Answer: [tex]20x-21y+14[/tex]
Step-by-step explanation:
[tex]\frac{1}{5}(150x-80y+50-50x-25y+20)\\\\=\frac{1}{5}(100x-105y+70)\\ \\ =20x-21y+14[/tex]
The area of a rectangular room is 750 square feet. The width of the room is 5 feet less than the length of the room. Which equations can be used to solve for y, the length of the room? Select three options. y(y + 5) = 750 y2 – 5y = 750 750 – y(y – 5) = 0 y(y – 5) + 750 = 0 (y + 25)(y – 30) = 0
The equation that can be used to solve for y, the length of the room is;
y² - 5y = 750
How to solve Algebra Expressions?The formula for the area of a rectangle is;
Area = L * W
where;
L is length
W is width
The width of the room is 5 feet less than the length of the room. Thus;
Width = Length - 5
If length is y, then;
Width = y - 5
Area = y(y - 5)
y(y - 5) = 750
y² - 5y = 750
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Jordan has an extension ladder that currently reaches a height of 1135 feet. She needs the ladder to extend to a height of 1515 feet. How much longer, in feet, does the ladder need to be extended
Answer: 380 ft
Step-by-step explanation: To find the length in between, you simply subtract the numbers.
1,515 - 1,135 = 380
Therefore, the ladder needs to be extended 380 ft.
given the following codes, what would be the final value of z? x = 5 y = 7 z = x - y 2.00
Z would ultimately have a value of 2, since 5 minus 7 equals 2.
x = 5; y = 7; z = x - y z = 5; y z = 7; z = 2;Consequently, z's final value is 2.
Given that x is 5 and y is 7, the final value of z would be 2. These two numbers are divided by two, giving the answer 2. Subtraction is the action of comparing two integers to determine their differences. In this instance, since x and y differ by 2, the ultimate value of z is also 2. The solution is 2, which can alternatively be written as 5 - 7 = 2. In this case, the ultimate value of z is 2, since the difference between x and y is 2, which can be found using the useful mathematical technique of subtraction.
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4) Which equation is true when x not when x = -10?
Answer:
x^3 = 1000
Step-by-step explanation:
describe a situation that represents 7 x -8
use the graph to write a linear function that relates y to x
Answer:
f(x) = -4[tex]x[/tex] - 2 or y = -4[tex]x[/tex] - 2
Step-by-step explanation:
In this question, you should use the graph to write the function/equation in slope intercept form.
y = mx + b where m is the slope and b is the y intercept
To calculate the slope, you can use rise/run between any two points. I will use the points (-2, 6) and (0, -2). In these points, the "rise" would be -8 as that is the number of units they are away from each other vertically. It is negative because the line obviously has a negative slow as it is travelling from up to down. The run in this case would be 2 as that is the distance the two points are away from each other horizontally.
Then, substitute.
[tex]\frac{-8}{2}[/tex] = -4, so m = -4
Now we will find the b value.
B is the y-intercept, or what the y value of the coordinate of the point that the line touches the y-axis. The coordinate is (0, -2). Therefore, the b value is 2.
You deposit $3000 in an account that pays 3.25% annual interest. Find the balance after 7 years if the interest is compounded quarterly.
Work Shown:
A = P*(1+r/n)^(n*t)
A = 3000*(1+0.0325/4)^(4*7)
A = 3762.91169916373
A = 3762.91
Build a function that describes Karas finances of the scenario where money is the y variable and the amount of skateboards is X
A variable is an alphabet or phrase used to represent an unknown quantity, unknown value, or unknown number in mathematics.
What is the difference between function and variable?The values of one or more independent variables determine the values of a single dependent variable in a mathematical connection known as a function. Function denotes a relationship between two variables where one influences expression the other (s).
Here,
Given :
=> 50 assembly kit be y
and => 20 profit be x
Thus,
Equation is = > 50y + 20y = 15
In mathematics, a variable is an alphabet or phrase that denotes an unknowable quantity, unknowable value, or unknowable number. In the case of algebraic expressions or algebra, the variables are employed specifically.
A graph is considered to be a function if any vertical line formed can cross it at most one point. The graph is not a function if it contains any locations where a vertical line can pass through it twice or more.
An expression, rule, or law in mathematics that specifies the relationship between an independent variable and a dependent variable (the dependent variable).
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What is the rule for the following pattern by 9 18 12 24 18 36 30?
The rule for the pattern is to add 6 to each number.
What is the rule for the following pattern by 9 18 12 24 18 36 30?The pattern for this sequence is that it follows a multiplication by two rule. This means that each term in the sequence is twice the previous term. This rule is also known as the exponential rule, because each term is the result of multiplying the previous term by two.This pattern is an example of exponential growth, which is defined as a growth rate that increases by a fixed rate over a period of time. In this case, the fixed rate is a multiple of two, and the growth rate is increasing by a factor of two each time.Exponential growth is important in mathematics and science because it can be used to predict the growth of populations, the spread of disease, the growth of financial investments, and the growth of technology. It is also important in the study of natural phenomena such as climate change and the evolution of life.Exponential growth can be represented as a graph, which will show a curved line with a steep slope. This is because the growth rate is increasing exponentially. As the sequence progresses, the rate of growth will become increasingly steep.The rule for this pattern is that each term is twice the previous term, and this type of pattern is called exponential growth. It is important in mathematics, science, and other fields because it can be used to predict the growth of populations, the spread of disease, the growth of financial investments, and the growth of technology.To learn more about the exponential rule refer to:
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how many liters is 79.1 ml? calculate and type your answer with correct significant numbers. (show your work for full credit)
79.1 mL is equal to 0.0791 litres with correct significant figures.
Unit conversion is a process with multiple steps involving multiplication or division by a numerical factor, particularly a conversion factor. The procedure may also demand the selection of the correct number of substantial digits and rounding. Different units of conversion are used to calculate different parameters.
We convert the units of any quantity to understand better. For example, the length of a table is measured in inches; on the other hand, the length of a garden is measured in yards to make it simple to comprehend. We cannot calculate the length of a finger in miles.
79.1 mL is equal to 0.0791 litres. To convert millilitres to litres, we divide the number of millilitres by 1000:
79.1 mL / 1000 = 0.0791 liters
So, 79.1 mL is equal to 0.0791 litres with correct significant figures.
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What expression represents the verbal phrase? One-fourth times a number n, minus thirty
Answer:
The expression that represents the verbal phrase "One-fourth times a number n, minus thirty" is (1/4)n - 30.
5. Use the graph to find the cost of 8 hats.
a. $7.50
b. $8.00
c. $60.00
d. $75.00
Answer:
c. $60
Step-by-step explanation:
Go along the x-axis until you get to 8, then go straight up until you hit the line, now go straight over to the left until you hit the y-axis. Your horizontal line will hit the y-axis at y=$60.
From a station, hikers Oliver and Roel, who both have uniform hiking, speed walk in opposite directions - Oliver speed walks eastward whereas Roel speed walks westward. After walking 3 kilometers each, both take left turns at different angles. Oliver at angle 30° and Roel at 40°. Both continue hiking and cover another 4 kilometers each after taking a rest. Which of the hikers is farther from their station? Why?
Oliver is farther from the station.
The distance from the station for each hiker can be calculated using the Law of Cosines.Let's call the initial distance from the station for Oliver and Roel as d1 and d2, respectively. The Law of Cosines states:
d1^2 = 3^2 + 4^2 - 2 * 3 * 4 * cos(30°)
d2^2 = 3^2 + 4^2 - 2 * 3 * 4 * cos(40°)
By solving the above equations, we can determine the distances d1 and d2. The hiker who is farther from the station will have the larger value of d1 or d2.
In this case, it can be seen that d1 > d2, meaning Oliver is farther from the station than Roel.
This is because the angle of 30° is larger than the angle of 40°, so the cosine of 30° is smaller than the cosine of 40°.
Therefore, Oliver is farther from the station.
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a one story house recently sold for $348,000. what is the price per square foot of the house, if the house measures 25' x 68'…?
The price per square foot of the house is $51.18.
The price per square foot of the house is determined by taking the total price of the house, $348,000, and dividing it by the total square footage of the house, 25' x 68' and we get $51.18.
For example- The total square footage is 1700, so when divided into the total cost, $348,000, the price per square foot of the house is $204.71. This means that for every square foot of the house, the buyer paid $204.71. The total cost of the house is a combination of the price per square foot in addition to any additional fees, such as taxes and closing costs.
When purchasing a home, it is important to know the price per square foot as this can help to determine the value of the home.
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Solve the polynomial equation. x^4+7x^2-144=0
Answer:
x = 3
Step-by-step explanation:
Let's check
3^4 + 7(3)^2 - 144 = 0
81 + 63 - 144 = 0
144 - 144 = 0
0 = 0
So, x = 3 is the correct answer.
how many hexadecimal strings of length 9 have exactly three a’s, no b’sand two 7’s
There are approximately 368,739,406 possible hexadecimal strings of length 9 with exactly three a’s, no b’s and two 7’s.
Hexadecimal is a numbering system that uses 16 symbols (0-9 and A-F) instead of the standard 10 symbols in decimal.
A hexadecimal string of length 9 with exactly three a’s, no b’s and two 7’s can be represented as
=> XaXaXaX7X7,
where X can be any of the hexadecimal symbols other than a and 7.
To calculate the number of possible combinations, we need to calculate the number of possible values for X.
In total, there are 16 possible hexadecimal symbols, but we need to subtract 3 (a’s) and 2 (7’s) to find the number of possible values for X.
So, the number of possible values for X is
=> 16-3-2 = 11.
With 9 positions to fill and 11 possible values for X, the total number of combinations is 11⁹, which is approximately 368,739,406.
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the base radius and height of a right circular cylinder are measured as 8 cm and 16 cm, respectively, with a possible error in measurement of as much as 0.2 cm each. use the total differential to estimate the maximum error in the calculated volume of the cylinder.
The total differential to estimate the maximum error in the calculated volume of the cylinder is 200.96.
The base radius of a right circular cylinder are measured as 8 cm.
The height of a right circular cylinder are measured as 16 cm.
The possible error in measurement of as much as 0.2 cm each.
We have to calculate the maximum error in the calculated volume of the cylinder.
The formula of volume of cylinder is:
V = πr^2h
The value of dr = 0.2 and dh = 0.2. So;
dV(max) = ∂V/∂r dr + ∂V/∂dh dh
dV(max) = ∂(πr^2h)/∂r dr + ∂(πr^2h)/∂dh dh
On differentiating
dV(max) = 2πrh dr + πr^2 dh
r = 8 cm, π = 3.14 and h = 16 cm.
Now putting the value
dV(max) = 2×3.14×8×16×0.2 + 3.14×(8)^2×0.2
dV(max) = 160.768 + 40.192
dV(max) = 200.96
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Which of the following would be classified as categorical data?
Choose the correct answer below.
A. Hair color
B. Number of suitcases on a plane
C. Tree height
D. Amount of rainfall
Hair color Categorical data is a type of data that can be stored into groups or categories with the aid of names.
Statistical information made up of categorical variables—data that have been divided into categories—is known as categorical data. A set of grouped data is one of example. More specifically, countable qualitative data or quantitative data clustered within predetermined intervals could be used to create category data. The information is condensed into a probability table. However, the word "categorical data," which is used to describe data sets, is used when discussing data analysis. It should be noted that although the data set includes some categorical variables, it may also include non-categorical variables.
Categorical data is a collection of information that is divided into groups. I.e, if an organization or agency is trying to get a biodata of its employees, the resulting data is referred to as categorical. This data is called categorical because it may be grouped according to the variables present in the biodata such as sex, state of residence, etc.
A. Hair color Categorical data is a type of data that can be stored into groups or categories with the aid of names.
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7. Write 3 x 3 x 3 x 3 x 3 x 3 using
exponents.
O A. 6³
O B. 3^3
O C. 12³
O D. 9^4
Answer:
(All given options are incorrect)
Correct answers: [tex]3^6[/tex] or [tex]9^3[/tex]
Step-by-step explanation:
There are several ways to write [tex]3\times3\times3\times3\times3\times3[/tex].
The first is as a power of 3. An exponent represents the number of times a number is multiplied by itself. This would be written as [tex]3^6[/tex].
The second is as a power of 9. Combining each pair of [tex]3\times3[/tex] gives:
[tex]9\times9\times9[/tex] which is equal to [tex]9^3[/tex].
None of the given options are correct for [tex]3\times3\times3\times3\times3\times3[/tex]. Please double check that your question and answer options are written correctly. Correct answer options would be [tex]3^6[/tex] or [tex]9^3[/tex].
Log x+y = logbx − logbyGiven log630 ≈ 1.898 and log62 ≈ 0.387, log615 =____.
Log x+y = logbx − logbyGiven log630 ≈ 1.898 and log62 ≈ 0.387, log615 ≈ 2.086.
Given log 630 ≈ 1.898 and log 62 ≈ 0.387,
We have log 630 = log (6 * 62 * 10) = log 6 + log 62 + log 10 = 1 + 0.387 + 1 = 2.387
And log 615 = log (6 * 62 * 5) = log 6 + log 62 + log 5 = 1 + 0.387 + 0.699 = 2.086
So, log 615 ≈ 2.086
In the example given, log 630 ≈ 1.898 and log 62 ≈ 0.387. These logarithmic values are used to simplify other logarithmic expressions and, the logarithm of 615 was found to be approximately 2.086.
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Determine all intervals on which f(x)[tex]\leq[/tex]0.
The required interval for which the function is f(x) ≤ 0 are (-∞, -2) and (2, 7).
What are functions?Functions are the relationship between sets of values. e g y=f(x), for every value of x there is its exists in a set of y. x is the independent variable while Y is the dependent variable.
Here,
From the graph, the portion of the function below the axis shows the f(x) ≤ 0.
So the interval where f(x) ≤ 0, from the graph, is given as,
(-∞, -2) and (2, 7)
Thus, the required intervals for which the function is f(x) ≤ 0 are (-∞, -2) and (2, 7).
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Factor out a negative 1 from each expression
1: 7 + (-6)
2: -4 - (5 + 3)
3: -9 - 1
4: 8 - (-6)
5: 3 + (-4 + 8)
Use the distributive property to show that your answers to Questions one through 5 are
correct.
Factoring out negative 1 from the expression -4-(5+3) is -1(12).
What are factors?A factor is a number that divides another number, leaving no remainder. In other words, if multiplying two whole numbers gives us a product, then the numbers we are multiplying are factors of the product because they are divisible by the product.
A) 7+(-6)
= 7-6
= 1
2) -4-(5+3)
= -4-8
= -12
= -1(12)
3) -9-1
= -10
= -1(10)
4) 8-(-6)
= 8+6
= 14
5) 3+(-4+8)
= 3+4
= 7
Therefore, factoring out negative 1 from the expression -4-(5+3) is -1(12).
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What coefficients correctly balance this reaction?
CH₂OH + 0₂
_CO, + _ _ _H,O
1
2
3
4
-
1; 2; 1; 2
3; 3; 2; 4
2; 3; 2; 4
1; 3; 1; 2
8²
Answer:
Step-by-step explanation:
i wish i knew! i wish i knew you wanted me
Short Explanation:Marcelino did not win the game 2 day ago. Marcelino did not win the game yeterday. Therefore, Marcelino will win the game today
This is a false conclusion. Just because Marcelino did not win the game 2 days ago or yesterday, it does not necessarily mean he will win the game today. There could be many other factors at play that determine the outcome of the game.
Marcelino Game Win False ConclusionThis statement is referring to a hypothetical game and the outcome of it, but the conclusion that Marcelino will win today is not logically deduced from the information given (that Marcelino did not win 2 days ago or yesterday). The outcome of a game can be influenced by many factors such as the skill level of the players, the strategies used, and luck. Simply not winning in the past does not guarantee a win in the future.
This statement is not related to mathematics. It is a logical conclusion based on the given information about a hypothetical game, but the conclusion does not follow logically from the information provided.
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PLS HELP ME!!!!
2 x3x5² is the prime factorization of what composite number? OA) 120 OB) 180 OC) 450 OD) 600
2³ × 3 × 5² is the prime factorization of the composite number 600.
What is the composite number?Composite numbers are whole numbers that can be divided evenly by numbers other than 1 or themselves. For example, 4 is a composite number because it can be divided evenly by 1, 2, and 4. Other examples of composite numbers are 6, 8, 9, 10, 12, 14, 15, and so on.A composite number is a positive integer that has more than two divisors. It is the product of two or more prime numbers. Examples of composite numbers include 4, 6, 8, 9, 10, 12, 14, 15, 16 and so on.
2³ × 3 × 5² = 2 × 2 × 2 × 3 × 5 × 5
= 600
Thus, 2³ × 3 × 5² is the prime factorization of the composite number 600.
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write an equation for a linear function h where h(7)=329 and h(11)=553
An equation for a linear function is, [tex]h(x)[/tex] = 56[tex]x[/tex] - 63 where h(7)=329 and h(11)=553.
Given that,
h(7)=329 and h(11)=553
Linear function, y = [tex]mx + c[/tex]
Let, h = y and [tex]x =x[/tex]
Define Linear function :A function whose graph is a straight line and which is represented by an equation of the form y = mx + c where a and b are constants, m does not equal zero, and x is any real number.
The standard form for linear equations in two variables is Ax+By=C. For example, 2x+3y=5 is a linear equation in standard form. When an equation is given in this form, it's pretty easy to find both intercepts (x and y).
So,
[tex]h(x)[/tex] = [tex]mx + c[/tex]
When,
[tex]x[/tex] = 7 , [tex]h(x)[/tex] = 329
( [tex]x_{1}[/tex] , [tex]h(x_{1} )[/tex] ) = ( 7 , 329 ) (Equation-1)
When,
[tex]x[/tex] = 11 , [tex]h(x)[/tex] = 553
( [tex]x_{2}[/tex] , [tex]h(x_{2} )[/tex] ) = ( 11 , 553 ) (Equation-2)
Linear function,
[tex]\frac{h(x)-h(x_{1} )}{x-x_{1} }[/tex] = [tex]\frac{h(x_{2} )-h(x_{1} )}{x_{2} -x_{1} }[/tex]
We can substitute equation -1 and 2
[tex]\frac{h(x)-329}{x-7}[/tex] = [tex]\frac{553-329}{11-7}[/tex]
[tex]\frac{h(x)-329}{x-7}[/tex] = 224/4
[tex]\frac{h(x)-329}{x-7}[/tex] = 56
[tex]h(x)[/tex] - 329 = 56 ( [tex]x-7[/tex] )
[tex]h(x)[/tex] - 329 = 56[tex]x[/tex] - 392
[tex]h(x)[/tex] = 56[tex]x[/tex] - 392 + 329
[tex]h(x)[/tex] = 56[tex]x[/tex] - 63
Therefore,
An equation for a linear function is, [tex]h(x)[/tex] = 56[tex]x[/tex] - 63 where h(7)=329 and h(11)=553.
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Identify the initial value and rate of change for the graph shown. (4 points) A coordinate plane is shown. A line passes through the y-axis at 2 and passes through the point 2 comma 4. a Initial value: 1, rate of change: 2 b Initial value: 2, rate of change: 1 over 2. c Initial value: 2, rate of change: 1 d Initial value: 1 over 2., rate of change: 2
Answer: the initial value is 2 and the rate of change is 1.
please solve step by step
The expression x² + 6x + 9 / 4 ÷ 3x + 9 / 8 can be simplified as 2(x + 3) / x .
How to solve an expression?To simplify an expression means to write an equivalent expression which contains no similar terms. In other words, we have to reduce the expression to the simplest form.
Therefore,
x² + 6x + 9 / 4 ÷ 3x + 9 / 8
Let's convert the division sign to multiplication.
Therefore,
x² + 6x + 9 / 4 × 8 / 3x + 9
Let's factorise the numerators and the denominators expression
x² + 6x + 9 = (x +3)² = (x + 3)(x + 3)
3x + 9 = 3(x + 3)
Therefore,
(x + 3)(x + 3) / 4 × 8 / x(x + 3)
Hence,
(x + 3)(x + 3) / 4 × 8 / x(x + 3) = 2(x + 3) / x
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An 8-foot ladder is leaning against a wall so that the top of the ladder is 5 feet above the ground. If a 15-foot ladder is leaned against the wall and forms the same angle with the wall, how high up the wall does this ladder reach? Enter your answer in the box. Show your answer to thousandths.
Which of the following terms completes the sentence below?
To fill out a function's______
and after each of the function's
, you will need to use test numbers before
and asymptotes.
O A. rational equation; values
OB. sign chart; values
OC. rational equation; zeros
O D. sign chart; zeros
Answer:
D. sign chart; zeros
Step-by-step explanation:
To fill out a function's sign chart, you will need to use test numbers before and after each of the function's zeros and asymtopes
What is Number system?A number system is defined as a system of writing to express numbers.
The term that completes the sentence and makes it grammatically and conceptually correct is "sign chart; zeros".
To fill out a function's sign chart; zeros and after each of the function's zeros, you will need to use test numbers before and after the zero to determine the sign of the function on each interval.
Hence, to fill out a function's sign chart, you will need to use test numbers before and after each of the function's zeros and asymtopes
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