[tex]\large\underline{\sf{Solution-}}[/tex]
Given:
[tex]\rm\longmapsto 4(x-3)<x+3, x\in \mathbb{W}[/tex]
[tex]\rm\longmapsto 4x-12<x+3[/tex]
[tex]\rm\longmapsto 4x-12-x<x+3-x[/tex]
[tex]\rm\longmapsto 3x-12<3[/tex]
[tex]\rm\longmapsto 3x-12+12<3+12[/tex]
[tex]\rm\longmapsto 3x<15[/tex]
[tex]\rm\longmapsto \dfrac{3x}{3}<\dfrac{15}{3}[/tex]
[tex]\rm\longmapsto x<5, x\in\mathbb{W}[/tex]
[tex]\large\underline{\sf{Answer-}}[/tex]
Therefore:
[tex]\rm\longmapsto x=\{0,1,2,3,4\}\ \ \ [/tex]
Helen counted six dollars and four cents in her purse. She recorded this amount in decimal form as $6.40. Did she record it correctly? If she made a mistake, what is the correct way
to record this amount of money as a decimal?
Pls answer will give brainiest
Answer:
6 dollars and 4 cents
Step-by-step explanation:
SOCCER TRACK GOLF 112 74 59 # OF STUDENTS There are 450 7th graders at Lakeside Middle School. The chart above shows the number that participate in a certain sport Find and fix the incorrect statement #1. About 55% of 7 graders do not play a sport #2: Of the students who play a sport, 24% play golf #3: Of the students who play a sport, 46% play soccer #4: About 16% of all 7 graders run track HURRYYYYYYYYYYYYY
Answer: about 14% of the 7 grade don't play sports
Step-by-step explanation: i think
x-10/3=5x+2/2 I need help with he next step please
Answer:
x2 the left side and x3 the right side of the equation
Answer:
X = -2
First you cross multiply, and then you expand to get 15x+6
after that its basic algebra with adding/subtracting from each side, simplifying, and then divide both sides by -13.
A boy dressed in a robot costume weighs a total of 50 7/8 lb. If the costume itself weighs 3 1/2 lb, how much does the boy weigh?
The weight of the boy in the robot costume is 351/8 lb or 43 7/8 lb.
To find the weight of the boy, we need to subtract the weight of the costume from the total weight of the boy in the costume.
Total weight of boy and costume = 50 7/8 lb
Weight of costume = 3 1/2 lb
To find the weight of the boy, we can subtract the weight of the costume from the total weight:
Weight of boy = Total weight - Weight of costume
Convert both the total weight and the weight of the costume to improper fractions:
Total weight = 50 + 7/8 = 400/8 + 7/8 = 407/8 lb
Weight of costume = 3 + 1/2 = 6/2 + 1/2 = 7/2 lb
Now, subtract:
Weight of boy = (407/8) lb - (7/2) lb
To perform subtraction, we need to have a common denominator, which is 8 in this case:
Weight of boy = (407/8) lb - (56/8) lb
Now, subtract the fractions:
Weight of boy = (407 - 56)/8 lb
Weight of boy = 351/8 lb
To learn more about fraction click on,
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Answer:
we know that it is 0.6 km
so we convert into meters
and then get 600 m
Hope that helps
Answer:
ok thank u ig
Step-by-step explanation:
Given the following exponential function, identify whether the change represents growth or decay, and determine the percentage rate of increase or decrease.
y=21(0.97)^x
what is the % increase
Answer:
Step-by-step explanation:
As the number under the exponent is less than 1, this is a decay function.
y decreases by (1 - 0.97)100 = 3% for each unit increase in x
so the increase would be -3%
2/3x + 7 = -1/5x + 3
if there is any doubt leave a comment
Write an inequality to show: The population of China (p) is at least 1,000,000,000 people.
I'll try to mark brainiest
Answer:
p ≥ 1,000,000,000
Step-by-step explanation:
since it says "at-least" that is implying that, that is the estimate and there is most likely more people and it is not exactly 1,000,000,000 so we need to use ≥ to show that it could be greater than or equal to 1,000,000,000.
please help me calculation completing square?
x²+2x-24=0?
Answer:
x = 4, -6
Step-by-step explanation:
x = 4, -6
Describe the slope of the line.
Answer:
-3/5
Step-by-step explanation:
Just ask.
Hope this helps! :)
Suppose `h\left(t\right)=-5t^{2}+10t+3`is an expression giving the height of a diver above the water (in meters), t seconds after the diver leaves the springboard.
a. How high above the water is the springboard? Explain how you know.
Answer:
Step-by-step explanation:
a) The height of the springboard above the water should be h(0) : Read, the height at t = 0
h(0) = -5(0) + 10(0) + 3
h(0) = 0 + 0 + 3
h(0) = 3
a) 3 meters
b) The time it takes the diver to hit water should be, the positive 0 solution for t. Remember, in a quadratic equation, there are two values for t where a parabola crosses the horizontal axis, which in this case would be t. Just by looking at the function, h(t) = -5t2 + 10t + 3 , one should be able to see that it cannot be factored easily, so it requires the Quadratic Formula to find the zeros ; x = -b ±√(b2-4ac) / 2a
Substitute t for x, and use the coefficients for a, b, c:
t = (-10 ± √((102 - 4(-5)(3)))/2(-5)
t = (-10 ±√(100 + 60))/-10
t = (-10 ±√160)/-10) ; Now factor the 160 to simplify:
t = (-10 ±√(10*16))/-10
t = (-10 ±4√10)/-10 ; Factor out leading coefficient of -2 from the numerator:
t = -2(5 ± 2√10)/-10
t = (5 ± 2√10)/5
Using a calculator to find the zeros, and disregarding the negative zero (because t starts at 0):
t ≈ 2.265
b) approx. 2.265 seconds for diver to hit water.
c) To find this, set the function equal to 3 to find what other value for t would be equal to 3 (we know one is 0).
-5tt + 10t + 3 = 3
-5t2 + 10t = 0 ; factor out t
t(-5t + 10) = 0
We know t = 0:
We also know that -5t + 10 = 0
-5t = -10
t = 2
c) 2 seconds. This is the time that diver would equal height of t=0 which is where he started, and where he equals the height of the springboard.
d and e) The peak of the dive (parabola), is determined using the formula h = -b/2a (Derived from the Quadratic Formula) to find the y value (in this case, the h value, answering e) and then using that result in the function to find the x value (in this case, the t value answering d) of the point where the parabola (dive path) reaches a maximum(height), or minimum(in upward opening parabolas).
h = -10/2(-5)
h = -10/-10
h = 1
h(1) = -5(1)2 + 10(1) + 3
h(1) = -5 + 10 + 3
h(1) = 8
d) At t = 1 second, diver will have reached peak of dive.
e) At t = 1 second, diver will have reached a maximum height of 8 meters.
Help please please need quick
a car travels 55 miles per hour for 2 hours. How far did it travel in 1 1/2 hours
Answer:
82.5 miles in 1 1/2 hours
Step-by-step explanation:
Using the information the question gives us we can find the appropriate answer to this question by dividing the miles per hour by two, and then add that number to the additional miles per hour.
55 miles = one hour
2 hours = 110 miles
1 1/2 hours = 55 ÷ 2 = 27.5
55 + 27.5 = 82.5 miles
82.5 miles
Hope this helps
Expand the function.
f(x) = (2x + 3)4
Answer:
y = 8x + 12
Step-by-step explanation:
y = (2x + 3)4
Distribute the 4 to the 2x and 3
y = 8x + 12
^ Expanded form
2yx= 4 is it a linear function?
Answer:
No, it is not a linear function, rather a rational function
Step-by-step explanation:
Because the term on the left-hand side contains both x and y, then neither variable varies directly with the other, hence, it's a rational function:
2yx=4
yx=2
y=2/x
Please help me do this question
Step-by-step explanation:
We need to break up the given expression into two separate fractions so that when they are added together, we will get the original expression.
Note that the denominator is made up of two factors, [tex](2x - 1)[/tex] and [tex](x^2 + 1).[/tex] But note that the 2nd factor is a 2nd order polynomial so as a rule, the numerator of the fraction containing this factor must be an (n - 1)-order polynomial, where n is the order. With that in mind, we can write the general form of the partial fractions as follows:
[tex]\dfrac{x + 7}{(2x - 1)(x^2 + 1)} = \dfrac{Ax + B}{x^2 + 1} + \dfrac{C}{2x - 1}[/tex]
[tex]\:\:\:\:=\dfrac{2Ax^2 + Bx - Ax - B + Cx^2 + C}{(2x - 1)(x^2 + 1)}[/tex]
Here, we combined the two fractions to form the equation above. Next, we compare the numerators on either side. Note that we satisfy the equality if we impose the following conditions:
[tex]2A + C = 0\:\:\:\:\:\:\:\:\:\:\:\:\:\:(1)[/tex]
[tex]2B - \:A = 1\:\:\:\:\:\:\:\:\:\:\:\:\:\:(2)[/tex]
[tex]-B + C = 7\:\:\:\:\:\:\:\:\:\:\:\:\:\:(3)[/tex]
To find the values of the constants A, B and C, we need to solve this system of equations. We start by multiplying Eqn(3) by 2 and then adding it to Eqn(2) to get
[tex]-A + 2C = 15\:\:\:\:\:\:\:\:\:\:\:\:\:\:(4)[/tex]
Then, multiply Eqn(1) by -2 to get
[tex]-4A - 2C = 0\:\:\:\:\:\:\:\:\:\:\:\:\:\:(5)[/tex]
Add Eqn(4) to Eqn(5) and we will get
[tex]-5A = 15 \Rightarrow A = -3[/tex]
Now that we know the value of A, we can use this in Eqn(2) to get
[tex]2B - (-3) = 1 \Rightarrow B = -1[/tex]
Next, to solve for C, we use the value of A in Eqn(1) to get
[tex]2(-3) + C = 0 \Rightarrow C = 6[/tex]
Therefore, the given expression can be written as
[tex]\dfrac{x + 7}{(2x - 1)(x^2 + 1)} = \dfrac{6}{2x - 1} + \left(\dfrac{-3x - 1}{x^2 + 1}\right)[/tex]
As a check, let's combine the two fractions together:
[tex]\dfrac{x + 7}{(2x - 1)(x^2 + 1)} = \dfrac{6}{2x - 1} + \left(\dfrac{-3x - 1}{x^2 + 1}\right)[/tex]
[tex]= \dfrac{6x^2 + 6 - 6x^2 - 2x + 3x + 1}{(2x - 1)(x^2 + 1)}[/tex]
[tex]= \dfrac{x + 7}{(2x - 1)(x^2 + 1)}[/tex]
As expected, we got the original expression.
12Q. Sweeti covered 2/7 of the running track by walking and rest by running and the length of the track is 630 m. Find the distance covered by running ?
Step-by-step explanation:
Given that :
Total length of the track = 630 m
Distance covered by Sweeti by walking = 2/7 of the running track
2/7 of 630 m
⇛ (2/7)×630
⇛ (2×630)/7
⇛ 1260/7
⇛ 180 m
Distance covered by walking = 180 m
Remaining distance =
Total distance - Distance covered by walking
⇛630 m - 180 m
⇛ 450 m
The total distance covered by running by Sweeti is 450 m.
Read more:
Similar Question
You can burn about 450 calories if you run 5 miles. How many miles will you need to run to burn 630 calories? Justify your reasoning.....
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What are the solutions to the quadratic function. f(x) = x^2+4x-12
Answer:
2, -6
Step-by-step explanation:
x^2 + 4x - 12
A = 1
B = 4
C = -12
i used the "X" method to solve for the solutions. i think it's easier than using the quadratic formula but it doesn't always work
for the "X" method you have to multiply your A value and your C value together so 1 x (-12) = -12. that is going to be the top part of the X
the bottom part of the x will be your B value which is 4
we have to find multiples of -12 that will also add to 4
so -2 and 6 multiply to -12 but also add to 4 so we know these numbers will work
i added added two drawings to show how i found the solutions using the "X" method and the quadratic formula
5/7 times 7/8 in simple form
Answer:
609
Step-by-stepStep-by-step explanation:
nope
A department store marked down all of its summer clothing 23%. The following week the remaining items were marked down again
15% off the sale price. When Jorge bought two tank tops on sale, he presented a coupon that gave him an additional 20% off. What
percent of the original price did Jorge save?
Answer:
58%
Step-by-step explanation:
fast hurry no link no bot please right
9514 1404 393
Answer:
(d) 972π in³
Step-by-step explanation:
The formula for the volume of a sphere is ...
V = 4/3πr³
The sphere has a diameter of 18 in, so a radius of 9 in. Its volume is ...
V = (4/3)π(9 in)³ = (4/3)729π in³ = 972π in³
The container can hold 972π in³ of water.
A punch recipe requires 2 cups of cranberry juice to make 4 gallons of punch. Using the same recipe, what is the amount of cranberry juice needed for 12 gallon of punch
Answer:
we need 6 cups of cranberry juice for 12 gallons of punch
What's the negative reciprocal of 5? Question 12 options: A) 1∕5 B) –5 C) –1∕5 D) 5
Answer:
[tex]\huge\boxed{C)\ -\dfrac{1}{5}}[/tex]
Step-by-step explanation:
The reciprocal of 5: [tex]\dfrac{1}{5}[/tex]
The negative reciprocal of 5: [tex]-\dfrac{1}{5}[/tex]
How to factor out a polynomial with a 3rd degree.
Answer:
How to factor out a polynomial with a 3rd degree-• well here is a For example, let G(x) = 7x³ – 125. Then factoring this third degree polynomial relieve on a differences of cubes as follows: (2x – 5) (4x² + 20x + 25), where ²x is the cube-root of 8x³ and 5 is the cube-root of 1256
Answer:
long division is probably the simplest method of finding out the factors
Step-by-step explanation:
For example, let G(x) = 8x³ – 125. Then factoring this third degree polynomial relies on a difference of cubes as follows: (2x – 5) (4x² + 10x + 25), where 2x is the cube-root of 8x³ and 5 is the cube-root of 125. Because 4x² + 10x + 25 is prime, you are done factoring.
Mr. Jameson has an apple orchard on his farm. He hires his daughter, Rachel, to pick apples and offers her two payment options:
Option A: $1.50 per bushel of apples picked
Option B: 1 cent for picking one bushel, 3 cents for picking two bushels, 9 cents for picking three bushels, and so on, with the amount of money tripling for each additional bushel picked
HELP ASAP
Answer:
Part A: f(x) = 1.50x/g(x) = 0.01(3)^x-1
Part B: Option A: $9
Part C: Option B: $1,771.47
Part D: The eighth bushel picked is when the exponential function exceeds the linear function.
Step-by-step explanation:
Part A: Write a function to model each option.
Option A: f(x) = 1.50x, where x is the number of bushels of apples picked
Option B: g(x) = 0.01(3)^x-1, where x is the number of bushels of apples picked.
--------------------------------------------------------------------------------------------------------------
Part B: If Rachel picks six bushels of apples, which option should she choose?
Option A: $9 Option B: $2.43
Option A is better since what the number is would be higher.
1.50x6 = 9. If I were to do the same for option b, option a would end up higher.
--------------------------------------------------------------------------------------------------------------
Part C: If Rachel picks twelve bushels of apples, which option should she choose?
Option A: $18 Option B: $1,771.47
After calculating both of them by multiplying by 12 for each, option B ends up to be much better.
--------------------------------------------------------------------------------------------------------------
Part D: How many bushels of apples does Lucy pick to make option B better for her than option A?
The eighth bushel picked is when the exponential function exceeds the linear function.
a man walks for 45 minutes at a rate of 3 mi/h then jogs for 75 minutes at a rate of 5 mi/h then rests for 30 minutes and finally walks for 90 minutes at a rate of 3 mi/h. Write a piecewise-defined function expressing the distance he traveled as a function of time.
Answer:
Sorry need points
Step-by-step explanation:
PLEASE HELP ME
It snowed 2/3 of a foot in January and 1/2 of a foot in February. How much more did it snow in January than in February?
Answer:
Step-by-step explanation:
2/3 - 1/2 ?=?
4/6 - 3/6 = 1/6 ft more
I have 7 friends. I owe 3 of my friends a dollar and 4 of my friends owe me a dollar. I can tell the difference between my friends. How many ways can I settle all the debts given that I start with 0 dollars
Answer:
2
Step-by-step explanation:
either the four friends give you the money first then you give it to the three friends That is one Or youcan ask your parental figure to own you three dallors then you will have more money at the End.
The student government snack shop sold 64 snacks this week. 8 of the snacks sold were fruit cups. What percentage of all snacks sold were fruit cups?
Rewrite the equation as a division equation.
Answer:
8/64 = 0.125 = 12.5%
Step-by-step explanation:
8/64 = 0.125 = 12.5%
Find the domain of the function.
f(x) = -5x + 3
Enter a problem...
Calculus Examples
Popular Problems Calculus Find the Domain and Range f(x)=5x-3
f
(
x
)
=
5
x
−
3
The domain of the expression is all real numbers except where the expression is undefined. In this case, there is no real number that makes the expression undefined.
Interval Notation:
(
−
∞
,
∞
)
Set-Builder Notation:
{
x
|
x
∈
R
}
The range is the set of all valid
y
values. Use the graph to find the range.
Interval Notation:
(
−
∞
,
∞
)
Set-Builder Notation:
{
y
|
y
∈
R
}
Determine the domain and range.
Domain:
(
−
∞
,
∞
)
,
{
x
|
x
∈
R
}
Range:
(
−
∞
,
∞
)
,
{
y
|
y
∈
R
}
