Answer:
3
Step-by-step explanation:
f(x)-g(x)=3-cos(x)
when u limit it
u have
3-cos180
which is 3-0
3
A pygmy hippo and a regular hippo were recently born. The pygmy hippo had a mass of 5 1/2 kg at birth. The regular hippo had a mass of 24 1/2 kg at birth. Complete the comparison. At birth, the regular hippo massed ? times as much as the pygmy hippo.
The mass of the regular hippo at birth to that of the pygmy hippo is 49/11
What is an equation?
An equation is an expression that shows the relationship between two or more numbers and variables.
An independent variable is a variable that does not depend on any other variable for its value while a dependent variable is a variable that depends on other variable.
The pygmy hippo had a mass of 5 1/2 kg at birth = 5.5 kg.
The regular hippo had a mass of 24 1/2 kg at birth = 24.5 kg
Hence:
Ratio of regular hippo to pygmy hippo = 24.5 / 5.5 = 49/11
The mass of the regular hippo at birth to that of the pygmy hippo is 49/11
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Answer:
49/11 or 4 5/11
Step-by-step explanation:
just did it on khan Academy.
please help!
Amara needs 90 kilograms of meat to feed her 4 pet dragons each day. Each pet dragon eats the same amount of meat. How many kilograms of meat does Amara need to feed 2 pet dragons each day?
45 kilograms of meat is required to feed 2 pet dragons each day.
Amara needs 45 kilograms of meat to feed 2 pet dragons each day.
What is unitary method ?Unitary method is a mathematical way of deriving a single unit then obtaining the required units by multiplying it with the single unit.
According to the given question Amara needs 90 kilograms of meat to feed her 4 pet dragons each day.
Also given that each pet dragon eats the same amount of meat.
∴ 1 pet dragon eat 90/4 kilograms of meat which is
= 22.5 kilograms of meat.
So, Amara need (22.5×2) = 45 kilograms of meat to feet 2 pet dragons.
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Joy is training for a triathlon. she runs a distance of 2x miles, cycles a distance of (x2 7) miles, and swims a distance of (x − 2) miles. which simplified expression is equivalent to the total distance, in miles, joy covers? x2 3x 5 x2 3x 9 3x2 5 3x2 9
The simplified expression that is equivalent to the total distance, in miles, Joy covers is (A) x² + 3x + 5 miles.
What is an expression?An expression or mathematical expression is a finite combination of symbols that is well-formed according to context-dependent norms.To find the simplified expression:
Given -
Distance cycled = x² + 7 milesDistance ran = 2x milesDistance swam = x - 2 milesThus,
Total distance she covers = x² + 7 + 2x + x - 2Total distance = x² + 3x + 5 milesTherefore, the simplified expression that is equivalent to the total distance, in miles, Joy covers is (A) x² + 3x + 5 miles.
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The complete question is given below:
Joy is training for a triathlon. She runs a distance of 2x miles, cycles a distance of (x2 + 7) miles, and swims a distance of (x - 2) miles. Which simplified expression is equivalent to the total distance, in miles, Joy covers?
(A) x2 + 3x + 5
(B) x2 + 3x + 9
(C) 3x2 + 5
(D) 3x2 + 9
Answer:
The person on top is right.
ITS A
Step-by-step explanation:
Rajani is making smoothies. Each smoothie uses 3/5 cup of yogurt. How much yogurt
does she need to make 13 smoothies?
Answer:
Rajani needs 7.8 (39/5) cups of yogurt to make 13 smoothies.
Step-by-step explanation:
3/5 = 0.6
The amount of cups of yogurt needed to make 13 smoothies = 13 x 0.6
This equals to 7.8 cups or 39/5 cups of yogurt to make 13 smoothies.
Hope this helps!
If U = Set of integers from -10 to 10 A=Set of integers from -1 to 1.
B=Set of first ten whole numbers
Prove that ( A intersection B)©=A©UB©
Hey c is complement
Answer:
(A∩B)' = A'∪B'
Step-by-step explanation:
U is the universal set
A and B are two subsets of U
let A' be the complement subset of A
and B' be the complement subset of B
U = {-10,-9,…,-1,0,1,…,9,10}
A = {-1,0,1}
B = {1,2,…,9,10}
Then
A∩B = {1}
Then
the complement of A∩B :
(A∩B)' = {-10,-9,…,-1,0,2,…,9,10}
(notice the absence of 1)
On the other hand,
A' = {-10,…,-2}∪{2,…,10}
B' = {-10,…,0}
Then
A'∪B' = {-10,-9,…,-1,0}∪{2,…,10}
= {-10,-9,…,-1,0,2,…,9,10}
Conclusion:
(A∩B)' = A'∪B'
Solve the following system using the algebraic method of substitution. Verify your solution.
x + 2y = -5
3x - y = -1
Solve the following linear system using the algebraic method of elimination. Verify your solution.
x + 2y = 2
3x + 5y = 4
I've done it on the attached pages.
I hope this helps you...
How many species go extinct in an average day? a. 3 b. 72 c. 1000 d. 20000 please select the best answer from the choices provided a b c d
It has been estimated that every year 20,000 species are going extinct and 72 species are going extinct on an average day.
What are species?
Species exist as organisms that contain similar characteristics and exist capable of interbreeding. A common example is human beings.
It has been observed that over the years, species have been going extinct due to human reasons such as excessive hunting, environmental factors such as natural disasters, global warming, and also due to changes in their genetic makeup or reduced reproduction.
It has been estimated that every year 20,000 species are going extinct and 72 species are going extinct on an average day.
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Answer: Edge 2022, B. 72
Minnie bought 6 postcards during 3 days of vacation. After 8 days of vacation, how many total postcards will Minnie have bought?
A. 12
Answer:
16
Step-by-step explanation:
6/3 = 2 postcards per day
2x8 = 16 postcards
Which of the graphs below shows the solution set for -36 ≤ 2x + 4(x-3)?
A.
B.
-10-9-8-7-6-5-4-3-2-1 0
-10-9-8-7-6-5-4-3-2-1 0
C. A++
▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬
-10-9-8-7-6-5-4-3-2-1 0
D. +++
-10-9-8-7-6-5-4-3-2-1 01
Considering the given inequality, the solution is given by graph D.
What is the solution to the inequality?The inequality is given by:
-36 ≤ 2x + 4(x-3)
Applying the operations:
-36 ≤ 2x + 4x - 12
-24 ≤ 6x
6x >= -24
x >= -24/6
x >= -4.
Hence option D is correct.
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What's the total surface area of a covered box with a length of 4 ft, a width of 3 ft, and a height of 6 ft?
Answer: 108 square feet
===============================================
Work Shown:
L = 4 = length
W = 3 = width
H = 6 = height
SA = surface area of the box
SA = 2*(LW + LH + WH)
SA = 2*(4*3 + 4*6 + 3*6)
SA = 108
Solve the system of equations.
\begin{aligned} &-5x-3y - 9=0 \\\\ &4x-18y-54=0 \end{aligned}
−5x−3y−9=0
4x−18y−54=0
Answer:
(0, - 3 )
Step-by-step explanation:
- 5x - 3y - 9 = 0 → (1)
4x - 18y - 54 = 0 → (2)
multiplying (1) by - 6 and adding to (2) will eliminate y
30x + 18y + 54 = 0 → (3)
add (2) and (3) term by term to eliminate y
34x + 0 + 0 = 0
34x = 0 ⇒ x = 0
substitute x = 0 into either of the 2 equations and solve for y
substituting into (2)
4(0) - 18y - 54 = 0
- 18y - 54 = 0 ( add 54 to both sides )
- 18y = 54 ( divide both sides by - 18 )
y = - 3
solution is (0, - 3 )
Answer:
(0, -3)
Step-by-step explanation:
This system of equations consists of two equations. There are 3 main ways to solve a system of equations:
Graphing (The solution is the point where the two lines intersect)Substitution EliminationFirst, start by having the variables on one side.
[tex]-5x-3y-9=0 \Rightarrow \text{Add 9 to both sides} \Rightarrow -5x-3y=9\\4x-18y-54=0 \Rightarrow \text{Add 54 to both sides} \Rightarrow 4x-18y=54 \Rightarrow \text{Simplify} \Rightarrow 2x-9y=27[/tex]
Solve Using EliminationThis method is the easiest to use in this situation.
In this method, we increase equations by a certain factor in order to eliminate one variable.
We can see that 3y in the first equation can be multiplied by 6 in order to obtain the 18y in the second equation. Therefore, we can multiply the whole first equation by 6:
[tex]-30x-18y=54\\4x-18y=54[/tex]
Now, subtract the two equations to eliminate y.
[tex]-34x=0\\x=0[/tex]
Plug in 0 to x in either of the equations to solve for y:
[tex]-5(0)-3y=9\\0-3y=9\\-3y=9\\ \text{Divide both sides by -3}\\y=-3[/tex]
OR
[tex]4(0)-18y=54\\0-18y=54\\-18y=54\\\text{Divide both sides by -18}\\y=-3[/tex]
Therefore:
(x, y) = (0, -3)
What is the following simplified product? Assume x 20.
(√6x² +4√8x³)(√9x-x√5x^5)
O 3x√√6x+x²√30x+24x²2x+8x³10x
O 3x√6x+x√30x+24x²√2+8x5/10
O 3x√√6x-x+√30x+24x² √2-8x² 10
O3x6x-x30x+24x²2x-8x510x
The simplified product of (√6x² +4√8x³)(√9x-x√5x^5) is 3x√6x + 24x^2√2 - x^4√30x - 8x^5√10
How to determine the simplified product?The product expression is given as:
(√6x² +4√8x³)(√9x-x√5x^5)
Evaluate the exponents
(√6x² +4√8x³)(√9x-x√5x^5) = (x√6 +8x√2x)(3√x - x^3√5x)
Expand the brackets
(√6x² +4√8x³)(√9x-x√5x^5) = x√6 * 3√x + 8x√2x * 3√x - x√6 * x^3√5x - 8x√2x * x^3√5x
This gives
(√6x² +4√8x³)(√9x-x√5x^5) = 3x√6x + 24x^2√2 - x^4√30x - 8x^5√10
Hence, the simplified product of (√6x² +4√8x³)(√9x-x√5x^5) is 3x√6x + 24x^2√2 - x^4√30x - 8x^5√10
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Use the graph to write the explicit rule of the arithmetic sequence.
Question 19 options:
A)
ƒ(n) = 9 + 2(n – 1)
B)
ƒ(n) = 5 + 3(n – 1)
C)
ƒ(n) = –3 + 2(n – 1)
D)
ƒ(n) = 3 + 2(n – 1)
Answer: D
Step-by-step explanation:
The first term is 3 and the common difference is 2.
Substituting into the explicit formula for an arithmetic sequence gives D as the correct answer.
A rectangle is 5 inches long and 2x inches wide. The value of the perimeter
(in inches) is equal to the value of the area (in square inches). Find x.
Answer:
Area=length× berngth
A=5×2x
A=10x square
Solve the proportion.
A. 12
B. 2
C. 8
D. 16
D. 16
Cross multiply, to cancel the denominator; so if you multiple by 6 on one side, to cancel the division of 6 - you must also multiply the other side by 6 & vice versa.
You get:
8(x-4) = 6x
Expand bracket to get:
8x - 32
Now solve for x :
8x - 32 = 6x
- 8x
- 32. = - 2x
÷ - 2
16 = x
Or
8x - 32 = 6x
+ 32
8x. = 6x + 32
- 6x
2x. = 32
÷2
x =16
Check:
16 - 4 = 12, then ÷ 6 is 2
16/8 = 2
Hope this helps!
Use the recursive formula to find the first five terms in the arithmetic sequence.
The first five terms of the given arithmetic sequence are:
1/5, 2/5, 3/5, 4/5, 1 (Fourth option)
The arithmetic sequence is given as follows,
f(n) = f(n-1) + 1/5 ............ (1)
Now, for finding the first five term of this arithmetic sequence, we will substitute n as 1, 2, 3, 4, and 5 one by one. Using the above formula for the arithmetic sequence, we can deduce the first five terms.
It is already given that f(1) = 1/5 ......... (2)
f(1) is the first term of the sequence.
Now, putting n=2 in equation (1), we get,
f(2) = f(2-1) + 1/5
f(2) = f(1) + 1/5
Substitute f(1) = 1/5 from equation (2)
⇒ f(2) = 1/5 + 1/5
f(2) = 2/5
To find the third term of the arithmetic sequence, put n = 3 in equation (1)
f(3) = f(3-1) + 1/5
f(3) = f(2) + 1/5
⇒ f(3) = 2/5 + 1/5
f(3) = 3/5
Similarly, we can find the fourth and fifth terms of the arithmetic sequence by substituting n = 4 and n = 5 respectively.
∴ f(4) = f(3) + 1/5
⇒ f(4) = 3/5 + 1/5
f(4) = 4/5
Likewise, f(5) = f(4) + 1/5
⇒f(5) = 4/5 + 1/5
f(5) = 1
Thus, using the recursive formula, the first five terms of the arithmetic sequence come out to be:
1/5, 2/5, 3/5, 4/5, 1
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Tickets to the movies cost $24 for 1 adult. The price of 1 child was 2/3 of that price. How much did a family with 2 adults and 2 children have to pay?
Find the values of x and y.
Write answers in simplest radical form.
x=______ y=_____
Using the Geometric mean theorem and the Pythagorean theorem:
x = 3√3, and y = 6.
What is the Right Triangle Altitude Theorem/Geometric Mean Theorem?The Geometric mean theorem or the right triangle altitude theorem states that the geometric mean of the the two segments equals he length of the altitude of a right triangle.
The geometric mean theorem is expressed by the equation, h = √(ab), where:
a is the length of one segmentb is the length of the other segmenth is the length of the altitude of the right triangle.Given the following:
h = x
a = 9
b = 3
x = √(9 × 3)
x = 3√3
Find y using the Pythagorean theorem
Based on the Pythagorean theorem, we would have the following:
y = √(x² + 3²)
y = √((3√3)² + 3²)
y = √(27 + 9)
y = √(36)
y = 6
Thus, in the simplest radical form, the value of x = 3√3, and y = 6.
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There are 6 dogs and 5 cats.
In how many different orders can these animals be placed in line if any animal can be next to any other animal?
In how many different orders can these animals be placed in line if the dogs and cats are lined up alternately?
(Hint - The first animal MUST be a dog)
In how many different orders can these animals be placed in line if the first and last animal in line must be a cat?
Using the arrangements formula, the number of orders is given as follows:
39,916,800 if no restrictions.86,400 if they are lined up alternatively.7,257,600 if the first and last must be cats.What is the arrangements formula?The number of possible arrangements of n elements is given by the factorial of n, that is:
[tex]A_n = n![/tex]
When there are no restrictions, the number of ways is:
[tex]A_{11} = 11! = 39,916,800[/tex]
When they must be lined alternatively, the 6 dogs can be arranged in 6! ways, and the 5 cats in 5! ways, hence the number of orders is:
[tex]A_6A_5 = 6! \times 5! = 86,400[/tex]
When the first and last are cats, we have that:
For the first and last animals, there are 5!/2! = 20 ways.For the middle 9 animals, there are 9! ways.Hence:
20 x 9! = 7,257,600.
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Classify the expression: 5x 2. linear expression quadratic expression cubic expression quartic expression
The given expression is a (A) linear expression.
What are linear expressions?A linear expression is an algebraic expression in which each term is a constant or a variable raised to the first power. To put it another way, none of the exponents may be greater than 1. x2 is a variable raised to the second power, whereas x is a variable raised to the first power. A constant is represented by the number 5.Reduce the equation as much as feasible to the form y = mx + b. Examine your equation for exponents. It is nonlinear if it has exponents. Your equation is linear if it contains no exponents.2x - 3 = 0, 2y = 8, m + 1 = 0, x/2 = 3, x + y = 2, 3x - y + z = 3 are some instances of linear equations.Therefore, the given expression is a (A) linear expression.
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The correct question is given below:
Classify the expression: 5x 2.
(A) linear expression
(B) quadratic expression
(C) cubic expression
(D0 quartic expression
HELP HELP ASAP
Figure BBB is a scaled copy of Figure AAA.
What is the scale factor from Figure AAA to Figure BBB?
Answer:
figure A = 3 units
figure B = 9 x 3 = 27 units
scale factor =
[tex] \frac{3}{27 } = \frac{1}{9} [/tex]
so the scale factor = 9
What is the least positive integers which , when subtracted 7300 would make a result a perfect square?
75 is the least positive integers which , when subtracted 7300 would make a result a perfect square
What is the least positive value?So normally the least positive integer of all the numbers is the number 1 but when you talk about least positive integer, often times you are talking about the special function called the ceiling function
Least positive integer:
The smallest of the numbers in the set {1, 2, 3, …} is 1.
So, the number 1 is the smallest positive integer.
7300
If we Take Square root of 7300 we have to subtract 75 from 7300 to get a perfect square.
7300-75=7225
(85)^2=7225
75 to be subtracted
√7300 ≥ 85
Perfect Square = 85² = 7225 or (7300-7225 = 75)
75 is the least positive integers which , when subtracted 7300 would make a result a perfect square
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A function is shown: f(x) = 36x² - 1.
Choose the equivalent function that best shows the x-intercepts on the graph
Based on the given function, the equivalent function that best shows the x-intercepts on the graph is f(x) = (6x - 1)(6x + 1)
What are equivalent functions?Equivalent functions are different functions that have equal values when evaluated and compared
How to determin the equivalent function that best shows the x-intercepts on the graph?
The function is given as:
f(x) = 36x^2 - 1
Express 1 as 1^2
f(x) = 36x^2 - 1^2
Express 36x^2 as (6x)^2
f(x) = (6x)^2 - 1^2
Apply the difference of two squares.
This is represented as:
(a + b)(a - b) = a^2 - b^2
So, we have the following equation
f(x) = (6x - 1)(6x + 1)
Based on the given function, the equivalent function that best shows the x-intercepts on the graph is f(x) = (6x - 1)(6x + 1)
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x-1/x-2+x+3/x-4=2/(x-2).(4-x)
The given equation x-1/x-2+x+3/x-4=2/(x-2).(4-x) is correct. the answer is proved.
According to the statement
we have given that the equation and we have to prove that the given answer is a correct answer for those equivalent equation.
So, The given expression are:
[tex]\frac{x-1}{x-2} +\frac{x+3}{x-4} = \frac{2}{(x-2).(4-x)}[/tex]
And we have to prove the answer.
So, For this
[tex]\frac{x-1}{x-2} +\frac{x+3}{x-4}[/tex]
[tex]\frac{({x-1}) ({x-4}) +({x+3})({x-2})} {(x-2) (x-4)}[/tex]
Then the equation become
[tex]\frac{x^{2} -4x -x +4 + x^{2} -2x + 3x -6 }{(x-2) (x-4)}[/tex]
Now solve it then
[tex]2x^{2} - 4x -2 / (x-2) (x-4)[/tex]
Now take 2 common from answer then equation become
[tex]\frac{x-1}{x-2} +\frac{x+3}{x-4} = \frac{2}{(x-2).(4-x)}[/tex]
Hence proved.
So, The given equation x-1/x-2+x+3/x-4=2/(x-2).(4-x) is correct. the answer is proved.
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At a walk-in interview, 12% of candidates can be selected, and 28% of candidates can be put on hold for the next hiring date. if 75 candidates are interviewed, about how many are expected to be rejected?
45 candidates are expected to be rejected.
What is a percentage in math?
percentage, a relative value indicating hundredth parts of any quantity. One percent (symbolized 1%) is a hundredth part. 100 percent represents the entirety and 200 percent specifies twice the given quantity.Here, we want to calculate the number of candidates to be rejected
The number of candidates to be rejected can be calculated from;
100% - (28% + 12%) = 60%
So 60% of the 75 interviewed are to be rejected
Thus, we have
60/100 * 75
= 45
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The system of equations below has no solution.
StartLayout enlarged left-brace 1st row two-thirds x + five-halves y = 15 2nd row 4 x + 15 y = 12
Which equation could represent a linear combination of the system?
The equation that could represent a linear combination of the system 2/3x + 5/2y = 15 and 4x + 15y = 12 is 0 = 26
What are linear equations?Linear equations are equations that have constant average rates of change, slope or gradient
How to determine the linear combination to the system?A system of linear equations is a collection of at least two linear equations.
In this case, the system of equations is given as
2/3x + 5/2y = 15
4x + 15y = 12
Multiply the first equation by 6, to eliminate the fractions.
6 * (2/3x + 5/2y = 15)
This gives
4x + 15y = 90
Subtract the equation 4x + 15y = 90 from 4x + 15y = 12
4x - 4x + 15y - 15y = 12 - 90
Evaluate the difference
0 + 0 = -78
Evaluate the sum
0 = -78
The above equation is the same equation as option (b) 0 = 26
This is so because they both represent that the system of equations have no solution
Hence, the equation that could represent a linear combination of the system is 0 = 26
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Find the value of the trigonometric ratio. Make sure to simplify the fraction if needed.
generally, tanA=opposite/adjacent
answer:tanC=36/15=12/5
Answer:
[tex]Tan \space\ \theta =\frac{\boxed{12}}{\boxed5}}[/tex]
Step-by-step explanation:
The tangent (Tan) of an angle is the ratio of the opposite side and the adjacent side, so that:
[tex]\boxed{Tan\space\ \theta = \frac{opposite}{adjacent}}[/tex].
In this case, with respect to angle C:
• opposite = AB = 36 units
• adjacent = CB = 15 units.
Substituting the values into the equation:
[tex]Tan \space\ C = \frac{36}{15}[/tex]
= [tex]\bf \frac{12}{5}[/tex] (simplified)
Solve the system of equations.
y equals x plus 8
y equals 3 x plus 2
Answer:
The answer is (3,11) or x = 3, y = 11
Step-by-step explanation:
:)
Answer:
(3, 11 )
Step-by-step explanation:
y = x + 8 → (1)
y = 3x + 2 → (2)
substitute y = 3x + 2 into (1)
3x + 2 = x + 8 ( subtract x from both sides )
2x + 2 = 8 ( subtract 2 from both sides )
2x = 6 ( divide both sides by 2 )
x = 3
substitute x = 3 into either of the 2 equations and solve for y
substituting into (1)
y = 3 + 8 = 11
solution is (3, 11 )
please I need to know how to do this !!
[tex]\frac{6xyz}{2xy-y}.\frac{2x^{2}-7x+3 }{3xz - 9z} = 2x[/tex]
How to simplify an expression?The expression can be simplified as follows:
[tex]\frac{6xyz}{2xy-y}.\frac{2x^{2}-7x+3 }{3xz - 9z}[/tex]
Hence,
[tex]\frac{6xyz}{y(2x-1)}.\frac{(x-3)(2x-1)}{3z(x-3)}[/tex]
Therefore.
[tex]\frac{6xyz}{y(2x-1)}.\frac{(2x-1)}{3z}[/tex]
Hence,
[tex]\frac{2xy}{y(2x-1)}.\frac{(2x-1)}1=2x[/tex]
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HELP WITH THE BONUS PLEASE!!!!
Based on the stock price and its growth rate, the function that models the situation is 48 (1 + 8%) ^ n. The price of the stock 6 years from now is $76.17.
What is the best function for the stock's growth?The value of a stock in future can be calculated using several types of formulas that take into account the various characteristics of the stock.
For this stock, the value of the stock at any given year is:
= Current price of stock x ( 1 + growth rate) ^ number of years from now
Assuming the number of years is n, the function becomes:
= 48 x ( 1 + 8%) ^n
In 6 years, the price will be:
= 48 x ( 1 + 8%) ⁶
= $76.17
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