Write a function(x) that calculates the cost of learning the machine for x months

Write A Function(x) That Calculates The Cost Of Learning The Machine For X Months

Answers

Answer 1

The question provides that an initial fee of $1000 and a monthly fee of $115 is paid.

Since the initial fee is a one-time payment and the monthly fee is a recurring payment, over x months, the fee that would have been paid is given o be:

[tex]C(x)=1000+115x[/tex]

After 1 year, 12months would have passed. This means that we can scalculate the cost using x = 12 in the equation:

[tex]\begin{gathered} x=12 \\ \therefore \\ C(x)=1000+115(12)=1000+1380 \\ C(x)=2380 \end{gathered}[/tex]

ANSERS

(a) The function is:

[tex]C(x)=1000+115x[/tex]

(b) At the end of one year, he would have paid $2,380.


Related Questions

THE GILBERTS PURCHASED A CAR. IF THE TOTAL COST, INCLUDING A 5% SALES TAX, WAS $14,512, FIND THE COST OF THE CAR BEFORE TAX

Answers

The cost of the car the Gilberts purchased before tax is  $13,820.52.

What is the cost before tax?

Tax is a compulsory amount that is levied on a good or service by the government. A sales tax is a tax that is levied on the purchase of a good and service. Taxes increase the cost of a good or service.

The equation that can be used to determine the cost of the car after tax is:

(1 + sales tax) x cost before tax = cost after tax

(1 + 0.05) x c = $14,512

1.05c = $14,512

In order to determine the value of c, divide both sides of the equation by 1.05:

c = $14,512 / 1.05

c = $13,820.52

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find all the zeros of the[tex]y = x^2 - x - 20[/tex] quadratic function

Answers

TO find the zeros of a quadratic function we should factorize the function

[tex]x^2-x-20=(x-)(x+)[/tex]

So we have to find numbers that multiplied are -20 and added are -1. So we get -5 and 4

[tex]x^2-x-20=(x-5)(x+4)[/tex]

so the zeros of the function are 5 and -4

Sam is installing a walkway around a rectangular flower patch in his garden. The flower patch is 12 feet long and 6 feet wide. The width of the walkway is x feet.

Sam created function A to represent the total area taken up by the flower patch and walkway by multiplying the functions modeling the new total length and width.

What does represent in this function?

A.
the area of the walkway along the width of the flower patch
B.
the total area of the walkway
C.
the total area of the flower patch
D.
the area of the walkway along the length of the flower patch

Answers

The function represents the area of the walkway along the width of the flower patch.

What is function?

Rule, or law that establishes the link between an independent variable and a dependent variable is known as function.

Functions can be found everywhere in mathematics, and they are essential for building physical connections in the sciences.

The German mathematician Peter Dirichlet initially offered the contemporary definition of function in 1837.

The total area taken up by the flower patch and walkway by multiplying the functions modeling the new total length and width represents  the area of the walkway along the width of the flower patch.

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a wood cutter has 1/4 + 2/4 + 3/4 of wood And goes to the store and buys 1/4 + 2/4 + 3/4 And adds all of his wood up.

Answers

Answer: I believe the answer is 3.

Step-by-step explanation:

a wood cutter has 1/4 + 2/4 + 3/4 So we add those up to get 6/4.

Then he buys the same amount again which would make 12/4.

We are not done probably, so we MUST simplify.

how many times can 4 fit into 12? 3! so we have whole number 3 and since 4 fit into 12 3 times perfectly all we have is 3

A model rocket is launched straight up into the air. The height y (in feet) of the rocket after t seconds can be modeled by y=-16t^2+128t. How many seconds is the rocket in the air?

Answers

Answer:

8

Step-by-step explanation:

To find the time the rocket is in the air, we can find the time when the height is 0 (remember this time is not 0).

[tex]-16t^2+128t=0 \\ \\ t^2-8t=0 \\ \\ t(t-8)=0 \\ \\ t=0,8 \\ \\ t \neq 0 \implies t=8[/tex]

helppppppppppppppppppypyppyoyoyoyoy

Answers

We are to solve using completing the square:

1/4x² + x + 1/4 = 0

Let's collect like terms:

1/4x² + x = -1/4

Divide both sides by the coefficient of x-squared:

x² + 4x = -1

Take half of the coefficient of x, square it, then add to both sides:

x² + 4x + 4 = -1 + 4

factor the left side of the equation:

(x + 2)² = 3

Take the root of both sides;

x + 2 = ±√3

Add 2 to both sides:

x = ±√(3) - 2

x = -2 + √3 or x = -2 - √3

herefore, the correct option is B, which is x = -2 + √3 or x = -2 - √3

3.656 X 10^-5 written in standard form

Answers

To write  3.656 X 10^-5 in standard form 0.00003656

What is Standard Form ?

A mathematical item's canonical, normal, or standard form refers to how the object is typically expressed mathematically in both mathematics and computer science. It is frequently the one that offers the most straightforward illustration of the thing while yet enabling distinctive identification.

Move the decimal in the number that many spaces to the right when multiplying a number by 10 to the power of a positive exponent

(for example, (10)^3)).

For example, 4.5x(10)^3=4500.

Move the decimal in the number (the absolute value of) that many spaces to the left when multiplying a number by 10 to the power of a negative exponent

(for example, (10)^4)).

For example, (4.5x10)^4=(0.00045)

Move the decimal five spaces to the left for (3.656x 10)^-5:

0.00003656

Hence , 0.00003656 is Standard form of  (3.656x 10)^-5

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A designer has designed different tops, pants, and jackets to create outfits. How many different outfits can the models wear if she has designed the following pieces?

seven tops, two pants, eight jackets

There are a total of different outfits

Answers

The most appropriate choice for combination will be given by-

Models can wear 112 different types of outfit.

What is combination?

Combination determines the number of ways of selecting some number of particular items from a group of given item, here the order of selection do not matter.

If there are n objects and from there, r objects are chosen, number of ways will be given by

                                  [tex]n \choose r[/tex] = [tex]\frac{n!}{(n - r)! \times r!}[/tex]

Here,

Number of tops = 7

Number of pants = 2

Number of jackets = 8

From 7 tops the designer can choose 1 top in [tex]7 \choose 1[/tex] ways

                                                                        = [tex]\frac{7!}{(7-1)!\times 1 !}[/tex]

                                                                        = [tex]\frac{7!}{6!}[/tex]

                                                                        = [tex]7[/tex]

From 2 pants the designer can choose 1 pant in [tex]2 \choose 1[/tex] ways

                                                                        = [tex]\frac{2!}{(2-1)!\times 1 !}[/tex]

                                                                        = [tex]\frac{2!}{1!}[/tex]

                                                                        = [tex]2[/tex]

From 8 jackets the designer can choose 1 jacket in [tex]8 \choose 1[/tex] ways

                                                                        = [tex]\frac{8!}{(8-1)!\times 1 !}[/tex]

                                                                        = [tex]\frac{8!}{7!}[/tex]

                                                                        = [tex]8[/tex]

Total number of different outfits models can wear = [tex]7 \times 2 \times 8[/tex]

                                                                             = 112

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Tanisha earns $3,000 per month
after taxes. She saves $720. What
percent of her budget is savings?

Answers

Answer:

[tex]{ \tt{\% savings = \frac{savings}{total \: income} \times 100\%}} \\ \\ { \tt{ = \frac{720}{3000} \times 100\%}} \\ \\ = { \tt{24\%}}[/tex]

Answer:

24%

Step-by-step explanation:

[tex]\boxed{\sf Percent=\left(\dfrac{Value}{Total\:value}\right) \times 100}[/tex]

Given information:

Value (savings) = $720Total value (earnings) = $3,000

Substitute the given values into the formula and solve for percent:

[tex]\begin{aligned}\implies \textsf{Percent} & =\dfrac{720}{3000} \times 100\\\\& = \dfrac{720\times 100}{3000} \\\\& = \dfrac{72000}{3000} \\\\& = \dfrac{72}{3} \\\\& = 24\% \end{aligned}[/tex]

Therefore, 24% of Tanisha's budget is savings.


If the quotient of a number and 8 is added to 1/4 the result is 7/8. Find the number.

Answers

Answer:

5

Step-by-step explanation:

Let n be the unknown number.

The quotient is the result obtained by dividing one number by another.

Therefore, the quotient of a number and 8 is ⁿ/₈.

If the quotient of a number and 8 is added to 1/4 the result is 7/8:

[tex]\implies \dfrac{n}{8}+\dfrac{1}{4}=\dfrac{7}{8}[/tex]

To solve, make the denominators of all the fractions the same:

[tex]\implies \dfrac{n}{8}+\dfrac{1 \cdot 2}{4 \cdot 2}=\dfrac{7}{8}[/tex]

[tex]\implies \dfrac{n}{8}+\dfrac{2}{8}=\dfrac{7}{8}[/tex]

[tex]\textsf{Apply the fraction rule} \quad \dfrac{a}{c}+\dfrac{b}{c}=\dfrac{a+b}{c}:[/tex]

[tex]\implies \dfrac{n+2}{8}=\dfrac{7}{8}[/tex]

Multiply both sides by 8:

[tex]\implies \dfrac{8(n+2)}{8}=\dfrac{7 \cdot 8}{8}[/tex]

[tex]\implies n+2=7[/tex]

Subtract 2 from both sides:

[tex]\implies n+2-2=7-2[/tex]

[tex]\implies n=5[/tex]

Therefore, the number is 5.

Jaxon was taking his boat out around the lake. The boat is able to drive for 18 minutes for every gallon of gas. Jaxon has 8 gallons of gas in his boat so he bought another 12 gallons. How long can the boat run for now? (In minutes)

Answers

Answer:

hi

Step-by-step explanation:

i dot no because i dot spak in english because im frach

Aidan scored 390 points in 20 games what is his scoring rate in points per game?

Answers

Answer:

19.5

Step-by-step explanation:

HELP PLEASE!!!

In a recent year, 26% of all college students were enrolled part-time. If 4.4 million college students were enrolled part-time that year, what was the total number of college students? Round your answer to the nearest million.

Answers

Answer: 17 million

Step-by-step explanation:

      We will set up a proportion to solve. We also will divide 26% by 100 to get a decimal, 0.26. We know that 26% of college students was 4.4 million, but we want to find 100%.

     [tex]\displaystyle \frac{0.26}{4.4\text{ million}} =\frac{1}{x\text{ million}}[/tex]

      Now, we will cross-multiply.

0.26 * x = 1 * 4.4

0.26x  = 4.4

      Lastly, we will divide both sides of the equation by 0.26. Then, we will round to the nearest million.

x = 16.923

x ≈ 17 million

Write an equation for each line

Answers

The equation for each line will be y=-x+2.

What is a linear equation?

It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.

If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.

It is given that,

The coordinate of the points are (2,0) and (0,2)

The slope of the line is,

[tex]\rm m =\dfrac{y_2-y_1}{x_2-x_1} \\\\ m = \frac{2-0}{0-2} \\\\ m = -1[/tex]

The standard equation of the line is,

y-y₁ = m(x-x₁)

y-0=-1(x-2)

y=-x+2

Thus, the equation for each line will be y=-x+2.

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Complete.
:14=15:21
Someone please answer how to solve

Answers

Answer:

The missing number is 10

Step-by-step explanation:

Given ratio

x : 14 = 15 : 21

Multiply both sides by 14 to find the missing value:

x = 14*15/21       x = 10

Lerato begins a new cycling programme with 2 km on the first day. Each day, he will increase his cycling by 500 m. How many kilometres will he cycle on day 30 of his programme?

Answers

He will cover total 247.5  kilometers on day 30 of his programe .

What is arithmetic progression ?

When there are identical differences between every two next words, the series is known as an arithmetic progression (AP). There is a chance to find a formula for the nth term of the AP using this kind of development. The series 2, 6, 10, 14, etc., for instance, is an example of an arithmetic progression (AP) because it follows a pattern in which each number is acquired by adding 4 to the preceding word. Nth term in this series equals 4n-2.

Given that :Lerato begins a new cycling programme with 2 km on the first day. Each day, he will increase his cycling by 500 m.

The formula to find Sum of an arithmetic progression is

S = [tex]\frac{n}{2}[2a+(n-1)d][/tex]

here , a = 2km

n = 30

d = 0.5km

S =[tex]\frac{30}{2}[2(2)+(30-1)0.5][/tex]

S = 247.5 km

He will cover total 247.5  kilometers  on day 30 of his programe

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Simplify -16.26-(-5.82)-(4.20) - (-6.85).

Answers

Answer:

Step-by-step explanation:

=−10.44−4.2−(−6.85)

=−14.64−(−6.85)

=−7.79

Answer:

-7.79

Step-by-step explanation:

Given problem,

→ -16.26 - (-5.82) - (4.20) - (-6.85)

Let's simplify the problem,

→ -16.26 - (-5.82) - (4.20) - (-6.85)

→ -16.26 + 5.82 - 4.20 + 6.85

→ -10.44 + 2.65 = -7.79

Hence, the answer is -7.79.

So I’m doing this assignment and got stuck on this question can anyone help me

Answers

Explanation:

The question involves dividing radicals

To resolve the question, we will follow the steps below

Step 1: Write the expression

[tex]\sqrt{50x^3}\div\sqrt{32x^2}[/tex]

Step 2: simplify the expression in parts and apply the laws

[tex]\begin{gathered} \sqrt{50x^3}=\sqrt{25\times2\times x^2\times x} \\ =\sqrt{25\times2\times x^2\times x}=\sqrt{5^2\times2\times x^2\times x}=\sqrt{5^2}\times\sqrt{x^2}\times\sqrt{2x} \end{gathered}[/tex]

Thus

[tex]\begin{gathered} \sqrt{50x^3}=\sqrt{5^2}\times\sqrt{x^2}\times\sqrt{2x}=5\times x\times\sqrt{2x} \\ Therefore \\ \sqrt{50x^3}=5x\sqrt{2x} \end{gathered}[/tex]

For the second part

[tex]\sqrt{32x^2}=\sqrt{16\times2\times x^2}[/tex]

simplifying further

[tex]\sqrt{16\times2\times x^2}=\sqrt{16}\times\sqrt{x^2}\times\sqrt{2}[/tex]

Hence, we have

[tex]\sqrt{16}\times\sqrt{x^2}\times\sqrt{2}=4\times x\times\sqrt{2}=4x\sqrt{2}[/tex]

Finally, we will combine the simplified terms, so that we will have

[tex]\sqrt{50x^3}\div\sqrt{32x^2}=5x\sqrt{2x}\div4x\sqrt{2}[/tex]

Hence, we will have

[tex]\frac{5x\sqrt{2x}}{4x\sqrt{2}}=\frac{5}{4}\times\frac{x}{x}\times\frac{\sqrt{2}}{\sqrt{2}}\times\frac{\sqrt{x}}{1}[/tex]

By canceling out the common parts, we will have the answer to be

[tex]\frac{5}{4}\sqrt{x}[/tex]

What is the quotient of 2.538\times 10^92.538×10

9

and 2.7 \times 10^22.7×10

2

expressed in scientific notation?

IF U DON"T KNOW THE ANSWER DON"T ANSWER & work it out plss

Answers

The quotient of 2.538 ×10^9 and 2.7×10^2 expressed in scientific notation is : 0.94 × 10^6.

Scientific notation

Given:

2.538 × 10^ 9 and 2.7 × 10^ 2

We have to first of all formulate before determining the scientific notation

(2.538 × 10^ 9) ÷ (2.7 × 10^2)

Rewrite as fraction

2.538 × 10^9 ÷ 2.7 × 10^2

simplify

2.538 ÷ 2.7 × 10^ 9-2

=  2.538 ÷ 2.7 × 10^7

Convert the fraction to decimal

0.94 × 10^7

Now let express it in scientific notation

Scientific notation = 94 × 10^6

Therefore the scientific notation is 94 × 10^6.

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The correct question is:

What is the quotient of 2.538 ×10^9 and 2.7×10^2 expressed in scientific notation

The area of a rectangle is solved by multiplying the length and width of a rectangle. A rectangular field has an area of 57,600 square feet. If its width is 160 feet, what is its length? ​

Answers

Answer:

360ft

Step-by-step explanation:

Here,

Given,

→Area=57600ft²

→Width=160ft

Now,

→Length=Area/Width
→Length=57600ft²/160ft=360ft

out of water park 243 out of 675 tickets were sold child tickets what percentage of the tickets were child tickets

Answers

Total ticket = 675

Child tickrt sold = 243

percentage of child tickets sold

[tex]\begin{gathered} =\text{ }\frac{243}{675}\text{ x 100\%} \\ \\ =\text{ }\frac{243\text{ x 100}}{675} \\ =\text{ }\frac{24300}{675} \\ =\text{ 36\%} \end{gathered}[/tex]

point a of a triangle is at 2, to point via that a reflection of a point across the X axle a c is 5 unit directly to the left of the point B what are the triangles Dimensions you may you wish to plot the point on your own piece of graph paper

Answers

From the question;

Point A is at (2,2)

Point B is the reflection of point A across the x-axis;

The rule for reflection across the x-axis is;

[tex](x,y)\rightarrow(x,-y)[/tex]

So, point B will be;

[tex]A(2,2)\rightarrow B(2,-2)[/tex]

The point C is 5 units directly left of point B;

So, point C will be;

[tex]\begin{gathered} (x,y)\rightarrow(x-5,y) \\ B(2,-2)\rightarrow C(2-5,-2) \\ B(2,-2)\rightarrow C(-3,-2) \end{gathered}[/tex]

Therefore, the coordinates of the Points A, B and C are;

[tex]\begin{gathered} A(2,2) \\ B(2,-2) \\ C(-3,-2) \end{gathered}[/tex]

Shown as;

So, the length AB is;

[tex]AB=2-(-2)=4[/tex]

The length BC is;

[tex]undefined[/tex]

3. A rectangle that is 2 cm by 3 cm has been scaled by a factor of 5. What are the dimensions of the new rectangle?

Answers

New width: 10 cm, new length: 15 cm

Or new width 15 and new length 10

1) Since this rectangle, has been scaled up by a factor k=5 (since 5 >1 then the rectangle has been enlarged)

2) Then we can write the following about their new dimensions:

w = 2 x 5 = 10

l = 3 x 5 = 15

3) So the answer is 10 x 15

Choose the expression that is equivalent to a fraction with six raised to the negative third power in the numerator and the quantity three raised to the negative second power times six squared end quantity in the denominator and the entire fraction is cubed.

three raised to the sixth power divided by six raised to the fifteenth power

three squared divided by six raised to the fifth power

negative three raised to the sixth power divided by six raised to the fifteenth power

negative three squared divided by six raised to the fifth power

Answers

The value of the expression in the options is (a) three raised to the sixth power divided by six raised to the fifteenth power

How to determine the equivalent expression of the expression?

The expression is given as

A fraction with six raised to the negative third power in the numerator and the quantity three raised to the negative second power times six squared end quantity in the denominator and the entire fraction is cubed.

Rewrite the expression properly

So, we have

[6^-3/(3^-2 x 6^2)]^3

Apply the law of indices to the expression

So, we have

[6^-3/(3^-2 x 6^2)]^3 = [6^(-3 - 2)/(3^-2)]^3

Evaluate the difference

[6^-3/(3^-2 x 6^2)]^3 = [6^-5/(3^-2)]^3

Apply the change of power rule

[6^-3/(3^-2 x 6^2)]^3 = [3^2/6^5]^3

Evaluate the product of exponents

[6^-3/(3^-2 x 6^2)]^3 = 3^6/6^15

In words, the result is (a) three raised to the sixth power divided by six raised to the fifteenth power

Hence, the value of the expression is (a)

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The formula to show the height and time an object is in the air is given byh(t) = -16t2 + 48t + 50 where h(t) is the height of an object and t is the timein seconds. Find how long the object is in the air before it hits the ground.

Answers

The formula to show the height and time an object is in the air :

[tex]h(t)=-16t^2+48t+50[/tex]

when the object hits the ground the height will become 0

so, put h(t) = 0

and simplify :

[tex]\begin{gathered} h(t)=-16t^2+48t+50 \\ 0=-16t^2+48t+50 \\ -16t^2+48t+50=0 \end{gathered}[/tex]

Simplfy the equation by using discrimination rule :

The general form of quadratic equation is : ax² + bx + c

and the roots are express a s :

[tex]x=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a}[/tex]

On compare the given equation with the general equation we get :

a = -16, b = 48 and c = 50

Substitute the value and simplify :

[tex]undefined[/tex]

The width of a rectangle is fixed at 5 cm. Determine​ (in terms of an​ inequality) those lengths for which the area will be less than 125 cm2.

Answers

The lengths of the rectangle for which the area will be less than 125 cm² is 5 < m < 25

In this question, we have been given the width of a rectangle is fixed at 5 cm.

We need to determine​ (in terms of an​ inequality) those lengths for which the area will be less than 125 cm²

Let 'm' be the length of the rectangle.

The area of the rectangle is:

A = length × width

The area of the rectangle should be less than 125 cm²

5 × m < 125

Divide both the sides of the inequality by 5

m < 25

This means, the length of rectangle should be less than 25 cm

But length is always greater than the width of the rectangle.

So, we get an inequality 5 < m < 25

Therefore, the lengths of the rectangle for which the area will be less than 125 cm² is 5 < m < 25

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Name the rule for this sequence.

27, 21, 15, 9, 3,…
A. divide the previous term by 0.06
B. divide the previous term by 0.6
C. add 6 from the previous term
D. subtract 6 from the previous term

Answers

D.

27 - 6 = 21
21 - 6 = 15
15 - 6 = 9
9 - 6 = 3

C. add 6 from the previous term

To get the next term in the sequence, you subtract 6 from the previous term.

Give an example of each survey question type below that would relate to an organic produce farmer.

a) Dichotomous

b) Multiple choice

c) Rating scale

d) Completion

e) Open-ended

Answers

Examples of each survey question that relates to organic farm produce are as follows;

a) Dichotomous

Do you prefer organic farm produce?

Yes/No

b) Multiple choice

How many of your colleagues make use of organic farm produce

OneTwoThreeFourFive

c) Rating scale

On a scale of 1 to 5, with 10 being happiest, how happy are you about our customer service?

1, 2, 3, 4, 5

d) Completion

Eating organic produce _______ improve my health

Will

Will not

e) Open-ended

Tell us why you prefer organic farm produce ___________

What is a statistical survey?

A survey involves the administration of questions or the examination of a process that is aimed at obtaining data with regards to a service, process or product.

a) Dichotomous questions are questions that can have only two possible responses. Such questions are used in a survey in which the two possible responses are stated such as Agree/Disagree, Yes/No, Fair/Unfair, True/False, or Cold/Hot. Based on the definition of the responses, the opinion of the responder is made clear

An example of a dichotomous question asked with respect to organic farm produce is 'Do you prefer organic farm produce?'

The possible responses are; Yes/No

b) Multiple choice survey question

Multiple choice questions provide the opportunity for a respondent to have more options to choose a response from. The multiple choice questions also allow researcher to obtain detailed information on the subject.

An example of multiple choice question is as follows;

How many of your colleagues make use of organic farm produce

OneTwoThreeFourFive

c) Rating Scale

In rating scale survey questions the respondents are asked to select a rating of their experience in a response that offers a rating such as 1 to 10 or 1 to 100

An example of a rating scale question in a survey is as follows;

On a scale of 1 to 5, with 10 being happiest, how happy are you about our customer service?

1, 2, 3, 4, 5

d) Completion

Completion type question assesses the level of cognition on a subject matter

Example;

Eating organic produce _______ improve my health

WillWill not

e) Open–ended

Open–ended questions gives respondents the latitude to express themselves with regards to the question in written text in a detailed or in a brief response.

Example;

Tell us why you prefer organic farm produce ___________

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Determine the values of m in the equation m2 = 16. m = ±4 m = 4 m = ±8 m = 8

Answers

The values of m that can fit into the equation m² = 16 will be m = ±4.

How to compute the value?

It should be noted that a equation is simply used to illustrate the relationship between the variables that are given. From the information, it should be noted that the equation is illustrated as m² = 16.

Since m² = 16, we need to find the square root. This will be illustrated as:

m² = 16

m = ✓16

m = 4

It should be noted that (-4) × (-4) = 16 and 4 × 4 = 16.

Therefore, the correct option is m = ±4

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Factor the trinomials:
1) [tex]x^2 -2x-2[/tex]
2)[tex]x^2-6x+4[/tex]

Answers

Given that equation

1) [tex]x^{2} - 2x - 2[/tex]  using the general quadratic equation, x = 1

2)[tex]x^{2} -6x -4[/tex] using the general quadratic equation, x= [tex]\frac{6 - \sqrt{20} }{2}[/tex]

According to the question, given that

1) [tex]x^{2} - 2x - 2[/tex]

2)[tex]x^{2} -6x -4[/tex]  

this equation cannot be factored but using general quadratic equation. we solved it easily.

When asked to solve a quadratic equation that you just can’t seem to factor (or that just doesn’t factor), you have to employ other ways of solving the equation, such as by using the quadratic formula. The quadratic formula is the formula used to solve for the variable in a quadratic equation in standard form.

Given a quadratic equation in standard form ax2 + bx + c = 0,

[tex]x = \frac{- b - \sqrt{b^{2} - 4 ac } }{2a}[/tex] and  [tex]x = \frac{- b + \sqrt{b^{2} - 4 ac } }{2a}[/tex]

solve [tex]x^{2} - 2x - 2[/tex] = 0, you first say that a = 1, b = –2, and c = 2. The a, b, and c terms simply plug into the formula to give you the values for x:

    1) [tex]x^{2} - 2x - 2[/tex]    

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

[tex]x = \frac{2 + \sqrt{4 -4} }{2}[/tex]

x = [tex]\frac{2}{2}[/tex]

[tex]x = 1[/tex]

and    [tex]x = \frac{- (-2) - \sqrt{(-2)^{2} - 4 (1)(1) } }{2(1)}[/tex]

         [tex]x = \frac{2 - \sqrt{4 -4} }{2}[/tex]

         x = [tex]\frac{2}{2}[/tex]

         [tex]x = 1[/tex]

equation  [tex]x^{2} - 2x - 2[/tex]  and x= 1

2)[tex]x^{2} -6x -4[/tex]  

solve [tex]x^{2} - 6x - 4[/tex] = 0, you first say that a = 1, b = –6, and c = 4. The a, b, and c terms simply plug into the formula to give you the values for x:

[tex]x^{2} -6x -4[/tex]  

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

[tex]x = \frac{6 + \sqrt{36 - 16} }{2}[/tex]

x = [tex]\frac{6 \sqrt{20} }{2}[/tex]

and    [tex]x = \frac{- (-6) - \sqrt{(-6)^{2} - 4 (1)(4) } }{2(1)}[/tex]

         [tex]x = \frac{6 - \sqrt{36 - 16} }{2}[/tex]

         x = [tex]\frac{6 - \sqrt{20} }{2}[/tex]

equation  [tex]x^{2} - 6x + 4[/tex]  and x= [tex]\frac{6 - \sqrt{20} }{2}[/tex]

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