3|x−1|+6≤0
Rewrite the inequality in standard form and determine if there is a solution.
The inequality 3 |x−1| + 6 ≤0 Has no solutions.
How to rewrite the inequality?Here we have the absolute value inequality:3 |x−1| + 6 ≤ 0
We need to isolate x,
so let's do that:3 * |x - 1| ≤ -6 |x - 1| ≤ -6/3 |x - 1| ≤ -2
Now notice that it is clear that the absolute value is always a number equal to or larger than zero.
Then there is no absolute value such that the outcome is smaller than -2, so that inequality has no solutions As we can see from the foregoing above in the detailed solution shown.
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The expression, 2/3, can mean which of the following?
A. 2 parts of size 3 each
B. 3 parts of size 2 each
C. 3 parts of size each
D.2 parts of size each
(PLEASE I NEED HELP)
Answer:
i am pretty sure its B..............
4+5(6p+2=24
........
Answer:
\(4+5\left(6p+2\right)=24\)
\(4+5\left(6p+2\right)-4=24-4\)
\(5\left(6p+2\right)=20\)
\(\frac{5\left(6p+2\right)}{5}=\frac{20}{5}\)
\(6p+2=4\)
\(6p+2-2=4-2\)
\(6p=2\)
\(p=\frac{1}{3}\)
PLEASE HELP TODAY!!!! WILL GIVE BRAINLIST
Hello!
We will go tu use the pythagorean theorem!
So:
BA² = BC² + AC²
AC² = BA² - BC²
AC² = 52² - 20²
AC² = 2304
AC = √2304
AC = 48
how do i solve 1-(1+.04/12)^-12x10
To solve the expression 1 - (1 + 0.04/12)^(-12x10), you can follow these steps: Step 1: Simplify the exponent. In this case, -12x10 simplifies to -120.
Step 2: Evaluate the term within the parentheses first. 0.04/12 simplifies to 0.0033333 (approximately).
Step 3: Add 1 to 0.0033333 to get 1.0033333.
Step 4: Raise 1.0033333 to the power of -120.
Step 5: Calculate the value inside the parentheses using a calculator or software. The result is approximately 0.742657.
Step 6: Subtract the value obtained in Step 5 from 1.
1 - 0.742657 = 0.257343 (approximately).
Hence, the value of the expression 1 - (1 + 0.04/12)^(-12x10) is approximately 0.257343.
It's important to follow the order of operations (PEMDAS/BODMAS) when solving mathematical expressions. In this case, the exponent is evaluated first, followed by addition and subtraction. Utilizing a calculator or software that supports exponentiation and parentheses can help simplify complex expressions and obtain accurate results efficiently.
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linda Put $610 in a savings account that pays 1.2% interest each year. Enrique puts $590 in a high-yield account that pays 3.9% interest each year.
PART A: After one year who has more money? How much more?
PART B: After a second year who has more money? How much more?
PART A: Linda has $4.41 more than Enrique after one year.
PART B: Enrique has $12.10 more than Linda after the second year.
PART A: After one year, we can calculate the amount of money each person has in their respective accounts.
For Linda's account:
Principal amount = $610
Interest rate = 1.2%
\(Interest $ earned = Principal $ amount \times (Interest rate/100) = $610 \times (1.2/100) = $7.32\)
\(Total $ amount after one year = Principal amount + Interest earned = $610 + $7.32 = $617.32\)
For Enrique's account:
Principal amount = $590
Interest rate = 3.9%
\(Interest $ earned = Principal amount \times (Interest rate/100) = $590 \times (3.9/100) = $22.91\)
Total amount after one year = Principal amount + Interest earned = $590 + $22.91 = $612.91
Comparing the two amounts, after one year Linda has more money.
The difference in the amount is:
$617.32 - $612.91 = $4.41
Therefore, Linda has $4.41 more than Enrique after one year.
PART B: After a second year, we need to calculate the amounts again.
For Linda's account:
Principal amount = $617.32
Interest rate = 1.2%
\(Interest earned = Principal amount \times (Interest rate/100) = $617.32 \times (1.2/100) = $7.41\)
Total amount after the second year = Principal amount + Interest earned = $617.32 + $7.41 = $624.73
For Enrique's account:
Principal amount = $612.91
Interest rate = 3.9%
\(Interest earned = Principal amount \times (Interest rate/100) = $612.91 \times (3.9/100) = $23.92\)
Total amount after the second year = Principal amount + Interest earned = $612.91 + $23.92 = $636.83
Comparing the two amounts, after the second year Enrique has more money.
The difference in the amount is:
$636.83 - $624.73 = $12.10
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Which graph represents a function?
Answer:
The fourth graph since it passes the vertical line test.
Each input has one output.
Hope this helps :)
Mary spends 2 2 3 hours on math homework every week. She also spends 3 1 3 hours on art homework every week. How much time does Mary spend in total on math and art over 4 weeks?
Answer: This is the answer. please give me the brainliest. Thanks
church,
"From Martina's World"
Martina, a 3-year-old with flaming red hair and bright blue eyes, is admitted to the pediatric unit w
bronchitis. In addition to her medical condition, Martina has autistic disorder. Martina does not seem
nurse's presence in the room but is intensely occupied with a blue stuffed dog. The nurse is prepar
ister scheduled oral medications to the child. Martina's mother is present in the room.
What approach would help the nurse to establish a trusting relationship with Martina
To establish trust with Martina, the nurse should show respect, use non-verbal communication, incorporate play, involve the parent, and individualize the approach.
To establish a trusting relationship with Martina, the nurse can employ several approaches:
Respect and empathy: The nurse should approach Martina with genuine respect and empathy, recognizing her unique needs and individuality. This can be conveyed through a calm and patient demeanor.
Non-verbal communication: Since Martina may not be responsive to verbal cues, the nurse can utilize non-verbal communication to establish connection and trust. This can include maintaining eye contact, using gentle touch, and respecting Martina's personal space.
Play and familiar objects: Given Martina's engagement with the blue stuffed dog, the nurse can incorporate play into their interactions. Bringing familiar objects or toys that Martina finds comforting can help create a sense of familiarity and security.
Parental involvement: Involving Martina's mother in the care process can be beneficial. The nurse can communicate with the mother, seek her input, and involve her in the administration of medications. This helps build trust not only with Martina but also with her caregiver.
Individualized approach: Recognizing Martina's autistic disorder, the nurse should tailor their approach to her specific needs. Understanding her sensory sensitivities and preferences can help create a safe and comfortable environment.
By implementing these strategies, the nurse can foster trust and a positive therapeutic relationship with Martina, promoting her overall well-being and care.
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Complete Question:
What approach would help the nurse establish a trusting relationship with Martina, a 3-year-old with bronchitis and autistic disorder, who is intensely occupied with a blue stuffed dog and does not seem responsive to the nurse's presence in the room, while the mother is also present?
Lani had a box that contained: 1 blue marble 1 green marble 1 purple marble 1 yellow marble 2 red marbles Lani removed one marble without looking and she recorded the result. She placed the marble back in the box and repeated the procedure one more time. What is the probability that she removed a red marble followed by a blue marble?
Answer:
16.66 and 0.33 im pretty sure
Step-by-step explanation:
A square and a rectangle have the same area. If the dimensions of the rectangle are 4 ft by 16 ft, how long is a side of the square?
A 10 ft
B. 8 ft
C 32 ft
D. 6ft
E 20 ft
9514 1404 393
Answer:
B. 8 ft
Step-by-step explanation:
The area of the rectangle is ...
A = LW = (16 ft)(4 ft) = 64 ft²
The area of the square in terms of its side length is ...
A = s²
For the square to have the area of the rectangle, its side length must be ...
64 ft² = s²
s = √(64 ft²) = 8 ft
A side of the square is 8 feet long.
find the area of the parallelogram. The figure is not drawn to scale.
Answer:
1330 in.
Step-by-step explanation:
38 x 35 = 1330
Answer:
1330
Step-by-step explanation:
area = b x h
base (38)
height (35)
38 x 35 = 1330
A radio tower is located on a coordinate system measured in miles. The range of a signal in a particular direction is modeled by a quadratic function where the boundary of the signal starts at the vertex at (4, 2). It passes through the point (5, 4). A linear road connects points (–3, 7) and (8, 2). Which system of equations can be used to determine whether the road intersects the boundary of the tower’s signal?
StartLayout Enlarged Left-Brace 1st Row y minus 2 (x minus 4) squared = 2 2nd Row 5 x + 11 y = 62 EndLayout
StartLayout Enlarged Left-Brace 1st Row y minus (x minus 4) squared = 2 2nd Row 5 x + 11 y = 62 EndLayout
StartLayout Enlarged Left-Brace 1st Row y minus (x minus 4) squared = 2 2nd Row 11 x + 5 y = 2 EndLayout
StartLayout Enlarged Left-Brace 1st Row y minus 2 (x minus 4) squared = 2 2nd Row 11 x + 5 y = 2 EndLayout
Modeling this scenario with a system of equations using a linear function and a quadratic function yields the following:
y = 2(x - 4)² + 2.
5x + 11y = 62.
What is the quadratic equation?A quadratic function with vertex (h,k), may be represented by the equation:
y = a(x - h)² + k
Because the vertex of this issue is located at (4,2), we may deduce that h = 4 and k = 2, and the equation for this problem is as follows:
y = a(x - 4)² + 2.
Because it goes through the location characterized by its coordinates (5, 4), we may determine a by establishing that when x = 5, y = 4.
4 = a + 2.
a = 2.
Thus the equation is:
y = 2(x - 4)² + 2.
The slope, denoted by m, is the rate of change, or the degree to which y deviates from its initial value for each unit of x that is added.
The y-intercept, denoted by the letter b, is the value of the variable y when the variable x is equal to zero. It may also be construed as the beginning value of the function.
Because the road links the locations (–3, 7) and (8, 2), the slope may be calculated as follows:
m = (2 - 7)/(8 - (-3)) = -5/11.
Then:
y = -5/11x + b.
When x = 8, y = 2, hence we use it to find b as follows:
2 = -40/11 + b
b = 62/11.
Then the equation is:
y = -5/11x + 62/11.
5x + 11y = 62.
The system of equations is:
y = 2(x - 4)² + 2.
5x + 11y = 62.
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Answer:
a edge
Step-by-step explanation:
Rewrite the expression with a single base and exponent. (3^2*3^3)^3
The expression can be rewritten by given term as; 3^15
We need to simplify the expression below:
(3^2 x 3^3)^3
Remember that we can add these exponents, so we get:
(9 x 9)^3 = 81^3
Then we can rewrite this as:
531441
Takin the product between the exponents we will get:
(3^5)^3
Thus, the solution is 3^15
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which one is it help ASAP
Answer:
The solution is (>)
Step-by-step explanation:
It can be said this is bigger because the number 7 is bigger than 6. The language is simple like this, for example we ignore the 2, the number 75 and 60 is clearly bigger than 75. It's the same as 2.75 with 2.6. So the number is 2.75 bigger than 2.6
simplify the following expression. (9x^2-2x+7)+(4x^2+7x+2)
Select all the correct measures of center and variation for the following data set.
10, 20, 31, 17, 18, 5, 22, 25, 14, 43
First quartile = 12
IQR = 11
Median = 19
Third quartile = 25
MAD = 7
Answer:
Median = 19
IQR = 11
Third quartile = 25
Step-by-step explanation:
Just caculate it...
find the vertexform (x)=x2-12x+36
Answer:
Vertex form pf y = x^2 + 12x + 36.
Step-by-step explanation:
y = (x + 6)^2
x-coordinate of vertex:
(x + 6) = 0--> x = - 6
y-coordinate of vertex: y = y(-6) = 36 - 72 + 36 = 0
Vertex form: y = (x + 6)^2
Answer:
2
Step-by-step explanation:
X=x 2-12x+36
X+X+12x=38
14x=38
X=38/14
X=2
The ratio of red pens to blue pens in maxs drawer is 4 to 5 how many red pens and how many blue pens are there in the drawer if there are 342 pens altogether? HELP PLEASE
There are 152 red pens and 190 blue pens in Max's drawer, given that there are a total of 342 pens altogether.
Let's solve the problem step by step:
Identify the given information:
The ratio of red pens to blue pens is 4 to 5.
There are a total of 342 pens in the drawer.
Set up the ratio equation:
Let's assume the number of red pens is 4x, and the number of blue pens is 5x.
Here, 'x' is a scaling factor that allows us to find the actual number of pens.
We can write the equation as: 4x + 5x = 342.
Simplify and solve the equation:
Combining like terms, we have 9x = 342.
Divide both sides of the equation by 9 to solve for 'x':
x = 342 / 9 = 38.
Calculate the number of red pens and blue pens:
Now that we have the value of 'x', we can find the number of red and blue pens:
Number of red pens: 4x = 4 × 38 = 152.
Number of blue pens: 5x = 5 × 38 = 190.
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A new car is purchased for $26,000 and over time its value depreciates by one half
every 5 years. What is the value of the car 7 years after it was purchased, to the
nearest hundred dollars?
Answer: $203
Step-by-step explanation: We first start out with the exponential decay model which is y=a(1-r)^t, then plug in the numbers of your problem:
-y=26,000(1-0.50)^7
-y=26,000*0.50^7
-y=26,000*0.0078125
-y=203.125
Then, after rounding to the nearest hundred dollars you get your answer....
:) hope this helped a bit
The value of the car 7 years after it was purchased will be $203.
What is exponential decay?A quantity lowers gradually at first during exponential decay before rapidly declining after that. Half-life may be calculated using the exponential decay formula, which is also used to estimate population decrease.
It is given that, A brand-new car costs $26,000 to buy, and every five years, its value decreases by 50%.
We have to find the value of the car 7 years after it was purchased
The exponential decay model, y=a(1-r)t, is where we begin. The data from your problem are then entered.
y=-26,000(1-0.50)^7
y=-26,000*0.50^7
y=-26,000*0.0078125
y=-203.125 (-ve shows the value is declining)
Thus, the car will be worth $203 seven years after it was bought.
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The youth group is going on a trip to the state fair. The trip costs $63. Include in that price is $13 for a concert ticket and the cost of 2 passes, one for the rides and one for the game booths. Each of the passes costs the same price. Write an equation represents the cost of the trip, and determine the price of one pass. Solve your equation by showing your work and steps.
Answer: 13 + 2x = 63 and the cost of one ticket is $25 (x=25)
Step-by-step explanation:
Build the equation from what it tells you.
The entire trip costs $63
The concert ticket that is included costs $13
Two passes cost the same amount, use x for what you don't know, 2x.
So, 13 + 2x = 63.
Find x = cost one pass.
13 + 2x = 63
-13. -13
2x= 50
2x/2= 50/2
x= 25
solve the following inequality for z. write your answer in simplest form. -9-(2z-7)>-2z-6-5z
Answer:
z > -4/5
Step-by-step explanation:
-9 - (2z - 7) > -2z - 6 - 5z
Get rid of the parenthesis
*There is the number one in front of the parenthesis.-9 - 2z + 7 > -2z - 6 - 5z
Combine like terms:
-2 - 2z > -7z - 6
+2 > +2
Add 2 to both sides.
-2z > -7z - 4
+7z > +7z
Add 7 to both sides.
5z > -4
Divide both sides by 5 to get z.
z > -4/5
The sign stays the same unless you divide by a negative number---------------------------------
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Hope this helps! :)
5
Enter the correct answer in the box.
Solve the quadratic equation by completing the square.
2x² + 12x = 66
Fill in the values of a and b to complete the solutions.
x=a-√b
x=a+√b
The values of a and b are a = -3 and b = 42. The solutions for x can be written as:
x = -3 - √42
x = -3 + √42
To solve the quadratic equation 2x² + 12x = 66 by completing the square, we need to follow these steps:
Step 1: Move the constant term to the right side:
2x² + 12x - 66 = 0
Step 2: Divide the equation by the leading coefficient (2):
x² + 6x - 33 = 0
Step 3: To complete the square, we take half of the coefficient of x, square it, and add it to both sides of the equation:
x² + 6x + (6/2)² = 33 + (6/2)²
x² + 6x + 9 = 33 + 9
x² + 6x + 9 = 42
Step 4: Rewrite the left side as a perfect square:
(x + 3)² = 42
Step 5: Take the square root of both sides:
√(x + 3)² = ±√42
x + 3 = ±√42
Step 6: Solve for x:
x = -3 ± √42.
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Simplify.
9a +4b+4+4a +5b+7
Answer:
13a + 9b + 11
Step-by-step explanation:
9a + 4a = 13a4b + 5b = 9b4 + 7 = 11Put them together: 13a + 9b + 11I hope this helps!
Answer:
13a+ 9b+ 11
Step-by-step explanation:
9a+4a= 13a
4b+ 5b= 9b
4+7=11
Aisha's softball coach can buy equipment for 8 players for $3080 or for 6 players for $2430. Which option is the better deal? Explain.
Answer:
Equipamiento para 8 jugadores
Explanation:
Porque la diferencia de dinero no es muy grande ni muy pequeña, por lo que obtienes equipamiento para más jugadores a un buen precio.
a) (10 pts) Re-express the given differential equation as a first order differential equation by utilizing matrix
and vector notation and in accordance with ()
= () form.
b) (10 pts) Is the system obtained in (a) stable, neutrally stable of unstable? Determine this using matrix.
c) (10 pts) Compute the eigenvalues and eigenvectors of matrix.
d) (10 pts) Using the results computed in (c) find and matrices and show that =
−
relationship
(i.e., the diagonalization relationship) is a valid relationship.
a) To re-express the given differential equation as a first-order differential equation using matrix and vector notation, we can rewrite it in the form:
\(x' = Ax\)
where x is a vector and A is a square matrix.
b) To determine the stability of the system obtained in part (a), we need to analyze the eigenvalues of matrix A.
If all eigenvalues have negative real parts, the system is stable.
If at least one eigenvalue has a zero real part, the system is neutrally stable.
If at least one eigenvalue has a positive real part, the system is unstable.
c) To compute the eigenvalues and eigenvectors of matrix A, we solve the characteristic equation
\(det(A - \lambda I) = 0\),
where λ is the eigenvalue and I is the identity matrix.
By solving this equation, we obtain the eigenvalues.
Substituting each eigenvalue into the equation
\((A - \lambda I)v = 0\),
where v is the eigenvector, we can solve for the eigenvectors.
d) Once we have computed the eigenvalues and eigenvectors of matrix A, we can construct the diagonalization relationship as follows:
\(A = PDP^{(-1)}\)
where P is a matrix whose columns are the eigenvectors of A, and D is a diagonal matrix whose diagonal elements are the eigenvalues of A.
To show that this relationship is valid, we can compute \(PDP^{(-1)}\) and verify that it equals A.
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Suppose water flows from a shower at a rate of 0.44 cubic feet per minute. Do you use more water by
taking an 8-minute shower or by filling a bathtub with 0.45 cubic yards of water, and by how much?
well, if the water is coming out at 0.44 ft³ per minute, and you take a shower for 8 mins, that simply means you used 8*0.44 ft³, or namely 3.52 ft³.
what if you instead fill the bathtub with 0.45 yd³? is that more or less than 3.52ft³?
\(\begin{array}{ccll} yard&(yard)^2&(yard)^3\\ \cline{1-3} (3~ft)&(3~ft)^2&(3~ft)^3\\ 3~ft&3^2~ft^2&3^3~ft^3\\ &9~ft^2&27~ft^3 \end{array}\)
so then, there are that many ft³ in a yd³, so how many will there be in 0.45yd³ anyway?
\(\begin{array}{ccll} yd^3&ft^3\\ \cline{1-2} 1&27\\ 0.45&x \end{array}\implies \cfrac{1}{0.45}=\cfrac{27}{x}\implies x=27(0.45)\implies x=12.15~ft^3\)
well, then you'd use more water with the 0.45yd³ and some soap btw, by how much more? 12.15 - 3.52 = 8.63 ft³.
Taking an 8-minute shower uses less water than filling a bathtub with 0.45 cubic yards of water.
Given that;
Suppose water flows from a shower at a rate of 0.44 cubic feet per minute.
For the shower, the flow rate is 0.44 cubic feet per minute, and you take an 8-minute shower.
So, the total amount of water used in the shower is:
0.44 cubic feet/minute × 8 minutes
= 3.52 cubic feet
Now let's convert cubic feet to cubic yards since the bathtub is measured in cubic yards.
There are 27 cubic feet in 1 cubic yard, so:
3.52 cubic feet × (1 cubic yard / 27 cubic feet)
= 0.1304 cubic yards
Therefore, the water usage for an 8-minute shower is 0.1304 cubic yards.
On the other hand, when filling a bathtub with 0.45 cubic yards of water, that is the exact amount of water used.
Comparing the two scenarios, we can see that taking an 8-minute shower uses less water than filling a bathtub with 0.45 cubic yards of water.
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please help me with this
Answer:
F
Step-by-step explanation:
64x³ = -1
x³ = -1/64
x = ∛-1/∛64
x = -1/4
Answer:
x = - \(\frac{1}{4}\)
Step-by-step explanation:
64x³+1=0
Add 1 to both sides:
64x³=-1
Divide both sides by 64:
x³=-\(\frac{1}{64}\)
Find cubed root of both sides:
x=-\(\sqrt[3]{\frac{1}{64}}\)
Note that \(\sqrt[n]{\frac{a}{b}}=\frac{\sqrt[n]{a}}{\sqrt[n]{b}}\) :
x=-\(\frac{\sqrt[3]{1} }{\sqrt[3]{64} }\)
Evaluate:
x = - \(\frac{1}{4}\)
A quadrilateral is shown.
H
6.5
5.51
What is the area of the quadrilateral? Enter the answer in the box.
The calculated area of the quadrilateral is 35.82 square units.
What is the area of the quadrilateral?Given that
BAse = 6.5
Height = 5.51
To find the area of a quadrilateral, we need to multiply the base by the height.
Area of quadrilateral = base x height
Substituting the given values, we get:
Area = 6.5 x 5.51
Area = 35.815
Rounding to the nearest hundredth, the area of the quadrilateral is 35.82 square units.
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help with his math question please
Answer:
Exact: -41/20 Decimal: -2.05
Step-by-step explanation:
Answer:
41
----------_______
20
Decimal: :-2.05