Answers
Given:
[tex]6x\text{ + }\frac{1}{4}(4x\text{ + 8) > 12}[/tex]First, let's open the bracket:
[tex]\begin{gathered} 6x\text{ + }\frac{1}{4}\times\text{ 4x + }\frac{1}{4}\times8\text{ > 12} \\ 6x\text{ + x + 2 > 12} \end{gathered}[/tex]Collect like terms:
[tex]\begin{gathered} 6x+x\text{ > 12 - 2} \\ 7x\text{ > 10} \end{gathered}[/tex]Divide both sides by 7:
[tex]\begin{gathered} \frac{7x}{7}\text{ > }\frac{10}{7} \\ x\text{ > }\frac{10}{7} \end{gathered}[/tex]Solution:
x > 10/7
Related Questions
A chord in circle T has a length of 16 cm and the diameter of the circle 20 cm. How far is the chord from the center of the circle
Answers
ANSWER
[tex]6\operatorname{cm}[/tex]EXPLANATION
First, let us make a sketch of the circle:
Since the diameter of the circle is 20 cm, the radius of the circle is 10 cm, as shown above.
The two radii and the chord of the circle form a triangle. Also, the distance from the center to the chord forms a right triangle with the radius and half the length of the chord:
Now, we can solve for d by applying the Pythagoras theorem:
[tex]10^2=d^2+8^2[/tex]Solve for d:
[tex]\begin{gathered} d^2=10^2-8^2 \\ d^2=100-64=36 \\ d=\sqrt[]{36} \\ d=6\operatorname{cm} \end{gathered}[/tex]That is the distance from the chord to the center of the circle.
Fill in the blanks. Multiplicative inverse applies to multiplication and division because by multiplying or dividing a number to its_______, the numbers cross_____. They factor to 1.
identity, divide
reciprocal, cancel
opposite, multiply
null, zero
Answers
Answer:
The correct answer is
reciprocal, cancel
A coin will be tossed three times, and each toss will be recorded as heads () or tails ().
Give the sample space describing all possible outcomes.
Then give all of the outcomes for the event that the first toss is tails.
Use the format to mean that the first toss is heads, the second is tails, and the third is heads.
If there is more than one element in the set, separate them with commas.
Answers
(A). Sample Space: {HHH, HHT, HTH, THH, TTH,THT,HTT,TTT}.
(B). Outcome: {HHH, HHT, THH, THT}
What is termed as the sample space?A sample space is a set of all possible outcomes from a random experiment. The sample space is denoted by the symbol "S." An experiment's events are the sub - set of possible outcomes. Depending on the experiment, a sample space could contain a variety of outcomes.The sample spaces for just a random experiment are enclosed in curly braces " { } ".For the given question;
The coin is tossed thrice.
The outcome of head is denoted by 'H'.
The outcome of tail is denoted by 'T'.
(A). Sample Space for coin is tossed 3 times.
{HHH, HHT, HTH, THH, TTH,THT,HTT,TTT}
(B). Outcome for second toss is Head
{HHH, HHT, THH, THT}
Thus, the values for the sample space of the coin tossed thrice are obtained.
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Consider the following parametric equations:x = V1 -2 and y = 41-2Step 2 of 2: Determine the domain and range of the equation obtained by eliminating the parameter. Please write your answer in interval notation.
Answers
Answer:
Explanation:
Find the greatest common factor of these three expressions.6,63x^2, and 9x
Answers
According to the given expressions, we need to find the greatest common factor. Since one of the expressions is an independent term (it is only a number, no variables present) the common factor is an independent term.
To find the common factor, we need to find the greatest common divisor of the independent term and the coefficients of the rest of the expressions:
According to this the greatest common factor is 3
Evaluate the expression below for x = -4 and y = 8 -X +5y + 2x
Answers
Here, given the values of x and y, we are told to evaluate the given expression
What we need to do here is to simply substitute the values of x and y into the given expression
Thus;
we have -x + 5y + 2x
By substitution, this becomes;
-(-4) + 5(8) + 2(-4)
= 4 + 40 -8
= 44 - 8
= 36
Given x = -4 and y = 8 , the expression -X +5y + 2x = 36
Analyze the diagram below and answer the question that follows.DGВЬ12.412.410.2F НA10.2СЕWhich two triangles are congruent by the HL theorem?
Answers
The answer is D. None of the triangles are congruent by the HL theorem.
Because even though a and b have the same hypothenuse, they don't have the same leg, so they are not congruent and in the HL theorem they have to be equal in the hypothenuse and one of the legs.
The polar equation r = 7 sin (2theta) graphs as a rose.What is the length of the petals of this rose?Enter your answer in the box.
Answers
This problem is about a polar equation. It's important to know that polar coordinates depend on two variables, the angle of the vector and its distance.
[tex](r,\theta)[/tex]Where r represents the distance and theta represents the angles.
In this case, the angle is 20°, according to the problem.
So, first, we need to graph this equation in the polar system, to then measure the length of the petals
[tex]r=7\sin (2\theta)[/tex]The graph of this equation is shown in the image attached below.
In the image above, you can observe the polar equation graphed, with the coordinated system behind, this will allow us to find the length of each (which are symmetrical). You can observe that the petal on the third quadrant is at (-5,-5).
Now, we use the following formula to find the distance
[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]Replacing the points, we have
[tex]d=\sqrt{(-5)^2+(-5)^2}=\sqrt{25+25}=\sqrt{2(25)}=5\sqrt{2}\approx7.07[/tex]Therefore, the length of each petal is 7.07 units, approximately.what is the slope of the line represented by the equation f(x)=-3x+7?
Answers
Answer: -3
Step-by-step explanation:
Slope intercept form is:
y = mx + b
Which in this case m is the coefficient of x so -3
License plates in a particular state are to consist of 2 digits followed by 3 uppercase letters. a) How many different license plates can there be in this state if repetition of letters and numbers is permitted? b) How many different license plates can there be in this state if repetition of letters and numbers is not permitted? c) How many different license plates can there be in this state if the must be , and repetition of letters and numbers is not permitted? d) How many different license plates can there be in this state if the first digit cannot be , and repetition of letters and numbers is not permitted?
Answers
As per the concept of probability,
a) There are 1757600 number of possible license plates can there be in this state if repetition of letters and numbers is permitted
b) There are 1404000 number of possible license plates can there be in this state if repetition of letters and numbers is not permitted.
Probability:
Probability refer the possible way of occurring the particular event.
Given,
License plates in a particular state are to consist of 2 digits followed by 3 uppercase letters.
Here we need to determine the number of possible license plates for both repetition phase and non repetition phase.
Here we know that, license plates consist of 3 letters followed by 2 digits.
Let us consider the numbers on license plates be N
Let us consider the letters on license plates be L
Then the license plate consisting of 3 letters and 2 digits will be writen as,
=> LLLNN.
We know that the letters can be anything from A to Z.
There are 26 letter combinations for the first letter.
Again second and third letters can be anything from the 26 letters.
So, combination for letters = 26 × 26 × 26 = 17576
Similarly, the numbers can be anything from 0 to 9.
There are 10 combinations for both places.
Then the combination for numbers = 10 × 10 = 100
Therefore, the total number of combination for letters and numbers
=> 17576 × 100 = 1757600.
Therefore, there are 1757600 license plates can be made with repetition.
Similarly, for non repetition mode,
The number of letters for each place is reduced before,
So, the combination for the letter is,
=> 26 x 25 x 24 = 15600
Similarly, the combination of numbers is,
=> 10 x 9 = 90
Therefore, the total number of combination is,
=> 15600 x 90 = 1404000
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What is the interquartile range (IQR) of the data set represented by this box
plot?
44
51
56
72
81
Ο Α. 16
OB. 56
C. 51
OD. 21
Answers
Based on the given data set in the box plot, the interquartile range (IQR) can be found to be D. 21
How to find the interquartile range?The box plot is not given. However, based on the similar box plot attached, we can infer that the upper quartile in the box plot is 72.
The lower quartile can also be inferred to be 51.
The interquartile range can be found by subtracting the lower quartile from the upper quartile. The interquartile range is:
= Upper quartile - Lower quartile
= 72 - 51
= 21
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What system of measurement is most commonly used in the United States?
Military system
Metric system
Celsius
English system
Answers
The system of measurement is most commonly used in the United States is Metric system.
Answer: metric system hope this help a had this problem
15 points
What is the slope of the line on the graph?
Enter your answer in the box.
Answers
The slope of the line on the graph is - 2
How to determine the slope?The given parameter is the line on the graph
From the above graph, we have the following points
(x₁, y₁) = (0, 0)
(x₂, y₂) = (3, -6)
The slope of a line can be calculated using the following slope formula
Slope = (y₂ - y₁)/(x₂ - x₁)
Where
(x₁, y₁) = (0, 0) and (x₂, y₂) = (3, -6)
Substitute the known values in the above equation
So, we have the following equation
Slope = (-6 - 0)/(3 -0)
Evaluate the quotient
Slope = -2
Hence, the slope is -2
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Please help I don't get this
Find the difference or type
"impossible"
[3 –8] + [4 - 5 -6]
? ? ?
It’s a matrice
Answers
The difference of the two matrices [3 -8] and [4 -5 -6] is an impossible operation to execute as per arithmetic rules.
As per the question statement, we are provided with two matrices, [3 -8] and [4 -5 -6].
We are either required to calculate the difference of the above mentioned matrices, or else, determine if the operation is impossible to perform.
To solve this question, we need to know about the order of a matrix first.
The Order of a matrix is the representation of the number of rows and columns of that matrix, in the form of "m×n" and read as (m by n), where "m" is the number of rows in that matrix while "n" is the number of columns. It also tells us about the total number of entries or elements in a particular matrix, which we can calculate by performing the multiplication of it's order, i.e., (m * n)Now, one basic rule of matrix subtraction is that, matrices having the same order can only be subtracted from each other.Here, in our case, matrix [3 -8] is of the order (1×2) while matrix [4 -5 -6] is of the order (1×3), i.e., the orders of our concerned matrices are not same.
Hence, as per the above mentioned rule, we cannot execute the difference of [3 -8] and [4 -5 -6], and yes, it is an impossible task.
Matrix: In Mathematics, a matrix is a rectangular array or tabular representation of numbers, symbols, and/or expressions, arranged in rows and columns, which is used to determine a mathematical object or a property of such an object.To learn more about Difference of Matrices, click on the link below
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BRAINLIEST (statistics) (please help fast) A brand of frozen green beans lists a weight of 32 ounces on its bag. Because of variability in the manufacturing process, the bags often contain slightly more, or less, than 32 ounces of green beans. An inspector takes a random sample of 25 bags of green beans and records their weights. The weights and their relative frequencies are summarized in the histogram.
A histogram titled Green Beans has actual weight (ounces) on the x-axis, and relative frequency on the y-axis. 31.8 to 31.9, 0.04; 31.9 to 32.0, 0.04; 32 to 32.1, 0.12; 32.1 to 32.2, 0.2; 32.2 to 32.3, 0.36; 32.3 to 32.4, 0.23.
What is the shape of the distribution of bag weight?
uniform
skewed left
skewed right
roughly symmetric
Answers
What is the shape of the distribution of bag weight?
uniform
skewed left
skewed right
roughly symmetric
From the data and graph given, the shape of distribution is skewed left. Meaning, the left side of the graph is wider than that of the side to the right of the highest value.
Answer: Skewed left
Step-by-step explanation: less data towards the left side of the histogram
You have a normal distribution with a mean of 58 and a standard deviation of 12. Aparticular value of x is 50. What is the z-score of 50 given that normal distributions?Users
Answers
To do this you can use the following formula that is used to standardize a random variable which has a normal distribution
[tex]Z=\frac{x-\mu}{\sigma}[/tex]Where
[tex]\begin{gathered} \mu\text{ represents the mean and, } \\ \sigma\text{ represents the standard desviation} \end{gathered}[/tex]So, replacing you have
[tex]Z=\frac{x-\mu}{\sigma}=\frac{50-58}{12}=-\frac{8}{12}[/tex]Simplifying you have
[tex]Z=-\frac{8}{12}=-\frac{2}{3}=-0.67[/tex]A botanist has determined that there is a relationship between how much a certain plant grows and how much water it receives. Identify the independent quantity and the dependent quantity in this problem situation.
Answers
Answer:
the dependent variable is how much the plant grows. The independent variable is the amount of water the plant is given.
Step-by-step explanation:
The amount the plant grows depends on the amount of water
also plus ultra
Chantelle has 458 pennies she puts 26 pennies in each jar. how many jars does Chantell fill. how many pennies are left over
Answers
We have to find the quotient of 458 by 26 and the residue:
we have that Chantelle used 17 jars and she got 16 pennies left.
Rachel has 37 videos and decides to purchase 2 more each week. Would this equation be Linear or Exponential?
Answers
The equation would be linear because every week, Rachel will purchase 2 more videos- resulting in this equation.
x = 37 + 2
Note: I assigned x as the total videos Rachel will have the following week.
The answer would be LINEAR.
you are ordering a new home theater system that consists of a tv, surround sound system and dvd player. you can choose from 17 different tv’s 7 types of surround sound systems and 13 types of dvd players. how many different home theater systems can you build?
Answers
Answer:
1,547 different home theater systems.
Explanation:
Given that you can choose between the following options:
• 17 different tv’s
,• 7 types of surround sound systems
,• 13 types of dvd players
Thus, to find the number of possible home theater systems that you can build, multiply the number of each item type.
[tex]17\times7\times13=1,547[/tex]You can build 1,547 different home theater systems.
The lines y=0.5x + 8 and y = 5-x are shown graphed to the right. Which of the following is the solution to the system comprised of these two lines?1) (0,5)2) (-2,7)3) (2,3)4) (4,10)
Answers
As we can see in the graph, the lines intersect in the ordered pair (-2,7). Then, the solution to the system comprised of these two lines is:
[tex]\begin{cases}x=-2 \\ y=7\end{cases}[/tex]MathematicallyTo solve the given system of equations, we can use the equalization method.
Step 1: Either variable is chosen and solved in both equations.
[tex]\begin{cases}y=0.5x+8\Rightarrow\text{ Equation 1} \\ y=5-x\Rightarrow\text{ Equation 2}\end{cases}[/tex]Step 2: The expressions are equalized, obtaining an equation with a variable.
[tex]0.5x+8=5-x[/tex]Step 3: We solve for x the resulting equation:
[tex]undefined[/tex]Are y’all able to help me out on this question pls?
Answers
Answer:
Step-by-step explanation:
if angle 1 and angle 2 are vertical angles, angle 2 and angle 3 are complementary angles, and the measure of angle 3 = 56, find the measure of angle 1
Answers
We know that
[tex]m\angle3=56[/tex]If angle 2 and angle 3 are complementary, then by its definition we can express the following.-
[tex]\begin{gathered} m\angle2+m\angle3=90 \\ m\angle2=90-m\angle3 \\ m\angle2=90-56=34 \end{gathered}[/tex]Then, angle 1 and angle 2 are equal by definition of vertical angles.
[tex]m\angle1=m\angle2=34[/tex]Therefore, angle 1 measures 34°.The survey results of the towns favorite holiday were displayed in a newspaper as described37% of people enjoy Fourth of July•28% of people enjoy New Years Eve42% of people enjoy Memorial DayC5% of people enjoy all three12 % of people enjoy New Years Eve and Memorial Day•18 % of people enjoy Fourth of July and New Years Eve13% of people enjoy Memorial Day onlyWhat percentage of people enjoy New Years Eve only?
Answers
In order to calculate the percentage that enjoy New Years Eve only, we can use the diagram and formula below:
Using F to represent Fourth of July, N to represent New Years Eve and M to represent Memorial Day, the formula is:
[tex]P(N\text{ only})=P(N)-P(F\text{ and }N)-P(M\text{ and }N)+P(all\text{ }three)[/tex]From the given data, we have:
P(N) = 28% = 0.28
P(F and N) = 18% = 0.18
P(M and N) = 12% = 0.12
P(all three) = 5% = 0.05
So P(N only) is:
[tex]\begin{gathered} P(N\text{ only})=0.28-0.18-0.12+0.05\\ \\ P(N\text{ only})=0.03=3\% \end{gathered}[/tex]Two friends shop for fresh fruit. Jackson buys a watermelon for $6.85 and 4 pounds ofcherries. Tim buys a pineapple for $2.25 and 3 pounds of cherries. Use the variable p to representthe price, in dollars, per pound of cherries. Write and simplify an expression to represent how muchmore Jackson spent.
Answers
Jackson
[tex]6.58+4p[/tex]Tim
[tex]2.25+3p[/tex]to know how much more Jackson spent we do a subtrac between Jackson and Tim
then
[tex](6.58+4p)-(2.25+3p)[/tex]solve the parenthesis
[tex]6.58+4p-2.25-3p[/tex]group posible operations
[tex](6.58-2.25)+(4p-3p)[/tex]and solve
[tex]4.33+p[/tex]Jackson spents $4.33 + 1 pund on cherries more
A total of $6000 is invested: part at 5% and the remainder at 10%. How much is invested at each rate if the annualinterest is $5902
Answers
Given:
Principal amount = $6000.
Let x be the amount invested at 5%.
So, 6000-x be the amount invested at 10%.
The annual interest is $590
The equation is written as,
[tex]\begin{gathered} 5\text{ \%x+(6000-x)10 \%=590} \\ \frac{5}{100}x+(6000-x)\frac{10}{100}=590 \\ 0.05x+(6000-x)0.1=590 \\ 0.05x+600-0.1x=590 \\ -0.05x=-10 \\ x=\frac{10}{0.05} \\ x=200 \\ 6000-x=6000-200=5800 \end{gathered}[/tex]Answer: At 5%, the amount invested is $200, and at 10%, the amount invested is $5800.
Help me please please its urgent im waiting to answer this question!!! :)
Answers
Answer:
m ∠6 = 55°
Step-by-step explanation:
Angles 2 and 6 are corresponding angles and equal
m ∠2 + 125° = 180° since they are linear supplementary angles
m ∠2 = 180 - 125 = 55°
Since m ∠2 = m ∠6
m ∠6 is also 55°
a) Plot the graph of y = 2^x+2 for-4 ≤ x ≤ 4
b) Draw the asymptote.
c) Write the equation of the asymptote.
I need help with question c only
Answers
Answer:
y = 2
Step-by-step explanation:
A horizontal asymptote is a horizontal line that the graph of a function approaches as x approaches ±∞.
Mathematically we write this as
[tex]f(x) \rightarrow a \text{ as } x \rightarrow \infty \text{ or } x \rightarrow -\infty[/tex]
A vertical asymptote at some constant a is where the function approaches ±∞.
Mathematically
[tex]f(x) \rightarrow \infty \text { or } f(x) \rightarrow -\infty \text{ as } x \rightarrow a[/tex]
The given function y = 2ˣ + 2 is an exponential function and exponential functions do not have a vertical asymptote
The horizontal asymptote can be found by determining what the function limit is as [tex]x \rightarrow \pm \infty[/tex]
As [tex]x \rightarrow +\infty[/tex] the function [tex]\rightarrow \infty[/tex]
As [tex]x \rightarrow -\infty[/tex] , [tex]2^x \rightarrow 0\\\\\\2^x + 2 \rightarrow 2\\\\[/tex]
So the equation for the horizontal asymptote is y = 2
The graph shows that at y = 2, the function is parallel to the line but does not touch the line
determine the range of y=√x/√x+2
Answers
Solution
[tex]y=\frac{\sqrt[]{x}}{\sqrt[]{x+2}}[/tex]For this case we can do the following:
[tex]y=\sqrt[]{\frac{x}{x+2}}[/tex]The minimum value should be 0 for y assuming that x>= 0
Then the range should be:
[tex]0\le y<1[/tex]You are taking a multiple-choice test that has 6 questions. Each of the questions has 5 answer choices, with one correct
answer per question. If you select one of these choices for each question and leave nothing blank, in how many ways
can you answer the questions?
Answers
Answer: 30
Step-by-step explanation:
If you multiply the amount of answer choices (5) by the amount of questions (6), you will get 30. 6 x 5 = 30
