0.03607
Step-by-step explanation:Absolute value is the distance of a number from zero. Since distance is always positive, the absolute value is the same number but positive.
Please note, for this problem I have rounded to 5 decimal points because the answer is irrational.
Subtracting
There are 2 different ways to approach this problem. You can either estimate the square root of 5 or plug this question straight into a calculator.
First, we can estimate [tex]\sqrt{5}[/tex] and round to 5 decimal places.
[tex]\sqrt{5}[/tex] ≈ 2.23607Then, take this value and subtract.
2.23607 - 2.2 = 0.03607Absolute Value
Now that we have solved the subtraction problem we have to find the absolute value. As stated above, the easiest way to find absolute value is to simply make the number positive. Since the answer is already positive, this is the final answer.
|0.03607| = 0.036078x+4y=7
6x-8y=41
using ELIMINATION METHOD
Answer:
([tex]\frac{5}{2}[/tex] , - [tex]\frac{13}{4}[/tex] )
Step-by-step explanation:
8x + 4y = 7 → (1)
6x - 8y = 41 → (2)
multiplying (1) by 2 and adding to (2) will eliminate y
16x + 8y = 14 → (3)
add (2) and (3) term by term to eliminate y
22x + 0 = 55
22x = 55 ( divide both sides by 22 )
x = [tex]\frac{55}{22}[/tex] = [tex]\frac{5}{2}[/tex]
substitute this value into either of the 2 equations and solve for y
substituting into (1)
8([tex]\frac{5}{2}[/tex] ) + 4y = 7
20 + 4y = 7 ( subtract 20 from both sides )
4y = - 13 ( divide both sides by 4 )
y = - [tex]\frac{13}{4}[/tex]
solution is ( [tex]\frac{5}{2}[/tex] , - [tex]\frac{13}{4}[/tex] )
Directions: Find the missing angle in each of the following problems.
1. QR = 36 ; PR = 45 ; PQ = 21, Sin __?___ = 21 / 45
2. QR = 16 ; PR = 2 ; PQ = 8, tan __?__ = 8 / 16
3. QR = 15 ; PR = 28 ; PQ = 15, Cos __?__ = 15 / 28
4. QR = 47 ; PR = 64 ; PQ = 38, tan __?__ = 38 / 47
5. QR = 4 ; PR = 17 ; PQ = 12, Sin __?___ = 12 / 17
6. QR = 36 ; PR = 59 ; PQ = 20, Cos __?___ = 36 / 59
7. QR = 82 ; PR = 63 ; PQ = 29, tan __?__ = 29 / 82
8. QR = 10 ; PR = 28 ; PQ = 8, Sin __?___ = 8 / 28
9. QR = 51 ; PR = 42 ; PQ = 9, tan __?__ = 9 / 51
10. QR = 16 ; PR = 20 ; PQ = 17, Cos __?___ = 16 / 20
11. QR = 12 ; PR = 84 ; PQ = 60, Sin __?_ = 60 / 84
12. QR = 19 ; PR = 32 ; PQ = 45, Cos __? = 19 / 32
13. QR = 76 ; PR = 27 ; PQ = 64, tan __ ?_ = 64 / 76
14. QR = 26 ; PR = 48 ; PQ = 37, Cos __?_ = 37 / 48
15. QR = 19 ; PR = 66 ; PQ = 23, Cos __?__= 23 / 66
The missing angles are listed below:
sin 27.818° = 21 / 45
tan 26.565° = 8 / 16
cos 57.607° = 15 / 28
tan 38.956° = 38 / 47
sin 44.901° = 12 / 17
cos 52.398° = 36 / 59
tan 19.477° = 29 / 82
sin 16.601° = 8 / 28
tan 10.008° = 9 / 51
cos 36.870° = 16 / 20
sin 35.538° = 60 / 84
cos 53.576° = 19 / 32
tan 40.101° = 64 / 76
cos 39.571 = 37 / 48
cos 69.605° = 23 / 66
How to find the measure of missing angles by definition of inverse of trigonometric functions
In this question we must find the measure of the angle associated to the rational numbers seen in the statement. There are two methods to estimate such measures: (i) Drawing an equivalent right triangle and estimate the measure of the angle by definition of trigonometric functions, (ii) Using inverse trigonometric functions and numerical methods since they are trascendent variables.
Herein we decided to use the second method by reasons of rapidness and effectivity:
sin 27.818° = 21 / 45
tan 26.565° = 8 / 16
cos 57.607° = 15 / 28
tan 38.956° = 38 / 47
sin 44.901° = 12 / 17
cos 52.398° = 36 / 59
tan 19.477° = 29 / 82
sin 16.601° = 8 / 28
tan 10.008° = 9 / 51
cos 36.870° = 16 / 20
sin 35.538° = 60 / 84
cos 53.576° = 19 / 32
tan 40.101° = 64 / 76
cos 39.571 = 37 / 48
cos 69.605° = 23 / 66
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change the following fraction to a percent 4/50
Answer:
For finding Percentage u have to multiply the number with 100
e.g.,
[tex] \frac{4}{50} \times 100[/tex]
[tex]4 \times 2 = 8\%[/tex]
Hopefully this helps u...
Please mark me as brainlist
divide 360 in the ratio 1:7
Answer:
45:315
Step-by-step explanation:
Add up the ratio to get the total ratio.
1+7=8
Divide the 360 by the total ratio.
360÷8=45
The number 45 tells you how many times to multiply both sets of the ratio to get a total of 360.
1×45=45
7×45=315
so,
45:315
Hope this helped. Comment below if you need more assistance! :)
A recent survey by the U.S. Census Bureau determined that the median monthly housing rent was $628. If the first quartile for monthly housing rent was $481, find the percent of monthly housing rents that were the following values.
(a) more than $481
%
(b) less than $628
%
(c) between $481 and $628
%
domain of f(x)=(1/4)^x
What is the domain of f(x)
O A. x>0
OB. All real numbers
O C. y>0
O D. x<0
? Need help asap
Answer: B
Step-by-step explanation:
The domain of a function is the set of x-values.
The graph of f(x) = x2 is translated to form g(x) = (x – 5)2 + 1. On a coordinate plane, a parabola, labeled f of x, opens up. It goes through (negative 2, 4), has a vertex at (0, 0), and goes through (2, 4). Which graph represents g(x)? On a coordinate plane, a parabola opens up. It goes through (2, 10), has a vertex at (5, 1), and goes through (8, 10). On a coordinate plane, a parabola opens up. It goes through (2, 8), has a vertex at (5, negative 11), and goes through (8, 8). On a coordinate plane, a parabola opens up. It goes through (negative 8, 10), has a vertex at (negative 5, 1), and goes through (negative 2, 10).
The graph is shown in the attached image.
(2 Fruit juice A is composed of 2 parts apple juice and 1 part grape juice.
Fruit juice B is composed of 1 part apple juice and 2 parts grape juice.
When A and B are mixed, the new mixture has 10 kg of apple juice and
8 kg of grape juice. How many kilograms does each type of original
fruit juice weigh
The amount of kilograms of each type of original fruit juice weighs; 12 kg of Apple and 6 kg of grape
How to Solve Algebra Word Problems?
The concentrations of apple and grape juice in the two different juice types are given as;
Juice A:
(2/3) apple
(1/3) grape
Juice B:
(1/3) apple
(2/3) grape
Let a be how much juice A is in the mixture;
Let b be how much juice B is in the mix.
Thus;
²/₃a + ¹/₃b = 10 ------(eq 1)
¹/₃a + ²/₃b = 8 ------(eq 2)
Solving both equations simultaneously gives us;
a = 12 and b = 6
Thus, the amount of kilograms of each type of original fruit juice weighs; 12 kg of Apple and 6 kg of grape
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In a triangle, the measure of the first angle is twice the measure of the second angle. The measure of the third angle is 76° more than the measure of the second angle. Use the fact that the sum of the measures of the three angles of a triangle is 180° to find the measure of each angle.
Answer:
First angle: 52°
Second angle: 26°
Third angle: 102°
Step-by-step explanation:
Let the measure of the second angle = x.
Measure of the first angle: 2x
Measure of third angle: x + 76
2x + x + x + 76 = 180
4x + 76 = 180
4x = 104
x = 26 second angle
2x = 2 × 26 = 52 first angle
x + 76 = 26 + 76 = 102 third angle
A motorist travels from town A to town B, which are 84km apart. If he has completed 7/8 of his journey, what is the distance he has travelled?
The distance that he has traveled exists 73km 500m.
What is the distance?
Distance exists described as the amount of space between two items or the condition of existing far apart. The distance of an object can be described as the complete path traveled by an object.
Given: A motorist travels from town A to town B, which exists 84km apart. He has finished 7/8 of his journey.
To estimate the distance that he has traveled
He covered 7/8 out of 84 km
So, 7/8 × 84 = 73.5 km
The distance he has traveled = 73 km 500 m
Therefore, the distance that he has traveled exists 73km 500m.
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help please it would make my day pleaes help me
Answer:
I think it would be D
A two-digit number has two less units than tens. The difference
between twice the number and the number reversed is 93. Find
the number.
The required two-digit number is 75.
What is arithmetic?In mathematics, it deals with numbers of operations according to the statements.
let the number in tenth place be x.
And has two fewer units than tens.
= x - 2
The two-digit number can be given as
= 10x + (x - 2)
= (11x - 2)
Reversing the digits
= (x - 2)10 + x
= 11x -20
The difference between twice the number and the number reversed is 93.
[tex]2(11x - 2) - (11x - 20) = 93\\22x-4-11x+20 = 93\\11x+16 = 93\\11x = 93-16\\11x = 77\\x = 7[/tex]
Now the required two-digit number is,
= 11x -2
= 11*7 - 2
= 77 -2
= 75
Thus the required two-digit number is 75.
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A 25-year old woman burns 200−20t cal/hr while walking on her treadmill. Her caloric intake from drinking Gatorade is 110t calories during the t th hour. What is her net decrease in calories after walking for 5 hours?
The net decrease in calories after walking for 5 hours is 50 calorie.
According to the statement
we have given that the
A 25-year old woman burns 200−20t cal/hr and Her caloric intake from drinking Gatorade is 110t calories during the t hour.
And we have to find the net decrease in calories after walking for 5 hours.
So, For this purpose,
We know that the
calories burns in one hour = 200−20t
calories burns in 5 hours = 5(200−20t)
calories burns in 5 hours = 1000 - 100t
Now,
Calorie intake in t hours = 110t
And
net decrease in calories after walking for 5 hours = 100t - 1000 + 110t
put t is 5 then
net decrease in calories after walking for 5 hours = 210(5) - 1000
net decrease is 50 cal.
So, The net decrease in calories after walking for 5 hours is 50 calorie.
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A one to one function is given. Write an equation for the inverse function
M(x)=4x^3-3
Step-by-step explanation:
M(x) = 4x^3 - 3
let M(x) = Y
Y = 4x^3 - 3...swap places of x & y.
X = 4y^3 - 3
look for x in terms of y.
4y^3 = x + 3
Y^3 = x + 3 / 4...put both sides under cube root.
y = ( x + 3 / 4 )^1/3
Solve the following proportion for v.
11/v = 5/13 Round your answer to the nearest tenth.
what is the midpoint of a segment with endpoints (-3, 2) and (7, -5)?
Answer:
[tex](2,-1.5)[/tex]
Step-by-step explanation:
The midpoint formula goes as follows:
[tex](x,y)=(\frac{x1+x2}{2} , \frac{y1+y2}{2})[/tex]
Lets plug in our values, let x1 be -3, x2 be 7, y1 be 2, y2 be -5.
[tex](\frac{-3+7}{2} , \frac{2+-5}{2})[/tex]
Solve numerators
[tex](\frac{4}{2} , \frac{-3}{2})[/tex]
Solve
[tex](2 , -1.5)[/tex]
Therefore the midpoint must be at [tex](2,-1.5)[/tex]
If you are taking a 3 credit college class and fail, and you have a 3.3 GPA. How mush will it affect it?
Answer:
it depend on your total credit load u register, if it's d only credit load it affect your gpa alot
Sarah is spending the day at a state fair. While at the fair, she can play games or ride rides. When Sarah arrives at the fair, she purchases 15 tickets and wants to use all of the tickets that she purchases. Playing a game at the fair requires three tickets, and riding a ride at the fair requires six tickets. To make her trip to the fair worthwhile, Sarah decides she must participate in seven activities at the fair.
Sarah requires the purchase of additional 12 tickets to ensure her participation in the seven activities at the fair.
How are the additional (missing) tickets determined?The additional tickets required by Sarah can be determined as follows:
Number of tickets purchased initially = 15
Number of tickets for playing a game = 3
Number of tickets for riding a ride = 6
Sarah can play five (5) games with 15 tickets (15/3).
Sarah can then purchase 12 additional tickets (6 x 2).
The later action enables Sarah to participate in 5 games and 2 rides, making it a total of 7 activities.
Thus, by purchasing additional 12 tickets, Sarah can participate in 5 games and 2 rides, making it a total of 7 activities.
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Question Completion:How many more tickets does Sarah require to ensure her participation in the seven activities at the fair?
Nisha collects comic books, and she convinced her friend Hakim to start collecting as well. Every week, they go to the store together, and they each buy a new comic book. This table shows how many books they each have:
By using the given table, we will get the linear equation:
h = n - 9
How to find the equation for Hakim?
We know that they always get comic books together, so always that Nisha's collection increases by one, Hakim's collection will also increase by one, so we will have a linear equation.
Now, if you look at the given table, you can see that Hakim's collection is always 9 units less than Nisha's collection, then the linear equation that models the relation between the two collections, h and n, is really straightforward, it will be:
Hakim's collection = Nisha's collection - 9
Using the variables, we get:
h = n - 9
That is the linear equation Hakim wanted.
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Answer:
h=n-9
Step-by-step explanation:
A _[blank 1]_ is a number whose only factors are 1 and itself. If a number has other factors besides 1 and itself, it is called a _[blank 2]_. You can use divisibility rules or _[blank 3]_ to help you determine whether a number is prime or composite.
Match each blank with the option that correctly fills in that blank.
1. the sieve of Eratosthenes.
2.whole number.
3. composite number.
4.counting number.
5. the standard algorithm
6. prime number.
Numbers whose only factors are 1 and itself is known as prime numbers , numbers whose factors besides 1 and itself are composite numbers, we can use the sieve of Eratosthenes to determine whether the number is prime or composite.
Given a paragraph in which there are blanks:
A _____ is a number whose only factors are 1 and itself. If a number has factors besides 1 and itself, it is called a _____. You can use divisibility rules or _______ to help you determine whether a number is prime or composite.
We are required to fill the blank with appropriate options.
We have to fill "prime numbers" in the first blank.
We have to fill "composite numbers" in the second blank.
We have to fill "the sieve of Eratosthenes" in the third blank.
Hence numbers whose only factors are 1 and itself is known as prime numbers , numbers whose factors besides 1 and itself are composite numbers, we can use the sieve of Eratosthenes to determine whether the number is prime or composite.
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plssssssssssssss help
Answer:
b. 30 m²
Step-by-step explanation:
find the area of the rectangle and triangle first
area of rectangle = length x height
aR = 10 x 6
aR = 60
area of triangle = base x height x 1/2
aT = 10 x 3 x 1/2
aT = 30
now, to find the area of the shaded area subtract the triangle from the rectangle
area = rectangle - triangle
a = 60 - 30
a = 30
A man weighs 51 kilograms. His brother weighs 10 percent more. How heavy is the brother? 5.1 kilograms 51.6 kilograms 55.6 kilograms 56.1 kilograms
Answer: 56.1 kilograms
Step-by-step explanation:
Solution 1: Multiply 51 by 10% and we'll get 5.1. Then, add 51 and 5.1 and we'll get 56.1
Solution 2: Multiply 51 by 110% and we'll get 56.1
(we can multiply 51 by 1 + 10% because multiplying 51 by 1 is the same thing as multiplying 51 by 100%. So you can just use this slicker formula for solving problems like this)
The area of a circle is 28.26 square miles. What is the circle's diameter?
Use 3.14 for л.
miles
A = 28.26 miz
During a drought, the water level in a reservoir dropped 3 in. each week for 5 straight weeks. Express the overall change in water level as a signed number.
Answer:
v = -3w
Step-by-step explanation:
water level/volume = -3 x weeks
v = -3w
A glass vase weighs 0.17 lb. How much does a similarly shaped vase of the same glass weigh if each dimension is 6 times as large?
Answer:
7,647.4?
Step-by-step explanation:
Question
A scientist needs 60 liters of a 40% solution of alcohol. He has a 30% solution and a 60% solution available.
How many liters of the 30% solution and how many liters of the 60% solution should he mix to make the 40% solution?
Provide your answer below:
30% solution: liters, 60% solution:
4 Previous
liters
ba
77°F 940)
I
9:0
8/2
Answer:
40 liters of 30% solution.
20 liters of 60% solution.
Step-by-step explanation:
Let x = amount of 30% solution.
Let y = amount of 60% solution.
Equation of amounts of solutions.
x + y = 60
Equation of amounts of alcohol in the solutions.
0.3x + 0.6y = 0.4 × 60
x = 60 - y
0.3(60 - y) + 0.6y = 24
18 - 0.3y + 0.6y = 24
0.3y = 6
y = 20
x + y = 60
x + 20 = 60
x = 40
Answer:
40 liters of 30% solution.
20 liters of 60% solution.
An equation is a mathematical statement that is made up of two expressions connected by an equal sign.
The number of liters of the 30% solution and the number of liters of the 60% solution to mix to make the 40% solution is 40 liters and 20 liters.
What is an equation?An equation is a mathematical statement that is made up of two expressions connected by an equal sign.
Example:
2x + 4 = 7 is an equation.
We have,
Let 30% solution = m
Let 60% solution = n
Now,
A scientist needs 60 liters of a 40% solution of alcohol.
He has a 30% solution and a 60% solution available.
This means,
m + n = 60 _____(1)
30% of m + 60% of n = 40% of 60
0.30m + 0.60n = 0.40 x 60
0.30m + 0.60n = 24 ____(2)
From (1) and (2) we get,
m + n = 60
m = 60 - n _____(3)
Putting (3) in (2) we get,
0.30m + 0.60n = 24
0.30(60 - n) + 0.60n = 24
18 - 0.30n + 0.60n = 24
18 + 0.30n = 24
0.30n = 24 - 18
0.30n = 6
n = 6/0.30
n = 20
Putting n = 20 in (3) we get,
m = 60 - 20
m = 40
Now,
The number of liters of the 30% solution is 40.
The number of liters of the 60% solution is 20.
Thus,
The number of liters of the 30% solution and the number of liters of the 60% solution to mix to make the 40% solution is 40 liters and 20 liters.
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Give the standard form for 7000+300+40+2
Answer:
7×10³+3×10²+4×10¹+2×10 or 7.342×10³
There are 40 students in a class. 30 of them can swim while the rest are non-swimmers. i) ii) What percentage of the students can swim? What percentage of the students cannot swim?
Answer:
The percentage of the students that can swim is 75%
The percentage of students that can't swim is 25%
Step-by-step explanation:
100÷40=2.5
2.5×30=75
The percentage of the students that can swim is 75%
100-75=25
The percentage of students that can't swim is 25%
Please comment below if you don't understand or want me to clarify. :)
Determine the real life solutions of 9x^2+6x+1=0
Answer:
1 (double root)
Step-by-step explanation:
Given quadratic equation:
[tex]9x^2+6x+1=0[/tex]
To find the solutions to the given quadratic equation, factor the equation.
To factor a quadratic in the form [tex]ax^2+bx+c[/tex], find two numbers that multiply to ac and sum to b.
[tex]\implies ac=9 \cdot 1=9[/tex]
[tex]\implies b=6[/tex]
Therefore, the two numbers are: 3 and 3.
Rewrite the middle term as the sum of these two numbers:
[tex]\implies 9x^2+3x+3x+1=0[/tex]
Factor the first two terms and the last two terms separately:
[tex]\implies 3x(3x+1)+1(3x+1)=0[/tex]
Factor out the common term (3x + 1):
[tex]\implies (3x+1)(3x+1)=0[/tex]
Therefore:
[tex]\implies(3x+1)^2=0[/tex]
This means that the curve has one root with multiplicity 2. So the curve touches the x-axis and bounces off the axis at one point. (See attached graph).
Apply the zero-product property:
[tex]\implies 3x+1=0 \implies x=-\dfrac{1}{3}[/tex]
Therefore there is one real solution of the given quadratic equation.
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A stamp collection consisting of 23 stamps includes 4¢ stamps and 9¢ stamps. The total value of the stamps is $1.27. Find the number of each type of stamp in the collection.
A simultaneous equation is a set of equations that has to be solved in relation to each other at the same time. Thus the required number of stamps are:
4¢ stamps = 16
5¢ stamps = 7
A simultaneous equation is a set of equations that has to be solved in relation to each other at the same time. This process is required so as to determine the values of two unknowns e.g x and y.
From the given question, let the number of 4¢ stamps be represented by n, and that of the 9¢ stamp be represented by m.
So that,
n + m = 23 ............ 1
But 100¢ = $1, so that;
4¢ = x
x = [tex]\frac{4}{100}[/tex]
= $0.04
also,
9¢ = x
x = [tex]\frac{9}{100}[/tex]
= $0.09
Thus, we have;
0.04n + 0.09m = 1.27 ......... 2
From equation 1, make n the subject of the formula, such that;
n = 23 - m ........... 3
Substitute equation 3 into equation 2
0.04(23 - m) + 0.09m = 1.27
0.92 - 0.04m + 0.09m = 1.27
collect like terms to have;
0.05m = 1.27 - 0.92
= 0.35
m = [tex]\frac{0.35}{0.05}[/tex]
m = 7
Now substitute the value of m into equation 3
n = 23 - m ........... 3
= 23 - 7
n = 16
Therefore the number of 4¢ stamps is 16, while that of the 5¢ stamps is 7.
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