Solve 2x - 1 < 7 and 5x + 3 < 3. {x | x < 0} {x | x < 4} {x | 0 < x < 4}
Answer:
Solution for givrn system of inequalities: [tex]\{x ~| ~x < 0\}[/tex]
Step-by-step explanation:
We are given a system of two inequalities:
[tex]2x-1 < 7\\5x+3 < 3[/tex]
Solving the inequalities individually:
[tex]2x-1 < 7\\2x<7+1\\2x < 8\\x < 4\\\text{In interval notation: } x \in (-\infty, 4) \\\\5x + 3 < 3\\5x < 3-3\\5x < 0\\x< 0\\\text{In interval notation: } x \in (-\infty, 0)[/tex]
The intersection of the two solution will give us the solution to the system of inequalities:
[tex]x \in (-\infty, 4) \cap (-\infty, 0)\\ x \in (-\infty, 0) \\\{x ~| ~x < 0\}[/tex]
Margot is sewing a ribbon on a seam along the perimeter of a square pillow. The side length of the pillow is 2x^2+1 inches, and its perimeter is 4(2x^2+1) inches. If x=3.5, how much Robbin does she need?
A room contains 5 cats and 2 dogs. If the ratio is 5 to 2 the rate can be expressed as 5 cats __ 2 dogs
Answer:
Per is the answer (Apex)
Step-by-step explanation:
The volume of
100
drops of a liquid is
0.1
fluid ounce.
What is the volume of
10,000
drops?
Final answer:
The volume of 10,000 drops of liquid, given that 100 drops equal 0.1 fluid ounce, is calculated to be 10 fluid ounces.
Explanation:
The question is asking to calculate the volume of 10,000 drops of a liquid, given that the volume of 100 drops is 0.1 fluid ounce. First, we determine the volume of a single drop. Then, we multiply that volume by 10,000 to find the total volume.
To start, we have the following relationship:
100 drops = 0.1 fluid ounce.
Next, we calculate the volume of one drop:
1 drop = 0.1 fluid ounce / 100 drops.
Then, we multiply the volume of one drop by 10,000 to find the volume of 10,000 drops:
10,000 drops * (0.1 fluid ounce / 100 drops) = 10 fluid ounces.
Therefore, the volume of 10,000 drops of the liquid is 10 fluid ounces.
Write the phrase as an algerbraic expression. 4 times the sum of a number and 20
write an equation with an even product
product is multiplication:
2 * 2 = 4
Find the quotient of quantity of negative 5 times x to the 3rd power plus 15 times x to the 2nd power minus 10 times x all over negative 5 times x. (5 points)
x2 + 3x − 2
x2 − 3x + 2
−x2 + 15x − 10
x2 − 15x + 10
Answer:
x^2 - 3x +2
Step-by-step explanation:
[tex]\frac{-5x^3+15x^2-10x}{-5x}[/tex]
We divide the whole expression by -5x
When we divide by negative the sign of each term changes
We divide each term separately by -5x
-5x^3 / -5x = x^2
15x^2 / -5x = -3x
-10x/ -5x = +2
So the expression becomes x^2 - 3x +2
Anybody know? Also, what pattern?
Joyce has as much money as George; then they bet 5 cents each and George lost. If, after the bet, George has x cents, how much does Joyce have ?
Joyce would have x + 5 cents after the bet.
Explanation:To determine how much money Joyce has after the bet, we need to consider the information given in the question. It states that Joyce has as much money as George, and after they bet 5 cents each, George lost and ended up with x cents. Since they both bet the same amount and George lost, it means Joyce must have won the bet and still has the original amount of money they each had, plus the 5 cents George lost.
Therefore, Joyce has x + 5 cents after the bet.
Needing this for tomorrow thanks help me please is hurry
39) 6 *15 = 90 in deposits
40) 5 + 10 + 15 = 30 withdrew
41) 35 +90 = 125 - 30 = 95 in the account
If you have 24 square pieces of wood, describe all the different ways you could make a rectangle by placing them side by side
You have 24 square pieces of wood. You could lay them out in the following fashion. First number is the number of rows. Second number is the number of columns. For example:
1,24 is 1 row by 24 columns. Here goes:
1,24
2,12
3,8
4,6
6,4
8,3
12,2
24,1
i believe that's all.
It winds up being the number of ways you can multiply two integers to get 24.
I need some help please
answer (0,10) see pic:
This is the 3rd one I have helped with, you should start seeing a pattern with the answers.
Parallelogram FGHI on the coordinate plane below represents the drawing of a horse trail through a local park: (Via Image)
In order to build a scale model of the trail, the drawing is enlarged on the coordinate plane. If two corners of the trail are at point A(0, 4) and point D(−6, −5), what is another point that could represent a corner of the trail?
1) (4, 4)
2) (11, 4)
3) (6, −5)
4) (−17, −5)
Answer:
Correct choice is 3)
Step-by-step explanation:
Enlargment is a dilation. A dilation is a transformation that preserves parallel lines and each side length of the pre-image parallelogram is multiplied by the same coefficient.
Note that
[tex]\overrightarrow{IF}=(-7-(-9),5-2)=(2,3);\\ \\\overrightarrow{DA}=(0-(-6),4-(-5))=(6,9)=3\cdot (2,3)=3\overrightarrow{IF}.[/tex]
From this statement you can conclude that the factor of dilation is 3.
Since
[tex]\overrightarrow{FG}=(-3-(-7),5-5)=(4,0),[/tex]
then
[tex]\overrightarrow{AB}=3\overrightarrow{FG}=3(4,0)=(12,0)\ \text{or}\ \overrightarrow{BA}=(12,0)[/tex]
and
[tex]\overrightarrow{DC}=(12,0)\ \text{or}\ \overrightarrow{CD}=(12,0)[/tex]
Yhis gives you that B(12,4) (or B(-12,4)) and C(6,-5) (or C(-18,-5)).
Find the excluded value of the rational expression 2x + 6/4x - 8
Answer:
for connections
1.a
2.c
3.d
4.c
Step-by-step explanation:
The total mass of Abdul and his baby brother is 15.25kg . The mass of Abdul and his father is 72.25kg . The mass of Abdul's father is 13 times as heavy as Abdul's baby brother. What is Abdul's mass?
What is the solution to the linear equation?
Phil and Lorena are playing golf. Phils score after the first round is -1 Lorena score is -4 the player with the lower score is the winner Who wins?
Lorena with the score of -4 is the winner.
To determine the winner of the match, we need to look at the following given details:
In golf, the player with the lower score wins. Let's compare Phil and Lorena's scores:Phil's score: -1Lorena's score: -4We know that in negative numbers, the higher count number is lower in value than lower count.For example: -50 is lower than -20.
Hence, we know that -4 is less than -1, Lorena has the lower score and thus wins the game.
Esmerelda rents a car from a company that rents cars by the hour. She has to pay an initial fee of $50, and then they charge her $9 per hour. She has $200 available to spend on car rental. What is the greatest number of hours for which she can rent the car? (The car cannot be rented for part of an hour.)
The correct answer is 16 hours
A piggy bank containing only quarters had a mass of 850 grams when empty and 7822 grams when filled. If a quarter weighs 5.6 grams , estimate the amount of money inside the piggy bank
What is the domain of the function f(w) = 0.5(35 – 2w)? Explain your answer.
If the graph of f(x) has the point (2,7) then what is one point that will be on the graph of f-1(x)
The graph of f^-1 (x) is called the inverse function of f (x). The relationship between the two is that the point (x,y) is on the graph of f (x) if and only if the point (y,x) is on the graph of f^-1 (x).
This means that if the point (2, 7) is on f (x), therefore the point (7, 2) is on f^-1 (x).
Answer: (7, 2)
Answer: The required point is (7, 2).
Step-by-step explanation: Given that the graph of f(x) has the point (2, 7).
We are to find one point that will be on the graph of [tex]f^{-1}(x).[/tex]
We know that
if a point (a, b) lies on the graph of a function g(x), then the point (b, a) will always lie on the the graph of the inverse function [tex]g^{-1}(x).[/tex]
Therefore, the one point that will lie on the graph of [tex]f^{-1}(x)[/tex] is (7, 2).
Thus, the required point is (7, 2).
Think of the number seven. Now add eight to it. Now add four more. Now subtract nine. Now add three. Your answer is _____.
Answer:
7+8+4-9+3=13
Step-by-step explanation:
We have given the statements and we have to figure out the answer.
Think of the number seven i.e. 7
Now add eight to it i.e. 7+8
Now add four more i.e. 7+8+4
Now subtract nine i.e. 7+8+4-9
Now add three i.e. 7+8+4-9+3
Simplification of expression 7+8+4-9+3
Add the terms,
7+8+4-9+3=22-9
Subtract the terms,
7+8+4-9+3=13
Therefore, The answer is 13.
mrs. Williams uses the following recipe for crispy rice treats. She decided to make 2/3 of the recipe. 2 cups of melted butter, 24 oz marshmallow, 13 cups rice crispy treats.
Fraction number is used to represent the part of a whole. For cook the 2/3 of the recipe Mr. Williams need 4/3 cups of melted butter, 16 oz marshmallow, and 26/3 cups of rice crispy treats.
Given -To cook full recipe Mr. Williams needs the 2 cups of melted butter, 24 oz marshmallow, and 13 cups rice crispy treats.
In the given question Mr. Williams wants to cook 2/3 of the recipe. For this he need to add all the ingredients in the 2/3 value as compare to the original recipe units.
Fraction numberFraction number is used to represent the part of a whole.
Required cups of melted butter is,[tex]\rm Butter = \dfrac{2}{3} \times 2[/tex]
[tex]\rm Butter = \dfrac{4}{3}[/tex]
Hence, the for the above question we need 4/3 cups of melted butter.
Required oz marshmallow-[tex]\rm oz \ marshmallow= \dfrac{2}{3} \times 24[/tex]
[tex]\rm oz \ marshmallow= 16[/tex]
Hence, the for the above question we need 16 units of oz marshmallow.
Required cups of rice crispy treats-[tex]\rm Rice \ crispy \ treats=\dfrac{2}{3} \times 13[/tex]
[tex]\rm {Rice \; crispy \; treats}=\dfrac{26}{3}[/tex]
Hence, for cook the 2/3 of the recipe Mr. Williams need 4/3 cups of melted butter, 16 oz marshmallow, and 26/3 cups of rice crispy treats.
Form more about the measurement follow the link-https://brainly.com/question/5014667
A student runs 100 meters in 11 second s . What is the speed of the student
For f(x)=3x+1 and g(x)=x^2-6, find (f/g)(x)
A. 3x+1/x^2-6, x≠±√6
B. x^2-6/3x+1
C. x^2-6/3x+1, x≠-1/3
D. 3x+1/x^2-6
Answer:
Answer is A
Step-by-step explanation:
Solve the inequality for b 10 < -2/3(9+12b)
Final answer:
To solve the inequality 10 < -2/3(9+12b), distribute -2/3 inside the parentheses, simplify, and divide by -8, which reverses the inequality. The solution is b < -2.
Explanation:
To solve the inequality 10 < -2/3(9+12b), we must first distribute the -2/3 across the parentheses:
Multiply -2/3 by 9 to get -6.
Multiply -2/3 by 12b to get -8b.
The inequality now looks like this: 10 < -6 - 8b. Next, we simplify by moving the constant term -6 to the left side:
Add 6 to both sides: 10 + 6 < -8b.
Combine like terms: 16 < -8b.
Finally, we divide both sides by -8, remembering that this reverses the inequality symbol:
Divide by -8: -2 > b or b < -2.
Therefore, the solution to the inequality is b < -2.
Eva has borrowed 200 songs from her friend. She plans to download an equal number of songs on her music player each week for 5 weeks. The graph shows the number of songs left to download, y, for a certain number of weeks, x: A graph titled Song Downloading shows Number of Weeks on x-axis and Number of Songs Left to Download on y-axis. The x-axis scale is shown from 0 to 5 at increments of 1, and the y-axis scale is shown from 0 to 280 at increments of 40. A straight line joins the ordered pairs 0, 200 and 1, 160 and 2, 120 and 3, 80 and 4, 40 and 5, 0. Part A: What is the rate of change and initial value of the function represented by the graph, and what do they represent in this scenario? Show your work to find the rate of change and initial value. (6 points) Part B: Write an equation in slope-intercept form to model the relationship between x and y. (4 points)
PART A)
The rate of change is -40 songs each week, because the amount of songs left to be downloaded decrease by 40 every week.
the initial value is 200 at 0 weeks, which means that there are 200 songs to be downloaded at the beginning
PART B)
calculate the slope:
Answer:
Each week the amount of songs that need to download decreases by 40. So The rate of change is -40 songs each week. The initial value is 200 because that is the number of songs left to download.
Part B:
y = -40x + 200
Rita's mother is 4 times as old as she is. Her grandmother is twice as old as her mother. If the sum of their age is 194, how old are Rita, her mother, and her grandmother?
Through setting up and solving an algebraic equation, we find that Rita is 15 years old, her mother is 60 years old, and her grandmother is 120 years old. These ages satisfy the conditions that the sum of their ages is 194, Rita's mother is 4 times her age, and her grandmother is twice the age of her mother.
Explanation:Let's use algebra to solve the problem of finding the ages of Rita, her mother, and her grandmother. We will start by defining the variable x to represent Rita's age. According to the information provided, Rita's mother's age is 4 times as old as Rita, so we can express that as 4x. The grandmother is twice as old as the mother, which can be written as 2(4x) or 8x.
Next, we need to use the fact that the sum of their ages is 194. We can set up the following equation based on all the information we have:
x (Rita's age) + 4x (Mother's age) + 8x (Grandmother's age) = 194
Combining like terms, we get:
13x = 194
Now, we solve for x by dividing both sides of the equation by 13:
x = 194 / 13
x = 14.923 (As ages are typically expressed as whole numbers, we would round this to the nearest whole number if necessary, but in this case, 194 is evenly divisible by 13, so x = 15).
Now that we know Rita's age, we can find out her mother's and grandmother's ages:
These are the ages of Rita, her mother, and her grandmother.
Define a simulation to represent correct answers on a true-or-false quiz. Use the simulation to find the probability of getting exactly 4 correct answers on a ten-question quiz.
A steel cylinder with a moveable piston on top is filled with helium (He) gas. The force that the piston exerts on the gas is constant, but the volume inside the cylinder doubles, pushing the piston up.
Which of the following answers correctly states the cause for the change described in the scenario?
The temperature increased.The density of the helium atoms decreased.The pressure decreased.The helium atoms increased in size.Final answer:
To determine the probability of passing a 10-question true-false quiz with at least a 70% score when guessing, we calculate the probabilities of getting 7, 8, 9, and 10 answers correct and sum them, using the binomial probability formula.
Explanation:
A student takes a 10-question true-or-false quiz and guesses randomly without studying. To find the probability of getting exactly 4 correct answers out of 10 questions, we can use a binomial probability formula which is P(X=k) = (n choose k) * p^k * (1-p)^(n-k), where 'P(X=k)' is the probability of 'k' successes in 'n' trials, 'p' is the probability of success on a single trial, and '(1-p)' is the probability of failure on a single trial.
In this case, guessing true or false correctly is a 50% chance or 'p' equals 0.5, since there are only two possible outcomes, and 'n' is 10. To calculate the probability of passing the quiz with at least a 70 percent score, we need at least 7 correct answers out of 10. We will calculate the probabilities of getting exactly 7, 8, 9, and 10 correct answers and then sum these probabilities.
The calculation for P(X=7) would be (10 choose 7) * 0.5^7 * 0.5^(10-7). Similarly, we would calculate P(X=8), P(X=9), and P(X=10) using the same formula with different values for 'k'. Once we have these probabilities, we can add them up to find the total probability of scoring at least 70 percent on the quiz.
Remember to round answers to relative frequency and probability problems to four decimal places for accurate results.
suppose an investment of $8200 doubles in value every 7 years. how much is the investment worth after 28 years
Answer:
After 28 years, it will be $131,200
Step-by-step explanation:
It is given that the investment doubles in value every 7 years.
So, after 7 years, it will be 8200 × 2 = 16,400
After 14 years, it will be 16,400 × 2 = 32,800
After 21 years, it will be 32,800 × 2 = 65,600
After 28 years, it will be 65,600 × 2 = 131,200
Hence, the investment is $131,200 worth after 28 years.