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4 years ago

Solve 1/2x+8≤ 10 What is x equal to?

Mathematics

2 answers:

Salsk061 [2.6K]4 years ago

7 0

Answer:

x ≤ 4

Step-by-step explanation:

1/2 x + 8 ≤ 10

1/2 x ≤ 10 - 8

1/2 x ≤ 2

x ≤ 4

Luba_88 [7]4 years ago

5 0

Answer:

x ≤ 4

Step-by-step explanation:

Step 1: Subtract 8 from both sides

1/2x + 8 - 8 ≤ 10 - 8

1/2x ≤ 2

Step 2: Multiply both sides by 2

1/2x * 2 ≤ 2 * 2

x ≤ 4

Answer: x ≤ 4

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In parallelogram ABCD,AB^4+AD^2+AB^2*AD^2=AC^2*BD^2.If angle ABC=x,find the product of all possible values of x

almond37 [142]

Answer:

Hello,

Step-by-step explanation:

AB=DC=b, AD=BC=a

p=BD, q=AC

angle ABC=x

$AB^4+AD^4+AB^2*AD^2=AC^2*BD^2\\\\b^4+a^4+b^2a^2=(a^2+b^2+2abcos(X))(a^2+b^2-2abcos(X)\\\\(a^2+b^2+2a^2b^2)-a^2b^2=((a^2+b^2)^2-4a^2b^2*cos^2(X))\\\\\\4a^2b^2cos^2(X)=a^2b^2\\\\\\cos^2(X)=\dfrac{1}{4} \\\\(cos(X)-\dfrac{1}{2} )(cos(X)+\dfrac{1}{2} )=0\\cos(x)=\frac{1}{2} \ or\ cos(X)=\dfrac{-1}{2} \\\\\\X=60^o =\dfrac{\pi}{3} rad \ or \ X=120^o=\dfrac{4\pi}{3} rad\\\\\\\\Product=\dfrac{\pi}{3}*\dfrac{4\pi}{3} =\boxed{\dfrac{4\pi^2}{9}}\\$

8 0

3 years ago

Find two consecutive even integers such that the square of the second, decreased by twice the first is 52

Fiesta28 [93]

Let the first integer be $x$ . So, the next even number is $x+2$

Let's translate the formula: the square of the second is $(x+2)^2$ , twice the first is $2x$ . So, the equation is

$(x+2)^2 - 2x = 52$

Expand the square to get

$x^2+4x+4-2x = 52 \iff x^2+2x+4 = 52 \iff x^2+2x - 48 = 0$

The solutions to this equations are

$x = -8,\quad x = 6$

So, the possible consecutive even numbers are

$-8\text{ and } -6\quad\text{or}\quad 6\text{ and } 8$

8 0

3 years ago

every ninth person in line at a movie theater gets free popcorn. Every sixth person gets free apple juice. Which customer will e

lys-0071 [83]

We are told that every 9th person gets free popcorn and every 6th person gets free apple juice at the movie theater. We want to show if the 36th person is the first to get both free popcorn and apple juice.
Since every 9th gets free popcorn, then the 9th and 18th and 27th and 36th people get it. We can use numbers and show this as multiples of 9.
9, 18, 27, 36, 45, 54, ...
And we repeat it for every 6th and the free juice.
6, 12, 18, 24, 30, 36,....
Shani thinks 36 comes first, and she's wrong. 18 appears on the list before 36 as something that's common. What are we finding is the lowest common muliple of 6 and 9.
6 = 2 x 3
9 = 3 x 3
The lowest common multiple will have a 2, a 3, and a second 3 (because we don't double count). 2 x 3 x 3 = 18. This matches up to the list of multiples.

Thus, Shani is wrong that the 36th person gets both free items, as she did not account for the 18th person gettting both free items

8 0

3 years ago

Suppose a 5-digit number is formed using the digits from 1 to 9 (without replacement). What is the probability that it will be a

zhuklara [117]

Answer:

First take 5 empty. Digits.
The no of digits are 9 (1-9).
The last no must be even so . The total no of even no’s . Are 4 (2,4,6,8)
The probability of last digit is 4
There are remaing 8 digits so. Place them where. U required. The probability are. 8, 7,6,5(no reputations)
The final answer is 4*8*7*6*5=6720 ways

6 0

2 years ago

Read 2 more answers

Simplify the product using FOIL. (2x – 7)(5x 5)

Reptile [31]

FOIL is an 'acronym'. It helps you remember how to multiply
two binomials ... like (2x-7) and (5x+5) .

FOIL stands for "First, Outside, Inside, Last". Here's how it's used
to multiply these particular two binomials:

   (2x - 7) (5x + 5)

First: (2x) (5x) = 10x²

Outside: (2x) (5) = 10x

Inside:   (-7) (5x) = -35x

Last: (-7) (5) = -35

Add them all together, and you have the product:

   10x² + 10x -35x -35

Simplify the sum: 10x² - 25x -35

   or 5(x² - 5x - 7) .

3 0

3 years ago