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Irina18 [472]
2 years ago
8

What is the reason for each step in the solution of the inequality? 4(x+6)>−5(x+5)−14 Select the reason for each step from th

e drop-down menus.
​ 4(x+6)>−5(x+5)−14 ​ ​Given
​​ ​ 4x+24>−5x−25−14 choose ​
​ 4x+24>−5x−39 ​ choose
​​ ​ 4x+63>−5x Addition Property of Order
​ 63>−9x ​ Subtraction Property of Order
​​​​ −7<x      choose
Mathematics
2 answers:
Nesterboy [21]2 years ago
8 0

Hey there!!

The equation given :

4 ( x + 6 ) > -5 ( x + 5 ) - 14

... 4x + 24 > -5x - 25 - 14

... 4x + 24 > - 5x - 39

Add 39 on both sides

... 4x + 63 > - 5x

Subtract 4x on both sides

... 63 > - 9x

Divide by -9 on both sides

When we divide both sides by a negative number, we switch the signs.

... -7 < x

Hope my answer helps!!

Serhud [2]2 years ago
4 0

4(x + 6) > −5(x + 5) − 14 ​ ​Given

(4)(x) + (4)(6) > (-5)(x) + (-5)(5) - 14

​​4x + 24 > −5x − 25 − 14 Distributive property ​

4x + 24 > -5x - (25 + 14)

4x + 24 > −5x − 39 ​ Simplify right side

4x + 24 + 39 > -5x -39 + 39

4x + 63 > −5x  Addition property of equality

4x - 4x + 63 > -5x - 4x

​ 63 > −9x ​ Subtraction property of equality

63 : (-9) < -9x : (-9)    /-9 < 0 → switch the signs/

−7 < x      Division property of equality

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mario62 [17]

Answer:

23 people.

Step-by-step explanation:

T=125 + 5.25p

p=23

She'd spend a total of 245.75.

7 0
2 years ago
What are the solutions of the equation (2x + 3)2 + 8(2x + 3) + 11 = 0? Use u substitution and the quadratic formula to solve.
zvonat [6]

Answer:

x=-2.38

x=-4.62


Step-by-step explanation:

The question is  (2x+3)^2+8(2x+3)+11=0

<em>We let u=2x+3, so the equation becomes:</em>

u^2+8u+11=0

Where a=1, b=8, c=11


Putting it in the quadratic formula, we have:

<u>Quadratic formula:</u> \frac{-b+-\sqrt{b^2-4ac} }{2a}

Substituting we have: \frac{-8+-\sqrt{(8)^2-4(1)(11)} }{2(1)}\\=\frac{-8+-\sqrt{20} }{2}\\=\frac{-8+-2\sqrt{5} }{2}\\=-4+\sqrt{5}, -4-\sqrt{5} }


<em>We let u=2x+3, so x is:</em>

<em>u=2x+3\\(-4+\sqrt{5})=2x+3\\x=\frac{-7+\sqrt{5}}{2}=-2.38</em>

<em>and</em>

<em>u=2x+3\\(-4-\sqrt{5})=2x+3\\x=\frac{-7-\sqrt{5}}{2}=-4.62</em>


The solutions of the equation is x=-2.38 (rounded to 2 decimal places), and x=-4.62 (rounded to 2 decimal places)

6 0
2 years ago
While shopping for clothes Tracy spent $38 less than three times what Daniel spent right and solve an equation to find how much
Gnom [1K]

Answer:

y=3x-38

Step-by-step explanation:

We know that Tracy spent $38 in less than 3 times than what Daniel spent. Given this information we can put our eqaution together.

Y=3x-38

Hope this helps! :)

6 0
2 years ago
A spherical container has a radius of 9 centimeters. It is filled with a solution that costs $2.10 per cubic centimeters.
vitfil [10]
Hello! For this question, first, we have to find the area of the spherical container. The formula for finding the area of a sphere is 4/3πr³. We raise the radius to the 3rd power and multiply it by pi (3.14). The radius is 9 cm. 9³ is 729. There's that number. Now, we multiply 81 by 3.14 to get the total area of the square. 729 * 3.14 is 2,289.06. Now, multiply that by 4/3. 2,289.06/1 * 4/3 is 3,052.08. The volume of the sphere is 3,052.08 cubic centimeters. Which brings us to the next part. Now, we can find the price of the solution by multiplying the area by the price. 3,052.08 * 2.10 is 6,409.368 or 6,409.37 when rounded to the nearest cent. The total value of the solution in the container is $6,409.37.
6 0
2 years ago
Read 2 more answers
I) Solve the equation sin2x + 3cos2x = 0 (for 0 till 360°)
galina1969 [7]
Get rid of cos2x by dividing both the values. So Sin2x/cos2x +3cos2x/cos2x.
Tan2x = 3
2x = -71.5 so x is -35.6
Use the quadrant method and add 360 twho the two values tou get.
7 0
2 years ago
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