Answer:
B) (2x + 3)(4x² - 6x + 9)-----------------------------------
Given sum of cubes, use identity a³ + b³ = (a + b)(a² - ab + b²):
8x³ + 27 = (2x)³ + 3³ = (2x + 3)((2x)² - (2x)(3) + 3²) = (2x + 3)(4x² - 6x + 9)The matching choice is B.
Answer:
B) (2x + 3)(4x² - 6x + 9)
Step-by-step explanation:
Given expression:
[tex]8x^3+27[/tex]
Rewrite 8 as 2³ and 27 as 3³:
[tex]\implies 2^3x^3+3^3[/tex]
[tex]\textsf{Apply exponent rule} \quad a^nc^n=(ac)^n:[/tex]
[tex]\implies (2x)^3+3^3[/tex]
[tex]\boxed{\begin{minipage}{5 cm}\underline{Sum of Cubes Formula}\\\\$a^3+b^3=(a+b)(a^2-ab+b^2)\\\end{minipage}}[/tex]
Therefore:
a = 2xb = 3Using the Sum of Cubes formula:
[tex]\begin{aligned}\implies (2x)^2+3^3&=(2x+3)((2x)^2-2x(3)+3^2)\\&=(2x+3)(4x^2-6x+9)\end{aligned}[/tex]
Marissa's mom purchased coffee from the local coffee shop. The first cup of coffee was $3.75. Each refill is $1.50. She also decided to get a bagel for $3.15. If Marissa's mom had 2 refills and a $0.50 discount as part of the rewards program, how much did she spend at the coffee shop?
$11.40
$10.65
$9.90
$9.40
Answer: ($9.40) or (d)
Step-by-step explanation:
Darren ha a piece of wood that i 7 in by 8 in. Explain how he could divide thi large rectangle into two maller rectangle
On solving the provided question, we got that - he could divide the large rectangle into two smaller rectangle by cutting into 7 inches by 4 inches each.
What is rectangle?The opposite sides of a rectangle are equal and parallel, making it a form of quadrilateral. Four of its sides are equal to 90 degrees, making it a four-sided polygon. Two-dimensional shapes include rectangles.
We know that Darren has a wood piece that measures 7 inches by 8 inches. We are expected to explain how he managed to separate these two enormous rectangles into smaller ones.
Let's imagine that a huge rectangle has a width of 8 inches and a length of 7 inches.
Darren needs to cut two rectangles that are each 4 inches wide and 7 inches long to divide a giant rectangle into two smaller rectangles.
In order to make two smaller rectangles that are each 7 inches long and 4 inches broad, Darren can cut a larger rectangle.
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PLEASE HELP
Fill in the blanks below with the correct units.
Answer:
a) Liters.
b) Kilograms.
c) Kilometers.
Step-by-step explanation:
I'm not completely sure about C). But after some researching and calculating these answers seem the most correct. But I'm pretty sure A) and B) are right.
There are 28 right-handed students in a class of 3 1. What is the probability that a student
chosen at random will be left-handed?
31/28
28/31
3/28
3/31
Answer:
3/31
Step-by-step explanation:
31 - 28 = 3 left handed students
31 total students
probability that a student chosen at random will be left-handed is 3/31
I REALLY NEED HELP WITH THIS
Cecil started from Point A and moved according to the expression 10 + (−5) + 19 + 6 + (−19) + 5 + (−10). What one additional step
does Cecel need in order to return to the starting point?
The number of steps in order to return to the starting point will be negative 16.
What is a number line?A number line refers to a straight line in mathematics that has numbers arranged at regular intervals or portions along its width. A number line is often shown horizontally and can be postponed in any direction.
Cecil started from Point A and moved according to the expression 10 + (−5) + 19 + 6 + (−19) + 5 + (−10).
Let 'x' be the number of steps in order to return to the starting point. Then the equation is given as,
x + 10 + (−5) + 19 + 6 + (−19) + 5 + (−10) = 0
Simplify the equation, then the equation is given as,
x + 10 − 5 + 19 + 6 − 19 + 5 − 10 = 0
x + 40 − 24 = 0
x + 16 = 0
x = − 16
The number of steps in order to return to the starting point will be negative 16.
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An ice cream shop sells a small bowl of ice cream for $2.25 and a large bowl for $3. One day, the shop sold 63 bowls of ice cream and made $159. How many of each size bowl did the shop sell?
The number of small size and large size bowls of ice cream sold in the shop is 40 and 22 respectively.
How to determine the number of each bowl size sold?let
Number of small bowl = x
Number of large bowl = y
x + y = 63
2.25x + 3y = 159
From (1)
x = 63 - y
Substitute into (2)
2.25x + 3y = 159
2.25(63 - y) + 3y = 159
141.75 - 2.25y + 3y = 159
- 2.25y + 3y = 159 - 141.75
0.75y = 17.25
divide both sides by 0.75
y = 17.25 / 0.75
y = 23
Substitute y = 23 into (1)
x + y = 63
x + 23 = 63
subtract 23 from both sides
x = 63 - 23
x = 40
In conclusion, The ice cream shop sold 40 small size bowls and 23 large size bowls
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the ratio of the four sides of a trapezoid is 2:1:1:1 the area of the trapezoid is 27sqrt(3) find the length of the median of the trapezoid
Answer:
9
Step-by-step explanation:
;)
During a class trip to an apple orchard, a group of
students picked 2436 apples. They packed them into
6 boxes to take to the local food bank. If each box
held the same number of apples, how many apples
were in each box?
2) 46
3) 460
4) 406
5) 14,616
The answer is 406 apples.
2436 apples divided by 6 boxes gives you the number of apples in each box.
A cylindrical can with height 12 cm has capacity 600 mL. What is its radius, to the nearest millimetre? [Remember that 1 mL = 1 cm³.]
The required radius of the cylindrical can is 4 millimeters.
What is cylinder?A cylinder is a three-dimensional solid in mathematics that maintains, at a given distance, two parallel bases connected by a curving surface. These bases often have a circular form (like a circle), and a line segment known as the axis connects the centers of the two bases.
Given that,
The height of the cylinder h = 12 cm.
And volume of the cylinder v = 600 mL
Since, 1 mL = cm³
The volume v = 600 cm³.
Let radius of cylinder is r,
To find the radius, use formula,
Volume of cylinder V = π x r² x h
22/7 x r² x 12 = 600
22/7 x r² = 50
r² = 350 / 22
r² = 15.909
r = 3.98
or r = 4 millimeters.
The radius of the cylinder is 4 millimeters.
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Pat and Sandy took a break for lunch.
They spent of an hour resting and
of an hour eating. What fraction
of an hour was their break?
Answer:
50%
Step-by-step explanation:
I’m so smart fr
HELP please last question for sparx due at midnight :)) i’ll give brainiest
Check the picture below.
so let's check the middle of the picture, inscribed angle "b" is intercepting the purple arc, wait a second!!! angle 22° is intercepting the same arc! ahaaa!.
now let's check the right of the picture, inscribed angle "a" is intercepting that brown arc, wait a second!!! angle 45° is intercepting the same arc!! ahaa!!.
well, you can see what's "c" and "d".
Point A has coordinates
(-4, -2). Point B has
coordinates (6, 3). Find the coordinates of
point P on directed line segment AB that
partitions AB so that AP: AB is 3:5.
what percent of twenty is 11
Answer:
55%
Step-by-step explanation:
first, you set up the problem as two fractions: 11 is to 20 as x is to 100. you cross multiply the 11 and 100, then divide that by 20 which gives you 55, which you divide by 100 for the percentage answer.
PLEASEEEEHELP OMG
I NEED THE ANSWER ASAPAPPAPP
Answer:
A- negative
B-positive
C- zero
Step-by-step explanation:
Going up= positive
Going down= negative
Horizontal line= zero
vertical line= undefined
Which sentence contains an allusion?
A. The cat went as still as a statue as the bird drew dangerously close.
B.The shower spit in anger whenever someone tried to run hot water
C. She had a thousand questions to ask the senator, but time was up.
D. Let me see if I can Thomas Edison my way out of this situation.
what is the probability that a randomly selected person will have a birthday in august? assume that this person was not born in a leap year. express your answer as a simplified fraction or a decimal rounded to four decimal places.
the probability of a randomly selected person having a birthday in August is 1/12 or 0.0833 rounded to four decimal places.
The probability of a randomly selected person having a birthday in August is 1/12. There are 12 months in a year and August is one of them. Therefore, The probability of a randomly selected person having a birthday in August is 1/12 because there are 12 months in a year and August is one of them. Each month has an equal chance of being chosen since they all have the same number of days. This probability remains the same regardless of whether or not it is a leap year. Therefore, the probability of a randomly selected person having a birthday in August is 1/12 or 0.0833 rounded to four decimal places.The probability of a randomly selected person having a birthday in August is calculated by dividing the number of days in August (31) by the total number of days in a year (365). This works out to be 1/12 or 0.0833 rounded to four decimal places.
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How do I do y=mx+b in these type of questions
1. y<-3/4x+2
2. y≤5
3. x+y>6
With linear inequalities in two variables, you still have y=mx+b and it still tells you the same thing.
The inequality portion adds two additional layers on top of the y=mx+b line.
If the inequality is > or <, then you draw the line as a dashed line.
If the inequality is ≥ or ≤, then you draw the line as a solid line.
The difference is that points on the > or < line do NOT make the inquality true, while points on the ≥ or ≤ line do.
The other piece is that all the points on one side of the line will also make the inequality true.
If you have "y>mx+b" or "y≥mx+b", then you shade above the line.
If you have "y<mx+b" or "y≤mx+b", then you shade below the line.
So there are three parts:
1. Where is the line?
2. Is the line solid or dashed?
3. Do you shade above or below the line?
The three graphs are attached.
Is 3 : 9 and 6 : 36 equivalent ratios?
Answer: False
Step-by-step explanation: they are not the same because if you times 3:9 ratio times 2 then it makes it 6 and 18 and does not make 6 : 36
Your welcome - your friend green
How do you solve the following:
−3+ |n-2 | >5
Please help!!!!
Step-by-step explanation: To solve this inequality, we can first isolate the absolute value term on one side of the inequality by subtracting |n-2| from both sides of the inequality. This gives us the inequality -3 + |n-2| > 2. Then, we need to consider two cases: when |n-2| is positive and when |n-2| is negative.
If |n-2| is positive, then we can drop the absolute value bars and rewrite the inequality as -3 + (n-2) > 2. Solving this inequality, we find that n > 7.
If |n-2| is negative, then we must reverse the direction of the inequality because subtracting a negative number is the same as adding a positive number. This gives us the inequality -3 - (n-2) > 2. Solving this inequality, we find that n < -1.
Therefore, the solution to the inequality is the set of all numbers that are greater than 7 or less than -1, which is the interval (-1, 7).
What is 6/2(19x6+17)
In it's first four games, a netball team scores an average of 31 points per game. After the fifth game, the average for the first five games is 30. How many points did the team score in the fifth game?
The netball team scored 26 points in their fifth game.
What is the arithmetic mean or average?Arithmetic mean or average can be obtained by adding all the given values and then dividing the total sum by the number of values.
Let x be the no. of points the netball team scores in the fifth game.
∴ (31 + 31 + 31 + 31 + x)/5 = 30.
(124 + x)/5 = 30.
124 + x = 150.
x = 26.
So, They scored 26 points in their fifth game.
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i have no clue how to do this please help me out :))
Answer:
∆QRS / ∆XZY = 1/2
Step-by-step explanation:
You want the similarity ratio of ∆QRS to ∆XZY. Side lengths are marked in the diagram.
The similarity ratio will be the ratio of two corresponding side lengths.
Corresponding sidesYou can find corresponding sides several ways:
Use the similarity statement to identify corresponding vertices. A side will be defined by 2 of them. Use vertex identifiers that are in the same positions in both triangle names: QR : XZ (first two vertices listed), for example.Use the markings in the figure to identify corresponding sides. Corresponding sides will have the same angle marks at either end. For example, the side marked 1 in ∆QRS has 1-arc and 3-arc angle markings at its ends. The side marked 2 in ∆XZY also has 1-arc and 3-arc angle markings at either end. It will be the corresponding side.Use side lengths. When both triangles have their side lengths sorted into increasing order, the corresponding numbers are corresponding sides. The side lengths in ∆QRS are {1, 2, 2}. In ∆XZY, they are {2, 4, 4}.The ratios of corresponding sides are 1:2, 2:4, and 2:4. The 2:4 ratios reduce to 1:2, which is the answer you're looking for. Written as a fraction, the ratio is ...
1/2 . . . . ratio of ∆QRS to ∆XZY
guys pls help!! i really need help on these two questions
In order to prove the opposite sides are congruent, the two diagonals of parallelogram ABCD needed.
The given quadrilateral WXYZ is a parallelogram.
What is a parallelogram?A parallelogram is a quadrilateral with opposite sides parallel.
The quadrilateral ABCD have congruent opposite sides only when the diagonals are bisect.
Given that the diagonals of quadrilateral WXYZ intersect at point R.
Since the R is the midpoint.
The opposite sides are equal and opposite angles are equal.
Hence we can say that the given quadrilateral WXYZ is a parallelogram.
Similarly, in order to prove the opposite sides of the parallelogram ABCD is congruent, both diagonal required.
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When do I divide in right trigonometry
The answer to this question which is based on Trignometry is that we divide when we want to calculate Trignometric Ratios
How many Trignometric ratios are available?
There are six basic trigonometric ratios: sine (sin), cosine (cos), tangent (tan), cotangent (cot), secant (sec), and cosecant (csc). These ratios are used to calculate angles and sides of a right triangle.
Whenever we need to calculate Trignometric ratios we have to divide the length of 2 sides of a triangle and one more the Trignometric ratios can be only found in Right Angled triangle
Hence we can just find the Trignometric ratios for any Triangle we can only do it for right Triangles
The values of Trignometric ratios can be negative also and it depends on the angle for which we want to find the Trignometric ratios.
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What is the simplified form of the expression the quantity x squared plus 10x plus 21 end quantity divided by 4 times the quantity x plus 3 end quantity?
the quantity x minus 7 end quantity divided by 4 the quantity x plus 7 end quantity divided by 4 the quantity x plus 7 end quantity divided by quantity x plus 3 end quantity the quantity x minus 7 end quantity divided by quantity x plus 3 end quantity
Answer:
[tex]\frac{x+7}{4}[/tex]
(B) is your answer :)
Step-by-step explanation:
do you need me to work it out?
Answer:
b
Step-by-step explanation: took the test
A small coffee shop sells a variety of different pastries and treats. The banana bread is sold
by the loaf, and each loaf is sold for the same price. The cookies are sold by the dozen, and
each dozen is sold for the same price.
On Friday, the bakery collected $260 from selling 40 loaves of bread and 35 dozen cookies.
On Saturday, the bakery collected $360 from selling 64 loaves of bread and 42 dozen
cookies.
At what price does the bakery sell each item for?
Using system of linear equations, the price of bread is $3 and cookies is $4
System of Linear EquationThe system of linear equations is the set of two or more linear equations involving the same variables. Here, linear equations can be defined as the equations of the first order, i.e., the highest power of the variable is 1.
Let;
x = bread y = cookiesWe can write a system of linear equation with this;
40x + 35y = 260 ....eq(i)
64x + 42y = 360 ...eq(ii)
Solving equation (i) and (ii)
The value of x is 3 and y is 4
This shows that the price of bread is $3 and cookies is $4
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Write an equation in slope-intercept form of the line that is perpendicular to the one given and passes through the given point. (4,8); y=-2x - 4
An equation in slope-intercept form of the line perpendicular to y = 2x-4
is y =(-1/2)x+10.
What are lines and their slopes?We are aware that there are many types of equations for lines, with the
general type being Ax+ By + C = 0, and the slope-intercept form equation
being y = mx + b.
m is the slope, and b is the y-intercept.
The y-intercept is the point (0,b) where the line intersects the y-axis when
x = 0, and the slope is the rate of change of the y-axis relative to the x-axis.
We are aware that the slopes of perpendicular lines are oppositely negative.
The slope of the given line, y = 2x-4, is 2.
Consequently, the given line will pass through point with a slope of (-1/2). (4,8).
∴8= (-1/2)(4)+b
8= -2+b
b = 10.
∴ y =(-1/2)x+10 is our required line.
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Selected values of the continuous function f are shown in the table below. Determine the validity of the following statement:
f(x)=0 has at least two solutionsin the interval {2,9}
True
False
could be true or false
Function may return true or false.
What does "continuous function" mean?A continuous function is one in which a continuous variation of the input (i.e., a change without a jump) results in a continuous modification of the function's value. This indicates that there aren't any discontinuities, or sudden changes in value.
Here, the function f(x) is continuous.
It follows that if x = 2 then f(x) = 3,
if x = 5 then f(x) = -9,
if x = 7 then f(x) = -15,
if x = 9 then f(x) = -13.
There are at least two solutions in the interval {2,9} for the graph of the function cross x axis f(x) = 0, hence it is not provided.
Therefore, it may be true or false.
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Dee chose A as the correct answer. What was her error? Answer in a complete sentence.
Number of square feet of wall painted in 1 hour is 243 square feet. Therefore, option C is the correct answer.
Given that, it takes Zach 10 minutes to paint [tex]40\frac{1}{2}[/tex] square feet of his bedroom wall.
What is the unitary method?The unitary method is a technique for solving a problem by first finding the value of a single unit, and then finding the necessary value by multiplying the single unit value.
Here, [tex]40\frac{1}{2}[/tex] square feet = 40.5 square feet
Rate at which he paints the wall =40.5/10
= 4.05 square feet per minute
As we know 1 hour =60 minutes
Now, number of square feet
= 4.05×60
= 243 square feet
Number of square feet of wall painted in 1 hour is 243 square feet. Therefore, option C is the correct answer.
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