The first step in solving the inequality is to distribute –4 to get -8x + 4 > 5 - 3x
Solution:
Given inequality is:
[tex]-4(2x - 1) > 5 - 3x[/tex]
The first step in solving the inequality is to distribute -4 to terms inside the bracket in left side of equation
This is done according to BODMAS rule
According to Bodmas rule, if an expression contains brackets ((), {}, []) we have to first solve or simplify the bracket followed by of (powers and roots etc.), then division, multiplication, addition and subtraction from left to right
Thus in given inequality, brackets has to solved first
This is done by using distributive property
a(b + c) = ab + bc
Therefore,
[tex]-4(2x - 1) = (-4 \times 2x) +(-4 \times -1) = -8x + 4[/tex]
Thus, the inequality becomes,
[tex]-4(2x - 1) > 5 - 3x\\\\-8x + 4>5-3x\\\\-5x>1\\\\x<\frac{1}{5}[/tex]
Thus solution to given inequality is found
2(x−3)=(x−1)+7
x = ___
Answer:
x=12
Step-by-step explanation:
Answer:
x = 12
Add 6 to both sides, simplify then subtract x from both sides
If y is an nonnegative , would it be describing a inequality or interval notation?
Mrs. Lin is sewing costumes for her grandchildren. She is making 3 lion costumes, 1 zebra costume, and 2 bear costumes. Fabric costs $7.49 per yard. How much fabric does Mrs. Lin need?
Answer:
rtetrt343444
Step-by-step explanation:
rewrew
Mrs. Lin needs a total of [tex]6 \frac{13}{24} \text{ yards}[/tex] yards of fabric for all the costumes.
To find out how much fabric Mrs. Lin needs for all the costumes, we need to calculate the total yardage required for each type of costume and then sum them up.
Given:
- Bear costume requires 2 1/4 yards.
- Lion costume requires 1 2/3 yards.
- Zebra costume requires 2 5/8 yards.
Let's calculate the total yardage required for each type of costume:
1. Bear costume:
[tex]\[ \text{Yardage for bear} = 2 \frac{1}{4} \text{ yards} \][/tex]
2. Lion costume:
[tex]\[ \text{Yardage for lion} = 1 \frac{2}{3} \text{ yards} \][/tex]
3. Zebra costume:
[tex]\[ \text{Yardage for zebra} = 2 \frac{5}{8} \text{ yards} \][/tex]
Now, let's convert all these mixed numbers into improper fractions:
1. Bear costume:
[tex]\[ \text{Yardage for bear} = 2 + \frac{1}{4} = \frac{8}{4} + \frac{1}{4} = \frac{9}{4} \text{ yards} \][/tex]
2. Lion costume:
[tex]\[ \text{Yardage for lion} = 1 + \frac{2}{3} = \frac{3}{3} + \frac{2}{3} = \frac{5}{3} \text{ yards} \][/tex]
3. Zebra costume:
[tex]\[ \text{Yardage for zebra} = 2 + \frac{5}{8} = \frac{16}{8} + \frac{5}{8} = \frac{21}{8} \text{ yards} \][/tex]
Now, let's sum up the yardages for all the costumes:
[tex]\[ \text{Total yardage} = \text{Yardage for bear} + \text{Yardage for lion} + \text{Yardage for zebra} \][/tex]
[tex]\[ \text{Total yardage} = \frac{9}{4} + \frac{5}{3} + \frac{21}{8} \text{ yards} \][/tex]
To add these fractions, we need to find a common denominator, which is 24:
[tex]\[ \text{Total yardage} = \frac{9 \times 6}{4 \times 6} + \frac{5 \times 8}{3 \times 8} + \frac{21 \times 3}{8 \times 3} \][/tex]
[tex]\[ \text{Total yardage} = \frac{54}{24} + \frac{40}{24} + \frac{63}{24} \][/tex]
Now, let's add the fractions:
[tex]\[ \text{Total yardage} = \frac{54 + 40 + 63}{24} \][/tex]
[tex]\[ \text{Total yardage} = \frac{157}{24} \][/tex]
Now, let's convert the improper fraction to a mixed number:
[tex]\[ \text{Total yardage} = 6 \frac{13}{24} \text{ yards} \][/tex]
So, Mrs. Lin needs a total of [tex]6 \frac{13}{24} \text{ yards}[/tex] yards of fabric for all the costumes.
complete question given below:
Mrs. Lin is sewing costumes for her grandchildren. She is making three lion costumes, one zebra costume, and two bear costumes. Fabric costs $7.49 per yard. How much fabric does Mrs. Lin need?
Bear= 2 1/4 yards
Lion= 1 2/3 yards
Zebra= 2 5/8 yards
The variable x represents the number of long sleeve shirts Nancy bought and the variable y represents the number of short sleeve shirts she bought.
Nancy bought 531 shirts for her business. She bought 2 times as many short sleeve shirts as long sleeve shirts.
How many of each type of shirt did she buy?
Final answer:
Nancy bought 177 long sleeve shirts and 354 short sleeve shirts for her business by solving a system of linear equations based on the provided constraints that she bought a total of 531 shirts and twice as many short sleeve shirts as long sleeve shirts.
Explanation:
The student's question involves solving a system of linear equations to find out how many of each type of shirt Nancy bought for her business. Following the given relationships between long sleeve shirts (x) and short sleeve shirts (y), we understand that Nancy bought a total of 531 shirts and that she bought twice as many short sleeve shirts as long sleeve shirts. The two equations that can represent this scenario are:
Equation 1: x + y = 531
Equation 2: y = 2x
To solve this system, we substitute Equation 2 into Equation 1 to get:
x + 2x = 531
Which simplifies to:
3x = 531
Dividing both sides by 3, we find that:
x = 531 / 3 = 177
Using the value of x to find y from Equation 2, we get:
y = 2 * 177 = 35
Therefore, Nancy bought 177 long sleeve shirts and 354 short sleeve shirts.
Complete the statements about the cone.
-The height is___
units.
-The radius is___
units.
-The volume is___
Pi cubic units.
Answer:
The height is 6 units.
The radius is 8 units.
The volume is 128 Pi cubic units
Step-by-step explanation:
The height is 6 units.
Use Pythagorean Theorem to find the radius.
6² + x² = 10²
36 + x² = 100
-36 -36
x² = 64
x = 8
V = πr²h/3
V = π(8)²6/3
V = π(64)2
V = 128π
Answer:
6,8,128
Step-by-step explanation:
Cynthia has the choice of taking out a 25-year loan for $155,000 at 4.4%
interest, compounded monthly, or the same loan at 20 years for a higher
monthly payment. If she would pay a total of $100,831 in interest on the 25-
year loan, how much in total would she pay in interest on the 20-year loan?
Answer:
D. Less than $100,831
Step-by-step explanation:
There is an equation for calculating monthly payment:
x = p • r • (1+r)^n / (1+r)^n - 1
It may seem a bit complicated, but let's explain it step by step:
- p is the amount of loan, in this case $155,000
- r is monthly interest rate, in this case (4.4/12) / 100, which is 0.00367
- n is the number of months for paying back, or in this case 20 • 12 = 240
Now that we know all the values, all that's left is to plug them in and solve it on the calculator:
x = 155,000 • 0.00367 • (1.00367^240) / (1.00367^240) - 1
x = $972.27
So, the monthly payment is around $972.3. We now multiply it by the number of months to get total payment:
$973.3 • 240 = $233,352
So, the total amount, loan plus interest, is 233,352 dollars.
To only find amount of interest, we simply subtract loan from total amount:
$233,352 - $155,000 = $78,352
24 ⅗ + 43 x (8 ⅕ - 2)
Answer: -14/5
Step-by-step explanation:
24 ⅗ + 43 x (8 ⅕ - 2)
= 72/5 + 43 * (8/5 - 2)
= 72/5 + 43 * (8 - 10/5)
= 72/5 + 43 * (-2/5)
= 72/5 - 86/5
= -14/5
When graphing two systems the break even point:
A. is the point of intersection of the two lines
B. includes the points greater than the line
C. includes points less than the line
Round 37,748 to the tens
Answer:
37750
Step-by-step explanation:
Susan uses a credit card with an APR of 22.2%. What is the monthly percentage rate on the card?
Answer:
1.85 %
Explanation:
APR refers to the "Annual Percentage Rate." This refers to the rate that is being charged to the borrower on a yearly basis.
It is very easy to get the monthly percentage rate once you know the APR. All you have to do is to divide the APR by the total number of months.
In the situation above, we just have to divide the APR of 22.2% by 12 (number of months on one year).
22.2% ÷ 12 months = 1.85 % per month (this is the monthly percentage rate on the card. Thus, this is the answer.A ball is dropped off the side of a bridge. after falling 1.55 s, what is its velocity?
Use the basic kinematic equation of
Final velocity = initial velocity + acceleration * time (shown in image)
simply plug the numbers in to get
Velocity(final) = 0 + -9.80 m/s^2 * 1.55 s
to give us
-15.19 m/s for our final velocity
How do you graph Y is less than 3/4 X +2
(It's a fraction). 5/2 + 5/7
Answer:
3 3/14
Step-by-step explanation:
First look for the LCM of the denominators 2 Andy 7. The LCM is 14.
then , divide the denominators by 14 and add the results to the numerators of both fractions divided by 14.
you‘ll have something like this 35+10/14
=45/14
= 3 3/14
=
a total of 345 tickets were sold for the school play. they were either adult tickets or student tickets. the number of student tickets sold was two times the number of adult tickets sold. how many adult tickets were sold?
Answer:
115
Step-by-step explanation:
a + s = 345
s = 2a
a + 2a = 345
3a = 345
a = 345/3
a = 115 <===== adult tickets
s = 2a
s = 2(115)
s = 230......student tickets
Estimate what’s 32.27/7
Answer:
The answer we can solving the above division is 4.61
Step-by-step explanation:
Given:
The given divider is 7 and the given dividend is 32.27.
To find:
Quotient and remainder
Formula:
The basic division formula that we all know is,
Quotient + Remainder/Divisor = Dividend/Divisor
where we know both dividend and divisor.
By using normal division method we get,
= 32.37/7
= 4.61
Thus we got the quotient as four and remainder as six.
Simplify 15 × 1316 in decimal form
Answer:
i multiplied them together and the result is 19740 but in decimal it would be 19740.0
Final answer:
To simplify 15 × 1316, you multiply to get 19740, which is rounded to 19700 when limited to three significant figures.
Explanation:
To simplify the expression 15 × 1316 in decimal form, you need to perform basic multiplication. Multiplying 15 times 1316 gives you a result of 19740.
However, to express this answer in terms of significant figures, specifically limiting to three significant figures, you would round this number to 19700, as the number 740 does not contribute to the first three significant digits.
What 2 numbers multiply to get -12 and add up to get 11
Answer:
12 and -1
Step-by-step explanation:
12(-1) = -12
12 + (-1) = 11
CAN SOMEONE PLEASE HELP ME WITH THIS QUESTION :::(((((
A typical traffic signal is programmed on a timer so that it is red 50% of the time, green 42% of the time, and yellow 8% of the time. The bulbs for each color are LED and are designed to last 100,000 hours. How many years does each color light last? Give your answer in years and months (rounded to the nearest month). What is the problem asking? What do we know? How did you solve the problem? Explain your steps.
Please answer this question for me
The problem is asking to identify how many years would each color light last. We know that a red light turns on 50% of the time, a green light is 42% of the time, and yellow is 8% of the time. Each light lasts 100,000 hours.
Although this question gives a lot of information, we really don't need the percentages of the lights. They simply are there to throw you off. Each light lasts 100,000 hours. We will use the following conversions:
1 day = 24 hours
1 year = 365 days
100,000 hours divided by 24 hours = 4166.67 days
4166.67 days divided by 365 days = 11.4 years (the 4 is 4 months).
A local grocery store kept track of the types of items sold in 2 hours. Express the ratio that compares the amount of produce sold to the total number of grocery items sold.
Answer:
Step-by-step explanation:
Tracking sales in a small convenience store does not require sophisticated sales monitoring software or expensive computer equipment, although basic point of sale software can save time and prevent mathematical errors. Daily monitoring of inventory, saving sales receipts and using a simple spreadsheet may be all you need to track sales. Depending on the size of your store and foot traffic the store receives each day, tracking sales may take only an hour or so each day.
Expression equivalent to 5(3m + n)
Answer:
Step-by-step explanation:
5(3m + n) = 15m + 5n
Final answer:
The expression equivalent to 5(3m + n) is found by applying the distributive property, resulting in 15m + 5n, where the 5 is multiplied by each term inside the parentheses.
Explanation:
The expression 5(3m + n) is an example of the distributive property in algebra. To find an expression equivalent to this, we need to distribute the 5 across the terms inside the parentheses. This means we multiply 5 by each term inside the parentheses.
Multiply 5 by 3m, which gives us 15m.Multiply 5 by n, which gives us 5n.Putting these two results together, the equivalent expression is 15m + 5n. This is a straightforward application of the distributive property, which is a fundamental concept in algebra.
Riding an exercise bike burns 6 calories per min how many calories will a person burn if he/she bikes for 23 1/2 minuets
Answer: 141
Step-by-step explanation:
23 1/2 *6=141
9+ (- 3/4+1.25)-6 please help you need to evaluate the solution
answer: 9+(-3/4+1.25)-6= 3.5
Answer:
Step-by-step explanation:
9+ (- 3/4+1.25)-6 = 9 + (-0.75 + 1.25) - 6
= 9 + 0.50 - 6
= 3.50
What is the inverse of the function f(x) = 2x – 10?
Answer:
f^-1 (x)=1/2x+5
Step-by-step explanation:
y=2x-10
x=2y-10
2y=x+10
y=1/2x+10/2
y=1/2x+5
How to tell the ordered pair represent an exponential function
Exponential functions include numbers that are doubled. For example, an ordered pair such as (2, 4), (3, 8), (4, 16) the y values are doubled, so it is an exponential funcion.
Ashley had a summer lemonade stand where she sold small cups of lemonade for 41.25 AND LARGE CUPS FOR $2.50. If Ashley solf a total of 155 cups of lemonade for $265, how many cups of each tpe did she sell?
Question:
Ashley had a summer lemonade stand where she sold small cups of lemonade for $1.25 and large cups for $2.50. If Ashley sold a total of 155 cups of lemonade for $265, how many cups of each did she sell
Answer:
The number of small cups of lemonades is 98
The number of Large cups of lemonades is 57
Step-by-step explanation:
Given:
Cost of small lemonade cups = $1.25
Cost of large Lemonade cups = $2.50
Total number of lemonade cups = 155 cups
The total cost for which the lemonade is sold = $265
To Find:
Number of each types of lemonade sold = ?
Solution:
Let the number of small cups of lemonade sold be x
the number of large cups of lemonade sold be y
Then according to the question,
x+y = 155-----------------------------(1)
Then the amount earned by selling small and large lemonade cups is $265
Then
1.25x+2.50y = 265------------------(2)
From (1)
y = 155-x----------------------------------(3)
Substituting (3) in (2), we get
1.25x+ (155-x)2.50 = 265
1.25 + (387.5 -2.50x) =265
-1.25x + 387.5 = 265
-1.25x= 265 -387.5
-1.25x = -122.5
[tex]x = \frac{-122.5}{-1.25}[/tex]
x= 98--------------------------------(4)
Substituting (4) in (3)
y = 155-98
y =57
(-4+6i) + (-6-2i)
How do I solve
Answer:
(-4+(-6))+(6i-2i)
(-10+4i)
Answer:
-10+4i = -2(5-2i)
Step-by-step explanation:
(-4+6i) + (-6-2i)
Collecting like terms
(-4-6) + (6i-2i)
-10+4i
-2(5-2i)
A train leaves a station and travels north at a speed of 45 mph. Two hours later, a second train leaves on a parallel track and travels north at 75 mph. How far from the station will they meet?
Both trains will meet in 3 hours.
Step-by-step explanation:
Given,
Speed of train A = 45 mph
Distance covered in two hours = 2*45 = 90 miles
Let,
x be the number of hours for both trains.
A(x) = 45x+90
Speed of train B = 75 mph
B(x) = 75x
For same distance;
A(x) = B(x)
[tex]45x+90=75x\\90=75x-45x\\90=30x\\30x=90[/tex]
Dividing both sides by 30
[tex]\frac{30x}{30}=\frac{90}{30}\\x=3[/tex]
Both trains will meet in 3 hours.
Keywords: function, division
Learn more about division at:
brainly.com/question/10081622brainly.com/question/10341324#LearnwithBrainly
if (x +5) -2(4x-1)=0 what is the value of x
Answer: x=1
Step-by-step explanation:
(X+5)-2(4x-1)=0
(-2•4x) (-2•-1)
X+5-8x+2=0
X-8x+5+2=0
(5+2)=7
X-8x=-7
-7x= -7
X=1
Simplifying the given expression (x +5) -2(4x-1)=0 we get the solution of this expression is x = 1.
A relation between a collection of inputs and outputs is known as a function. A function is, to put it simply, a relationship between inputs in which each input is connected to precisely one output.
The given expression,
(x +5) -2(4x-1)=0
Distributing the number inside the bracket we get,
x + 5 - 8x + 2 =0
Simplifying the like terms,
-7x + 7 = 0
Subtract 7 on both sides,
-7x = -7
Divide by -7 on both sides we get,
x = 1
Hence,
The solution of the expression is x = 1.
To learn more about the function visit:
https://brainly.com/question/8892191
#SPJ4
a sprinkler in a backyard turns through 180 degrees. the sprinkler has turned 96 degrees so far. how many more degrees will the sprinkler turn through to reach 180 degrees?
I owe my friend Miguel $4.00. I also owe my friend Gloria $7.50. Which equation correctly shows this relationship?
A. -4 - 7.50 = 11.50
B. 7.50 - 4 = 3.50
C. 4 + (-7.50) = -3.50
D. -4 + (-7.50) = -11.50