The answer is a ≤ 30.
An inequality is a mathematical expression that compares two values or expressions using an inequality operator. In this case, the inequality would be a ≤ 30. This means that the area of the triangle must be less than or equal to 30 square inches.
This can be solved by finding the area of the triangle. To do this, we need to know the lengths of the sides of the triangle. Suppose we have sides p, q, and r. Then the area of the triangle can be found using the formula:
a = 1/2 × b × h
where q is the base of the triangle and r is the height. To ensure that the area of the triangle is no more than 30 square inches, the inequality must be satisfied. That is, 1/2 × b × h ≤ 30. This inequality can be rewritten in terms of the side lengths by substituting 1/2 × q × r for h. This gives us a ≤ 30.
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Mark each of the following graphs as (a) a function, but not one-to-one, (b) one-to-one function, or (c) not a function. In each case, explain how you know. (1 point each)
The graph is forming a function but it is not an one-one function.
If the vertical line test is satisfied, then the graph represents a function and a vertical line will cross it at most once.
If a horizontal line crosses the graph in no more than one spot, the function is one-to-one and passes the horizontal line test.
The graph in this case is made up of several horizontal, non-overlapping lines. It is a function and passes the vertical line test, however a horizontal line can cross the graph at any number of locations (is not one-to-one).
However, the graph is not a one-to-one function.
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Squares $ABCD$ and $EFGH$ are equal in area. Vertices $B$, $E$, $C$, and $H$ lie on the same line. Diagonal $AC$ is extended to $J$, the midpoint of $GH$. What is the fraction of the two squares that is shaded
The fraction of the two squares that is shaded exists 5/16 area shaded.
What is the difference between diagonal and vertices?A diagonal is a line segment connecting two opposite corners (vertexes) of a polygon, however it is not an edge (side). In other words, it connects any two non-adjacent polygonal vertices. Therefore, by connecting any two vertices in a polygon directly (i.e., without using a side), we create a diagonal.
A line segment known as a diagonal joins two polygonal vertexes (corners), although it is not an edge (side). To put it another way, it joins any two polygonal vertices that are not adjacent. Therefore, by connecting any two vertices in a polygon directly (i.e., without using a side), we create a diagonal.
The triangle on the bottom exists 1/2 × 1/2 × 1/2 of the original area of the lower square = 1/8 of the lower square
2 square = [1/2 (square) + 1/8 (square) ] / 2 square
= 5/16 area shaded
Therefore, the fraction of the two squares that is shaded exists 5/16 area shaded.
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The fraction of the two squares that is shaded exists 5/16 area shaded.
What is the difference between diagonal and vertices?A diagonal is a line segment that joins two opposed polygonal corners (vertexes), although it is not an edge (side). In other words, it joins any two polygonal vertices that are not neighbouring. As a result, we can make a diagonal by directly joining any two vertices of a polygon (i.e., without utilising a side).
Although it is not an edge, a line segment known as a diagonal connects two polygonal vertexes (corners) (side). In other words, it connects any non-adjacent pair of polygonal vertices. As a result, we can make a diagonal by directly joining any two vertices of a polygon (i.e., without utilising a side).
The triangle on the bottom exists 1/2 × 1/2 × 1/2 of the original area of the lower square = 1/8 of the lower square
2 square = [1/2 (square) + 1/8 (square) ] / 2 square
= 5/16 area shaded
Therefore, the fraction of the two squares that is shaded exists 5/16 area shaded.
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The scale factor of the blueprint of a garage door to the actual garage door is 0.05. The area of the actual garage door is 220 ft2 . What is the area of the garage door on the blueprint
The area of the garage door on the blueprint is 0.55 ft^2.
The size of a patch on a surface is determined by its area. The area of an open surface or the boundary of a three-dimensional object is referred to as the surface area, whereas the area of a plane region or plane area refers to the area of a form or planar lamina.
Given in question,
Scale factor = 0.05
Since this scale factor is for length.
The scale factor for the area = 0.05*0.05
= 0.0025
Original Area = 220
The area on the blueprint = 0.0025*220
= 0.55
Hence, the area of the garage door on the blueprint is 0.55 ft^2.
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a pair of sneakers in on sale as shown the sale price is $51. This is 75% of the original price. what was the original price of the shoes
pls help, explanation required
Is log e and log same?
The log function with base 10 is called the “common logarithmic functions” and the log with base e is called the “natural logarithmic function”. The logarithmic function is defined by, if logab = x, then ax = b.
The log with a base "e" (log e) is the same thing as In
The natural logarithmic function log e refers to its logarithmic function of the base of the constant e. For this equation to be equivalent in logarithm;
We can say that:
log e = ln
Logarithm may alternatively be defined as the exponent power to which a base must be raised in order to produce a given number.
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What is the inverse of the logarithmic function f x log9x?
The inverse of the logarithmic function f x log9x is f-1(x)=9^x.
The inverse of a logarithmic function is the exponential function. To find the inverse of the logarithmic function f x log9x, we can use the following equation: f-1(x)=9^x. This equation states that the inverse of the logarithmic function f x log9x is the exponential function f-1(x)=9^x.
The inverse of the logarithmic function f x log9x is f-1(x)=9^x, which is the exponential function.This means that for any value of x, the inverse of the logarithmic function f x log9x is equal to 9 raised to the power of x. For example, if x=2, then the inverse of the logarithmic function f x log9x is 9^2, or 81. Similarly, if x=3, then the inverse of the logarithmic function f x log9x is 9^3, or 729. In general, the inverse of the logarithmic function f x log9x is 9 raised to the power of x, for any value of x.
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Answer: f –1(x) = 9x
Step-by-step explanation:
Help with a bit of math??
Answer:
b.x=30
c.x=21
Step-by-step explanation:
What are the 3 possible solutions when solving a system of equations?
Three possible solutions when solving a system of equation are: one solution, no solution, and infinite solutions.
The 3 possible solutions of a system of equations are:
- Unique or one solution
- Infinite solutions
- No solution
In case of a system of linear equations, we can determine the type of its solution as follows:
- If the slopes are different, then their graphs will intercept in one point. Hence, the system of linear equation will have one solution.
- If the slopes are the same but the equation of the lines are different, the lines are parallel, hence they will not intercept. Therefore, there is no solution.
- If the linear equations are exactly (or can be transformed to exactly) the same equations, the solution is infinite.
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Express 1/2 loga16 + 1/3loga27 as logab
Answer:
[tex]log_{a}[/tex] 12
Step-by-step explanation:
using the properties of logarithms
• nlog x ⇔ log[tex]x^{n}[/tex]
• log x + log y = log (xy)
[tex]\frac{1}{2}[/tex] [tex]log_{a}[/tex] 16 + [tex]\frac{1}{3}[/tex] [tex]log_{a}[/tex] 27
= [tex]log_{a}[/tex] [tex]16^{\frac{1}{2} }[/tex] + [tex]log_{a}[/tex] [tex]27^{\frac{1}{3} }[/tex]
= [tex]log_{a}[/tex] [tex]\sqrt{16}[/tex] + [tex]log_{a}[/tex] [tex]\sqrt[3]{27}[/tex]
= [tex]log_{a[/tex] 4 + [tex]log_{a}[/tex] 3
= [tex]log_{a}[/tex] (4 × 3)
= [tex]log_{a}[/tex] 12
What does this symbol mean ∈?
A hat symbol (^) is used to represent an estimated value in regression analysis.
We know that in regression analysis, the predicted values are the y-hat values.
Here y is the output variable or dependent variable
A 'hat' symbol (^) is used to denote an estimator.
A ^ symbol is placed over the variable name to denote the estimated value.
In matrix system, a hat matrix is nothing but the projection matrix.
It projects the vector of observations, y, onto the vector of predictions, y^
We know that a vector has magnitude and direction. A ^ symbol is used is represent the direction of unit vector.
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please help me with this question!
Answer:
|5-2x|<_11
=5+2x<11
=2x=11-5
2x=6
=X<-3
How do you solve X easily?
To solve x easily, shift the variables to one side, and shift all the other values including constants to the other side.
Solve for x means finding the value of x in an equation involving one variable that is x or with different variables like finding x in terms of y. Whatever the case is you are required to find the value of x, for which the given equation holds true.
For example, if the equation is given as: 2x - 50 = 4
Now solve the tjis equation for x by keeping the term with variable x to one side, and shifting all the other values such as constants to the other side.
now
2x = 4 + 50
2x = 54
x = 54/2
x= 27
This is the required value of x which is obtained after solving the equation for x.
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What are the 4 types of problem solving?
The four types of problem solving can be named as Trial and Error , Algorithms , Inductive Reasoning and Deductive Reasoning .
What is Problem Solving ?
The Problem solving can be defined as the act of defining a problem , finding cause of problem, identifying, prioritizing and selecting the alternatives for solution and implementing it .
The four types of problem solving are :
(i) Trial and Error : It is defined as trying the different ways of doing something until we find the best solution .
(ii) Algorithms : The algorithm can be defined as a set of step by step procedures which provides correct answer to a particular problem.
(iii) Inductive Reasoning : It is defined as a process where we come to a conclusion where a general statement is reached from specific result.
(iv) Deductive Reasoning : It is defined as a process where we get specific results from general statements .
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Alaska is the biggest state in the United States of America. Write the given definition as a biconditional. A. A state is Alaska if and only if it is the smallest state in the United States of America. B. A state is the biggest state in the United States of America if and only if it is not Alaska. C. If a state is Alaska, then it is the biggest state in the United States of America. D. A state is Alaska if and only if it is the biggest state in the United States of America
D. A state is Alaska if and only if it is the biggest state in the United States of America is the correct biconditional statement.
Give reason for your answer.This is the correct biconditional statement because it accurately reflects the information given. The statement states that a state is Alaska if and only if it is the biggest state in the United States of America. This is true, as the given information states that Alaska is the biggest state in the United States of America.
Option A is incorrect because it says that a state is Alaska if and only if it is the smallest state in the United States of America which contradicts the given information.Option B is incorrect because it says that a state is the biggest state in the United States of America if and only if it is not Alaska, and that is not true. Alaska is the biggest state in the United States of America and it contradicts the given information.Option C is correct, but it is not a biconditional statement, it is a conditional statement, it states that if a state is Alaska, then it is the biggest state in the United States of America, but it doesn't have the "if and only if" part.Therefore, statement D is the correct biconditional statement that reflects the given information that Alaska is the biggest state in the United States of America.
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On a negatively skewed curve, which is true?
The mean of negatively skewed facts can be less than the median. If the information graphs symmetrically, the distribution has 0 skewness, no matter how lengthy or fat the tails are.
What is a curve ?
Curve can be defined as the path on which it is usually generated by the equation.
In statistics, a negatively skewed (also called left-skewed) distribution is a sort of distribution wherein more values are targeting the right side (tail) of the distribution graph while the left tail of the distribution graph is longer.
negatively skewed distribution refers to the distribution kind where greater values plot at the graph's proper facet, the tail of the distribution is longer on the left aspect, and the suggest is decrease than the median and mode. It is probably 0 or poor due to the data being distributed negatively.
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Find the first three terms of the sequence:
a₁ = 2.25, an = an-1 +0.5
The first three terms of the sequence are 2.25, 2.30, and 2.35.
What is an arithmetic sequence?It is a sequence where the difference between each consecutive term is the same.
Example:
2, 4, 6, 8, 10 is an arithmetic sequence.
We have,
a(1) = 2.25
a(n) = a(n - 1) + 0.5
Now,
The first term = 2.25
The second term.
a(2) = a(1) + 0.5
= 2.25 + 0.5
= 2.30
The third term.
a(3) = a(2) + 0.5
= 2.30 + 0.5
= 2.35
Thus,
The first three terms are 2.25, 2.30, and 2.35.
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A woman looking out from the window of a height 30m, observed that the angle of depression of the top of a flagpole was 44°. if the foot of the pole is 25m from the foot of the building and on the same horizontal ground, find, correct to the nearest whole number, the angle of depression of the foot of the pole from the woman
Answer:
here is your answer = 56.7m
What is the relationship between points and lines?
Answer:
Points identify starting and ending positions, and a line (in this case line segment) connects such points to show the distance between the two points.
Step-by-step explanation:
One-fifth of a bread loaf was shared equally among Herb, Dara, Mark, and Lily. What fraction of the original bread loaf did each person get?
Using the provided values and information, The answer is each person would receive 1/5 of the original bread loaf.
What do you mean by proportion?A proportion is a mathematical statement that compares two ratios. It is an equation that states that two ratios are equal, such as "a/b = c/d." Proportions are often used to solve problems involving fractions, decimals, and percentages. For example, if you know that a particular recipe calls for two cups of flour for every one cup of sugar, you can use this proportion (2/1 = x/3) to figure out how much sugar you need if you want to triple the recipe. The proportion can also be written as 2:1 = x:3.
What do you mean by ratio?A ratio is a mathematical comparison of two or more quantities, typically represented as a fraction. It is a way to compare the size of two or more things. For example, if a recipe calls for 2 cups of flour to 1 cup of sugar, the ratio of flour to sugar is 2:1. This means that for every 2 units of flour, there is 1 unit of sugar. Ratios can also be written using the colon symbol (:) or the word "to". For example, the ratio 2:1 can also be written as 2/1 or 2 to 1. Ratios can be simplified by dividing both the numerator and denominator by a common factor and can be used to compare quantities in different units.
Each person would get 1/5 of the original bread loaf. If the bread is divided equally among four people, then each person would receive 1/4 of the total amount. Since 1/5 is the same as 4/20, and 4 people are receiving the bread, then each person would receive 1/5 of the original bread loaf.
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Find the Values of x and y
The values of x and y could be 25 and 113
What are parallel lines ?
parallel lines can be stated as , they both are equi distant from each other and which never intersect.
From the given figure,
y+12 = 3x + 50
as both are parallel to each other.
y-3x = 38
and 5x = y + 12
as vertically opposites are always equal .
y = 3x + 38
y = 5x - 12
hence,
5x - 12 = 3x +38
2x = 50
x = 25
put x = 25 in y = 3x + 38
y = 3 * 25 + 38
y = 113
hence the values of x and y are 25 and 113 respectively.
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Is a polynomial yes or no?
we can find out the polynomial by the degree of the Polynomial.
Polynomial
A polynomial is defined as an expression which is composed of variables, constants and exponents, that are combined using mathematical operations such as addition, subtraction, multiplication and division
Degree of polynomial
The degree of a polynomial is defined as the highest exponent of a monomial within a polynomial. Thus, a polynomial equation having one variable which has the largest exponent is called a degree of the polynomial.
Types of polynomial
Depending upon the number of terms, polynomials are divided into the following categories:
1-Monomial
2-Binomial
3-Trinomial
4-Polynomial containing 4 terms (Quadronomial)
5-Polynomial containing 5 terms (pentanomial ) and so on.
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Hays is standing outside on a sunny day. he is 6 ft tall and casts a 4 ft shadow. what is the distance from the top of hays's head to the end of his shadow? round to the nearest tenth, if necessary. responses
a. 4.5 ft
b. 4.5 ft
c. 5 ft
d. 5 ft
e. 7.2 ft
f. 7.2 ft
g. 10 ft
Options e and f is the correct answers. The distance from the top of hays' head to the end of his shadow is 7.21ft
Hays' body and his shadow are perpendicular.
So if we imagine the line from the top of his head to the end of his shadow on the ground, we have a right triangle, and the imaginary line is the hypotenuse.
Then you can stand back and let Pythagoras figure out the length of the line for you, using c² = a² + b²
(Distance)²=(Hay's height)²+(length of his shadow)²
(Distance)²=(6 ft)² + (4 ft)²
(Distance)²=(36 ft²) + (16 ft²)
(Distance)=52 ft²
Distance =√(52 ft)²
Distance = 7.21 ft
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The quotient of 25 and 5 increased by 3
Answer: 8
Step-by-step explanation: Based on the given conditions, formulate 25/5+3 Reduce the sum or difference: to 8 therefore the answer is 8
Answer:
down below
Step-by-step explanation:
The quotient means the total amount that comes from dividing two things. In this case, the problem is asking for 25 and 5 to be divided. 25 divided by 5 is 5. You can check this by multiplying 5 and 5 to get 25. So, you know it's right. Now, take 5 and add 3 to it. 5 + 3 = 8. So, the answer is 8.
Hope this helps! :)
Select the values that make the inequality a > − 6 true
Answer:
a ≥ -5
Step-by-step explanation:
Think like this is a number line
--------------------------------------------------------------------------------------------------------
-6 -5 -4 -3 -2 -1 0 1 2 3 4
and all the inequality says is for it to be bigger than -6 so than is -5, -4, -3, -2 -1, 0,1 and so on. So the answer is a>-6 or a≥-5
Do the values in the table represent a proportional relationship?
x 2 3 4 5
y 5 6 7 8
Select from the drop-down menu to correctly complete the statement.
All of the y-values
Choose.
a constant multiple of the corresponding x-values, so the relationship
Choose
Values of x and y in table does not represent a proportional relationship.
From the table x values 2, 3, 4 and 5 corresponds to values of y 5, 6, 7 and 8 respectively. The ratio of x value and y value is
2/ 5 = 0.4
3/ 6 = 0.5
4/ 6 = 2/ 3 ≈ 0.67
5/ 8 = 0.625
As the ratio is not constant, the values in table does not represent a directly proportional.
The value of xy is
2×5 = 10
3×6 = 18
4×7 = 28
5×8 = 40
Again as the value of xy is not constant, so they are not inversely proportionally.
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3 1/2 x 1 1/2 as a mixed number in simplest form
Answer: 8 3/4 because first find your common denominator, then solve the math and you will get 8 3/4
if the minimum charge of 175 calls is Rs 180 and Rs 1.50 per calls for additional calls then find the cost of calls including the charge of TSC 10% and VAT 13% as the former reading the total calls a land line phone is 5577 and the present reading 7577.Also,find the amount of payment including 20% fine
The total amount of payment for calls is Rs 648
How to find the total amount for paymentFrom the problem, the following information is deduced to help solve the problem
the minimum charge of 175 calls is Rs 180 and Rs 1.50 per calls for additional calls
The total call reading
= present reading - former reading
= 7577 - 5577
= 2000
the number of 175 calls in 2000
= 2000 / 175
= 11 3/7 approximately 12
Total cost of calls
175 calls = Rs 180 + Rs 1.50 * 12
= 180 + 1.50 * 12
= Rs 180
Adding other charges to Rs 180
= 180 * 1.1 + 180 * 1.3 + 180 * 1.2
= Rs 648
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Question 3(Multiple Choice Worth 5 points) (05.01)A window is 4 feet wide and 8 feet tall. A rectangle is shown. The length of the rectangle is labeled 4 feet. The width of the rectangle is labeled 8 feet. A manufacturer wants to use a scale factor of 1.5 to enlarge a window. What will the area of the window be after it is enlarged
Answer: 72 feet²
Step-by-step explanation: Area scale factor = 1.5² = 2.25 Area of the window after it is enlarged = Original area × 2.25 The original area = 8 feet × 4 feet = 32 feet² Area of the window after it is enlarged = 32 feet² × 2.25 = 72 feet²
set an expression negative -4n +3+9n-4 is equivalent to 4N. What error did Maria likely make?
The error that Maria likely make is that she subtracted 1n from 5n.
How to infer the error?In Mathematics, it is important to note that an expression is simply used to show the relationship between the variables that are provided or the data given regarding an information. In this case, it is vital to note that they have at least two terms which have to be related by through an operator.
The value of the expression will be:
= -4n +3+9n-4
= 5n - 1
The error was because 1n was minus from 5n
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What is the expression for f(x)f(x)f, left parenthesis, x, right parenthesis when we rewrite \left(\dfrac{1}{49}\right) ^{x}\cdot \left(\dfrac{1}{7}\right)^{6x 11}( 49 1 ) x ⋅( 7 1 ) 6x 11 left parenthesis, start fraction, 1, divided by, 49, end fraction, right parenthesis, start superscript, x, end superscript, dot, left parenthesis, start fraction, 1, divided by, 7, end fraction, right parenthesis, start superscript, 6, x, plus, 11, end superscript as \left(\dfrac{1}{7}\right)^{f(x)}( 7 1 ) f(x) left parenthesis, start fraction, 1, divided by, 7, end fraction, right parenthesis, start superscript, f, left parenthesis, x, right parenthesis, end superscript ? f(x)=
The expression for f(x) using exponent properties is 8x+11.
Let's first simplify the following statement in order to determine f(x):
[tex]\[\left(\frac{1}{49}\right)^x \cdot \left(\frac{1}{7}\right)^{6x + 11}\][/tex]
Rewrite now with [tex]\(\left(\frac{1}{49}\right)^x\)[/tex] and [tex]\(\left(\frac{1}{7}\right)^{6x + 11}\)[/tex] as a single term's powers:
[tex]\[\left(\frac{1}{7^2}\right)^x \cdot \left(\frac{1}{7}\right)^{6x + 11} \][/tex]
Now, using the rule for exponents [tex](a^{(m*n)} = (a^m)^n)[/tex],
Combine the following words using the same base (1/7 in this case):
[tex]\[ \left(\frac{1}{7}\right)^{2x} \cdot \left(\frac{1}{7}\right)^{6x + 11} \][/tex]
Add their exponents to multiply phrases with the same base:
[tex]\[ \left(\frac{1}{7}\right)^{2x + (6x + 11)} \][/tex]
[tex]\[ \left(\frac{1}{7}\right)^{(8x + 11)} \][/tex]
Now, the given expression becomes:
[tex]\[ \left(\frac{1}{7}\right)^{(8x + 11)} \][/tex]
Now, compare [tex]\(\left(\frac{1}{7}\right)^{f(x)}\)[/tex],and [tex]\(f(x) = 8x + 11\)[/tex] gives f(x) = 8x+ 11.
So, the expression for f(x) is: [tex]\[ f(x) = 8x + 11 \][/tex].
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The question attached here is in appropriate form the appropriate form is
Find the expression for f(x) when rewriting the following expression in the form [tex]\(\left(\dfrac{1}{7}\right)^{f(x)}(7^1) ^{\dfrac{1}{49}^x \cdot \dfrac{1}{7}^{6x+11}}\):[/tex]
[tex]\(\left(\frac{1}{49}\right)^x \cdot \left(\frac{1}{7}\right)^{6x + 11}\)[/tex]