Answer: [tex]3 \le x \le 5[/tex]
x is any real number between 3 and 5, including both endpoints
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Explanation:
If A < B, then 1/A > 1/B. Applying the reciprocal flips the inequality sign.
For example, if 2 < 3, then 1/2 > 1/3. It might help to look at the decimal representations
1/2 = 0.500
1/3 = 0.333
We see that 1/2 is larger.
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The inequality [tex]x < y < z[/tex] is the same as [tex]x < y \ \text{ and } \ y < z[/tex].
We've broken the single inequality into two smaller parts.
The given inequality breaks down into [tex]\frac{1}{6} \le \frac{1}{x+1}[/tex] and [tex]\frac{1}{x+1} \le \frac{1}{4}[/tex]
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Let's solve the first inequality for x
[tex]\frac{1}{6} \le \frac{1}{x+1}\\\\6 \ge x+1\\\\6-1 \ge x\\\\5 \ge x\\\\x \le 5[/tex]
Repeat for the other inequality as well
[tex]\frac{1}{x+1} \le \frac{1}{4}\\\\x+1 \ge 4\\\\x \ge 4-1\\\\x \ge 3\\\\[/tex]
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We found that [tex]x \ge 3 \ \text{ and } \ x \le 5[/tex]
This is the same as [tex]3 \le x \ \text{ and } \ x \le 5[/tex] which combines to [tex]3 \le x \le 5[/tex]
The Fairview Library is getting ready to move to a bigger building. So, the librarians need to pack 2 tons of books into cardboard boxes. Each box can safely hold about 25 pounds of books. If they already packed 50 boxes, how many more boxes should they expect to use?
Given :
The librarians need to pack 2 tons of books into cardboard boxes. Each box can safely hold about 25 pounds of books. If they already packed 50 boxes.
To Find :
How many more boxes should they expect to use.
Solution :
We know, 1 ton = 2000 pounds
So, 2 ton = 4000 pounds
Minimum number of boxes required for safe handling :
[tex]n=\dfrac{4000}{25}\\\\n=160[/tex]
So, total 160 boxes required.
Therefore, 160 - 50 = 110 many more boxes should they expect to use.
Hence, this is the required solution.
Answer:
110 more boxes
Step-by-step explanation:
llene is making bows for gift wrapping. She uses 1 feet of ribbon for each 3 bow. How much ribbon will she need to make 12 bows?
Answer:
4 feet
Step-by-step explanation:
Because if she used 1 feet of ribbon for 3 bows you need to multiply by 4 to 1 foot and you will get 12 bows
Answer:
4 feet of ribbon
Step-by-step explanation:
Because she uses 1 feet of ribbon for each 3 bows, we can create a fraction.
1 ft / 3 bows = x ft / 12 bows
Cross multiplying, we get: 3x = 12
Divide by 3 and we get x = 4 (x in this case is in feet)
Luka buys a special pass to a fair for $7 that allows him to go on every ride for $1 each. How many rides will Luka need to ride in order to spend $20?
Answer:
He would have to do 13 rides.
Step-by-step explanation:
If he initially pays $7, which lets him pay only $1 for each ride, so when he spends $20, he would have done 13 rides.
There are 13 rides will Luka need to ride in order to spend $20.
What is an expression?Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
Luka buys a special pass to a fair for $7 that allows him to go on every ride for $1 each.
Here, Luka need to ride in order to spend $20.
Let number of rides = x
So, We can formulate;
⇒ $7 + $1x = $20
⇒ 7 + x = 20
Solve for x as;
⇒ x = 20 - 7
⇒ x = 13
Learn more about the mathematical expression visit:
brainly.com/question/1859113
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Write the expression as a power with the base of 3 and find its value in the table of cubes
27·243
Answer:
27 · 243 = 3
=
Answer:
3^8 and 6,561
Step-by-step explanation:
1) Calculate, 3 to the power of what is 27?
Make a table of all of 3's powers until 10. i.e. 3^1 = 3, 3^2 = 9 ......
You will find that 3^3 = 27 and 3^5 is 243
3) Use the formula x^m * x^n = x^m+n and substitue our value.
It should look like this: 3^3 * 3^5 = 3^3+5 = 3^8
4) Make a table as described in step 2 and calculate all of 3's powers up to 10. Look at your table and you will find that 3^8 is equal to 6,561
5) The expression written as a power is
3^8 and
the value: 6,561
Enjoy :)
Lois builds a cage for her hamster. The cage is a right rectangular prism. The height of the cage is 2 feet. The length and width are both x feet more than the height. Which expression represents the volume, in cubic feet, of the cage?
A. x^2 +6
B.2x^2+4x+4
C.x^2+4x+6
D.2x^2+8x+8
Answer:
[tex]V=2x^2+8x+8[/tex]
Step-by-step explanation:
The volume of a right rectangular prism is given by :
[tex]V=lbh[/tex]
Where,
l is length, bis breadth and h is height
ATQ,
Height of the cage is 2feet
The length and width are both x feet more than the height.
l = b = (x+2)
So,
[tex]V=(x+2)(x+2)2\\\\V=(x+2)^22\\\\V=(x^2+4+4x)2\\\\V=2x^2+8+8x[/tex]
So, the correct option is (D).
Answer:
Your Ans is
Option D.....
PLZZZ SEND HELPPP ANSWER QUICKK
Answer:
The answer is C 2^3
hope this helps!!!
Answer:
2^3
Step-by-step explanation:
Ok, let's jump right in!
Multiply 2^6 by 2^−3 by adding the exponents.
Use the power rule a^m a^n = a^m+n to combine exponents. Therefore, we get:
2^ 6-3
Subtract 3 from 6.
2^3
TIP: For next time remember that when you have to multiply exponents you that have the same base number you really just have to add the exponents.
A _______ cuts one angle into two equal angles
A ferris wheel has a diameter of 80 meters. How far does a rider travel in one complete rotation around the ferris wheel?
Given parameter:
Diameter of the ferris wheel = 80m
Unknown:
Distance covered in one complete rotation = ?
Solution:
One complete rotation will sweep through the circumference of the wheel.
So,
One complete rotation = Circumference of circle = 2 [tex]\pi[/tex] r
Where r is the radius;
Radius here is [tex]\frac{80}{2}[/tex] = 40m
So circumference = 2 x [tex]\pi[/tex] x 40 = 80[tex]\pi[/tex]
The distance the wheel sweeps through will be 80π m
12 divided by 3 +6 times 2 simplified
Answer:
16
Step-by-step explanation:
12/3 +6×2
4+12=16
Hope it helps
PLEASE ANSWER THIS FOR ME!!
If 12 = 17 - 5, then 17 - 5 = 12 What math property is this?
Answer:
Symmetric property of equality
Step-by-step explanation:
The symmetric property of equality states values are still equal no matter which side of the equal sign they're on.
HELP ASAP
How much interest is earned on a $500 investment made at a 3.5% simple interest
rate over the course of 2 years?
A$3500
B $350
C$35
D$3.50
Answer:
C
Step-by-step explanation:
500* (0.035)
17.5*2
35
Someone please help?
Answer:
57
Step-by-step explanation:
x= 180-123
x=57
The sum of 5x and 2x is at least 14.
Answer:
it will be 40
Step-by-step explanation:
If two angles are supplementary and one of the angles measures 62 degrees, What is the measure of the other angle?
answer choices
28 degrees
38 degrees
118 degrees
128 degrees
Answer:
118 degrees
Step-by-step explanation:
Supplementary = sum of the angles equal 180 degrees
180 - 62 = 118
118 degrees is your answer
Hope this helps!
Answer:
118°
Step-by-step explanation:
i’m different
Sam purchases a used video game for GameStop. In order to make a profit,
GameStop marksup their used game 50% before reselling them. Sam paid $45 (without
tax). What was the original price of the game?
Answer:
$22.50
Step-by-step explanation:
50/100 = x/45
cross multiply
50 × 45 = 100 × x
2250 = 100x
divide both sides by 100
22.5 = x
*note: marksup the price means that $45 should be more than what the value of x is. $45 is more than $22.50. you can also check your work by looking at the fact $22.50 is exactly half (50%) the amount of $45*
If f (x) = x over 2 - 2 and g(x) = 2x squared + x - 3, find (f + g) (x)
[tex]f(x) = \frac{x}{2} - 2 \\ [/tex]
[tex]g(x) = 2x + {(x - 3})^{2} [/tex]
[tex]f(x) + g(x) = (f + g)(x)[/tex]
[tex]( \frac{x}{2} - 2) +( 2x + ({x - 3})^{2} \: ) = \\ [/tex]
[tex] \frac{x}{2} - 2 + 2x + {x}^{2} - 6x + 9 = \\ [/tex]
[tex] {x}^{2} - 6x + 2x + \frac{x}{2} + 9 - 2 = \\ [/tex]
[tex] {x}^{2} - 4x + \frac{x}{2} + 7 = \\ [/tex]
[tex] {x}^{2} - \frac{8}{2}x - \frac{1}{2}x + 7 = \\ [/tex]
[tex](f + g)(x) = {x}^{2} - \frac{9}{2}x + 7 \\ [/tex]
_________________________________
Done....
♥️♥️♥️♥️♥️
Simplify negative 4 over 3 divided by 2 over negative 6
Answer:
-4 x 3= 12 divid 2= 6 x -6 =12
Step-by-step explanation:
Write an expression for the perimeter of the triangle shown below:
6.9x − 16
6.9x + 16
0.1x − 16
0.1x + 16
Answer:
The answer is 0.1x-16
Step-by-step explanation:
-3.4x+3x+.5x=0.1x and -25+9 is -16 which is 0.1x-16
HELP !! ASAP !!
Find the zeros of the function f(x) = -5x2 + 4x - 1 by completing the square.
(leave in fraction form if necessary)
Answer:
The roots are;
x = (2 + i)/5 or (2-i)/5
where the term i is the complex number representing the square root of -1
Step-by-step explanation:
Here, we want to use the completing the square method to solve the quadratic equation;
f(x) = -5x^2 + 4x -1
Set the function to zero
0 = -5x^2 + 4x - 1
So;
-5x^2 + 4x = 1
divide through by the coefficient of x which is -5
x^2 - 4/5x = -1/5
We now take half of the coefficient of x and square it
= -2/5^2 = 4/25
add it to both sides
x^2 - 4x/5 + 4/25= -1/5 + 4/25
(x- 2/5)^2 = -1/5 + 4/25
(x - 2/5)^2 = -1/25
Take the square root of both sides
x - 2/5 = √( -1/25
x - 2/5 = +i/5 or -i/5
x = 2/5 + i/5 or 2/5 - i/5
Help please. I will give brainliest.
Answer:
if you answer my most recent question ill answer this one.
Step-by-step explanation:
the creamery ice cream shop in walnut creek sold 501 ice creams last Wednesday. they sold half as many chocolate cones as vanilla. First write the equation.
I need the complete answer, thanks!!
Answer:
9 is the constan trate of change.
Step-by-step explanation:
Assuming two points of the graph with the form as P=(x,y) you can find the constant rate m using the slope formula.
m=(y2-y1)/(x2-x1)
Lets say that P1=(0,0) and P2=(1,9), then:
m= (9 – 0)/(1-0)
m=9
Therefore, the point (0,0) means that when you are not buying any t-shirt then you dont have any waste of money. The point (1,9) means that when you are buying one t-shirt then you have to pay 9 then its result that cost of each t-shirt is 9 so when you are buying two t-shirt then you have to pay 18, when you are buying three you have to pay 27 likewise.
There are 25 female performers in a dance recital. There ratio of men to women is 2:5. How many men are in dance recital.
Answer:
There are 10 men in the dance recital.
Step-by-step explanation:
The ratio 2:5 means that for every 5 women there are 2 men.
We will divide 25 by 5 to figure out how many groups there will be.
[tex]25/5=5[/tex]
[tex]x*y=z[/tex]
x = amount of groups.
y = amount of men per group
z = total amount of men.
[tex]5*2=10[/tex]
This means that there are 10 men in the dance recital.
a
1.80 x 5= 2.16
b
1.80 ÷ 5= 2.16
c
1.80 ÷ 2= 0.90
d
1.80 ÷ 5= 0.36
Answer:
heidnejfrbfj
Step-by-step explanation:
heudbdbeb
Help me plzzzzzzz.thank you
A ship travels 685 nautical miles. How many feet has the ship traveled? If a nautical mile equals 1,852 meters, how many meters has the ship traveled?
Answer:
1,268,620
Step-by-step explanation:
Multiply 1,852×685
Answer:
1268620 meters
Step-by-step explanation:
685x1852= 1268620
What is the slope of the line that passes through the points (3,-2) and (1,8)
Answer:
10/-2= -5
Step-by-step explanation:
slope= change of y/ change of x
Solve the inequality 2x + 10 < 5x + 1
Answer:
3 < x
Step-by-step explanation:
Jennifer received a coupon for 40% off her purchase of a regularly priced item from her favorite
store. If Jennifer wants to order a shirt from the store that is originally $30, how much would
she have to pay for the shirt after the coupon?
Answer:
18$
Step-by-step explanation:
Explain! Prize! Thank you!
Answer:
60 pages in 2 days
Step-by-step explanation:
120 pages in 4 days is equivalent to a 30 pages in 1 day rate (divide both by 4). The only other rate that is equivalent to a 30 pages in 1 day rate is 60 pages in 2 days because 60 = 30*2 and 2 = 1*2.
Answer:
60 pages in 2 days is the answer