Solve the equation by extracting the square roots. when a solution is irrational, list both the exact solution and its approximation rounded to two decimal places.

Answers

Answer 1

The polynomial that is given here in which the goal is to find out the roots of the equation is x2 = 196 where x is the root of the equation. we transform the given equation into its standard form that is x^2 - 196 = y in which y should be equal to 0 in order to get x.
In this case,

x^2 - 196 = 0
x^2 = 196
we take the square root of both sides in order to extract x
square root x^2 = square root 196
x = +- 14
there are two roots in this function which are positive and negative numbers.
square of a positive number leads to a positive number while the square of a negative number also yields to a positive number.

Related Questions

True or False? The distribution whose five-number summary is shown below has at least one outlier. 21.7, 55.3, 73.4, 89.3, 142.2 A. True B. False

Answers

Answer:

True

Step-by-step explanation:

Apex approved

Answer:

this answer is true

Step-by-step explanation:

i say this because 142.2 is an outlier.

Conjectures and Postulates are accepted as true without formally proving they are true.
True or False

Answers

The answer is false, it is only true for postulates, not conjectures.

Answer:

False; only true for postulates!!!

Step-by-step explanation:

On BYU :)

Where are the x-intercepts for f(x) = −4cos(x − pi over 2) from x = 0 to x = 2π? (?

Answers

consider the function [tex]f(x)=-4cos(x- \frac{ \pi }{2})[/tex]

the x-intercepts of the graph of f, are the zeros of f, that is the solutions of f(x)=0.

so we solve

[tex]-4cos(x- \frac{ \pi }{2})=0[/tex]

[tex]cos(x- \frac{ \pi }{2})=0[/tex]

at this point we ask ourselves, keeping the unit circle in mind, "cosine of what is 0?"

In the unit circle, from 0 to 2π radians,

cos 90° = cos (π/2) rad = 0

and

cos 270° = cos (3π/2) rad = 0

this means that

i)
[tex]x- \frac{ \pi }{2}= \frac{ \pi }{2}[/tex]

[tex]x= \pi [/tex]

and

ii)
[tex]x- \frac{ \pi }{2}= 3\frac{ \pi }{2} [/tex]

[tex]x=3\frac{ \pi }{2} +\frac{ \pi }{2}=2 \pi [/tex]

ii) also, check that [tex]f(0)=-4cos(0- \frac{ \pi }{2})=-4cos(-\frac{ \pi }{2})[/tex] is also 0, because cos (-pi/2)= cos (-90°)=cos 270°=0

Answer:

x=0, x=π, and x=2π

[tex]-2y + y - 3 = 6
[/tex]

Answers

Combine like terms. -2y+y=-y. The equation is now -y-3=6. You need to get the y by itself so add 3 to both sides. The equation is now -y=9. You are solving for y so divide both sides by -1. The equation will be y=-9. The answer is y=-9. Hope this helps! ;)

Can some one please help me with this question answer What is 40%of 320

Answers

40% = 40/100 = 0.4

320 * 0.4 = 128 ← answer

320*0.4=128
Final answer: 128

The formula for the nth term of an arithmetic sequence can be found using the formula a(n)=a (1)+(n-1)d. Which of the following is equivalent to this equation?
a. n=a(n)
b. n=a(n)+a(1)-d/d
c. n=a(n)-a(1)
d. n=a(n)-a(1)+d/d

Answers

The formula is given as

[tex] a_{n} = a_{1}+(n-1)d [/tex] , multiplying out the bracket gives
[tex]a_{n}= a_{1}+nd-d [/tex], rearranging to make [tex]n[/tex] the subject
[tex] a_{n}- a_{1}+d=nd [/tex]
[tex] \frac{ a_{n}- a_{1}+d }{d}=n [/tex]

Hence, the correct answer is option d

Answer:

Step-by-step explanation:

It takes an older employee 13 hours to shovel the snow from a sidewalk, but a younger employee can shovel the same sidewalk in 10 hours. how long will it take them to clear the walk if they work together?

Answers

Time taken by both of the older employee and younger employee is 5.6 hrs

What is Componendo-dividendo rule?

Componendo-dividendo rule: A theorem based on the topic of proportions permits a faster way to carry out the calculations and cut down the count of expansions required. It is helpful in situations involving equations with fractions or rational functions. The componendo and dividendo rule are used while studying ratios and proportions. If the ratio of any two given numbers is the same as the ratio of the other 2 numbers, then the ratios of the sum total of the numerator and denominator to the difference of the numerator and denominator of the two rational numbers are equal in nature.

Given, older employee needs 13 hours to shovel the snow.

So in 1 hr the older employee will shovel = 1/13

Younger employee needs 10 hours to shovel the snow.

So in 1 hr the younger employee will shovel = 1/10

Now, when they work together

[tex]1/13+1/10 = 1/x \\(10+13)/130 = 1/x \\3/130 = 1/x\\x = 130/23 = 5.6 hrs[/tex]

Hence, the time taken by both of them together is 5.6 hrs

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Final answer:

Two employees working together can clear the sidewalk in approximately 6 hours and 31 minutes. This is determined by finding the individual work rates, combining them, and then taking the reciprocal of the combined rate to find the total time worked together.

Explanation:

To find out how long it will take two employees to shovel snow together, we need to determine their combined work rate. The older employee takes 13 hours, and the younger employee takes 10 hours. First, we calculate each of their work rates per hour by taking the reciprocal of their time.

So, the older employee's work rate is 1/13 sidewalks per hour and the younger employee's 1/10 sidewalks per hour. To find their combined work rate, we add these two rates together:

Combined work rate = (1/13) + (1/10) = (10 + 13) / (13 × 10) = 23/130 sidewalks per hour

Now, to find the total time taken to shovel the sidewalk when working together, we take the reciprocal of the combined work rate:

Time taken working together = 1 / (23/130) = 130/23 hours

To make this more interpretable, we can convert it into a mixed number:

Time taken working together = 5 hours and (130/23 - 5 × 23/23) hours = 5 hours and 35/23 hours

We can convert 35/23 hours into minutes by multiplying by 60:

Additional minutes = (35/23) × 60 minutes = approximately 91 minutes

Therefore, the time taken working together is roughly 5 hours and 91 minutes, which simplifies to 6 hours and 31 minutes.

Identify the standard form of the equation by completing the square

Answers

[tex]4 x^{2} -9 y^{2} -8x-36y-68=0[/tex]

[tex]4 x^{2} -8x-(9 y^{2} +36y)-68=0[/tex]

[tex](2x)^{2} -2*(2x)*2-((3y)^{2} +2*(3y)*6)-68=0[/tex]

add and subtract 2^ to the x-expression and 6^ to the second expression to complete the square.

[tex][(2x)^{2} -2*(2x)*2+4]-4-((3y)^{2} +2*(3y)*6+36-36)-68=0[/tex]

[tex](2x-2)^{2} -4-((3y+6)^{2} -36)-68=0[/tex]

[tex](2x-2)^{2} -(3y+6)^{2} -4+36-68=0[/tex]

[tex](2x-2)^{2} -(3y+6)^{2} -36=0[/tex]

[tex](2x-2)^{2} -(3y+6)^{2} = 6^{2} [/tex]

divide by 6 squared

[tex]( \frac{2x-2 }{6} )^{2} -( \frac{3y+6}{6} )^{2} =1[/tex]

[tex]( \frac{x-1 }{3} )^{2} -( \frac{y+2}{2} )^{2} =1[/tex]

[tex] \frac{ (x-1)^{2} }{9} - \frac{(y+2)^{2}}{4} =1[/tex]

Answer: A

A card is drawn from a standard deck of 52 cards. what is the probability that it is a heart? type in your answer to two decimal places!

Answers

There are 13 hearts in a deck, so 13/52 which is just 1/4 which is 0.25

4 suits in a deck
1 suit is a heart

so the probablity is 1 out of 4 or 25% or 0.25

The graph shows the location of Jacob's, Kent's, and Hakim's houses. Each unit on the graph represents 1 kilometer. A coordinate plane is shown. Hakims house is located at negative 3, 1, Jacobs house is located at 1, 5, and Kents house is located at 1, 1. Line segments connect the points to form a right triangle.

Answers

The distance between any two points is:

d^2=(x2-x1)^2+(y2-y1)^2 so in this case we have:

d^2=(5-1)^2+(1-3)^2, d^2=(1-5)^2+(1-1)^2, d^2=(1-3)^2+(1-1)^2

d^2=(16+4), d^2=16, d^2=4

So the total distance or perimeter, p, is:

p=√20+√16+√4

p=√20+4+2

p=6+√20 km (exact)

p≈10.47 km (to nearest hundredth of a kilometer)

Answer:

14 km

Step-by-step explanation:

I did FLVS

"It was you who awoke me last summer out of a life-long stupid dream" write the conclusion for this quote

Answers

The person that "awoke [the author]" helped change the authors life around and helped him find the purpose for his life

hope this helps

How to divide fractions with whole numbers

Answers

To divide fractions with whole numbers, write the whole number as a fraction, then it should be more solveable

To divide fraction with whole number write the whole number as a fraction like write 2 as 2/1.

Hope this helps.

Felicia put $175 into a CD that pays 4% interest, compounded semiannually. According to the rule of 72, approximately how long will it take for her money to double?

Answers

The compound interest is given by:
A=p(1+r/100)^n
where;
A=amount
p=principle
r=rate
n=time
therefore the time taken for Felicia's money to double will be:
350=175(1+4/100)^n
350/175=1.04^n
2=1.04^n
therefore introducing natural longs we get:
ln2=nln1.04
n=(ln2)/(ln1.04)
n=17.7 years
The answer is 17.7 years

Answer:

the answer is 18 years

Step-by-step explanation:

i just did this on 12/8/18 good luck to cheaters

Will give brainliest!

What is the x-coordinate at the point of intersection of y1= 2(5x + 3) and y2= x2 − 15? Consider only the positive value of x, and round the value to nearest hundredth.

Answers

so when does y1 = y2?

at
2 (5x + 3) = (x2 -15)

solve and advise answer in comments and will assist further

Solution

The equation of two curves are

[tex]y_{1}=y=2 \times (5 x+3)\\\\y_{2}=y=x^2-15[/tex]

Equating the two curves that is y values, to find their point of Intersection

→ 2 × (5 x+3)=x²-15

→10 x +6=x²-15⇒⇒Used distributive property of multiplication with respect to addition

→x² -10 x -15 -6=0

→x² -10 x-21=0

For a Quadratic equation of the type

[tex]\rightarrow ax^2+b x +c=0\\\\x=\frac{-b \pm \sqrt{D}}{2 a}\\\\D=b^2-4ac[/tex]

Using discriminant method to solve the problem

[tex]x=\frac{-(-10)\pm\sqrt{(-10)^2-4 \times 1 \times (-21)}}{2 \times 1}\\\\x=\frac{10 \pm \sqrt{100+84}}{2}\\\\x=\frac{10 \pm \sqrt{184}}{2}\\\\x=5 \pm \sqrt{46}\\\\x_{1}=5+6.78\\\\x_{1}=11.78\\\\x_{2}=5-6.78\\\\x_{2}=-1.78[/tex]

The x coordinate of point of intersection are, 11.78 and -1.78.

a ratio is a rate, sometimes,never, or always?

Answers

Never True.
Ratio can be rate but rate can never be ratio. In essence, rate is comparison between ratios. While ratio is comparison between two or more numbers. Further, ratio on one hand, involves numbers either in amount, size, measurement, degrees, percentages or fractions with the absence of specific unit of measurement. On the contrary, rate is comparing quantities, amounts or unit of events happened expressed in a specific measurement or expressed under time. Take for instance, an example, Joe eats 2 while John eats 4 meals in a day. The ratio can be Joe: John, 2:4 meals. While the rate, is Joe eats 2 meals/day and John 4 meals/day.

If a weighted score for a project is based on just two criteria, fit with strategy, weighted 70% and roi, weighted 30%, what would be the weighted score for a project with scores of 80 on fit with strategy and 50 on roi?

Answers

When dealing with weighted averages, we multiply the score of each item by the percentage that it's been weighted and add the scores together. 80/100 X 70/100 = 5600/10000 or 56/100 50/100 x 30/100 = 1500/10000 or 15/100 56 + 15 = 71 and so your grade would be 71%

Final answer:

To calculate the weighted score for a project, apply the weights to the scores for each criterion and sum the results. The calculated weighted score for a project with scores of 80 on 'fit with strategy' (70% weight) and 50 on 'ROI' (30% weight) is 71.

Explanation:

To calculate the weighted score for a project based on the provided criteria, you need to apply the weights to the scores for each criterion and then sum the results. In this case, the criteria are 'fit with strategy' which has a weight of 70% and 'ROI' which has a weight of 30%.

The weighted score for 'fit with strategy' is calculated as follows:
(Score for 'fit with strategy' × Weight of 'fit with strategy') = (80 × 0.7) = 56.

The weighted score for 'ROI' is calculated as follows:
(Score for 'ROI' × Weight of 'ROI') = (50 × 0.3) = 15.

To find the total weighted score for the project, you add these two results together: 56 (from fit with strategy) + 15 (from ROI) = 71.

Therefore, the total weighted score for the project is 71.

Which Act protects consumers against inaccurate and unfair practices from credit card companies and lenders? The ______ in Lending Act protects consumers against inaccurate and unfair practices from credit card companies and lenders.

Answers

I'm pretty sure the answer is The Truth in Lending Act.
Hope this helped!

Answer:

Truth

Step-by-step explanation:

A geometric sequence has a common ratio of 2/9 and the first term is 729 what is the 8th term?

Answers

This is the concept of sequences and series. The formula for geometric series is given by:
an=ar(n-1)
where;
a=first term
r=common ratio
n=nth term
thus the 8th term will be:
8th=728*(2/9)^(8-1)
=728*(2/9)^7
=128/6561

"if the price of mints was raised from 5 cents each to 15 cents for two, what was the increase in price per mint?"

Answers

15 cents for two mints gives 7.5 cents for one mint
7.5 cents is an increase of 2.5 cents from the previous price 5 cents for one mint and it is a 50% increase

Answer:

Increase in price per mint is 2.5 cents .

Step-by-step explanation:

The price of mints is raised from 5 cents each to 15 cents for two.15 cents is the rice in price for two mints .Hence rise in price for each mint is 15÷2=7.2 cents.

Rise in price for each mint = 7.2-5=2.5cents.

Percent increase = [tex]\frac{2.5}{5} (100)=50[/tex]

There is 50% increase in price per mint.

Explain 2 other ways other than rotating 180 degrees counterclockwise or clockwise, that would allow the point to find it’s way to the same place from its original position. Hint: You may combine transformations.

Answers

check picture 1

Notice that a 180° rotation clockwise or counterclockwise (around the origin) send any point P(a, b) to a point with coordinates (-a, -b).

this means the number values of the respective x and y coordinates are the same, but the signs are different.

for example rotating point P(-3, 17) 180 degrees results in point (3, -17)

check picture 2.

reflecting point P(a, b) with respect to :

the y-axis results in point (-a, b)

the x-axis results in point (a, -b)

for example , consider point P(-3, 17)

reflecting this point with respect to the y axis, results in (3, 17)

reflecting (3, 17) with respect to the x-axis results in (3, -17)

So the effect of reflecting with respect to the y axis, the x axis (the other way around is the same) results in the same point as rotating 180 degrees.

Answer:

1) reflect with respect to the y-axis, then reflect this last point with respect to the x-axis

2) reflect with respect to the x-axis, then reflect this last point with respect to the y-axis

In a horse race, how many different finishes among the first 33 places are possible if 20 horses20 horses are running? (exclude ties)

Answers

To solve this problem, let us break this down one by one.

There are 20 possible horses that could win in first place. Therefore this means that for each of these possibilities, there are now 19 horses that could come in second. So meaning there are 20 x 19 possible combinations for the first 2 places.

20 x 19 = 380. And for each of those combinations, there are also 18 possible horses that could come in the third place. So

20 x 19 x 18 = 6,840

There are 6,840 possible horse combinations for the first 3 places in the race.

PLEASE HELP NEED ASAP! 10 PTS!
Solve each system by elimination.
1. -9x+2y= -1.
18x-7y=17

2. 4x+18y= -28
2x+9y= -14

3. 20x+y= -11
-10x-3y= -17

4. -3x+y=7
-6x+2y=12

Thank you!

Answers

Problem 1
-9x + 2y = -1 (1)
18x - 7y = 17 (2)
To eliminate x, multiply (1) by 2 to obtain
-18x + 4y = -2
18x - 7y = 17
Add the two equations.
-3y = 15
y = -5
From (2), obtain
18x = 17 + 7y = 17 + 7*(-5) = -18
x = -1

Answer: x= -1, y = -5

Problem 2.
4x + 18y = -28 (1)
2x + 9y = -14 (2)
Divide (1) by 2 to obtain the system of equations
2x + 9y = -14
2x + 9y = -14
These two equations re identical.
Therefore there are an infinite number of solutions.

Answer:
There is no unique set of solutions.

Problem 3.
20x + y = -11 (1)
-10x - 3y = -17 (2)
Multiply (2) by 2 to obtain
20x + y = -11
-20x - 6y = -34
Add the two equations to eliminate x.
-5y = -45
y = 9
From (1), obtain
20x = -11 - y = -11 - 9 = -20
x = -1

Answer: x = -1, y = 9

Problem 4
-3x + y = 7 (1)
-6x + 2y = 12 (2)
Divide (2) to obtain the system of equations
-3x + y = 7
-3x + y = 6
Because 7 ≠ 6, th set of equations is nonsensical (inconsistent).

Answer:
The set of equations is invalid, and it has no solution.

I NEED THIS ANSWER NOWWWW PICTURE ATTACHED

Which system of inequalities is represented by the graph?

y ≤ 3x
y > –2x – 1
y > 3x
y ≤ –2x – 1
y < –3x
y ≥ 2x – 1
y > –3x
y ≤ 2x – 1

Answers

So first, you need to notice the blue line is y = 2x, and the other one is y = -2x - 1

For the purple area, let's choose a point (1,0), which is in the area.

For y = 2x -> 2 >0, so the inequality will be y ≤2x

For y = -2x - 1 -> -3 < 0, so the inequality will be y ≥ -2x - 1

You can use the similar approach to find other area representations

3/5x+19−3/20x−7/35x+19−3/20x−7 simplified is

Answers

Final answer:

To simplify the expression, combine like terms and then simplify to get (1/4)x+24.

Explanation:

To simplify the expression, 3/5x+19−3/20x−7/35x+19−3/20x−7, we can combine like terms and then simplify:

Combine 3/5x−3/20x−7/35x to get (3/5−3/20−7/35)x = (12/20−3/20−4/20)x = (5/20)x = (1/4)x.Combine 19+19 to get 38.Combine −7−7 to get −14.Combine the results: (1/4)x+38−14 = (1/4)x+24.

So, the simplified expression is (1/4)x+24.

What is the factorization of the polynomial below?

x^3-4x^2+45x

Answers

The method of factorization is used to find the roots of a given polynomial. Roots are the solutions of the function. Graphically, these roots are where the curve passes the x-axis. The first step to do is to find the common factor of the equation. That would be x. So you place it outside of the parenthesis.

x³-4x²+45x = x(x² - 4x + 45)

If you solve the quadratic equation inside the parenthesis using the quadratic formula, the roots are imaginary. Therefore, the quadratic equation is already a prime polynomial.

The final answer is x(x² - 4x + 45).

Hope This Helps You!(

Manuel and rita bought cds at the music store. rita's cds originally cost three times more than manuel's cds, but she received a $9 discount. if rita spent $21 total, which equation can be used to find the amount manuel spent

Answers

3m - 9 = 21 <=== ur equation
3m = 21 + 9
3m = 30
m = 30/3
m = 10 <== ur solution

Answer with Step-by-step explanation:

Let cost of Manuel's cds=m

Rita's cds originally cost three times more than Manuel's cds, but she received a $9 discount.

i.e. Rita's cds cost=3m-9

Rita spent $21 total.

i.e. 3m-9=21

Adding 9 on both sides, we get

3m=30

Dividing both sides by 3, we get

m=10

Hence, equation which can be used to find the amount Manuel spent is:

3m-9=21

Lukas graphed the system of equations shown. 2x + 3y = 2 y = x + 3 What is the solution to the system of equations? (–2, 2) (0, 0.67) (0, 3) (1, 0)

Answers

The closest answer that I could find would be (-2, 2). The answer to the system is (-1.4, 1.6)

The solution to the given system of linear equations is (-1.4, 1.6).

What is a linear system of equations?

A system of linear equations consists of two or more equations made up of two or more variables such that all equations in the system are considered simultaneously. The solution to a system of linear equations in two variables is any ordered pair that satisfies each equation independently.

The given system of equations are 2x+3y=2 -----(i) and y=x+3 -----(ii)

Substitute, equation (ii) in equation (i), we get

2x+3(x+3)=2

2x+3x+9=2

5x=-7

x=-7/5

x=-1.4

Substitute x=-1.4 in equation (ii), we get

2(-1.4)+3y=2

-2.8+3y=2

3y=2+2.8

3y=4.8/3

y=1.6

So, the solution is (-1.4, 1.6)

Therefore, the solution to the given system of linear equations is (-1.4, 1.6).

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the price of a television decreased from 1000.00 to 800.00.what is the percent of decrease.

Answers

Percentage change = 100((New Value - Original Value) / Original Value)
So....
100((800 - 1000) / 1000)
= 100(-1/5) = -20%
Considering the question asks what is the percentage 'decrease' and thus has mentioned that the price is decreasing, you should just give the answer as 20%. If it was not mentioned that the value increases or decreases, it would be correct to put it as -20%

Answer:

The decrease is 20%

Step-by-step explanation:

If the problem is 7+(-5) how many spaces do you move to the right or left

Answers

Start at seven and move 5 spaces to the left.

Addition of a negative is the same as subtraction.

The graph represents a person's heart rate in beats per minute during 30 minutes of exercise.

Which statement best describes the relationship between heart rate and time doing exercise?

Answers

Looking at the graph closely we can see that the heart rate increases from 0 to 6 min then became steady from 6 to 25 min then finally decreases from 25 to 30 min. Therefore the correct answer is:

“The heart rate increases for 6 minutes, remains constant for 19 minutes, and then gradually decreases for 5 minutes.”

In real life cardiac exercises, we can interpret that the period from 0 to 6 min is the period where the person is still warming up thus leading to an increase in heart rate. At 6 min, the person is fully warmed up hence reaching a stable heart rate. Then at 25 min, the person starts cooling down which means that the exercise is ending soon.

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