on expanding polynomial (6x^2−11y^3)(−6x^2−11y^3) or [tex](6x^2-11y^3)(-6x^2-11y^3)[/tex] is [tex]121y^6 -36x^4[/tex] .
Step-by-step explanation:
We have , (6x^2−11y^3)(−6x^2−11y^3):
[tex](6x^2-11y^3)(-6x^2-11y^3)[/tex]
⇒ [tex](6x^2-11y^3)(-6x^2-11y^3)[/tex]
We know that :
[tex](a +b)(c+d) = (ac+ad+ad+bd)[/tex]
⇒ [tex](6x^2(-6x^2) - 11y^3(-6x^2) )+(6x^2(-11y^3) + (-11y^3)(-11y^3))[/tex]
⇒ [tex](-36x^4+66x^2y^3 -66x^2y^3 + 121y^6)[/tex]
⇒ [tex](-36x^4+ 121y^6)[/tex]
⇒ [tex]121y^6 -36x^4[/tex]
Therefore, on expanding polynomial (6x^2−11y^3)(−6x^2−11y^3) or [tex](6x^2-11y^3)(-6x^2-11y^3)[/tex] is [tex]121y^6 -36x^4[/tex] .
The values in the table represent a linear function. How does the value of y change in relation to a change in the value of x? A) for every change in x by 4, y changes by 3 B) for every change in x by 3, y changes by 4 C) for every change in x by −4, y changes by 3 D) for every change in x by −3, y changes by 4
Answer:
C
Step-by-step explanation:
Answer:
D
Step-by-step explanation:
A computer programmer worked for 10 hours and earned $70,which is a rate of dollars per hour.
When a programmer works for 10 hours and earns $70, the rate of dollars per hour earned by the programmer is $7.
A computer programmer worked for 10 hours and earned $70.
To calculate the rate per hour, we divide the total earnings by the number of hours worked. In this case,
$70 ÷ 10 hours = $7 per hour.
Therefore, the programmer earned $7 per hour.
Use the Distributive Property to solve the equation
4(x+2)=16
Answer:
Step-by-step explanation:
4(x+2) = 16
4x + 8 = 16
4x =16-8
4x = 8
x = 8/4
x = 2
The solution to the equation 4(x + 2) = 16 is x = 2.
The Distributive Property states that a(b + c) = ab + ac. Apply this to the equation:
4(x + 2) = 4 * x + 4 * 2.
Thus, the equation becomes:
4x + 8 = 16.
To solve for x, first subtract 8 from both sides of the equation:
4x + 8 - 8 = 16 - 8
4x = 8.
Divide both sides of the equation by 4:
4x / 4 = 8 / 4
x = 2.
At a campground, a rectangular fire pit is 3 feet by 2 feet. What is the area of the largest circular fire that
can be made in this fire pit? Use 3.14 for it. Round to the nearest square Inch.
The area of the largest circular fire pit is 452 square inches.
Explanation:
Given that at a campground, a rectangular fire pit is 3 feet by 2 feet
The radius is given by 1 feet.
Area:
The area of the largest circular fire is given by
[tex]A=\pi r^2[/tex]
Substituting the values in the formula, we get,
[tex]A=(3.14)1^2[/tex]
[tex]A=3.14 \ ft^2[/tex]
Thus, the area of the largest circular fire is 3.14 square feet.
To convert feet to inches:
The feet can be converted into inches by multiplying by 12.
Thus, we have,
[tex]1 \ft= 12 \ inches[/tex]
Hence, we have,
[tex]Area= 3.14\times 12^2[/tex]
Simplifying,we get,
[tex]Area= 3.14\times144[/tex]
[tex]Area=452.16 \ in^2[/tex]
Rounding off to the nearest square inch.
Thus, we have,
[tex]Area= 452 \ in^2[/tex]
Thus, the area of the largest circular fire pit is 452 square inches.
Whats the product of 2/3 × 36
Answer:
24 :)
Step-by-step explanation:
2 / 3 x 36 = ?
First of all, note that 36 is the same as 36/1 since 36 divided by 1 is 36. Therefore, start by setting up the problem like this:
36 / 1 x 2 / 3
Multiply the numerators together (36 x 2 = 72) and multiply the denominators together (1 x 3 = 3) and make it into one fraction like so:
72 / 3
The greatest common factor of 72 and 3 is 3. Minimize the fraction by dividing the numerator and the denominator by its greatest common factor to get:
24 / 1
Convert the improper fraction above to a whole number to get the answer:
24
Hope this helps :)
1.1.11
Question Help
Cars Paloma wants to buy a car. She is considering two different models. Model Ais
decimal. Which car is wider?
ft wide. Model B is 63 in wide Express the width of each car in ft Using a
Answer:
Model B is wider car I think for the question which ones wider
Monday
What time is 72 hours
before 2:12 am?
Hi
72 Hours before 2:12 am, Monday is 2:12 am, Friday, because 72 hours before is 3 days in the past.
Find the sum of the interior angles of a decagon
Answer:
1440 degrees
Step-by-step explanation:
The sum of the interior angles of a polygon can be found by
(n-2)*180
where n is the number of sides
a decagon has 10 sides, so n=10
(10-2) *180
8*180
1440
The sum of all the interior angles of a decagon is calculated as (n-2) × 180°. For a decagon, where n is 10, the sum is 1440°.
The correct option is (C).
The sum of all the interior angles of a decagon can be found using the formula for calculating the sum of interior angles of any polygon, which is (n-2) × 180°, where n is the number of sides of the polygon. In the case of a decagon, n is 10. Therefore, the sum of all the interior angles of a decagon is (10-2) × 180° = 8 × 180° = 1440°. Thus, the correct answer is C.1440°.
complete question given below:
The sum of all the interior angles of a decagon is
A.1000∘
B.960∘
C.1440∘
D.1200∘
What is the simplified form of (2 X 102)2 in standard notation? Do not use commas in your answer. (HAS TO BE A NUMBER)
Answer:
40000
Step-by-step explanation:
[tex](2 \times {10}^{2} )^{2} \\ = {2}^{2} \times {10}^{2 \times 2} \\ = 4 \times {10}^{4} \\ = 40000[/tex]
help porfavor, please
Answer:
Option A, (-7, -3)
Step-by-step explanation:
The answer is: Option A, (-7, -3)
Samuel has a life insurance policy that will pay his family $40,000 per year if
he dies. If interest rates are at 4.0% when the insurance company has to pay,
what is the amount of the lump sum that the insurance company must put
into a bank account?
O
A. $1 million
O
B. $350,000
O
C. $3.5 million
O
D. $1.4 million
Answer: A 1 million
Step-by-step explanation:
The amount of the lump sum that the insurance company must put
into a bank account is $1 million.
Option A is the correct answer.
What is an expression?An expression contains one or more terms with addition, subtraction, multiplication, and division.
We always combine the like terms in an expression when we simplify.
We also keep all the like terms on one side of the expression if we are dealing with two sides of an expression.
Example:
1 + 3x + 4y = 7 is an expression.
3 + 4 is an expression.
2 x 4 + 6 x 7 – 9 is an expression.
33 + 77 – 88 is an expression.
We have,
We can use the present value formula for an annuity to find the lump sum that the insurance company must put into a bank account:
PV = PMT / r
where PV is the present value, PMT is the annual payment, and r is the interest rate.
Substituting the given values, we get:
PV = 40,000 / 0.04
= $1,000,000
Therefore,
The amount of the lump sum that the insurance company must put
into a bank account is $1 million.
Learn more about expressions here:
https://brainly.com/question/3118662
#SPJ7
A 45 foot ladder is used to clean the
gutters at your house. How far away from
the house should you put the ladder in
order for it to reach the 40 foot high
gutter? Round your answer to the nearest
tenth.
5 feet.
Answer:
20.62
Step-by-step explanation:
In this instance, we are going to use the pythagorean theorem.
The height of the gutter will be a leg of the triangle, and the ladder will be the hypotenuse. The formula is
[tex]a^{2} + {b}^{2} = {c}^{2} [/tex]
While A and B are legs and C is the hypotenuse. We are trying to find B, the distance from the house.
So plug A and C in:
[tex] {40}^{2} + {b}^{2} = {45}^{2} [/tex]
Now figure it out: first you square 40 and 45:
[tex]1600 + {b}^{2} = 2025[/tex]
Isolate the B term: subtract 1600 from both sides
[tex] {b}^{2} = 425[/tex]
Now take the square root of both sides to find B
[tex]b = 20.62[/tex]
And that's your answer
Answer:
20.6 feet
Step-by-step explanation:
The Pythagorean theorem can tell you the distance from the house the base of the ladder may be for it to reach 40 feet up. If that distance is represented by x, then it tells you ...
45^2 = x^2 + 40^2
x = √(2025 -1600) = √425
x ≈ 20.6
The ladder will reach to 40 feet high when the base is 20.6 feet from the house.
_____
Comment on ladder distance
The ladder safety association recommends an angle with the ground of about 75°. That corresponds to a distance from the house of about 10 feet. If the ladder is 20 feet away, it will barely reach the gutter, so placing it at that distance would probably not be safe.
An appropriate answer to this question is "10 feet", not based on math, but based on safety. At that distance the end of the ladder will extend about 3.7 feet beyond the gutter.
Without multiplying, tell which is greater: 4/5 x 45 or 2/3 x 45. Explain.
Answer: It is 4/5 x 45
Step-by-step explanation: Hope i helped please mark brainliest!
I know there is suppose to be no multiplying but if you mulitply in your head 4/5 x 45 is 36 and 2/3 x 45 is 30
therefore, 4/5 x 45 is greater!
also, if not multiplying 0.8(5/4) is greater than 0.667(2/3). Therefore, 4/5 is greater than 2/3.
Without multiplying, 4/5 x 45 is greater than 2/3 x 45 because the fraction 4/5 is greater than 2/3 when both are compared using a common denominator.
Explanation:To answer which is greater without multiplying, we can look at the fraction multiples of 45 in the problems 4/5 x 45 and 2/3 x 45. Since both expressions involve the same whole number (45), we can compare the fractions 4/5 and 2/3 to determine which product is greater. By converting the fractions to have a common denominator, we can see that 4/5 is equivalent to 24/30, and 2/3 is equivalent to 20/30. Therefore, 4/5 is greater than 2/3, meaning that 4/5 x 45 is greater than 2/3 x 45.
3. Lamar has 3.6 meters of string. He makes a square with congruent sides. What
is the length of each side?
Plz help ???!!!
using a graph to solve the equation 45=5x+10
Answer:
X=7 and y=45
Step-by-step explanation:
5(7)+10=45
35+10=45
I have attached a graph
What is an equivalent expression for the quotient? 4²/4⁵
Answer:
[tex] \frac{1}{ {4}^{3} } [/tex]
Step-by-step explanation:
[tex] \frac{ {4}^{2} }{ {4}^{5} } = \frac{1}{ {4}^{ - 2} \times {4}^{5} } = \frac{1}{ {4}^{(5 - 2)} } = \frac{1}{ {4}^{3} } [/tex]
Madeline invested $920 in an account paying an interest rate of 3.6% compounded continuously. Assuming no deposits or withdrawals are made, how much money, to the nearest cent, would be in the account after 11 years?
Answer:
$1,367
Step-by-step explanation:
The compound amount formula applying to continuous compounding is
A = Pe^(r*t), where P is the principal, r is the interest rate as a decimal fraction, and t is the time in years.
Here we have A = $920e^(0.036*11), or $1,367
=
Answer:
The correct answer would be 1367.
Step-by-step explanation:
Grandma says Baby Bertha (BB) should get $1000 at birth plus $50 per year. Grandpa disagrees; he thinks BB should get $1000 at birth plus an additional 4% of the accumulated amount each year. Grandma and Grandpa will continue to contribute additional funds into the account as long as BB doesn’t make a withdrawal. Which option should BB’s parents select? Why?
BB's parents should choose Grandpa's option, where Baby Bertha (BB) receives $1000 at birth plus an additional 4% of the accumulated amount each year.
Explanation:In Grandpa's option, the annual contribution grows dynamically with the accumulated amount, creating compounding growth. Let's denote the accumulated amount at the end of year \(n\) as A_n. The contribution at year \(n\) can be expressed as \(0.04 \times A_n\). BB's total amount at the end of year \(n\) can be written as:
\[A_n = 1000 \times (1 + 0.04)^{n}.\]
This formula considers the initial $1000 and the 4% annual growth on the accumulated amount. With compounding, this option ensures that BB's fund grows significantly over time.
Grandma's option, on the other hand, provides a fixed annual amount of $50, which does not consider the potential growth through interest or investment. Over time, the fixed contribution might not keep up with inflation, and the fund may not accumulate as much as Grandpa's option.
In summary, Grandpa's option is financially advantageous due to compounding growth, allowing BB's fund to grow more substantially over the years. This strategy aligns with long-term financial planning, providing a better financial foundation for Baby Bertha's future.
A triangle has the following angle measures: 125°, 15°, and 40°. Which of the following statements best describes its drawing? There is one possible triangle with these angle measures. It is impossible to construct a triangle with these angle measures. There are many possible similar triangles with these angle measures. There are many possible triangles with these angle measures.
Answer:
There is only one triangle with the degrees
Step-by-step explanation:
All angles must add up to 180 degrees
Write two different mixed numbers where the LCD (lowest common denominator) is 12
Two mixed numbers as [tex]\frac{5}{6}[/tex] and [tex]\frac{5}{12}[/tex] the least common denominator (LCD) is 12.
Step-by-step explanation:
The least common denominator (LCD) is the smallest number that can be a common denominator for a set of fractions. Also known as the lowest common denominator, it is the lowest number you can use in the denominator to create a set of equivalent fractions that all have the same denominator.
Steps to find the LCD of fractions, integers and mixed numbers:
Convert integers and mixed numbers to improper fractionsFind the LCD of all the fractionsRewrite fractions as equivalent fractions using the LCDLet's us have two mixed numbers as [tex]\frac{5}{6}[/tex] and [tex]\frac{5}{12}[/tex].
Equivalent Fractions with the LCD
[tex]\frac{5}{6}[/tex] = [tex]\frac{10}{12}[/tex]
[tex]\frac{5}{12}[/tex] = [tex]\frac{5}{12}[/tex]
For the denominators (6, 12) the least common multiple (LCM) is 12. Therefore, the least common denominator (LCD) is 12.
Final answer:
The mixed numbers 1 1/4 and 2 1/3 can be converted to have the lowest common denominator of 12, resulting in 1 3/12 and 2 4/12 respectively.
Explanation:
To write two different mixed numbers where the lowest common denominator (LCD) is 12, we can choose denominators that are factors of 12 and numerators that result in proper fractions (where the numerators are less than the denominators). An example would be 1 1/4 and 2 1/3. Here's how these mixed numbers have 12 as their common denominator:
For 1 1/4, the denominator 4 is a factor of 12. To convert 1/4 to a denominator of 12, multiply the numerator and denominator by 3. So, 1 1/4 becomes 1 3/12.For 2 1/3, the denominator 3 is also a factor of 12. To convert 1/3 to a denominator of 12, multiply the numerator and denominator by 4. So, 2 1/3 becomes 2 4/12.Now we have two mixed numbers with the LCD of 12.
Which values of a, b, and c correctly complete the division?
Answer:
Option 1
Step-by-step explanation:
1/6 × 5/3
Step-by-step explanation:
[tex] \frac{1}{6} \div \frac{3}{5} [/tex]
[tex] \frac{1}{6} \times \frac{5}{3} [/tex]
a= 6,b=5,c=3 option A
What is the surface area of the breadbox
to the nearest square inch? Check your
answer for reasonableness.
Answer:
Step-by-step explanation:
surface area of two sides=2[(8×8)+π×8²/4]
=2[64+16π]
=128+32π
surface area of curved surface=2πrh/4
surface along length=base (16×16)+2×(16×8)+2×π×8/4 ×16
=256+256+64π
=512+64π
Total surface area=128+32π+512+64π
=640+96π
≈640+302
≈942 in²
I need some help! Evaluate the expression: -11²
Answer: -121
Step-by-step explanation:
Simplify by combining like terms 4s + 1/6s + 2 3/5s
Solution:
Given expression is:
[tex]4s + \frac{1}{6}s + 2\frac{3}{5}s[/tex]
We have to simplify by combining the like terms
From given,
[tex]4s + \frac{1}{6}s + 2\frac{3}{5}s[/tex]
Convert the mixed fraction to improper fraction
[tex]4s + \frac{1}{6}s + \frac{13}{5}s[/tex]
Make the denominator same
[tex]\frac{4s \times 30 }{30} + \frac{1s \times 5}{6 \times 5} + \frac{13s \times 6}{5 \times 6}\\\\\frac{120s}{30} + \frac{5s}{30} + \frac{78s}{30}\\\\\frac{203}{30} = 6.7667[/tex]
Thus the solution is 6.7667
Danielle has 3/5kg of beads. She shares the beads evenly between 5 friends.
How many Kilograms does each friend receive?
Answer:
0.12
Step-by-step explanation:
3/5=0.6
0.6/5=0.12
Ariel and ber friends purchased some drinks and pizza slices at the snack bar each drink cost $2 and each pizza slice $4 they purchased 9 items and spent a total of $28
Answer:
5 peices of pizza for $4 each
and 4 drinks for $2
Step-by-step explanation:
Gabriella expects to earn $50 in tips during her shift as a waitress today. In addition to tips, she earns $8.00 an hour. If she wants to make at least $114 today, how many hours must she work at a minimum?
Answer:
She needs to work 8 hours
An=a^1*r^n-1 that’s the formula for the equation I kinda dunno how to exactly solve it though
Answer:
see explanation
Step-by-step explanation:
The n th term of a geometric sequence is
[tex]a_{n}[/tex] = a[tex](r)^{n-1}[/tex]
where a is the first term and r the common ratio
Here a = 15, thus
[tex]a_{5}[/tex] = 15[tex](r)^{4}[/tex] = [tex]\frac{243}{125}[/tex] ( divide both sides by 15 )
[tex]r^{4}[/tex] = [tex]\frac{243}{1875}[/tex], thus
r = [tex]\sqrt[4]{\frac{243}{1875} }[/tex] = [tex]\frac{3}{5}[/tex]
Multiply the previous term by [tex]\frac{3}{5}[/tex] to obtain the next term
15 × [tex]\frac{3}{5}[/tex] = 9
9 × [tex]\frac{3}{5}[/tex] = [tex]\frac{27}{5}[/tex]
[tex]\frac{27}{5}[/tex] × [tex]\frac{3}{5}[/tex] = [tex]\frac{81}{25}[/tex]
[tex]\frac{81}{25}[/tex] × [tex]\frac{3}{5}[/tex] = [tex]\frac{243}{125}[/tex]
Thus the sequence is
15, 9, [tex]\frac{27}{5}[/tex], [tex]\frac{81}{25}[/tex], [tex]\frac{243}{125}[/tex]
Solve each system by graphing, check your answer
Y=3x+13
Y=x-3
Answer:
x = -8
Y = -11
Step-by-step explanation:
Given
Y = 3x + 13
Y = x - 3
Substitute x - 3 for Y in the first equation
We have
Y = 3x + 13
x - 3 = 3x + 13
Add 3 to both sides
x - 3 + 3 = 3x + 13 + 3
x = 3x + 16
Subtract 3x from both sides
x - 3x = 3x - 3x + 16
-2x = 16
Divide both sides by -2
x = 16/-2
x = -8
Now substitute -8 for x in any of the above equations to get Y.
Using the second equation, we have
Y = x - 3
Y = -8 - 3
Y = -11
The glee club needs to raise money for the spring trip to Europe, so the members are assembling holiday wreaths to sell. Before lunch, they assembled 15 regular wreaths and 15 deluxe wreaths, which used a total of 135 pinecones. After lunch, they assembled 15 regular wreaths and 20 deluxe wreaths, using a total of 160 pinecones. How many pinecones are they putting on each wreath?
Answer:
5 pinecones on the deluxe wreath and 4 pinecones on the regular wreath
Step-by-step explanation:
Answer:
Regular: 4
Deluxe: 5
Step-by-step explanation:
15x + 15y = 135
15x + 20y = 160
5y = 25
y = 5
15x = 135 - 15(5)
15x = 60
x = 4