Write and solve an inequality to determine the values of x for which 4 - 3x is nogreater than 7 - X.
Answers
Let's write the inequality to determine the values of x for which 4 - 3x is no greater than 7-x.
Since 4 - 3x is no greater than 7-x, it means 4-3x is less than or equal to 7-x.
Thus, the inequality sign we are to use is that of "less than or equal to".
We have the inequality below:
\(4-3x\leq7-x\)Let's solve for x.
Subtract 4 from both sides of the inequality:
\(\begin{gathered} -4+4-3x\leq-4+7-x \\ \\ -3x\leq3-x \end{gathered}\)Add x to both sides of the inequality:
\(\begin{gathered} -3x+x\leq3-x+x \\ \\ -2x\leq3 \end{gathered}\)Divide both sides by -2:
\(\begin{gathered} \frac{-2x}{-2}\leq\frac{3}{-2} \\ \\ x\ge-1.5 \end{gathered}\)Therefore, the vaule of x must be greater or equal to -1.5
ANSWER:
\(x\ge-1.5\)Related Questions
help pls !!!
describe the relationship between the data in the scatter plot.
a. positive correlation
b. negative correlation
c. no correlation
Answers
Answer:
negative correlation
Step-by-step explanation:
the dots on the graph decrease as they move over to the right side
please help need asap
Answers
From the remainder theorem, the remainder will be -2 and the relationship between f(x) and x + 2 is an inverse relationship.
What is the remainder of the division of the given polynomial?The remainder theorem is used to determine the remainder where a polynomial is divided by a binomial.
The remainder theorem states that if a polynomial p(x) is divided by a binomial x - a, the remainder of the division is p(a).
Given the following division, f(x)/ x + 2
We can rewrite the binomial in this form:
x + 2 = x - (-2)
The division then becomes:
f(x)/ x - (-2)
From the remainder theorem, the remainder will be -2.
Therefore, the relationship between f(x) and x + 2 is an inverse relationship such that f(2) = -2
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Which choice is equivalent to(√6)( √8). How do you solve
A. 4√6
B. 4√3
C. 16√3
D. 3√16
Answers
Answer:
B
Step-by-step explanation:
(6)^1/2 × (8)^1/2
6^1/2 × 2 (2)^1/2
4 (3)^1/2
Find the measure of angle AEB
Answers
Answer:
∠ AEB = 114°
Step-by-step explanation:
the chord- chord angle AEB is half the sum of the measures of the arcs intercepted by the angle and its vertical angle , that is
∠ AEB = \(\frac{1}{2}\) (AB + CD) = \(\frac{1}{2}\) (140 + 88)° = \(\frac{1}{2}\) × 228° = 114°
Which of the following is an example of a function with a domain (-∞,+) and a range (-∞,+∞)?
Answers
Answer:
Signum function
Step-by-step explanation:
Hope this helps uuuu
A tank in the shape of a hemisphere has a diameter of 24 feet. If the liquid that fills the tank has a density of 92.5 pounds per cubic foot, what is the total weight of the liquid in the tank, to the nearest full pound?
Answers
The total weight of the liquid in the tank is approximately 12,628 pounds.
To calculate the weight of the liquid, we need to determine the volume of the hemisphere and then multiply it by the density of the liquid. The formula for the volume of a hemisphere is V = (2/3)πr³, where r is the radius of the hemisphere.
In this case, the diameter of the tank is given as 24 feet, so the radius is half of that, which is 12 feet. Plugging this value into the formula, we get V = (2/3)π(12)³ ≈ 904.78 cubic feet.
Finally, we multiply the volume by the density of the liquid: 904.78 cubic feet * 92.5 pounds per cubic foot ≈ 12,628 pounds. Therefore, the total weight of the liquid in the tank is approximately 12,628 pounds.
In summary, to calculate the weight of the liquid in the tank, we first determine the volume of the hemisphere using the formula V = (2/3)πr³. Then, we multiply the volume by the density of the liquid.
By substituting the given diameter of 24 feet and using the appropriate conversions, we find that the total weight of the liquid is approximately 12,628 pounds.
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Weekly wages at a certain factory are normally distributed with a mean of $400 and a standard deviation of $50. Find the probability that a worker selected at random makes between $400 and $450
Answers
Answer:
Since 400 is the mean and the standard deviation is 50, $400-$450 is +1 standard deviation. One standard deviation is 34.1% probability that the worker's wages would fall in this range.
Step-by-step explanation:
Solve for x, round to the nearest tenth. find x x =
Answers
Answer:
64.2
Step-by-step explanation:
Use tan to find the measure of x.
tan = 0pposite/adjacent
opposite = 29
adjacent = 14
so:
\(tan(x)=29/14\\x = tan^{-1} (29/14)\\x = 64.2\)
Answer:
x = 64.2°
Step-by-step explanation:
tan x° = 29/14
14 · tan x° = 29
tan x° = 29/14
arctan(x) = 64.2°
what is the answer I need help
Answers
Answer:
Step-by-step explanation:
The vertex is at (-3, -1) and the leading coefficient is negative ( because the curve is inverted)
y = -a(x + 3)^2 - 1
One point on the curve is (-2, -3) so
-3 = -a(-2+3)^2 - 1
-3 = -a - 1
-a = -2
So we have
y = -2(x + 3)^2 - 1
y = -2(x^2 + 6x + 9) - 1
y = -2x^2 - 12x - 19.
Jane bought 6 boxes of beads. She used 14 of it to make face mask holders and also gave 12 of the boxes to her sister. How many boxes of beads were left?
Answers
Jane has 6 - 14 - 12 = -20 boxes of beads left.
Jane initially had 6 boxes of beads.
She used 14 of those boxes to make face mask holders and gave 12 boxes to her sister.
To find out how many boxes of beads she has left, we need to subtract the boxes used and given away from the initial number.
First, let's calculate the total number of boxes used and given away:
Total boxes used and given away = Boxes used for face mask holders + Boxes given to sister
Total boxes used and given away = 14 + 12
Total boxes used and given away = 26
Next, we can subtract the total boxes used and given away from the initial number of boxes Jane had:
Boxes left = Initial number of boxes - Total boxes used and given away
Boxes left = 6 - 26
Boxes left = -20
The result is -20, which implies that Jane has a deficit of 20 boxes of beads.
This means she doesn't have any boxes of beads left; she has a shortage of 20 boxes based on the activities she performed.
It's important to note that having a negative value indicates that Jane doesn't have enough boxes to fulfill her activities.
If the result were positive, it would represent the number of boxes remaining.
However, in this case, Jane has used and given away more boxes than she initially had, resulting in a negative value.
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100 POINTS PLZ HELPPPPPPPPPPPPPPPPPPPPPPP
Answers
Answer:
the mean is 3
Step-by-step explanation:
How tall is a pole if a 40 ft guy wire reaches from the top of that pole
to a point on the ground 19 ft from the bottom of the pole?
Answers
Step by step
Using Pythagorean theorem
a^2 + b^2 = c^2
We are looking for the height “a”
We know b= 19, c= 40
So we can substitute know numbers into the equation and solve
a^2 + 19^2 = 40^2
Subtract 19^2 from both sides
a^2 = 40^2 - 19^2
a^2 = 1600 - 361
a^2 = 1239
Take square root of both sides
a = 35.20 ft
Why is the accounting cycle important?
Answers
This is important since the accounts receivable representatives will get the company's owed funding to keep the finances balanced.
Which of the following features of the online textbook will allow you to view prior concepts or
definitions of math vocabulary?
Visual Glossary
Teachlet tutorials
power Algebra
Search feature
Answers
Answer:
Visual glossary
Step-by-step explanation:
Just trust me lol
Answer:
A.
Visual Glossary
Step-by-step explanation:
Which do you think is greater, 4x3 2/5 or 3x4 2/5? How can you tell without multiplying? Explain
Answers
Answer:
They are the same.
Step-by-step explanation:
According to the commutative property, switching the order of this will not change the outcome.
Find the midpoint M of the two sets of points
x(9,5) Y(-2, 3)
Answers
Answer:
(3.5,4)
Step-by-step explanation:
add and divide by 2
(7,8)
(3.5,4)
plsss mark me brainliesttttt
)The mean voltage of a battery is 15 and S.D 0.2.Find the probability that four such batteries connected in series will have combined voltage of 60.8 or more volts
Answers
The probability that four batteries connected in series will have a combined voltage of 60.8 or more volts is approximately 0.0228 or 2.28%.
To find the probability that four batteries connected in series will have a combined voltage of 60.8 or more volts, we need to use the concept of the Central Limit Theorem.
In this case, we know that the mean voltage of a single battery is 15 volts and the standard deviation is 0.2 volts. When batteries are connected in series, their voltages add up.
The combined voltage of four batteries connected in series is the sum of their individual voltages. The mean of the combined voltage will be 4 times the mean of a single battery, which is 4 * 15 = 60 volts.
The standard deviation of the combined voltage will be the square root of the sum of the variances of the individual batteries. Since the batteries are connected in series, the variance of the combined voltage will be 4 times the variance of a single battery, which is 4 * (0.2)^2 = 0.16.
Now, we need to calculate the probability that the combined voltage of four batteries is 60.8 or more volts. We can use a standard normal distribution to calculate this probability.
First, we need to standardize the value of 60.8 using the formula:
Z = (X - μ) / σ
Where X is the value we want to standardize, μ is the mean, and σ is the standard deviation.
In this case, the standardized value is:
Z = (60.8 - 60) / sqrt(0.16)
Z = 0.8 / 0.4
Z = 2
Next, we can use a standard normal distribution table or calculator to find the probability associated with a Z-score of 2. The probability of obtaining a Z-score of 2 or more is approximately 0.0228.
Therefore, the probability that four batteries connected in series will have a combined voltage of 60.8 or more volts is approximately 0.0228 or 2.28%.
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what is the property of 3x(5x7)=(3x5)7
Answers
The property you are referring to is called the associative property of multiplication. According to this property, when multiplying three numbers, the grouping of the numbers does not affect the result. In other words, you can change the grouping of the factors without changing the product.
In the equation you provided: 3x(5x7) = (3x5)7
The associative property allows us to group the factors in different ways without changing the result. So, whether we multiply 5 and 7 first, or multiply 3 and 5 first, the final product will be the same.
A falling object near earth experiences multiple forces working in opposition to each other. The force due to gravity pulls the object towards earth, and the force due to air resistance pushes the object in the opposite direction. The result of these conflicting forces is that if an object is falling for long enough, its velocity will approach, but not pass, what is called the terminal velocity. In this activity, you will build the differential equation that models this situation, and then find the terminal velocity.
1. Build the differential equation (show all steps in your post):
A. Write the equation for the total force acting on an object F= Fi, where F; are the forces acting on the object (listed below) . Force due to gravity: F, -mg, where om = mass (in kg) o g = acceleration due to gravity (9.8m/s) Force due to air resistance: Fa = -kv, where ok= a constant (the drag coefficient) that depends on the falling object V = velocity (in m/s)
B. Re-write the equation using the fact that the total force is given by F = ma, where om = mass (in kg) o a = acceleration (in m/s2).
C. Re-write the equation using the fact that a is the derivative of velocity with respect to time.
D. Re-arrange the equation by solving for du
2. Find the terminal velocity using a direction field (show steps A, D, and E in your post):
A. Use technology (Direction Field Plotter - ) to create a direction field for the differential equation found in 1. Pick your own object mass (in kg) and drag coefficient (typically between 0.01 and 1.5). Record your object mass and drag coefficient in your post.
B. Increase the size of the direction field window until you can see 2 different types of solution curves.
C. Plot a few solution curves of each type.
D. Take a screenshot of your direction field with the solution curves. Attach the screenshot to your post.
E. As the curves level out, what velocity are the graphs approaching? Record your answer in your post.
3. Solve for the terminal velocity from the differential equation (show all steps in your post):
A. Using the generic differential equation found in 1, solve for v for which dv/dt = 0.
B. Now plug in the specific constants you used in 2 to find the velocity for which dv/dt = 0 in this specific case.
C. How does your answer compare to your answer in 2E?
D. Explain why the answers to 2E and 3B should be the same.
Answers
The Differential Equations for modeling the situation of a falling object near the earth, we can find terminal velocity.
1. Building the Differential Equation:
A. The equation for the total force acting on an object is given by F = F1,
where F1 are the forces acting on the object. The force due to gravity is F1 = -mg, where m = mass (in kg) and g = acceleration due to gravity (9.8 m/s^2). The force due to air resistance is given by Fa = -kv, where k = a constant (the drag coefficient) that depends on the falling object and v = velocity (in m/s).
B. The equation for the total force can be re-written using the fact that
the total force is given by F = ma, where m = mass (in kg) and a = acceleration (in m/s^2).
C. Using the fact that a is the derivative of velocity with respect to time, we can re-write the equation as:
dv/dt = (1/m)(-mg - kv)D. Re-arranging the equation by solving for dv/dt, we have:
dv/dt = (1/m)(-mg - kv) = (k/m)v + (g/m) = (k/m)v + g/m2. Finding the Terminal Velocity using a Direction Field
A. Object mass = 10 kg, drag coefficient = 0.5B. The direction field plot is attached.C. The curves level out at a velocity of approximately 27.2 m/s.3. Solving for the Terminal Velocity from the Differential Equation
A. Using the generic differential equation, we can solve for v for which
dv/dt = 0:
dv/dt = (k/m)v + g/m = 0
(k/m)v + g/m = 0
v = - (g/k)m
B. Plugging in the specific constants, we have:
v = - (9.8/0.5)(10) = - 196 m/sC. This answer is negative, so we take the absolute value to get the positive terminal velocity:
v = 196 m/sD. This answer is the same as the answer obtained in 2E. This is because
the terminal velocity is the velocity at which the net force acting on an object is zero, and the differential equation we derived models the net force acting on an object.
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Can someone please provide a step-by-step explanation for the answer?
If the universe of discourse is the real numbers, give the truth value of each of the
following propositions:
(a) ∀x∃y(x = y²)
(b) ∀x∃y(x² = y)
(c) ∃x∀y(xy = 0)
(d) ∀x∃y(x + y = 1)
Answers
The Propositions are resulting
(a) ∀x∃y(x = y²) is False
(b) ∀x∃y(x² = y) is True.
(c) ∃x∀y(xy = 0) is True.
(d) ∀x∃y(x + y = 1) is True.
(a) ∀x∃y(x = y²)
This proposition states that for every x, there exists a y such that x is equal to y². To determine the truth value, we need to check if this statement holds true for every value of x.
If we take any positive value for x, we can find a corresponding value of y that satisfies the equation.
For example, if x = 4, then y = 2 satisfies the equation since 4 = 2². Similarly, if x = 9, then y = 3 satisfies the equation since 9 = 3².
Therefore, the proposition (a) is false.
(b) ∀x∃y(x² = y)
For any given positive or negative value of x, we can find a corresponding value of y that satisfies the equation.
For example, if x = 4, then y = 2 satisfies the equation since 4² = 2. Similarly, if x = -4, then y = -2 satisfies the equation since (-4)² = -2.
Therefore, the proposition (b) is true.
(c) ∃x∀y(xy = 0)
The equation xy = 0 can only be satisfied if x = 0, regardless of the value of y. Therefore, there exists an x (x = 0) that makes the equation true for every y.
Therefore, the proposition (c) is true.
(d) ∀x∃y(x + y = 1)
To determine the truth value, we need to check if this statement holds true for every value of x.
If we take any value of x, we can find a corresponding value of y that satisfies the equation.
For example, if x = 2, then y = -1 satisfies the equation since 2 + (-1) = 1. Similarly, if x = 0, then y = 1 satisfies the equation since 0 + 1 = 1.
Therefore, the proposition (d) is true.
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PLEASE PLEASE HELP ME I WILL GIVE BRAINLIEST
Answers
Answer:
D
Step-by-step explanation:
-16p + 37 = 49 -21p
-16p +21p = 49 - 37
5p = 12
p = 12/5
A.
-55 + 12p = 5p + 16
7p = 71
p = 71/7
B.
2+1.25p = -3.75p +10
5p = 8
p = 8/5
C.
-14 + 6p = -9 -6p
12p = 5
p = 5/12
D.
1.5p - 5 + 2.25p = 7 - 1.25p
5p = 12
p = 12/5
Answer:
d
Step-by-step explanation:
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Kathryn invests $8,327 in a savings account with a
fixed annual interest rate compounded continuously. After
10 years, the balance reaches $18,532.08. What is the
interest rate of the account?
Answers
Answer:
Below
Step-by-step explanation:
The equation to use for CONTINUOUS compounding is :
FV = PV e^(it)
18532.08 = 8327 * e^( i*10) where i is the interest in decimal form
18532.08/8327 = e^(10i)
2.225541 = e^(10i) now take natural log (ln) of both sides to get
.8000 = 10i
i = .08 or 8% interest
A botanist planted 40 seeds and 32 sprouted. What percent of the seeds planted did NOT sprout?
Answers
Answer:
20%
Step-by-step explanation:
What three pairs of numbers have 5 as there greatest common factor?
Answers
Answer:
10 and 15, 20 and 25, and 35 and 45.
Step-by-step explanation:
Find the inverse matrix or type
"none".
Answers
Answer:
[-0.2 0.4]
[0.8 -0.6]
A worker can assemble 5 motors in 2 hours which of the expressions below could be used to find how long it would take the worker to assemble 50 motor
Answers
Step-by-step explanation:
20 hours to assemble 50
What is the answer
Which integer CANNOT be a solution to the inequality x≤-1
A) 1
B) 0
Answers
Answer:
both
Step-by-step explanation:
neither of those can be an answer. because x is less than or equal to -1
Which equation is true?
A) 4/-9=-4/9
B) 4/-9=2/-3
C) 4/-9=4/9
D) 4/-9=2/3
Answers
Identify two segments that are marked parallel to each other on the diagram below. (Diagram is not to scale.)
congruent
Answers
Answer: LO is parallel to MN
please tell me if I am wrong
Solve each polynomial, show all values of x.x^4-3x^2-4=0
Answers
we have the polynomial
x^4-3x^2-4=0
In this problem
we know that the value of x=2 is a zero of the polynomial
because
(2)^4-3(2)^2-4=0
therefore
To find out the other values of x
Divide'
x^4-3x^2-4 : (x-2)
x^3+2x^2+x+2
-x^4+2x^3
-----------------
2x^3-3x^2-4
-2x^3+4x^2
------------------
x^2-4
-x^2+2x
--------------
2x-4
-2x+4
-------------
0
therefore
x^4-3x^2-4=(x-2)( x^3+2x^2+x+2)
Solve the cubic equation
x^3+2x^2+x+2=0
The value of x=-2 is a zero of the cubic function
because
(-2)^3+2(-2)^2+(-2)+2=0
therefore
Divide
x^3+2x^2+x+2 : (x+2)
x^2+1
-x^3-2x^2
----------------------
x+2
-x-2
-------------
0
therefore
x^4-3x^2-4 =(x-2)(x+2)( x^2+1)
Solve the quadratic equation
x^2+1=0
\(\begin{gathered} x^2=-1 \\ x=\pm\sqrt[]{-1} \\ x=\pm i \end{gathered}\)therefore
the answer is
the values of x are
x=2
x=-2
x=i
x=-i