Exponents and power - [tex]12y^3 - 4y^3 = 8y^3[/tex]
What are exponents and power?
Exponents and powers are two techniques for simplification of extremely big or extremely small numbers. For instance, we can write 3 x 3 x 3 x 3 as [tex]3^{4}[/tex], where 4 is the exponent and 3 is the base, to demonstrate 3 x 3 x 3 x 3 in a straightforward manner. There is a claim of power throughout the entire sentence [tex]3^{4}[/tex].
How do you perform exponentiation operations?
Rule 1: All operations enclosed in parenthesis must be simplified.
Rule 2 states that all exponents should be simplified, starting from the left.
Rule 3: When multiplying and dividing, always go from left to right.
Rule 4: Always add and subtract by moving from left to right.
[tex]8y^{3}[/tex] is the correct answer to the given equation.
[tex]12y^{3} - 4z^{3}\\ = (12-4)y^{3}\\= (8)y^{3}\\ =8y^{3}[/tex]
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QUESTION: William started with 40 pieces of candy and gave away x pieces. Hannah had 70 pieces of candy and gave away three times as many pieces as William did.
How many pieces of candy did William give away if they had the same number of pieces of candy left?
A. 30
B. 18
C. 15
D. 8
The pieces of candies that William gave away is 15.
How many pieces of candy did William give away?The linear expression that can be used to determine the number of candies left is:
Pieces of candies left = initial pieces of candies - number of candies given out
Pieces of candies left when William gave out candies : 40 - x
Pieces of candies left when Hannah gave out candies : 70 - 3x
If they have the same pieces of candies left, the two above expressions would be equal.
40 - x = 70 - 3x
3x - x = 70 - 40
2x = 30
x = 15
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5(x-2)+7=5x-11 what is the answer
Marta went to the local discount store to stock up on school supplies. She bought four spiral notebooks at $1.50 each, a package of pens for $3.95, three felt tip markers at $.99 each, and a three-ring binder for $5.00. The sales tax is 6.5%. What was the total price Marta paid at the checkout counter?
Answer: 18.7598
Step-by-step explanation:
4 x 1.50= 6
6+ 3.95=9.95
3x 0.99= 2.97
2.97 + 9.95= 12.92
12.92+ 5= 17.92
6.5% of 12.92= 0.8398
6.5% of 12.92 + 17.92= 18.7598.
if your heart beats 700 times in 10 minutes how many times in 2 minutes
Answer:
your heart beats 140 times in two mintutes or 70 times per minute
Step-by-step explanation:
to find how many beats per minute :
700/10= 70
and then to find for two minutes :
70x2= 140
Hope this helped
Use the slope-intercept form to graph the equation
Question content area bottom left
Part 1
Use the graphing tool to graph the line. Use the slope and y-intercept when drawing the line.
The graph of the equation y = -6/7x + 2 that shows the slope and y-intercept is shown in the image attached.
What is the Slope-Intercept Form of the Equation of a Line?y = mx + b represents the equation of a line in slope-intercept form. In y mx + b, we have the following parameters of the line it represents:
m = the slope of the line, which is the change in y / the change in x or rise/run of the line.b = the point the line intercepts at the y-axis which is the y-intercept where x = 0.Given the equation of a line in slope-intercept form as y = -6/7x + 2, it means that the graph of the line you are to plot would have a negative slope (m) of -6/7, and must intercept the y-axis at y = 2.
So, to draw the line of the equation that was given in slope-intercept form as y = -6/7x + 2, you have to use a slope of -6/7 that show the steepness of the line, and a y-intercept of 2, that shows where the line intercepts the y-axis of the graph at y = 2, of which the corresponding x-coordinate must be equal to zero.
Therefore, the graph of y = -6/7x + 2 is shown below.
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Question 1 : given the replacement set {0,1, 2, 3, 4} . solve 5x - 6 = 9
Question 2: Given the replacement set {2, 3, 4, 5} . Solve 8x + 4 = 5x - 6
The solution to the equations are x = 3 and no solution in the set, respectively
How to solve the equations using the replacement sets?Question 1
The equation is given as:
5x - 6 = 9
The replacement set is given as
{0,1, 2, 3, 4}
So, we replace the variables using the elements in the replacement set
When x = 0, we have
5(0) - 6 = 9
- 6 = 9 -- false
When x = 1, we have
5(1) - 6 = 9
- 1 = 9 -- false
When x = 2, we have
5(2) - 6 = 9
4 = 9 -- false
When x = 3, we have
5(3) - 6 = 9
9 = 9 -- true
Hence, the value of the equation is x = 3
Question 1
The equation is given as:
8x + 4 = 5x - 6
The replacement set is given as
{2, 3, 4, 5}
So, we replace the variables using the elements in the replacement set
When x = 2, we have
8(2) + 4 = 5(2) - 6
20 = 4 -- false
When x = 3, we have
8(3) + 4 = 5(3) - 6
28 = 9 -- false
When x = 4, we have
8(3) + 4 = 5(4) - 6
28 = 14 -- false
When x = 5, we have
8(5) + 4 = 5(5) - 6
44 = 19 -- false
Hence, the value of the equation is not in the solution set
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suppose you walk at the of 210 ft/min. you need to walm 10,000 ft. how many more minutes will it take you to finish if you have already walked 550 ft.
It will take you 45 more minutes to finish walking the remaining distance.
If you have already walked 550 ft, subtracting it to the total distance you need to walk, then the remaining distance will be:
10,000 ft - 550 ft = 9450 ft
Rate is the relationship between two quantities of different units. Rate of speed is the amount of distance over total time.
If you walk at the rate of 210 ft/min, then the time it will take you to finish the remaining distance will be:
rate = distance/time
time = distance/rate
time = 9450 ft/(210 ft/min)
time = 45 mins
Hence, it will take you 45 more minutes to finish the walk.
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Divide using either synthetic division or long division
(3x^3+4x^2-x+7)/(x+2)
Answer:
3x^2-2x+3 with a remainder of 1/x+2
Step-by-step explanation:
Which equation represents the line through (2, - 4) and (0, 4)?
Answer: Option D is correct.
y = -4x + 4
Answer:
y = -4x + 4
Step-by-step explanation:
D. is your answer ^^
find the perimeter pls i need help
Answer: 70 in.
Step-by-step explanation:
So we know that the perimeter of a rectangle =2(Length*Breadth)
Given =
Area of the rectangle = 35 [tex]in.^{2}[/tex]
Length = 7 in.
Area of a rectangle = Length*Breadth
35 = 7*Breadth
[tex]\frac{35}{7}[/tex] = Breadth
5 = Breadth
Now we can find out the perimeter of the rectangle =
= 2(Length*Breadth)
= 2(7*5)
= 2*35
= 70 in.
What are the dimensions of the matrix?
[−163049−1−2]
Enter your answer by filling in the boxes.
Answer: 2 x 4
Reason:
There are 2 rows and 4 columns. The order is important since 4x2 is different from 2x4.
(2x + 12y = −17) (3x + 2y = 7) value of x and y
Answer:
x = (59/16)
y = (-65/32)
Step-by-step explanation:
2x + 12y = −17
3x + 2y = 7
--------------------------
(2x + 12y = −17) × 3
6x + 36y = -51
(3x + 2y = 7) × -2
-6x - 4y = -14
----------------------------------
6x + 36y = -51
-6x - 4y = -14
-----------------------
32y = -65
÷32 ÷32
--------------------------
y = (-65/32)
3x + 2y = 7
3x + 2(-65/32) = 7
3x - (65/16) = 7
+(65/16) +(65/16)
-------------------------------
3x = (177/16)
÷3 ÷3
---------------------------
x = (59/16)
I hope this helps!
A cash discount of 8% is allowed on an item which costs £45. How much money is saved if a customer decides to pay in cash? How much more can he save if the discount is 9%?
well, if she decides to pay in cash, the savings is 8%!!!! yeah!!!, well hell how much is that?
[tex]\begin{array}{|c|ll} \cline{1-1} \textit{\textit{\LARGE a}\% of \textit{\LARGE b}}\\ \cline{1-1} \\ \left( \cfrac{\textit{\LARGE a}}{100} \right)\cdot \textit{\LARGE b} \\\\ \cline{1-1} \end{array}~\hspace{5em}\stackrel{\textit{8\% of 45}}{\left( \cfrac{8}{100} \right)45}\implies \text{\LARGE \pounds 3.6}[/tex]
what if 9%? well, how much is 9%?
[tex]\begin{array}{|c|ll} \cline{1-1} \textit{\textit{\LARGE a}\% of \textit{\LARGE b}}\\ \cline{1-1} \\ \left( \cfrac{\textit{\LARGE a}}{100} \right)\cdot \textit{\LARGE b} \\\\ \cline{1-1} \end{array}~\hspace{5em}\stackrel{\textit{9\% of 45}}{\left( \cfrac{9}{100} \right)45}\implies 4.05~\hfill \underset{\textit{more in savings}}{\stackrel{4.05~~ - ~~3.6}{\text{\LARGE \pounds 0.45}}}[/tex]
rereciporical of 3.5??
Answer:
B
Step-by-step explanation:
3 5/6 = 23/6
Reciprocal: 6/23 i hope you pass(ﾉ◕ヮ◕)ﾉ*:･ﾟ✧
What is the area of the shaded part of the figure
Answer: 102in
Step-by-step explanation:
the rectangle in the top right corners dimensions are 3in by 4in therefore that area is 12in then moving onto the larger rectangle the dimensions at the bottom are 10in and the dimensions for the side are 9in (6+3) so the area of the larger rectangle is 90. adding the two areas together gives a total shaded area of 102in
Answer: the area of the shaded part of the figure is 102in
Step-by-step explanation:
6+3=9 (length of the sides of the figure)
10+4= 14 (length of the bottom of the figure)
9x14 = 126 (area of entire figure)
4x6= 24 (area of the white part of the figure)
126-24 = 102 (area of the shaded part of the figure)
hope this helps!
What is the range of the following function:
A.) –1 ≤ y ≤ 1
B.) {–1, 1}
C.) y is all numbers.
D.) y > –1
Answer:
A is the correct answer.
someone give me the answer pls
The measure of the triangle for the value of x is x = 11.
What is defined as the triangle?A triangle is a 2-dimensional closed shape with three sides, three angles, and three vertices. A triangle is a type of polygon.
The sum of a triangle's three interior angles is always 180°.The sum of any two triangle sides is always larger than the length of a third side.A triangle's area is equal to half the product of the its base and height.For the given value of triangle;
The three angles are given as;
3x + 84x + 1184By the sum of all angles of triangle property.
The sum of all three angles of the triangle is 180°
Thus,
3x + 8 + 4x + 11 + 84 = 180
Simplifying;
7x = 180 - 103
7x = 77
x = 11
Thus, the solution of x of the given triangle is found as x = 11.
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Rebecca keeps all of her line drawings in portfolio
folders. She was recently asked to show the
drawings at an upcoming exhibit. She notices as
she sorts through the drawings that, in each folder,
4 out of 9 drawings are human portraits.
If Rebecca has sixty-three line drawings in one of
her portfolio folders, how many of them are human
portraits?
Answer:
28 human portraits
Step-by-step explanation:
If 9x7=63,
Then you would multiply the 4 human portraits by 7 which gets you 28 human portraits.
Find the quotient and remainder - Enter your answers as a whole
number followed by the letter R (for remainder) and then the
remainder.
13) 4,297
Explanation:
The long division is shown below.
You can also use your calculator to find that 4297/13 = 330.538 approximately which rounds down to 330. This is the quotient.
The remainder is 4297-330*13 = 7
HELP ASAP NEEDS TO BE DONE BEFORE TONIGHT
Answer:
neither
Step-by-step explanation:
Answer:
neither
Step-by-step explanation:
I graphed it on desmos. It showed the lines intersecting each other. Intersection is not the same as perpendicular. Intersecting goes all the way through while perpendicular doesn't.
Sorry, I see my mistake now.
Hope this helps! :)
The points (h,0) and ( – 9, – 6) fall on a line with a slope of 6. What is the value of h?
Answer:
-8
Step-by-step explanation:
[tex]\frac{-6-0}{-9-h} = 6\\6(-9-h)=-6\\-9-h=-1\\-h=8\\h=-8[/tex]
Answer:
Step-by-step explanation:
Given:
x1 = h
y1 = 0
x2 = - 9
y = - 6
k = 6
_______
h - ?
y = k*x + b
y = 6*x + b
1)
y2 = 6*x2 + b
-6 = 6*(-9) + b
-6 =- 54 + b
b = 54 - 6
b = 48
2)
y = 6*x + 48
y1 = 6*x1 + 48
0 = 6*h + 48
6*h = - 48
h = - 8
The quotient of 1 and the square of a number
Answer: 1
Step-by-step explanation: The reciprocal squared of an integer may be found by taking the quotient of 1 and the square of the number. A number's inverse, also known as the number that must be multiplied by in order to get 1, is referred to as the number's reciprocal.
Which statement describes the graph of y= -x+3 and y=-x+6?
Responses
They intersect at point ( 3 ,6 )
They are parallel
They are perpendicular
They intersect at point (6,3).
Considering the definition of parallel line, the statement "They are parallel" describes the graph of y= -x+3 and y=-x+6.
Linear equationA linear equation o line can be expressed in the form y = mx + b
where:
x and y are coordinates of a point.m is the slope.b is the ordinate to the origin and represents the coordinate of the point where the line crosses the y axis.Parallel lineParallel lines are two lines that are always at the same distance from each other and that prolonged towards infinity never touch.
Two lines are parallel if they have the same slope or value of m and different y-intercepts or value of b.
This caseIn this case, you know:
y= -x+3 has a slope of -1 and an ordinate to the origin of 3.y=-x+6 has a slope of -1 and an ordinate to the origin of 6.Two lines are parallel if they have the same slope and different y-intercepts. Then, both lines are parallel.
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please answer question with answer
Answer:
48[tex]cm^{2}[/tex]
Step-by-step explanation:
1. We need 2 integers (full number) when added gives us 7
this is 4 and 3
2. so the width of the rectangle is 3cm and the length is 4cm
3. to find one area of a rectangle we do
4cmx3cm= 12[tex]cm^{2}[/tex]
4. There is 4 rectangles, so we do
4x12[tex]cm^{2}[/tex]= 48[tex]cm^{2}[/tex]
5. so the total area of the pattern is
= 48[tex]cm^{2}[/tex]
A triangle has an area of 20in every dimension of the triangle is multiplied by a scale factor, and the new triangle has an area of 180in . what was the scale factor
If a triangle has an area of 20in every dimension of the triangle is multiplied by a scale factor, and the new triangle has an area of 180in . the scale factor is 3.
Scale factorFirst step is to calculate the area
Area:
Area = New triangle /Old triangle
Area = 180 / 20
Area = 9
Second step is to calculate the ratio of areas
Ratio of areas :
Ratio of areas = 9
Ratio of areas = (3)²
Hence,
Scale factor : 3
Therefore the scale factor is 3.
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4x12=6 x n guys please help me on this im in 4th grade and dont know it
Answer:
4x12=6x
48=6x
x=48/6
x=8
Ariana owns a food truck that sells tacos and burritos. She only has enough supplies
to make 120 tacos or burritos. She sells each taco for $3.75 and each burrito for
$7.25. Ariana must sell no less than $580 worth of tacos and burritos each day. If x
represents the number of tacos sold and y represents the number of burritos sold,
write and solve a system of inequalities graphically and determine one possible
solution.
One possible solution to the system of inequalities is (90, 50)
How to solve the system of inequalities graphically?From the question, we have the following parameters:
Supplies = 120 tacos or burritos
This means that
x + y = 120
Where x represents the number of tacos and y represents the number of burritos
Also, we have
She must sell no less than $580
This means that
3.75x + 7.25y >= 580
So, we have the system of inequalities to be given as
x + y = 120
3.75x + 7.25y >= 580
Next, we plot the system of inequalities on a graph
See attachment for the system of inequalities on a graph
From the attached graph, we have both lines of the graph intersect at (82.857, 37.143)
When the point is moved to the shaded region, we have one of the possible points to be (90, 50)
Hence, the solution to the system of inequalities is (90, 50)
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You harvest 50 cherry tomatoes from your garden. you randomly inspect 15 tomatoes and find that 3 have bad spots on them. what is the experimental probability that a tomato has a bad spot?
Answer: 1 out of 5
Step-by-step explanation: 15 divided by 3 is 5. Which also means out of the 50 cherry tomatoes, 10 of them have bad spots.
(f o g)(x):
f(x)=x^2+9 and g(x)=x^2-9
The composite result function of ( f ° g )(x) in the given functions f( x ) = x² + 9 and g( x ) = x² - 9 is x⁴ - 18x² + 90.
What is the composite result function of ( f ° g)(x) in the given function?A function is simply a relationship that maps one input to one output.
Given the data in the question;
f( x ) = x² + 9g( x ) = x² - 9( f ° g)(x) = ?First, we set up the composite result function f(g(x)).
f( x ) = x² + 9
f( g(x) ) = f( x² - 9 ) = ( x² - 9 )² + 9
f( g(x) ) = ( x² - 9 )² + 9
Expand the parenthesis
f( g(x) ) = ( x² - 9 )( x² - 9 ) + 9
f( g(x) ) = ( x²( x² - 9 ) -9( x² - 9 ) + 9
f( g(x) ) = x⁴ - 9x² - 9x² + 81 + 9
Collect and add like terms
f( g(x) ) = x⁴ - 18x² + 81 + 9
f( g(x) ) = x⁴ - 18x² + 90
Therefore, ( f ° g )(x) in the given functions is x⁴ - 18x² + 90.
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9 customers entered a store over the course of 18 minutes. At what rate were the customers entering the store in minutes per customer?
Answer:
0.5 entrances per minute
Step-by-step explanation:
9 customers entered a store over the course of 18 minutes. At what rate were the customers entering the store in minutes per customer?
9/18 = 0.5 entrances per minute
Answer: 2 minutes/Customer
Step-by-step explanation:
Total time passed: 18 minutes
Total customers entered: 9 nos.
using unitary method, number of minutes requires for one customer to enter or minutes per customer is:
18/9 that is , 2 minutes/customer.
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