MATHEMATICS MIDDLE SCHOOL

Find the solution set of this inequality|10x+20| ≤10

Answers

Answer 1

Answer:

Answer:

solution is

[-3,-1]

Step-by-step explanation:

we are given

$|10x+20|\leq 10$

Firstly, we will find critical values

so, let's assume it is equal

$|10x+20|= 10$

now, we can break absolute sign

For $|10x+20|= -(10x+20)$ :

$-(10x+20)= 10$

we can solve for x

$-10x-20= 10$

Add both sides by 20

$-10x-20+20= 10+20$

$-10x= 30$

Divide both sides by -10

and we get

$x=-3$

For $|10x+20|= (10x+20)$ :

$(10x+20)= 10$

we can solve for x

$10x+20= 10$

Subtract both sides by 20

$10x+20-20= 10-20$

$10x= -10$

Divide both sides by 10

and we get

$x=-1$

so, critical values are

$x=-3$

$x=-1$

now, we can draw a number line and locate these values

and then we can check inequality on each intervals

For $(-\infty,-3)$ :

We can select any random value from this interval and plug that in inequality

and we get

we can plug x=-5

$|10* -5+20|\leq 10$

$|-50+20|\leq 10$

$30\leq 10$

so, this is FALSE

For $[-3,-1]$ :

We can select any random value from this interval and plug that in inequality

and we get

we can plug x=-2

$|10* -2+20|\leq 10$

$|-20+20|\leq 10$

$0\leq 10$

so, this is TRUE

For $(-1,\infty)$ :

We can select any random value from this interval and plug that in inequality

and we get

we can plug x=0

$|10* 0+20|\leq 10$

$|0+20|\leq 10$

$20\leq 10$

so, this is FALSE

so, solution is

[-3,-1]

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What is 2.75 rounded to the nearest hundredth

Answers

Well first off we need to know how to round or what rounding is. Rounding is the approximation of numbers usually decimals to a approximate cut off number for numbers that are too long or hard to work with/remember. To round a number you simply need to look at the number behind that number whether its a whole number (integer) or a decimal, either one will work. Now continuing on (on) how to round the number, look at the number after it and if it is 5 or above the number rounds up +1 and all numbers behind that turn to 0. For example 3.25500 round to the nearest hundredth, 3.26(000). Now if the number is 4 or smaller then you don't do anything at all (no rounding) and all the numbers after the being rounded number turn to 0's like so, 3.254(0000) rounded to the nearest hundredth, 3.25(00000). So now that we know how to round and what rounding is we need to look at are hundredth place on are number here and see what the next number is after that, in this case it is 0 because there is no stated number there the default next number is 0 like so,
2.750 and because 0 is under 5 we don't do any rounding at all here and just leave it as it is. So 2.75 rounded to the nearest hundredth is 2.75

Enjoy!=)

The sum of two numbers is 264. One number ends with a zero. If this zero is erased, you get the second number. Find these numbers.

Answers

Answer:

240; 24

Step-by-step explanation:

Given that:

Sum of two numbers = 264

One number ends with '0'

Second number = first number without '0'

Let the first number be 'a'

Since the second number is the first number with '0' erased, then,

Second number = (a ÷ 10)

Therefore, the expression becomes :

a + a/10 = 264

Multiply the equation by 10

10a + a = 2640

11a = 2640

a = 2640/11

a = 240

Therefore ;

a = 240 ;

a/10 = 240/10 = 24

The numbers are 240 and 24

Log8 2^6x-3 = 4 helpppp

Answers

x/729-3 = 4 is the answer. lograythms are fun!

-3q + 12 greater than equal too 4q - 30 solve for q

Answers

Solving the inequality $-3q+12\geq 4q-30$ the value of q is $q\leq 6$

Step-by-step explanation:

We need to solve the inequality: $-3q+12\geq 4q-30$ and find value of q

Solving:

$-3q+12\geq 4q-30\nAdding\,\,-12\,\,on\,\,both\,\,sides:\n-3q+12-12\geq 4q-30-12\n-3q\geq 4q-42\nAdding\,\,-4q\,\,on\,\,both\,\,sides:\n-3q-4q\geq 4q-42-4q\n-7q\geq -42\nDivide\,\,both\,\,sides\,\,by\,\,7\n(-7q)/(7)\geq (-42)/(7)\n -q\geq -6\nMultiply\,\,both\,\,sides\,\,by\,\,-1\,\,and\,\,reverse\,\,the\,\,inequality:\nq\leq 6$

So, solving the inequality $-3q+12\geq 4q-30$ the value of q is $q\leq 6$

Keywords: Solving inequality

Learn more about solving inequality at:

#learnwithBrainly

2x + (3 - x) how do I do this

Answers

okay so you would do it like this

2x + (3 - x)

2x + 3 - x

x + 3

the answer would be x + 3

hope this helps!

Following PEMDAS, the parentheses comes first. Essentially, (3 - x) is times 1, which removes the parentheses. So 2x + 3 - x. Subtract the x first. This leaves x + 3.

The Yu family and the Sainz family went on vacation together and each family leased a car. The leasing company charged a flat rental fee for the week, plus a charge for each mile driven. The Yu's drove 222 miles; their car cost $110.30 for the week. The Sainz's drove 147 miles; their car cost $99.05. What is the linear equation that represents the cost of a rental car? Round to the nearest hundredth

Answers

Answer:

y = 0.15x+77 is the equation linear connecting total cost y and miles driven x

Step-by-step explanation:

Given that the leasing company charged a flat rental fee for the week, plus a charge for each mile driven.

Let flat rental fee be c and cost per mile driven = m and miles driven = x

Total cost =y

Then y = mx+C is the linear equation.

to find m and c, we use the fact that y =110.30 when x = 222

i.e. 110.30 = c+222x

and similarly 99.05 = c+147x

Subtract to eliminate c

11.25 = 75 x

0.15 =x

Substitute in I equation

110.30 = c+222(0.15)

c = 77

y = 0.15x+77 is the equation linear connecting total cost y and miles driven x

Answer:

y=0.15x + 77.00

Step-by-step explanation:

I did it on edge that is the correct answer promise.

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