Answer:
the remainder is 8
Step-by-step explanation:
2222 x 2223 x 22 x 24 = 2,608,059,168
2,608,059,168 ÷ 10 = 260,805,916.8
so the remainder is 8
What is the length of st given s (-3, 4) and t (1, 0)
[tex]~~~~~~~~~~~~\textit{distance between 2 points} \\\\ (\stackrel{x_1}{-3}~,~\stackrel{y_1}{4})\qquad (\stackrel{x_2}{1}~,~\stackrel{y_2}{0})\qquad \qquad d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2} \\\\\\ d=\sqrt{[1 - (-3)]^2 + [0 - 4]^2}\implies d=\sqrt{(1+3)^2 +(-4)^2} \\\\\\ d=\sqrt{32}\implies d\approx 5.66[/tex]
Andrei wants to fill a glass tank with spherical marbles and then fill the remaining space with water.
The variable "w" models the amount of water (in liters) Andrei uses if he uses n marbles.
w = 32 - 0.05n
What is the volume of each marble?
The volume of each marble is 0.05 liter
How to determine the volume?The volume function is given as:
w = 32 - 0.05n
The variable n represents the number of marbles.
This means that 0.05n represents the volume of n marbles and 32 represents the total volume of the glass tank
To get the volume of each marble, we divide 0.05n by n
i.e.
Volume = 0.05n/n = 0.05
Hence, the volume of each marble is 0.05 liter
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1. Which shows the factoring pattern for the sum of cubes?
1. (a+b)(a2–ab+b2)
2. (a+b)(a2–ab–b2)
3. (a–b)(a2–ab+b2)
4. (a+b)(a+b)(a+b)
2. Select all the solutions of x3+2x2−9x=18.
1. x=2
2. x=−3
3. x=3
4. x=−2
3. If x=−1 is a root of the polynomial 0=x3+2x2−5x−6, what are the other roots?
1. x=3, x=−2
2. x=−3, x=2
3. x=−1, x=−3, x=2
4. x=0, x=−3, x=2
4. Subtract: (x2–1)–(x3–2x+1)
1. –x^3 – x^2 + 2x
2. –x^3 – x^2 + 2x + 2
3. –x^3 + x^2 + 2x – 2
4. –x^3 + x^2 – 2x – 2
5. What is the largest multiplicity in the factored polynomial y=(x2−1)(x+2)(x+4)?
1. 4
2. 1
3. 0
2. 0
The solution to the questions are:
The expression that represents the factoring pattern is (a + b)(a² - ab + b²)The solutions of the equation x³ + 2x² - 9x = 18 are x = -3, x = 3 and x = -2The other roots are x = -3 and x = 2The result of subtracting the expressions is - x³ + x² + 2x - 2The largest multiplicity is 1Factoring pattern for the sum of cubesAs a general rule, the sum of cubes x³ and y³ is:
x³ + y³= (x+y)(x² - xy + y²)
Replace x with a and y with b
a³ + b³= (a + b)(a² - ab + b²)
Hence, the expression that represents the factoring pattern is (a + b)(a² - ab + b²)
The solutions of the polynomialThe equation is given as:
x³ + 2x² - 9x = 18
Subtract 18 from both sides
x³ + 2x² - 9x - 18 = 0
Factorize the expression
x²(x + 2) - 9(x + 2) = 0
Factor out x + 2
(x²- 9)(x + 2) = 0
Express x²- 9 as a difference of two squares
(x + 3)(x - 3)(x + 2) = 0
Split
(x + 3) = 0 or (x - 3) = 0 or (x + 2) = 0
Remove brackets
x + 3 = 0 or x - 3 = 0 or x + 2 = 0
Solve for x
x = -3, x = 3 and x = -2
Hence, the solutions of the equation x³ + 2x² - 9x = 18 are x = -3, x = 3 and x = -2
The other roots of the polynomialThe polynomial equation is given as:
0 = x³ + 2x² - 5x - 6
Rewrite as:
x³ + 2x² - 5x - 6 = 0
Factorize the expression on the left-hand side
(x + 3)(x + 1)(x - 2) = 0
Split
x + 3 = 0 or x + 1 = 0 or x - 2 = 0
Solve for x
x = -3 or x = -1 or x = 2
Hence, the other roots are x = -3 and x = 2
Subtract the expressionsThe expression is given as:
(x² - 1) - (x³ - 2x + 1)
Expand
x² - 1 - x³ + 2x - 1
Collect like terms
- x³ + x² + 2x - 1 - 1
Evaluate the like terms
- x³ + x² + 2x - 2
Hence, the result of subtracting the expressions is - x³ + x² + 2x - 2
The largest multiplicity of the polynomialThe polynomial is given as:
y = (x² - 1)(x + 2)(x + 4)
Express x² - 1 as a difference of two squares
y = (x - 1)(x + 1)(x + 2)(x + 4)
The power of each factor in the above expression is 1.
This means that the largest multiplicity is 1
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Which expression is equivalent to
4^sqrt 6 / 3^sqrt2
Answer: Choice C
[tex]\frac{\sqrt[12]{55,296}}{2}[/tex]
==========================================================
Explanation:
Recall the process to rationalize the denominator is to multiply top and bottom by the denominator expression. This only works if we have a square root in the denominator.
For cube roots, we'll need to multiply two copies of the denominator to top and bottom. This will get us three copies of [tex]\sqrt[3]{2}[/tex] so that the cube root goes away.
Check out the steps below to see what I mean:
[tex]\frac{\sqrt[4]{6}}{\sqrt[3]{2}}\\\\\\\frac{\sqrt[4]{6}\sqrt[3]{2}\sqrt[3]{2}}{\sqrt[3]{2}\sqrt[3]{2}\sqrt[3]{2}}\\\\\\\frac{6^{1/4}*2^{1/3}*2^{1/3}}{\left(\sqrt[3]{2}\right)^3}\\\\\\\frac{6^{3/12}*2^{4/12}*2^{4/12}}{2}\\\\\\\frac{\left(6^3*2^4*2^4\right)^{1/12}}{2}\\\\\\\frac{\left(55,296\right)^{1/12}}{2}\\\\\\\frac{\sqrt[12]{55,296}}{2}\\\\\\[/tex]
In short,
[tex]\frac{\sqrt[4]{6}}{\sqrt[3]{2}}=\frac{\sqrt[12]{55,296}}{2}[/tex]
We have the 12th root of 55,296 all over top the integer 2. The "2" is not part of the 12th root. This shows why choice C is the final answer.
Answer:
C
Step-by-step explanation:
Use the given information to determine which of the following relationships
can be proved and why.
ZL= 20
ZME P
M
Answer:
C. ∆LMN ~ ∆OPQ, because of AA
Step-by-step explanation:
All of the triangle congruence postulates require at least one pair of corresponding sides be congruent (in addition to other requirements). Triangle similarity can be proved if there are two pairs of congruent corresponding angles.
__
congruenceNo sides are given as congruent, so no congruences can be proved.
similarityTwo pairs of corresponding angles are said to be congruent, so we can say ...
∆LMN ~ ∆OPQ, because of AA
Hey can someone help me I dont really undertstand this, (thank you ^^)
Answer:
exact area = 81π in.²
approximate area = 254.34 in.²
Step-by-step explanation:
Exact:
area = πr²
r = radius = diameter/2 = 18 in./2 = 9 in.
area = πr²
area = π × (9 in.)²
area = 81π in.²
exact area = 81π in.²
Approximate:
π = 3.14 (approximately)
area = πr²
area = 81π in²
area = 81 × 3.14 in.²
approximate area = 254.34 in.²
find the value of x and y
Answer:
x= 131
y = 49
Step-by-step explanation:
X and 49 form a straight line so they add to 180
x+49 = 180
x = 180-49
x =131
49 and y are alternate interior angles and alternate interior angles have the same value
y = 49
Step-by-step explanation:
please mark me as brainlest
_____ teaspoon is equivalent to 5 ml.
Answer:
1.01 teaspoons is equal to 5 ml
Step-by-step explanation:
it goes up by ( 0.202884 )
1 ml 0.202884 tsp
2 ml 0.405768 tsp
3 ml 0.608653 tsp
4 ml 0.811537 tsp
5 ml 1.0144 tsp
6 ml 1.2173 tsp
7 ml 1.4202 tsp
Hope This Helped
Please don’t lie to me and tell the right answer and if you do get it correct I will give you a shout out thanks
Answer:
Part A = 7
Part B = 1
I hope this is right, sorry if it isn't
Answer:
See below
Step-by-step explanation:
5 cups cheese / ( 2/3 cup cheese/plate ) =
5 * 3/2 = 15/2 = 7 1/2 or 7 full plates
2/3 cup cheese / plate * 9 plates =
2/3 * 9 = 6 cups cheese total
she has 5 cups to start.....she will need 1 cup more
what are the coefficients of the expression 7x-4x2?
Answer:
Coefficients: 7, -4.
Step-by-step explanation:
In the expression 7x-4x^2, the terms are 7x and -4x^2. There are no constants here, which would just be a number by itself. Coefficients are integers written alongside or multiplied by the variable.
In this expression, the variable x has two coefficients (one per term). These are 7 and -4.
Answer:
7
Step-by-step explanation:
a numerical or constant quantity placed before and multiplying the variable in an algebraic expression (e.g. 4 in 4x y).
please simplify and keep the answer with exponents.
(6^7 * 6^12)/ 6^8
Answer:
6¹¹
Step-by-step explanation:
Simplifying the numerator :
When two terms with the same base are multiplied, the powers are added6⁷ x 6¹²6¹⁹Solving the expression :
When two terms with the same base are divided, the powers are subtracted6¹⁹ / 6⁸6¹¹Ariana has 4 posters she wants to hang on the wall how many different ways can the posters be arranged
Answer:
4 different ways
Step-by-step explanation:
there are four different ways she can post it because there are four posters she want to hang on the wall.
Allison earned a score of 95% on a test where the mean was only an 82%. How far above average was her score?
Answer:
The correct answer is 13%.
Step-by-step explanation:
We can easily put in the equation:
95 - 82 = 13
Hope this helps:) Goodluck!
Classify the triangle by its sides and by its angles
Answer:
Scalene obtuse.
Step-by-step explanation:
Scalene means that none of the sides are the same. You can tell by looking at the triangle that none of the sides are the same. An obtuse triangle is a triangle with one obtuse angle. It is a close call between obtuse and right, but I believe that I can definitely say that the angle is a little more than 90 degrees, and is therefore obtuse.
High school geometry. help is needed, please and thank you.
50 POINTS HELP ME PLEASE ITS GEOMETRY
Answer:
x is the midpoint of a segment in the diahram
Answer:
x is mid point
Step-by-step explanation:
I hope it's helpful for
which of the following is located over the center of the base of a regular pyramid
A vertex
B slant height
C face
D edge
Vertex is located over the center of the base of a regular pyramid.
What is Vertex Angle?
Vertex angle is defined as the angle formed by two lines or rays that intersect at a point. These two rays make the sides of the angle.
Here, Vertex is the point which is located over the center of the base of a regular pyramid.
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Erica buys a package of note cards costing $1.44. She gives the cashier
$5.00. The cashier gives her her change using the least number of coins and
bills possible. How many of each coin or bill does she receive?
Answer:
See below.... several options
Step-by-step explanation:
Change is $3.56
3 dollar bills one 50 c piece one nickel one penny
(though 50 cent pieces are uncommon.....this may be 2 quarters)
[For a while , there was $ 2 bills
so it could be one 1 dollar bill and one $ 2 bill instead of three dollar bills]
The graph shows a proportional relationship between the number of plants and the number of flowers on the plants. What is the constant of proportionality in terms of flowers per plant?
The constant of proportionality in terms of the number of flowers per plant is 5.
What is the proportional relationship?If two quantities varies directly to each other i.e if y varies proportional to x then
y =kx .....[1] where, k is the constant of proportionality.
Suppose, y represents the number of roses and x represents the number of plants.
Given is the graph shows a proportional relationship between the number of plants and the number of flowers on the plants. The graph attached below has the coordinates points,
(0, 0)
(1, 5)
(2, 10)
(3, 15)
(4, 20)
Substitute any coordinate points like (3, 15) in above equation to find k.
15 =k x 3
k = 5
Therefore, the constant of proportionality in terms of the number of flowers per plant is 5.
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Answer:
5
Step-by-step explanation:
Nathan needs some paint for his bedroom. He finds two cans of white paint, four cans of green paint and three cans of pink paint in his garage. If he chooses a can of paint without looking at the color, what is the chance that he will paint his bedroom pink?
A. 1/3
B. 2/9
C. 2/3
D. 6/9
The probability of randomly selecting a can of pink paint is P = 1/3, so the correct option is A.
What is the chance that he will paint his bedroom pink?Assuming that all the cans of paint have the same probability of being randomly selected, the probability that he will choose a pink can is equal to the quotient between the number of pink cans and the total number of cans.
There are 2 cans of white, 4 cans of green, and 3 cans of pink, so a total of 9 cans.
Then the probability is:
P = 3/9 = 1/3.
The correct option is A.
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The volume of this right prism is 2,500 ft³. What is the height, x, of the prism? x = ft
The height x of the right prism is 10 ft if the volume of this right prism is 2,500 ft³.
What is a rectangular prism?It is defined as the six-faced shape, a type of hexahedron in geometry.
It is a three-dimensional shape. It is also called a cuboid.
From the figure:
Volume = 2500 cubic ft
(10)(x)(25) = 2500
250x = 2500
x = 10 ft
Thus, the height x of the right prism is 10 ft if the volume of this right prism is 2,500 ft³.
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the dimensions of a high school football field are represented by a width of 2x - 40 feet and a length of 3x + 60 feet
what expression represents the binomial factors you would multiply to find the area of the football field?
Solving System of Equations Using Subtraction.
X + 4y = 11
X - 6y = 11
Answer:
x=11
y=0
Step-by-step explanation:
Don't know if this is what you're looking for but this is correct if you plug it in.
X + 4y = 11 Get x by itself. x=-4y+11 and plug it into the bottom.
X - 6y = 11
simplify -4y+11-6y=11
11-10y=11
-10y=0
y=0 plug it into the original and you will get
x=11
x=11
Somebody please answer quick, will mark whoever is first Brainliest. Select the correct answer from the drop-down menu
The graphed linear equation is
A. 3x - 2y = -12
B. 2x - 3y = -12
C. 3x + 2y = 12
D. 3x + 3y = -12
Answer:
C. 3x + 2y = 12
explanation:
Solve for X
1.1x + 1.4x = 350
Answer:
X= 140
Step-by-step explanation:
I hope this helps. =D
Answer:
x=140
Step-by-step explanation:
1.1x+1.4x=350 1. combine like terms which 1.1x+1.4x
2.5x=350 2. /2.5 on both sides
x=140
(Please help!!!)
Select the correct answer.
Simplify the following expression.
3x(4x-3)
A. 12+ 13x
B. 12x²-5x
C. 12x² + 5x
D. 12x²-9x
I need help please help me and thank you :))
Answer:
see explanation
Step-by-step explanation:
∠ CZD = 90° , then
∠ CZF = 90° - ∠ FZD = 90° - 40° = 50°
∠ FZD and ∠ AZG are vertically opposite angles and are congruent , so
∠ AZG = 40°
∠ CZF and ∠ GZE are vertically opposite angles and are congruent , so
∠ GZE = 50°
E
∠ AZB + ∠ BZC = 90° , that is
3x - 2 + 32 = 90
3x + 30 = 90 ( subtract 30 from both sides )
3x = 60 ( divide both sides by 3 )
x = 20
Which expression represents the growth of an investment of $8,000 at 7.5% per year for a period of t years? 8000(1.075t) 8000(1.075)t 8000(0.075)t
Answer:
its b
Step-by-step explanation:
because im feeling generous enjoy
If anyone is good at grade 8 math problems pls help answer these questions thanks!! :DD
WILL MARK BRAINLIEST TO WHOEVER CAN ANSWER THIS CORRECTLY!!!!
Answer:
53 Meters.
Step-by-step explanation:
34*34 + 41*41 = 2837.
1156 + 1681 = 2837.
The square root of 2837 would be your answer.
34*34 + 41*41 = 53.26349 * 53.26349
a*a + b*b = c*c.
a² + b² = c².
Answer:
21.74
Step-by-step explanation:
AC^2 = AB^2 + BC^2
AC^2 = 34^2 + 41^2
AC^2 = 1156 + 1681
AC^2 = 2837
AC = Square root of 2837
AC = 53.26..
meters saved by walking through the pond = (AB+BC)-53.26
=> (34+41)-53.26
=> 75 - 53.26
=> 21.74
hope this helps:)
Nadya has 19 1/4 yards of ribbons she cuts into pieces that each measure 1 3/4 yards. How many pieces of ribbon does Nadya have
Answer:
Nadya have 11 pieces of ribbon