Solve each inequality. Check your solution. 4x - 2 > 1/2
The inequality given by 4x - 2 > 1/2 has the solution x > 5/8 or (5/8 , +∞).
Inequality refers to the relationship between two non-equal expressions. It can be denoted by > for greater than, < for less than, >/= for greater than and equal to, and </= for less than and equal to.
To solve an inequality is to find the values of x such that when we substitute that number for x we have a true statement.
Given the inequality 4x - 2 > 1/2, add 2 to both sides.
4x - 2 + 2 > 1/2 + 2
4x > 5/2
Multiply both sides by 1/4.
1/4(4x) > 1/4(5/2)
x > 5/8
To check, let x = 3/4
x = 3/4 ≥ 5/8
Substitute this value to the inequality.
4x - 2 > 1/2
4(3/4) - 2 > 1/2
3 - 2 > 1/2
1 > 1/2
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Jaya has a points card for a movie theater.
. She receives 70 rewards points just for signing up.
• She earns 7.5 points for each visit to the movie theater.
• She needs at least 175 points for a free movie ticket.
Use the drop-down menu below to write an inequality representing v, the number of
visits she needs to make in order to get a free movie ticket.
The inequality that shows the number of visits she needs to make in order to get a free movie ticket is 7.5v + 70 ≥ 175
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
Let v represent the number of visits she needs to make in order to get a free movie ticket.
She needs at least 175 points for a free movie ticket. Hence:
7.5v + 70 ≥ 175
The inequality that shows the number of visits she needs to make in order to get a free movie ticket is 7.5v + 70 ≥ 175
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Sanjay's dad has asked sanjay and his little brothers to rake the leaves in their yard. they rake all afternoon and fill a number of bags with leaves. then, when sanjay isn't looking, his brothers empty 4 of the bags to make a giant leaf pile! sanjay is frustrated that only 6 bags of leaves remain. which equation can you use to find the total number of bags b that sanjay and his brothers fill with leaves?
The given situation presents a word problem and can be solved by converting the word problem into an equation.
Word problem is a few sentences representing a real-life scenario where a problem needs to be solved by method of a mathematical calculation.
According to the given situation:
Total number of bags – number of bags emptied=number of bags left
Total number of bags filled= b
Number of bags emptied=4
Number of bags left=6
Hence,
b-4=6
Solving the equation,
b=6+4
b=10
Note: The provided question does not include the options of equation. Possible options are:
4b=6; b+4=6; b/4=6; b-4=6
Hence, the equation used to determine the numbers of bags initially filled is b-4=6 and number of bags are 10 bags.
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The length of a rectangle is 3 times the width. The perimeter is 96 cm. Find the length.
Answer:
W=12cm
L=36cm
Step-by-step explanation:
We are told L=3W
and P=96
so 96=2⋅W+2⋅3⋅W
8W=96
so W=968=12cm
and L=3⋅12=36cm
hope this helps :)
7 divided by 9 long division
in exercises 14 and 15, the value of the surface area of the cylinder is equal to the value of the cylinder. Find the surface area of the cylinder
Considering that the surface area and the volume of the cylinders are equal, the surface areas are given as follows:
14. 108π ft².
15. 250π ft².
What are the surface area and the volume of a cylinder?For a cylinder of radius r and height h, the surface area is given by:
S = 2πr(h + r).
The volume is given by:
V = πr²h.
For item 14, the parameters are given as follows:
r = 6 ft, h = x ft.
Hence we solve for x equaling the surface area and the volume as follows:
V = S
36πx = 12π(x + 6)
3x = x + 6
2x = 6.
x = 3.
Hence the surface area is:
S = 12π(3 + 6) = 108π ft².
For item 15, the parameters are given as follows:
r = 10 ft, h = x ft.
Hence we solve for x equaling the surface area and the volume as follows:
V = S
100πx = 20π(x + 10)
5x = x + 10
4x = 10.
x = 2.5.
Hence the surface area is:
S = 20π(2.5 + 10) = 250π ft².
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Determine the slope of the line that contains the given points.
A(0,6), B(4,0)
The slope of the line that contains the given points A(0,6), B(4,0) is -3/2.
It is given in the question that the line contains the points A(0,6) and B(4,0).
We know that:-
The formula to find the slope of a line that contains points (a,b) and (c,d) is given by:-
m = (d-b)/(c-a)
Here, we have
m = slope of the line
(a,b) = (0,6)
(c,d) = (4,0)
Hence, putting the values of (a,b) and (c,d) , we get
Slope of the line that contains the given points A(0,6), F(4,0) is given by:-
(0-6)/(4-0) = -6/4 = -3/2
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I need this answered please
The entrance fee to the fair is $15. You pay $2.50 for each ride you ride. Create a table and graph to represent the total paid as a function of the number of rides you ride.
The cost for x rides is modeled by the linear function:
c(x) = $15 + $2.50*x
A table and a graph for that function are provided below.
How to create a table and graph that represents the amount you pay?Here we know that the entrance fee to the fair is $15, and the cost of each ride on the fair is $2.50
So, if you go to the fair and enter in x rides, the total cost for that will be modeled by the linear function:
c(x) = $15 + $2.50*x
Now let's find a table, to do that we just need to evaluate the function in some values of x, I will use x = 0, x = 1 and x = 2, we will get:
C(0) = $15 + $2.50*0 = $15
C(1) = $15 + $2.50*1 = $17.50
c(2) = $15 + $2.50*2 = $20.00
Then we can write the table:
Number of rides ||| Cost
0 $15
1 $17.50
2 $20.00
Now that we have the table, we just need to graph these 3 points on a coordinate axis, and connect them with a line.
The graph can be seen below.
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Write an equation of a parabola with its vertex at the origin and the given characteristics.directrix y=-1
Answer:
ue7e66eywgwgwgwjw7wh3he
question is in the picture
Answer:
after 4 years her salary would be $48,000
salary after t years: y=2000t+40000
Write each equation in y intercept form x+2y=10
Answer:
y
=
1
2
x
−
5
Step-by-step explanation:
Answer:
y=x+5
Step-by-step explanation:
divide by 2 on each side
The height of a binary search tree is given as h. what is the maximum number of nodes in the tree?
The greatest number of comparisons each operation in the method add needs, given a binary search tree with n nodes and height h, is O. (h).
What is a binary search?Computer scientists utilize the search method known as binary search to locate a target value within a sorted array. Binary chop, logarithmic search, and half-interval search are other names for it. The binary search compares the target value to the array's center member. If not, the half where the target cannot lie is eliminated, and the search is then carried out on the remaining half while once again comparing the center element's value to the target value. Up till the goal value is found, this process is repeated. if, at the end of the search, the remaining half is empty.
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Find the value of n:
1/(3^√7)^5 = 7^n
Step-by-step explanation:
[tex]n = \frac{ - 5}{3} [/tex]
ATTACHED IS THE SOLUTION!!
The value of a certain stock tripled. If you knew what the stock used to be worth, how would you find how much it is
worth now?
I really need help with how to do this . I am confused . Thank you
Answer:
You could measure the distance from both of the lasers and divide by 2 to know the middle of the line. Then draw a straight line from the middle of the line joining the lasers, to you.
if a movie starts
at 7:45 and is
I hour and 43
mins what time
will it end
9:28 would be the time the movie ends
Answer:
9:28
Step-by-step explanation:
First, add an hour to 7:45. Then, find how much time there is until you reach the next hour. After that, take the remaining time and add it on. 7:45 plus one hour is 8:45. There is fifteen minutes until the next hour, so subtract that from the forty three minutes. Add that fifteen minutes on and you are at nine o'clock. There is twenty eight minutes left. Add it in to nine o'clock. You now have the time the movie will end
Hope this helps! :)
If the probability that it will snow on Tuesday is 4/13, then what is the probability that it will not snow?
A 4/9 C 13/9 E 13/4
B 9/13 D 13/5
The correct option is (B) 9/13.
The probability that it will not snow on Tuesday is 9/13.
What is defined as the probability?The ratio of the quantity of favorable outputs to the overall number of possibilities of an event is defined as probability.
The number of favorable results for an experiment with 'n' outcomes is denoted by x.
The following formula is used to determine the probability of an event.
Probability(Event) = Favorable Outcomes/Total Outcomes = x/n.
Some properties of the probability are mentioned below-
The sum of the probability of an event occurring and not occurring is equal to one.The probability of any event occurring is always between 0 and 1.The probability about an impossible event occurring or of an event not occurring will always be equal to zero.A certain event's probability will always be equal to one.Now, for the stated question;
The probability that it will snow on Tuesday is 4/13.
Use property 1;
Then, the probability that it will not snow on Tuesday is;
= 1 - 4/13
= (13 - 4)/13
= 9/13
Therefore, the probability that it will not snow on Tuesday is 9/13.
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BRAINLIEST EXPLAIN HOW U GOT ANSWER
Complete the following:
Write an exponential expression: Let 10 be the base and an even number between 1 and 10 be the exponent.
Then write the exponential expression in expanded form and standard form.
Answer:
10^2 . . . . see below for additional information or versions of the answer(s)
Step-by-step explanation:
You seem to want 10^exponent, where exponent is an even single digit, not zero.
We choose exponent = 2, so your expression is ...
10^2
__
There are several versions of expanded form. One uses exponents. In that form, the expression above is the expanded form.
Another uses multipliers of 1, 10, 100, 1000, and so on. In that form, the expression expands as ...
10^2 = 1×100
Another expanded form uses individual digits of the expanded form with others set to zero
10^2 = 100
The standard form is ...
10^2 = 100.
_____
We suppose your exponential expression might have another multiplier, such as 2.98:
exponential expression: 2.98×10^2
standard form: 298
expanded form 1: 2×10^2 + 9×10^1 +8×10^0
expanded form 2: 2×100 +9×10 +8×1
expanded form 3: 200 + 90 + 8
Please please please help please asap!!!
........................................................................................
Answer:
Options 3 and 6
[tex]3i\sqrt{3} \\-3i\sqrt{3}[/tex]
Step-by-step explanation:
hope this helps
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Uranium-238 (U-238) has a half-life of 4.5 billion years. Geologists find a rock containing a mixture of U-238 and lead, and determine that 71% of the original U-238
remains; the other 29% has decayed into lead. How old is the rock?
The rock is ___ billion years old.
(Round to three decimal places as needed.)
Answer: 2.223 billion years old
Step-by-step explanation:
since 71 percent of the rock is remaining, the half life hasn't been reached yet. Hence, we know uranium isn't 4.5 billion years old yet. However, every-time 4.5 billions years pass, the rock get smaller by 2 times(a scale factor of 1/2). Hence, you can express that in a log equation:
[tex]\log_{2}(100/(percent of rock remaining))=[/tex] Fraction of 4.5 billions years of time passed
[tex]\log_{2}(100/50)=1[/tex] ==> 100% of 4.5 billion years passed. When 50% of rock remains, 4.5 billion years have passed.
[tex]\log_{2}(100/100)[/tex] =
[tex]\log_{2}(1)=0[/tex] ==> 0% of 4.5 billion years passed. When the rock hasn't decayed at all yet, that means that it is 0 years old.
[tex]\log_{2}(100/71)=0.494[/tex] ==> 49.4 % of 4.5 billion years passed
0.494*4.5 billion =2.223 billion years passed
2.223 billion years old
Find the measure of the numbered angle, and name the theorems that justify your work. (Lesson 2-8)
∠2 and ∠3 are supplementary; m∠2=149
When two straight lines or rays intersect at a shared endpoint, an angle is generated. The measure of ∠3 is 31°.
What is an angle?When two straight lines or rays intersect at a shared endpoint, an angle is generated. An angle's vertex is the common point of contact. Angle is derived from the Latin word angulus, which means "corner."
Given that ∠2 and ∠3 are supplementary angles. Therefore, the sum of the two angles will be 180°. Thus, we can write the sum of the two angles as,
∠2 + ∠3 = 180°
Also, it is mentioned in the question that the measure of ∠2 is 149°. Therefore, substitute the value of ∠2 in the above equation.
149° + ∠3 = 180°
∠3 = 180° - 149°
∠3 = 31°
Hence, the measure of ∠3 is 31°.
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542.84−39.93 pls help
Answer:
answer is 502.91
Step-by-step explanation:
answer is 502.91
Answer:
502.91
Step-by-step explanation:
You make $7.25/hr and your boss
promises at least 3 hours but no
more than 18 hours per week.
Payroll (FICA) taxes of 7.65% are
withheld from your paycheck.
Be sure to deduct your tax
The question's payroll (FICA) taxes total 0.2295.
Considering the information provided,
7.65% of payroll (FICA) taxes
Boss promises a minimum of 3 hours each week and not more than 18 hours.
We have, 3 × 0.0765
= 0.2295
Amount of payroll taxes that will be taken out of your paycheck.
= 0.2295
FICA Taxes: The Federal Income Contributions Act, also known as FICA, is the name of the payroll tax deduction used in the United States to pay for Social Security and Medicare. Tens of millions of seniors, Americans with disabilities, and children receive financial and medical benefits from those well-known government programs. Both employees and the employers they work for are jointly liable for FICA taxes.
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can someone please help me
Answer:mhmm cool b
Step-by-step explanation:
What is the domain of function f?
ƒ(x) = 2|x − 1| + 3
write 1/16 as a power of 2
Answer:
256
Step-by-step explanation:
According to the rule of exponents: 16 to the power of 2 can be written as 162.
URGENNTTT !!! ITS EASY BUT I NEED CLARIFICATION
You can solve this by isolating the variable.
1.
30 + a = 40
You can isolate a by subtracting 30 from each side
30 + a - 30 = 40 - 30
a = 10
2.
500 + b = 200
Subtract 500 from each side
500 + b - 500 = 200 - 500
b = -300
3.
-1 + c = -2
Add 1 to each side
-1 + c + 1 = -2 + 1
c = -1
4.
d + 3567 = 0
Subtract 3567 from each side
d + 3567 - 3567 = -3567
d = -3567
Pls help me this is due Monday 9/12/22
It’s about statements in geometry and I’m confused
Answer:
what are the given options? :)
Write an equation in slope-intercept form for a line parallel to y=4 x-5 containing (-1,5) .
The equation in slope-intercept form is y = 4x + 1
Given,
Points (x, y) = (-1, 5)
Parallel to y = 4x - 5
Now,
Recall that a parallel line to the one given has to have the same slope. The slope of the line given is "4" (the coefficient that accompanies "x").
Therefore the equation of a parallel line has to be of the form:
y = 4x - b
5 = 4(-1) - b
5 = -4 - b
b = -4 - (-5)
b = -4 + 5
b = 1
So the equation now becomes:
y = 4x + 1
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