3(x + 6) — 2(x + 2) > 10
Answers
Answer:
x > -4
Step-by-step explanation:
Step 1: Simplify both sides of the inequality.
x + 14 > 10
Step 2: Subtract 14 from both sides.
x + 14 − 14 > 10 − 14
x > −4
Hope it helps!
Related Questions
F(x)=2(3-x),find f(-7)
Answers
Answer:
\(f(-7) = 20\)
Step-by-step explanation:
Given:
\(f(x) = 2(3 -x)\)
Solving for \(f(-7)\):
\(f(-7) = 2(3 -(-7)) \\ f(-7) = 2(3 +7) \\ f(-7) = 2(10) \\ f(-7) = 20\)
convert to the unit in the brackets
(1) 6 438m in (kg)
(2) 8,187km in (m)
(3) 6,75m in (cm)
(4) 77cm in (m)
(5) 0,345km in (m)
(6) 127cm² in (mm)²
(7) 144m² in (km)²
(8) 123m³ in (mm)³
(9) 12 430 000cm³ in (m)³
Answers
Answer:
1) 6.438km 2)818,700m 3)6750cm
First is brainliest :) and ill leave a thanks for them. Please and thank you!
(BTW This is one question)
Answers
Answer:
D
Step-by-step explanation:
The y-intercept is the initial amount and the rate of change is the amount she saved each week so that eliminates A and B. Since the y-intercept is 20 the answer is D.
Make a 4-by-4 logic grid on your own paper. Use it to help solve the logic
puzzle and answer the question.
A barbershop, a coffee shop, a flower shop, and a nail salon each have a sign
of a different color: blue, green, red, or purple (but not necessarily in that
order)
The coffee shop and the barbershop are next to the shop with the green sign.
The nail salon is not next to any of the other shops.
The barbershop's sign is either blue or red.
The store with the purple sign is next to the store with the green sign.
Which shop has the purple sign?
A. The coffee shop
B. The flower shop
C. The nail salon
D. The barbershop
Answers
Answer:
A
Step-by-step explanation:
#21
In the diagram, line g is parallel to line h.
Answers
Answer:
2, 3, 4, 5
Step-by-step explanation:
Answer:
I believe 4 of these are correct,
answer choice, 2,3,4and
Step-by-step explanation:
2 and 3 are correct because of the inverse of the parallel theorem and answer choice 4 is just a straight line has an angle of 180. Since angle 3 corresponds to angle 7 also meaning they are congruent. We can say angle 1 and 7 add up to 180. As for answer 5, it is the same side interior thereom
7) What does a multiplier of \( 1.2 \) mean?
Answers
A multiplier of 1.2 means the value is multiplied or increased by a factor of 1.2.
A multiplier is a term used to represent a factor by which a value is multiplied or increased. It is a numeric value that indicates the extent of the increase or expansion of a given quantity. Multiplication by a multiplier results in scaling or changing the magnitude of the original value.
A multiplier of 1.2 indicates that a value will be increased by 20% or multiplied by a factor of 1.2. This means that when the multiplier is applied to the original value, the resulting value will be 1.2 times the original.
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Letg(x) be the reflection of f(x)=x2+6 in the y axis. What is the function of rule for g(x)?
Answers
practice using linear combinations to solve systems of equations. which constants can be multiplied by the equations so one variable will be eliminated when the systems are added together? 5x 13y
Answers
The constants that have to multiply to eliminate one variable from the system are 12 and 5.
The equations are
5x+13y = 232
12x + 7y = 218
Elimination Method
The elimination method is the process of eliminating one of the variables in the system of linear equations using the addition or subtraction methods in conjunction with multiplication or division of coefficients of the variables
Both x term and y terms, choose x terms and apply the elimination method
The coefficient of x in the first equation is 5 and 12 in the second equation
Coefficient is a number that is being multiplied by the variable. 2x+6x+14. The 2x, 6x, and 14 are terms because they are being added together. 2 and x; 6 and x are factors because they are being multiplied together. 2 from 2x and 6 from 6x are the coefficients because they are being multiplied by the variable.
To make it the same
Prime factorization
Prime factorization is a process of writing all numbers as a product of primes.
5 = 5×1
12 = 2×2×3
LCM (5, 12 ) = 2×2×3×5 = 60
Multiply the first equation by 12 and the second equation by 5
60x + 156y = 2784
60x + 35y = 1090
Subtract equation 2 from equation 1
121y = 1694
Eliminated x term
The constants that we have to multiply to eliminate one variable from the system are 12 and 5
The complete question is:
Which constants can be multiplied by the equations so one variable will be eliminated when the systems are added together? 5x + 13y = 232
12x + 7y = 218
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Find an equation of the line that passes through the point (2, -8) and is perpendicular to the line 2x-6y=10
Answers
9514 1404 393
Answer:
3x +y = -2
Step-by-step explanation:
First of all, it is helpful to put the given equation in standard form. We can do that by dividing it by 2 to eliminate the common factor from the numbers.
x -3y = 5
Next, since you want the perpendicular line, you can swap the coefficients of x and y, and negate one of them. This can give you ...
3x +y = (some constant)
The constant will be found using the given point.
3x +y = 3(2) +(-8) = -2 . . . the perpendicular line
An equation is ...
3x +y = -2
Blue points, blue line segments, red points, and red line segments arranged on a Cartesian coordinate plane. Here are the blue points and their coordinates. Point A: (negative nine, 3). Point B: (negative 11, 3). Point C: (negative 10, 3). Point D: (negative 10, 5). Point F: (negative 10, 4). Point E: (negative 11, 4). Here are the red points and their coordinates. Point A-1: (negative 1, 6). Point A-2: (negative 3, 4). Point B-1: (negative 2, 4). Point B-2: (negative 5, 4). Point C-2: (negative 3, 3). Point D-1: (negative 5, 5). Point D-2: (negative 5, 3). Point E-1: (negative 6, 6). Point F-1: (negative 5, 6). A semicircle that lies below its line of symmetry AB. A semicircle that lies above its line of symmetry B-2 A-2. A triangle DEF. A triangle D-1 E-1 F-1. Line segments are drawn from C to D, from A-1 to B-1, from A-2 to B-2, and from C-2 to D-2. Triangle DEF, segment CD, and the semicircle with line of symmetry BA are arranged so that they look like a boat.1.What transformations would you use on the blue triangle to get it to match with the red triangle? Explain your movement using the coordinates of the vertices.
Answers
Transformation blue triangle.
Point D.
coordinates(-10,5)
and the point D1 have coordinates: (-5,5)
The transformation will be over the x-axis:
\(\begin{gathered} D(-10,5) \\ D(-10+5,5)=(-5,5) \end{gathered}\)Point F.
Coordinates(-10,4 ).
Ans the point F1 have coordinates: ( -5,6)
The transformation will be over both axis, x and y:
\(\begin{gathered} F=(-10,4) \\ F(-10+5,\text{ 4+2 })=(-5,\text{ 6}) \end{gathered}\)Point E.
Coordinates: (-11,4)
The point E1 have coordinates: (-6, 6),
The tranformation will be over both axis once again.
\(\begin{gathered} E(-11,\text{ 4}) \\ E(-11+5,\text{ 4+2})=(-6,6) \end{gathered}\)Conclusion: on the x-axis, it shifts 5 points to the right, while on the y-axis it shifts up 2 points only for points E and F.
4.2 Puzzle Time
What Did The Wall Say To The Bookcase?
Answers
"He said he thic," the wall says to the bookcase.
What about the Puzzle Time?A mathematical or numerical puzzle is one that requires strong mathematical reasoning, thought, or consideration to solve. Mathematics is the study of abstract concepts such as numbers, shapes, quantity, space, and change. Young children can investigate key early math concepts such as shapes, sizes, and how and where one puzzle piece fits with another to form pictures or designs using puzzles. Spatial reasoning is required for this type of math. Number puzzles follow a set of rules; you must first figure out the pattern before answering the puzzle.Therefore, "He said he thic," is the correct answer.
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The U.S. Senate has 100 members. For a bill to pass with a supermajority, at least twice as many senators must vote in favor of the bill as vote against it. If each of the 100 senators votes either in favor of or against a bill, how many must vote in favor for it to pass with a supermajority
Answers
At least 67 senators must vote in favor for a bill to pass with a supermajority.
How is the minimum number of senators needed to pass a bill with a supermajority?A supermajority is a voting requirement that surpasses a simple majority and sets a higher threshold for passing certain decisions. In the case of the U.S. Senate, which consists of 100 members, a bill must garner the support of at least twice as many senators voting in favor as those voting against in order to pass with a supermajority. Therefore, to achieve a supermajority, a minimum of 67 senators must vote in favor of the bill.
The purpose of a supermajority requirement is to ensure that significant decisions have substantial support and broad consensus among legislators. By raising the threshold, it becomes more challenging for a small minority to block the passage of a bill, making it more likely that measures with broad support can be enacted into law.
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The dot plot represents the amount of rain recorded by rain gauges in different locations around a city. A number line going from 0. 25 to 2. 75. 0 dots are above 0. 25. 3 dots are above 0. 5. 1 dot is above 0. 75. 3 dots are above 1. 0 dots are above 1. 25. 1 dot is above 1. 5. 2 dots are above 1. 75. 3 dots are above 2. 2 dots are above 2. 25. 1 dot is above 2. 5. 0 dots are above 2. 75. How many rain gauges recorded rainfall? 2 8 11 16.
Answers
The dot plot indicates rainfall recorded by rain gauges. Counting the dots above each value reveals that 16 rain gauges recorded rainfall.
To determine the number of rain gauges that recorded rainfall based on the given dot plot, we need to count the number of dots above each value on the number line.Starting from 0.25, we see that 0 dots are above it. Moving to 0.5, we find 3 dots. Continuing, there is 1 dot above 0.75, 3 dots above 1.0, 0 dots above 1.25, 1 dot above 1.5, 2 dots above 1.75, 3 dots above 2.0, 2 dots above 2.25, 1 dot above 2.5, and finally 0 dots above 2.75.
By adding up the number of dots above each value, we find the total count of rain gauges that recorded rainfall. Summing these values, we get 0 + 3 + 1 + 3 + 0 + 1 + 2 + 3 + 2 + 1 + 0 = 16.Therefore, based on the given dot plot, the number of rain gauges that recorded rainfall is 16.
It's important to note that the brief solution provided assumes that each dot in the dot plot represents a unique rain gauge. If there are multiple dots representing the same rain gauge, the count would need to be adjusted accordingly.
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The results of a company’s study shows that it sells its product to 58% ofall people who make telephone enquiries to them.(i) What is the percentage of enquiries where no sale is made?(ii) If in a month 2800 enquiries are made, how many sales would the company expect to make?
Answers
i) The percentage of enquires where no sale is made is 42%.
ii) If in a month 2,800 inquiries are made, the company would expect to make sales of 1,624.
What is the percentage?The percentage refers to the quotient of a number or value multiplied by 100.
The quotient is the result of a division operation that compares a portion of a quantity with the whole.
The percentage of people who make telephone enquires and buy the company's products = 58%
i) The percentage of the people who make telephone inquiries but do not buy the company's products = 42% (100% - 58%)
ii) The number of inquiries made in a month = 2,800
The expected number of sales for the month = 1,624 (2,800 x 58%)
Thus, based on the percentage of expected sales, when 2,800 inquiries are made, the company should make 1,624 sales.
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Consider the curve defined by x2 + y2 - 3x + 11y = 17. (a) Find dy dx dy dx (b) Under what condition on x is the tangent line to the curve horizontal? The curve has a horizontal tangent line when is -Select- X = (c) Under what condition on y is the tangent line to the curve vertical? The curve has a vertical tangent line when dy is --Select-- dx Y 11 which occurs when which occurs when F
Answers
(a) dy/dx = (3 - 2x) / (2y + 11) (b) The tangent line to the curve is horizontal when x = 3/2. (c) The tangent line to the curve is vertical when y = -11/2.
(a) To find dy/dx, we need to differentiate the equation of the curve with respect to x:
x^2 + y^2 - 3x + 11y = 17
Differentiating both sides implicitly with respect to x:
2x + 2yy' - 3 + 11y' = 0
Rearranging the terms and isolating y':
2yy' + 11y' = 3 - 2x
Factoring out y':
y'(2y + 11) = 3 - 2x
Dividing both sides by (2y + 11):
y' = (3 - 2x) / (2y + 11)
So, dy/dx = (3 - 2x) / (2y + 11).
(b) The tangent line to the curve will be horizontal when dy/dx = 0.
Setting dy/dx = 0:
(3 - 2x) / (2y + 11) = 0
For the numerator to be zero, we have:
3 - 2x = 0
2x = 3
x = 3/2
Therefore, the tangent line to the curve is horizontal when x = 3/2.
(c) The tangent line to the curve will be vertical when the denominator of dy/dx, which is (2y + 11), is equal to zero.
Setting 2y + 11 = 0:
2y = -11
y = -11/2
Therefore, the tangent line to the curve is vertical when y = -11/2.
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Which is the balanced equation for S3 + O2 – SO2?
O O O O
S8 + 016 — 8S02
Se + O₂ → S₂ + O2
Se + O₂ → S₂0₂
Sg + 802 – 8802
Answers
S3 + 3O2 ——-> 3SO2
18. Expand each of the following logarithmic expressions: (49.23 (a) log7 y (b) In (x2(2 + x)) (c) In 81x8y
Answers
The expanded forms are:(a) log7 y(b) 2 ln x + ln (2 + x)(c) ln 81 + 8 ln x + ln y.
(a) expand log7 y:using the logarithmic property logb(xⁿ) = n logb(x), we have:log7 y = log7 (y¹) = 1 log7 y = log7 y.
(b) expand ln (x²(2 + x)):using the logarithmic property ln (ab) = ln a + ln b, we have:ln (x²(2 + x)) = ln (x²) + ln (2 + x) = 2 ln x + ln (2 + x).
(c) expand ln 81x⁸y:using the logarithmic property ln (aⁿ) = n ln a, we have:ln 81x⁸y = ln 81 + ln (x⁸y) = ln 81 + ln (x⁸) + ln y = ln 81 + 8 ln x + ln y.
logarithmic expressions: (49.23 (a) log7 y (b) In (x2(2 + x)) (c) In 81x8y
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The length of perpendicular drawn from the opposite vertex to any side is a) altitude b) median c) perpendicular d) angle bisector
Answers
Answer:
Step-by-step explanation:
Altitude or height
Answer
It is known as altitude
There are three such altitudes and the point of intersection of these altitudes
is called as orthocentre
1. Is x = 2, y = 6, z = 1 a solution to the system of equations? Explain.
1.5x + y-z = 8
x + 3y = 18
2y + z = 13
2. If y = 6, find the values of and z.
x
4x+y=z=15
x + 2y + z = 38
Answers
The solution to the system of equation is x = 6, y = 4, z = 5
The equation is
1.5x + y - z = 8
x + 3y = 18
2y + z = 13
From this we have,
y = 8 - 1.5x + z
x + 3y = 18
2y + z = 13
x + 3(8 - 1.5x + z) = 18
2(8 - 1.5x + z) + z = 13
Apply the Distributive Property
x + 24 - 4.5x + 3z = 18
16 - 3x + 2z + z = 13
Combine like terms
-3.5x + 24 +3z = 18
16 - 3x + 3z = 13
Rearrange variables to the left side of the equation
-3.5x + 3z = 18 - 24
-3x + 3z = 13 - 16
Subtract the two equation
-3.5x + 3z - (-3x + 3z ) = 18-24 - ( 13-16)
-3.5x + 3z + 3x -3z = 18 - 24 - 13 + 16
-3.5x + 3x = 18 - 24 - 13 + 16
x = 6
Substitute the value of x in one of the equation
-3×6 + 3z = 13 - 16
-18 + 3z = -3
3z = 15
z = 5
Now put the value of x and z
y = 8 - 1.5x + z
y = 8 - 1.5×6 + 5
= 8 -9 + 5
= 4
Therefore the solution to the system of equation is x= 6, y = 4 and z = 5
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Future dollars can be converted to constant-value dollars by using this equation:Constant-value dollars = future dollars/ (1+n)^2TrueFalse
Answers
The statement "Future dollars can be converted to constant-value dollars by using this equation: Constant-value dollars = future dollars / (1+n)^2" is False. The correct equation to convert future dollars to constant-value dollars, also known as present value, is: Constant-value dollars = future dollars / (1 + n)^t.
In this equation, 'future dollars' represents the amount of money you have in the future that you want to convert to its equivalent value in today's dollars. The 'n' represents the discount or interest rate per period, and 't' represents the number of periods (typically years) in the future.
The (1 + n)^t term in the denominator is the present value factor, which accounts for the time value of money. It discounts the future dollars to their equivalent value in today's dollars. By dividing the future dollars by this present value factor, you obtain the constant-value dollars or present value.
It's important to note that the exponent 't' in the present value factor can vary depending on the compounding frequency. For example, if the interest rate is an annual rate and the compounding is done annually, then 't' would represent the number of years. If the compounding is done semi-annually, 't' would represent the number of half-years, and so on.
In summary, the correct equation to convert future dollars to constant-value dollars (present value) is: Constant-value dollars = future dollars / (1 + n)^t, where 'n' represents the discount or interest rate, and 't' is the number of periods (typically years) in the future.
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The sixth-grade class is competing in the school field day. There are 32 girls and 56 boys who want to participate. Each team must have the same number of girls and boys. What is the greatest number of teams that can be formed? How many boys and how many girls will be on each team?
Answers
Answer:
8 teams each team will have 4 girls and 4 boys
Step-by-step explanation:
We use GCD to solve this
the GCD of 32 and 24 = 8
8 is the greatest number of teams.
each team must have equal number of boys and girls so divided by two
8/2 = 4
4 girls and 4 boys
I have attached how to do GCD.
If you need any clarification or more explanation pls do mention at the comment section
Hope this helps and if it does pls mark as brainliest answer thx
Which value of x makes this inequality true? 12x-6 < 30 A. X< 36 B. x > 2 C. x 24
Answers
ezra determined that the graph shown below is vertically compressed by a factor of 1/3 from the graph of y=|x| do you agree or disagree? why?
Answers
Answer:
Step-by-step explanation:
no graph was shown
4, 13, 22, ...
Find the 35th term.
Answers
Answer:
im thinking its 40.. tho im not sure im pretty sure it is so im sorry if its wrong
Step-by-step explanation:
Answer:
310
Step-by-step explanation:
1.Find your constant difference of the sequence by subtracting from left to right which is 9
2. find your fomula by using Tn=bn+C (b is your constant difference you can find C by C=T1 -b ) which will then give us 9n-5
3. T(35)=9n-5=9(35)-5=310
Use the graphs to evaluate the expressions below.
Answers
Answer:
\(f(g(4) = \boxed{\bold{0}}\)
\(g(f(3)) = \boxed{\bold{2}}\)
\(f(f(5)) = \boxed{\bold{5}}\)
\(g(g(1)) = \boxed{\bold{4}}\)
Step-by-step explanation:
All the expressions are composite functions where the output of one function is fed as input to the other function to get the composite output
To explain better, I will use the specific values and the graphs of f(x) and g(x)
-----------------------------------------------------------------------------------------------------
f(g(4))
Let's take the first expression \(\displaystyle {f(g(4))}\). The innermost function, \(g(x)\) is first evaluated at \(x = 4\), then this value is used to find the value of the outer function \(f(x)\)
To find the value of this expression
Look at the \(g(x)\) graph on the right, find out the value for g(4). On this graph we see that when x = 4, \(g(x)\) is 3.So \(g(4) = \bold{3}\)
Use this value of \(\bold{3}\) to determine what the value of \(f(x)\) is when
\(x = 3\) .
From the\(f(x)\) graph on the left we see that when
\(x = 3, f(x) = 0\)
So \(f(3) = 0\)
This means that \(f(g(4)) = 0\)
Answer: 0
-----------------------------------------------------------------------------------------------------
The other expressions can be evaluated using similar reasoning.
g(f(3))
First evaluate\(f(x) \:at\: x = 3 == > f(3) = 0 == > g(0) = 2\)
Answer: 2
-----------------------------------------------------------------------------------------------------
f(f(5))
This is a function which is a composite of itself
Find \(f(5) = 2 == > f(2) = 5\)
Answer: 5
-----------------------------------------------------------------------------------------------------
g(g(1))
\(g(1) = 5 == > g(5) = 4\)
Answer: 4
if sarah went to the shop and there was a 10% sale. she was going to buy 7 CDs for $60
Answers
Answer:
10 % of 60$ => 10/100 × 60$ => 6$
6$ for 7 cds => 42 $
Please help. worth 30 pts!!!
Select the correct answer.
Which function is represented by this graph?
A line is graphed in an x y plane, where the x and the y axes range from negative 10 to 10 in increments of 2. The line rises through (negative 10, negative 3), (negative 7, 0) to (1, 8), and then it falls through (9, 0), and (10, negative 1).
A.
f(x) = -|x − 1| + 8
B.
f(x) = -|x − 8| + 1
C.
f(x) = -|x + 8| − 1
D.
f(x) = -|x + 1| − 8
Answers
Answer: ß
Step-by-step explanation:
HELP!
calculate the area of kite ABCD in terms of k, given that the diagonals intersect at point e
Answers
The area of kite ADCD in terms of k is (k + 2) x √(10k² - 16k + 10) square units.
What is a kite?The area of a kite can be calculated by multiplying the lengths of the diagonals and dividing by 2, or by multiplying half the product of the diagonals by the sine of the angle between them.
Equation:Since we are given the lengths of the diagonals, we can use the first method to find the area of kite ADCD.
Let BD = 2k + 4 be the length of the non-vertex diagonal, and AC be the other diagonal
Since the diagonals intersect at point E, they divide each other into two equal parts. Therefore, AE = EC.
Let AE = x = k + 1, and EC = x = 3k - 3.
Using the fact that the diagonals of a kite are perpendicular bisectors of each other, we can find the length of the other diagonal, AC:
AC² = AE² + EC²
AC² = (k + 1)² + (3k - 3)²
AC² = k² + 2k + 1 + 9k²- 18k + 9
AC² = 10k² - 16k + 1
AC = √(10k² - 16k + 10)
Now we can find the area of kite ADCD:
Area = (BD x AC) / 2
Area = ((2k + 4) x √(10k² - 16k + 10)) / 2
Area = (k + 2) x √(10k² - 16k + 10)
Therefore, the area of kite ADCD in terms of k is (k + 2) x √(10k²- 16k + 10) square units.
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find the distance between each pair of points in the coordinate plane.(3,1) and (3,-5)
Answers
We have the following:
\(d(P_1,P_2)=\sqrt[]{(x_2-x_1)^2+(y_2-y_1)^2}\)Now,
\(\begin{gathered} P_1=(3,1)=(x_1,y_1) \\ P_2=(3,-5)=(x_2,y_2) \end{gathered}\)replacing:
\(\begin{gathered} d=\sqrt[]{x_2-x_1)^2+(y_2-y_1)^2} \\ d=\sqrt[]{(3-3)^2+(-5-1_{})^2} \\ d=\sqrt[]{0^2+(-6)^2} \\ d=\sqrt[]{36} \\ d=6 \end{gathered}\)Therefore, the answer is 6 units
what is the potential-energy function for f⃗ ? let u=0 when x=0 . express your answer in terms of α and x .
Answers
Potential energy can be defined as energy that is stored inside an object due to its position or configuration.The potential energy function for f⃗ is given by:-U = α (x^2 / 2)
Given a force vector f⃗ and its corresponding potential energy function u(x,y,z), the force is defined as the negative gradient of the potential energy function. In order to get the potential energy function for f⃗ , we need to integrate force with respect to distance. We know that force is equivalent to the derivative of potential energy with respect to distance, so we can use the fundamental theorem of calculus to solve for u(x).We are given that u=0 when x=0, so we can define our initial condition. Using the above equation, we get:-du/dx = f(x)⇒ du = -f(x)dx Integrating both sides, we get: u(x) = -∫f(x)dx + Cwhere C is a constant of integration. We can solve for C using our initial condition: u(x=0) = 0 = CSo, the potential energy function for f⃗ is:u(x) = -∫f(x)dx + 0Now, we can express f⃗ in terms of α and x, which yields :f⃗ = -αxî where î is the unit vector in the x-direction. Substituting this value for f⃗ into our equation for potential energy function, we get:u(x) = -∫(-αx)dx = 1/2αx² + C.
Therefore, the potential-energy function for f⃗ when u=0 at x=0, and expressed in terms of α and x, is given by u(x) = 1/2αx².
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