The factοrs οf the expressiοn is 4x(2xy+3y-4z).
What is factοrizatiοn?Tο factοrise an algebraic statement, we first identify the terms' highest cοmmοn factοrs and then arrange the terms intο grοups in accοrdance with thοse grοups. In plain English, factοrizatiοn is the prοcess thrοugh which an algebraic expressiοn gets expanded in the οppοsite directiοn.
Here the given expressiοn is ,
=> [tex]8x^2y+12xy-16xz[/tex]
Nοw factοrizing the given expressiοn then,
=> 4×2×x×x×y+4×3×x×y-4×4×x×z
=> 4x(2xy+3y-4z)
Hence the factοrs οf the expressiοn is 4x(2xy+3y-4z).
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The sum of twice a number,n, and 14 is 30. Write an equation that models this statement.Then explain how you might use reasoning to find the value of n.
Answer:
2n + 14 = 30
Step-by-step explanation:
Since you know that 2n + 14 = 30, we can determine the values by first subtracting 14 from 30. Our equation would then be 2n = 16. Divide 2 from both sides and n = 8.
This model represents the total on the top and the 2 parts on the bottom.
Which two statements best describe Michael’s height while on the two roller coasters?
It switches between negative and positive every 40 seconds. it switches between positive and negative every 80 seconds. So correct statements are B and E.
Describe Algebra?Mathematics' branch of algebra deals with symbols and the formulas used to manipulate them. It is an effective tool for dealing with issues involving mathematical expressions and equations. In algebra, variables—which are typically represented by letters—are used to represent unknowable or variable quantities.
Equations represent mathematical relationships between variables in algebra. An equation is made up of two expressions, one on either side of an equal sign, separated by an equation. Algebraic expressions can involve constants, variables, and mathematical operations such as addition, subtraction, multiplication, and division.
As we can see from the first roller coaster's graph, Michael's height changes from positive to negative after 40 seconds, whereas it was positive for the first 40. It remains negative between 40 and 80 seconds. It continues to be positive from 80 to 120, and so forth.
As a result, every 40 seconds it alternates between negative and positive.
B is accurate.
We can see from the second roller coaster's table that it stays positive from 0 to 80. It continues to be negative from 80 to 160, and so forth.
As a result, every 80 seconds it alternates between positive and negative.
E is accurate.
The complete question is:
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A bank account gathers compound interest at a rate of 5% each year. Another bank account gathers the same amount of money in interest by the end of each year, but gathers compound interest each month. If Abraham puts £4300 into the account which gathers interest each month, how much money would be in his account after 2 years and 5 months? Give your answer in pounds to the nearest 1p.
Answer:
$6235 1
' 1 . ' 8
Answer:
Step-by-step explanation:
what is the solution to this
Answer:
-2
Step-by-step explanation:
The proof shows that ABCD is a rhombus. Which of the following is the
missing reason?
A. Reflective property
B. Symmetric property
C. Transitive property
D. Addition property
The correct answer is B. Symmetric property.
The symmetric property states that if a = b, then b = a. In the context of geometry, this property can be used to show that if one side of a figure is congruent to another side, then the second side is also congruent to the first. In the case of the given proof, it is possible that the symmetry of the figure is used to show that opposite sides of the rhombus are congruent.
The reflective property (A) is not typically used to prove that a figure is a rhombus, as it relates to the reflection of a figure across a line. The transitive property (C) and the addition property (D) are also unlikely to be used in this context, as they relate to the properties of equality and addition, respectively, rather than geometric properties of figures.
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Dave bought a new game for $28. The tax rate was %7. How much was the tax and the total price?
The tοtal price οf the game including tax is $29.96.
What are the variοus types οf taxes?Physical assets such as prοperty and transactiοns such as the sale οf stοck οr a hοme are subject tο taxatiοn. Taxes include incοme, cοrpοrate, capital gains, prοperty, inheritance, and sales taxes.
Because the tax rate is 7%, the tax amοunt is 7% οf the purchase price. Tο calculate the tax, multiply the purchase price by the tax rate expressed as a decimal:
0.07 x $28 = $1.96 in taxes
As a result, the purchase tax is $1.96.
Tο calculate the tοtal price, add the purchase price and the tax:
Purchase price + Tax = Tοtal Price
Tοtal cοst: $28 + $1.96 = $29.96
As a result, the tοtal cοst οf the game, including tax, is $29.96.
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Who knows this? I need help
#16
Answer:
Step-by-step explanation:
adjacent: [tex]\angle BOC, \angle EOD[/tex] (both are adjacent)
complementary: [tex]\angle BOC[/tex]
supplementary: [tex]\angle EOD[/tex]
vertical angles: [tex]\angle AOE[/tex]
Ice cream is packaged in cylindrical gallon tubs. A tub of ice cream has a total surface area of 183.69 square inches.
If the diameter of the tub is 6 inches, what is its height? Use π = 3.14.
A 2.25 inches
B 4.5 inches
C 6.75 inches
D 12.75 inches
Answer:
6.75 inches.
Step-by-step explanation:
[tex]183.69 = 2*3.14*3^2 + 2*3.14*3*h[/tex]
[tex]= 56.52 + 18.84h[/tex]
[tex]183.69 - 56.52 = 18.84h[/tex]
[tex]127.17 = 18.84h[/tex]
[tex]=\frac{127.17}{18.84}[/tex]
[tex]=6.75[/tex]
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Which of the following choices lists the values of the side lengths of a triangle with 45-45-90 degree angles and a leg = 5?
A) 5, 5, 5
B) 5, 1, 5
C) 1, 5, 5
D) 1, 1, 5
The side lengths of such a triangle with a leg length of 5 and angles of 45, 45, and 90 are not listed in any of the options.
Explain about property of the right triangles?The right angle is established when 2 straight lines cross at a 90° angle or when they are perpendicular at the intersection. The symbol is used to indicate a right angle.
A triangle's (of all varieties) cumulative sum of angles is 180°.The length of a triangle's two longest sides added together is longer than for third side.Similar to this, the length of a third side of a triangle's third side is shorter than the difference between its two sides.For the given question:
Triangle with degree angles - 45-45-90
It means two legs are of same length 5 units.
Then, hypotenuse H will be:
H² = 5² + 5²
H² = 25 + 25
H² = 50
H = 5√2
Thus, the correct third side of the triangle will be 5√2.
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88.128 x 0.5 Multiplication question
Answer:
44.064x
Step-by-step explanation:
Answer: when you time 88.128 by 0.5, it gives you an answer of 44.064
Hope this helps :)
To amend a country’s constitution, 7/9 of the 84 states in that country must approve the amendment. If 66 states approve the amendment, will the constitution be amended?
Answer:
Since only 66 states approve the amendment, it falls short of the required 7/9 majority. Therefore, the constitution will not be amended.
Step-by-step explanation:
To determine whether the constitution will be amended, we need to compare the number of states that have approved the amendment to the required number of states needed for approval.
The requirement is that 7/9 of the 84 states must approve the amendment. So, we need to calculate 7/9 of 84 to find out how many states need to approve the amendment:
(7/9) x 84 = 66.67
Rounding up, we see that 66.67 is equivalent to 67 states. This means that in order for the amendment to be approved, at least 67 states must approve it.
Since only 66 states approve the amendment, it falls short of the required 7/9 majority. Therefore, the constitution will not be amended.
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The value of M is
A) 14
B) 18
C) 20
D) 28
Answer:
I got 28
Step-by-step explanation:
use the formula k=y/x. 6/8=0.75
21/0.75=
What is the inverse of each statement below: Be sure to label your
answers as a, b, c, and d.
a.) Add 25
b.) Divide -18
c.) Subtract 3
d.) Multiply 14
The term “inverse” in mathematics generally refers to an operation that undoes or reverses another operation. However, the phrase "inverse of maths tools" doesn't really make sense because “maths tools” is not a specific mathematical operation.
What is the inverse of maths tools?Mathematical tools can refer to various instruments or techniques used in mathematics, such as calculators, rulers, compasses, graph paper, software, etc. Each of these tools has its own purpose and may or may not have an inverse operation or tool associated with it.
For example, the inverse of addition is subtraction, the inverse of multiplication is division, and the inverse of differentiation is integration. However, it's not clear what the inverse of a “maths tool” would be.
Therefore, a) The inverse of “Add 25” would be “Subtract 25.”What is the b) The inverse of “Divide -18” would be “Multiply -18.” c) The inverse of “Subtract 3” would be “Add 3.” d) The inverse of “Multiply 14” would be “Divide 14.”
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The function S=m^(2)+6m+8 models the growth of book sales in m months, where S is an amount in thousands of dollars. In how many months do book sales reach $80,000 ?
Answer:
We are given the function S = m^2 + 6m + 8 which models the growth of book sales in m months, where S is an amount in thousands of dollars. We want to find in how many months book sales reach $80,000.
We can set up an equation as follows:
S = m^2 + 6m + 8 = 80
Subtracting 80 from both sides, we get:
m^2 + 6m - 72 = 0
We can factor this quadratic equation as:
(m + 12)(m - 6) = 0
This gives us two possible solutions:
m + 12 = 0 or m - 6 = 0
Solving for m in each case, we get:
m = -12 or m = 6
Since we are looking for a number of months, we can discard the negative solution.
Therefore, book sales reach $80,000 in 6 months.
So, the answer is: 6 months.
The surface area of a cylinder is given by the formula SA = 2r2 + 2rh. A cylinder has a radius of 12 cm and a surface area of 1,632 cm^2 . Find the height of the cylinder.
A. 52 cm
B. 56 cm
C. 59 cm
D. 34 cm
In ΔLMN, n = 27 inches, l = 70 inches and ∠M=149°. Find ∠N, to the nearest degree.
Using trigonometric functions, we can find that the value of the angle N is 3°.
What are trigonometric functions?The six fundamental trigonometric operations make up trigonometry. Trigonometric ratios are useful for describing these methods. The sine, cosine, secant, co-secant, tangent, and co-tangent functions are the six fundamental trigonometric functions. On the ratio of a right-angled triangle's sides, trigonometric identities and functions are founded. Trigonometric formulas are used to determine the sine, cosine, tangent, secant, and cotangent values for the perpendicular side, hypotenuse, and base of a right triangle.
Here, using the cosine theorem:
CosM = n² + l² - m²/2nl
⇒ Cos 149° = 27² + 70² - m²/2 × 27 × 70
⇒ -0.981 = 729 + 4900 - m²/3780
⇒ 5629 - m² = -3708
⇒ m² = 9337.
Now Cos N = m² + l² - n²/2ml
= (9337 + 4900 - 729) / (2 × √9337 × 70)
= 0.9985
Cos N = 0.9985
Putting [tex]Cos^{-1}[/tex] on both sides:
[tex]Cos^{-1}[/tex] Cos N = [tex]Cos^{-1}[/tex] 0.9985
⇒ N ≈ 3°
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The complete question is:
In ΔLMN, n = 27 inches, l = 70 inches and ∠M=149°. Find ∠N, to the nearest degree.
75909931 rounded to the nearest hundred thousand
Answer:
the answer is supposably 75900000
Rachel ran 3 miles when she was training for a race. How many feet did she run?
15,840 feet
5,280 feet
10,560 feet
14,840 feet
To convert miles to feet, we need to multiply the number of miles by the number of feet in one mile. There are 5,280 feet in one mile. So, to find out how many feet Rachel ran, we can multiply 3 miles by 5,280 feet/mile:
3 miles x 5,280 feet/mile = 15,840 feet
Therefore, Rachel ran 15,840 feet. Answer: 15,840 feet.
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Answer:
The notation Σ-2 (3η + 5) is incorrect for representing the arithmetic series 8 + 11+ ... + 29.
The correct notation for the arithmetic series 8 + 11 + ... + 29 should be:
Σ_{i=1}^{11} (6i + 2)
The series has 11 terms, and each term can be found by adding 3 to the previous term, starting with the first term 8. Therefore, the general form of the series is 6i + 2, where i represents the index of the term in the series.
In contrast, the notation Σ-2 (3η + 5) appears to have multiple errors. The use of a negative index (-2) is not valid, as the index should start from 1 or 0. Also, the use of the Greek letter eta (η) instead of i as the index variable is unconventional and likely to cause confusion. Finally, the expression inside the parentheses does not appear to correspond to the terms of the arithmetic series.
The correct notation for the arithmetic series 8 + 11 + ... + 29 should be:
Σ_{i=1}^{11} (6i + 2)
To explain the error in the given notation Σ-2 (3η + 5), we can break it down as follows:
The use of a negative index (-2) is incorrect. The index of summation should always be a non-negative integer.
The use of the Greek letter eta (η) instead of i as the index variable is unconventional and may cause confusion or errors.
The expression inside the parentheses, 3η + 5, does not represent the terms of the arithmetic series. In particular, it does not involve the index variable i or the common difference 3.
Therefore, the correct notation for the given arithmetic series is Σ_{i=1}^{11} (6i + 2).
Consider a circle whose equation is x2 + y2 – 2x – 8 = 0. Which statements are true? Select three options. The radius of the circle is 3 units. The center of the circle lies on the x-axis. The center of the circle lies on the y-axis. The standard form of the equation is (x – 1)² + y² = 3. The radius of this circle is the same as the radius of the circle whose equation is x² + y² = 9.
Answer:
To determine which statements are true, we can use the standard form of the equation of a circle:
(x - h)^2 + (y - k)^2 = r^2
where (h, k) is the center of the circle and r is the radius.
Using this form, we can rewrite the given equation as:
(x - 1)^2 + y^2 = 3^2 + 1^2 = 10
Comparing this to the standard form, we can see that the center of the circle is (1, 0), so the statement "The center of the circle lies on the x-axis" is true. However, the statement "The center of the circle lies on the y-axis" is false.
To find the radius, we can rearrange the equation as follows:
x^2 - 2x + y^2 = 8
Completing the square for x, we get:
(x - 1)^2 + y^2 = 9
This shows that the radius of the circle is 3, so the statement "The radius of the circle is 3 units" is true, as well as the statement "The radius of this circle is the same as the radius of the circle whose equation is x² + y² = 9."
Therefore, the three true statements are:
1.The radius of the circle is 3 units.
2.The center of the circle lies on the x-axis.
3.The radius of this circle is the same as the radius of the circle whose equation is x² + y² = 9.
Step-by-step explanation:
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Each year, the school has a goal to have a third as many students in remedial mathematics courses as the year before. Currently the school has 1,200 students in remedial math. Approximately how many students will be enrolled in four years?
(a) 44 (b)15 (c) 32,400 (d) 1
Answer:
44 students
Step-by-step explanation:
1200 for the first year
a third of that is 400
400 for the second year
a third of that is 133.4
133.4 for the third year
a third of that is 44
Someone please help me answer this question
The two statements that are both true are as follows: line
AC is perpendicular to line HB and line AC is parallel to FG. That is option A.
What is a perpendicular line?A perpendicular line is defined as the line that forms angle 90° where it meets with another line in a plane.
A line is said to be parallel to each other when they do not intercept as they are both on the same plane.
From the given diagram, line AC is perpendicular to line HB because they form angle 90° at the point of intersection.
Also, line AC is parallel to FG, because they can never intersect till infinity.
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What is tan(49°)?
O A. 0.75
OB. 0.66
O C. 1.15
OD. 0.82
Answer:
Find the Exact Value tan(49). tan(49) tan ( 49 ). Step 1. The result can be shown in multiple forms. Exact Form: tan(49) tan ( 49 ). Decimal Form:
Step-by-step explanation:
Need help pls
geometry
#23
Answer: I think its C
Answer:
Step-by-step explanation:
C is false. [tex]\angle BEC = \angle AED=126[/tex] (vertically opposite).
The rest are correct.
What is the area of the real object that the scale drawing models? Scale factor. 1:5 Area = 10 square cm Scale drawing Real object
Answer:
D. 50 square centimeters
If you place a 26-foot ladder against the top of a building and the bottom of the ladder is 20 feet from the bottom of the building, how tall is the building? Round to the nearest tenth of a foot. help please now.
Answer: The building is approximately 16.6 feet tall.
Step-by-step explanation:
Use Pythagorean theorem (a²+b²=c²) to solve this.
We know that the ladder is 26 feet long so that would be our hypotenuse (c²). and the distance between the ladder and the building is 20 feet. So, this is the base. The remaining side is x.
Your equation would be: 20²+x²=26²
subtract 20² from 26² --> 276=x²
then take the square root --> 16.6=x
At age 25 , someone sets up an IRA (individual retirement account) with an APR of 4 %. At the end of each month he deposits $95 in the account. How much will the IRA contain when he retires at age 65? Compare that amount to the total deposits made over the time period.
Question content area bottom
Part 1
After retirement the IRA will contain $
enter your response here.
(Do not round until the final answer. Then round to the nearest cent as needed.)
The formula for the future value of an annuity is FV = Pmt * (((1 + r)n - 1) / r) to calculate the balance of the IRA at age 65. To compare this amount to the total deposits made over the time period, Total Deposits = Pmt * n = $45,600.
How will you calculate the balance of the IRA?To calculate the balance of the IRA at age 65, we need to use the formula for the future value of an annuity:
FV = Pmt * (([tex](1 + r)^n[/tex] - 1) / r)
Where:
Pmt = $95 (the monthly deposit amount)
r = 4% / 12 = 0.003333 (the monthly interest rate)
n = (65 - 25) * 12 = 480 (the total number of months, assuming retirement at age 65)
Plugging in these values, we get:
FV = 95 * (([tex](1 + 0.003333)^480[/tex] - 1) / 0.003333)
FV = $98,052.52
Therefore, the IRA will contain $98,052.52 at age 65.
Part 2
To compare this amount to the total deposits made over the time period, we can calculate the total deposits as:
Total Deposits = Pmt * n
Plugging in the values, we get:
Total Deposits = 95 * 480
Total Deposits = $45,600
Therefore, the IRA will contain significantly more than the total deposits made over the time period, due to the power of compounding interest.
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Simplify 1/cos x + 1/cos x -1
Answer:
-2cotxcscx
Step-by-step explanation:
Step 1: Find a common denominator
Step 2: Simplify
Researchers comparing the effectiveness of two pain medications randomly selected a group of patients who had been complaining of a certain kind of joint pain. They randomly divided these people into two groups, then administered the pain killers. Of the 112 people in the group who received medication A, 84 said this pain reliever was effective. Of the 108 people in the other group, 66 reported that pain reliever B was effective.
(a)Find a 95% confidence interval for the difference in the proportions of people who may find these medications effective. Interpret your interval.
(b) Does this interval contain zero? What does that mean for the hypothesis test of the difference in proportions?
(a) The 95% confidence interval for the difference in proportions of people who may find these medications effective is 0.029 to 0.231, which suggests that medication A is more effective than medication B in relieving joint pain.
(b) No, the interval does not contain zero, which means that the difference in proportions is statistically significant and supports the hypothesis that medication A is more effective than medication B.
solve for x; (a+bx)/(a+b)=(c+dx)/(c+d) if cb=ad
Answer:
To solve for x, we can start by cross-multiplying the equation to eliminate the denominators:
(a+bx)(c+d) = (c+dx)(a+b)
Expanding the terms on both sides:
ac + adx + bc + bdx^2 = ac + abx + cdx + bd
Simplifying and rearranging the terms:
adx + bdx^2 - abx - cdx = bd - ac
dx(ad - ab - c) = bd - ac
Now, since we know that cb=ad, we can substitute ad=cb into the equation:
dx(cb - ab - c) = bd - ac
dx(cb - ab - c) = b(cd - ac)
x = b(cd - ac)/(d(cb - ab - c))
Therefore, the solution for x is:
x = b(cd - ac)/(d(cb - ab - c))