 players, and k is the number of items to choose, which here is 5 players.

The formula for a combination is:

C(n, k) = n! / (k!(n-k)!)

where ! denotes factorial, which is the product of all positive integers up to that number.

So for our specific question:

C(10, 5) = 10! / (5!(10-5)!) = 10! / (5!*5!) = (10*9*8*7*6) / (5*4*3*2*1) = 252

Therefore, there are 252 different possible ways the coach can choose a team of 5 players from a pool of 10.

Answer:

(14, 6)

Step-by-step explanation:

If you plug in 6 for y you get:

6 = x/2 - 1

Add 1 to both sides:

7 = x/2

Multiply 2 on both sides:

14 = x

The answer is (14, 6)

[tex]\Huge{\underline{\underline{\tt{\orange{Answer:}}}}}[/tex]

Reason :

__________________________________________

The reciprocal of the given fraction 11/7 is 7/11.

The reciprocal of any quantity is, one divided by that quantity. For any number ‘a’, the reciprocal will be 1/a. If the given number is multiplied by its reciprocal, we get the value 1.

The given fraction is 11/7.

The reciprocal of the given fraction is the fraction that results from switching or reversing the numerator and denominator.

The reciprocal of the fraction is 7/11.

Therefore, the reciprocal of the fraction is 7/11.

Learn more about the reciprocal property here:

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Answer:

[tex]Z = -2.2[/tex]

Step-by-step explanation:

Problems of normally distributed samples are solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

In this problem, we have that:

[tex]\mu = 3600, \sigma = 500[/tex]

Use the information on the right to find the z-score of a 2,500 g baby.

This is Z when X = 2500. So

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{2500 - 3600}{500}[/tex]

[tex]Z = -2.2[/tex]

Answer:

Step-by-step explanation:

-2

ur welcome ;)

Answer:

7.25h = e

If e = $166.75, h = 23 hours

Step-by-step explanation:

7.25h = e

However many hours he works, he'll earn 7.25 times that number.

If he wants to know how many hours he must work to get the video game system where e = 166.75, we model this with

7.25h = e

7.25h = 166.75

Divide both sides by 7.25.

h = 23 hours

Final answer:

Explanation of the equation relating hours worked to earnings and interpretation of variables.

Explanation:

Equation: e = 7.25h - 166.75

Explanation: The equation that models the relationship between the number of hours worked h and the amount earned e can be represented as e = 7.25h - 166.75. This equation captures the idea that Marvin earns $7.25 per hour and wants to buy a video game system costing $166.75.

Independent and dependent variables: Hours worked (h) is the independent variable, and the amount earned (e) is the dependent variable. The y-intercept is -166.75, and the slope is 7.25, indicating that for each additional hour worked, Marvin earns $7.25.

Answer:

9 pigs

Step-by-step explanation:

We have the following numbers of heads:

pigs (p) + chickens (c) = 16 animal heads (1)

And the following numbers of feet:

4p + 2c = 50 animal feet   (2)

From equation (1):

p = 16 - c (3)

By entering equation (3) into (2) we have:

4(16 - c) + 2c = 50

64 - 4c + 2c = 50

c = 7

Now, entering the value of c into equation (3) we have the next value of p:

p = 16 - c

p = 16 - 7

p = 9

Therefore, the number of pigs that Henry has is 9.

I hope it helps you!  

Answer:

Step-by-step explanation:

The formula for determining simple interest is expressed as

I = PRT/100

Where

I represents interest paid on the amount of money invested.

P represents the principal or amount of money invested.

R represents interest rate on the investment.

T represents the duration of the investment in years.

From the information given,

P = $14000

R = 2.5%

T = 7 years

Therefore,

I = (14000 × 2.5 × 7)/100

I = $2450

The total amount that the CD would be worth after 7 years is

14000 + 2450 = $16450

Answer:

Value of CD in total at the end of 7 years when the CD matures is $16646

Step-by-step explanation:

This is based on the formula A= P(1+r)^ n

where r = annual rate of interest,

           P = Principal amount,

           n = number of years

p = 14000

r = 2.5

n = 7

A = 14000 ( 1+ 0.025) ^ 7

= 14000 ( 1.025)^7

=14000 x 1.189

=16646

A = $16646

Answer:   y-value=36

Step-by-step explanation:

If you take the unit rate of these set of numbers, (it can be any set of the numbers on the table), let's use 2 and 12. To find the unit rate all you have to do is divide. 12 divided by 2 is 6. This also works for 4 and 24. 24 divided by 4 is 6. Therefore 6 times any number in the x column will give you the y-value.

Plugging in the unit rate would look look this 6(6)=y

                                                                           36=y

Therefore your missing value, or the y-value that is not filled in would be 36.

The solution to the Quadratic equation [tex]x^2+4x-40=-8[/tex] is -8 & 4. correct option is C.

To solve the quadratic equation x^2+4x-40=-8 using the quadratic formula, we first need to rearrange the equation so that it is in the form [tex]ax^2+bx+c=0.[/tex]

So, the equation becomes [tex]x^2+4x-32=0.[/tex]

Now, we can identify the values of a, b, and c.

In this case, a=1, b=4, and c=-32.

Next, we can substitute these values into the quadratic formula: x = (-b±√([tex]b^2-4ac[/tex]))/(2a).

Using the formula, we can calculate the solutions for x.

After performing the calculations, we find that the solutions are x = -8 and x = 4.

Therefore, the correct answer is option c) -8 & 4.

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