Explain the deifferences between properties of equality of equality and properties of inequality when solving the equations and inequality

Answer:

s = 1.17, -23.17

Step-by-step explanation:

s^2 + 22s = 27

Take the coefficient of s

22

Divide by 2

22/2 =11

Square it

11^2 =121

Add this to both sides

s^2 + 22s+121 = 27+121

s^2 + 22s+121  = 148

(s+11)^2 = 148

Take the square root of each side

sqrt((s+11)^2) = ±sqrt(148)

s+11 =  ±sqrt(148)

Subtract 11 from each side

s+11-11 = -11  ±sqrt(148)

s =  -11  ±sqrt(148)

s = -11 + sqrt(148) = 1.1655

   - 11 - sqrt(148)=-23.166

Rounding to the nearest hundredth

s = 1.17, -23.17

Answer:

[tex]0.926[/tex]

Step-by-step explanation:

[tex]1-7.4/100[/tex]

[tex]1-0.074[/tex]

[tex]=0.926[/tex]

Answer:

A

d = 2

Step-by-step explanation:

Formula

l = a + (n - 1)d

Givens

n = 10

a = - 5

l = 13

Solution

13 = - 5 + (10 - 1)d       Substitute

13+5 = -5+5 + 9d       Add 5 to both sides

18 = 9d                      Divide by 9

18/9 = 9/d

d = 2

Answer:

1.375 pounds

Step-by-step explanation:

We want to find how many pounds of candy he has left.

He bought 5 pounds.

He gave out 3 pounds.

He ate 10 ounces. Converting 10 ounces to pounds:

1 ounce = 0.0625 pounds

10 ounces = 10 * 0.0625 = 0.625 pounds

Therefore the amount of candy he has left is:

5 - (3 + 0.625)

= 5 - (3.625)

= 1.375 pounds

Answer:

121

Step-by-step explanation:

5x-54=3x+16

5x-3x=16+54

2x=70

x=35

-------

mAB= 5x-54= 5*35-54= 175-54= 121

Answer:

3/5

Step-by-step explanation:

The constant of proportionality is the slope

m = (y2-y1)/(x2-x1)

   = (3-0)/(5-0)

   =3/5

Answer:

Look up how  to find volume and you'll get the answer right away

Step-by-step explanation:

Answer:

see below

Step-by-step explanation:

4. If ∠AYX = 25.5° that means that ∠XYZ = 25.5 * 2 = 51° because YA is the angle bisector.

5. If ∠XYZ = 64°, ∠AYZ = 64 / 2 = 32°.

6. You can construct ∠P and PQ by using a protractor. I'm not sure how to attach an image so I'll just tell you the answer I got for c which is about 3 cm.

Answer:

simplified expression for √x^2+6x+9 if x≥3

is x+3

Step-by-step explanation:

[tex]\sqrt{x^2+6x+9} \\=>\sqrt{x^2+3x+3x+9} \\=>\sqrt{x(x+3)+3(x+3)} \\=>\sqrt{(x+3)(x+3)} \\=>\sqrt{(x+3)^2}\\=>(x+3) \ or -(x+3)[/tex]

but given that x≥3

then we have to negate solution -(x+3)\

Then simplified expression for √x^2+6x+9 if x≥3

is x+3

Answer:

0.001728 is the cube of [tex]\frac{3}{25}[/tex]

Step-by-step explanation:

0.001728 = [tex]\frac{1728}{1000000}[/tex]

break down each using LCD

1728 / 2 = 864

864 / 2 = 432

432 / 2 = 216

216 / 2 = 108

108 / 2 = 54

54 / 3 = 27

27 / 3 = 9

9 / 3 = 3

3 / 3 = 1

1000000 / 2 = 500000

500000 / 2 = 250000

250000 / 2 = 125000

125000 / 2 = 62500

62500 / 2 = 31250

31250 / 5 = 15625

15625 / 5 =3125

3125 / 5 =625

625 /2 = 125

125 / 5 =25

25 / 5 = 5

5 / 5 = 1

*don't forget to add another 2 for each group*

[tex]\frac{1728}{1000000}[/tex] = [tex]\frac{2 * 2 * 2 * 2 * 2 * 2 * 3 * 3 * 3}{2 * 2 * 2 * 2 * 2 * 2 * 5 * 5 * 5 * 5 * 5 * 5}[/tex]  

= [tex]\frac{3 * 3 * 3}{5 * 5 * 5 * 5 * 5 * 5}[/tex]

= [tex]({\frac{3x^{3} }{5x^{3} * 5x^{3} })^{3}[/tex]

= [tex]\sqrt[3]{\frac{1728}{1000000} } = (\frac{3}{5 * 5} )^{3}[/tex]

=[tex]\sqrt[3]{\frac{1728}{1000000} } = \frac{3}{5 * 5}[/tex]

= [tex]\sqrt[3]{0.001728} = \frac{3}{25}[/tex]

Answer: the  answer is -0.04 ,1 ,-0.04 ,loss of 0.04 gallons of fuel for every 1 mile

Step-by-step explanation:

From the given table we can noticed that the fuel remaining (gallons) decreases as distance (miles).

It is clear that the distance increases by 1 mile for each next row and the remaining fuel is changed for each next row

The change in fuel remaining from one row to the next in the table is -0.04 gallons.

1) The change in fuel remaining from one row to the next in the table is -0.04 gallons.

2) The change in distance from one row to the next in the table is 1 mile.

3) The slope of the line that runs through the points given in the table is -0.04.

4) The slope is -0.04 it means the remaining fuel decreases by 0.04 gallons in each mile.

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Now,

From the given table we can noticed that the fuel remaining (gallons) decreases as distance (miles).

Hence, It is clear that the distance increases by 1 mile for each next row and the remaining fuel is changed for each next row is,

⇒ 13.46 - 13.50

⇒ - 0.04

Thus, The change in fuel remaining from one row to the next in the table is -0.04 gallons.

And, The change in distance from one row to the next in the table is 1 mile.

Hence, The slope is the rate of change of remaining fuel with respect to change in distance is,

⇒ m = - 0.04/1

⇒ m = - 0.04

Thus, The slope of the line that runs through the points given in the table is -0.04.

And, The slope indicates a Change in the fuel remaining in each mile. The slope is -0.04 it means the remaining fuel decreases by 0.04 gallons in each mile.

Learn more about the mathematical expression visit:

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Answer:

2. 13

Step-by-step explanation:

The least number of classes need for all of the students to be registered in a class is 13 since you want all of the stuednts to be registered so no one should be left out. If we do 12*12 (12 students in each class and there are 12 classes), that would only let 144 students take the swimming classes and 8 students would be left out. We don't want that though since we want all of the students to be registered. So let's go to 12*13 (12 students in each class and  there are 13 classes), that would let 156 students take the swimming class. 156>152 so therefore, 13 classes would allow for all 152 students to be registered and it is the least number of classes needed for all the students to be registered in a class (plus you would have 4 seats left for anyone who wants to register in the future but the remainder doesn't matter).  

Step-by-step explanation:

let's subtract it from the first one

8x -4y -(-3x + 4y) = -4 -5

8x -4y +3x - 4y= -9

11x -8y =-9

Answer:

D

Step-by-step explanation:

B needs to be 0 or else there is an extra constant term which makes the equation non proportional

Answer:

- 8/5

Step-by-step explanation:

A line has x-intercept -8 and y-intercept 5.

It means the line has passes through:

Slope as per slope formula:

Perpendicular lines have slopes negative reciprocal to each other

So the slope of the perpendicular line is:

Answer:

y = -319/20| x = 377/20

Step-by-step explanation:

/| 7/2-x-y-(3/5) = 0| -11*x-(13*y) = 0

We try to solve the equation: 7/2-x-y-(3/5) = 0

29/10-x-y = 0 // - 29/10-x

-y = -(29/10-x) // * -1

y = 29/10-x

We insert the solution into one of the initial equations of our system of equations

We get a system of equations:

/| -(13*(29/10-x))-11*x = 0| y = 29/10-x

-1*13*(29/10-x)-11*x = 0

2*x-377/10 = 0

2*x-377/10 = 0 // + 377/10

2*x = 377/10 // : 2

x = 377/10/2

x = 377/20

We insert the solution into one of the initial equations of our system of equations

For y = 29/10-x:  

y = 29/10-377/20

y = -319/20

We get a system of equations:

/| y = -319/20| x = 377/20

Answer:

Macy’s

Step-by-step explanation:

let’s find the cost of each shirt

JCPenny’s: 14.99 x 0.80 = $11.99

                   11.99 x 1.06 = $12.70

                   The final cost of the JCPenny shirt is $12.70

Macy’s: 17.99 x 0.65 = $11.69

             11.69 x 1.07 = $12.51

             The final cost of the Macy’s shirt is $12.51

$12.51 is less than $12.70

So, the Macy’s shirt is the better deal :)

Answer:

Step-by-step explanation:

x+y≥ 10

2x+3y≤24

Answer:

x+y≥ 10

2x+3y≤24

Step-by-step explanation:

Answer:

see below

Step-by-step explanation:

if its perimeter is 60 each side is 60/3 = 20.

Its height will be 10√3 so area is 20 * 10√3 / 2 = 100√3

Answer: False

Step-by-step explanation:

If ABC is congruent to DEF, then BC is congruent to EF.

And A would be congruent to D.

Answer:

see below

Step-by-step explanation:

A

Add the students who passed french, german, both

add 17+19+11 = 47

Subtract this from 55 to get b

b = 55-47 =8

b =8

B

P( passed french and german)

    = number that passed french and german / total

    = 19/55

P( french or german) =

  = number that passed french or german / total

    = (17+11)/55 =28/55

Answer:[tex]\frac{85}{81}[/tex]

Step-by-step explanation:

To find the slope of a line, you would use [tex]\frac{y_{2} -y_{1} }{x_{2}-x_{1} }[/tex].

We use out coordinates to plug into this equation.

[tex]\frac{84-(-1)}{98-17} =\frac{85}{81}[/tex]

Answer:

[tex] = \frac{85}{81} [/tex]

Step-by-step explanation:

[tex](17 \: \: \: \: \: - 1) = > (x1 \: \: \: \: \: \: y1) \\ (98 \: \: \: \: \: \: \: \: \: 94) = > (x2 \: \: \: \: \: \: y2)[/tex]

[tex]slope \\ = \frac{y1 - y2}{x1 - x2} \\ = \frac{ - 1 - 84}{17 - 98} \\ = \frac{ - 85}{ - 81} \\ = \frac{85}{81} [/tex]

hope this helps

brainliest appreciated

good luck! have a nice day!

Answer:

12/13

Step-by-step explanation:

The probability of not drawing an ace is =

1 minus the probability of drawing an ace.

there are 4 aces in a deck

hence the probability of not drawing an ace =

1 - [tex]\frac{4}{52}[/tex]

= 48/52 = 12/13

The required probability of not drawing an ace would be 12/13.

Probability is defined as the possibility of an event being equal to the ratio of the number of favorable outcomes and the total number of outcomes.

You draw a card from a standard deck of 52 playing cards.

The probability of not drawing an ace is P(E)

There are 4 aces in a deck

So the number of favorable outcomes n(E)= 4

And the total number of outcomes n(S) = 52

Thus, the probability of drawing an ace = n(E)/n(S) = 4 / 52

The probability of not drawing an ace will be:

⇒ P(E) = 1 - n(E)/n(S)

⇒ P(E) = 1 - 4 / 52

⇒ P(E) = 48/52

⇒ P(E) = 12/13

Therefore, the required probability of not drawing an ace would be 12/13.

Learn more about the probability here:

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Answer:

x=-9

Step-by-step explanation:

2x+6+5x=6x-3

7x+6=6x-3

7x-6x=-3-6

x=-9

Answer:

x= -9

Step-by-step explanation:

2(x+3)+5x=3(2x-1)

2x+6+5x=6x-3

7x+6=6x-3

7x-6x= -3-6

x= -9

Resolviendo un sistema de ecuaciones, veremos que el número de dos cifras es 97.

¿Como encontrar el sistema de ecuaciones?

Podemos escribir un número de dos cifras como:

a*10 + b

Donde a y b son dos numeros de una cifra.

Entonces podemos escribir las restricciones:

"Si un número de dos cifras se disminuye en 17 y esta diferencia se divide por la suma de sus cifras, el cociente es 5"

((a*10 + b) - 17)/(a + b) = 5

"si el número disminuido en 2 se divide por la cifra de las unidades disminuida en 2, el cociente es 19"

(a*10 + b - 2)/(b - 2) = 19

Entonces tenemos un sistema de ecuaciones, que vamos a escribir como:

a*10 + b - 17 = (a + b)*5

a*10 + b - 2 = 19*(b - 2)

Donde pase los denominadores a la derecha, así es más simple de leer.

Para resolver esto, primero debemos simplificar ambas ecuaciones, vamos a obtener:

a*10 + b - 17 = a*5 + b*5

a*10 + b - 2 = 19*b - 38

Moviendo los terminos con variables a la izquierda y los constantes a la derecha:

a*10 + b - a*5 - b*5 = 17

a*10 + b - 19*b = -38 + 2

Terminamos de simplificar:

a*5 - b*4 = 17

a*10 - b*18 = -36

Ahora debemos aislar una de las variables en una de las ecuaciones, vamos a aislar a en le primera:

a = (17 + b*4)/5

Ahora reemplazamos esto en la otra ecuación y resolvemos para b:

10*(17 + b*4)/5 - b*18 = -36

2*(17 + b*4) - b*18 = -36

34 + b*8 - b*18 = -36

34 - b*10 = -36

-b*10 = -34 - 36 = -70

b = -70/-10 = 7

Para encontrar el valor de a usamos la ecuación:

a = (17 + b*4)/5 = (17 + 7*4)/5 = 9

Entonces podemos concluir que el número es 97.

Sí quieres aprender más sobre sistemas de ecuaciones, puedes leer:

https://brainly.com/question/13729904

Step-by-step explanation:

8:15::16:x

8x = 15 x 16

8x = 240

x = 240/8

x = 30

Answer:

x=2

Step-by-step explanation:

3x+2=8

Subtract 2 from both sides

3x=6

Divide 3 from both sides

x=2

Answer:

see attachments

Step-by-step explanation:

Multiply 25 total students by 40% to find thew number that like science:

25 x 0.40 = 10

10 students like science.

You are told 15 students like math.

More students like math.

Answer:

A

Step-by-step explanation:

x² + 16 = 0

x² = - 16

x² = i² * 4²            {i²  = -1}

x² = (4i)²

x=√(4i)²

x=±4i

x² + 16 = (x + 4i)(x - 4i)