Answer: The polynomial has 3 terms and a degree of 10.
Step-by-step explanation:
The given polynomial: [tex]5s^6t^2 + 6st^9 - 8s^6t^2 - 6t^7[/tex]
Here, two terms [tex]5s^6t^2[/tex] and [tex]8s^6t^2[/tex] have same power for s and t i.e. they are like terms.
Combine like terms , we get
[tex]6st^9 - 3s^6t^2 - 6t^7.[/tex] i.e. there are 3 terms.
Degree of [tex]6st^9[/tex] is 1+9=10;
Degree of [tex]- 3s^6t^2[/tex] is 6+2=8;
Degree of [tex]- 6t^7[/tex] is 7.
Since degree of the polynomial = highest degree i.e. 10
Hence, the polynomial has 3 terms and a degree of 10.
The statement which is true about the polynomial 5s⁶t² + 6st⁹ – 8s⁶t² – 6t⁷ is; It has 4 terms and a degree of 10.
Discussion:
By counting the number of terms in the polynomial;
We can conclude that the polynomial has 4 terms and hence can be called a tetranomial.Additionally, the degree of the polynomial is 10.
This is from the term with the highest degree which is; 6st⁹; where s has degree 1 and t has degree 9; total of which is; 10.
Read more on polynomial degree;
https://brainly.com/question/10937045
if the edges of the base of a rectangular prism are 8 cm and 6 cm, and the diagonal is 10√2, what is the volume of the solid?
Answer:
221.12 cm^3
Step-by-step explanation:
Imagine that you have the 6cm side of the prism base facing you, and that you cut the prism in half through the vertex. Doing this will form two triangles. The hypotenuse of the triangle is the same as the "diagonal" that is 10√2 cm. The base of this triangle is half of the 6" side, or 3 cm.
Use the Pythagorean Theorem to determine the height (h) of the prism:
h^2 + 3^2 = (10√2)^2, or
h^2 = 200-9 = 191
Then the height is √191 cm
and the base area is 6cm times 8 cm, or 48 cm^2
and so we end up with the volume V = (1/3)(base area)(height), or
V = (1/3)(48 cm^2)(√191 cm), or
roughly 221.12 cm^3
IDK what to put up here any more so imma copy-paste this
Answer:
its 3 units.
Step-by-step explanation:
Answer: 3 units
Step-by-step explanation:
Points A and B have the same y value. Thus, subtract the x-values from each other to get 5 - 2 = 3.
Hope it helps <3
Which expression is equivalent to ....
Answer:
Its the first answer 24
describe the y-intercept in terms of knots and rope length
Answer:
what is the y-intercept sorry i can't help there isn't enough information
Step-by-step explanation:
Horatio wants to ship a batch of 8 machine parts. The packaging for each part weighs 2 pounds. If each part weighs x pounds, which expression represents the total weight of the parts and their packaging? And if each part weighs 6 pounds, what will the total weight of the shipment be? A. The expression is 2(x + 8), and the weight is 28 pounds. B. The expression is 8(x – 2), and the weight is 32 pounds. C. The expression is 8x – 2, and the weight is 46 pounds. D. The expression is 8x + 2, and the weight is 50 pounds. E. The expression is 8(x + 2), and the weight is 64 pounds. Reset Next
Answer: E. The expression is 8(x + 2), and the weight is 64 pounds.
Step-by-step explanation:
Given: Number of machine parts in a batch = 8
weight of packaging for each part = 2 pounds
Let x be the weight of each part ( in pounds).
Weight of each part with packaging = x+2
Then, Total weight of the parts and their packaging = (Number of machine parts) x (Weight of each part with packaging )
= 8(x+2)
If each part weighs 6 pounds, then put x= 6
Total weight of the parts and their packaging = 8(6+2)
= 8 x 8 = 64 pounds
Hence, If each part weighs 6 pounds, then the total weight of the shipment will be 64 pounds .
Here is what we know:
8 machine parts
each part = x pouunds
packaging for each part is 2 pounds so 16 pounds for packaging
If y=total weight wiith that information we can form this equation
y=8x + 16
If each part equals 6 pounds the total shipment will be
y=8x+16
y=8(6) + 16
y= 48 + 16
y=64
Find the critical numbers for f(x)=cos(x)+sin^2(x) on the interval [0,2pi]
Answer:
Step-by-step explanation:
Rad [0,2[tex]\pi[/tex]]
f(x)=cos(x)+sin²(x)=cos(x)+1-cos²(x)
--[cos(x)-1/2]²+5/4=f(x)
when cos(x)=1/2,the f(x) has Max=5/4
cos(x)=1/2,x=[tex]\pi[/tex]/3(Rad) or 60°(Deg)
HELP ASAP!!! Alex bought a notebook containing 96 pages, and numbered them from 1 through 192. Bob tore out 25 pages of Alex’s notebook, and added the 50 numbers he found on the pages. Could Bob have gotten 2012 as the sum? Show your logic steps on how you draw your conclusion.
=====================================================
Explanation:
Page 1 is labeled with 1 and 2, which sum to 1+2 = 3
Page 2 is labeled with 3 and 4 which sum to 3+4 = 7
Page 3 is labeled with 5 and 6 which sum to 5+6 = 11
and so on until we reach
Page 96 is labeled with 191 and 192, which sum to 191+192 = 383
Note how each page has an odd page number label and an even number label (odd on the front side; even on the back side). Adding any odd number to an even number will result in an odd number. We can prove it as such
x = some odd number = 2m+1, m is any integer
y = some even number = 2n, n is an integer
x+y = 2m+1+2n = 2(m+n)+1 = some other odd integer because it is in the form 2p+1 with p = m+n as an integer
This explains why the results 3,7,11,..,383 are all odd.
------------------------
So we effectively have this set of values {3,7,11,...,383}. This is an arithmetic sequence with 3 as the first term and 4 as the common difference.
If we add two odd numbers together, we get an even number (proof is similar to one shown above)
odd + odd = even
But if we add in another odd number, then we'll go back to an odd result
odd + odd + odd = odd
If we have an odd number of odd numbers added up, then the result will be odd. In this case, we're adding 25 values from the set {3,7,11,...,383}. The value 25 is odd, so we have an odd number of values from {3,7,11,...,383} being added up. Therefore, the result Bob will get will always be odd. There is no way to get a sum of 2012 because this value is even.
A cylinder has a volume of 675.1 cubic centimeters. The diameter of the cylinder is 10 cm. What is the height of the cylinder? (Assume = 3.14)
Answer:
8.6 cm
Step-by-step explanation:
V=pi r-squared h
diameter of 10 means radius of 5
675.1=3.14x5x5xh
675.1=78.5h
8.6
fleur wants to make tables and chairs. She has a total of 150 wooden boards and 330 nails. 17T + 6C ≤ 150 represents the number of tables T and chairs C she can make with 150 Wooden boards. 34T + 27C ≤ 330 represents the number of tables and chairs she can make with 330 nails. Does Fleur have enough boards and nails to make 3 tables and 9 chairs? Choose 1 answer: (Choice A) Fleur has enough boards and nails. (Choice B) Fleur has enough boards but not enough nails. (Choice C) Fleur has enough nails but not enough boards. (Choice D) Fleur has neither enough boards nor enough nails.
Answer::
Choice B : fleur has enough boards but not enough nails
Answer:
Fleur has enough boards but not enough nails.
Step-by-step explanation:
T = 3
C = 9
substitute
Mark decided to donate a lot of his shirts to two different organizations and keep
the rest. First he 1/10 donated of his shirts to his church, and then he donated 2/3 of
what was left to a consignment shop.
1) What fractional part of his shirts did he donate to the consignment shop?
2) What fractional part of his shirts did he keep?
3) If Mark kept 15 shirts, how many shirts did he donate?
(also please help me with drawing a picture that's a fraction to shade in for the problem)
Answer:
1.) 3/5
2.) 3/10
3.) 50
Step-by-step explanation:
i believe my answers are right, they might be wrong. I'm not that old so I can't solve most of these problems.
1.) to get this, you need to multiply the remaining shirts and 2/3
2.) subtract 1/10, and 3/5 from 1, which equals 3/10
3.) is 3/10 is equal to 15, then 1/10 is equal to 5, 5*10=50
Answer:
1) 3/5
2) 3/10
3) 35
Step-by-step explanation:
For majority of the questions, you just have to multiply the numbers together. I think all of them is right... T-T
sry if its wrong.. :|
Can someone help me with the question please
Answer:
Purple line: 4
Red dashed line: 2
Blue line: 1/2
Step-by-step explanation:
The purple line is the steepest line, therefore it has the biggest constant of proportionality or slope. Since 4 is the biggest number among the others, we attribute it to the purple line (the one with the point C on it).
Think of it this way:
[tex]y = ax+b \\[/tex]
here [tex]b = 0[/tex] so [tex]y = ax[/tex]
The greater a is, the greater y is. So for any value of x, y will be become bigger and bigger if we increase the value of a.
Take for example this one:
[tex]y = 2x \\[/tex]
Take [tex]x=2\\[/tex] therefore [tex]y =4[/tex]
Now take [tex]y = 4x[/tex] and take [tex]x =2[/tex] therefore [tex]y = 8[/tex]
When we increased this constant of proportionality, as you can see from 2 to 4, the value of y increase from 4 to 8.
Hope this is helpful. Think of it really carefully, and I'm sure you'll grasp the concept.
The height of the trunk is 26 inches the length of the trunk is 50 inches. The tv is 54 inches wide. And 96 inches in height. Assuming the trunk is at least 96 inches deep can the tv fit into the trunk? Explain
Answer:
It states that assuming the trunk is 96" long. So with that information assuming the trunk is at least 96 inches deep and the tv is 96” long and the length of the trunk diagonal is 56.36” which is greater than the TV length 56”, so the TV will fit diagonally in the trunk.
Step-by-step explanation:
The length of the diagonal of the trunk is 56.356011 inches.
What is Pythagoras Theorem?A theorem stating that the square of the length of the hypotenuse of a right triangle is equal to the sum of the squares of the lengths of the other sides.
Given:
height of the trunk= 26 inches
length of the trunk= 50 inches
using Pythagorean theorem,
diagonal length of the trunk=√(height² +length²)
=√(26²+50²)
=√3176
=56.356011 inches
Hence, the length of the diagonal of the trunk is 56.356011 inches.
Learn more about this concept here:
https://brainly.com/question/17106915
#SPJ2
Rachel made $110 for 5 hours of work. At the same rate, how many hours would she have to work to make $264 ?
Answer: she needs to work 8 hours
Step-by-step explanation:
9. Find the value of x. Using that value, what is the
measurement of ZUTQ?
thank you <3
Answer:
92°
Step-by-step explanation:
We know that [tex]\overline{QV}[/tex] is a straight line which means that we know that ∠QTU + ∠VTU = 180
11x+4+∠VTU = 180
∠VTU = 180-11x-4
∠VTU = 176-11x
Then, using the triangle inequality, we know that ∠VTU+∠TUV+∠UVT = 180
3x+14+54+176-11x=180
-8x+244=180
-8x = -64
x=8
Now we can substitute and solve for ∠UTQ
11(8)+4 = 88+4 = 92°
Answer: 92°
Step-by-step explanation:
Line 'L' is horizontal and passes through (-5,8). Line 'L is vertical and passes through $(4,-1)$. Find the point of intersection of $\ell_1$ and $\ell_2$.
Every y coordinate on the horizontal line is the same, so each point has a y coordinate of y = 8. This is to be able to pass through (-5,8)
Every x coordinate on the vertical line is the same, so each point has an x coordinate of x = 4. This is to be able to pass through (4,-1)
Put this together to get the answer (x,y) = (4,8)
Answer:
The two lines intersect at (4,8).
What is the measure of Angle X W Y? Triangle X W Y. The exterior angle to angle W is 74 degrees. 16 degrees 74 degrees 106 degrees 116 degrees
The exterior of angle XWY is 74 degrees, so the angle XWY itself is 180-74 = 106 degrees. The two angles form a 180 degree straight line or angle.
Answer:
the answer is 74
Step-by-step explanation:
i did the cumulative test
Please help with the questions on the picture, it's very urgent......Thank you✨
Answer:
2. sinθ= cos 35°
sinθ= sin(90°-35)
θ= 55°
3. cos4θ= sin5θ
cos 4θ= cos (90-5θ)
4θ=90°-5θ
collect like terms
4θ+5θ=90°
9θ=90° (divide both sides by 9)
therefore θ=10°
PLEASE HELP!!!
Which graph represents the solutions to the inequality |2x - 6| < 10? (5 points)
Answer:
3
Step-by-step explanation:
To do this you would take absolute value so you get [tex]2x+6\leq 10[/tex] then you would subtract 6 from both sides so you get [tex]2x\leq 10[/tex] then you would divide 2 from both sides so you would get [tex]x\leq 2[/tex] so graph 3 would be the write answer
In how many ways can you put seven marbles in different colors into four jars? Note that the jars may be empty.
Answer: 16384
Step-by-step explanation:
Given: Total marbles = 7 (All are distinct)
Total jars = 4
Assume that, the jar is empty.
When we put marbles in the jar, we need to choose jar each time.
For each marble, total choices = Total jars = 4
Then, by using the fundamental counting principle,
The number of ways to put seven marbles in different colors into four jars =
[tex]4^7[/tex]
= 16384
Hence, the required number of ways =16384
Answer:
your answer is 16384
Step-by-step explanation:
have a nice day.
is x=-3 a function plz respond in one minute
Answer:
x = -3 is not a function because, for one thing, its graph does not pass the vertical line test.
Step-by-step explanation:
Please help me fast!
Answer:
39.5
Step-by-step explanation:
Let's figure out the equations of l and m first.
For line l, we see that the coordinates (0, 5) and (3, 0) are on the line. The equation of a line is y = mx + b where m is the slope and b is the y-intercept.
We can find the slope, which is the difference in the y-coordinates divided by the difference in the x-coordinates:
m = slope = (5 - 0) / (0 - 3) = 5/-3 = -5/3
The y-intercept of a line is the place where the line crosses the y-axis. For line l, it is at (0, 5), so b = 5. Our equation is thus: y = (-5/3)x + 5.
For line m, we see that the coordinates (0, 2) and (7, 0) are on the line. The slope is:
m = slope = (2 - 0) / (0 - 7) = 2/-7 = -2/7
The y-intercept is at (0, 2), so b = 2. Our equation is hence: y = (-2/7)x + 2.
Taking the two equations, let's set 15 equal to y and solve for x:
y = (-5/3)x + 5 ⇒ 15 = (-5/3)x + 5 ⇒ 10 = (-5/3)x ⇒ x = -6
y = (-2/7)x + 2 ⇒ 15 = (-2/7)x + 2 ⇒ 13 = (-2/7)x ⇒ x = -91/2
Let's find the difference:
-6 - (-91/2) = 39.5
The answer is thus 39.5.
~ an aesthetics lover
Help help help help
Plz
Answer:
Step-by-step explanation:
Probability of getting any number less than 6 = 2/6 =1/3
So, It is unlikely
Answer:
2/6 or 1/3
Step-by-step explanation:
the two umbers less than 6 or 2 and 4. In total on the dice there is 6 numbers. so 2/6 is tha answer and then we spimlify
Sam's total expenses last month were $1840. What was his total variable cost for last
month?
Expense
Amount
Rent
$100
Groceries and drinks
$1000
$10
Insurance premiums
Loan interest payment
Clothes
$30
$200
&
Utilities
$300
Home security fee
$200
Answer:
$1500
Step-by-step explanation:
It is given that
Rent = $100
Groceries and drinks = $1000
Insurance premiums = $10
Loan interest payment =$30
Clothes = $200
Utilities = $300
Home security fee = $200
Fixed cost are costs that does not vary and variable cost are costs that vary with goods and services.
In the given problem, rent , insurance premiums, loans interest payment ad home security fee are fixed cost.
Groceries and drinks, clothes and utilities are variable cost.
So, total variable cost for last month is
[tex]\text{Total variable cost}=\$1000+\$200+\$300=\$1500[/tex]
Therefore, total variable cost for last month is $1500.
Answer:
$1500
Step-by-step explanation:
I just took the test and got it right
The function f(x) is given by the set of ordered pairs. {(1,0), (–10,2), (0,6), (3,17), (–2,–1)} Which equation is true?
Answer:
y = -6x + 6
Step-by-step explanation:
To make an equation you need to find the slope first
To do that use the expression y2-y1/x2-x1 (-6)
Now plug that in to y = mx + b
Lastly you substitute any coordinate and find b
y = -6x + 6
Answer:C
Step-by-step explanation:
Find the correct algebraic representation of the rotation shown below.
a. (y, -x)
b. (-x, -y)
c. (-y, x)
d. (y, x)
Answer:
-y, x
Step-by-step explanation:
x values go from negative to positive and the y values remain negative
One student ate 3/20 of all candies and another 1.2 lb. The second student ate 3/5 of the candies and the remaining 0.3 lb. What weight of candies did they each eat? PLEASE HELP!!
Let the total weight of the candy = x
We know the total weight is:
X = 3/20x + 1.2 + 3/5x+ 0.3
Simplify:
X= 3/20x + 1.2 + 12/20x + 0.3
X = 15/20x + 1.5
Subtract 15/20x from both sides:
5/20x = 1.5
Divide both sides by 5/20:
X = 1.5 / 5/20
X = 6
Total = 6 pounds.
Pls help with this question thank u all
Answer:
4 cm (A)
Step-by-step explanation:
triangle BAC is just a larger version of triangle EAD. given that ED is 5cm, and BC is 10cm, triangle BAC must be twice the size of EAD. since the ratio of AD to ED is 4:5, and BC is twice the size, all we need to do is multiply both sides by 2 to find length AC. 4*2 = 8. now we can subtract length AD from AC to get CD. 8 - 4 = 4.
sorry if what i wrote is a little confusing
Write the function f(x) = x^2 + 8x + 12 in vertex form. Enter all work. Please help me.
Hello!
Answer:
f(x) = (x + 4)² - 4
Step-by-step explanation:
Write the equation f(x) = x² + 8x + 12 in vertex form by completing the square:
f(x) = (x² + 8x + (8/2)²) + 12 - (8/2)²
Simplify:
f(x) = (x² + 8x + 16) + 12 - 16
Subtract to find the 'k' value:
f(x) = (x + 4)² - 4. This is the equation in vertex form.
SOMEONE PLS HELP I WILL GIVE BRAINLIEST
factor x^(n+2)+x^(2)
pls explain too :>
Answer:
x² (x^n + 1)
Step-by-step explanation:
factor x^(n+2) + x²
= x^(n+2) + x²
= x^n • x² + x² (using law of indices)
= x²(x^n + 1)
please help with this too
Answer:
Step-by-step explanation:
Garden roller is in the shape of cylinder.
So, one revolution = Curved surface area of the cylinder
diameter = 70 cm
radius = 70/2 = 35 cm
h = 100 cm
Curved surface area of the cylinder = 2πrh
= [tex]2*\frac{22}{7}*35*100[/tex]
= 22000 square cm
Area covered in 15 revolutions = 15 * 22000
= 330000 square cm
2) Coin
diameter = 22 mm
r = 22/2 = 11 mm
Volume of coin = 66 mm
πr²h = 66
[tex]\frac{22}{7}*11*11*h=66\\\\\\h=\frac{66*7}{11*11*22}\\h=0.17 mm[/tex]