Two steps in solving the inequality: simplify the algebraic expressions by combining like terms and isolating the target variable, then applying the mathematic operators.
Steps in solving the inequality:- Simplify the expression by: open the parentheses of algebraic expression, combine the terms like, and isolate the target variable.
- Use mathematic operators such as: addition, subtraction, multiplication, and division. All mathematic operations must be done on both sides. Addition and subtraction do not change the inequality. Multiplication and division with positive numbers will not change the inequality.
Multiplication and division with negative numbers will change the sign of the inequality.
Example:
Solve the inequality: 3x + 2 < 5x - 8
Step one: Subtract both sides with 5x and 2, this operation does not change the inequality sign
3x + 2 - 5x - 2 < 5x - 8 - 5x - 2
-2x < -10
Step two: Divide both sides with (-2). Since we divide with negative numbers, flip the inequality sign.
-2x/(-2) > -10/(-2)
x > 5
Hence, the solution is x> 5
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Answer the following questions. Make sure to show all your work. 1. When is it best to solve a system of equations using graphing? 2. When is it best to solve a system of equations using substitution? 3. When it is best to solve a system of equations using elimination? When it is 4. Solve the following system of equations graphically. y=3x+4 y=-2x-5
Andrew is going to invest in an account paying an interest rate of 2.2% compounded quarterly. How much would Andrew need to invest, to the nearest hundred dollars, for the value of the account to reach $93,000 in 19 years?
Andrew would need to invest $61,300 for the account to reach $93,000.
What is Compound Interest?Compound interest is defined as the amount of interest which has been calculated on the principal amount as well as the amount accumulated over the previous period is also included.
The equation to find final amount in compound interest is,
A = P (1 + r/n)^(n t)
Here A is the final amount, P is the initial amount, r is the rate of interest, n is the number of times compounding is done in a year, t is the time in years.
Given, A = $93,000
t = 19 years
r = 2.2% = 0.022
n = 4 (since compounding is quarterly)
93,000 = P [1 + (0.022/4)]^(4×19)
93,000 = P [1.0055]^(76)
93,000 = P (1.517)
P = 61,297.8516
To the nearest hundred dollars, P = $61,300
Hence the principal amount Andrew need to invest is $61,300.
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HELP NOW PLS (100 POINTS)
The function f(x) = 20x + 80 represents the distance in miles a drone flew.
The function g(x) = x + 2 represents the time the drone flew in hours.
Part A: Find f(2) and g(2). Show your work. (2 points)
Part B: Find f divided by g of 2. Show your work. (2 points)
Part C: What is the domain of f divided by g of x? (2 points)
Answer:
A) f(2) = 120, g(2) = 4.
B) f'(x) = 5x + 20
C) R - {-2}.
Step-by-step explanation:
A) Just apply given value and resolve:
[tex]f(2) = 20 \times 2 + 80 = 40 + 80 = 120 \\ g(2) = 2 + 2 = 4[/tex]
B) g(2) is 4, so just divide f(x) by 4:
[tex] \frac{1}{4} f(x) = \frac{1}{4} (20x + 80) = \frac{20}{4} x + \frac{80}{4} = 5x + 20[/tex]
C)
[tex] \frac{f(x)}{g(x)} = \frac{20x + 80}{x + 2} [/tex]
Polynomials have full domain. A Quotient of polynomials is defined when denominator is not zero. In this sample, denominator is zero when x = -2, so -2 is not part of the domain. All other real numbers are part, hence R - {2}.
1. The value of F(2) = 120 and g(2) = 4.
2. The division is 5(x+4)
3. The domain is real number except -2.
What is Function?In mathematics, a function is an expression, rule, or law that establishes the relationship between an independent variable and a dependent variable. In mathematics, functions exist everywhere, and they are crucial for constructing physical links in the sciences.
The function f(x) = 20x + 80 represents the distance in miles a drone flew.
The function g(x) = x + 2 represents the time the drone flew in hours.
1. F(2)= 20(2)+ 80= 40+ 80= 120
and, g(2)= 2 + 2 = 4
2. The division is
= F(x) / g(2)
= (20x + 80)/ (2+2)
= 20 (x+4) / 4
= 5 (x+4)
3. The domain of F(x) / g(x) is all real number except -2.
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Cómo resolver esta factorizacion
Therefore , the solution of the given problem of factorization comes out to be x=0 and x=1/3.
What is factorization, exactly?The breaking or decomposition of an entity (such as a number, a matrix, or a polynomial) into a product of another entity, or factors, whose multiplication results in the original number, matrix, etc., is known as factorization or factoring in mathematics.
Here,
Given:
thus . We do factorization of given expression and
we come on a result
=> 3x - 9x²
=> 3x (1 -3x)
x=0 and x=1/3
Therefore , the solution of the given problem of factorization comes out to be x=0 and x=1/3.
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√x = √3x
What is the solution to the equation above?
Answer:
[tex]x=0,\;x=\dfrac{1}{3}[/tex]
Step-by-step explanation:
Given equation:
[tex]\sqrt{x}=\sqrt{3}x[/tex]
Square both sides:
[tex]\implies \left(\sqrt{x}\right)^2= \left(\sqrt{3}x\right)^2[/tex]
[tex]\implies x= \left(\sqrt{3}\right)^2 \cdot \left(x\right)^2[/tex]
[tex]\implies x=3x^2[/tex]
Subtract x from both sides:
[tex]\implies x-x=3x^2-x[/tex]
[tex]\implies 0=3x^2-x[/tex]
[tex]\implies 3x^2-x=0[/tex]
Factor out the common term x:
[tex]\implies x(3x-1)=0[/tex]
Apply the zero-product property:
[tex]\implies x=0[/tex]
[tex]\implies 3x-1=0 \implies x=\dfrac{1}{3}[/tex]
Answer:
[tex] \sf \: x = \frac{1}{3} \: (or) \: x = 0[/tex]
Step-by-step explanation:
The equation given is,
→ √x = √3x
Now the value of x will be,
→ √x = √3x
→ x = (√3x)²
→ x = 3x²
→ 3x² = x
→ 3x² - x = 0
→ (3x - 1)(x) = 0
→ 3x - 1 = 0 || → x = 0
→ 3x = 0 + 1 || → [ x = 0 ]
→ 3x = 1 ||
→ [ x = 1/3 ] ||
These are the values of x.
Solve for y.
y−58.8=62
Enter your answer in the box.
y =
Answer:
y = 120.8
Step-by-step explanation:
y − 58.8 = 62
Add 58.8 to both sides
y = 120.8
Let's check
120.8 - 58.8 = 62
62 = 62
So, y = 120.8 is the correct answer.
Answer:y= 120.8 I hope this helps
Step-by-step explanation:
y-58.8=62
Move the constant to the right-hand side and change its sign
Like this
Y=62+58.8
Then Add the numbers 62 and 58.8
Which will give you
Plus bring down your y
Your answer is y=120.8
Chad bought a box of donut hole that contain 60% glazed and the ret powdered ugar. The box ha 12 powdered ugar donut hole. How many glazed donut hole are in the box Chad bought?
The box has 18 glazed donut hole that Chad bought.
The percentage of glazed donut holes = 60%
The percentage of powdered sugar donut hole = (100 - 60) % = 40%
Let us consider the total number of donut hole in the box bought by Chad to be 'x'
Number of powdered sugar donut hole = 12
Hence, we can say that the number of powdered sugar donut hole in the box Chad bought is:
(40% of x) = 12
Therefore, x = (12 x 100) / 40 = 30
Since the total number of donut hole in the box = 30
The number of glazed donut hole = 30 - 12 = 18
Thus, the box that Chad bought had 18 glazed donut hole.
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Peter has 18 dimes. He uses 12 dimes to buy a drink. The number of dimes he has left is one-half the number of Pennie’s he has. How many Pennie’s does Peter have? *Put this in a 5th grade understanding*
18-12=6, peter now has 6 dimes left after buying a drink. Since the number he has left is ONE HALF of the number of pennies he has. 6x2=12.
peter has 12 pennies. hoped that helped
Which point is the reflection of (- 3 2 over the y-axis?
The reflection of (-3, 2) over the y-axis is (-3, -2).
The reflection of a point (x, y) over the y-axis is (x, -y).
Therefore, the reflection of (-3, 2) over the y-axis is (-3, -2).
To calculate the reflection of (-3, 2) over the y-axis, we first use the formula (x, -y).
In this case, x = -3 and y = 2, so the reflection of (-3, 2) over the y-axis is (-3, -2).
We can also calculate the reflection of (-3, 2) over the y-axis using the distance formula.
The distance formula is d = √(x2-x1)2 + (y2-y1)2
In this case, x1 = -3, x2 = 0, y1 = 2, and y2 = 0.
Therefore, the distance d = √(02-(-3)2 + (02-2)2 = √(9 + 4) = √13
The reflection of (-3, 2) over the y-axis is (-3, -2). This can be verified using the distance formula.
d = √(x2-x1)2 + (y2-y1)2 = √(-3-0)2 + (-2-0)2 = √(9+4) = √13
The distance d is equal to the distance between (-3, 2) and (-3, -2). Hence, the reflection of (-3, 2) over the y-axis is (-3, -2).
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What is 0 to the 0 exponent and why?
0 to the 0 exponents is undefined or indeterminate, and it's not considered as a valid mathematical operation.
The value of 0 to the 0 exponents is undefined or indeterminate. The reason for this is that the mathematical definition of exponentiation states that any number to the power of 0 is equal to 1, except for 0, which is undefined. However, when we try to apply this rule to 0 to the power of 0, it creates a paradox.
If we assume that 0 to the 0 exponents is 1, then any number raised to the power of 0 would be equal to 1, which is not true. For example, 2 to the power of 0 is not equal to 1, but 2, so this assumption doesn't hold true.
On the other hand, if we assume that 0 to the 0 exponents is 0, then any number multiplied by 0 would be 0, which is not true either. For example, 2 multiplied by 0 is not equal to 2.
Therefore, 0 to the 0 exponents is undefined or indeterminate, and it's not considered as a valid mathematical operation.
It's important to note that in some fields of mathematics such as limit, the value of 0 to the 0 exponent is defined as 1, but this is limited to the context of limit and not in general math.
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Three times the measure of a supplement of an angle is 8 times the measure of a complement of the angle. Find the measure of the angle .
Answer:
3x of 180=8x of 90
Use this equation
please help! Which equation could you use to find the original amount of ounces of rice in a box, when the current box holds 85 ounces, 25% less rice.
The equation which is use to find the original amount of ounces of rice in a box, when the current box holds 85 ounces, 25% less rice is
y = 0.25*85.
What is percentage?
A number or ratio expressed as a fraction of 100 is known as a percentage in mathematics. Though the abbreviations "pct.", "pct.", and occasionally "pc" are also used, the percent sign, "%," is frequently used to indicate it. An amount that is a percentage is dimensionless and has no assigned measurement.
Given:
The current box holds 85 ounces, 25% less rice.
We have to find the equation which is use to find the original amount of ounces of rice in a box, when the current box holds 85 ounces, 25% less rice.
Let, y be the original amount of ounces of rice in a box.
The current box holds 85 ounces.
The 25% less than 85 ounces are 85*0.25.
So, the equation becomes y = 0.25*85.
Hence, the equation which is use to find the original amount of ounces of rice in a box, when the current box holds 85 ounces, 25% less rice is
y = 0.25*85.
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In 1967 a pair of slacks sold for $8.00. Ten years later, the price increased by 65%. How much more did a pair of slacks sell for ten years later?
A company ha two manufacturing plant with daily production level of 5x 14 item and 3x - 5 item, repectively. The firt plant produce how many more item daily than the econd plant?
As per the given equation, the first plant is produce 2x+21 more items than second plant.
The term equation is known as a mathematical statement that shows that two mathematical expressions are equal.
Here we have given that the first plant produces 5x+14 items daily
And the second plant produces 3x-7 items daily
In order to find the number of items produced on first plant, then we have to calculate the differences between number of items by the two plants daily, then it can be written as by using the equations,
=> (5x+14) - (3x-7)
Now, we have to expand the equations, then we get
=> 5x+14 - 3x+7
=> 2x+21
Therefore, first plant produces 2x+21 more items daily than the second plant.
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I need help only have 2 hours left
Answer:
[tex]\begin{array}{|c|c|c|c|c|c|}\cline{1-6} \vphantom{\dfrac12} x&-4&1&2&3&6 \\\cline{1-6} \vphantom{\dfrac12} f(x)&-20&5&10&15&30 \\\cline{1-6}\end{array}[/tex]
Step-by-step explanation:
Given function:
[tex]f(x)=5x[/tex]
To complete the function table, substitute each given value of x into the given function:
[tex]x=-4 \implies f(-4)=5(-4)=-20[/tex]
[tex]x=1 \implies f(1)=5(1)=5[/tex]
[tex]x=2 \implies f(2)=5(2)=10[/tex]
[tex]x=3 \implies f(3)=5(3)=15[/tex]
[tex]x=6 \implies f(6)=5(6)=30[/tex]
Completed table:
[tex]\begin{array}{|c|c|c|c|c|c|}\cline{1-6} \vphantom{\dfrac12} x&-4&1&2&3&6 \\\cline{1-6} \vphantom{\dfrac12} f(x)&-20&5&10&15&30 \\\cline{1-6}\end{array}[/tex]
Please help! Please! Thank you! :) 30+ points
Answer:
x=6 z=73
Step-by-step explanation:
9x+53=6x+71
3x+53=71
3x=18
x=6
9(6)+53
54+53
107
107+z=180
z=73
there are two drama groups in school one group were 36 boys and 48 girls in the other 3/7 of students are boys others girls
ann says "the ratio of the number of boys to the number of girls is the same for both groups"
is ann correct
Answer:
UMMMM Wait IM sorry What grade are you in? I'm in fifth.
Step-by-step explanation:
What is an example of inequality math?
Answer: 5x − 4 > 2x + 3
Step-by-step explanation:
The expression 5x − 4 > 2x + 3 looks like an equation but with the equals sign replaced by an arrowhead. It is an example of an inequality. This denotes that the part on the left, 5x − 4, is greater than the part on the right, 2x + 3.
What is the exponential form for 8x8x8x8 taking base as 2?
The exponential form of 8x8x8x8 is 2^(4*3) = 2^12.
A group of researchers investigated the effect of media usage (whether or not subjects watch television or use the Internet) in the bedroom on "Tiredness" during the day (measured on a 50 point scale
a. Identify each of the variables, state whether the variables are quantitative or categorical, and identify each variable as either explanatory or response variables. nterviewed
b. To collect these data, the researchers randomly selected homes to visit and i the adult member of the household whose birthday was nearest. Is this an experiment or an observational study? Briefly explain.
YES, This is an observational study.
The variables in this study are:
Media usage: categorical (explanatory variable)
Tiredness: quantitative (response variable)
This is an observational study. The researchers are observing and measuring the relationship between media usage and tiredness, but they are not manipulating or controlling any variables. They are collecting data by randomly selecting homes to visit and interviewing the adult member of the household whose birthday was nearest.
An observational study draws conclusions from a sample of a population in disciplines like epidemiology, social sciences, psychology, and statistics when the independent variable is not under the researcher's control due to ethical considerations or practical limitations. One typical observational study examines how a therapy may affect its participants, but the researcher has no control over which group the subjects are assigned to—the treated group or the control group. Unlike experiments like randomized controlled trials, when each subject is arbitrarily assigned to either a treated group or a control group, this does not happen. Observational studies naturally create challenges for inferential analysis because they lack an assignment mechanism.
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lines AB and BC are perpendicular. the dashed rays bisect angles ABD and CBD. explain why the measure of angle EBF is 45 degrees.
Angle EBF is 45 degrees because angle ABC is 90 degrees and line D divides each side into two equal parts.
How to determine angles?Given that lines AB and BC are parallel. Angles ABD and CBD are bisected by the dashed rays. Angle EBF is measured at 45 degrees because angle ABC is 90 degrees, line D divides each side into two equal parts, and half of 90 degrees is 45 degrees.
As a result, the angle EBF is 45 degrees because angle ABC is 90 degrees and line D divides each side into two equal parts, and half of 90 degrees is 45 degrees.
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How do I solve (3.4) (6.7) using standard algorithm?
To solve the equation (3.4)(6.7) using the standard algorithm, first multiply 3.4 and 6.7. Then, the result is 22.78.
How to solve for the standard algorithm?The standard algorithm for multiplication is a step-by-step process that involves breaking down the numbers being multiplied into simpler parts, and then multiplying those parts together.
First, you would need to multiply the ones place of the first number (4) by the ones place of the second number (7), which would give you 28.
Next, you would need to multiply the ones place of the first number (4) by the tens place of the second number (6), which would give you 24.
Then, you would add the two products from steps 1 and 2 to get the result: 28 + 24 = 52.
Alternatively, you can use the distributive property of multiplication to simplify the problem.
(3.4)(6.7) = 3.46 + 3.40.7 = 22.8
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What is the mirror image of point 2 3 under origin?
The mirrors image of points (2, 3) under the origin is (-2, -3)
What is a mirror image?
A mirror image is a reflected duplicate of a seemingly identical item that is turned the other way in the plane perpendicular to the mirror surface. It manifests as an optical effect as a result of reflection off of materials like a mirror or water.
Here,
We have to find the mirror image of points (2, 3) under the origin.
We concluded that the mirror image of a point(2,3) is (-2,-3).
The coordinates of the origin are denoted by (0, 0). It means that at origin, x=0 and y=0.
Hence, the mirrors image of points (2, 3) under the origin is (-2, -3)
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Juan has $24 to spend at the bookstore. If books cost $6 each how many books cam he buy?
4Answer:
Step-by-step explanation:
24 divided by 4 = 6
A zip code for eagar, Arizona is 85925. Which digit is in the "hundreds" place?
TEST RN What is the equation of the line that passes through the point (6.0) and had a slope of -5/6? HELPP PLEASE TEST RN
An equation of the line that passes through the point (6, 0) and had a slope of -5/6 is y = -5x/6 + 5.
What is the point-slope form?Mathematically, the point-slope form of a straight line can be calculated by using this mathematical expression:
y - y₁ = m(x - x₁)
Where:
m represents the slope.x and y are the points.Given the following parameters:
Point (x, y) = (6, 0)Slope = -5/6Substituting the given parameters into the point-slope formula, the equation of the line is given by;
y - y₁ = m(x - x₁)
y - 0 = -5/6(x - 6)
y = -5x/6 + 5
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8. What is the converse of this
statement?
If Sarah keeps practicing gymnastics,
she will win a medal.
Answer:
Step-by-step explanation:
Sara will win a medal if she keeps practicing gymnastics.
Which graph represents the equation y equals one half times x plus 2? graph of a line passing through the points negative 2 comma negative 2 and 0 comma negative 1 graph of a line passing through the points negative 2 comma 0 and 0 comma 1 graph of a line passing through the points negative 2 comma negative 3 and 0 comma negative 2 graph of a line passing through the points negative 4 comma 0 and 0 comma 2
The correct graph is the third one: graph of a line passing through the points negative 2 comma negative 3 and 0 comma negative 2.
A graph is what?News grapher using a function with inputs and outputs to depict a function. A function is a connection between two variables in which the input determines the output. In a graph, the y-axis shows the output, while the x-axis shows the input.
An unweighted, undirected graph with no graph loops or numerous edges is referred to as a simple graph (also known as a strict graph; Tutte 1998, p. 2; West 2000, p.
The line that connects the coordinates (x, y) = (-2, -3) and (y = 1/2x + 2) on this graph expresses the equation y = 1/2x + 2. (0, -2). When we enter those coordinates into the equation, we get the points on the graph, y = 1/2(-2) + 2 = -3 and y = 1/2(0) + 2 = 2.
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Show two
different ways to find the answer to the problem below.
Dog and cat food are sold in 20-pound bags. There are 14 bags of dog food and 12 bags of cat food on the store shelves. How many pounds of dog and cat food are on the shelves?
Answer: There are 520 pounds of dog and cat food
Step-by-step explanation:
1. 14+12= 26
2. 26x20=520
what is 999,999,999 x 600277798128
Answer:
6.000277798 x 10^20