The area of the rectangle is equal to b² · (b + 1) · (b + 0.628) · (b + 6.372).
What is the area of the rectangle?
The area of the rectangle is equal to the product of the height and the width, each of them represented by polynomials. In this question we must apply algebraic handling to simplify the product of the two polynomials:
A = h · w (1)
Where:
h - Heightw - WidthIf we know that h = b³ + b² and w = b² + 7 · b + 4, then the area of the rectangle is:
A = (b³ + b²) · (b² + 7 · b + 4)
A = b² · (b + 1) · (b + 0.628) · (b + 6.372)
The area of the rectangle is equal to b² · (b + 1) · (b + 0.628) · (b + 6.372).
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What is the slope of the line that contains the points (1, −9) and (−3, 3)?
3
−3
one third
negative one third
[tex](\stackrel{x_1}{1}~,~\stackrel{y_1}{-9})\qquad (\stackrel{x_2}{-3}~,~\stackrel{y_2}{3}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{3}-\stackrel{y1}{(-9)}}}{\underset{run} {\underset{x_2}{-3}-\underset{x_1}{1}}} \implies \cfrac{3 +9}{-4}\implies \cfrac{12}{-4}\implies -3[/tex]
Answer:
-3
Step-by-step explanation:
ya
Please help describe each transformation in order 1-3
Answer:
A translation 4 units right and 5 units down followed by a rotation of 90 degrees clockwise about the top left vertex of triangle 2
Jeffrey simplified the algebraic expression and made an error. Find and fix the mistake.
(-2x²y³)*(3.5xºy)
(-2x8y¹2)(3.5y12)
(-2.3.5) (x³)(y¹².y)
13 -7.5x8y¹3
Using exponent properties, the simplified expression is given as follows:
-7x²y^4.
What is the property for the multiplication of exponents?For multiplication of exponents, when two terms of same base but different exponents are multiplied, we have to do two steps:
Maintain the base as is.Add the exponents.If the exponents also have constants multiplying each other, the constants are multiplied.
For this problem, the two factors are given as follows:
-2x²y³ and 3.5x^0y.
Hence:
Multiplying the constants: -2 x 3.5 = -7.For the exponents of x, we have that: x^(2 + 0) = x².For the exponents of y, we have that: y^(3 + 1) = y^4.Multiplying each term found above, we have that that the simplified expression is given as follows:
-7x²y^4.
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What are the roots of the function f(x) = (log(3^x
) − 2 log(3)) - (x^
2 − 1) with x ∈ R
The sum of the angles of a regular hexagon is 720 degrees. Solve for x
Answer:
x = 32
Step-by-step explanation:
Measure of each interior angle of a regular hexagon is 120°-> (4x - 8)° = 120°-> 4x - 8 = 120-> 4x = 120 + 8-> 4x = 128-> x = 128/4-> x = 32Convert the following expression to scientific notation.
0.000000000001 =
Choice 'A'
Choice 'B'
Choice 'C'
Choice 'D'
1.0 × 10-12
10.0 × 10-12
10.0 × 10-10
1.0 x 1010
Answer:
none of them
Step-by-step explanation:
(X₁ + X₂)²
Find the square.
Show your work
Step-by-step explanation:
[tex]{ \purple{ \tt{(X₁ + X₂)²}}}[/tex]
This above problem is in the form of
[tex]{ \blue{ \tt{ {(a + b)}^{2}}}}[/tex]
where the expanded form of
[tex]{ \blue{ \tt {(a + b)}^{2}}} = { \green{ \bold{ {a}^{2} + {b}^{2} + 2ab}}} [/tex]
then the (X₁ + X₂)² answer will be
[tex]{ \purple{ \tt{(X₁ + X₂)²}}} = { \purple{ \tt{ {X₁}^{2} + {X₂}^{2} + 2X₁X₂}}}[/tex]
find an expression in terms of n for the nth term of this sequence, 15,19,25,33,43
Answer:
Hello,
Step-by-step explanation:
P(n)=ax²+bx+c (quadratic sequence)
with a=1,b=1,c=13
[tex]\\\boxed{u_n=n^2+n+13}\\[/tex]
Answer:
tₙ = n² + n + 13=============================
Given sequence:
15, 19, 25, 33, 43, ...We can see this not AP or GP as the difference or ratio of consecutive terms is not common.
But we can see the difference between terms has common difference of 2:
19 - 15 = 425 - 19 = 633 - 25 = 843 - 33 = 10and
10 - 8 = 28 - 6 = 26 - 4 = 2It means the sequence is of the second degree, in other words it is quadratic.
In general it is of the form:
tₙ = an² + bn + c, where a, b, c are coefficients, n - is the number of the terms.Use the terms of the given sequence to work out unknown coefficients.
t₀ = 15 - (4 - 2) = 15 - 2 = 13
a(0)² + b(0) + c = 13c = 13It gave us the value of c.
t₁ = 15
a(1)² + b(1) + c = 15a + b + c = 15a + b + 13 = 15a + b = 2t₂ = 19
a(2)² + b(2) + c = 194a + 2b + c = 194a + 2b + 13 = 194a + 2b = 6Compare the last two equations and solve for a and b:
a = 2 - b4(2 - b) + 2b = 68 - 4b + 2b = 62b = 8 - 62b = 2b = 1Then
a = 2 - 1 a = 1So we know the coefficients:
a = 1, b = 1, c = 13The nth term equation is:
tₙ = n² + n + 13What is the area of the composite figure whose vertices have the following coordinates? (2,-2), (2,1), (4,2), (6,2), (4,-1)
Enter your answer in the box.
__Units Sqared
The area of the composite figure whose vertices have the (2,-2), (2,1), (4,2), (6,2), (4,-1) coordinates is 6 square units
We first need to plot all the given points A (2,-2), B (2,1), C (4,2), D (6,2)and E (4,-1) which is coordinate geometry
After joining the Points which is a pentagon and it can be divided in two shapes one is triangle CDE and a quadrilateral ABCE
Using the distance formula
BC = [tex]\sqrt{(y2-y1)^{2}+(x2-x1)^{2} }[/tex] = [tex]\sqrt{(2-1)^{2} + (4-2^{2} }[/tex] = √5
Since BC = AE and BC ll AE , we can say ABCE is a parallelogram
area of a parallelogram = base × Altitude
= 2 × 2= 4
Area of triangle CDE where CD is perpendicular and CE is the base
= 1/2 ( 2×2)
= 1/2 (4)
= 2 square units
So the area of ABCDE = Area of ABCE + area of CDE
= 4 square units + 2 square units
= 6 square units
Hence, the area of the composite figure whose vertices have the (2,-2), (2,1), (4,2), (6,2), (4,-1)coordinates is 6 square units
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Which of the following would be the least consistent with a rising salt mass origin for the Arizona crater discussed in the textbook?
a) shattered rocks formed at very high pressures in the crater walls
b) a mass of salt beneath the crater
c)rock layers bent backward along the rim of the crater
The option that will be the least consistent with a rising salt mass origin for the Arizona crater discussed in the textbook is C. rock layers bent backward along the rim of the crater.
How to illustrate the information?It should be noted that the solidified magma that lie under the create flow will be consistent with the volcanic origin.
In this case, the option that will be the least consistent with a rising salt mass origin for the Arizona crater discussed in the textbook is the rock layers bent backward along the rim of the crater.
In conclusion, the correct option is C.
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60 as product of prime factors
Answer:
[tex] {2 }^{2} \times 3 {}^{1} \times 5[/tex]
PLS HELLP!!
Which expression is equivalent to sum of quantity negative three and one third times n plus one sixth end quantity plus quantity one and three sixths times n minus three twelfths end quantity?
negative twenty nine sixths times n minus one twelfth
negative twenty nine sixths times n plus one twelfth
negative eleven sixths times n minus one twelfth
negative eleven sixths times n plus five twelfths
The equivalent expression is negative eleven sixths times n minus one twelfth. Option C
What are algebraic expressions?Algebraic expressions are expressions that comprises of variables, terms, constants, coefficients and factors.
They are also made up of arithmetic operations such as division, multiplication, addition, subtraction, bracket, etc.
Equivalent expressions are expressions with the same solution but different arrangement of elements.
Given the expression
{ -3 1/3n + 1/6} + { 1 3/6n - 3/12 }
expand the bracket
-3 1/3n + 1/6 + 1 3/6n - 3/12
collect like terms
-10/3n + 1/6 + 9/6n - 3/12
-10/3n + 9/6n + 1/6 - 3/12
find the lowest common multiple
-20n + 9n/6 + 2 - 3 /12
-11n/6 - 1/12
Thus, the equivalent expression is negative eleven sixths times n minus one twelfth. Option C
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2) Use three functions above to evaluate the following: input f(x)=x-3_soupat f(3) = -3 p(0) = p(x)=0, x= function p(-4)= x/g(x) p(x)=5, x= 5 2 -3 f(x)=12, x=-4 f-3 = 12 -3 36207 g(-3)= p(1)= | p(3)= g(x)= -3, x = 95 = -3 p(x)=1, x= p(x)=2, x=
Answer:
f(3) = 3 - 3 --> f(3) = 0
f(x) = 12, x = 15 (because 15 - 3 would equal 12)
g(-3) = 2 (because in the chart for g(x), an x of -3 is 2)
g(x) = -3, x = 5 (because in the chart for g(x), a g(x) of -3 is an x of 5)
For the graph questions, p(0)= means that the 0 is the x integer and you must find the y when x=0
p(0) = 3
p(-4) = 5
p(1) = 3
p(x) = 1, x = 2
For the graph questions, p(x)=0 means that the 0 is the y integer and you must find the x when y=0
p(x) = 0, x = 2.5
p(x) = 5, x = -4
p(3) = -1
p(x) = 2, x = 1.5
I need to find the missing angles
Answer:
g=93 h=87 k=122 m=58
Step-by-step explanation:
Employees in 2012 paid 4.2% of their gross wages towards social security (FICA tax), while employers paid another 6.2%. How much will someone earning $39,000 a year pay towards social security out of their gross wages?
Someone who is earning $39,000 a year, would pay $1,638 towards social security out of their gross wages
Employees in 2012 paid 4.2% of their gross wages towards social security tax.
As the gross yearly wages of an employee is $39,000 and he have to pay the 4.2% of his gross wages towards social security or FICA tax.
Percentage means division by 100 and to know the contribution of the employee we need to multiply the percentage with the gross wages of the employee
He paid towards social security = 4.2% of 39000
= 4.2/100×39000
= 0.042 × 39000
= $1,638.00
He would pay $1,638 towards social security tax out of their wages.
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A garden store Sells bags of potting soil in flats. There are 7 Bags in each flat . each palette has 7 flats the garden store sold 17 pallets on Saturday and 23 How many bags of potting soil did the gardner sell in all ?
The garden store was able to sell a total of 1,960 bags of potting soil on Saturday and Sunday.
What is distributive property of multiplication over addition ?
If we multiply a number by the sum of more than two, we use the distributive property of multiplication over addition.
In order to find the number of bags of potting soil sold over those two days, the first step is find out the number of pallets store sold there potting soil :
= 17( on Saturday) + 23 (Sunday)
= 40 palettes
Each palettes has 7 flats so the total number of flats sold is:
= 40 x 7
= 280 flats
Each flat then contains 7 bags so the total number of bags sold is:
= Number of flats sold x 7
= 280 x 7
= 1960 bags
In conclusion 1,960 bags of potting soil were sold.
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Instead of raising the number to a second power, he doubled it. His 2 digit answer had the same digits as the correct answer but in reverse order. What was the correct answer
Answer: 81 ==> correct answer
Step-by-step explanation:
n=number
n^2+n*2=n*11 ==> the sum of a 2 digit number and the reverse of the two digit number is a multiple of 11. For example, 21+12=33. 33/11=3, so 33 is a multiple of 11.
n*n+2n=11n
n(n+2)=11n
n+2=11
n=9
n^2=
9^2=81 ==> correct answer
Which number rounds to 42.7 when rounded to the nearest tenth? (10 points)
a 42.07
b 42.62
c 42.64
d 42.73
Answer:
d 42.73
Step-by-step explanation:
if you were to round off the first 3 you wouldn't get 42.7 due to them not being above 5, but, if you were to round off 42.73 you would get 42.7 due to 3 being lower than 5 and it changing into 0
Dontavious has a box of colored pencils. He uses 53 pencils and has 118 pencils left in the box. Write an equation showing how many pencils are in the box before he starts drawing.
53 + p = 118
118 + p = 53
p − 53 = 118
p = 118 − 53
An equation showing the number of pencils that are in the box before he starts drawing is p - 53 = 118.
We are given that:
Dontavious has a box of colored pencils.
Dontavious uses 53 pencils.
Pencils still left in the box = 118.
Let the total number of pencils in the box be p.
So, the equation representing the situation given will be:
p - 53 = 118
As from p pencils, 53 pencils have been used and 118 pencils still remain at the end.
Therefore, we get that, an equation showing the number of pencils that are in the box before he starts drawing is p - 53 = 118.
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Which of the following represents an INEFFICIENT point of production?
a. Point A
b. Point B
c. Point D
d. None
e. Point C
The point that represents an INEFFICIENT point of production is point A.
The correct answer is an option (a)
In this question we have been given a graph of Skateboards vs. Bikes.
We need to find the point that represents an INEFFICIENT point of production.
Inefficient production means the economy can be producing more goods without using any additional resources.
In given production possibility curve, an INEFFICIENT point of production is point A.
Therefore, the point that represents an INEFFICIENT point of production is point A.
The correct answer is an option (a)
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I really need help from someone please
Answer:
b
Step-by-step explanation:
Use the graph of the function to find its domain and range. Write the domain and range in interval notation.
Pls someone help me asap
Answer:
Domain: (-infinity, 5]Range: [-6, infinity)Step-by-step explanation:
The domain is the set of x values and the range is the set of y values.
what have the same solution as 3x - 12 = 24
Answer: 12
add 12 to the left side to cancel out the -12 then add 12 to 24 to get 36, then divide 3x from 36 to get 12 (x=12)
Find the value of k the diagram is not to scale
○ 42
○ 70
○ 118
○ 58
Answer:
70
Step-by-step explanation:
We can actually solve this based on two “rules” that are present in triangles and lines.
The first rule is that the three angles inside a triangle will always add up to 180.
In this case, we have 2 out of 3 angles given like so: 52 + 58 + k = 180
Solve for k and that gives 70
Another rule that reinforces this is that a straight line will have an angle of 180 degrees. With the 180 that is given, we can solve for k again using: 110 + k = 180
Answer:
70°
Step-by-step explanation:
Total angles of a triangle = 180°
Then, 180° = 58° + 52° = k
➟ 180° = 58° + 52° = k
➟ 180° - 180° + k =180° - (58° + 52°)
➟ k = 180° - 110°
➟ k = 70°
the actual length of a teacher's table is 1.42m and its width is 2m. ashiru wishes to find out how accurate he can measure using a meter rule. he measures the length of the table to be 1.38m and it's width to be 0.98m
The area of rectangle is 1.42×2=2.84
Given,
The area of rectangle is 1.42×2=2.84
The length of rectangle is 1.38×.98=1.3524
A rectangle is a quadrilateral with equal angles and opposing sides that are equal and parallel. There are several rectangle items all around us. Each rectangle form is distinguished by two dimensions: length and breadth. The length of the rectangle is the longer side, while the width is the shorter side. We will study about the rectangle form and its features in this chapter.
The rectangle is a four-sided closed two-dimensional shape. A rectangle's opposite sides are equal and parallel to one other, and all of its angles are equal to 90°.
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Which of the following is not an example of an experiment? Multiple choice question.
Picking a team that will win the World Series.
Selecting a card from a deck of cards.
Pick the team that won last year's World Series.
Buying a computer based on repair history.
The answer option which is not an example of an experiment is to: C. pick the team that won last year's World Series.
What is an experiment?An experiment can be defined as a scientific investigation which typically involves the process of manipulating an independent variable (the cause), so as to determine or measure the dependent variable (the effect).
In this scenario, some examples of an experiment include the following:
"Picking a team that will win the World Series.""Selecting a card from a deck of cards.""Buying a computer based on repair history."In conclusion, "picking the team that won last year's World Series" is not an example of an experiment because it does not connote a scientific investigation or observation
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Please Help ASAP!!!!!!
It should be noted that sbsolute risk is the probability of an event.
How to illustrate the information?It should be noted that absolute risk is used for the number of events which occurred in a group which is divided by the number of people in that group.
The response variable is the focus of a question in the experiment and an explanatory variable is one which explains changes in that variable.
The types of bar graph include:
Vertical Bar Graph: It represents the grouped data in a vertical form.Horizontal Bar Graph: It represents grouped data horizontally. Stacked Bar Graph: Every bar in the graph is a whole, while the segments in the bar are the different parts of that whole.The steps involved for the pie chart include:
Convert the data to percentages.Calculate the angle for each pie segment.Draw the pie chart.Learn more about probability on:
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5. Which value is an integer but not a whole
number?
A. 75%
B. 5¹.10
C. √20
D. -4³/16
Answer: √20
Step-by-step explanation:
The square root of 20 is 4.47213595 which is a decimal and not a whole number.
Fairfield Company’s raw materials inventory transactions for the most recent month are summarized here:
Beginning raw materials $ 20,000
Purchases of raw materials 90,000
Raw materials issued
Materials requisition 1445 25,000 For Job 101
Materials requisition 1446 35,000 For Job 102
Materials requisition 1447 30,000 Used on multiple jobs
Required:
How much of the raw materials cost would be added to the Work in Process Inventory account during the period?
How much of the raw materials costs would be added to the Manufacturing Overhead account?
Compute the ending balance in the Raw Materials Inventory account.
direct materials?
indirect materials?
ending balance?
The direct and indirect material costs and the ending balance will be $60,000, $30,000, and $20,000, respectively.
What is direct and indirect material cost, and ending balance?The most recent month's raw resources supply operations for Fairfield Business are listed here:
Beginning raw materials $ 20,000
Purchases of raw materials 90,000
Raw materials issued
Materials requisition 1445 25,000 For Job 101
Materials requisition 1446 35,000 For Job 102
Request for Materials 1447 30,000 used for a variety of jobs
The direct material cost is given as,
The direct raw materials used are the sum of the Materials requisition 1445 For Job 101 and Materials requisition 1446 For Job 102.
Direct raw materials used = $25,000 + $35,000
Direct raw materials used = $60,000
The indirect material cost is given as,
Amount to add to the Manufacturing Overhead account = Indirect materials used = $30,000
The ending balance is given as,
Ending raw materials balance = Beginning raw materials + Purchases of raw materials - Direct raw materials used - Indirect materials used = $20,000 + $90,000 - $60,00 - $30,000 = $20,000
The direct and indirect material costs and the ending balance will be $60,000, $30,000, and $20,000, respectively.
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9-3-3-3 = 0 written as a division problem
The value of 9-3-3-3=0 written as division problem is the value of 0.333
According to the Honor algebra:
The symbols for variables used in algebra, which may be found in Greek and Latin literature, can be used to date the creation of algebra to the height of Greek or Latin culture.
9-3-3-3=0 as written as division
⇒ 9÷3÷3÷3 =0
⇒ 9÷3 =3÷3
⇒ 3=1
⇒ x=1/3
⇒ x=0.333
so, the value of 9 divide by 3 and divided by 3 equals to 3 divvied by 3 is the value of 0.333.
When things are more realistic, algebra becomes much more intriguing. With a two-pan balance, some mystery bags, and a ton of jelly beans, solving linear equations is much more enjoyable.
Therefore, the 9-3-3-3=0 written as division is the value of 0.333.
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