The solution of factorization of x ³ + 64 is ( x + 4 )( x ² - 4 x + 16 ) [ Option C ].
The question asks to factorize the given polynomial, that is, x ³ + 64.
The question clearly states that we need to use the sum of cubes formula to factor the given polynomial x ³ + 64.
Sum of cube formula is given as
a ³ + b ³ = ( a + b ) ( a ² - a b + b ² ).
Substitute the values of variable a and b from the given polynomial x ³ + 64
x³ + 64 can be written as x ³ + 4 ³
=> a = x and b = 4
=> x ³ + 4 ³ = ( x + 4 ) ( x ² - 4 x + 4 ² )
=> x ³ + 4 ³ = ( x + 4 ) ( x ² - 4 x + 16 )
This matches with the option c among the multiple choices for this question.
Therefore, we get the solution of factorization of x ³ + 64 as ( x + 4 )( x ² - 4 x + 16 ).
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jackie has fewer than 20 h to work on her jewelry. it takes her half an hour to make a necklace and an hour to make a bracelet. she wants to make x necklaces and y bracelets, and she wants at least twice as many bracelets as necklaces. select all inequalities that model this situation.
The inequalities that model the given situation are 0.5x+y<20, y≥2x and x>0.
Let Jackie wants to make x necklace and y bracelets.
Now, Since it take her half an hour to make a necklace and one hour to make a bracelet.
Also since she has fewer than 20 h total to work on the jewelry. So we have
0.5x + 1y < 20
=> 0.5x + y < 20
and she want at least twice as many bracelets as necklace, so we have
y ≥ 2x
also the number of necklace should be greater than 0. So x > 0
So the required inequalities are:
0.5x + 1y < 20
y ≥ 2x
and x > 0
Hence, The inequalities that model the given situation are 0.5x+y<20, y≥2x and x>0.
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10. Shade the models to show that 0.7 and
0.70 are equivalent.
In a figure we can see that 0.7 and0.70 are equivalent, we have shade in the figure.
Given that,
To illustrate that 0.7 and 0.70 are equivalent, shade the models.
We have 0.7
We can say 7/10
For example, take a square and divide it by 10 part in column and shade 7 column.
Draw horizontal lines connecting the model's dots using a ruler.
Now divide it into 100 equal pieces.
So,
70/100
Shade the 7 rows and column.
Shaded at 70 or 0.70.
Therefore, in a figure we can see that 0.7 and0.70 are equivalent.
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Write in terms of i.
Simplify your answer as much as possible.
√-63
Answer:
3 i √7
Step-by-step explanation:
sqrt (-63) = sqrt ( -1 * 3 * 7 *3) = sqrt (-1) * 3 * sqrt 7 = 3 i sqrt 7
Benito drove 14 miles and his car used 5 gallons of gas. How many miles can he drive with 16 gallons of gas?
Answer:70
Step-by-step explanation:
70 divided by 5 equals 14
12 = -4(-6X - 3) what is x
Answer:
x=0
Step-by-step explanation:
12 = -4(-6x-3)
12 = 24x+12
-12 -12
0 = 24x
/ /
24 24
0 = x
Check
12 = -4(-6(0)-3)
12 = -4(0-3)
12 = 0 + 12
12 = 12
Solve each equation. If necessary, round to the nearest ten-thousandth. 8x=444
The solution of the given equation by rounding off it to the nearest ten-thousandth is 55.5000.
What is a round-off of the digit?
In mathematics, a round-off is defined as an approximation of the given number to a fewer number of significant digits by taking into consideration some rules.
For eg: 13.58 ~ 13.6
Solving the given equation: 8 x = 444
We are given that 8 x = 444 —- 1
x = 444 / 8
= 55.5
Hence, the solution of the given equation rounded off to the nearest ten-thousandth is 55.5000.
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please help with this question its worth 50 points
An audience of 482 people were at a concert.
How many people were in the audience, to the
a) nearest 100?
b) nearest 1000?
Answer
482 rounded off to nearest 100 is 500 and 482 rounded off to nearest 1000 is zero.
By maintaining a number's value while moving it closer to the next number, rounding off makes the number easier to understand. It is done for entire numbers as well as decimals at different places such as hundreds, tens, and tenths. To maintain the major figures, numbers are rounded off.
At a concert there were 482 people in the audience:
(a) With a number line, 482 was rounded to the nearest hundred.
Find the two consecutive 100-multiples that surround 482.Between 400 and 500 is 482.The halfway point between 400 and 500 is 450.482 is greater than the midway, as shown on the number line (450)The result is 500 when 482 is rounded to the nearest hundred.(b) Since 4 is the hundredth value of 482 and there is no previous thousand to 499. So when 499 is rounded to the nearest thousand, equals 0.
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Factor the ff.
1.) 2x² + 17x + 35
2.) 2y² - 5y - 3
3.) 3x² - 8x + 4
1.
[tex] 2x {}^{2} + 17x + 35 \\ = 2x {}^{2} + 10x + 7x + 35 \\ = 2x(x + 5) + 7(x + 5) \\ = (2x + 7)(x + 5)[/tex]
2.
[tex]2y {}^{2} - 5y - 3 \\ = 2y {}^{2} -6y + y - 3 \\ = 2y(y - 3) + 1(y - 3) \\ = (2y + 1)(y - 3)[/tex]
3.
[tex]3x {}^{2} - 8x + 4 \\ = 3x {}^{2} - 6x - 2x + 4 \\ = 3x(x - 2)( - 2)(x - 2) \\ = (3x - 2)(x - 2)[/tex]
Solve the system of equations using a matrix
x+5 y=-4
x+6 y=-5
The solution of system of equations is (1,-1).
Given that the system of equations is x+5y=-4, x+6y=-5.
The system of equations can be written in matrix form as
x+5y=-4
x+6y=-5
[tex]\left[\begin{array}{ll}1&5\\ 1&6\end{array}\right]=\left[\begin{array}{l}-4\\ -5\end{array}\right][/tex]
Write the matrix on the left as the product of coefficients and variables.
[tex]\left[\begin{array}{ll}1&5\\ 1&6\end{array}\right]\left[\begin{array}{l}x\\ y\end{array}\right]=\left[\begin{array}{l}-4\\ -5\end{array}\right][/tex]
Firstly, find the inverse of the coefficient matrix.
The inverse of [tex]\left[\begin{array}{ll}1&5\\ 1&6\end{array}\right][/tex] is
[tex]\begin{aligned}\left[\begin{array}{ll}1& 5\\ 1&6\end{array}\right]&=\frac{1}{6(1)-5(1)}\left[\begin{array}{ll}6&-5\\ -1&1\end{array}\right] \\ &=\left[\begin{array}{ll}6&-5\\ -1&1\end{array}\right]\end{aligned}[/tex]
Next, multiply each side of the matrix equation by the inverse matrix . Since matrix multiplication is not commutative, the inverse matrix should be at the left on each side of the matrix equation.
[tex]\begin{aligned}\left[\begin{array}{ll}6&-5\\ -1& 1\end{array}\right]\left[\begin{array}{ll}1&5\\ 1&6\end{array}\right]\left[\begin{array}{l}x\\ y\end{array}\right]&=\left[\begin{array}{ll}6&-5\\ -1& 1\end{array}\right]\left[\begin{array}{l}-4\\ -5\end{array}\right]\\ \left[\begin{array}{ll}1&0\\ 0&1\end{array}\right]\left[\begin{array}{l}x\\ y\end{array}\right]&=\left[\begin{array}{l}1\\ -1\end{array}\right]\end{aligned}[/tex]
The identity matrix on the left verifies that the inverse matrix was calculated correctly.
[tex]\left[\begin{array}{l}x\\ y\end{array}\right]=\left[\begin{array}{l}1\\ -1\end{array}\right][/tex]
The solution is (1,-1).
Hence, the solution of the system of equtions using matrix is x+5y=-4, x+6y=-5 is (1,-1).
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Please help me asap and I will try to give brainliest!
Answer:
0.1 or 1/10
Step-by-step explanation:
-2/5 + 1/2 is also - 4/10 + 5/10 which is 1/10
Step-by-step explanation:
-2x2/5x2+1x5/2x5
-4/10+5/10
1/10
SOMEONE PLEASE HELP ME
1st - 3
2nd-1
3rd-4
5th-2
HELP ME PLEASE I NOT SPEAK ENGLISH, THE ENGLISH IS DIFFICULT FOR ME
The value of the expression (4x^6) * 3y^5/6x^3y^3 is 2x^3y^2
How to evaluate the expression?The expression is given as
(4x^6) * 3y^5/6x^3y^3
Divide 3 and 6 by 3
So, we have
(4x^6) * 3y^5/6x^3y^3 = (4x^6) * y^5/2x^3y^3
Apply the law of indices to the exponents
(4x^6) * 3y^5/6x^3y^3 = (4x^6) * y^2/2x^3
Remove the bracket
(4x^6) * 3y^5/6x^3y^3 = 4x^6 * y^2/2x^3
Divide 4 and 2 by 2
So, we have
(4x^6) * 3y^5/6x^3y^3 = 2x^6 * y^2/x^3
Apply the law of indices to the exponents
(4x^6) * 3y^5/6x^3y^3 = 2x^3y^2
Hence, the value of the expression (4x^6) * 3y^5/6x^3y^3 is 2x^3y^2
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By rounding each number to the nearest 10, estimate the value of 197 + 10.3 Optional working Answer: 19.1
200+10=210 this is the answer
please like it if it is correct
The estimated value of 197 + 10.3 is 210.
What is Rounding off?Although the term "rounding" is a general one, we typically use the terms "round up" or "round down" to indicate whether the number has gone up or down after being rounded. The supplied number is said to be rounded up when the rounded number is increased, and it is said to be rounded down when the rounded number is dropped.
Given:
197 + 10.3
Now, rounding off nearest 10
197---> 200
and, 10.3 ----> 10
So, 197+ 10.3 = 200+ 10 = 210
Hence, the estimated value is 210.
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A seventh-grade class has reached 6/7 of its quota in a Read-a-Thon. An eighth-grade class has reached 7/8 of its quota. If both classes have the same quota, which class is closer to reaching its quota?
Answer:
Eighth Grade ( [tex]\frac78[/tex] )
Step-by-step explanation:
The larger the denominator is, the smaller one "piece" of it is.
If we imagine a cake, for instance, then one piece of a cake that is split into 8 pieces would be smaller than a piece of a cake that is split into 7 pieces.
Therefore, if the piece is smaller, the closer the fraction is to being equal to 1, meaning, [tex]\frac78 > \frac67[/tex]
How do I solve this?
Answer:times 5 and 5 =25 7 and 7=49 add answers 74
Step-by-step explanation:
help plssssssssssssss ty
Answer:
associative property
Step-by-step explanation:
because the variables match
What is the equation of a line that passes through the point (2, −10) and is parallel to 14x+2y=6?
The the equation of a line that passes through the point (2, −10) and is parallel to 14x+2y=6 is 7x + y + 8 = 0.
A straight line is just a line with no curves. So, a line that extends to both sides till infinity and has no curves is called a straight line.
The equation of a line parallel to a given line will have the same slope as the given.
The equation of a line having a slope m and passing through the point (x', y') is written as
y - y' = m (x - x').
This is called point - slope equation of a straight line.
In the given equation,
14x+2y=6
⇒ 2y = -14x + 6
⇒ y = -7x + 3
Comparing it with standard equation of a straight line; y = m x + c, the slope m of the given line = -7
Therefore equation of the line parallel to the given line and passing through point (x', y') = (2, -10) would be:
y - (-10) = -7x + 2
⇒ y + 10 = -7x + 2
⇒ 7x + y + 8 = 0
Hence the required equation of line 7x + y + 8 = 0
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Solve each equation.
3²x=6561
After solving the given equation 3²x=6561, the value of x=729.
What is an equation, exactly?A mathematical statement made up of two expressions joined by an equal sign is known as an equation.3x - 5 = 16 is an example of an equation.We get the value of the variable x as x = 7 after solving this equation.So,
Given: 3²x=6561Then,
3²x=65619x=6561x=6561/9x=729Therefore, after solving the given equation 3²x=6561, the value of x=729.
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Dae collects x number of peaches from his yard, sells them, and adds the profits to his bank account, which then contains y dollars. The amount of money in his bank account can be represented by the equation y = 2x + 350. How many peaches did Dae sell if he ends up with $650 in his account?
Which of the following functions are continuous for all real numbers?
f(x) = e²
g(x)=√x
Choose 1 answer:
f only
g only
Both f and g
Neither f nor g
A parking area at a department store is shaped like a quarter circle with a radius of 123 meters. Due to the fact that the department store is to be rebuilt, the parking area must be temporarily reduced to 1/3 of its original area. What is the radius of the new parking area assuming it is still a quarter circle?
a. 91 m
b. 71 m
c. 77m
d. 82 m
The radius of the new parking area is 82 meters
How to determine the radius of the new parking area?The radius of the old parking area is given as
Radius, R = 123 meters
From the question, we understand that:
The parking area must be temporarily reduced to 1/3 of its original area
This means that
New Radius = Old radius - Old radius * 1/3
So, we have
New Radius = 123 meters - 123 meters * 1/3
Evaluate the product
So, we have
New Radius = 123 meters - 41 meters
Evaluate the difference
New Radius = 82 meters
Hence, the radius of the new parking area is 82 meters
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George jumps off a tire swing into a circular pond causing circles of waves. One of the waves travels at a rate of 16 ft/sec .
d. If the area of the pond is 22,000 square feet, how long will it take the circle to cover the area of the pond? Use this information to determine the diameter of the pond.
The wave will take 5.23 seconds to cover the area of the pond and the diameter of the lake is 167.52 feet when the area of the lake is given as 22000 feet.
We are given that the area of the pond = 22,000 square feet
Area = 22,000 feet²
π r² = 22,000
22 / 7 r² = 22,000
r² = 22000 × 7 / 22
r² = 7000
r = √ 7000
r = 10 √70
r = 83.76 feet
Also, since the wave travels 16 feet per second,
Time taken to cover the entire area = 83.76 / 16 = 5.23 seconds
The diameter of the lake = 83.76 + 83.76
d = 167.52 feet
Therefore, we get that the wave will take 5.23 seconds to cover the area of the pond and the diameter of the lake is 167.52 feet when the area of the lake is given as 22000 feet.
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dave earns his salary by making a 12.5% commision on all of his sales.if he sells $25000 this month,how much did he earn this month
PLEASE SHOW WORK
The total amount did he earn this month is $3125.
What is arithmetic?Arithmetic is the branch of mathematics that deals with the study of numbers using various operations on them. Basic operations of math are addition, subtraction, multiplication and division. These operations are denoted by the given symbols.
Given:
Dave earns his salary by making a 12.5% commission.
sales= $25000 this month.
According to given question we have
The basic formula is
Sales × Commission Percent/100 = Commission
$25000 ×12.5/100= Commission
Commission=$3125
Therefore, the total amount did he earn this month is $3125.
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7
[tex]7 \sqrt{6 } - 4 \sqrt{6} = [/tex]
[tex] - 0.7 \sqrt{7} + 2.3 \sqrt{7} = [/tex]
[tex] \sqrt{45} + \sqrt{20} = [/tex]
What are answers to these formulas
The answer to the formula are-
7√6 - 4√6 = 3√6-0.7√7 + 2.3√7 = 1.6√7√45 + √20 = 5√5How to add square roots?Square roots, like "regular" numbers, can be added together. However, you may not be able to reduce the addition to a single number.Because the radical in each term is the same, these are "like" terms.Part 1: 7√6 - 4√6
As both the digits have the same value √6. It means they can simply be added with sign to solve.
= 7√6 - 4√6
Take √6 common from both;
= √6(7 - 4)
= 3√6
Thus, the simplification of the expression is 3√6.
Part 2: -0.7√7 + 2.3√7
Here, also the common term is √7.
= √7( -0.7 + 2.3)
Simply add the number with sign.
= 1.6√7.
Thus, the simplification of the number is 1.6√7.
Part 3: √45 + √20
In thus, first write the number in its prime factors;
= √3×3×5 + √2×2×5
Take the root of 3 and 2 from the first and second digits of expression.
= 3√5 + 2√5
Now, both have the same term √5.
= √5(3 + 2)
Do the addition;
= 2√5
Thus, the simplification of given expression is 2√5.
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i need help and this is IXL how do you do this?
Answer:
Q= (1, -1), R = (7,-1), S = (7,-10), P =. (1,-10)
Step-by-step explanation:
Look at the coordinate grind then look at the coordinates (x) vertically, then look at the coordinates(y) horizontally.
then plot it as (x, y)
SOS URGENT PLS HELP ASAP THANKS ILL GIVE BRAINLIEST DUE TOMORROW PLSSSS TYSM
Step-by-step explanation:
you can ask any questions for clarification
Tyrone solved the equation 4x=2−4(2−3x).
Match the property with each of Tyrone's steps for solving the equation.
PLEASE I NEED A ANSWER FAST thank you
The property with each of Tyrone's steps for solving the equation is;
Multiplication property of equalitySubtraction property of equalitycombine like termsdivision property of equalityProperty of equality4x = 2 - 4(2 - 3x)
Apply Multiplication property of equality4x = 2 - 8 + 12x
Apply Subtraction property of equality4x = - 6 + 12x
Apply combine like terms4x - 12x = -6
-8x = - 6
Apply division property of equalityx = -6 / - 8
x = 3/4
Therefore, the solution to Tyrone's equation for x is 3/4
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What is the circumference of this circle? r = 2 km
Answer:
12.56 km
Step-by-step explanation:
C = 2πr
= 2 x 3.14 x 2
= 12.56 km
Answer:
12.56km or 12,560m
Step-by-step explanation:
c = 2πr
c = (2)(3.14)(2)
c = (6.28)(2)
c = 12.56
X and Y are two geometrically similar solid
shapes.
The total surface area of shape X is 450 cm²
The total surface area of shape Y is 800 cm²
The volume of shape X is 1350 cm³
Calculate the volume of shape Y
Shape Y has a volume of 3200 cm3.
What is volume?Volume is a measurement of three-dimensional space that is occupied. It is frequently expressed mathematically using imperial or SI-derived units. The volume of a container is typically thought of as its capacity, not as the amount of space it takes up. In other words, the volume is the amount of fluid (liquid or gas) that the container may hold.
What is Surface Area?A solid object's surface area is a measurement of the overall space that the object's surface takes up.
Scale Factor Formula
Scale up (Smaller to larger) = (lager figure measurement)/(smaller figure measurement)
Scale down (Larger to smaller) = (smaller figure measurement)/(larger figure measurement)
A ratio greater than 1 is the scale factor for scaling up. A ratio of less than 1 is the scale factor for scaling down.
Given data:
The total surface area of shape X is 450 cm².
The total surface area of shape Y is 800 cm².
The volume of shape X is 1350 cm³.
Scale Factor for Area = (Surface area of shape x)/(surface area of shape y)
=450/800
=16/9
Scale factor for Length = [tex]\frac{\sqrt{16}}{\sqrt{9} }[/tex]
= 4/3
Scale factor for volume =4³/3³
= 64/27
Volume of shape y = volume of shape x*scale factor for volume
=1350×(64/27)
=450×(64/9)
=50×64
=3200 cm³.
Therefore, the volume of shape Y is 3200 cm³.
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