Answer:
b. x=2
Step-by-step explanation:
Step 1- Move the variable to one side.
12x-8= 3x+10
-3x -3x
9x-8= 10
Step 2- Add 8 to both sides.
9x-8= 10
+8 +8
9x= 18
Step 3- Divide to both sides.
9x= 18
9 9
x= 2
Solve 2x−1<4 and −5x−3>−3 and write the solution in interval notation. If there is no solution, type ∅.
2x - 1 < 4
First, let's add 1 to both sides.
2x < 5
Divide both sides by 2
x < 5/2 or (-∞, [tex]\frac{5}{2}[/tex])
-5x - 3 > -3
Add 3 to both sides.
-5x > 0
Divide both sides by -5
x < 0 or (-∞, 0)
The solution set of the given set of linear inequations 2x - 1 < 4 and -5x - 3 < -3 is [tex]\left ( -\infty , 0 \right )[/tex].
What are equations and inequations?Algebraic expressions can be related to each other in many ways. When two expressions are equal to each other, they are called equations and are represented with an equal sign between them (=). When two expressions are not equal, they are called inequations and are represented by non-equal signs between them (>, <, ≥, ≤).
How to solve the given question?In the question, we are asked to solve the given inequations:
2x - 1 < 4 ... (i), and -5x -3 > -3 ... (ii).
First, we will solve (i), in the following ways:
2x - 1 < 4.
or, 2x - 1 + 1 < 4 + 1 (Adding 1 to both sides of the inequation)
or, 2x < 5 (Simplifying)
or, 2x/2 < 5/2 (Dividing both sides of the inequation by 2)
or, x < 5/2 (Simplifying)
or, x ∈ [tex]\left ( -\infty , \frac{5}{2} \right )[/tex] ...(iii)
Now, we will solve (ii), in the following ways:
-5x -3 > -3.
or, -5x - 3 + 3 > -3 + 3 (Adding 3 to both sides of the inequation)
or, -5x > 0 (Simplifying)
or, -5x/(-5) < 0/(-5) (Dividing both sides of the inequation by -5, sign of the inequality reverses as we are dividing by a negative number)
or, x < 0 (Simplifying)
or, x ∈ [tex]\left ( -\infty , 0 \right )[/tex] ...(iv)
For the solution set, we need the intersection of (iii) and (iv)
[tex]\left ( -\infty , \frac{5}{2} \right )[/tex] ∩ [tex]\left ( -\infty , 0 \right )[/tex]
= [tex]\left ( -\infty , 0 \right )[/tex]
∴ The solution set of the given set of linear inequations 2x - 1 < 4 and -5x - 3 < -3 is [tex]\left ( -\infty , 0 \right )[/tex].
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I NEED THIS ANSWER ASAP DUE IN 3 HOURS!!!!!
Read this description of the life cycle of a mushroom. 1. A mushroom begins to grow underground as a single-celled "spore.” 2. The spore grows into multicellular structures called "hyphae.” 3. The hyphae absorb nutrition and detect when conditions are right to sprout a mushroom above ground. 4. The sprouted mushroom then forms new spores that can enter the ground and begin the life cycle again. Which sentence about this life cycle shows that mushrooms need energy and respond to stimuli? A mushroom begins to grow underground as a single-celled “spore.” The spore grows into multicellular structures called “hyphae.” The hyphae absorb nutrition and detect when conditions are right to sprout a mushroom above ground. The sprouted mushroom then forms new spores that can enter the ground and begin the life cycle again.
The correct answer is C. The hyphae absorb nutrition and detect when conditions are right to sprout a mushroom above ground.
Explanation:
Two key features of living organisms are energy processing and response to stimuli. These two features imply organisms require nutrients, which can be taken from the environment or created through a process such as photosynthesis and they sense their surroundings and respond to it.
Moreover, these two features are exemplified by mushroom (fungi) in the sentence "The hyphae absorb nutrition and detect when conditions are right to sprout a mushroom above ground" because the first section shows the developing mushroom takes nutrients from the soil or its environment and this is essential for growing and survival. Also, the second section of the sentence shows the developing mushroom can sense its environment and respond by developing only in appropriate conditions.
Answer:
C
Step-by-step explanation:
Got it right on edge 2020
Please help!!! I would like an explanation along with your answer. Thanks
Answer:
11.2 feet
Step-by-step explanation:
The two furthest corners of the bed are at (8, 6) and (5, 10). To determine which is the furthest from the origin, use the distance formula.
d = √((x₂ − x₁)² + (y₂ − y₁)²)
d = √((8 − 0)² + (6 − 0)²)
d = 10
d = √((x₂ − x₁)² + (y₂ − y₁)²)
d = √((5 − 0)² + (10 − 0)²)
d = 5√5
d ≈ 11.2
Therefore, the corner at (5, 10) is the furthest from the origin, about 11.2 feet away.
What are the odds of two people having the same birthday?
Answer:
In a room of just 23 people there's a 50-50 chance of at least two people having the same birthday. In a room of 75 there's a 99.9% chance of at least two people matching. Put down the calculator and pitchfork, I don't speak heresy.
Step-by-step explanation:
Use logarithmic differentiation to find dy/dx. y = (x + 1)(x − 4)/ (x − 1)(x + 4) , x > 4 dy dx =
Answer:
dy/dx = (x + 1)(x-4)/(x-1)(x+4)[1/(x+1) + 1/(x-4) -1/(x-1) -1/(x+4)
Step-by-step explanation:
Here, we want to find the derivative using logarithmic differentiation.
What we will do here is to first take the natural logarithm of both sides, then we proceed to differentiate afterwards.
Please check attachment for complete solution and step by step explanation.
Jasmine knows that the area of a rectangle is the product of its base and height. Help her write an expression that represents the area of this rectangle, and then use the expression to find the area when b = 10. Select the correct answer from each drop-down menu. The expression that represents the area of this rectangle is . When b = 10, the area of the rectangle is square units.
Answer:
8b and 80
Step-by-step explanation:
Answer:
The expression that represents the area of this rectangle is 8b
When b = 10, the area of the rectangle is 80 square units.
Step-by-step explanation:
If you get this, you are a critical thinker. I enter the garden. There are 34 people. You kill 30. How many people are in the garden?
Good luck!
If you get it correct your answer will be deleted, and l will message you to continue the game. Don't play if you are not going to continue!
Answer:
Step-by-step explanation:
is it 34 because you haven't moved the bodies. however including you there's 35???
This is a simple algebra problem. The answer is 5.
We know that:
Initially, there are 34 people in the garden.
Then you enter, so now there are 35.
Then we lose 30 of these people, so the final number of people in the garden will be: 35 - 30 = 5
Finally, there are 5 people in the garden.
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Which statement is true?
A function is a relation where each output value is assigned to exactly one input value.
The domain of a function is the set of all output values, or y-values, for which the function is defined.
The range of a function is the set of all input values, or x-values, for which the function is defined.
To write the equation y = ax + b in function notation, substitute f(x) for y.
Answer:
To write the equation y = ax + b in function notation, substitute f(x) for y
Step-by-step explanation:
The only true statement is the last one.
__
A function assigns exactly one output value to each input value.
The domain is the set of all input, or x-values.
The range is the set of all output, or y-values.
y=ax+b can be written in function notation by replacing y with f(x).
Answer:
The last one: To write the equation y = ax + b in function notation, substitute f(x) for y.
Step-by-step explanation:
A relation is a mapping from a set of input values, called the domain, to a set of output values, called the range. In a relation, each element in the domain can be assigned to one or more elements in the range.
A function is a relation where each input value is assigned to exactly one output value.
The domain of a function is the set of all input values, or x-values, for which the function is defined.
The range of a function is the set of all output values, or y-values, for which the function is defined.
To write the equation y = ax + b in function notation, substitute f(x) for y, resulting in the function f(x) = ax + b.
16. (x4 - 3x° – 7x - 14) = (x - 4) 4
An automobile manufacturer introduces a new model that averages 27 miles per gallon in the city. A person who plans to purchase one of these new cars wrote the manufacturer for the details of the tests, and found out that the standard deviation is 3 miles per gallon. Assume that in-city mileage is approximately normally distributed. What is the probability that the person will purchase a car that averages less than 20 miles per gallon for in-city driving
Given :
An automobile manufacturer introduces a new model that averages 27 miles per gallon in the city.
Standard deviation , S.D = 3 miles per gallon .
To Find :
The probability that the person will purchase a car that averages less than 20 miles per gallon for in-city driving.
Solution :
We have to find the probability , [tex]P(X\leq 20)[/tex] .
Here , we will use the excel function
So ,
[tex]P(X\leq 20)=NORMADIST( 20, 27 , 3 , 1 )=0.009815[/tex] .
Therefore , probability is 0.009815 .
These triangles are scaled copies of each other.
For each pair of triangles listed, the area of the second triangle is how many times larger than the area of the first?
Answer/Step-by-step explanation:
Recall: the ratio of the areas of two similar figures = the square of the ratio of the corresponding sides of the similar figures.
This will give us the scale factor.
The scale factor indicates how many times larger the second triangle is than the area of the first.
Let's find how many times larger is the area of the second triangle is to the first:
1. ∆ G And ∆ F
[tex] \frac{Area_{F}}{Area_{G}} = \frac{side_{F}^2}{side_{G}^2} [/tex]
[tex] \frac{Area_{F}}{Area_{G}} = \frac{6^2}{3^2} [/tex]
[tex] = \frac{36}{9} = 4 [/tex]
∆F is 4 times larger than ∆G
2. ∆ G And ∆ B
[tex] \frac{Area_{B}}{Area_{G}} = \frac{side_{B}^2}{side_{G}^2} [/tex]
[tex] \frac{Area_{B}}{Area_{G}} = \frac{2^2}{4^2} [/tex]
[tex] = \frac{4}{16} = 0.25 [/tex]
∆B is 0.25 times ∆G
3. ∆ B And ∆ F
[tex] \frac{Area_{G}}{Area_{B}} = \frac{side_{F}^2}{side_{B}^2} [/tex]
[tex] \frac{Area_{F}}{Area_{B}} = \frac{8^2}{2^2} [/tex]
[tex] = \frac{64}{4} = 4 [/tex]
∆F is 16 times larger than ∆B
4. ∆ F And ∆ H
[tex] \frac{Area_{H}}{Area_{F}} = \frac{side_{H}^2}{side_{F}^2}} [/tex]
[tex] \frac{Area_{H}}{Area_{F}} = \frac{2^2}{6^2} [/tex]
[tex] = \frac{4}{36} = \frac{1}{9} [/tex]
∆H is ⅑ times ∆F
5. ∆ G And ∆ H
[tex] \frac{Area_{H}}{Area_{G}} = \frac{side_{H}^2}{side_{G}^2} [/tex]
[tex] \frac{Area_{H}}{Area_{G}} = \frac{2^2}{3^2} [/tex]
[tex] = \frac{4}{9} [/tex]
∆G is 4/9 times ∆G
6. ∆ H And ∆ B
[tex] \frac{Area_{B}}{Area_{H}} = \frac{side_{B}^2}{side_{H}^2} [/tex]
[tex] \frac{Area_{B}}{Area_{H}} = \frac{1.5^2}{2^2} [/tex]
[tex] = \frac{2.25}{4} = 0.6 [/tex] (nearest tenth)
∆B is 0.6 times ∆H
The solution to an inequality is graphed on the number line. What is another way to represent this solution set? O {x | X 4.5) O x | x2 4.5) 5 -3 -2 -1 0 1 2 3 4 5
Answer: Choice B [tex]\{x | \ x \le 4.5\}[/tex]
=============================================
Explanation:
The endpoint is at 4.5 and this endpoint is a filled in circle. So we'll have "or equal to" as part of the inequality sign. This is because we are including the endpoint as part of the shaded solution region.
The other part of the inequality sign is "less than" because the shading is to the left of the endpoint. Any point in the shaded region is less than 4.5, or it could be equal to 4.5
Put another way: x is either 4.5 or smaller
We write that as [tex]x \le 4.5[/tex] which is read out as "x is less than or equal to 4.5"
Surrounding this in curly braces tells the reader we're dealing with a set of values. The first part "x |" means "x such that"
All together we end up with the answer [tex]\{x| \ x \le 4.5\}[/tex] which translates to "x such that x is less than or equal to 4.5"
Answer:
B
Step-by-step explanation:
If f(x)=-2x-3 find the value f(4y)
Answer:
f(4y) = -8y - 3
Step-by-step explanation:
Step 1: Define variables
f(x) = -2x - 3
f(4y) = x = 4y
Step 2: Plug in x = 4y
f(4y) = -2(4y) - 3
f(4y) = -8y - 3
13times the difference of a number n and 20 is 322. Write as an equation.
Answer:
13(n-20)=322
Step-by-step explanation:
13 times n-20 equals 322
A car driving at 50 miles per hour drives 2 hours. What distance did it cover?
Answer: It travels 100 miles
Step-by-step explanation:
If it drives 50 miles an hour it would drive 100 miles an hour if it were driving for 2 hours.
Based on the speed of the car and the amount of time it was travelling, the car travelled 100 miles in 2 hours.
The distance that the car travelled can be calculated by:
Distance = Speed x Time
Speed = 50 miles per hour
Time = 2 hours
Distance = 50 x 2
= 100 miles
In conclusion, the car would have gone 100 miles.
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Determine whether the given ordered pair is a solution to the system of equations.
Yes or no?
(6,-1)
x-y=3
2x+5y=6
Introduction to Interval Notation
What is the domain and range?
2.
The domain of this function is 3≤x≤5 in interval notation that is [3,5]
The range is -3≤y≤3. In interval notation that is [-3,3]
4.
The domain of this function is -5≤x≤-1 in interval notation that is [-5,-1]
The range is 1≤y≤5. In interval notation that is [1,5]
:)
The admission fee at an amusement park is $1.50 for children and $4 for adults. On a certain day, 332
people entered the park, and the admission fees collected totaled 898.00 dollars. How many children and
how many adults were admitted?
Answer:
172 kids and 160 adults
Step-by-step explanation:
We can create two equations with the information given.
1.5x + 4y = 898
x + y = 332
We can then bring the x in the second equation over to the other side.
y = 332 - x
We can now plug this equation into the one before.
1.5x + 4(332 - x) = 898
We now do the distributive property on the equation and result with
1.5x + 1328 - 4x = 898
Then we can combine like terms and add 1.5x and -4x together and bring 1328 over by subtracting it from 898.
-2.5x = -430
-430 / 2.5x = 172
x = 172
x is defining how many children when to the park.
Now we just need to figure out y by subtracting it from the total amount of people (aka plugging it into the second equation)
y = 332 - 172
y= 160
We end up with
x = 172
y = 160
172 children and 160 adults
How do I solve this? Solve for x 2/3+5/3x=9
Answer:
5
Step-by-step explanation:
5. Natalie has a pound bag of 1/8 pound bag of gummy worms, a 1/2 pound bag of twizzlers, and a 2/3 pound bag of chocolate. How many pounds of candy does Natalie have in all?
Step-by-step explanation:
1. Add all the different candies together
1/8 + 1/2 + 2/3=
2. Find the lowest common multiple of all the denominators
All the denominators can evenly multiply to 24 so 24 is the Lowest Common Denominator.
3. Multiply to make all the denominators 24
8x3=24 2x12=24 3x8=24
4. Whatever you did to the denominators, do the same thing to the numerators of that specific denominator.
1x3/8x3 1x12/2x12 2x8/3x8
5. Now that the denominators are the same for all the fractions, add all the numerators together.
3/24 + 12/24 + 16/24
3+12+16= 31
ANSWER: Natalie had 31/24 pounds of candy in all
Note: The decimal form is 1.292 pounds
HELP hate geometry like uhhh what is this don’t understand #help
Answer:
CE would be half of AD.
Step-by-step explanation:
A, E and D are all points on the circumference of the circle.
AD is the diameter.
CE is the radius.
CE would be half of AD.
which systems of equations have no Solutions
Answer:
Inconsistent System of Equations
Explanation:
There is no solution for the system of equations that graphs as parallel lines.
Parallel lines never cross, therefore there is no intersection. This is an inconsistent system of equations.
Scott invested a total of $5400 at two separate banks. One bank pays simple interest of 12% per year while the other pays simple interest at a rate of 9% per year. If Scott earned $576.00 in interest during a single year, how much did he have on deposit in each bank?
Answer:
648 im each bank
Step-by-step explanation:
Shea bought x candy bars for $1.50 each. Write an
algebraic expression for the total amount Shea spent.
What’s the answer?
Jill, Cathy, and Sandy were in line for a roller coaster ride. How many ways could they be seated if the ride held 3 people in each seat?
Answer:
6
Step-by-step explanation:
1x2x3=6
Someone help me on thissss
Each gallon of gasoline costs $2.35. The equation y=2.35x can be used to represent this situation.
Answer:
Yes
Step-by-step explanation:
If y is the total cost, then this would be correct.
Jamie is playing a card gameJamie's score changes by - 12 points for 8 turns in a row. What is the total of jamies score? Plz answer fast
Answer:
-96
Step-by-step explanation:
Assuming that the scores start at 0,
-12 x 8 = -96
Total of Jamies score in card game is -96
Given that;
Each turn score = -12
Number of turn = 8
Find:
Total of Jamies score
Computation:
Total of Jamies score = Each turn score × Number of turn
Total of Jamies score = -12 × 8
Total of Jamies score = -96
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PLEASE HELP QUICK!!! 3x − 2(6 − x) = 7x + 2(5 + x) − 6
Answer:
it would be x=-4
hope i helped ya
Answer:
x = -4
Step-by-step explanation:
3x -2(6-x) = 7x +2(5+x) -6
Distribute -2 through the parentheses 3x -12 +2x = 7x +2(5+x) -6
Distribute 2 through the parentheses 3x -12 +2x = 7x +10 +2x -6
3x -12 +2x = 7x +10 +2x -6 cancel equal terms on both sides of the equation
3x -12 = 7x +10 -6 subtract the numbers 3x -12 = 7x +4
Move variable to the left left handed side and change its sign
3x -7x-12 = 4 --> 3x -7x = 4 + 12 --> -4x = 4+12 --> -4x = 16
Divide both sides of the equation by -4 --> x = -4