Step-by-step explanation:
First expression ...
[tex] = {ax}^{3} y[/tex]
[tex] = a \times x \times x \times x \times y[/tex]
Second expression.....
[tex] = b {x}^{4} {y}^{3} [/tex]
[tex] = b \times x \times x \times x \times x \times y \times y \times y[/tex]
HCF = common factor...
[tex] = x \times x \times x \times y[/tex]
[tex] = {x}^{3} y[/tex]
[tex]hence \: {x}^{3} y \: is \: the \: answer....[/tex]
Answer: HCF =
x³y
Step-by-step explanation:
HCF of ax³y and bx⁴y³
ax³y = a . x . x . x . y
bx⁴y³ = b . x . x . x . x . y . y . y
Common Factors = x . x . x . y
HCF = x . x . x . y
HCF = x³y Answer
therefore, the HCF of ax³y and bx⁴y³ is x³y.
hope that helps...
note: the dot (.) represents multiplication.
Which phrase best describes this polygon?
concave octagon
concave nonagon
convex nonagon
convex octagon
Answer:
Concave octagon
Step-by-step explanation:
Concave octagon:
This polygon has 8 sides. So it is a octagon. If one interior angle measures more than 180, then it is concave polygon.So, this is a concave octagon
The area of a rectangular shop in the mall is 160 square meters. The perimeter is 52 meters. What are the dimensions of the shop?
Answer:
width = 10 m
length = 16 m
Step-by-step explanation:
Formula
[tex]\textsf{Area of a rectangle} = wl[/tex]
[tex]\textsf{Perimeter of a rectangle}=2(w+l)[/tex]
(where [tex]w[/tex] is width and [tex]l[/tex] is length)
Given:
Area = 160 m²Perimeter = 52 mSubstituting the given values into the formulae to create two equations:
[tex]\textsf{Equation 1}: \quad wl=160[/tex]
[tex]\textsf{Equation 2}: \quad 2(w+l)=52[/tex]
Rearranging Equation 1 to make w the subject:
[tex]\implies w=\dfrac{160}{l}[/tex]
Substituting expression for w into Equation 2 and solving for [tex]l[/tex]:
[tex]\implies 2\left(\dfrac{160}{l}+l\right)=52[/tex]
[tex]\implies \dfrac{160}{l}+l=26[/tex]
[tex]\implies 160+l^2=26l[/tex]
[tex]\implies l^2-26l+160=0[/tex]
[tex]\implies l^2-10l-16l+160=0[/tex]
[tex]\implies l(l-10)-16(l-10)=0[/tex]
[tex]\implies (l-10)(l-16)=0[/tex]
[tex]\implies l=10, 16[/tex]
According to Equation 1:
If length = 10 m ⇒ width = 16 mIf length = 16 m ⇒ width = 10 mAs width < length, the dimensions of the shop are:
width = 10 mlength = 16 mWhich of the following describes the function shown in the table below? x y -4 16 -1 2 2 0.25 4 0.0625 5 0.03125 exponential, there is a continual rate of growth exponential, there is a continual rate of decay or decrease quadratic, there is a second degree change in the y-values quadratic, there is a constant difference between consecutive y-values
A statement which best describes the function shown in the table is: B. exponential, there is a continual rate of decay or decrease.
What is an exponential function?An exponential function is a mathematical function whose numerical values (numerals) are generated by a constant that is raised to the power of an argument.
Given the following table:
X : -4 -1 2 4 5
Y : 16 2 0.25 0.0625 0.03125
Next, we would calculate the rate of decay for the y-values:
16/2 = 2/0.25 = 0.25/0.0625 = 0.0625/0.03125 = 8
Rule: The y-values constantly decreases by 1/4 or 0.25 of the previous number.
In conclusion, we can logically deduce that the function shown in the table is exponential, there is a continual rate of decay or decrease.
Read more on exponential functions here: https://brainly.com/question/12940982
#SPJ1
Answer: It's B
Step-by-step explanation:
I got it right
Solve the radical equation.
√x − 1 + 5 = 9
Answer:
17
Step-by-step explanation:
square root of x-1 +5=9
square root of x-1 = 4multiple by power of 2 because square root is cancled by 2.
x-1=16,x=17
ow is the product of 3 and –2 shown using integer tiles?
3 positive tiles and 2 negative tiles.
3 negative tiles and 2 positive tiles.
3 sets of 2 negative tiles.
3 sets of 2 positive tiles.
The correct answer is option C which is 3 sets of 2 negative tiles.
What is multiplication?Multiplication is the process of determining the product of two or more numbers in mathematics.
We have the product of 3 and -2. We can represent this as 3 is equivalent to -2 negative tiles.
When we add -2 three times -2 - 2 -2 = -6 we will get -6 that is 3 sets of 2 negative tiles.
So when we multiply it by 3, we end with 3 sets of 2 negative tiles. This is because the order of the factors does not change the product.
Therefore the correct answer is option C which is 3 sets of 2 negative tiles.
To know more about multiplication follow
https://brainly.com/question/10873737
#SPJ1
Find the value of each trigonometric ratio. 18) cos X Y 24 24 25 24 A) C) 25 B) D) 24 25 25
Answer:
Step-by-step explanation:
41 is a prime number found in the middle of a list of 7 consecutive numbers. find the 7 consecutive numbers
Answer: 29, 31, 37, 41, 43, 47, 53.
Step-by-step explanation:
Solve for x: -24 = 6x
1/4
-4
4
- 1/4
Answer:
-4
Step-by-step explanation:
[tex]~~~~~-24 = 6x\\\\\\\implies -\dfrac{24} 6 = \dfrac{6x}6\\\\\\\implies x = -4[/tex]
what are the prime factors of 30
Step-by-step explanation:
Stay safe, stay healthy and blessed.Have a good day !Thank you♡ #jennifer ♡
Which is the graph of y = [X] - 2?
Answer:
Top right graph
Step-by-step explanation:
Graph is in attached image.
Solve. 5/8 +3/4 over -2/3 - 5/6
The solution of the fraction 5/8 +3/4 over -2/3 - 5/6 is -11/12
How to solve fractions5/8 + 3/4 ÷ -2/3 - 5/6
(5+6) / 8 ÷ (-4-5) / 6
= 11/8 ÷ -9/6
= 11/8 ÷ -3/2
= 11/8 × 2/-3
= 22/-24
= -11/12
Therefore, the solution of the fraction 5/8 +3/4 over -2/3 - 5/6 is -11/12
Learn more about fraction:
https://brainly.com/question/11562149
#SPJ1
can you simplify 8/15+1/6
Answer:
Yes and the answer is 16/5
Step-by-step explanation:
Find the reciprocal of the divisor
Reciprocal of 1/6 : 6/1
Now, multiply it with the dividend
8/15 ÷ 1/6 = 8/15 × 6/1
And after that you get 48/15 but after reducing the fraction, the answer is 16/5. ( In mixed form, 3 1/5 )
I hope this helps and I am a middle school student answering this question.
Answer:
7/10Step-by-step explanation:
can you simplify 8/15+1/6
8/15 + 1/6 =
(16 + 5)/30 =
21/30 =
semplify (21:3 and 30:3)
7/10
Andrew is showing his work in simplifying -4.5 + 4.2 + 5.6 - 7.3. Identify
any errors in his work or in his reasoning. Write feedback to Andrew
explaining the mistake he made and how to correct his work.
Answer:
hence the answer for given problem is -2, but andrew get -21.6 which is wrong
Step-by-step explanation:
What is the equation of a line that is parallel to -x + 3y = 6 and passes through the
point (3, 5)?
1.y=1/3x + 4
2.y = 3x + 4
3.y = -1/3x-4
4.y = -3x - 4
Answer:
Two lines are parallel if and only if they have the same slope.therefore the original line y=1/3x+2
so option 1 is the answer
The table shown below lists the time, in days, that it takes for
a package to be delivered based on its mode of transport and
whether it is international or domestic. Some additional
information is provided.
1. The cost per package by air is $100; by train, $50; by
truck, $10; and by boat, $20.
2. Fragile packages cannot be transported by air.
3. Shipping fragile packages costs an extra $20.
4. Shipping international packages costs an extra $30.
Tim needs to transport a fragile package, and he needs it to
arrive as soon as possible. He is shipping domestic. Which of
the following shipping methods should he use?
Answer:gotchu g there it is
Step-by-step explanation:
Answer:sike gtf
Step-by-step explanation:
I NEED THIS ANSWER FAST PLEASE
Fill in the missing coordinates of the x-intercept of the line defined by the equation y = x – 4
Answer:
the answer might be (-4,0) for x coordinates
Write the following expression without negative exponents and without parentheses.
(9x)^-1
Answer:
1/9x
Step-by-step explanation:
The parenthesis around the 9x means that the -1 exponent goes to the whole thing (the 9x) To "fix" a negative exponent push the 9x across a fraction bar to make the exponent positive. When you push the 9x down across a fraction bar that leaves a 1 on top of the fraction, that has nothing to do with the 1 exponent. Its a 1 on top because when you push the 9x down there is nothing left on top so it is a 1.
(9x)^-1
= 1/9x
To be clear, this is a 1 one top and a 9x on the bottom of a fraction.
George is building a fence around a rectangular dog run. He is using his house as one side of the run. The area of the dog run will be 240 square feet. The length of the run is 30 feet, and the width is (30 minus x) feet. The diagram below shows his plan.
Recall the formulas for area and perimeter: A = lw and P = 2l + 2w.
A rectangle labeled Dog run has a length of 30 feet and width of (30 minus x) feet.
How many feet of fencing will George need for the dog run?
The length of the fencing needed for the dog run will be 76 feet
What is the length?
The measure of the size of any object or the distance between the two endpoints will be termed the length.
Given that:-
Area of Dog Run = 240
Length of Dog Run = 30
The solution will be done as below:-
Width of Dog Run = 30 - x
Area of Dog Run: 30 * (30 - x) = 240
240 / 30 = 30 - x
8 = 30 - x
x = 24
Width of Dog Run = 8
How many feet of fencing will George need for the dog run?
Perimeter of Dog Run = 2Length + 2Width
Perimeter of Dog Run = (2 * 30) + (2 * 8)
Perimeter of Dog Run = 60 + 16
The perimeter of Dog Run = 76
Therefore the length of the fencing needed for the dog run will be 76 feet
To know more about length follow
https://brainly.com/question/2217700
#SPJ1
Answer:
C. 76 feet
Step-by-step explanation:
windows
A toy rocket is shot vertically into the air from a launching pad 6 feet above the ground with an initial velocity of 88 feet per second. The height h, in feet, of the rocket above the ground at t seconds after launch is given by the function h(t)=−16t*2 + 88t +6. How long will it take the rocket to reach its maximum height? What is the maximum height?
Question content area bottom
Part 1
The rocket reaches its maximum height at ? second(s) after launch.
Answer:
Step-by-step explanation:
For 95% of all randomly selected samples of n = 130 students, the mean amount of sleep will be between? Use the empirical rule.
For 95% of all randomly selected samples of n = 130 students, the
amount of sleep will be between [tex]P(\mu - 2\sigma < X < \mu + 2\sigma) \approx 95\%\\\\\\[/tex].
What is the empirical rule?According to the empirical rule, also known as the 68-95-99.7 rule.
The percentage of values that lie within an interval with 68%, 95%, and 99.7% of the values lies within one, two or three standard deviations of the mean of the distribution.
For 95% of all randomly selected samples of n = 130 students, the
amount of sleep will be between can be
[tex]P(\mu - 2\sigma < X < \mu + 2\sigma) \approx 95\%\\\\\\[/tex]
Learn more about empirical rule here:
https://brainly.com/question/13676793
#SPJ1
Given matrix A below, and that A = B, find the value of the elements in B.
A =
9 −2 3
2 17 0
3 22 8
b11 =
9
b12 =
17
b13 =
b21 =
b22 =
b23 =
b31 =
b32 =
b33 =
The value of Matrix B = [tex]\left[\begin{array}{ccc}9&17&3\\2&17&0\\3&22&8\end{array}\right][/tex]
Given : Matrix A = Matrix B
matrix A= [tex]\left[\begin{array}{ccc}9&-2&3\\2&17&0\\3&22&8\end{array}\right][/tex]
The matrix A= [tex]\left[\begin{array}{ccc}9&-2&3\\2&17&0\\3&22&8\end{array}\right][/tex] (according to the question)
Since it is given A=B
and substituting the given values of elements of B
matrix B=[tex]\left[\begin{array}{ccc}9&17&?\\?&?&?\\?&?&?\end{array}\right][/tex]
According to the property of equality of matrices,
When the matrices are given to be equal, their corresponding elements are also equal
so
b13 = 3
b21 = 2
b22 = 17
b23 = 0
b31 = 3
b32 = 22
b33 =8
Substituting the found out values in place of the question marks,
Matrix B = [tex]\left[\begin{array}{ccc}9&17&3\\2&17&0\\3&22&8\end{array}\right][/tex]
Learn more about matrices at https://brainly.com/question/12661467
#SPJ10
Answer:
b11 =
9
b12 =
-2
b13 =
3
b21 =
2
b22 =
17
b23 =
0
b31 =
3
b32 =
22
b33 =
8
Step-by-step explanation:
Just need some help with this question.
A northbound train left at noon. Two hours later, a southbound train left the same station. At five o'clock the two trains were 210 miles apart. Find the rate of each train of the northbound train traveled 10 miles per hour faster than the southbound train.
The rate of each train of the northbound train traveled 10 miles per hour faster than the southbound train 26 miles per hour.
what is speed?
Speed is the time rate at which an object is moving along a path
Let the speed of southbound train is x miles/hour
so, northbound train has speed of x+10 miles/hour.
then, Speed of both train = Total distance/ total time
(x+10+x)=210/5
2x+10= 210/5
2x+10= 42
2x= 32
x= 16 miles per hour (southbound train)
northbound train: 16+10=26 miles per hour
Learn more about this concept here:
https://brainly.com/question/15544987
#SPJ1
Nell is analyzing a quadratic function f(x) and a linear function g(x) will they intersect
A fruit stand has to decide what to charge for their produce. They need \$10$10dollar sign, 10 for 4 apples and 4 oranges. They also need $12 for 6 apples and 6 oranges. We put this information into a system of linear equations.
Can we find a unique price for an apple and an orange?
Answer:
no
Step-by-step explanation:
The prices are inconsistent, so there is no unique price that can be set for either an apple or an orange that will give the total prices indicated.
__
The first relation can be written as ...
$10 = 4A +4O
$10 = 4(A +O) . . . . factor out 4
$2.50 = A +O . . . . divide by 4
The second relation can be written as ...
$12 = 6A +6O
$12 = 6(A +O) . . . . factor out 6
$2 = A +O . . . . . . . divide by 6
These two relations give different prices for 1 apple and 1 orange. There is no price that can be set for either fruit that will give this result.
No unique prices can be assigned.
Prove that for a triple element x, y, z the distributive law is always satisfied if one of the elements equals 0 or 1, or if two of the elements are equal.
The distributive law is satisfied if the numbers 1,2, and 3 are used as multyplying factors.
What is the distributive law?This is basic mathematical law that states:
A multiplied by (b+c) equals (a x b) + (a x c)Is this law satisfied if there are three numbers involved?The law is always satisfied if one of the numbers is 1. Here is an example
2 x (1+2+3) = 2 x 6 = 12or
(2x1) + (2x2) + (2x3)2+4+6 = 12Learn more about mathematical laws in: https://brainly.com/question/15190681
#SPJ1
The article What is i* if I =o
questions:you have been offered a scholarships to further your studies in Australia
write a diary entry sharing your experience about it
Drag the tiles to the correct boxes to complete the pairs.
Match each radical equation with the corresponding value of x.
5√x^4=81
3√x^4= 625
3√x^5=32
4√x^3=64
The value of x for each radical equation is 243 , 125,8,256 respectively.
The correct question is attached as an image with the answer.
What is a Radical Equation ?
When in an equation the variable is under a radical it is called a Radical Equation.
It is given in the question that
which radical matches to the solution
[tex]\rm \sqrt[5]{x^4} = 81 \\\\\sqrt[3]{x^4} = 625\\\\\sqrt[3]{x^5} = 32\\\\ \sqrt[4]{x^3}=64[/tex]
[tex]\rm x^4 = 81^5\\x = 243[/tex]
[tex]\rm x^4 = 625^3\\x = 125\\[/tex]
[tex]x^5 = 32^3\\x = 8\\[/tex]
[tex]\rm x ^3 = 64^4\\x = 256[/tex]
Therefore for each radical the value of x is determined.
To know more about Radical Equation
https://brainly.com/question/8606917
#SPJ1
20. THOUGHT PROVOKING There are 100 coins in a bag.
Only one of them has a date of 2010. You choose
a coin at random, check the date, and then put the
coin back in the bag. You repeat this 100 times. Are
you certain of choosing the 2010 coin at least once?
Explain your reasoning.
Answer:
yes
Step-by-step explanation:
yes, because there is a 99/1 chance. also, you can put 50 2010 coins in.
A cone will be inscribed in a sphere of radius 11 in.
Part A: Find the exact dimensions of the cone of largest volume that will fit inside the sphere. (20 points)
Part B: Find the maximum volume cone to the nearest tenth. (20 points)
The exact dimensions of the cone of largest volume that will fit inside the sphere will be 14.67 inches and 22✓2/3 inches.
How to calculate the dimensions?From the information given, the height of the cone will be:
h = 11 + x
h = 11 + 3 2/3
h = 14 2/3 inches
The radius of the base of the cone will be:
= ✓121 - ✓121/9
= 2✓2(11)/3
= 22✓2/3
Therefore, the dimensions of the cone aren't 14.67 inches and 22✓2/3 inches.
Learn more about cone on:
https://brainly.com/question/1082469
#SPJ1
Find the interquartile range (IQR) for the following data set: 52, 60, 24, 36, 48, 52, 72
Answer:
24
Step-by-step explanation:
The interquartile range defines the difference between the third and the first quartile.
Let's put this data set in ascending order:
24, 36, 48, 52, 52, 60, 72
The median is 52. The median of both the lower (1st quartile) and upper half (3rd quartile) of the data is 36 and 60.
Now we can subtract the first quartile from the third quartile (60 - 36) to get the interquartile range of 24.
Hope this helped! :)