The solution to the compound inequality is x < 3 and x >6. The graph of the solution is shown.
What is inequality?The relation between two unequal expressions is defined as inequality.
The given inequalities are 3x + 6 < 15 and 2x - 5 >7.
Solve the first inequality:
3x + 6 <15
3x < 15 -6
3x < 9
x < 3
Solve the second inequality:
2x - 5 > 7
2x > 7 + 5
2x > 12
x > 6
Hence, the solution to the compound inequality is x < 3 and x >6.
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Which graph represents the solution set of - 4x - y ≤ - 6?
Answer:
Step-by-step explanation:
Which graph represents the solution set of - 4x - y ≤ - 6?
find the horizontal asymptote
The horizontal asymptote is y = [tex]\frac{9}{4}[/tex].
Let f(x) = [tex]\frac{9x^{3}-5x-9}{4x^{3}-9x+4}[/tex]
Line y = L is a horizontal asymptote of the function y=f(x), if either [tex]\lim_{x \to \infty} f(x) = L[/tex] or, [tex]\lim_{x \to -\infty} f(x) =L[/tex] and L is finite.
We will calculate limits :
[tex]\lim_{x \to \infty}(\frac{9x^{3}-5x-9}{4x^{3}-9x+4}) = \frac{9}{4}[/tex]
[tex]\lim_{x \to -\infty}(\frac{9x^{3}-5x-9}{4x^{3}-9x+4}) = \frac{9}{4}[/tex]
Hence, horizontal asymptote is y = [tex]\frac{9}{4}[/tex].
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The table shows a proportional relationship. x 14 6 26 y 7 3 13 Describe what the graph of the proportional relationship would look like. A line passes through the point (0, 0) and continues through the point (7, 14). A line passes through the point (0, 0) and continues through the point (14, 7). A line passes through the point (0, 0) and continues through the point (3, 6). A line passes through the point (0, 0) and continues through the point (13, 26).
The graph of this proportional relationship would look like this: A line passes through the point (0, 0) and continues through the point (14, 7).
What is a graph?In Mathematics, a graph simply refers a type of chart that is typically used to graphically represent data points on both the horizontal and vertical lines of a cartesian coordinate, which are the x-coordinate (x-axis) and y-coordinate (y-axis).
Generally speaking, the graph of any proportional relationship is always characterized by a straight line with the data points passing through the origin (0, 0) because as the values on the x-coordinate (x-axis) increases or decreases, the values on the y-coordinate (y-axis) increases or decreases simultaneously.
By critically observing graph of this proportional relationship (see attachment), we can logically deduce that it passes through both points (0, 0) and (14, 7).
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Determine the value of x below. (only type the numerical value, do not include the degree sign)
By using the fact that the angles are supplementary, we can write and solve a linear equation to find that x = 62.
How to find the value of x?
In the image, we can see two supplementary angles, where by definition, two angles are supplementary if their addition is equal to a plane angle (an angle of 180°).
With that in mind, we can write the linear equation:
x + 118 = 180
So we just need to isolate x in that simple linear equation.
If we subtract 118 in both sides, we will get:
x + 118 - 118 = 180 - 118
x = 62
So the unknown angle has a measure of 62°.
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The seating capacity y for a banquet hall is represented by y = 8x + 56,
where x is the number of extra tables you need. How many extra tables
do you need to double the original seating capacity?
The number of extra tables that you need to double the original seating capacity will be 7.
What is the solution to the equation?The allocation of weights to the important variables that produce the calculation's optimum is referred to as a direct consequence.
The seating capacity y for a banquet hall is represented by y = 8x + 56, where x is the number of extra tables you need.
If the no extra table is there. Then the value of 'y' will be
y = 8 (0) + 56
y = 56
Then the number of extra tables do you need to double the original seating capacity will be
8x + 56 = 2 × 56
8x = 56
x = 7
Then the number of extra tables that you need to double the original seating capacity will be 7.
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8 (a) Write 0.000089 in standard form.
Answer: 0.000089
Step-by-step explanation: 0.000089 is already in standard form, if you want 0.000089 in the scientific form then that would be...
8.9 x 10⁻⁵
What is the angle θ in the triangle below?
Answer:
θ = 64.98310506 degrees (65 degrees rounded to unit)
Step-by-step explanation:
4.2 * tanθ = 9
4.2 * tanθ/ 4.2 = 9/4.2
tanθ = 2.142857
θ = arctan 2.142857
θ = 64.98310506
Step-by-step explanation:
using the SOH CAH TOA Rule,
tan 0=opp÷adj
tan 0=9÷4.2
tan 0=2.14
0=tan inverse of 2.14
If Tomas divides his stack of programs between himself and his 3 friends, what fraction of the original stack will each of his friends have? can someone help me.
As per the given information, Tomas divides one program among four people then each person will get fraction of ( 1/ 4) of the original stack if divided equally .
As given in the question,
Number of stacks of program to be divided = 1
Number of friends = 3
Number of people among whom stack of program is to be divided = 4
Let us consider stack of program divided equally
Fraction of stack of program each friend will get = 1 /4
As
( 1 / 4 ) + ( 1 / 4 ) + ( 1 / 4 ) + ( 1 / 4 )
= ( 1+ 1+ 1+ 1) / 4
= 4/4
= 1
Therefore, for the given information, Tomas divides one program among four people then each person will get fraction of ( 1/ 4) of the original stack if divided equally .
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Apply Laws of Exponents to write an equivalent expression for the given expression
Step-by-step explanation:
e⁰ = 1
so, we have
(f² / (f³gh⁶))⁸ = f¹⁶ / (f²⁴g⁸h⁴⁸) = 1 / (f⁸g⁸h⁴⁸)
FYI - depending on what your teacher wants to see as simplified answer, it could be also
1 / (fgh⁶)⁸
or
(1 / (fgh⁶))⁸
but normally it should be the first result form above
1 / (f⁸g⁸h⁴⁸)
The sum of four positive integers is 125. If you increase the first number by 4, decrease the second by 4, multiply the third by 4, and divide the fourth by 4, you produce four equal numbers. What is the smallest of the original numbers
Step-by-step explanation:
a + b + c + d = 125
a + 4 = b - 4 = 4c = d/4
a + 8 = b
a = b - 8
16c = d
b = 4c + 4
4a + 16 = d
b - 8 + 4c + 4 + c + 16c = 125
4c + 4 - 8 + 4c + 4 + c + 16c = 125
25c = 125
c = 5
d = 16c = 80
4a + 16 = d = 80
4a = 64
a = 16
b = a + 8 = 16 + 8 = 24
so, the numbers are
16, 24, 5, 80
James shares 5/8 of a cake between 6 people.
What fraction of the cake do they each receive?
Answer:
5/48
Step-by-step explanation:
The fraction of people getting cake will be 1/6 of 5/8 thus it will be 5/48.
What is a fraction?In such a fraction, the value that appears above the horizontal line is referred to as the numerator.
In another word, if we divide two numbers by each other then the upper word is called the numerator, and the lower word is called the denominator.
As per the given,
James shares 5/8 of a cake between 6 people.
Now, 1/6 of 5/8 will be as,
1/6(5/8) = 5/48
Hence "The fraction of people getting cake will be 1/6 of 5/8 thus it will be 5/48".
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Can someone sketch the graph plsss? I rlly need help to sketch it
Answer:
1. Plot x = 0
(A. IF YOU CAN EASILY FIND IT, PLOT Y = 0)
(B. BONUS: PLOT A FEW EASY TO CALCULATE POINTS LIKE X = 1 & X = -1)
2. Figure out what happens when x is really big (in the positive and negative direction)
3. Optional: look for any “significant” x-values
4. Connect the dots and finish!
Step-by-step explanation:
1. Plot x = 0
The first thing we want to do is get some points up on our graph, so we want to pick the ones that will be easy to calculate. For almost any equation, plugging in x = 0 and solving for y is fast and easy to do by eye, and almost always doable without a calculator. For our example equation:
So, the first point we’ll put on our graph is (0, -4).
Jose hopes to earn $600 in interest in 4.8 years time from $30,000 that he has available to invest. To decide if it's feasible to do this by investing in an account that compounds annually, he needs to determine the annual interest rate such an account would have to offer for him to meet his goal. What would the annual rate of interest have to be? Round to two decimal places.
Answer
The annual rate of interest have to be 3.87%.
How to determine the annual rate of interest?Mathematically, compound interest can be calculated by using this formula:
A = P(1 + r/n)^{nt}
Where:
A represents the future value.P represents the principal.r represents the interest rate.n represents the number of times compounded.T represents the time measured in years.Making the interest rate (r) the subject of formula, we have:
r = n[(A/P)^{1/nt} - 1]
Note: A = SI + P = 600 + 30,000 = $36,000
Substituting the given parameters into the formula, we have;
Interest rate, r = 1[(36,000/30,000)^{1/1 × 4.8} - 1]
Interest rate, r = [(1.2)^{0.20833333333} - 1]
Interest rate, r = [1.0387 - 1]
Interest rate, r = 0.0387
Interest rate, r = 3.87%.
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In the diagram a person who is ft tall is standing on the ground ft away from point . A line segment drawn from the top corner of the building to point creates two similar triangles.
The height of the building, using similar triangles, is given by:
36 feet.
What are similar triangles?Similar triangles are two triangles that share these two features, which are listed as follows:
Same angle measures.Proportional side lengths.The second bullet point, regarding proportional side lengths, is especially relevant in the context of this problem, as a proportional relationship is built to find the height h of the building.
From the similar triangles, the equivalent side lengths are presented as follows:
3 ft and 18 ft.6 ft and h ft.Hence the proportional relationship that models this situation is presented as follows:
3/18 = 6/h.
Applying cross multiplication, the height of the building is obtained as follows:
3h = 18 x 6
h = 6 x 6 (simplifying by 3)
h = 36 feet.
Missing InformationThe diagram is given by the image shown at the end of the answer.
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5 lily pads are found in a pond. Thirty days later, there are 16 lily pads. Find the exponential growth
model, L(t) = Aekt for the lily pad colony. Enter your answers as expressions or numbers rounded to four
decimal places.
A =
k=
The exponential model for the lily pad colony is L(t) = A[tex](1+r)^{kt}[/tex] and the values of A=5 and k=1.2.
What is meant by exponential growth?Over time, anything grows in quantity through an exponential growth process. When a quantity's rate of change over time (or derivative) is proportional to the quantity itself, this phenomenon takes place. A number that is increasing exponentially is referred to as a function, and the exponent, which stands for time, is the variable that represents time (in contrast to other types of growth, such as quadratic growth).
When a quantity decrements with time, it is considered to be experiencing exponential decay rather than a positive constant of proportionality. It is also known as geometric growth or geometric decay when the definition's discrete domain has equal intervals since the values of the function form a geometric progression.
Given, there are 5 lily pads that are found in a pond
And after 30 days, there are 16 lily pads in that pond
Here, a=5
r=(11-5)/5=1.2
f(x)=a(1+r)ˣ
f(x)=5(1+1.2)³⁰
From the above equation, A=5, and k=1.2
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Graph the line with slope 1/3 and y-intercept −2.
An ice cream factory has 4 machines that make the same type of ice cream. The rate of production for each machine is shown in the table. Based on the date given, which machine works atthe fastest rate?
Using division operations and based on the rates of production, given, Machine D works the fastest.
How is the rate of production determined?The rate of production can be computed using the division operation, which divides the dividend by the divisor, to obtain the quotient (rate).
The rate of production is the number of goods that can be produced during a given period of time.
The rate of production or production rate also refers to the time consumed in the production of a unit of goods or services.
There are, therefore, two ways of determining production rate. Firstly, we can divide the total production by the hours consumed.
Secondly, the production rate can be computed by dividing the total production time by the number of goods produced.
Units Production Rate of
Produced Hours Production
Machine A 10,000 15 667 cups per hour
Machine B 25,000 20 1,250 cups per hour
Machine C 30,000 30 1,000 cups per hour
Machine D 15,000 10 1,500 cups per hour
Thus, using division operation, Machine D produces at the fastest rate than the other three machines.
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Question Completion:Units Production
Produced Hours
Machine A 10,000 15
Machine B 25,000 20
Machine C 30,000 30
Machine D 15,000 10
I really need help to this answer ASAP.
(x - 5)²
Step-by-step explanation:
use formula
[tex](x - y) {2} = x {}^{2} - 2xy + y {}^{2} [/tex]
Find the slope of the line that contains the points named.
P(1, 2), Q(3, 4)
0-1
01
02
Answer:
If the coordinates of at least two points in the line are given, the slope (m) may be calculated by, m = (y2 - y1) / (x2 - x1
Fill in the blanks to solve 2,000x9
Answer: its 18,0000
Step-by-step explanation: Be smart 2x9= 18+ three 0,s?
Please help me I NEED HELP
Answer:
A= 6n
B= 9n
C= 15n
Step-by-step explanation:
It's just adding.
A= 6n
B= 9n
C= 15n
Factorise this expression as fully as possible
2xy^2 + 8y
2y(xy+4)
Hope this answers your question!
Answer:
2y(xy+4)
Step-by-step explanation:
First, Distribute
you get 2y(xy+4) because you have to isolate the like terms than find a gcf of the terms
A fish tank has a capacity of 154L.
What is the volume of the fish tank?
The volume of the fish tank required = 0.154 m^3.
A fish tank has a capacity = 154L.
Capacity of fish tank in Litre = Volume of the fish tank in meter cube
So the volume of the fish tank required in cubic meter.
For the volume we required a conversion of litre into meter cube.
Cubic meters and liters are two common metric units of volume.
1 cubic meter is 1000 liters.
To convert liters to cubic meters, you simply need to move the decimal point three places to the left. In other words, divide a value in liters by 1000 to get an answer in cubic meters.
1L = 0.001 m^3
So 154L = 0.154 m^3
So the volume of the fish tank required = 0.154 m^3.
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Rewrite this number in appropriate scientific notation:
answer=
464, 400,000
You may use either X or to represent multiplication.
Find the unit rate for this relationship
2/3 is the unit rate of the relationship
How to determine the unit rate of the relationship?
A unit rate is defined as the rate for one of something. For example, if 10 oranges cost $50, the unit rate will be $50/10 = $5 i.e. $5 for one orange.
On a linear graph, the unit rate is obtained by calculating the slope of the line. The slope is the change in y divided by the change in x:
Slope = y2-y1 / x2-x1
Thus, we can any two convenient points on the graph and use it calculate the slope as shown in the attached image:
Slope = y2-y1 / x2-x1
Slope = 6-2 / 9-3 = 4/6 = 2/3
Therefore, the unit rate for this relationship is 2/3. The 2nd option is the answer
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What is the x value of the solution to the following system
x + y =40
x - 3y = -4
Answer:
x=y , x-3y=4. x = y x = y , x − 3y = 4 x - 3 y = 4. Replace all occurrences of x x with y y in each equation. Tap for more steps... −2y = 4 - 2 y = 4. x = y x = y. Divide each term in −2y = 4 - 2 y = 4 by −2 - 2 and simplify. Tap for more steps... y = −2 y = - 2.
Step-by-step explanation:
Just smart
Answer:
C) 29
Step-by-step explanation:
1st equation - 2nd equation,
x+y - (x-3y) = 40-(-4)
x+y-x+3y = 40+4
4y = 44
y = 44÷4
y = 11
substituting y into the first equation,
x + 11 = 40
x = 40-11 = 29
answer is C
hope it helps. :)
Factor 18p-3618p−3618, p, minus, 36 to identify the equivalent expressions.
Choose 2 answers:
Choose 2 answers:
(Choice A)
A
3(9p-12)3(9p−12)3, left parenthesis, 9, p, minus, 12, right parenthesis
(Choice B)
B
9(2p-4p)9(2p−4p)9, left parenthesis, 2, p, minus, 4, p, right parenthesis
(Choice C)
C
2(9p-18)2(9p−18)2, left parenthesis, 9, p, minus, 18, right parenthesis
(Choice D)
D
18(p-2)18(p−2)
After simplification, the equivalent expression is 18(p-2). So the option D is correct.
In the given question,
We have to find factor 18p-36 equivalent expressions.
The given option is
A. 3(9p-12)
B. 9(2p-4p)
C. 2(9p-18)
D. 18(p-2)
The given expression is 18p-36.
We simplify the given expression to find their equivalent expression.
To simplify the expression we take out the common term from both terms.
We can see that 18 is a common multiply of both number 18 and 36. SO we take out 18 from both terms.
Taking common 18
18p-36 = 18(p-2)
Hence, the equivalent expression is 18(p-2). SO the option D is correct.
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Solve for j.
–3(j − 8) + –6 = –9
Answer:
j = 9
Step-by-step explanation:
Given equation,
→ -3(j - 8) + (-6) = -9
Let's solve for the value of j,
→ -3(j - 8) + (-6) = -9
→ -3j + 24 - 6 = -9
→ -3j + 18 = -9
→ -3j = -9 - 18
→ j = (-27)/(-3)
→ [ j = 9 ]
Hence, the value of j is 9.
Answer:
j = -9
Step-by-step explanation:
[tex] - 3(j - 8) + - 6 = - 9 \\ open \: brackets \\ - 3j + 24 + - 6 = - 9 \\ 3j + 24 = - 9 + 6 \\ 3j + 24 = - 3 \\ 3j = - 3 - 24 \\ 3j = - 27 \\ divide \: by \: 3 \\ j = - 9[/tex]
WILL MARK BRAINLIEST 30 POINTS
Each night Liz spends at least 45 minutes and no more than 120 minutes on her phone.
Choose which double inequality describes how long Liz spends on her phone each night.
"n" will be used as your variable.
WILL MARK BRAINLIEST
The double inequality describing the length of time (in minutes) that Liz spends on her phone each night is 45 ≤ f(x) ≤ 120.
What is double inequality?Double inequality is a mathematical expression that has two inequalities.
Double inequality is also known as a compound inequality. because there is more than one inequality in the expression
The form of double inequality is always written as: a ≤ f (x) ≤ b.
This double inequality gives the value of x as more than a and less than b.
The least number of minutes spent by Liz on her phone = 45 minutes
The maximum number of minutes spent by Liz on her phone = 120 minutes
Inequalities:Inequality 1: 45 ≤ f(x)
Inequality 2: f(x) ≤ 120
Thus, this double inequality 45 ≤ f(x) ≤ 120 shows Liz's time on the phone every night.
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A manufacturer produces 25-pound lifting weights. The lowest actual weight is 24 pounds, and the highest is 26 pounds. Each weight is equally likely so the distribution of weights is uniform. A sample of 100 weights is taken. Find the probability that the mean actual weight for the 100 weights is greater than 25.2
The probability that the mean actual weight for the 100 weights is greater than 25.2 is equal to 0.0136%.
How to determine the probability that the mean actual weight for the 100 weights?In order to determine the probability that the mean actual weight for the 100 weights is greater than 25.2, we would have to calculate the mean and standard deviation.
In a uniform distribution, the mean of a data set can be calculated by using this formula:
Mean, E(x) = [a + b]/2
Where:
a is the lowest boundary.b is highest boundary.Substituting the given parameters into the formula, we have;
Mean, E(x) = [24 + 26]/2
Mean, E(x) = 50/2
Mean, E(x) = 25.
For the standard deviation, we have:
Standard deviation, S(x) = √((b - a)²/12)
Standard deviation, S(x) = √((26 - 24)²/12)
Standard deviation, S(x) = √((2)²/12)
Standard deviation, S(x) = √(4/12)
Standard deviation, S(x) = 0.5774.
For the sample standard deviation, we have:
Standard deviation = S(x)/√n
Standard deviation = 0.5774/√100
Standard deviation = 0.5774/10
Standard deviation = 0.05774.
By applying the central limit theorem, we would determine the z-score as follows:
Z-score = (x - μ)/σ
Z-score = (25.2 - 25)/0.05774
Z-score = 0.2/0.05774
Z-score = 3.64
Therefore, the p-value is equal to 0.000136.
Probability (x > z) = 0.0136%.
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