Add the whole numbers 4 + 3 = 7
Add the fractions 1/2 + 1/4
Rewrite 1/2 to have a common denominator with 1/4
1/2 = 2/4
Now add 2/4 + 1/4 = 3/4
The answer would be 7 3/4
What is the algebraic equation for this math trick
Pick a number
Add 2
Multiply by 3
Subtract 3
Divide by 3
Subtract the original number
Answer:
it will always be 1
Step-by-step explanation:
lets make an equation
pick a number : x
add 2 : x+2
multiply by 3 : (x+2)*3
subtract 3 : (x+2)*3-3
divide by 3 : ((x+2)*3-3)/3
if you simplify, you will get 1
step by step simplification
(x+2)*3 = 3x+6
3x+6-3=3x+3
(3x+3)/3 = x+1
x+1-x=1
Final answer:
The algebraic equation for the given math trick is: (((((x + 2) * 3) - 3) / 3) - x).
Explanation:
To represent the math trick you described algebraically, we can use the variable x to represent the initial number you pick. Following the steps you provided, the algebraic equation would be: ((((x + 2) * 3) - 3) / 3) - x. Let's break down each step:
Start with the initial number x.Add 2: x + 2.Multiply by 3: (x + 2) * 3.Subtract 3: ((x + 2) * 3) - 3.Divide by 3: (((x + 2) * 3) - 3) / 3.Subtract the original number x: ((((x + 2) * 3) - 3) / 3) - x.the tempurature is changing every day by -3/16 degree farenheit. what will be the change in temerature after 4 days?
Answer:
After 4 days, the temperature will be 3/4 Fahrenheit degrees lower than today
Step-by-step explanation:
Let's calculate the change in temperature after 4 days, this way:
Today's temperature = t in Fahrenheit degrees
Tomorrow's temperature = t - 3/16 Fahrenheit degrees
The day after tomorrow's temperature = t - 2 * 3/16 = t - 3/8 Fahrenheit degrees
Therefore, the temperature after 4 days will be = t - 4 * - 3/16 = t - 3/4 Fahrenheit degrees
After 4 days, the temperature will be 3/4 Fahrenheit degrees lower than today
whats the square root of 49
Answer:
The square root of 49 is 7. 7*7=49
Hope this helps,
:)
A circle has a circumference of 44m. What
is its area?
A. 616m
B. 154m
C. 14m
D. 308m
================================
Work Shown:
C = 44 is the circumference
in general, the circumference of a circle is
C = 2*pi*r
Plug in C = 44 and solve for r.
C = 2*pi*r
44 = 2*pi*r
2*pi*r = 44
r = 44/(2pi)
r = 7.0028175 which is approximate
--------------------
Now plug this into the formula for the area of a circle
A = pi*r^2
A = pi*(7.0028175)^2
A = 154.061985
A = 154 rounding to the nearest whole number
Answer:
B
Step-by-step explanation:
Circumference = 2πr
And circumference = 44 m
44 = 2πr
so, r = 44/2π
r = 22/π
Radius is 22/π
Area of circle = πr²
Area of circle = π × (22/π)²
Area of circle = π × 22²/π²
Area of circle = 22²/π
Area of circle = 484/π
Area of circle = 154.14m²
The main road in Belleville is 7 3/10 Miles long so far 2 3/4 miles have been repaved. How many miles have not been repaved
Answer:
4 11/20
Step-by-step explanation:
The length of road unpaved is 7 3/10 less 2 3/4 miles The LCD of the fractions is 20 (both 10 and 4 divide evenly into 20).
Thus, the problem becomes 7 6/20 - 2 15/20.
We have to borrow 1 from that 7 because 15/20 is larger than 6/20. This results in
6 26/20 - 2 15/20, or
4 11/20
The total length of the main road in Belleville is [tex]7^{(3/10)}[/tex] miles. So far, [tex]2^{3/4}[/tex] miles have been repaved, leaving [tex]7^{(3/10)}[/tex] - [tex]2^{3/4}[/tex] miles that have not been repaved.
1. The total length of the main road is given as [tex]7^{(3/10)}[/tex] miles. In mathematical notation, [tex]7^{(3/10)}[/tex] represents the cube root of 7, which is then raised to the power of 3. So, the total length of the road is the cube root of 7, and then that result is cubed.
2. The length of the repaved portion is given as [tex]2^{3/4}[/tex] miles. In mathematical notation, [tex]2^{3/4}[/tex] represents the fourth root of 2, which is then raised to the power of 3. So, the repaved length is the fourth root of 2, and then that result is cubed.
3. To find the remaining length that has not been repaved, we simply subtract the repaved length from the total length:
Remaining length = [tex]7^{(3/10)}[/tex] - [tex]2^{3/4}[/tex]
Calculating the values, the total length is approximately 2.262 miles (rounded to three decimal places) and the repaved length is approximately 1.682 miles (rounded to three decimal places). Now, subtracting the repaved length from the total length, we get approximately 0.580 miles (rounded to three decimal places) as the length that has not been repaved.
Therefore, the remaining length that has not been repaved is approximately 0.580 miles (rounded to three decimal places).
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What is this ????????
The number of hours in d days and 6 hours how to write in algebraic expression
In a day, there are 24 hours. Then the number of hours in d days and 6 hours is 24d + 6.
What is Algebra?Algebra is the study of mathematical symbols and the rule involves manipulating these mathematical symbols.
The number of hours in d days and 6 hours. Then the algebraic expression will be
We know that in a day, there are 24 hours.
Let the number of the days be d. Then the algebraic expression will be
→ 24 d + 6
Then the number of hours in d days and 6 hours is 24d + 6.
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The graphs of f(x) and g(x) are shown below.
On a coordinate plane, a straight line with a positive slope represents f (x) = x minus 3. The line goes through (0, negative 3) and (3, 0). On a coordinate plane, a straight line with a negative slope represents g (x) = negative 0.5 x. The line goes through (negative 4, 2), (0, 0), and (4, negative 2)
For what interval is the value of (f – g)(x) negative?
(negative infinity, negative 1)
(negative infinity, 2)
(0, 3)
(2, infinity)
Answer:
(negative infinity, 2)
Step-by-step explanation:
The two functions are given by f(x) = x - 3 and g(x) = - 0.5x
So, (f - g)(x) = x - 3 - ( - 0.5x) = 1.5x - 3
Then, for (f - g)(x) to be negative (1.5x - 3) < 0
⇒ 1.5x < 3
⇒ x < 2
Therefore, the interval will be (negative infinity, 2) for which the function (f - g)(x) will be negative. (Answer)
Answer:
negative infinity 2
Step-by-step explanation:
just did the test
what is the solution to this system of equations?
5x-3y=10
3x+3y=3
Answer:
y = 5/2 , x= 7/2
Step-by-step explanation:
5x - 3y = 10…....(1)
3x + 3y = 3......(2)
solving by elimination, we subtract equation (2) from equation (1)
so, 2x = 7
dividing both sides by 2
x= 7/2
substitute x=7/2 for the value of y in equation (1)
5(7/2) - 3y = 10
multiply both sides by 2
35 - 6y = 20
rearranging
-6y = -15
dividing both sides by -6
y = 5/2
Find the Mid point of (-5,-9) (-7,-4)
Answer: ( -6 , -6.5 )
Step-by-step explanation:
The formula for calculating Mid - point is given by
M = ([tex]\frac{x_{1}+x_{2}}{2}[/tex] , [tex]\frac{y_{1}+y_{2}}{2}[/tex] )
[tex]x_{1}[/tex] = -5
[tex]x_{2}[/tex] = -7
[tex]y_{1}[/tex] = -9
[tex]y_{2}[/tex] = -4
substituting into the formula , we have
M = [tex]\frac{-5-7}{2}[/tex] , [tex]\frac{-9-4}{2}[/tex]
M = [tex]\frac{-12}{2}[/tex] , [tex]\frac{-13}{2}[/tex]
Therefore : mid point = ( -6 , -6.5 )
Teo earns 47.25$ in 7 h of work at Beck’s Burgers. How much will he earn in 12 hours?
Answer:
He will earn $81 in 12 hours.
Step-by-step explanation:
Given:
Teo earns 47.25$ in 7 hours of work at Beck’s Burgers.
Now, to find the money he will earn in 12 hours.
As, given Teo earns 47.25$ in 7 hours of work.
So, to get the money he will earn in 12 hours we solve by using unitary method:
If Teo earns in 7 hours $47.25.
Then, in 1 hour he earns = [tex]\frac{47.25}{7}[/tex]
Thus, in 12 hours he will earn = [tex]\frac{47.25}{7} \times 12[/tex]
= [tex]6.75\times 12[/tex]
= [tex]\$81.[/tex]
Therefore, he will earn $81 in 12 hours.
What is the complete factorization of 12x2 + 36x + 27?
A.
(x+3)(12x+ 9)
B. 3(2x + 3)2
C. 6(x + 2)2
D.
(6x + 3)(2x + 9)
Need help please
Answer:
B) 3(2x+3)^2
Step-by-step explanation:
12x^2+36x+27
factor out the 3 first,
3(4x^2+12x+9)
factor out the trinomial 4x^2+12x+9,
3(2x+3)(2x+3)
3(2x+3)^2
Answer:
B. 3(2x + 3)2
Step-by-step explanation:
how many solutions are there to the equation below. 9x+27=9(x+2)+9
Answer:
Infinitely many
Step-by-step explanation:
Evaluate the first expression for b = 5.
5b - 12.4
Answer:
12.6
Step-by-step explanation:
plug in 5 for b
5*5 = 25
25-12.4=12.6
Answer:
B= -2.48
Step-by-step explanation:
Divide 5 and -12.4 both by 5 then B=-2.48
chetan makes a necklace for his sister. twelve beads take up 5 inches of strings. how many beads fit on 1 foot of string.
Answer:
28 beads fit on the string.Step-by-step explanation:
12 inch = 1 ft.
12 inch can be be written as (5 + 5 + 2) inch.
It is given that, 5 inches require for 12 beads.
Hence, (12 + 12) = 24 beads will take up (5 + 5) = 10 inches.
There are 2 inches more to fill.
5 inches required for 12 beads.
1 inch required for [tex]\frac{12}{5}[/tex] beads.
2 inches will be required for [tex]\frac{24}{5}[/tex] beads.
[tex]\frac{24}{5} = 4.8[/tex].
Hence, there will 24 + 4 = 28 beads in total. (Only 4 is added instead of 4.8 because, the number can not be in fraction and there is no space for 29 beads in total).
Raymond just got done jumping at Super Bounce Trampoline Center. The total cost of his session was $43.25. He had to pay a $7 entrance fee and $1.25 for every minute he was on the trampoline.
Here is the equation:
43.25 = 1.25t + 7 where t is the number of minutes he was on the trampoline.
If you place a 89-foot ladder against the top of a 80-foot building, how many feet will
the bottom of the ladder be from the bottom of the building?
Answer:
[tex]\large \boxed{\text{39 ft}}[/tex]
Step-by-step explanation:
Let x be the distance from the foot of the ladder to the base of the building.
We have a right triangle, so we can use Pythagoras' Theorem.
[tex]\begin{array}{rcl}80^{2} + x^{2}& = & 89^{2} \\6400+ x^{2} & = & 7921\\x^{2} & = & 1521\\x & = & \sqrt{1521}\\& = &\mathbf{39}\\\end{array}\\\text{The foot of the ladder will be $\large \boxed{\textbf{39 ft}}$ from the base of the building,}[/tex]
Write the polynomial function, in standard form, that has zeros -2, 5, and 0.
Answer:
f(x) = x³ - 3x² - 10x
Step-by-step explanation:
Given that the zeros are x = - 2, x = 5 and x = 0 then the factors are
(x + 2), (x - 5) and (x - 0) = x
The polynomial is the product of it's factors, thus
f(x) = x(x + 2)(x - 5) ← expand factors using FOIL
= x(x² - 3x - 10) ← distribute parenthesis by x
= x³ - 3x² - 10x
asap, please and thank you
Answer: Here dimension of bigger triangle = 10
Dimension of smaller triangle = 5
Scale factor = 10/5 =2
Therefore
Center C and scale factor 2
which situation could be represented by 5 divided by 1/2=10
See explanation
Step-by-step explanation:
A situation where a farmer needs to divide his 5 acre land into 1/2 an acre to get 10 pieces of land where he can grow ten different crops.
In such a case; you divide 5 by 1/2
5/ 1/2 = 5*2 =10 pieces
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Answer:can someone help
Step-by-step explanation:
What solves 4 + 1/5x = -1 ?
Answer: [tex]x=-25[/tex]
Step-by-step explanation:
For this exercise it is necessary to remember the multiplication of signs:
[tex](+)(+)+\\(-)(-)=+\\(-)(+)=-\\(+)(-)=-[/tex]
Then, having the following equation provided in the exercise:
[tex]4 + \frac{1}{5}x = -1[/tex]
You need to solve for the variable "x" in order to find its value.
To solve the equation, you can follow the steps shown below:
Step 1: You need to subtract 4 from both sides of the equation. Then:
[tex]4 + \frac{1}{5}x-(4) = -1-(4)\\\\ \frac{1}{5}x=-1-4\\\\ \frac{1}{5}x=-5[/tex]
Step 2: This is the final step. You must multiply both sides of the equation by 5 in order to find the value of the variable "x".
Then, you get the following result:
[tex](5)( \frac{1}{5}x)=(-5)(5)\\\\x=-25[/tex]
the height of a parallelogram is 18 centimeters less than its base. if the area is 175 square centimeters, what is its height?
The height of a parallelogram can be found by solving the equation 'Area = base × height' given the area is 175 square centimeters and the height is 18 centimeters less than the base. The base 'b' and the height 'b - 18' form a quadratic equation that can be solved to find 'b', after which subtracting 18 will give the height.
Explanation:The question is asking to find the height of a parallelogram given its area and a relationship between the base and the height. The area of a parallelogram is found using the formula Area = base × height. According to the given information, we know that the area is 175 square centimeters. The relationship between the base and the height of the parallelogram is such that the height is 18 centimeters less than the base. Therefore, we can denote the base as 'b' and the height as 'b - 18'. Plugging these into the formula for the area we get 175 = b × (b - 18).
To solve for 'b', we can set up and solve a quadratic equation. After finding the value of 'b', we can calculate the height by subtracting 18 centimeters from our value for 'b'. Let's go through the steps:
175 = b × (b - 18).Distribute the 'b' on the right side of the equation: 175 = b^2 - 18b.Rearrange to form a quadratic equation: b^2 - 18b - 175 = 0.Solve the quadratic equation using the quadratic formula or factorization (if possible).Substitute the positive value of 'b' back into 'b - 18' to find the height.After solving the quadratic equation, we would get the value of 'b' and accordingly the value of 'b - 18' which is the height of the parallelogram in centimeters.
What is the area of a circle with a radius of 15 inches to the nearest 10th use 3.14
Step-by-step explanation:
The area of a cirkel is calculated with the formula \pi×r^2. Using the 15 inch radius given we get \pi×15^2=706.5 inches squared.
If f(x) = 5x + 4, which of the following is the inverse of f(x)
Answer:
f^-1 (x)=1/5x-4/5
Step-by-step explanation:
y=5x+4
x=5y+4
5y=x-4
y=1/5x-4/5
Answer:
I WOULD SAY THAT THE ANSWER IS C
Step-by-step explanation:
I GOT IT FROM A
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X
A fruit company delivers its fruit in two types of boxes: large and small. A delivery of 4 large boxes and 8 small boxes has a total weight of 197 kilograms. A delivery of 2 large boxes and 3 small boxes has a total weight of 83 kilograms. How much does each type of box weigh?
A large box of fruit weighs 18.25 kilograms and a small box weighs 15.5 kilograms.
Step-by-step explanation:
Let,
Weight of large box = x
Weight of small box = y
According to given statement;
4x+8y=197 Eqn 1
2x+3y=83 Eqn 2
Multiplying Eqn 2 by 2
[tex]2(2x+3y=83)\\4x+6y=166\ \ \ Eqn\ 3[/tex]
Subtracting Eqn 3 from Eqn 1
[tex](4x+8y)-(4x+6y)=197-166\\4x+8y-4x-6y=31\\2y=31[/tex]
Dividing both sides by 2
[tex]\frac{2y}{2}=\frac{31}{2}\\y=15.5[/tex]
Putting y=15.5 in Eqn 2
[tex]2x+3(15.5)=83\\2x+46.5=83 \\2x=83-46.5\\2x=36.5[/tex]
Dividing both sides by 2
[tex]\frac{2x}{2}=\frac{36.5}{2}\\x=18.25[/tex]
A large box of fruit weighs 18.25 kilograms and a small box weighs 15.5 kilograms.
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-f(x) = 2x + 6 Find f(-4)
Can someone plz help me with this problem?
Answer:
option (2)
Step-by-step explanation:
Given the area (A) of a circle is
A = πr² ← r is the radius ( divide both sides by π )
[tex]\frac{A}{\pi }[/tex] = r² ( take the square root of both sides )
[tex]\sqrt{\frac{A}{\pi } }[/tex] = r → option (2)
Javier asks his mother how old a tree in their yard is. His mother says, “The sum of 10 and two-thirds of that tree’s age, in years, is equal to 50.”
Javier writes the equation , where a is the tree’s age in years. His equation is not correct. What error did he make?
Answer:
[tex]10 + (\frac{2}{3}) a = 50[/tex] is the CORRECT equation.
Step-by-step explanation:
The given question is INCOMPLETE.
Javier asks his mother how old a tree in their yard is. His mother says, “The sum of 10 and two-thirds of that tree’s age, in years, is equal to 50.” Javier writes the equation { 10 + 2/3} where a is the tree’s age in years. His equation is not correct. What error did he make?
Now here:
a: The tree’s age in years.
Also, “The sum of 10 and two-thirds of that tree’s age, in years, is equal to 50.”
⇒ 10 + two-thirds of that tree’s age = 50
[tex]\implies 10 + (\frac{2}{3}) a = 50[/tex]
But in the equation written by Javier, the the third fraction is NOT MULTIPLIED by the age of the tree a in Years.
So, the written equation by Javier is Incorrect.
Now, solving the written correct equation for the value of a, we get:
[tex]\implies 10 + (\frac{2}{3}) a = 50\\\implies (\frac{2}{3}) a = 40\\\implies a = 40 \times (\frac{3}{2}) = 60\\\implies a = 60[/tex]
Hence the correct age of the tree = 60 years
Use >, <, and + signs to write inequalities for the relationships among
the sides of the triangles. Show your work below the numbers.
7. 1/2 _______________1/3 _______________1/5
8. 0.1 _______________ 0.15 _______________ 0.2
Answer:
7. [tex]\frac{1}{2}+\frac{1}{3}>\frac{1}{5}[/tex]
8. [tex]0.1+0.15>0.2[/tex]
Step-by-step explanation:
Given:
Three sides of the triangles are given.
For Question 7
1/2 _ 1/3 _1/5
For Question 8
0.1 _ 0.15 _ 0.2
We need to use >, <, and + signs to write inequalities for the relationships among the sides of the triangles.
Solution:
Part 7.
Property of the triangles.
Sum of two side of triangles must be greater than third side.
So, first, second and third side of the triangle is [tex]\frac{1}{2}, \frac{1}{3}\ and\ \frac{1}{5}[/tex]
[tex]\frac{1}{2}+\frac{1}{3}>\frac{1}{5}[/tex]
[tex]\frac{5}{6}>\frac{1}{5}[/tex]
So, its satisfy the triangle rule.
Therefore, Inequality is [tex]\frac{1}{2}+\frac{1}{3}>\frac{1}{5}[/tex]
Part 8.
Property of the triangles.
Sum of two side of triangles must be greater than third side.
So, first, second and third side of the triangle is [tex]0.1, 0.15\ and\ 0.2[/tex]
[tex]0.1+0.15>0.2[/tex]
[tex]0.25>0.2[/tex]
So, its satisfy the triangle rule.
Therefore, Inequality is [tex]0.1+0.15>0.2[/tex]
Use inequalities to compare sides of triangles with >, <, and + signs.
For 7:
1/2 > 1/3
1/3 > 1/5
1/2 + 1/3 > 1/3 + 1/5
For 8:
0.1 < 0.15
0.15 < 0.2
0.1 + 0.15 < 0.15 + 0.2
Am not good makeing word problems can you help me make one here we go 2/3 x 3 =c now help me make a word problem
Answer:
Emily decides marbles the ratio of marbles is 2 to 3 she adds 3 times more to that.
Step-by-step explanation:
Answer:
Step-by-step explanation:
I have 2/3 of milk and I need 6/3 so my neighbor gave me 3