a³ - b³ = (a - b) (a² + ab + b²)
You can see why this works if you expand the right side as
a (a² + ab + b²) - b (a² + ab + b²)
(a³ + a²b + ab²) - (a²b + ab² + b³)
Both the a²b and ab² terms cancel, leaving you with a³ - b³.
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ASK YOUR TEACHER
Consider a survey involving the cookie preferences of a sample of 1,214 adults. If 28% answered peanut butter" find the decimal and reduced fraction of that percentage
PRACTICE ANOTHER
The decimal fraction is 0.28 and reduced fraction is 7/25.
What is fraction?In mathematics, the fraction is generally a term which define the small part of something or amount of something. A fraction has generally two parts a numerator and a denominator.
The general syntax for fraction is : [tex]\frac{x}{y}[/tex]
where, x is the numerator part
y is the denominator part
The fraction has two types of notations:
Decimal notation : In the decimal notation of fraction the term is written as the decimal form of x / y. we generally try to reduce the decimal value upto the nearest tenth.Reduce notation: In the reduce notation the structure of term is x/y but in this we try to convert the fraction into smallest fraction form.In the question given,
Total number of samples = 1214
Adults who answered peanut butter = 28%
Now, the decimal fraction = 28 / 100 = 0.28
and, the reduce fraction = 28/100 = (7)(4) / (25)(4) = 7/25
Hence, The decimal fraction is 0.28 and reduced fraction is 7/25.
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A chef uses a recipe with the following ingredients then the chef decides to make more than 1 batch of recipe. if a total of 30 cups of mangoes and blueberries are used, how many batches of the recipe did the chef make? 3 cups used for 1 mango and 2 cups used for blueberries, 5 cups for apples and 1 cup used for blackberries
Answer:11 cups
Step-by-step explanation:
Srry if im wrong :)
Laura is 32 feet below the ground in a cave. If she ascends 8 feet, what is her new depth?
Answer:
40 feet
Step-by-step explanation:
Because 32+8=40
32
- 08
-----
40
Answer: -24 feet
Step-by-step explanation: ascending is rising so you would subtract feet, which in this case is 8 feet. after that you would consider that since she is underground the feet would be negative because she is below ground level which is zero. once you subtract it then you would get a grand total of -24 feet or 24 feet below the earth's surface but more than likely the answer would be -24 ft.
hope this was helpful :)- hailey <3
You have timed yourself and found that you can read 8 pages of a novel in 10 minutes. Your homework tonight is to read 42 pages in the novel. How many minutes should it take you? Round your answer to the nearest tenth if needed.
It will take 53 minutes to read 42 pages in a novel
Given,
The time taken to read 8 pages in a novel = 10 minutes
Therefore, the time taken to read 1 page = 10 ÷ 8 = 1.25 minutes
Now,
We have to find the time taken to read 42 pages of a novel.
Time to read 42 pages = 42 × 1.25
Time taken = 52.5 minutes
We can round it to nearest tenth, that is 53 minutes.
That is, the time taken to read 42 pages in a novel is 53 minutes.
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MARKING BRAINLEIST IF CORRECT
Answer:
C) corresponding angles
Step-by-step explanation:
AE is a transversal that crosses two parallel lines. Notice Angle ABC and BED are on the same corner. Hence, they are corresponding angles
for the dinner special at a restaurant, the customer must choose an appetizer, an entree, a side dish, and a dessert. here are the items to choose from
288 dinner specialist
1 Appetizer = 3 C₁
1 Salad = 2 C₁
1 Entree = 4 C₁
1 Side dish = 3 C₁
1 desert = 4 C₁
Total = 3 C₁ * 2 C₁ * 4 C₁ * 3 C₁ * 4 C₁
=3* 2 * 4 * 3 * 4
= 288 dinner specialist
What do you mean by possibility in mathematics?The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true. The probability of an occurrence is a number between 0 and 1, with 1 representing certainty and 0 representing impossibility. The higher the likelihood of an event, the more likely it is to occur. A straightforward illustration is tossing a fair (impartial) coin. Since there are no other conceivable outcomes and the coin is fair, the odds of both the possibilities, "heads" and "tails," are equally likely to occur. As a result, the probability of either occurrence is half.
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list the digits that repeat:
2/11 = 0. [?] [ ]
enter the number that belongs in the green box (or just boxes)
Answer:
0.18
Step-by-step explanation:
you just need to divide 2÷11 until 2 decimal places
find the value of x
(X-24) = 29 degrees
Answer:
X - 24 = 29
X = 29 + 24
X = 53 degrees
the shortest distance between two points on a sphere is group of answer choices a straight line an arc of a great circle an arc of a small circle
The shortest path between two points on the sphere is the arc of a great circle. Thus, option C is correct.
According to the statement
We have to find about the distance.
So, For this purpose, we know that the
The distance between two points is that the length of the path connecting them.
From the given information:
We have to search out that the the shortest distance between two points on a sphere.
Then we all know that the
Sphere is that the set of all points in three-dimensional space lying the identical distance from a given point, or the results of rotating a circle about one in every of its diameters.
Then
The shortest path between two points on the sphere is that the arc of a good circle.
According to this the option C is correct.
So, The shortest path between two points on the sphere is the arc of a great circle. Thus, option C is correct.
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x / −6 ≥−20
solve for x
Answer:
[tex]x\leq 120[/tex]
---------------------------
Hope this helps!
Have a great day and God bless! :)
Graph: y= lx+2l+1
what are the coordinates of the vertex of the graph? The vertex is
Can you guys help me on this one?
Answer:
The area is 12.57
The Circumference is 12.57
Step-by-step explanation:
How to do this exercise step by step?
which point on the number line represents the product (-4)(-2)(-1)?
Select all decimals that are equivalent to
9 x 100 + 2 x 10 + 3 x 10 + 5 x 1/100
A.92.35
B.920.350
C.902.35
D.92.350
E. 920.35
F.920.035
Answer:
E. 920.35
Step-by-step explanation:
Hope this helped :>
On a coordinate plane, 2 straight lines are shown. The first solid line has a positive slope and goes through (negative 1, negative 3) and (0, 0). Everything to the right of the line is shaded. The second dashed line has a negative slope and goes through (negative 2, 3) and (1, negative 3). Everything to the right of the line is shaded.
A school is planning for an addition in some open space next to the current building. The existing building ends at the origin. The graph represents the system of equations that can be used to define the space for the addition. What is the system of equations that matches the graph?
y ≤ 3x
y > –2x – 1
y > 3x
y ≤ –2x – 1
y < –3x
y ≥ 2x – 1
y > –3x
y ≤ 2x – 1
Using linear functions, the system of inequalities that matches the graph is given by:
y ≥ 3x.y > -2x - 1.What is a linear function?A linear function is modeled by:
y = mx + b
In which:
m is the slope, which is the rate of change, that is, by how much y changes when x changes by 1.b is the y-intercept, which is the value of y when x = 0, and can also be interpreted as the initial value of the function.Given two points, the slope is given by change in y divided by change in x. For the first line, the points are:
(-1, -3) and (0,0).
Hence the slope is:
m = (0 - (-3))/(0 - (-1))
m = 3.
When x = 0, y = 0, hence the y-intercept is of b = 0 and the line is given by:
y = 3x.
Everything to the right of the solid line is shaded, hence the values that are equal(line is solid) or greater than the line compose the inequality, as follows:
y ≥ 3x.
For the second line, the points are:
(-2,3) and (1,-3).
Hence the slope is:
m = (-3 - 3)/(1 - (-2)) = -6/3 = -2.
Then:
y = -2x + b.
When x = -2, y = 3, hence:
3 = -2(-2) + b
b = -1.
Hence the line is:
y = -2x - 1.
Everything to the right of the dashed line is shaded, hence the inequality is:
y > -2x - 1.
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Lorie ordered a shed to hold her gardening supplies. The shed had a length of 12.25 ft, a width of 10 ft, and a height of eight and one fifth ft.
Determine the volume, V, using the formula V = lwh.
30.45 ft3
100.45 ft3
960.05 ft3
1,004.5 ft3
The volume will be 1004.5 ft³.
How to calculate the volume?It should be noted that the volume is calculated as:
= Length × Width × Height
= 12.25 × 10 × 8.2
= 1004.5 ft³
Therefore, the volume will be 1004.5 ft³.
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help questions 3-5 (negative and positive numbers)
Answer:
good luck broooooooooo
Ruguru wants to rent a car for 3 days. The cost,C , in dollars, for the rental is shown in the box, where D is the number of days the car is rented If Ruguru has 115, how much more will he need to rent a car for 3 days?
Ruguru need $15 more to rent a car for 3 days.
Given,
Number of days Ruguru wants to rent a car = 3 days
The amount Ruguru has with him = $115
The cost for the rental of the car:
C = 25 + 35D
Where,
D is the number of days
Now,
Lets find the total rent of the car for 3 days
C = 25 + 35D
C = 25 + 35 × 3
C = 25 + 105
C = 130
The total rent of a car for 3 days is $130
We have to find the amount needed by Ruguru to rent a car for 3 days.
That is,
Total rent - Amount Ruguru has = Amount needed
130 - 115 = 15
Therefore,
Ruguru need $15 more to rent a car for 3 days.
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Kenneth's bank account is modeled by the following equation f(x) = 13x+30
where x in the number of weeks and f(x) is total amount. How much money
was in Kenneth's account when it was opened?
When Kenneth opened her account, her account balance was 30.
A function is an expression that assigns each input value, say x, a unique output value, say y. Mathematically, a function can be represented as-
F(x) = x + a
Here, we are given that Kenneth's bank account is modeled by the following equation-
f(x) = 13x + 30
here, x = number of weeks
and f(x) = total amount
When Kenneth must've opened his account, the number of weeks would've been zero.
⇒ x = 0
Substituting the value of x = 0 in f(x), we get-
f(0) = 13(0) + 30
f(0) = 0 + 30
f(0) = 30
Thus, when Kenneth opened her account, her account balance was 30.
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When you answer these, can you number them?
15+3(2x-9)=44 solutions or no solution
when we take x = 9.33, the equation becomes true, which means that the linear equation has one solution.
Does the given linear equation has solutions?
Here we have the following linear equation:
15 + 3*(2x - 9) = 44
And we want to see if this has a solution, it means that there is a value of x such that the equation becomes true. Let's see that.
To do it, we need to isolate the variable, x, in one of the sides of the equation.
Expanding the product we get:
15 + 3*2x - 3*9 = 44
Moving the terms without x to the right side:
15 + 6x - 27 = 44
6x = 44 + 27 - 15 = 56
Now we can divide both sides by 6 so we get:
x = 56/6 = 9.33
So, when we take x = 9.33, the equation becomes true, which means that the linear equation has one solution.
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Help please(work provided)
Answer is angle 2
Reason
two angles are adjacent angles when they share the common vertex and a side.
See attached picture
Express 28 + 42 as the product of the greatest common factor (GCF) of the two numbers and a sum of two numbers.
Answer:
14 is there (GCF) 28+42=70
Graph each integer and its opposite on the number tin
hi!
lets try and further analyze this.
The integer -2 would be graphed directly on the "-2" point on the line. also marking positive 2 (2) as for that's its opposite. Positive 3 (3) would be marked on the 3 and so would -3. Then -5 and positive 5 (5) and lastly -1 and positive 1 (1).
hope this helps!
side note: for actually graphing the point just use a filled in dot indicating where you mark it.
Situation 1: A number cube has sides labelled 1-6. After rolling 15 times, Tyler records his data:
1,1,1,1,2,2,3,3,4,4,5,5,5,6,20
Is there an outlier? (yes/no)
If so, what is it? (write N/A if there is no outlier)
Should any data points be investigated or removed? (investigated/removed)
Why? (non-plausible/not representative)
Answer:
There is an outlier. The outlier is 20. 20 should be removed because a dice only has 6 faces, and there is no side numbered 20.
Step-by-step explanation:
Use the laws of exponents to simplify the expression so that the base, x, appears once, and the exponent is positive. x^3/x^5
Can someone pls help me with this one T—T
Answer:
13. x = 2 - 5y
14. x= 6y + 2
A cone has a volume of 98 cm3.
The radius of the cone is 5.13 cm.
Work out an estimate for the height of the cone.
Answer: Height is equal to approximately 3.56.
Step-by-step explanation:
FIND formula for finding height on a cone:3 * [tex]\frac{V}{\pi r^{2} }[/tex]
2. INSERT Volume and Radius
3 * [tex]\frac{98}{\pi 5.13^{2} }[/tex]
3.CALCULATE Height
Pi*5.13^2= 82.676979798 / 82.6769797= 1.185335995041.18533599504 * 3= 3.556007985133.55600798513 rounds to 3.56Answer:
3.6cm=h
Step-by-step explanation:
v=1/3πr^2h
input your values
98=1/3×22/7×5.13×5.13×h
98=(22*5.13*5.13*h)/21
cross multiply
98*21=22*5.13*5.13*h
2058=22*5.13*5.13*h/22*5.13*5.13
3.6cm=h
hope it helps, please mark brainliest
what is the product of (2.5+y) and (1.1y)
The product of the expressions (2.5 + y) and (1.1y) will be 2.75y + 1.1y².
What is Algebra?The analysis of mathematical representations is algebra, and the handling of those symbols is logic.
It is also known as the product. If the object n is given to m times then we just simply multiply them.
The expressions are given below.
(2.5 + y) and (1.1y)
Then the product of the expressions (2.5 + y) and (1.1y) will be
⇒ (2.5 + y) × (1.1y)
⇒ 2.75y + 1.1y²
The product of the expressions (2.5 + y) and (1.1y) will be 2.75y + 1.1y².
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