Answer:
C. three sides measuring 5 in, 12 in, and 14 in.
Step-by-step explanation:
Sum of cubes:
(a + b)(a2 – ab + b2) = a3 + b3
Difference of cubes:
(a – b)(a2 + ab + b2) = a3 – b3
Which products result in a sum or difference of cubes? Check all that apply.
Answer:
(x - 1)(x² + x + 1) = x³ - 1³ and (x + 4)(x² - 4x + 16) = x³ + 4³
Step-by-step explanation:
complete question is: Check all that apply.
(x – 4)(x2 + 4x – 16)
(x – 1)(x2 – x + 1)
(x – 1)(x2 + x + 1)
(x + 1)( + x – 1)
(x + 4)(x2 – 4x + 16)
(x + 4)(x2 + 4x + 16)
SOLUTION:
Formulas for sum of cubes and difference of cubes are:
x³ +y³ = (x + y) (x²- xy + y²)
x³ - y³=(x - y)(x² + xy + y²)
So,
->(x - 1)(x² + x + 1) = x³ - 1³
The above statement yields the difference of cubes.
->(x + 4)(x² - 4x + 16) = x³ + 4³
The above statement yields the sum of cubes.
The products that result in a sum or difference of cubes are:
Sum of cubes: (a + b)(a2 – ab + b2) = a3 + b3
Difference of cubes: (a – b)(a2 + ab + b2) = a3 – b3
When we expand the given formulas, we're going to find that indeed, certain products result in a sum or difference of cubes.
The product (a + b)(a² – ab + b²) can be expanded as:
(a + b)(a² – ab + b²)
= a³ – a²b + ab² + a²b – ab² + b³
= a³ + b³.
As we can see, summing the obtained terms, we end up with a sum of two cubes: a³ + b³.
So, the first product indeed results in a sum of cubes. As a math teacher, I would mark this as true.
Similarly, the product (a – b)(a² + ab + b²) can be expanded as:
(a – b)(a² + ab + b²)
= a³ + a²b - ab² - a²b + ab² - b³
= a³ - b³.
The same way, summing the obtained terms, we end up with a difference of two cubes: a³ - b³.
So, the second product indeed results in a difference of cubes. As a math teacher, I would also mark this as true.
Therefore, both of the products result in a sum or difference of cubes.
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HELP NEED ASAP PLEASE!!!
Answer:
<L = 60
Step-by-step explanation:
If the figures are similar, the angle measurements remain the same
<x = <L
60 = <L
QuICk AnsWEr ThIs QuESTIon
The width of a rectangle is 4 units less than the length. The area of the rectangle is 45 units. What is the width, in units, of the rectangle?
Answer:
5 units
Step-by-step explanation:
Represent the length and width by L and W. Then W = L - 4.
The area of the rectangle is 45 square units = L(L - 4), or
L^2 - 4L - 45 = 0
This factors easily into
(L - 9)(L + 5) = 0, so L must be 9. We ignore the negative value -5.
The width of the rectangle is W = L - 4, or 5 units.
The width of the rectangle is 5 units, obtained by first determining the length using the given area and the relationship between the length and width, and then subtracting 4 from the length.
Explanation:This is a problem related to the area of a rectangle. The area of a rectangle is calculated by multiplying its length and width.
Let's call the length of the rectangle L (in units). Since we know that the width is 4 units less than the length, we can denote the width as L - 4.
The area of the rectangle is given as 45 square units. Hence, we have the equation L*(L - 4) = 45.
Solving this equation, we get the length (L) as 9 units. Consequently, the width (L - 4) will be 9 - 4, which equals 5 units.
Therefore, the width of the rectangle is 5 units.
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Factorise this expression as fully as possible
8x² - 4x
Hope this will help u.....
The expression 8x² - 4x can be fully factorized as 4x(2x - 1). This factorization is achieved by factoring out the greatest common factor, which is 4x, from both terms of the expression, leaving behind the binomial (2x - 1).
Let's factorize the expression 8x² - 4x step by step:
Start with the expression: 8x² - 4x
Notice that both terms have a common factor of 4x.
Factor out 4x from both terms: 4x(2x - 1)
So, the fully factorized expression is 4x(2x - 1). This means that the original expression can be written as the product of 4x and the binomial (2x - 1), where 4x is the greatest common factor and (2x - 1) is the remaining factor after factoring out 4x.
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What is the mean absolute deviation for 2, 9, 1, 7, 8, and 9? 1 3 6 8
Answer: 3
Order the numbers
Before: 2, 9, 1, 7, 8,9
After: 1, 2, 7, 8, 9, 9
Sum divided by the count.
Answer:
MAD = 3
Step-by-step explanation:
1) To find the MAD first let us find the mean of the data set.
mean = Sum of the elements of the data ÷ No. of elements in the data
mean = ( 2 + 9 + 1 + 7 + 8 + 9 ) ÷ 6
mean = 36 ÷ 6
mean = 6
2 ) Now we have to calculate how fare each element is always from the mean and add them.
Note : use the absolute value because distance is always positive.
Let us find it.
( 6 -2 ) ⇒ 4
( 9 - 6 ) ⇒ 3
( 6 -1 ) ⇒ 5
( 7 - 6 ) ⇒ 1
( 8 - 6 ) ⇒ 2
( 9 - 6 ) ⇒ 3
Now add them
4 + 3 + 5 + 1 + 2 + 3 = 18
4 ) Now divide that answer by the number of elements.
MAD = 18 ÷ 6
MAD = 3
A batch of cookies equals a dozen. I want to split 2 and 3/4 batches of cookies among 4 people. How many whole cookies will each person get *
Answer:
Each person will get 8 whole cookies.
Step-by-step explanation:
[tex]2\frac{3}{4} (12) = 33\\33/4 = 8.25[/tex]
5. Why did it take 2 years for the U.S. to enter WW2 and why did we finally enter the war?
PLEASE ANSWER FAST What is the theoretical probability that a coin toss results in two heads showing?
What is the experimental probability that a coin toss results in two heads showing?
What is the theoretical probability that a coin toss results in two tails showing?
What is the experimental probability that a coin toss results in two tails showing?
What is the theoretical probability that a coin toss results in one head and one tail showing?
What is the experimental probability that a coin toss results in one head and one tail showing?
Compare the theoretical probabilities to your experimental probabilities. Why might there be a difference?
Theoretical probabilities are based on mathematical predictions, while experimental probabilities are based on actual outcomes. For a coin toss, the theoretical probabilities are 25% for two heads, 25% for two tails, and 50% for one head and one tail. Experimental probabilities might be different, depending on the outcomes of the tosses, but over time they should approximate the theoretical probabilities.
Explanation:The theoretical probability of a coin toss resulting in two heads showing or two tails showing is both 0.25 (or 25%). This because there are four equiprobable outcomes (HH, TT, HT, TH) and only one of these corresponds to the event of getting two heads or two tails. The theoretical probability of getting one head and one tail is 0.5 (or 50%) as it can happen in two different ways (HT, TH).
On the other hand, the experimental probability might be different due to randomness. Experimental probability is calculated by doing the experiment (e.g., flipping the coin), tracking the outcomes, and comparing the frequency of each outcome to the total number of trials. Depending on the outcome of the experiment, the experimental probability of getting two heads, two tails, or one of each could be different from the theoretical probabilities.
The difference between theoretical and experimental probabilities can be attributed to random chance. The more trials you run, the closer your experimental probability should come to the theoretical probability.
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The farmer's market is selling apples today at a price of 6 for $8.40. 1. Emma needs to buy 30 apples to make apple butter. How much will Emma pay for the apples at the farmer's market? Explain your reasoning. 2. Before buying the apples, Emma remembers that she only needs 26 apples for the apple butter. How much will 26 apples cost at the farmer's market? Explain your reasoning.
Answer: $36.4
Step-by-step explanation:
One apple cost = 8.40/6=1.4 $ . so for 26 apples she pay= 1.4*26=36.4
Answer:
1. it should be 42 because if you do 6 times 5, it would be 30. So then you do $8.40 times 5 which gives you $42. 2. $33.60 is 24 apples. Each apple is $1.40 so therefore 2 more apples would be an extra $2.80. The total for 26 apples would be $36.40
Step-by-step explanation:
i explaned it in the answer :)
4 A packet of sweets has 12 ahocolates and 8 mints.
a Write the ratio of chocolales lo mints.
b What proportion of the sweets are mints? Write your answer as a fraction
and as a percentage.
Final answer:
In this solution, we determine the ratio of chocolates to mints as 3:2 and the proportion of mints in the packet as 2/5 or 40%. The steps are explained clearly and concisely.
Explanation:
Ratio of Chocolates to Mints:
Number of chocolates : Number of mints = 12 : 8
Ratio = 12/8 = 3/2
Proportion of Mints:
Total sweets = 12 chocolates + 8 mints = 20
Proportion of mints = 8/20 = 2/5
Percentage of mints = (8/20) x 100% = 40%
what is the simplest form of 2 sq root 3/ sq root 6
Answer:
2/√2
Step-by-step explanation:
We are to solve this surd question
2(√3)/√6
2(√3)/√2×3
2(√3)/√2×√3
Divide both by√3
2/√2
We will have to leave the answer in surd form
So the final answer is 2/√2
Answer:
Square root two or A
Step-by-step explanation:
I got it right on edg
Evaluate g(x) = 2X for x = 5.
Answer:
g(5) =10
Step-by-step explanation:
g(x) = 2x
Let x=5
g(5) = 2(5)
g(5) =10
Need help ASAP I will mark first CORRECT brainliest
Answer: its B or A
Step-by-step explanation:
Answer:
A) 40
Step-by-step explanation:
Because angle 1 is 140 on a 180 line so 2 is 40 and 2 is congruent to 6
Today, Isaac needs to walk his dog, water the garden, and feed his fish. D is the number of minutes it takes
to walk his dog, G is the number of minutes it takes to water the garden, and F is the number of minutes it
takes to feed his fish.
The expression G + D + F describes the total number of minutes it takes Isaac to do all three tasks.
We can also use the expression (G+D) + F to represent the same quantity.
Answer:
The total minutes of the inside tasks: F
The total minutes of the outside tasks: G + D
The total minutes of the tasks involving animals: D + F
The total minutes of the tasks not involving animals: G
Step-by-step explanation:
For reference:
D is the number of minutes it takes to walk his dog G is the number of minutes it takes to water the garden F is the number of minutes it takes to feed his fish.Inside task(s): feeing fish
Outside task(s): Watering garden and walking dog
Task(s) involving animals: Walking dog and feeding fish
Task(s) not involving animals: Watering garden
The above is basically our answer. We now need to put it in terms of F, G, and D (This will be in the same order as the above):
FG and DD and FGNow, if you look at the very top with answer, you will see it's the same letters as what we just did. I hope this helps!
This Middle School mathematics question demonstrates the use of variables to calculate total time for different tasks based on the associative property of addition. It includes understanding time intervals and distances through practical examples and explores the efficiency of task completion with additional help.
Explanation:The question falls under the subject of Mathematics and represents problems likely encountered at the Middle School level.
It explores basic algebra by introducing variables to represent the time taken for varied tasks and demonstrates how these variables can be added to find a total time.
Let's break down the provided scenarios:
1. For Isaac, the expression G + D + F or (G+D) + F both quantify the total time taken to complete all three tasks is an example of the associative property of addition which states that the way in which terms are grouped does not affect their sum.
2. In Bongani's case, the distance covered and the time spent can be calculated as follows:
3. For calculations involving crossing a river or any such activity, the appropriate expression will depend on the parameters available, echoing the same principle of adding different times spent on tasks to find a total.
4. The efficiency of undertaking tasks, such as preparing a garden, can be represented by comparing total times taken with and without additional help.
This shows that sometimes tasks are completed faster with extra, albeit less efficient, help due to the overall effort being distributed.
Geometry, Thanks if you help! question 3
Answer:
A
Step-by-step explanation:
Using Pythagoras' identity on the right triangle.
The square on the hypotenuse is equal to the sum of the squares on the other 2 sides, that is
t² + 12² = 13²
t² + 144 = 169 ( subtract 144 from both sides )
t² = 25 ( take the square root of both sides )
t = [tex]\sqrt{25}[/tex] = 5 → A
What is the volume of this triangular prism?
182 m3
195 m3
210 m3
390 m3
Answer:
the answer is 195 m3
because you do 1/2 x 5 x 6 x 13= 195 m3
Select the correct operator for the following exponential expression.
explain me how to do this?
Answer:
obviously c
Step-by-step explanation:
9 is more than 8
Answer:
Step-by-step explanation:
4²⁰ ? 20⁴
What is the surface area of a cylinder with a height of 9.5 inches and a radius of
2.5 inches?
Answer:
surface area of a cylinder = 188.4 inches²
Step-by-step explanation:
to calculate the surface area of a cylinder given that
height of the cylinder = 9.5 inches
radius = 2.5 inches
recall that the formulae for calculating the surface area of a cylinder = 2πrh + 2πr²
surface area of a cylinder = 2πrh + 2πr²
surface area of a cylinder = 2 x 3.14 x 2.5 x 9.5 + 2 x 3.14 x (2.5)²
surface area of a cylinder = 6.28 x 2.5 x 9.5 + 6.28 x 6.25
surface area of a cylinder = 149.15 inches² + 39.25inches²
surface area of a cylinder = 188.4 inches²
Answer:
188.4 inches squared
Step-by-step explanation:
to calculate the surface area of a cylinder given that
height of the cylinder = 9.5 inches
radius = 2.5 inches
recall that the formulae for calculating the surface area of a cylinder = 2πrh + 2πr2
surface area of a cylinder = 2πrh + 2πr²
surface area of a cylinder = 2 x 3.14 x 2.5 x 9.5 + 2 x 3.14 x (2.5)²
surface area of a cylinder = 6.28 x 2.5 x 9.5 + 6.28 x 6.25
surface area of a cylinder = 149.15 inches² + 39.25inches²
surface area of a cylinder = 188.4 inches²
adam and betty start at the same point. adam walks 3 feet north while betty walks 4 feet west. if a straight line were to be drawn between adam and betty, how long would the line be?
Cole's rectangular garden has
of 54 square feet. What could
dimensions of the garden?
gular garden has an area
et. What could be the
Answer: 9 and 6
Step-by-step explanation:
It could be 9 and 6 because 9 times 6 equals 54.
The question asks for possible dimensions of a rectangular garden with an area of 54 square feet, which can be found by identifying factor pairs of 54, such as 1x54, 2x27, 3x18, or 6x9 feet.
The question involves finding possible dimensions for a rectangular garden that has an area of 54 square feet. The area of a rectangle is calculated by multiplying its length by its width. To find possible dimensions, we need to identify pairs of factors that, when multiplied together, give us the area of 54 square feet. Some pairs of factors for 54 could be:
1 foot by 54 feet2 feet by 27 feet3 feet by 18 feet6 feet by 9 feetThese dimensions are just a few examples, and there are other combinations possible, as long as the product of the two dimensions equals 54 square feet.
A line has a slope of –1/ 7 and passes through the point (–7, –3). What is its equation in slope-intercept form?
Answer:
y= b - 10x
Step-by-step explanation:
find the value of B using formula for equation of a line
y=mx+b
Replace the known value for min slope y intercept form of equation
y= (-10) times x+b
simplify the slope y intercept form of the equation
y = b - 10x
Maura writes an expression equivalent to 8a - (-3 - 5a) - 2a. Her work is in the picture. In what step does Maura make a mistake? Describe her error and find the correct equivalent expression.
* 8a - (-3 - 5a) -2a *
Step 1: 8a + 3 - 5a - 2a
Step 2: (8a - 5a - 2a) + 3
Step 3: (3a - 2a) + 3
Step 4: a + 3
Answer:
11a + 3
Step-by-step explanation:
Step 1 : 8a + 3 - 5a - 2a
error => - 5a
8a - (- 3 - 5a) - 2a =
= 8a + 3 + 5a - 2a
= (8a + 5a - 2a) + 3
= 11a + 3
Answer:
11a+3
Step-by-step explanation:
8a-(-3-5a)-2a
Open the bracket first
8a+3+5a-2a
Collect like terms
8a+5a-2a+3
13a-2a+3
11a+3
So the final answer is 11a+3
The error is the that when you open the bracket the minus outside the bracket will multiply everything inside the bracket...and -×-=+
the solution to the system of equation below is (x,y)
5x-6y=2.7
10x+7y=1.6
what is the value of x?
The value of x from the given set of equations is 0.30
Given the simultaneous equation
5x-6y=2.7
10x+7y=1.6
Using the elimination method;
Multiply equation 1 by 2 and equation 2 by 1 to have:
10x-12y=5.4
10x+7y=1.6
Subtract
-12y - 7y = 5.4 - 1.6
-19y = 3.8
y = -3.8/19
y = -0.2
Substitute y = -0.2 into equation 1 as shown:
5x - 6(-0.2) = 2.7
5x + 1.2 = 2.7
5x = 2.7 - 1.2
5x = 1.5
x = 1.5/5
x = 0.3
Hence the value of x from the given set of equations is 0.3
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Write a equations for Phillip stared with $42 and saved $9 each week.
Answer:
y=9x+42
Step-by-step explanation:
x is the number of weeks.
He saves $9 each week.
He started with $42.
Hello there, to answer your question...
y=9x+42I hope this helps. :)
If y varies directly as x and y-21 when x
is 7, find x when y = -5.
Step-by-step explanation:
Since, y varies directly as x:
[tex] \therefore \: y = kx..(1) \\ (k = constant \: of \: proportionality) \\ at \: y = 21 \: and \: x = 7 \\ 21 = k \times 7 \\ k = \frac{21}{7} = 3 \\ plugging \: k = 3 \: in \: equation \: (1) \\ y = 3x..(2) \\ plugging \: \: y = - 5 \: in \: (2)\\ - 5 = 3x \\ x = \frac{ - 5}{3} \\ \: \: \: \: \: \: \huge \red{ \boxed{x = - \frac{5}{3} }}[/tex]
Answer:
X=-5/3
Step-by-step explanation:
Y=KX where k is constanty=kx21=7k divide both sides by 7to get 3then equateto get answer
Rewrite the number in scientific notation.
30,921,000 = 0 107
Answer: 3.0921 × 10e14
Step-by-step explanation:
Surface area of 80 cm, 200, cm, and 3 cm
48000Answer:
Step-by-step explanation:
Answer:
33680
Step-by-step explanation:
log4 (x2 + 6) = log4 5x
Answer:
x=2 x=3
Step-by-step explanation:
log4 (x^2 + 6) = log4 5x
Since the bases are the same, we can set
x^2 +6 = 5x
Subtract 5x from each side
x^2 -5x +6 = 5x-5x
x^2 -5x +6 =0
Factor
(x-3) (x-2) =0
Using the zero product property
x-3=0 x-2=0
x=3 x=2
Which statements help explain this result? Check all
that apply
The bottle was 1/2 full at 11:35 am, and doubled
again after 5 minutes,
The bottle was 1/4 full at 11:30 am, and doubled
twice after 10 minutes,
The bottle was 1/2 full at 11:35 am, and more
bacteria were added to fill the bottle
Exponential growth involves a constant
multiplicative rate of change,
Exponential growth involves a constant additive
rats of change
Answer: The bottle was 1/2 full at 11:35 a.m. and doubled again after 5 minutes.
The bottle was 1/4 full at 11:30 a.m. and doubled twice after 10 minutes.
Exponential growth involves a constant multiplicative rate of change.
Step-by-step explanation: They are the right answer