Please help.
Compare and contrast the processes of solving rational and radical equations

I only need like 2-3 sentences.

If a, b and c are the lengths of the sides of a triangle then

if a ≤ b ≤ c, then a + b > c.

1. a ≤ 3 ≤ 8 then a + 3 > 8 → a > 8 - 3 → a > 5 FALSE, because a ≤ 3.

2. 3 ≤ a ≤ 8 then 3 + a > 8 → a > 5 therefore  5 < a ≤ 8

3. 3 ≤ 8 ≤ a then 3 + 8 > a → 11 > a → a < 11 therefore 8 ≤ a < 11.

The range of possible links for the third side s is 5 < s < 11

A triangle is a polygon with three sides , three vertices and three angles.

It is known that if a, b and c are the lengths of the sides of a triangle and

then

a + b > c  

b+c > a  

c+a > b

Then the length of the third side lies between

8-3 < s < 8+3

5 < s < 11

Therefore the range of possible links for the third side s is 5 < s < 11

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The midpoint of line segment MN with endpoints M (6, 14) and N (-4, -4) can be calculated using the formula: ( (x1 + x2) / 2, (y1 + y2) / 2 ) which gives the midpoint coordinates as (1, 5).

In order to find the midpoint of a line segment in a 2-dimensional space, you can use the midpoint formula: ( (x1 + x2) / 2, (y1 + y2) / 2 ). For the given endpoints M (6, 14) and N(-4, -4), substitute the respective values into the formula:

X-Midpoint = (6 + -4) / 2 = 1

Y-Midpoint = (14 + -4) / 2 = 5

Thus, the coordinates of the midpoint of segment MN are (1, 5).

Note: The reference information provided does not apply to this question as it seems to be talking about different points and using the slope matrix, not the midpoint formula.

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s in the expression s • (16) = 2.5  represents the speed in miles per hour.

Speed is defined as when an object is in motion, the distance covered by that object per unit of time is called speed.

here,
A theme park has a tram that goes around the 2.5-mile perimeter of the park in 10 minutes.
So,
Speed = 2.5 miles / 10 minutes

Since, 1 hour = 60 minutes,
And 1 minute = 1/60 hours,

Now, converting the unit of speed of tram from miles per minute to miles per hour where,
Speed = 2.5 miles / 10 (1/60 hours)
Speed = s (say)

s = 2.5/ (1/6)
s (1/6) = 2.5

hence, s in the above expression represents the speed.

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Final answer:

The symbol 's' in the equation represents the speed of the tram in miles per minute

Explanation:

The student's question involves solving for the speed s of a tram that goes around the perimeter of a theme park. The equation provided is s (16) = 2.5, where s represents the speed of the tram in miles per minute. To find the value of s, we need to divide both sides of the equation by 16, which yields:

s = 2.5 / 16

Now, performing the division gives us:

s = 0.15625

Therefore, the speed of the tram is 0.15625 miles per minute.

Answer:

9 quarters and 12 nickles

Step-by-step explanation:

9 quarters = $2.25

12 nickles = .60

$2.25 + .60 = 2.85

12 is 3 more than 9

Answer: 8.50 dollars

The result is positive, so this is a gain (instead of a loss)

====================================

Explanation:

Focus on the "stock JKL" row only when it comes to the percentages we'll use. We need to convert them to decimal form

15% ---> 0.15

65% ---> 0.65

20% ---> 0.20

I just moved the decimal point over 2 spots, or you can divide by 100 (eg: 15% = 15/100 = 0.15)

Multiply each of these values by their corresponding loss or gain. Use negative numbers for losses

15% chance of losing $25 ---> 0.15*(-25) = -3.75

65% chance of winning $5 ---> 0.65*(5) = 3.25

20% chance of winning $45 ---> 0.20*(45) = 9

Now add up those results: -3.75+3.25+9 = 8.50

Answer:

The equation of the line would be y = 1/3x + 2

Step-by-step explanation:

To find this, we must first solve the original equation for y.

3x + y = 6

y = -3x + 6

This means the original slope is -3. Since the original slope is -3, we know that the perpendicular slope is 1/3. This is because perpendicular slopes are opposite and reciprocal.

Now we use the slope and the intercept in slope-intercept form to get the equation.

y = mx + b

y = 1/3x + 2

The equation of a line perpendicular to the line 3x + y = 6 and passing through the y-intercept of 2 is y = 1/3x + 2.

To find the equation of a line that is perpendicular to a given line and passes through a certain y-intercept, we first find the slope of the given line, and then use the negative reciprocal of that slope as the slope of the new line.

The given line is in standard form 3x + y = 6. To convert it to slope-intercept form, we isolate y: y = -3x + 6. Therefore, the slope of the given line is -3. The slope of any line perpendicular to this line is the negative reciprocal of this slope, or 1/3.

The new line must pass through the point where y = 2. So, we plug this value into the slope-intercept form of the equation: y = mx + b, where m is the slope and b is the y-intercept. As a result, the new equation is: y = 1/3x + 2.

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Is it asking about the slope of this vertical line? if so, then the answer is "undefined". The rise is any number you want, let's say 1, and the run is 0

slope = rise/run = 1/0 = undefined

you cannot divide by zero

Answer:

The value of [tex]s_{26}=84.5[/tex]

Step-by-step explanation:

We have given  [tex]a_{14}=4.1[/tex]

d=1.7

We have to find [tex]s_{26}[/tex]

So, [tex]a_{14}=a+13d[/tex] from the formula

[tex]a_n=a+(n-1)d[/tex]

When n=14

[tex]a_{14}=a+(14-1)(1.7)=a+13(1.7)[/tex]

[tex]4.1=a+22.1[/tex]

[tex]-18=a[/tex]

[tex]a=-18[/tex]

Using the formula:

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

When n=26

[tex]s_{26}=\frac{26}{2}[2(-18)+(26-1)(1.7)][/tex]

On simplification we get:

[tex]s_{26}=84.5[/tex]

Answer:

the maximum height is 1054.500 meters

Step-by-step explanation:

h ( t ) = − 4.9t^2 + 133t + 152

a= -4.9 , b= 133  and c= 152

To find maximum height , we find vertex

[tex]x= \frac{-b}{2a}=\frac{-133}{2(-4.9)}= 13.5714 [/tex]

Now plug in 13.5714 for 't' in h(t)

[tex]h(t) =-4.9t^2 + 133t + 152[/tex]

[tex]h(t)=-4.9( 13.5714)^2 + 133( 13.5714)+ 152=1054.500[/tex]

the maximum height = 1054.500 meters

The maximum height of the drone is approximately 1347.174 meters.

To find the maximum height of the drone, we need to find the vertex of the quadratic function h(t) = -4.9t^2 + 133t + 152. The vertex of a quadratic function in the form f(t) = at^2 + bt + c is given by the coordinates (t, f(t)) where t = -b/2a and f(t) is the maximum value.

Plugging in the values from our function, we have t = -133/(2*(-4.9)) = 13.67347. Substituting this value of t back into the function, we get h(13.67347) = -4.9*(13.67347)^2 + 133*(13.67347) + 152 = 1347.174 meters. Therefore, the maximum height of the drone is approximately 1347.174 meters.

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Answer:

a. $102  b. $38  c. 19/70.

Step-by-step explanation:

a. You spent  2/3 * 60 + 7/10 * 35 + 5/6 * 45

= $102.

b. Cost before the sale discount = 60 + 35 + 45 = $140 , so the amount you saved = 140 - 102 = $38.

c.  Fraction on original price saved = 38/140 = 19/70.

Money spent is $102. Money saved is $38. The fraction of the total original price saved is 19/70.

a. How much money did you spend?

Sneakers: 2/3 of $60 = $40

Sweater: 7/10 of $35 = $24.50

Jacket: 5/6 of $45 = $37.50

Total spent = $40 + $24.50 + $37.50 = $102

b. How much money did you save?

Original total price = $60 + $35 + $45 = $140

Amount saved = $140 - $102 = $38

c. What fraction of the total original price did you save?

Fraction saved = Amount saved / Total original price = $38 / $140 = 19/70

Answer:

500 pounds

Step-by-step explanation:

By proportion :-

15% of the tigers weight   = 75 pounds

1%    ....................................   = 75/15 pounds

100% ..................................   = 75*100 / 15 pounds

= 7500 / 15

= 500 pounds

Answer:

711,042,207 is the standard form.

Step-by-step explanation:

The expanded form can be compressed by simply adding the numbers together. When you add each of these together, you get the number above.

Answer:

Step-by-step explanation:

First of all, par and odd functions have their graphic particularities.

Specificially, if the grade of the polynomial is pair, then the function has a symmetric graph, the curve will have a returning point, like the parabola. On the other and, if the grade of the polynomial is odd, then the graph of the function won't have an symmetry like pair ones, and it won't have a returning points like parabolas

So, in this case, the raph doesn't have a returning point like a parabola or an U movement, that means possible answers are A and B.

Choice B cannot be the answer because the negative sign in the first term indicates a reflection accros the vertical axis, and the graph is showing an original function.

Therefore, the right answer is A. [tex]F(x)=2x^{9} -4x^{2} +4[/tex]

Answer:

D

Step-by-step explanation:

so basically to add up radicals you need to make the number inside the square root the same. what you have to do to do that is find squares inside the number as a factor.

13√80=13*2√20=13*2*2√5=52√5

3√125=3*5√5=15√5

√500=10√5

so all of them have 5 in the square root so you can add them up to equal 77√5

To find the perimeter of a triangle with given radical expressions for side lengths, simplify each expression and add them up. The correct answer is D) 77√5.

The perimeter of a triangle is the sum of the lengths of all three sides. So, to find the perimeter of the triangle given the side lengths as radical expressions, we need to simplify and add them up.

The given side lengths are: 13√80 , 3√125, and √500.

Simplify each radical expression:

13√80 = 13 * √(16 * 5) = 13 * (4 * √5) = 52√5

3√125 = 3 * √(25 * 5) = 3 * (5 * √5) = 15√5

√500 = √(100 * 5) = 10√5

Now, add up the simplified radical expressions: 52√5 + 15√5 + 10√5 = (52 + 15 + 10)√5 = 77√5.

Therefore, the correct answer is D) 77√5, which represents the perimeter of the triangle.

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Brainly keeps saying that my answer contains inappropriate words.

It doesn't!!!

I'll try again.

Answer:

Matt has 7/12 of the jar of marbles left.

Step-by-step explanation:

In order to find this, simply subtract the 3/4 from the full jar (1) and then add 1/3. They will need common denominators to complete this operation.

1 - 3/4 + 1/3 = Amount

12/12 - 9/12 + 4/12 = Amount

7/12 = Amount

Answer:

The center is at (5, -3) and the radius is 5

Step-by-step explanation:

The equation for a circle is given by

(x-h)^2 + (y-k)^2 = r^2

Where (h,k) is the center of the circle and r is the radius of the circle.

(x - 5)2 + (y + 3)2 = 25

Rewriting the equation

(x - 5)2 + (y -  -3)2 = 5^2

The center is at (5, -3) and the radius is 5

Answer:

$44.15 spend by tyrell if he buys the regular school lunch 9 days and buys ala carte 4 days .

Step-by-step explanation:

As given

When Tyrell buys the regular school lunch he spends $2.75.

On some days he buys ala carte he spends $4.85.

Tyrell buys the regular school lunch 9 days and buys ala carte 4 days.

Than

Tyrells spends money when he buys regular school lunch 9 days and ala carte 4 days = 9 × 2.75 + 4 × 4.85

                    = 24.75 + 19.4

                    = $44.15

Therefore $44.15 spend by tyrell if he buys the regular school lunch 9 days and buys ala carte 4 days .

Answer: x=9

Step-by-step explanation:

First, you should multiply 11.75 by 4 to include the shirts that Jolene needs to buy. then, add 11.75x to the equation and it should look like this:

Next, subtract 47 on each side of the equation.

Finally, divide each side by 11.75. Keep in mind that x isn't the only variable you can use.

You should get x=9, which is the number of shirts Keith can buy.

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Answer:

Median is sqrt61

Step-by-step explanation:

Answer:

it cost $39.95 in a month when you use the internet for 14 hours

Step-by-step explanation:

internet company charges $4.95 per month plus $2.50 for each hour

Let x be the amount of hours internet used

for 1 hour, charge is 2.50

for x hours , charge is 2.50x

To get linear equation we use y=mx+b

m is the slope and b is the fixed cost

fixed cost b= 4.95 and slope m = 2.50

So equation becomes y = 2.50x + 4.95

we need to find the cost y for 14 hours

So we plug in 14 for x  and find out y

y = 2.50(14) + 4.95= 39.95

Final answer:

The linear equation to model the monthly cost of internet use is y = 4.95 + 2.50x. For using the internet for 14 hours, the total cost would be $39.95.

Explanation:

The student is asking for a linear equation in slope-intercept form to model the monthly cost of internet usage based on the number of hours used. The internet company charges a monthly subscription fee plus an additional fee per hour of use. The equation to represent this situation is y = 4.95 + 2.50x, where y represents the total monthly cost in dollars and x represents the number of hours the internet is used. To calculate the cost for 14 hours of use in a month, we substitute x with 14: y = 4.95 + 2.50(14), which equals $39.95 for the month.

Answer: [tex]83\dfrac{1}{3}\ \text{days}[/tex]

Step-by-step explanation:

[tex]\dfrac{40\ \text{yards} \cdot \ 25\ \text{yards} }{12\ \text{yards}^2} = \dfrac{1000\ \text{yards}^2}{12\ \text{yards}^2}=\dfrac{1000}{12}=\dfrac{250}{3}=83\dfrac{1}{3}[/tex]

Answer:

Formula for the area of a rectangle

Your welcome:) TTM

9.

[tex]\begin{array}{c|c}\underline{Statement}&\underline{Reason}\\1. SJ=FJ&\text{1. Given}\\2.KS=3, KF=3&\text{2. Given}\\3.KS=KF&\text{3. Transitive Property}\\4.\angle SJK = \angle FJK&\text{4. Congruent sides }\\5.JK=JK&\text{5. Reflexive Property}\\6. \triangle SJK \cong \triangle FJK&\text{6. Side-Angle-Side Theorem}\\\end{array}[/tex]

10.

[tex]\begin{array}{c|c}\underline{Statement}&\underline{Reason}\\1.MA || TH&\text{1. Given}\\2. \angle MAX \cong \angle THX&\text{2. Alternate Interior Angles}\\ \text{3. x is midpoint of AH}&\text{3. Given}\\4.AX \cong HX&\text{4. Deefinition of midpoint}\\5. \angle AXM \cong \angle HXT&\text{5. Vertical angles}\\6. \triangle MAX \cong \triangle THX&\text{Angle-Side-Angle Theorem}\\\end{array}[/tex]

Answer:

4. x=2 y=3

5. x=-3, y=-6

6. x=0, y=6.5

Step-by-step explanation:

A system of equations is 2 or more equations for which the same x,y solution exists. We can solve the system in three ways: elimination, substitution, or graphing. To use substitution, we substitute a equivalent expression in for a variable and solve for the remaining variable. We then substitute again to find the other variable.

y=5x-7  & -3x-2y=-12

We will input for y, the expression 5x-7 into -3x-2y=-12. We will then isolate x to solve for it using inverse operations.

-3x-2(5x-7)=-12

-3x-10x+14=-12

-13x+14=-12

-13x+14-14=-12-14

-13x=-26

x=2

We substitute back in now to solve for y. y=5(x)-7=5(2)-7=10=7=3

-4x+y=6  & -5x-y=21

We will input for y, the expression 6+4x into -5x-y=21. We will then isolate x to solve for it using inverse operations.

-5x-(4x+6)=21

-5x-4x-6=21

-9x-6=21

-9x-6+6=21+6

-9x=27

x=-3

We substitute back in now to solve for y. y=4(x)+6=4(-3)+6=-12+6=-6

-7x-2y=-13  & x-2y=-13

We will input for x, the expression 2y-13 into -7x-2y=-13. We will then isolate y to solve for it using inverse operations.

-7(2y-13)-2y=-13

-7(2y)+-7(-13)-2y=-13

-14y+91-2y=-13

-16y+91=-13

-16y+91-91=-13-91

-16y=-104

y=6.5

We substitute back in now to solve for x. x=2y-13=2(6.5)-13=13-13=0.

Answer:

The Answer is c) 6

Step-by-step explanation:

Solve for x:

5 (x - 3) + 7 = 22

5 (x - 3) = 5 x - 15:

5 x - 15 + 7 = 22

Grouping like terms, 5 x - 15 + 7 = 5 x + (7 - 15):

5 x + (7 - 15) = 22

7 - 15 = -8:

5 x + -8 = 22

Add 8 to both sides:

5 x + (8 - 8) = 8 + 22

8 - 8 = 0:

5 x = 22 + 8

22 + 8 = 30:

5 x = 30

Divide both sides of 5 x = 30 by 5:

(5 x)/5 = 30/5

5/5 = 1:

x = 30/5

The gcd of 30 and 5 is 5, so 30/5 = (5×6)/(5×1) = 5/5×6 = 6:

Answer:  x = 6

Answer:

x=6

Step-by-step explanation:

7 + 5(x - 3) = 22

The first step is to distribute the 5

7+ 5x-5*3 =22

7+ 5x-15 =22

Combine like terms

5x-8 =22

Add 8 to each side

5x-8+8 =22+8

5x = 30

5x/5 = 30/5

x=6

Answer:

16 edges.

Step-by-step explanation:

We will use Euler's polyhedron formula to solve for the edges of our convex polyhedron.

Euler's polyhedron formula is: [tex]V+F-E=2[/tex], where,

V= Vertices of polyhedron,

F= Faces of polyhedron,

E= Edges of polyhedron.

Let us substitute V=6 and F=12 in Euler's formula to find number of edges of our polyhedron.

[tex]6+12-E=2[/tex]

[tex]18-E=2[/tex]

Let us subtract 18 from both sides of our equation.

[tex]18-E-18=2-18[/tex]

[tex]-E=2-18[/tex]

[tex]-E=-16[/tex]

[tex]E=16[/tex]

Therefore, our convex polyhedron will have 16 edges.

Answer:

[tex]\cos\left(\theta\right)=\frac{\sqrt{15}}{4}[/tex]

Step-by-step explanation:

Given that [tex]\sin\left(-\theta\right)=-\frac{1}{4}[/tex] and [tex]\tan\left(\theta\right)=\frac{\sqrt{15}}{15}[/tex]

Using those values we need to find value of [tex]\cos\left(\theta\right)[/tex]

So let's begin with equation of  [tex]\tan\left(\theta\right)=\frac{\sqrt{15}}{15}[/tex] and simplify it to get value of  [tex]\cos\left(\theta\right)[/tex]

[tex]\tan\left(\theta\right)=\frac{\sqrt{15}}{15}[/tex]

[tex]\frac{\sin\left(\theta\right)}{\cos\left(\theta\right)}=\frac{\sqrt{15}}{15}[/tex]

[tex]\sin\left(\theta\right)=\frac{\sqrt{15}}{15}\cos\left(\theta\right)[/tex]

[tex]\sin\left(\theta\right)\cdot\frac{15}{\sqrt{15}}=\cos\left(\theta\right)[/tex]

[tex]\cos\left(\theta\right)=\sin\left(\theta\right)\cdot\frac{15}{\sqrt{15}}[/tex]

[tex]\cos\left(\theta\right)=-\sin\left(-\theta\right)\cdot\frac{15}{\sqrt{15}}[/tex]  {since [tex]\sin\left(-\theta\right)=-\sin\left(\theta\right)[/tex] }

[tex]\cos\left(\theta\right)=-\sin\left(-\theta\right)\cdot\sqrt{15}[/tex]

[tex]\cos\left(\theta\right)=-\left(-\frac{1}{4}\right)\cdot\sqrt{15}[/tex]

[tex]\cos\left(\theta\right)=\frac{\sqrt{15}}{4}[/tex]

Answer:

[tex]\cos \theta = \frac{\sqrt{15}}{4}[/tex]

Step-by-step explanation:

The sine function is an odd function, that is:

[tex]\sin (-\theta) = - \sin \theta[/tex]

Then,

[tex]\sin \theta = \frac{1}{4}[/tex]

The cosine function is computed by the following relation:

[tex]\cos \theta = \frac{\sin \theta}{\tan \theta}[/tex]

[tex]\cos \theta = \frac{\frac{1}{4} }{\frac{\sqrt{15}}{15} }[/tex]

[tex]\cos \theta = \frac{\frac{1}{4} }{\frac{1}{\sqrt{15}} }[/tex]

[tex]\cos \theta = \frac{\sqrt{15}}{4}[/tex]

Answer:

As per the given statement: when the lights go out at the store at night there's a 15% off sign hanging out by the make up counter.

To find the number as a decimal and a fraction in simplest form.

Given the Number = 15%.

If we convert any number from percent to decimal divide by 100 and remove the % sign.

[tex]\frac{15}{100} = 0.15[/tex]

Then the given number in decimal is, 0.15

Now, to convert this percent into fraction;

[tex]\frac{15}{100}[/tex]

Divide both numerator and denominator by 5 to get;

[tex]\frac{\frac{15}{5} }{\frac{100}{5} } = \frac{3}{20}[/tex]

Therefore, the given number in fraction is; [tex]\frac{3}{20}[/tex]

Answer:

[tex]\left(-\frac{1}{2},\frac{\sqrt{3}}{2}\right)[/tex]

Step-by-step explanation:

We know that coordinate of any point on unit circle is given by

[tex]\left(\cos\left(\theta\right),\sin\left(\theta\right)\right)[/tex]

Given that [tex]\theta=-\frac{4\pi}{3}[/tex]

So we just need to plug the value of given angle [tex]\theta=-\frac{4\pi}{3}[/tex] into above formula:

[tex]\left(\cos\left(\theta\right),\sin\left(\theta\right)\right)[/tex]

[tex]=\left(\cos\left(-\frac{4\pi}{3}\right),\sin\left(-\frac{4\pi}{3}\right)\right)[/tex]

[tex]=\left(\cos\left(2\pi-\frac{4\pi}{3}\right),\sin\left(2\pi-\frac{4\pi}{3}\right)\right)[/tex]

[tex]=\left(\cos\left(\frac{2\pi}{3}\right),\sin\left(\frac{2\pi}{3}\right)\right)[/tex]

[tex]=\left(-\frac{1}{2},\frac{\sqrt{3}}{2}\right)[/tex]

Hence choice (3) is correct.

Answer:

-1/2, √3/2

Step-by-step explanation: