Answers
Answer:
The correct option is C
Step-by-step explanation:
81x²+72x+16
We have to break the middle term:
If we multiply 81 by 16 we get 1296:
The same answer we get when we multiply 36 by 36:
36*36=1296
And if we add 36+36 then we get the middle term which is 72.
So,
=81x²+72x+16
=81x²+36x+36x+16
=9x(9x+4)+4(9x+4)
=(9x+4)(9x+4)
Thus the correct option is C ....
Related Questions
7a3+56b3 factorize it plsss
Answers
Answer:
7(a + 2b)(a² - 2ab + 4b²)
Step-by-step explanation:
Given
7a³ + 56b³ ← factor out 7 from each term
= 7(a³ + 8b³) ← sum of cubes which factors in general as
a³ + b³ = (a + b)(a² - ab + b²)
8b³ = (2b)³ ⇒ b = 2b
a³ + 8b³ = (a + 2b)(a² - 2ab + (2b)²) = (a + 2b)(a² - 2ab + 4b²)
Hence
7a³ + 56b³ = 7(a + 2b)(a² - 2ab + 4b²) ← in factored form
Find all the real cube roots of -343.
Answers
The Cube Root Of -343 is ( -7)
Answer:
Cube root of -343 is -7
Step-by-step explanation:
If we square a negative value it becomes positive as ² is an even number
eg: -7² = -7 × -7
= +49
But if we cube it is the value becomes negative as ³ is an odd number
eg: -7³ = -7 × -7 × -7
= -343
Hope it helps u ...
Find the probability of each event. There are 4 red marbles, 2 black marbles, and 2 green marbles in a box. P(red) = P ( red or black) =
Answers
Answer: P(red): 1/2
P(red or black):3/4
Step-by-step explanation: Count the total number of marbles. There are 8. Since there are 4 red marbles out of the 8, put this into a fraction. It will be 4/8, but simplify to 1/2. The P(red) is 1/2.
Since there are 4 red marbles and 2 black marbles, add them. There are 6 out of the 8 marbles. The fraction is 6/8 simplify to 3/4. The P(red or black) is 3/4.
The probability of choosing a red marble from the box is 0.5 and the probability for choosing either a red or black marble is 0.75.
Explanation:The subject of this question refers to calculating probabilities which is a concept in Mathematics, specifically in the scope of Statistics. To calculate the probability of an event, we need to know the total amount of outcomes and the amount of favorable outcomes. In the context of the question, these outcomes are represented by marbles.
First, we need to add the total number of marbles, which is 4 red + 2 black + 2 green = 8 marbles in total.
To find the probability of picking a red marble, we divide the number of red marbles by the total number of marbles. Hence, P(red) = 4/8 or 0.5.
To find the probability of picking a red or black marble, we add the number of red and black marbles and divide by the total number of marbles. Hence, P (red or black) = (4 red + 2 black) / 8 total = 6/8 or 0.75.
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how do you convert 17 1/6 to a 3 decimal place
Answers
Answer:
17.167 rounded
Step-by-step explanation:
17+(1/6)
17+0,166
17.167
well, firstly convert the mixed fraction to improper fraction, and then simply divide the numerator by the denominator and round as needed.
[tex]\bf \stackrel{mixed}{17\frac{1}{6}}\implies \cfrac{17\cdot 6+1}{6}\implies \stackrel{improper}{\cfrac{103}{6}}~\hfill \stackrel{\textit{to a decimal}~\hfill }{103\div 6 = 17.166\overline{6}}\implies \stackrel{\textit{rounded up}}{17.167}[/tex]
Factor.
m4 - 36
a. (m2 - 18)(m2 - 18)
b. (m? + 6)(m2 - 6)
c. (m2 + 6)(m2 + 6)
d. (m2 + 18)(m2 - 18)
Answers
Answer:
b. (m^2 + 6)(m^2 - 6)
Step-by-step explanation:
m^4 - 36
m^2 ^2 -36
Replace m^2 with x
x^2 -36
This is the difference of squares
(x-6) (x+6)
Replace x with m^2
(m^2 -6) (m^2+6)
a = 310 rounded to the nearest 10
b = 66.1 rounded to 1 DP
Find the minimum (to 2 DP) of a÷b
Answers
To find the minimum of a divided by b, round a and b and then divide.
Explanation:To find the minimum of a divided by b, we need to divide the rounded values of a and b. First, round a to the nearest 10, which is 310. Next, round b to 1 decimal place, which is 66.1. Now divide 310 by 66.1 to get the minimum value. The result, rounded to 2 decimal places, is 4.69.
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using the side lengths determine whether the triangle is acute obtuse or right 24 30 18
Answers
Answer:
It is a Right Triangle.
Step-by-step explanation:
30^2 = 900
24^2 = 576
18^2 = 324
576 + 324 = 900
This satisfies the Pythagoras theorem so it is a Right Triangle.
Answer:
It's a right triangleStep-by-step explanation:
For a ≤ b ≤ c:
if a² + b² = c², then a triangle is a right triangle
if a² + b² < c², then a triangle is an obtuse triangle
if a² + b² > c², then a triangle is an acute triangle.
We have a = 18, b = 24, c = 30. Substitute:
18² + 24² = 324 + 576 = 900
30² = 900
18² + 24² = 30² → a² + b² = c²
Which graph is correct?
Answers
There are many ways to see it. First is the dotted and solid lines
The dotted lines mean that it doesn’t include the answer while the dotted line says it does.
When something is greater it’s going to be shaded on top of the line and when something is less it’s going to be shaded below the line
What is the value of f(x) = 9x when x = -2? A. 1 81 B. 81 C. 1 18 D. 18
Answers
Answer:
Step-by-step explanation:
The correct answer would be -18
To solve this, you would substitute x with the x value, which in this case is -2
That would make it so f(x)= 9(-2)
9*-2=-18
Therefore f(x)=-18
Note that f(x) is another way to write y, therefore...
y = 9x
To solve for this plug -2 in for x in this equation like so...
y = 9 * -2
When a positive number is being multiplied with a negative number the answer will be negative.
y = -18
C. is the answer (assuming that you meant to write -18 instead of 1 18)
Hope this helped!
~Just a girl in love with Shawn Mendes
f(x)=squarerootof(x−3), what is f(12)?
Answers
f(12)= square root of(12-3)
f(12)=square root of 9
f(12)=3
Answer:
3
Step-by-step explanation:
[tex]f(12) = \sqrt{12-3}=\sqrt{9} = 3[/tex]
The vertices of a polygon ABCD is A (1, 2), B (1,4), C(2,6), and D (5, 4). The polygon is dilated by a scale factor 3. Find the
coordinates of the dilated polygon...
Answers
(1,4) times 3 is (3,12)
(2,6) times 3 is (6,18)
(5,4) times 3 is (15,12)
The coordinates are (3,6) (3,12) (6,18) (15,12).
Hope this helps!
If polygon ABCD with vertices A (1, 2), B (1,4), C(2,6), and D (5, 4) is dilated by a factor 3, the coordinates of the dilated polygon are A' (3, 6), B' (3, 12), C' (6, 18), and D' (15, 12).
Explanation:When a polygon is dilated by a scale factor, all the coordinates of its vertices are multiplied by that scale factor. In this case, the scale factor is 3. Thus, we should multiply the x and y coordinates of each vertex by 3.
Let's calculate:
Vertex A (1, 2) dilated by scale factor 3 becomes A' (1*3, 2*3) => A' (3, 6)Vertex B (1,4) becomes B' (1*3, 4*3) => B' (3, 12)Vertex C (2,6) becomes C' (2*3, 6*3) => C' (6, 18)Vertex D (5, 4) becomes D' (5*3, 4*3) => D' (15, 12)So, the coordinates of the dilated polygon ABCD are A' (3, 6), B' (3, 12), C' (6, 18), and D' (15, 12).
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Eight hundred registered voters were asked whether they would vote yes or no on a certain measure. If 38% of those polled said yes, how many voters said no?
Answers
To find the decimal of 62%, we will have to divide 62 by 100 to get 0.62.
0.62(800)= 496.
Therefore, 496 people will vote no.
Hope this helps!
Final answer:
38% of eight hundred registered voters said yes, so 62% said no. By calculating 62% of 800, we find that 496 voters said no.
Explanation:
If 38% of eight hundred registered voters said yes to a measure, this means 62% said no because the total percentage must add up to 100%. To find out how many said no, we calculate 62% of 800. Here is the step-by-step calculation:
First, convert the percentage to a decimal by dividing it by 100: 62% / 100 = 0.62.
Next, multiply this decimal by the total number of voters to find the number who said no: 800 * 0.62 = 496.
Therefore, 496 voters said no to the measure.
a classroom is 19 ft long 2 ft wide and 10 feet high find the number of cubic feet of air in the room
Answers
Answer:
380 cubic feet of air
Step-by-step explanation:
Volume = height * width * length.
So
Volume = 10 * 2 * 19 = 380 cubic feet of air
Answer:
[tex]380\text{ ft}^3[/tex]
Step-by-step explanation:
We have been that a classroom is 19 ft long 2 ft wide and 10 feet high. We are asked to find the number of cubic feet of air in the room.
To find the number of cubic feet of air in the room, we will find the volume of the given room by multiplying all of its side as:
[tex]\text{Volume of the room}=\text{19 ft}\times \text{2 ft}\times\text{10 ft}[/tex]
[tex]\text{Volume of the room}=380\text{ ft}^3[/tex]
Therefore, there are 380 cubic feet of air in the room.
What does x ^2 + y^2 = 9 mean? What about x ^2 + y ^2 = 0 ? Can a circle have a radius of − 3 ? Why or why not?
Answers
Answer:
See below.
Step-by-step explanation:
Compare our equation with one standard form of a circle:
x^2 + y^2 = r^2 where r = the radius.
So x^2 + y^2 = 9 is the equation of a circle with it's center at the origin and it's radius is 3 units.
x^2 + y^2 = 0 is not a circle because r = 0 ( a radius of 0). A circle of radius 0 is really a point!!
The value of the radius of a circle must be positive so it cannot have a radius of -3.
Answer
[tex]x ^{2} + {y}^{2} = r^{2} [/tex]
since all the terms are squared so there can be a negative number
but in number line
...... -4,-3,-2,-1,0,1,2,3.......
as we know negative sign indicates only the direction so -3 means in which coordinates will it lie.
.
.
.
[tex] {x}^{2} + {y}^{2} = 9[/tex]
it means the origin is (0,0) and radius 3
Which of these are the intercepts of y = 2x − 6?
A. (3, 0), (0, 6)
B. (3, 0), (0, -6)
C. (4, 0), (0, 6)
D. (6, 0), (0, 12)
Answers
Answer:
B. (3, 0), (0, -6)
Step-by-step explanation:
Plug 0 in for each variable one at a time, and you will get both intercepts.
If a cone has the same radius and height as a cylinder, the volume of the cone is (one fourth, one third, half, or two thirds) the volume of the cylinder. If a cylinder and a sphere have the same radius and the cylinder’s height is twice its radius, then the volume of the sphere is (one fourth, one third, half, or two thirds) the volume of the cylinder.
Answers
The volume of the cone is one third of the volume of the cylinder when they have the same radius and height.
The volume of the sphere is two thirds the volume of the cylinder when the sphere and the cylinder have the same radius and the height of the cylinder is twice its radius.
If a cone has the same radius (r) and height (h) as a cylinder, then the volume of the cone is one third the volume of the cylinder.
This can be determined using the formula for the volume of a cone, which is V = (1/3)πr²h, compared to the volume of a cylinder, which is V = πr²h. Since we have the same 'r' and 'h' for both, the cone's volume will be one third of the cylinder's.
Similarly, if a cylinder and a sphere have the same radius and the cylinder’s height is twice its radius, we can say h = 2r. Thus, the volume of the sphere is calculated to be V = (4/3)πr³.
On the other hand, the cylinder's volume with h=2r would be V = πr²(2r) = 2πr³. The sphere's volume is two thirds of the cylinder's volume, because (4/3)πr³ is two thirds of 2πr³.
What is the equation of the line that is parallel to 8x-5y=2 and goes through the point (-5,-2)
Answers
Answer:
8x - 5y = - 30
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
Rearrange 8x - 5y = 2 into this form
Subtract 8x from both sides
- 5y = - 8x + 2 ( divide all terms by - 5 )
y = [tex]\frac{8}{5}[/tex] x - [tex]\frac{2}{5}[/tex] ← in slope- intercept form
with slope m = [tex]\frac{8}{5}[/tex]
• Parallel lines have equal slopes, hence
y = [tex]\frac{8}{5}[/tex] x + c ← is the partial equation of the parallel line
To find c substitute (- 5, - 2) into the partial equation
- 2 = - 8 + c ⇒ c = - 2 + 8 = 6
y = [tex]\frac{8}{5}[/tex] x + 6 ← in slope- intercept form
Multiply through by 5
5y = 8x + 30 ( subtract 5y from both sides )
0 = 8x - 5y + 30 ( subtract 30 from both sides )
8x - 5y = - 30 ← in standard form
Rosa is buying school supplies. Uf she needs x number of notebooks and each notebook cost a dollar and she needs y number if pens that cost b dollars, each write an equation for t, the amount of dollars she will spend
Answers
Answer:
t=x+yb
Step-by-step explanation:
I have answered ur question
Answer: Our required equation be t = x+yb.
Step-by-step explanation:
Let the number of notebooks be 'x'
Let cost of each notebook be $1
Let cost of pens be $b.
Let the number of pens be y.
Let the total amount be 't'.
So, According to question, equation becomes
[tex]t=x\times 1+y\times b\\\\t=x+yb[/tex]
Hence, our required equation be t = x+yb.
How many modes does the following data set have?
4,4,4,6, 6, 11, 11, 11, 134, 134
A.3
B.4
C.2
D.0
Answers
Answer:it would be C.2
Step-by-step explanation:
Final answer:
The data set has A) 3 modes, which are 4, 11, and 134.
Explanation:
The data set provided is: 4, 4, 4, 6, 6, 11, 11, 11, 134, 134. The mode is the number that appears most frequently in a set of numbers. In this data set, the modes are 4, 11, and 134, so the data set has 3 modes.
Given the frequency table, what percentage of the students in grades 9–10 like country music? Round to the nearest whole percent.
Band Preference for School Dance
Rap Rock Country Row totals
Grades 9–10 40 30 55 125
Grades 11–12 60 25 35 120
Column totals 100 55 90 245
a. 22%
b.44%
c.55%
d.61%
Answers
Answer:
b: 44%
Step-by-step explanation:
From grades 9-10 there are 55 students who like country music.
While there are 125 grades 9-10 students in total.
This gives us a percentage of (55/125) *100% = 44%
Answer:
b.44%
Step-by-step explanation:
44% of the students in grades 9–10 like country music.
Round to the nearest whole percent.
(55/125)
100% = 44%
Examine the steps used to solve the equation.
12.5x − 10.2 = 3(2.5x + 4.2) - 6
12.5x − 10.2 = 7.5x + 12.6 − 6
12.5x − 10.2 = 7.5x + 6.6
12.5x = 7.5x + 16.8 4. 5x = 16.8
5. x = 3.36
Analyze the steps to determine which properties or procedures were used to complete each step
Answers
Answer:
see below
Step-by-step explanation:
12.5x − 10.2 = 3(2.5x + 4.2) - 6
Use the distributive property to distribute the 3
12.5x − 10.2 = 7.5x + 12.6 − 6
Combine like terms
12.5x − 10.2 = 7.5x + 6.6
Add 10.2 to each side of the equation by using the addition property of equality
12.5x = 7.5x + 16.8
Subtraction 7.5x from each side of the equation by using the subtraction property of equality
5x = 16.8
Divide by 5 on each side by using the division property of equality
x = 3.36
Answer:
Step 1:
✔ distributive property
Step 2:
✔ combining like terms
Step 3:
✔ addition property of equality
Step 4:
✔ subtraction property of equality
Step 5:
✔ division property of equality
Step-by-step explanation:
Just did the assignment.
Using the slope and the y-intercept graph the line represents by the following equation then select the correct graph 2y + 4 =0
Answers
Answer:
Step-by-step explanation:
2y + 4 = 0 subtract 4 from both sides
2y = -4 divide both sides by 2
y = -2
The slope-intercept form of an equation of a line:
y = mx + b
m - slope
b - y-intercept → (0, b)
In the equation
y = -2
slope: m = 0
y-intercept: b = -2 → (0, -2)
y = -2 - it's a horizontal line
How much more area does a medium pizza with a 14 in. diameter have
than a small pizza with a 12 in diameter? Use the r key on your calculator
to approximate a Round your answer to the nearest square inch.
Answers
The medium pizza with a 14-inch diameter has approximately 41 square inches more area than the small pizza with a 12-inch diameter, using the formula for the area of a circle, πr², where r is the radius (half of the diameter).
Explanation:The subject of this question is area comparison between two circles, which is a topic in Mathematics. The areas of the two pizzas (which we can represent as circles) can be found using the formula for the area of a circle, which is πr^2, where r is the radius (half of the diameter).
For the medium pizza, the diameter is 14 inches, so the radius is 7 inches. The area is thus π*(7)^2 = 153.94 square inches. For the small pizza, the diameter is 12 inches, so the radius is 6 inches. The area is thus π*(6)^2 = 113.10 square inches.
So, the medium pizza has 153.94 - 113.10 = 40.84 square inches more area than the small pizza. Rounded to the nearest square inch, the medium pizza has approximately 41 square inches more area than the small pizza.
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1.
From a total yearly budget of
$360,000, the Kimball Foundation
spends $30,000 on leasing office
space. What is the ratio of dollars
spent on office space to dollars spent
on other costs?
A. 12:1
B. 11:1
C
Answers
Answer:
I think it would be 11:1.
Step-by-step explanation:
360,000 / 30,000 = 12
11/12 of the yearly budget was used on other costs
1/12 of the yearly budget was used for leasing office
space.
Answer:
Step-by-step explanation:
Okay so I may be wrong BUT since it's asking for the other costs, I'm assuming we're subtracting the $30,000 from the $360,000 first. Therefore the original ratio would be 30,000: 330,000 which is simplified to 1:11 ($ on office space: $ on other costs)
Plzzz help ASAP
Plz give answers
Answers
Answer:
4
Step-by-step explanation:
-5x/6=-10/3
or..5x/6=10/3
or..X/2=2
so X=4
Answer:
x = 4
Step-by-step explanation:
note that - [tex]\frac{5}{6}[/tex] x = [tex]\frac{-5x}{6}[/tex], hence
[tex]\frac{-5x}{6}[/tex] = [tex]\frac{-10}{3}[/tex] ( cross- multiply )
- 15x = - 60 ( divide both sides by - 15 )
x = [tex]\frac{-60}{-15}[/tex] = 4, that is
x = 4
The paragraph below comes from the rental agreement Susan signed when she opened her account at Super Video.
"All rentals are due back by midnight of the due date as printed on the transaction receipt. Any rental not received by midnight on the day it is due is subject to a late charge of $1.50 for each day it is late. Any rental not returned by the fifth day after the due date will be transferred to a sale. The Customer will then be required to pay the purchase price of the item in addition to five (5) days of late fees. The Customer will not be required to return the product once the total balance is paid."
As of today, Susan's movie is currently five days late. She knows that if she doesn't get the movie back tonight, she will be charged $9.99, the purchase price of the movie, plus five days' worth of late fees. A round trip cab ride to the video store will cost about $10.
Which of the following statements is true?
a.
Taking a cab to return the movie is the cheapest action. Susan should call a cab.
b.
It would cost about the same to keep or return the movie. Susan should keep it.
c.
Keeping the movie and paying the purchase price and late fees is the cheapest option.
d.
If Susan returns the movie, she should not have to pay late fees. She should return it.
Answers
Answer:
option B
Step-by-step explanation:
Given:
per day late costs= 1.50
Purchase price= 9.99
A round trip cab ride to the video store will cost = 10
5 day late cost= 5(1.50)
= 7.50
Payment after 5 day late= 5 day late cost + Purchase price
= 7.50 + 9.99
= 17.49
If she gets a cab, then total payment= 10 + 7.50
= 17.50
Hence both costs almost the same, option B is true
b.
It would cost about the same to keep or return the movie. Susan should keep it!
RS is the diameter of circle T. Point R is located at (11, 10) and point S is located at (5, 4). What are the coordinates of the center of this circle?
Answers
ANSWER
[tex]( 8 ,7 )[/tex]
EXPLANATION
Use the midpoint formula to find the center of this circle.
The midpoint formula is
[tex]( \frac{x_1+x_2}{2} ,\frac{y_1+y_2}{2} )[/tex]
The reason is that, the midpoint of the diameter RS gives the center of the circle.
Point R is located at (11, 10) and point S is located at (5, 4).
We plug in the values to get:
[tex]( \frac{11+5}{2} ,\frac{4+10}{2} )[/tex]
[tex]( \frac{16}{2} ,\frac{14}{2} )[/tex]
[tex]( 8 ,7 )[/tex]
Answer:
(8,7)
Step-by-step explanation:
I got it correct on founders edtell
Two fair dice are rolled 4 times and the sum of the numbers that come up are recorded. Find the probability of these events. A) the sun is 5 on each of the four rolls. B) the sun is 5 exactly three times in the four rolls.
Answers
Answer:
See below in bold.
Step-by-step explanation:
A. On one roll the possible ways to get a sum of 5 is (2,3, ) and (4, 1).
There are 36 possible outcomes from the one roll of the 2 dice.
So the probability of getting a sum of 5 on one roll = 2/36 = 1/18.
So the probability of 5 on 4 rolls = (1/18)^4
= 1/104976.
B.
The probability of the first 3 rolls being a 5 and the last one being not 5
= (1/18)^3 * (17/18)
= 17/104976
There are 4 ways to pick 3 out of 4 so the required probability
= 4 * 17/104976
= 68/104976.
Final answer:
The detailed answer explains the probability of rolling specific sums with two fair dice in four rolls, covering events A and B.
Explanation:
The Probability of Rolling Sums with Two Fair Dice
For event A, the probability of getting a sum of 5 on each of the four rolls is (4/36)⁴.
For event B, the probability of getting a sum of 5 exactly three times in the four rolls is 4*(4/36)³*(32/36).
Suppose you buy a CD for $500 that earns 2.5% APR and is compounded quarterly. The CD matures in 3 years. How much will this CD be worth at maturity?
Answers
Answer:
A=$538.82
Step-by-step explanation:
We're going to use the compounded interest formula:
A=P(1+r/n)^n*t
Where,
A = the future value of the investment/loan, including interest
P = the principal investment amount (the initial deposit or loan amount)
r = the annual interest rate (decimal)
n = the number of times that interest is compounded per unit t
t = t is the amount of time at which you're checking how much it's worth (yrs)
Using this information, we can use:
A=500(1+0.025/4)^3*4
A=500(1+0.00625)^12
A=500(1.00625)^12
A=500(1.07763259886)
A=538.82
A=$538.82....
Mary, Chau, and David have a total of $87 i their wallets. Marry has 9$ more than Chau. David has two times what Mary has. How much do they have in each wallet?
Answers
Answer:
Mary = 24
Chau = 15
David = 48
Step-by-step explanation:
The formula is
Mary + Chau + David = 87
And we know that
Chau = Mary - 9
David = Mary * 2
So when we fill this in
Mary + Mary - 9 + Mary * 2 = 87
4Mary - 9 = 87
4Mary = 96
Mary = 24
Chau = Mary - 9 = 15
David = Mary * 2 = 48
Final answer:
The problem is solved using basic algebra, yielding Chau has $15, Mary has $24, and David has $48, all adding up to the total amount of $87.
Explanation:
The question involves a three-person word problem focusing on algebraic relationships and equation solving. Mary, Chau, and David have a total of $87 in their wallets. Mary has $9 more than Chau, and David has twice what Mary has. To find out how much each person has, we'll let 'c' represent the amount that Chau has.
Accordingly, Mary has c + $9, and David has 2(c + $9). Together, they have a total of c + (c + $9) + 2(c + $9) = $87. Simplifying this, we get 4c + $27 = $87. Subtracting $27 from both sides gives us 4c = $60. Dividing both sides by 4, we find that Chau has $15.
Now, since Mary has $9 more than Chau, Mary has $24 ($15 + $9). David, having twice what Mary has, possesses $48 (2 x $24). These amounts add up to the total of $87.