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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The coordinates of the vertices of a triangle are (2, 3), (5, 1), and (6, 4). After one reflection, the coordinates of the vertices of the triangle's image are (2, -3), (5, -1), and (6,-4). Over what line has the triangle been reflected? Select the answer from the drop-down list to correctly complete the sentence. is it x-axis or y-axis
Answer: x-axis
Explanation:
The point (2,3) moves to (2, -3)
The x coordinate stays the same, but the y coordinate flipped from positive to negative. Therefore, the rule used is [tex](\text{x},\text{y}) \to (\text{x}, -\text{y})[/tex] which is a reflection over the horizontal x axis.
Write an absolute value inequality to represent each situation.
A friend is planning a trip to Alaska. He purchased a coat that is recommended for outdoor temperatures from -15⁰ F to 45⁰F . Let t represent the temperature for which the coat is intended.
Answer: |t - 15| ≤ 30 ; -30 ≤ t - 15 ≤ 30
Step-by-step explanation:
To set up the equation, we have to find the center, and the tolerance, so that we can use formula "|x - c| ≤ t"
First, we can find the tolerance by adding both number, then dividing by 2 --> -15 + 45 = 30 --> 30/2 = 15, so we now know that the center is 15
Next, we can find the tolerance by finding the distance between the center and one of the number --> 15 - (-15) = 30, so we now know that the tolerance is 30
Now we can set up our equation,
center (c) = 15
tolerance (t) = 30
|t - 15| ≤ 30
Now that we have our equation, we can set up the inequality
|x - c| ≤ t = -t ≤ x - c ≤ t
so,
-30 ≤ t - 15 ≤ 30
Hope this helps!
(sorry it was so long)
How do I solve this equation 10=-9-x
Answer:
Step-by-step explanation: 10=-9-x > add 9 to 10 > 19=-x> divide 19 by -x> x=-19
Question
Evaluate the expression when a=4, b=−5, and c=−8.
a+b=
???
Answer:
a+b= (-1)
Step-by-step explanation:
4+(-5)=
4-5= (-1)
Answer:
-1
Step-by-step explanation:
a = 4
b = -5
4 + -5 = -1 ( +- turns to -)
Amy wants to fence off a rectangular area that is 24 feet squared in size for a vegetable garden.
She is considering three garden lengths of 6 ft, 8 ft, and 12 ft. She wants to determine which garden would require the least amount of fencing.
Determine the dimensions of the garden that would require the least amount of fencing.
Length
12, 8, or 6ft
Width:
3, 4, or 2ft
Answer:
Let y = length of side parallel to the side with no fence
x = length of each of the other two sides
Then, y+2x = 64. So, y = 64-2x
Area = A = xy = x(64-2x)
The graph of the area function is a parabola opening downward with a highest point and with x-intercepts (0,0) and (32,0).
By the symmetry of the parabola, the x-coordinate of the maximum point lies halfway between the x-intercepts.
So, the area is maximized when x = 16 ft
y = 64 - 2x = 32 ft
Maximum area = xy = (16)(32) = 512 ft2
To maximize the area of the garden, the side of the fence parallel to the side of the house should be 32 ft long, and the other two sides should both have length 16 ft.
Function: g(x) = 2x² - 8
For x ≥ 0, the inverse function is f(x)=
For x ≤ 0, the inverse function is d(x)= -√√x +4
X
-8
0
10
f(x)
0
r
S
d(x)
q
-2
t
q=
= ין
=√√₂x + 4
S=
t =
1
870
Answer:
(5,15)
Step-by-step explanation:
we know that c=12 is 5 so your answer is 5,15
Reporte 184 caracoles entre 8 árboles c
cuántos caracoles tendrá cada árbol?
Answer:
23
Step-by-step explanation:
Porque 23 X 8 = 184
Espero te ayude
Hope this helps
Morgan, Phil, Callie, and Tyreese are sitting on the side of a pool in that order. Morgan is 2 feet from Phil. Phil is 4 feet from Callie. Callie is 3 feet from Tyreese. Oscar joins them.
a. Find the probability that 0scar sits between Morgan and Phil.
If Morgan, Phil, Callie, and Tyreese are sitting on the side of a pool in that order. the probability that 0scar sits between Morgan and Phil is 2/9 and the probability that Oscar sits between Phil and Tyreese is 7/9.
Probabilitya. 0scar sits between Morgan and Phil
First step is to calculate the total distance
Total distance=2 feet+4 feet+3 feet
Total distance=9 feet
Since Morgan is 2 feet from Phil.
Hence,
P(Oscar sits between Morgan and Phil)=2/9
b. Oscar sits between Phil and Tyreese.
First step is to calculate the distance between Phil and Tyreese
Distance= 4 feet + 3 feet
Distance =7 feet
Hence,
P(Oscar sits between Phil and Tyreese)=7/9
Therefore If Morgan, Phil, Callie, and Tyreese are sitting on the side of a pool in that order. the probability that 0scar sits between Morgan and Phil is 2/9 and the probability that Oscar sits between Phil and Tyreese is 7/9.
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The complete question is:
Morgan, Phil, Callie, and Tyreese are sitting on the side of a pool in that order. Morgan is 2 feet from Phil. Phil is 4 feet from Callie. Callie is 3 feet from Tyreese. Oscar joins them.
a. Find the probability that 0scar sits between Morgan and Phil.
b. Find the probability that Oscar sits between Phil and Tyreese.
If point B ( -3, -6) is translated 8 units up and 1 unit left what are the coordinates of B’?
Sammy wants to start walking to exercise. He finds a circular path with a radius of 50 ft that he wants to walk around. Using the information provided, how many laps around the path would Sammy need to complete in order to walk 628 ft?
Answer:
2 laps
Step-by-step explanation:
The equation for circumference of a circle is 2πr.
We can use this equation to find how many ft are in a lap, then determine with the circumference how many laps need to be completed.
This is simple algebra
2πr
2π(50)
2(3.14)(50)
314.
One lap is 314 feet, so Sammy needs to walk 2 laps.
Answer: 2 laps
Step-by-step explanation:
Length of a circular path is 2πR (R=50ft)
Length of a circular path is:
2*3.14*50=
314 ft
628:314=
2 laps
Determine whether each number is a solution of the inequality below.
Please help determine whether A, B and C (at the top) is a solution.
Answer: yes it is a solution
Given f(x)= 3 x 2 + 2, find the value of f(−2)
Answer:
f(- 2) = 14
Step-by-step explanation:
substitute x = - 2 into f(x)
f(- 2) = 3(- 2)² + 2 = 3(4) + 2 = 12 + 2 = 14
A scientist collected a 1 liter sample of sea water and then examined it to see how many viruses, bacteria, phytoplankton, and protozoa it contained, The scientist found that there were 5x10^5 protozoa and 3x10^9 viruses in the sample. How many times greater was the number of viruses than the number of protozoa that were found in the sea water sample? Estimate by rounding to the nearest whole number
In the sample that is used number of viruses were 6000 times greater than the number of protozoa.
Sampling is the process of choosing a subset of people (a statistical sample) from a statistical population in order to estimate characteristics of the entire population.
It is used in statistics, quality control, and survey technique. Statisticians try to get samples that are typical of the population under consideration.In situations where it is impractical to assess the complete population, sampling offers insights and is more affordable and quicker than doing so.Given the number of protozoa in the sample as 5 × 10⁵ and the number of viruses in the sample as 3x10⁹.
This is represented in the scientific notation.
To calculate the number of times the viruses in the sample is more than the protozoa in the sample we divide the amount of virus by the amount of protozoa.
∴ (3x10⁹) ÷ (5 × 10⁵)
= 6000
Therefore in the sample that is used number of viruses were 6000 times greater than the number of protozoa.
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g(x) =
2x²-8
x²-x+6
IN
2
Answer:
Use the formula L(x)=f(a)+f'(a)(x−a) to find the linearization.
L(x)=2
Step-by-step explanation:
Distance between the points
(a cos (0 + 25+), a sin (
3
2π
3
and
(acos (0+), asin (0+5)) is
3
3
1) 2a
2) 3a
3) a/2
4) a
Distance between the points [tex](a cos(0 +\frac{2\pi }{3} ), a sin(0+\frac{2\pi }{3}))[/tex] and [tex](a cos(0+\frac{\pi }{3}), a sin(0+\frac{\pi }{3}))[/tex] is [tex]a[/tex]. (Option D)
Distance between two points is the length of the line segment that connects the two points in a plane. The formula to find the distance between the two points is usually given by [tex]d= \sqrt{(x^{2}-x) ^{2}+(y^{2}-y) ^{2} }[/tex]. This formula is used to find the distance between any two points on a coordinate plane or x-y plane. This formula is called distance formula.
Let A= [tex](a cos(0 +\frac{2\pi }{3} ), a sin(0+\frac{2\pi }{3}))[/tex] and B= [tex](a cos(0+\frac{\pi }{3}), a sin(0+\frac{\pi }{3}))[/tex].
Putting values in above formula:
AB=[tex]\sqrt{a^{2}[cos(0+\frac{\pi }{3})-cos(0+\frac{2\pi }{3})]^{2}+a^{2}[sin(0+\frac{\pi }{3})-sin(0+\frac{2\pi }{3})]^{2} }[/tex]
AB= [tex]a\sqrt{cos^{2}(0+\frac{\pi }{3})+sin^{2}(0+\frac{\pi }{3})+cos^{2}(0+\frac{2\pi }{3})+sin^{2}(0+\frac{2\pi }{3})}[/tex]
AB= [tex]a\sqrt{cos(0+\frac{\pi }{3})cos(0+\frac{2\pi }{3})sin(0+\frac{\pi }{3})sin(0+\frac{2\pi }{3})}[/tex]
AB=[tex]a\sqrt{1+1-2cos(0+\frac{2\pi }{3}-0-\frac{\pi }{3}) }[/tex]
AB= [tex]a\sqrt{2-2cos\frac{\pi }{3} }[/tex]
AB= [tex]a\sqrt{2-2\frac{1}{2} }[/tex]
AB= [tex]a\sqrt{2-1} =a[/tex]
Hence, the distance between the two given points is [tex]a[/tex].
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A large cheese pizza costs $11.45. A premium
topping on the large pizza costs $2.75, while a
standard topping on the large pizza costs
$1.75. Beverly orders a large cheese pizza
with 3 premium toppings and 4 standard
toppings. How much will the pizza cost?
6) Magdalena runs 5 days per week. Her goal is to run a minimum of 60 km each
week. If she runs 50 days, what is the minimum distance she will run?
The required minimum distance she will run is 600 km.
Given that,
Magdalena runs 5 days per week. Her goal is to run a minimum of 60 km each week. If she runs 50 days, what is the minimum distance she will run is to be determined.
In mathematics, it deals with numbers of operations according to the statements. There are four major arithmetic operators, addition, subtraction, multiplication and division,
Here,
In 5 days she ran 60 km
In one day she ran = 60 / 5 = 12
Let the number of km run be x
for 50 days minimum run would be,
= 50 * 12
= 600 km
Thus, the required minimum distance she will run is 600 km.
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Jackson eats 1/4 part of a banana in 1/2 minute. How much time will he need to eat a full banana?
PLEASE HELP
ALSO DO THE CHECK UR BOX WORK AND SHOW ME
a. Write an equation of the line through (-2,6) with slope 2
Answer:
Step-by-step explanation:
Point slope form:
y - y1 = m(x-x1)
y - 6 = 2(x + 2)
y - 6 = 2x + 4
y = 2x +10
AOC and BOD are diameters of a circle, centre O.
Prove that triangle ABD and triangle DCA are congruent by RHS.
The RHS congruency criterion showed ABD ≅ DCA.
What is congruency?In geometry, two figures or objects are said to be congruent if their shapes and sizes match, or if one is the mirror image of the other.
The diameters of a circle with an O-centered center are AOC and BOD.
To Locate:
By RHS, ABD and DCA are congruent.
Solution:
The fact that AOC and BOD are a circle's diameters is a given.
BD = CA (circle circumferences)
"BAD = CDA" [90° angles in semicircle]
AD = AD (shared by both triangles)
[Using RHS congruence criterion] ABD ≅ DCA
As a result, the RHS congruency criterion showed ABD ≅ DCA.
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Alexa has 38 m of fencing to build a three-sided fence around a rectangular plot of land that sits on a riverbank. (The fourth side of the enclosure would be the river.) The area of the land is 140 square meters. List each set of possible dimensions (length and width) of the field.
The possible dimensions ( width and length) plot of land are 9.5 m and 19 m.
What is defined as the rectangle?A rectangle is a confined two-dimensional structure with four sides, four corners, and four right angles (90°). A rectangle's opposite sides are equal as well as parallel.
Area of a rectangle
area of rectangle = l×w
where, l = length and w = width.
Thus, the perimeter for 2 side of width and 1 side of length is;
perimeter = 2w+ l
Perimeter of river = 38 m.
38 = 2w + l
l = 38 - 2w
Hence, Put the value of l in the area.
area = w(38 - 2w)
The area of the land is 140 sq.m.
140 = 38w - 2w²
-2w² + 38w - 140 = 0
-w² + 19w - 70 = 0
The equation is in the form of quadratic. Thus use the relation of coefficients and the roots to evaluate the width.
w = - b / a
Comparing the coefficients;
where,
a = -1
b = 19
w = - 19 / 2( -1)
w = 9.5 meters
Then,
l = 38 - 2w
l = 38 - 2(9.5)
l = 19 meters
Therefore, the dimensions of the plot of land are 9.5 meters and 19 meters.
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Ms.Nishino uses Zipcar, a rental car service. She only wants to spend $75.00 each month.ziper charges $25 a month, plus $12.50 per hour of car rental.
Ms.Nishino can drive using Zipcar for 4 hours
How is the total cost of of car rental modelled?
The total cost of car rental can be viewed using a straight-line equation, such total cost comprises of the fixed monthly charge and the total cost of hours based on the fact that hourly fee is $12.50 of car rental
y=a+bx
y=total cost=$75.00
a=fixed charge per month for car rental=$25.00
b=hourly charge=$12.50
x=number of hours spent driving in a month=unknown
75=25+12.50x
75-25=12.50x
50=12.50x
x=50/12.50
x=4
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Concluding part of the question:
How many can she drive the rental car to get it in her budget?
9/4x -1/2y = -3
Find x and y intercepts
Answer:
x-int: (-12/9, 0)
y-int: (0, 6)
Step-by-step explanation:
x-int ==> on x-axis when y=0
y-int ==> on y-axis when x=0
9/4x -1/2y = -3
x-int: 9/4x -1/2(0) = -3
9/4x = -3
9x/4 = -3
9x*4/4=-3*4
9x=-12
x=-12/9 ==> x-int: (-12/9, 0)
y-int: 9/4(0) -1/2y = -3
-1/2y = -3
1/2y=3
y/2=3
y=6 ==> y-int: (0, 6)
Find the value of x .
24=2 x √2
Answer:5
Step-by-step explanation:
Add or Subtract.
7/24 - 5/36
Answer:
A product of a number and 12 is increased by 23
The height of one of these cylinders if its radius is 2 inches is inches .
Answer: 4 inches.
Step-by-step explanation:
If you are adding two fractions that are both less then 1/2 what must be true about the sum? Give three examples to support your thinking
Addition of two fractions which are both less than (1/2) must result in a fraction which is always less than 1.
What is fractions?A fraction represents a part of a whole or, more generally, any number of equal parts. A fraction describes how many parts of a certain size there are, for example, one-half, eight-fifths, three-quarters.
Given data
The fractions can be represented as follows;
x < ½ and y < ½
The sum of both of the inequalities is;
x + y < ([tex]\frac{1}{4}[/tex]) + ([tex]\frac{1}{4}[/tex])
x + y < ½
Examples are-
[tex]\frac{1}{5}[/tex]+ [tex]\frac{2}{3}[/tex] =[tex]\frac{13}{15}[/tex]
¼ + ½ = ¾
[tex]\frac{1}{2}[/tex] +[tex]\frac{1}{3}[/tex] = [tex]\frac{5}{6}[/tex]
Therefore, Addition of two fractions which are both less than (1/2) must result in a fraction which is always less than 1.
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Find the reciprocal of 3/5
y varies directly with x .
If y=25 when x=15 , find y when x=6 .
The required value of y is 10.
What is the constant of proportion?
A constant of proportion is illustrated as the ratio which relates two given quantities with each other in the relationship of proportion. Constant of proportion is also called constant variation, rate of change, and constant ratio.
Solving for the value of y
let k be the constant of proportion
When a quantity varies directly with others, then we have a relation, y = kx, —-- 1
Now, find k for given x = 15 and y = 25, we need to put these values in equation 1, i.e.
25 = k(15)
k = 25 / 15
k = 5 / 3
Further calculate y for given x = 6 and constant of proportion = 5/3 i.e.
y = (6)(5 / 3)
y = 10
Hence, the required value of y is 10.
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