Answer: 1.
Step-by-step explanation:
[tex]\displaystyle\\sin^2x(cot^2x+1)=\\\\sin^2x(\frac{cos^2x}{sin^2x}+1)=\\\\\frac{sin^2xcos^2x}{sin^2x}+sin^2x=\\\\cos^2x+sin^2x=\\\\1.[/tex]
Help with a bit of math??
Answer:
b.x=30
c.x=21
Step-by-step explanation:
The granola is selling for $2.88 and weighs 18 ounces. The
flaked cereal is selling for $4.32 and contains 24 ounces.
Which is the better buy? Show your thinking.
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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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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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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E) how to find the first 4 terms in the expantion of ( 1 + 2x ) to power 6 ?
the first 4 term is (1+2x)^6
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
In the diagram below, \overline{MN}
MN
is parallel to \overline{JK}
JK
. If MNMN is 1212 more than LNLN, LK=33LK=33, and JK=55JK=55, find the length of \overline{LN}
LN
. Figures are not necessarily drawn to scale. State your answer in simplest radical form, if necessary.
The value of the missing length LN of the similar triangles is; LN = 18
How to solve Similar Triangles?Similar triangles are defined as triangles that have the same shape, but their sizes may vary. This means therefore that, if two triangles are similar, then we can say that their corresponding angles are congruent and also their corresponding sides are in equal proportion.
In the given triangle attached, we can say that if we apply the concept of similar triangles, we will get;
LN/LK = MN/JK
We are told that;
MN is 12 more than LN. Thus; MN = 12 + LN
LK = 33
JK = 55
Thus;
LN/33 = (12 + LN)/55
55LN = 33(12 + LN)
55LN = 396 + 33LN
22LN = 396
LN = 396/22
LN = 18
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please help me with this question!
Answer:
|5-2x|<_11
=5+2x<11
=2x=11-5
2x=6
=X<-3
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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Solve for x in this triangle. Round your answer to the nearest tenth.
Answer:
Step-by-step explanation:
7
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:
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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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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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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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! :)
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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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
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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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]
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
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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Carolina is mowing lawns for a summer job.for every mowing job,she charges an initial fee plus $6 for each hour of work.her total fee for a 4-hour job,for instance is $32
The function Formula is, f(t) = 6t + 8.
What is Function?In mathematics, a function is represented as a rule that produces a distinct result for each input x. In mathematics, a function is indicated by a mapping or transformation. The collection of all the values that the function may input while it is defined is known as the domain. The entire set of values that the function's output can produce is referred to as the range. The collection of values that could result in a function's outputs is known as the co-domain.
Given:
Carolina charges an initial fee plus $6 for each hour of work
Her total fee for a 4-hour job = $32
So, if she work for 't' hours then linear equation will be of the form
f(t) = mt + b
Here m is the constant rate = 6
Now we plug in the values and find out b, m=6
f(t) = mt + b
32 = 6(4) + b
32= 24 + b
8 = b
So, the function is f(t) = 6 t+8.
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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
PROBLEM SOLVING Your friend has two standard decks of 52 playing cards and asks you to randomly draw one card from each deck. What is the probability that you will draw two spades
Answer:
[tex]\frac{1}{16}[/tex]
Step-by-step explanation:
We will start by calculating the probability of drawing a spade from one deck, and then square it since we need to get the chance of getting two spades. We know there are 13 spades in a deck, out of 52 cards, giving us:
[tex]\frac{13}{52}[/tex]
Which can be simplified to :
[tex]\frac{1}{4}[/tex]
Then, we will square this fraction since we need two spades in a row:
[tex]\frac{1}{4} * \frac{1}{4} = \frac{1}{16}[/tex]
So the probability is [tex]\frac{1}{16}[/tex].
Hope this helped!
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
How do you find the unknown part of a right triangle?
To find the unknown part of a right triangle, you can use the Pythagorean theorem or the trigonometric ratios.
A right triangle is a triangle that has one angle measuring exactly 90 degrees, this angle is called the right angle.
To find the unknown part of a right triangle, you can use the Pythagorean theorem, which states that in a right triangle, the sum of the squares of the lengths of the two shorter sides (legs) is equal to the square of the length of the longest side (the hypotenuse). The formula is:
a² + b² = c²
Where c is the length of the hypotenuse and a and b are the lengths of the legs.
You can use this theorem to find the length of a missing side, if you know the length of the other two sides. For example, if you know the lengths of the two legs (a and b) and you need to find the length of the hypotenuse (c), you can use the formula:
c = √(a² + b²)
Alternatively, if you know the length of the hypotenuse (c) and one leg (a), you can use the formula to find the length of the other leg (b):
b = √(c² - a²)
Another way to find the unknown part of a right triangle is the use of trigonometric ratios. As you know, in a right triangle, there are three main ratios: sine, cosine, and tangent. These ratios are defined as follows:
Sin(A) = a/c
Cos(A) = b/c
Tan(A) = a/b
Where A is one of the acute angles of the triangle, and a,b,c are the sides of the triangle. By using the known side and the known angle you could find the unknown side.
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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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Why is it important to use
estimation when solving problems?
Answer: Without estimation skills, students aren't able to determine if their answer is within a reasonable range.
Step-by-step explanation:
to make sure your answer at least make sense to the question