The value of expression 4 1/5 + 3 2/3 + 1 1/6 is 9 1/30
Given that,
to simplify: 4 1/5 + 3 2/3 + 1 1/6
Mixed fraction definition?
It is a type of fraction, and those that have both a fraction and a whole number are considered to be it.
How to convert Improper fraction to a mixed fraction?
Divide the fraction's numerator by its denominator, or 15/7, in step one.
Second Step: Since 2 is an integer, the answer's integer component will be a mixed fraction.
Step 3: The original denominator of seven will be used as the denominator.
Step 4: The incorrect fraction 15/7 is now a mixed fraction with the value 2 (1/7)
To simplify ,
4 1/5 + 3 2/3 = 7 13/15
7 13/15 + 1 1/6 = 9 1/30
Therefore the correct answer is 9 1/30
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Evaluate if x = 4. x² + x = [?]
Answer: The answer is 0.
X = 0 when evaluated.
Step-by-step explanation:
A barge is being towed by two tugboats, using ropes with force vectors as shown.
SOLUTION
From the question, we are given
[tex]\begin{gathered} F_1=(11,000,5000) \\ F_2=(14,500,-8,000) \end{gathered}[/tex]Now, to find the angle between the ropes, we will take the dot product of two vectors. This is given as
[tex]\begin{gathered} a.b=|a||b|cos\theta \\ so,\text{ we have } \\ cos\theta=\frac{a.b}{|a||b|} \end{gathered}[/tex]But writing the forces in vector form, we have
[tex]\begin{gathered} F_1=11,000i+5000j \\ F_2=14,500i-8,000j \end{gathered}[/tex]Applying the formula above, we have
[tex]\begin{gathered} cos\theta=\frac{a.b}{|a||b|} \\ cos\theta=\frac{(11,000)(14,500)+(5000)(-8000)}{\sqrt{11,000^2+5000^2)\sqrt{14500^2+(-8000)^2}}} \\ cos\theta=\frac{159,500,000-40,000,000}{\sqrt{121,000,000+25,000,000}\sqrt{210,250,000+64,000,000}} \\ cos\theta=\frac{119,500,000}{\sqrt{146,000,000}\sqrt{274,250,000}} \\ cos\theta=\frac{119,500,000}{12,083.04579\times16560.4952} \\ cos\theta=\frac{119,500,000}{200,101,221.806675} \\ cos\theta=0.5971977 \end{gathered}[/tex]Now, theta becomes
[tex]\begin{gathered} \theta=cos^{-1}0.5971977 \\ \theta=53.3305 \end{gathered}[/tex]hence the answer is option B, 53 degrees
SOLUTION
From the question, we are given
[tex]\begin{gathered} F_1=(11,000,5000) \\ F_2=(14,500,-8,000) \end{gathered}[/tex]Now, to find the angle between the ropes, we will take the dot product of two vectors. This is given as
[tex]\begin{gathered} a.b=|a||b|cos\theta \\ so,\text{ we have } \\ cos\theta=\frac{a.b}{|a||b|} \end{gathered}[/tex]But writing the forces in vector form, we have
[tex]\begin{gathered} F_1=11,000i+5000j \\ F_2=14,500i-8,000j \end{gathered}[/tex]Applying the formula above, we have
[tex]\begin{gathered} cos\theta=\frac{a.b}{|a||b|} \\ cos\theta=\frac{(11,000)(14,500)+(5000)(-8000)}{\sqrt{11,000^2+5000^2)\sqrt{14500^2+(-8000)^2}}} \\ cos\theta=\frac{159,500,000-40,000,000}{\sqrt{121,000,000+25,000,000}\sqrt{210,250,000+64,000,000}} \\ cos\theta=\frac{119,500,000}{\sqrt{146,000,000}\sqrt{274,250,000}} \\ cos\theta=\frac{119,500,000}{12,083.04579\times16560.4952} \\ cos\theta=\frac{119,500,000}{200,101,221.806675} \\ cos\theta=0.5971977 \end{gathered}[/tex]Now, theta becomes
[tex]\begin{gathered} \theta=cos^{-1}0.5971977 \\ \theta=53.3305 \end{gathered}[/tex]hence the answer is option B, 53 degrees
3a. Sketch the line that goes through the points A(4,3) and B( 8, 1)Find the slope and the equation of line AB3b. Find the length of segment AB3c. Find the midpoint of segment AB
Hello! First, let's remember:
We can write a point as a cartesian coordinate (x, y).
The exercise has given two points, A(4,3) and B(8,1).
a. Slope:To calculate the slope of a line, we can use the formula below:
[tex]\text{Slope}=\frac{y_2-y_1}{x_2-x_1}[/tex]Let's consider A equal to the first point (4, 3) = (x1, y1), and B will be the second point (8, 1) = (x2, y2). Replacing these values in the formula:
[tex]\text{Slope}=\frac{1_{}-(3)_{}}{8-(4)}=\frac{-2}{4}=-\frac{1}{2}[/tex]b. Lenght of segment AB:To find this length, we have to use another formula. Now we will calculate the distance between two points:
[tex]\text{Distance}=\sqrt[]{(x_2-x_1)^2+(y_2_{}-y_1_{})^2}[/tex]Still considering A (4, 3) = (x1, y1), and B (8, 1) = (x2, y2), let's replace the values in the formula:
[tex]\begin{gathered} \text{Distance}=\sqrt[]{(8_{}-4_{})^2+(1-3_{})^2} \\ \text{Distance}=\sqrt[]{(4_{})^2+(-2_{})^2} \\ \text{Distance}=\sqrt[]{(16^{}+4)^{}} \\ \text{Distance}=\sqrt[]{20} \\ \text{Distance}=2\sqrt[]{5} \end{gathered}[/tex]c. Midpoint of segment AB:This value will be the medium point. To calculate it, we'll use another formula:
[tex]x_m=(\frac{x_1+x_2}{2}+\frac{y_1+y_2_{}_{}}{2})[/tex]Still considering the same values for (x1, y1) and (x2, y2), let's replace them:
[tex]\begin{gathered} x_m=(\frac{8+4_{}}{2},\frac{3+1_{}}{2}) \\ \\ x_m=(\frac{12_{}}{2},\frac{4_{}}{2}) \\ \\ x_m=(6,2) \end{gathered}[/tex]The midpoint of segment AB will be at point X (6, 2).
You can see this line represented in a cartesian plan below:
PLS HELP, 50 POINTS + BRAINLY FOR CORRECT ANSWER!!!
jackson bikes 2 miles in 15 mins at that rate how many miles will a bike in 45 mins
Let's use Cross-multiplication:
2mi ------------------------>15min
x mi------------------------->45min
So:
2/x = 15/45
Solving for x:
Multiply both sides by x:
x*(2/x) = x* 15/45
2 = 15x/45
Multiply both sides by 45:
45*2 = 45*(15x/45)
90 = 15x
Divide both sides by 15:
90/15 = 15x/15
6 = x
x = 6mi
HOW ARE THESE GRAPHS THE SAME AND HOW ARE THEY DIFFERENT
In this case, we must analyze the graphs to find the solution.
Step 01:
Graph A
Dollars vs Months
If Months = 4 ===> 400 Dollars
Graph B
Months vs Dollars
If Dollars = 4 ===> 400 Months
If Months = 4 ===> The dollar amount is imperceptible on the graph.
The answer is:
The graphics are different.
In this case, we must analyze the graphs to find the solution.
Step 01:
Graph A
Dollars vs Months
If Months = 4 ===> 400 Dollars
Graph B
Months vs Dollars
If Dollars = 4 ===> 400 Months
If Months = 4 ===> The dollar amount is imperceptible on the graph.
The answer is:
The graphics are different.
Which graph represents the reflection of AABC over the line y = 0?
-54-3 -2 -1
S ON
CH
-3
LO
*
C
A
2 3
A
B
12
X
Answer:
The graph represents the reflection of triangle ABC over the line y=0 in graph (C).
The coordinates of the triangle ABC are:
A(1, -1), B(4, -1) and C(3, -3).
The rule of reflection over the line y = 0 is:
(x, y) ⇒ (x, -y)
So, we have:
A(1, -1) ⇒ (1, 1),
B(4, -1) ⇒ (4, 1)
C(3, -3) ⇒ (3, 3).
By comparing the above points to the list of options, the correct graph is a graph (c)
Step-by-step explanation:
hope this helps I hope
The graph C represents the reflection of triangle ABC over the line y = 0
What is Graph?Graph is a mathematical representation of a network and it describes the relationship between lines and points.
The coordinates of the triangle ABC are:
A(1, -1), B(4, -1) and C(3, -3).
The rule of reflection over the line y = 0 is:
(x, y) ⇒ (x, -y)
So, we have:
The coordinates after applying rule
A(1, -1) ⇒ (1, 1),
B(4, -1) ⇒ (4, 1)
C(3, -3) ⇒ (3, 3).
By comparing the above points to the list of options, the correct graph is a graph (c)
Hence, the graph C represents the reflection of triangle ABC over the line y = 0
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I need help!
Use the given information to select the factors of f(x). f(4)=0 f(-1)=0 f(3/2)=0. Make sure to select all correct answers for full credit.
The given information of the factors f ( x ) helped to get the following correct options:
( x + 1 ) ⇒ f ( -1 )( x - 4 ) ⇒ f ( 4 )( 2x - 3 ) ⇒ f ( 3/2 )What is a function in math?The term function as used n math refers to a relation consisting of variables. the variables are of two major types which include
The dependent variableThe independent variableSubstituting the functions we have:
f (-1 ) = ( 1 - 1 ) = 0
f ( 4 ) = ( 4 - 4 ) = 0
f ( 3/2 ) = (3 * 2/3 - 3 ) = 0
Other options fail to give the desired result of zero.
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Greg is at his house he gets in his car drives north 8.9 miles and stops at a store then he turns around and drives south 7.7 miles to his friends house how far is the friends house from Greg’s houses
The distance of the friends house from Greg’s houses is 1.2 miles.
How to illustrate the information?From the information illustrated, Greg is at his house he gets in his car drives north 8.9 miles and stops at a store then he turns around and drives south 7.7 miles to his friends house how
The distance will be the difference between the miles that are given.
This will be:
= 8.9 miles - 7.7 miles
= 1.2 miles
The distance is 1.2 miles.
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Solve the equation 5x = 85 for x.
−17
17
−90
80
x = 17
Step-by-step explanation:
5x = 85
x = 85/5
x = 17.
Hence, option (b) is correct answer
Answer: x=17 the answer is B
Hope this helped
Step-by-step explanation:
product of (-12)(-8)
[tex]\huge\text{Hey there!}[/tex]
[tex]\huge\textsf{GUIDE TO FOLLOW: }[/tex]
• [tex]\large\textsf{2 negatives equal positive}[/tex]
• [tex]\large\textsf{2 positives equal positive}[/tex]
• [tex]\large\textsf{1 negative \& 1 positive equal negative}[/tex]
• [tex]\large\textsf{1 positive \& 1 positive equal negative}[/tex]
[tex]\large\textsf{SOME OPERATIONS MAY BE DIFFERENT THAN OTHERS!}[/tex]
[tex]\large\textsf{ANYWHO, LET US ANSWER THIS QUESTION, SHALL WE? }[/tex]
[tex]\mathsf{(-12)(-8)}[/tex]
[tex]\mathsf{= 12(8)}[/tex]
[tex]\mathsf{= 96}[/tex]
[tex]\huge\textsf{Therefore, your answer should be: \boxed{\mathsf{96}}}\huge\checkmark[/tex]
[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]
~[tex]\frak{Amphitrite1040:)}[/tex]
Solve the inequality and graph the solution on the line provided.
3x+17_< 41
Tiana made lemonade for a party. Her family drank half of the lemonade. After the party, she gave one-third of the remaining lemonade to her neighbors. If Tiana has 210 ounces of lemonade remaining after the party and giving some away to her neighbors, how many ounces of lemonade did she start with? Show your work.
The amount of lemonade Tina made in the starting is 630 ounces.
Given that:-
Fraction of lemonade drank by her family = 1/2
Fraction of lemonade given to neighbors = 1/3 of remaining
Amount of lemonade left with her at the end = 210 ounces
We have to find the amount of lemonade Tina made in the starting.
Let the amount of lemonade Tina made in the starting be 6x.
Hence,
Amount of lemonade drank by her family = (1/2)*6x = 3x
Remaining lemonade = 6x - 3x = 3x
Amount of lemonade given to neighbors = (1/3)*3x = x
Remaining lemonade = 3x - x = 2x = 210 ounces
Hence,
x = 210/2 = 105 ounces
Amount of lemonade Tina made in the starting = 6x = 6*105 = 630 ounces.
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Dr. Choi just started an experiment. He will collect data for days. How many hours is this?
The data collected in [n] days is collected in 24n hours.
What is the SI unit of time?
The SI unit of time is Seconds. In 1 second, there are (1/60) minutes.
Given is Dr. Choi who just started an experiment and he will collect data for days.
Assume that he collects the data for [n] number of days. In one day, we have 24 hours. Therefore, in [n] number of days, there will be total of 24n hours.
Therefore, the data collected in [n] days is collected in 24n hours.
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According to the United States Treasury Department, the U.S. national debt was 1.815 x 10^13 dollars on September 30, 2015. On September 29,
2005, the national debt was 4.974 x 10^12 dollars. Find the amount of increase in the national debt from September of 2005 to September of 2015.
Write a sentence describing the increase in the national debt from 2005 to 2015 using scientific notation and using standard form.
The increase in the national debt from 2005 to 2015 using scientific notation is 1.3176 × 10^13.
What is scientific notation?Scientific notation simply means a way of expressing numbers that are either too large or too small.
The U.S. national debt was 1.815 x 10^13 dollars on September 30, 2015 and in September 29,
2005, the national debt was 4.974 x 10^12 dollars.
The increase will be the difference between the two notations. This will be:
= 1.815 x 10^13 - 4.974 x 10^12
= 1.3176 × 10^13
The increase is 1.3176 × 10^13.
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The required respective increase in the national debt of America for the period 2005 to 2015 is 1.3176 × 10¹³.
As of the given condition,
According to the United States Treasury Department, the U.S. national debt was 1.815 x 10^13 dollars on September 30, 2015. On September 29, 2005, the national debt was 4.974 x 10^12 dollars.
Here,
The required increase in the debt is evaluated as the arithmetic difference of the debt in the years 2015 and 2005.
So.
Increase in debt = 1.815 × 10¹³ - 0.4974 × 10¹³ = 1.3176 × 10¹³
Thus, the required respective increase in the national debt of America for the period 2005 to 2015 is 1.3176 × 10¹³.
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C)
to make the total value equal to 2. Re-write the statement 19 + 7 + 2 x 6 + 1 by including two pairs
of brackets
If you place brackets or parenthesis around the numbers 19+7 and 2*6+1. It would appear as follows: (19+7)/(2*6+1) = 26/13 = 2. It takes special parenthetical treatment to express the mathematical expression 19+7/26+1 to get a result of 2.
What is expression?An expression in mathematics is made up of numbers, variables, and functions (such as addition, subtraction, multiplication or division etc.) You can think of expressions as being similar to phrases. A phrase in language may contain an action on its own, but it does not constitute a complete sentence.
Here,
y=19+7/2×6+1
becomes
y=(19+7)/(2×6+1)
y=26/(12+1)
y=26/13
y=2
If you enclose the numbers 19+7 and 2*6+1 in parenthesis or brackets. It would look like this: (19+7)/(2*6+1) = 26/13 = 2. The mathematical expression 19+7/26+1 must be expressed with special parenthetical treatment to yield the number 2.
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a bakery uses 3 3/5 cups of oats to make 2 4/7 pounds of oatmeal cookies how many cups of oats are required per pound of cookies
Answer: 7/5 or 1 2/5
Step-by-step explanation:
Ok so the bakery uses 3 3/5 cups cups of oats for 2 4/7 POUNDS of cookies.
You need to find the unit price.
So to get from 2 4/7 to 1, you need to divide 2 4/7 by 2 4/7
You need to do the same thing to 3 3/5 cups.
3 3/5 as an improper fraction is 18/5
2 4/7 as an improper fraction is 18/7
Now to divide you need to keep, change, and flip
keep the 18/5, change the sign to multiplycation, and flip the 18/7 to 7/18
18/5*7/18=7/5
7/5 or 1 2/5 pounds of outs are required to make 1 pound of oatmeal cookies
Helpppppp x = – 3
y = – 1
The graphs of the equations are in the attached graph
'
How to plot the equations on the graph?Equation (2)
From the question, the equation is given as
x = -3
In the above equation, we can see that
The equation has only one variable and the highest power of the variable is 1
Since the variable is x, then it means that the line of the graph is a vertical line that passes through point x = -3
See attachment for the graph
Equation (3)
Here, we have
y = -1
Also in this equation, we can see that
The equation has only one variable and the highest power of the variable is 1
Since the variable is y, then it means that the line of the graph is a horizontal line that passes through point y = -1
See attachment for the graph
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What is the slope of the line through the points (6,5) and (4, 10)?
m=
The slope of the line through the points (6,5) and (4, 10) exists -5/2.
What is meant by the slope of a line?A line's slope in mathematics is defined as the ratio of the change in the y coordinate to the change in the x coordinate. Both the net change in the y-coordinate and the net change in the x-coordinate are denoted by Δy and Δx, respectively. where "m" represents a line's slope. So, the slope of a line is tan.
Determine the coordinates of two points along the line that you choose. Find the difference between these two points' y-coordinates (rise). Find the difference between these two points' x-coordinates (run). Divide the difference in x-coordinates (rise/run or slope) by the difference in y-coordinates.
Let the two points are (6, 5) and (4, 10)
(x1, y1) = (6, 5) and (x2, y2) = (4, 10)
The equation of slope of the line through the points (x1, y1) and (x2, y2) = y2 - y1 / x2 - x1
substitute the values in the above equation, and we get
= 10 - 5 / 4 - 6
= 5 / -2
Therefore, the slope of the line through the points (6,5) and (4, 10) exists -5/2.
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Which equation has no solution?
Answer:
The answer is the third one down
Step-by-step explanation:
l5-3xl = -8
Absolute value cannot equal a negative number.
Step-by-step explanation:
l5-3xl = -8
the | | is absolute value to it so it cant be negative number
General MathematicsProblem:What sum would have to be invested at 9% conpounded annually to provide an ordinary annuity at ₱8,000 per year for 5 years?
Given that a future value annuity of 8,000 is accrued at 9% compounded annually, the present value of the annuity is evaluated as
[tex]\begin{gathered} PV=P(\frac{1-(1+r)^{-n}}{r})\text{ ----- equation 1} \\ \text{where } \\ PV\text{ }\Rightarrow present\text{ value of the annuity} \\ P\Rightarrow value\text{ of each payment} \\ r\Rightarrow interest\text{ rate} \\ n\Rightarrow period \end{gathered}[/tex]Thus,
[tex]\begin{gathered} P=8,000 \\ r=9\text{\%}=\frac{9}{100}=0.09 \\ n=5 \\ PV\text{ is unknown} \\ \end{gathered}[/tex]Substitute the above value into equation 1, to solve for PV
[tex]\begin{gathered} PV\text{ = 8000(}\frac{1-(1+0.09)^{-5}}{0.09}) \\ \Rightarrow8000\times\frac{1-1.09^{-5}}{0.09} \\ =31117.21 \end{gathered}[/tex]Hence, the sum to be invested is 31117.21
Give an example of a percent problem involving the simple interest formula. Then solve your problem.
The example of the simple interest problem is: What will be the simple interest on $2500 invested at an interest rate of 6% for 2 years?
What is simple interest?
Calculating the amount of interest that will be owed on a sum of money at a certain rate and for a specific period of time is possible using simple interest. Contrary to compound interest, where we add the interest of one year's principal to the next year's principal to compute interest, the principal amount under simple interest remains constant.
Solution for the above problem is:
The formula to calculate simple interest is:
[tex]S.I. = P \times I \times T[/tex]
Here, S.I. is simple interest, P = principal amount, I = interest rate, T = time
Given in the question:
P = $2500
I = 6% = 0.06 (in decimals)
T = 2
Putting the value in the question:
S.I. = 2500(0.06)(2)
S.I. = 300
Therefore, the simple interest is $300.
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2x+y = -7
-4x -5y =23
Answer:
x = -2
y = -3
Step-by-step explanation:
If it is a simultaneous equation.
2x+y = -7-----equation 1
-4x -5y =23-----equation 2
5(2x+y = -7)
-4x -5y =23
10x+5y = -35
-4x -5y =23 +5y cancel -5y
10x= -35
-4x=23
6x = -12
x = -2
Solving for Y
Substitute the value of x in equation one or two.
equation two = -4x -5y =23
-4x -5y =23
-4(-2) -5y =23
8-5y=23
-5y = 23-8
-5y = 15
y = -3
Find the output when the input is n input 1,2,3,4,n output
-6,-8,-10,-12
The expression that represents the output value when the input is n is -4 - 2n
How to determine the output value for the input n?From the question, the input parameters are given as
Input 1,2,3,4,n
Similarly, the output parameters are given as
output: -6,-8,-10,-12
So, we have the following table of values
1,2,3,4,n
-6,-8,-10,-12
From the above table of values, we have the following parameters
Sequence type = arithmetic sequenceFirst term, a = -6Common difference, d = -2The output value for the input n is then calculated as
Tn = a + (n - 1) * d
So, we have
Tn = -6 + (n - 1) * -2
Open brackets
Tn = -6 - 2n + 2
Evaluate the like terms
Tn = -4 - 2n
Hence, the output value for the input n is -4 - 2n
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Which graph represents data used in a linear regression that produces a correlation coefficient closest to -1?
What does the letter "L" stand for in the simulation?
Answer: d
Step-by-step explanation: ion know man but i looked it up and got it right
Emma is scrapbooking. She has 9 inches of paper and needs to cut it into 2/5 inch strips of paper. how many whole strips will she be able to make?
ok
I erased the answer but it is 22 whole strips
arlett is playing a video game. She spends 900 minerals to create 18 workers. Each worker costs the same number of minerals.
Write an equation to describe the relationship between m, the amount of minerals, and w, the number of workers.
The required equation is m/w = 900/18
What is meant by an equation?
An equation is a formula in mathematics that expresses the equality of two expressions by linking them with the equals sign. The word equation and its cognates in various languages may have somewhat different definitions; for example, in French, an équation is defined as including one or more variables, but in English, an equation is any well-formed formula consisting of two expressions linked by an equals sign. Differential equations are equations in which one or more functions and their derivatives are involved. They are solved by locating a function expression that does not use derivatives. Differential equations are used to represent processes with variable rates of change in fields such as physics, chemistry, biology, and economics.
The required equation is m/w = 900/18
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4x > 28 solve the inequality for x and simplify your answer as much as possible
Answer:
x > 7
Step-by-step explanation:
x = 28 ÷ 4
x > 7
that's it
Hey there!
4x > 28
DIVIDE 4 to BOTH SIDES
4x/4 > 28/4
SIMPLIFY it
x > 28/4
x > 7
It is an open circle started at 7 & it’s going to the left of the number line
Therefore, your answer should be:
x > 7
Good luck on your assignment & enjoy your day!
~Amphitrite1040:)
Find the perimeter pf the regular polygon.
5 (x+2)
7x+4
The perimeter of the regular polygon is 108 units.
How to find the perimeter of a regular polygon?A regular polygon is a polygon that has all its sides equal to each other.
Therefore,
5(x + 2) = 7x + 4
5x + 10 = 7x + 4
5x - 7x = 4 - 10
-3x = -6
x = -6 / -3
x = 2
The perimeter of a regular polygon is the sum of the whole sides of the polygon.
Therefore,
each side of the regular polygon = 7(2) + 4
each side of the regular polygon = 14 + 4
each side of the regular polygon = 18
Hence the regular polygon has 6 sides
perimeter of the regular polygon = 18 × 6
perimeter of the regular polygon = 108 units
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The United States flag has a height : width ratio of 10 : 19. If a U.S. flag is 25 inches high, what is its area?
The area of the given flag is 1187.5 square inches.
Given that, the United States flag has a height : width ratio of 10 : 19.
What is the ratio?The ratio is defined as the comparison of two quantities of the same units that indicates how much of one quantity is present in the other quantity.
Let the sum of Height and width of flag be x.
Now, 10+19=29
⇒ 10/29 ×x = 25
⇒ 10x=29 × 25
⇒ x=72.5
So, width = 72.5-25 =47.5
Area of flag = Length × Width
= 25 × 47.5
= 1187.5 square inches
Therefore, the area of the given flag is 1187.5 square inches.
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