Which choice is the solution to the inequality below?
6x>72
OA. x< 12
OB. x> 12
OC. x2 72
OD. x>72
Answers
The solution to the inequality 6x > 72 is option B x > 12
What is an inequality?
An inequality in mathematics is a relation that compares two numbers or other mathematical expressions in an unequal way. The majority of the time, size comparisons between two numbers on the number line are made. Different types of inequalities are represented by a variety of notations, including:
The symbol a < b indicates that a is smaller than b.
When a > b is used, it indicates that a is bigger than b.
A is not equivalent to b in any scenario. Since a is strictly less than or strictly greater than b, these relationships are known as stringent inequalities. Equivalence is not considered.
There are two forms of inequality relations that are not strict, in contrast to strict inequalities:
The notation a ≤ b or a ⩽ b means that a is less than or equal to b (or, equivalently, at most b, or not greater than b).
The notation a ≥ b or a ⩾ b means that a is greater than or equal to b (or, equivalently, at least b, or not less than b).
Given, the inequality is 6x>72
6x > 72
Dividing by 6 on both sides of inequality, we get,
6x/6 > 72/6
⇒ x > 12
Hence, option B is correct.
The solution to the inequality 6x > 72 is option B, x > 12
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Related Questions
in the parallelogram ABCD is shown below, segment EB bisects angle ABC if m angle A = 40 degrees thenm angle BED is
1. 40 degrees
2. 70 degrees
3.110 degrees
4. 140 degrees
Answers
Answer:
110°
Step-by-step explanation:
\(m\angle C=40^{\circ}\) (opposite angles of a parallelogram are congruent)
[texm\angle ABC=140^{\circ}\) (adjacent angles of a parallelogram are supplementary)
\(m\angle EBC=70^{\circ}\) (angle bisector)
\(m\angle BED=110^{\circ}\) (exterior angle theorem)
what is the measure that is complementary to an 20 degree angle
Answers
algebraaaaaaaaaaaaaaaaaaaaaaaaaaa
Answers
The factors of the cubic function f(x) = 27x³ + 8 is (3x + 2) and (9x² - 6x + 4) .
How to find the factors of a cubic function?The factors of the cubic function f(x) = 27x³ + 8 can be found as follows:
Let's factorise the cubic function to find the factors. Hence,
27x³ + 8
Therefore, the cube root of 27 is 3 . This implies 3³ = 27. Also the cube root of x³ is x. The cube root of 8 is 2. This implies 2³ = 8
Using the cube root, let's factorise the cubic function as follows:
27x³ + 8 = (3x)³ + 2³ = (3x + 2)(9x² - 6x + 4)
Therefore, the factors are (3x + 2) and (9x² - 6x + 4)
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3 3 Given matrices 3 - 1 0 and B = 3 a 0. Find the values of c, d and e such that 0 10 AB=14I
Answers
Given:
The matrix A and B is,
\(A=\begin{bmatrix}{5} & {3} & {0} \\ {3} & {-1} & {0} \\ {0} & {0} & {2}\end{bmatrix},B=\begin{bmatrix}{c} & {3} & {0} \\ {3} & {d} & {0} \\ {0} & {0} & {e}\end{bmatrix}\)Take the matrix multiplication,
\(AB=\begin{bmatrix}{5c+9} & {15+3d} & {0} \\ {3c-3} & {9-d} & {0} \\ {0} & {0} & {2e}\end{bmatrix}\)Now, use the given condition,
\(\begin{gathered} AB=14I \\ \begin{bmatrix}{5c+9} & {15+3d} & {0} \\ {3c-3} & {9-d} & {0} \\ {0} & {0} & {2e}\end{bmatrix}=\begin{bmatrix}{14} & {0} & {0} \\ {0} & {14} & {0} \\ {0} & {0} & {14}\end{bmatrix} \\ \Rightarrow5c+9=14,15+3d=0 \\ 3c-3=0,9-d=14 \\ 2e=14 \\ \text{Take,}5c+9=14 \\ 5c=5 \\ c=1 \\ 15+3d=0 \\ 3d=-15 \\ d=-5 \\ And,2e=14\Rightarrow e=7 \end{gathered}\)Answer: c = 1, d = -5, e=7
=2x-1
7) through: (-4,-4), parallel to y=-
3
=2x-4
9) through: (-4,-4), parallel to y =
11) through: (5,-2), perp. to y =
y=²x-5
13) through: (-2, 5), perp. to y = x + 2
8) through: (1, 0), parallel to y = 2x - 1
5
10) through: (5, 5), perp. to y = --
y = ²√x + 4
12) through: (3,-2), perp. to y = -
14) through: (-4, 0), perp. to y = -
Answers
The equation of the lines parallel or perpendicular to another line and that pass through a point are listed below:
Case 7: y = (7 / 4) · x + 3
Case 8: y = 2 · x + 1
Case 9: y = (3 / 2) · x + 2
Case 10: y = (6 / 5) · x - 1
Case 11: y = - (2 / 5) · x
Case 12: y = - (5 / 2) · x - 19 / 2
Case 13: y = - x + 3
Case 14: y = - (5 / 4) · x - 5
How to derive the equation of a line
In this problem we have eight cases of line equations parallel or perpendicular to a line and that pass through a point. The equation of a line is an expression of the form:
y = m · x + b
Where:
x - Independent variable.y - Dependent variable.m - Slopeb - InterceptThere are the following relationships between two lines:
Two lines are parallel when they have the same slope.Two lines are perpendicular when the product of their slopes is equal to - 1.Now we proceed to determine the line equations:
Case 7
Slope
m = 7 / 4
m' = 7 / 4
Intercept
b = y - m · x
b = - 4 - (7 / 4) · (- 4)
b = - 4 + 7
b = 3
Equation of the line
y = (7 / 4) · x + 3
Case 8
Slope
m = 2
m' = 2
Intercept
b = 1 - 2 · 0
b = 1
Equation of the line
y = 2 · x + 1
Case 9
Slope
m = 3 / 2
m' = 3 / 2
Intercept
b = - 4 - (3 / 2) · (- 4)
b = - 4 + 6
b = 2
Equation of the line
y = (3 / 2) · x + 2
Case 10
Slope
m = - 5 / 6
m' = 6 / 5
Intercept
b = 5 - (6 / 5) · 5
b = 5 - 6
b = - 1
Equation of the line
y = (6 / 5) · x - 1
Case 11
Slope
m = 5 / 2
m' = - 2 / 5
Intercept
b = - 2 - (- 2 / 5) · 5
b = 0
Equation of the line
y = - (2 / 5) · x
Case 12
Slope
m = 2 / 5
m' = - 5 / 2
Intercept
b = - 2 + (- 5 / 2) · 3
b = - 2 - 15 / 2
b = - 4 / 2 - 15 / 2
b = - 19 / 2
Equation of the line
y = - (5 / 2) · x - 19 / 2
Case 13
Slope
m = 1
m' = - 1
Intercept
b = 5 - (- 1) · (- 2)
b = 3
Equation of the line
y = - x + 3
Case 14
Slope
m = 4 / 5
m' = - 5 / 4
Intercept
b = 0 - (- 5 / 4) · (- 4)
b = 0 - 5
b = - 5
Equation of the line
y = - (5 / 4) · x - 5
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If you can walk 5.3 miles in 2.5 hours, how many minutes does it take to walk 3.18 miles? Round to 1 decimal.
Answers
Answer:
90min
Step-by-step explanation:
we can solve the first part by means of the rule of three:
5.3miles ----2.5 hour
3.18miles----x
then
\(x=\frac{3.18*2.5}{5.3} \\x=\frac{7.95}{5.3} \\x=1.5 hours\)
Now we must convert hours to minutes:
1.5 hours = 1.5hours (1)
1.5 hours =1.5 hours \(\frac{60min}{1 hours}\)
1.5 hours =(1.5)(60) min
1,.5 hours =90min
What is the value of f(2)?
Answers
Question:
What is the equation?
Find the slope of the line in the picture
Answers
Answer: The slope is 0
Step-by-step explanation: hortizontal lines have a slope of 0 while vertical lines have undefined slope
A bowl contains an apple, a plum, a pear, and a banana. How many different pairs of fruit can be selected from the bowl
Answers
Based on the information given about the combination, the number of different parts of fruits that can be selected from the bowl will be 6.
Solving the combination.Since the bowl contains an apple, a plum, a pear, and a banana, the different pairs of fruit that can be selected from the bowl will be 4C2.
We can solve this further which will be:
= 4C2
= 4! /2! (4 - 2)!
= 4! / 2!2!
= (4 × 3 × 2)/ 2 × 2
= 24/4
= 6
Therefore, 6 different pairs of fruit can be selected.
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HELPPPP me pleaseeeee
Answers
Answer:
\(-2077\)
Step-by-step explanation:
\(i=1(-3-4)=-7(first)\)
\(i=2(-3-4*2)=-11\)
\(i=3(-3-4*3)=-15\)
\(i=31(-3-4*31)=-127(last)\)
Difference= -11-(-7)= -4
\(sum=\frac{n}{2}\)
\(= \frac{31}{2}[-7+(-127)]\)
\(=\frac{31}{2}*(-134)\)
\(=31*(-67)\)
\(= -2077\)
✧༝┉˚*❋ ❋ ❋┉༝✧
hope it helps..
have a great day!!
Compute the required rate of return on two stocks with beta values of 0.5 and 2 respectively assuming the risk-
free rate of 5% and the market return of 10% using the capital asset pricing model. Please show work. Thank you.
Answers
The required rate of return for the stock with a beta of 0.5 is 7.5% and for the stock with a beta of 2 is 15%.
What is Rate of return?Rate of return is the amount of profit or loss earned on an investment over a certain period of time, expressed as a percentage of the initial investment or total asset value.
What is stock?A stock is a type of security that represents ownership in a company. Investors buy stocks to become shareholders and share in the company's profits and losses.
According to the given information:
The Capital Asset Pricing Model (CAPM) is expressed as:
R = Rf + beta*(Rm - Rf)
Where:
R = Required rate of return
Rf = Risk-free rate of return
beta = Beta coefficient (systematic risk)
Rm = Expected market return
Using the given values, we can compute the required rate of return for each stock:
Stock with beta of 0.5:
R = 5% + 0.5*(10% - 5%)
R = 7.5%
Stock with beta of 2:
R = 5% + 2*(10% - 5%)
R = 15%
Therefore, the required rate of return for the stock with beta of 0.5 is 7.5%, and the required rate of return for the stock with beta of 2 is 15%.
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how to solve this question?
Answers
The revised Doubtful Debts Provision should be, $4,555.
Now, Using a net debtors value of $91,100 and a provision rate of 5%, use the calculation to get the adjusted Provision for Doubtful Debts (PDD):
Net Debts x Provision Rate equals Adjusted PDD.
The computation would then be:
= $91,100 x 0.05
= $4,555 is the adjusted PDD.
Because of the additional $550 in bad debt and the revised net debtors value of $91,100, the Provision for Doubtful Debts must be raised by ,
= $4,555 - $3,500
= $1,055
Hence, The revised Doubtful Debts Provision should be $4,555.
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find the derivative of tan^-1 x
Answers
Five less than twice the value of a number is equal to three times the quantity of 4 more than 1/2 the number what is the number let x be the number right and solve an equation to find x show your work.
Answers
The value of the number is x = 34.
Let's break down the problem and solve it step by step.
1. "Five less than twice the value of a number": This can be represented as 2x - 5, where x is the number.
2. "Three times the quantity of 4 more than 1/2 the number": This can be represented as 3 * (x/2 + 4).
According to the problem statement, the two expressions are equal. We can set up the equation as follows:
2x - 5 = 3 * (x/2 + 4)
Now, let's solve the equation:
2x - 5 = 3 * (x/2 + 4)
Distribute the 3 to both terms inside the parentheses:
2x - 5 = (3/2)x + 12
Multiply through by 2 to eliminate the fraction:
2(2x - 5) = 2((3/2)x + 12)
4x - 10 = 3x + 24
Next, let's isolate the x term by moving the constant terms to the other side of the equation:
4x - 3x = 24 + 10
Simplify:
x = 34
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How would you eliminate the
denominators of the equation:
2
1
2+4= Ta
3
4
Multiply each term by 4 only
Multiply each term by 3 only
multiply each term by the LCM of 3 and 4
which is 6
multiply each term by the LCM of 3 and 4
which is 12
Answers
Answer:
Multiply each term by LCM of 3 and 4 which is 12
Step-by-step explanation:
I neeed the answer plssss
Answers
Answer:
300km
Step-by-step explanation:
if 1 hr=80
then take 80 and multiply it by 3.75
hope this helps!
please give brainiest if you want<3
Answer:
300km
Step-by-step explanation:
one number is 10 more than another. their product is -25
Answers
Answer: resource - trust me bro
Step-by-step explanation: Let x = the smaller numberLet 2x + 10 = the larger numberx(2x + 10) = 1002x^2 + 10x - 100 = 0Divide both sides of the equation by 2.x^2 + 5x - 50 = 0(x - 5)(x + 10) = 0x - 5 = 0 or x + 10 = 0x = 5 or x = -10, not a positive number2x + 10 = 2(5) + 10 = 20
What is the probability that a randomly chosen balloon animal is yellow or is shaped like a dog?
Answers
from the question,
P(that the balloon animal is yellow) = 0.7
P(the balloon animal has a dog shape) = 0.6
P(that it is yellow and is shaped like a dog) = 0.5
We are to find the probability that a randomly selected balloon is yellow or is shaped like a dog is
\(\begin{gathered} P(\text{balloon yellow or is shaped like a dog) = 0.7 + 0.6 - 0.5} \\ P(\text{balloon yellow or is shaped like a dog) = 0.8} \end{gathered}\)Therefore, the probability that a randomly selected balloon is yellow or is shaped like a dog is 0.8
I'm having trouble answers these questions b-h. I've already answered a. I can provide a photo of a if needed. this assignment is over the pythagorean theorem.
Answers
With the triangles given:
Then, the proportion for first triangle and second triangle would be:
\(\begin{gathered} \frac{b}{c}=\frac{d}{b} \\ \text{Cross multiplication:} \\ b^2=d\cdot c \end{gathered}\)Proportin for first triangle and third triangle:
\(\begin{gathered} \frac{c}{a}=\frac{a}{e} \\ Cross\text{ multiplication} \\ c\cdot e=a^2 \end{gathered}\)f. The equations would be:
\(\begin{gathered} b^2=d\cdot c \\ a^2=c\cdot e \\ a^2+b^2=(d\cdot c)+(c\cdot e) \end{gathered}\)g. Then, factor out a common factor:
\(a^2+b^2=c(d+e)\)h. As a final step, replace the expression inside the parenthesis with one variable and then simplify:
\(\begin{gathered} a^2+b^2=c(c) \\ a^2+b^2=c^2 \end{gathered}\)
A School held an election for student president, there were 9 votes for Liz out of 12 votes in all.
What percent of the votes were for Liz?
Answers
Answer:
75%
Step-by-step explanation:
9/12 then multiply by 100 %
Graph the function -40x^2 + 640x. Label the vertex.
Answers
The graph is given below.
The vertex for the function is located at (8, 1280).
We have,
The given function is a quadratic function of form f(x) = ax² + bx + c, where a = -40, b = 640, and c = 0.
To find the vertex, we need to use the formula:
x = -b/2a
where a = -40 and b = 640.
So,
x = -b/2a = -640/(2(-40)) = 8
Now, we can find the y-coordinate of the vertex by plugging x = 8 into the function:
y = -40(8)^2 + 640(8) = 1280
Therefore,
The vertex for the function is located at (8, 1280).
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-) Aspirin has a half-life of 6 hours in the blood stream. If a person takes 625mg, how long will it take for there to be 150mg left in the bloodstream?
Answers
It will take approximately 25 hours and 1 minute for there to be 150mg of aspirin left in the bloodstream.
We have,
To determine how long it will take for there to be 150mg of aspirin left in the bloodstream, we can use the concept of half-life.
The half-life of aspirin is given as 6 hours, which means that after every 6 hours, the amount of aspirin in the bloodstream reduces by half.
Let's calculate the number of half-lives required to reach 150mg:
Initial amount of aspirin = 625mg
Final amount of aspirin = 150mg
625mg / 150mg = 4.17
This means it will take approximately 4.17 half-lives for the amount of aspirin in the bloodstream to reduce from 625mg to 150mg.
Since each half-life is 6 hours, we can calculate the total time it will take:
Total time = Number of half-lives * Half-life duration
Total time = 4.17 x 6 hours
Total time ≈ 25 hours and 1 minute
Therefore,
It will take approximately 25 hours and 1 minute for there to be 150mg of aspirin left in the bloodstream.
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I don’t know how to do this.
Answers
Answer:
sin(t) = √15/4,
cos(t) = - 1/4,
tan(t) = - √15
Step-by-step explanation:
The coordinates of the terminal point P(x, y) determined by t are x = - 1/4, and y = √15/4;
sin(t) = y = √15/4
cos(t) = x = - 1/4
tan(t) = y/x = √15/4 / - 1/4 = - √15
Chloe runs a farm stand that sells apples and peaches. Each pound of apples sells for
$3 and each pound of peaches sells for $4. Chloe sold 3 times as many pounds of
peaches as pounds of apples and she made $240 altogether. Graphically solve a
system of equations in order to determine the number of pounds of apples sold, x,
and the number of pounds of peaches sold, y.
pls help! plot on a line
Answers
Answer:
3x+4y=240; y=3x16 pounds of apples48 pounds of peachesStep-by-step explanation:
You want a system of equations and a graphical solution for the scenario that the weight of peaches sold (y) is 3 times the weight of apples sold (x), and the revenue from sales of apples at $3/lb and peaches at $4/lb was a total of $240.
EquationsThe revenue equation can be ...
3x +4y = 240
The relation between pounds of each fruit sold can be ...
y = 3x
GraphThe graph is attached. The solution is (x, y) = (16, 48).
16 pounds of apples and 48 pounds of peaches were sold.
__
Additional comment
We note that the 3x in the first equation can be substituted by y using the second equation. This gives 5y=240, or y = 48. Then 3x=48, so x=16. This agrees with the graphical solution, as it should.
A bag contains 3 green marbles and 5 white marbles. Paul picks a marble at random from the
bag and does not put it back in the bag. He then picks another marble from the bag.
a. Construct a probability tree of the problem.
Answers
A probability tree is a visual representation of the possible outcomes of an event or series of events. In this case, the event takes a marble out of the bag.
How to create the tree?The first step in building a probability tree is to create a starting point that represents the first state of the problem. In this case, the starting point is a bag containing 3 green marbles and 5 white marbles.
The next step is to branch from the starting point and show the possible results of the first event. This includes taking out the marble out of the bag. The probability of getting a green marble is 3/8 and the probability of getting a white marble is 5/8.
After the first event, the issue status changes. In this case, the bag contains 2 green marbles and 4 white marbles.
The next step is to branch out from the state after the first event and show the possible outcomes of his second event involving pulling another marble out of his pocket. The probability of getting a green marble is 2/6 and the probability of getting a white marble is 4/6. The final step is to label the endpoints of the tree with the possible outcomes of the problem and the probabilities of each outcome.
The probability tree starts with an sack of 3 green marbles and 5 white marbles, as shown in the design showing the possible outcomes of selecting a marble, the new state of the sack after each selection, and the probability of each outcome
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Phillip mixing 8 oz of Raisins 8 oz of sunflower seeds 12 ounces of almond and 12 oz of dried fruit for a recipe how many pounds of mixed does Philips make with this recipe chooses are2 pounds2 1/2 4 pounds 40 pounds
Answers
Phillip mixing 8 oz of Raisins 8 oz of sunflower seeds 12 ounces of almond and 12 oz of dried fruit for a recipe, therefore:
8 oz + 8oz + 12oz + 12oz = 40oz
Let's make a conversion:
\(undefined\)Which graph correctly represents the information from the table?
Time (s) Speed (m/s)
0 0
2 4
3 6
4 8
6 12
Answers
Answer:
A.
Step-by-step explanation:
A and C are the only graphs it could be because they are the only graphs starting with (0, 0)
Graph C does not have (2, 4) on it but Graph A does meaning that the only possible answer is Graph A
Answer:
Yes, ( A )would be the correct answer
Step-by-step explanation:
Took the test.
Which of the following statements best describes the effect of replacing the graph of y = f(x) with the graph of y = f(x) − 11?
The graph of y = f(x) will shift up 11 units.
The graph of y = f(x) will shift right 11 units.
The graph of y = f(x) will shift left 11 units.
The graph of y = f(x) will shift down 11 units.
Answers
9514 1404 393
Answer:
The graph of y = f(x) will shift down 11 units.
Step-by-step explanation:
The y-coordinate of a point on the graph is the distance above the x-axis. When 11 is subtracted from the y-coordinate, the distance above the x-axis is decreased by 11. That is, the point will shift down 11 units.
please help with this math question! and explain to me please so i understand
Answers
Answer:
360 - 98 = 262
Step-by-step explanation:
Which graph represents a function? Edge 2020
Answers
Answer:
Last Graph
General Formulas and Concepts:
Algebra I
Vertical Line Test - A function's x-values must have only 1 y-value corresponding to it. If the function fails to pass this, it is not a function.Step-by-step explanation:
When we apply the Vertical Line Test to the 1st graph, it does not pass it. Therefore, the 1st graph is not a function.
When we apply the Vertical Line Test to the 2nd graph, it does not pass it. Therefore, the 2nd graph is not a function.
When we apply the Vertical Line Test to the 3rd graph, it does not pass it. Therefore, the 3rd graph is not a function.
When we apply the Vertical Line Test to the 4th graph, it does pass it. Therefore, the 4th graph is a function.