The best answer from the choices provided is a = plus-or-minus 16 . Option C
What is a quadratic equation?A quadratic equation can be defined as an equation that can be rearranged in a standard form
Such that;
x represents an unknown value or variableThe variables, a, b, and c represent known numbersThe variable, a ≠ 0These quadratic equation are also described as polynomial equation having its highest degree as 2.
From the information given, we have that;
3a² - 21 = 27
collect like terms
3a² = 27 + 21
Add the values
3a² = 48
Divide both sides by 3
a² = 48/3
a² = 16
Hence, the value is a² = 16
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what are the properties of rational exponents and how are they used to solve problems
The properties of the rational exponents are given and a rational equation is of the form b = aˣ
What are the laws of exponents?When you raise a quotient to a power you raise both the numerator and the denominator to the power. When you raise a number to a zero power you'll always get 1. Negative exponents are the reciprocals of the positive exponents.
The different Laws of exponents are:
mᵃ×mᵇ = mᵃ⁺ᵇ
mᵃ / mᵇ = mᵃ⁻ᵇ
( mᵃ )ᵇ = mᵃᵇ
mᵃ / nᵃ = ( m / n )ᵃ
m⁰ = 1
m⁻ᵃ = ( 1 / mᵃ )
Given data ,
Let the rational exponent equation be A
Now , the properties of the exponent equations are
mᵃ×mᵇ = mᵃ⁺ᵇ
The powers of the exponents are added together
mᵃ / mᵇ = mᵃ⁻ᵇ
The powers of the exponents are subtracted together
( mᵃ )ᵇ = mᵃᵇ
The powers of the exponents are multiplied together
mᵃ / nᵃ = ( m / n )ᵃ
m⁰ = 1
Any number raised to the power of 0 is 1
m⁻ᵃ = ( 1 / mᵃ )
Hence , the exponents are solved
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Andre and diego were each trying to solve 2x 6=3x-8 describe the first step they each make to the equation
The final answer after solving the given equation could be 14.
What is Linear Equation ?
Linear Equation can be defined as the equation in which the highest degree of the variable is one. Linear equations are generally three types , they are standard form , slope intercept form , point slope form and linear equation is also called as the equation of straight line.
Given,
Given equation,
2x + 6 = 3x -8
separating the value into a similar term:
2x-3x = -8 - 6
subtracting the equation:
-x = -14
remove negative sign:
x = 14
Therefore , the final answer could be 14.
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what is the decrease of 3/2
Answer:
3/2
Step-by-step explanation:
3/2 is in the simplest form; it can't be decreased any more.
Tim's phone service charges $24.20 plus an additional $0.17 for each text message sent per month. If Tim's phone bill was $28.45, which equation could be used to find how many text messages, x, Tim sent last month? A. $0.17x + $24.20 = $28.45 B. $0.17x - $24.20 = $28.45 C. $24.20x + $0.17 = $28.45 D. $24.20x - $0.17 = $28.45
Answer:
A
Step-by-step explanation:
each text message is .17 text messages are x the total bill is 28.45. the service charges are 24.20.
.17x + 24.50 = 28.45
When treated with an anabiotic, 97% of all the dolphins are cured of an ear infection. if 6 dolphins are treated find the probability that exactly 3 are cured.
The probability is _____
(Round your answer to 4 decimal places.)
Answer:
0.0005
Step-by-step explanation:
this is a binomial experiment -- they are either cured or not, and the outcome is random
probability = n choose r * p^r * q^(n-r)
here, n = number of trials, r = number of successes desired, p = probability event occurs, and q = probability event doesn't occur
probability = n choose r * p^r * q^(n-r) = 6 choose 3 * 0.97^3 * 0.03^(6-3)
= 0.00049284342 rounding to 0.0005
A rectangle has an area of 7. 5m2.
One of the sides is 0. 3m in length.
Work out the perimeter of the rectangle.
The perimeter of rectangle could be 50.6 if a rectangle has an area of 7. 5 and One of the sides is 0. 3m in length.
What is Area of rectangle ?
area of rectangle could be the product of its sides that is length and breadth.
Given the area of rectangle is 7.5
one of its side, length = 0.3
let other side be x .
area = length*breadth
7.5 = 0.3 * x
x = 25
hence , other side could be 25.
perimeter of rectangle = 2 (length+breadth)
= 2 * (25+0.3)
= 2 * (25.3)
= 50.6
Hence, The perimeter of rectangle is 50.6
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What is the answer to 2/3x=-36
the answer to your question is 36
When 32 is subtracted from the square of a number, the result is 4 times the number. Find the positive solution
Step-by-step explanation:
x² - 32 = 4x
x² - 4x - 32 = 0
with a little bit experience we see immediately that this is
(x - 8)(x + 4) = 0
the positive x for this to be true is x = 8.
formally, the solution to a quadratic equation
ax² + bx + c = 0
is
x = (-b ± sqrt(b² - 4ac))/(2a)
in our case
x = (4 ± sqrt((-4)² - 4×1×-32))/(2×1) =
= (4 ± sqrt(16 + 128))/2 = (4 ± sqrt(144))/2 =
= (4 ± 12)/2 = 2 ± 6
x1 = 2 + 6 = 8
x2 = 2 - 6 = -4
we were right at the beginning.
the positive solution is x = 8.
When x 12" to the "-x^3+3x^2+5x+1"
The value of expression -x³+3x²+5x+1 is -1235 when x is 12
What is Expression?An expression is combination of variables, numbers and operators.
Given polynomial is -x³+3x²+5x+1
We need to find the value of the polynomial when x is 12.
To find this we just need replace x with 12
-(12)³+3(12)²+5(12)+1
Minus twelve cube plus three times of twelve square plus five times of twelve plus one
-1728+3(144)+5(12)+1
-1728+432+60+1
-1728+493
-1235
Hence, the value of expression -x³+3x²+5x+1 is -1235 when x is 12
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Carlton is using the following data samples to make a claim about the house values in his neighborhood:House ValueA $100,000B $600,000C $650,000D $700,000E $900,000Based on the data, should Carlton use the mean or the median to make an inference about the house values in his neighborhood?He should use the median because there is an outlier that affects the mean.He should use the mean because there are no outliers that affect the mean.He should use the mean because it is in the center of the data.He should use the median because it is in the center of the data.
The option A "He should use the median because there is an outlier that affects the mean." is correct.
It is clear from the data that option E's house is much more expensive than those in the other options. A $9,00,000 price is therefore an outlier in this set of data.
In symmetrically distributed data, an inference is made using the mean. Due to the inclusion of an outlier, the data is not symmetrical. As a result, the mean won't accurately depict the data's centre. As a result, we shall refrain from drawing conclusions about the pricing of the residences using the mean.
Therefore, since the median is unaffected by outliers, we shall use it.
Therefore, since there is an outlier that influences the mean, we will utilise the median. The answer is (A).
Your sincere criticism is crucial for better outcomes.
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The bill is 42 dollars, taxes is 9%, and the tip given is 18%. What's the Total?
The total cost of the bill that sells for $42 is $54.0204
How to determine the total cost of the bill?From the question, we have the following parameters that can be used in our computation:
Cost of the bill = $42
Sales tax = 9%
Tip = 18%
The total cost of the bill that sells for $42 is then calculated as
Total cost = Selling price * (1 + Sales tax) * (1 + tip)
Substitute the known values in the above equation, so, we have the following representation
Total cost = 42 * (1 + 9%) * (1 + 18%)
Evaluate
Total cost = $54.0204
Hence, the total cost is $54.0204
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if y varies jointly as x and the inverse of z and y = -5 and x = -5 and z = 6, find y when x = 5 and z = -8
Step-by-step explanation:
y varies inversely as x=
y= k/xz
-5= k(-5)/6
k= 6
y=6/xz
y=6/5×-8
y= -3/20
Optimization A cone is made from a circular sheet of radium R by cutting out a sector and gluing the cut edges. What is the maximum volume of the cone
The cone should have its maximum volume. V=1/*3r2h is the formula for calculating the volume V of a cone with height h and radius r.
How do you find the maximum volume of a cone?The cone has a volume of
V=πr2h/3
Therefore, we must calculate the values of r and h in terms of R. R is the diameter of the cone's top-circular circle, and h is the cone's height.
R is the cone's slant height, and it serves as the hypotenuse of a right triangle.
R2 = h2 + r2, or r2 = R2-h2.
So V = (1/3)π
[R2-h2]
h = (π/3)[R2h-h3]
You must take the derivative of the cone's volume, set it to zero, then solve for h to determine the cone's maximum volume.
dV/dh=(π/3)[R2-3h2]
R2-3h2=0 --> h2=R2/3 -> h = R/√3
Now we can determine r:
r2=R2-R2/3 = (2/3)R2
The volume formula with r and h substituted:
V = (π/3)
r2h = (π/3)(2R2/3)
(R/√3)
V(R)=2πR3/(9√3)
The complete question is:
A cone-shaped drinking cup is made from a circular piece of paper of radius R by cutting out a sector and joining the edges CA and CB. Find the maximum capacity of such a cup (Your answer may depend on R).
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Ver en español
On the coordinate plane, the segment from R(6,
–
16) to S(14,
–
1) forms one side of a rectangle. The rectangle has an area of 459 square units. Find the perimeter of the rectangle.
Write your answer as a whole number, decimal, or simplified radical. Do not round.
units
The perimeter of the rectangle, given the area and the segment from R ( 6, -16) to S (14, - 1 ) is 88 units
How to find the perimeter ?To find the perimeter, first find the distance between R ( 6, -16) to S (14, - 1 ) which will allow you to find the length of one side. This distance can be found by the formula :
= √((x2 – x1)² + (y2 – y1)²)
= √((14 – 6)² + (-1 – (-16))²)
= 17 units
This means that one side of the rectangle measures 17 units so the other side would be:
Area = Length x Width
459 = 17 x Width
Width = 459 / 17
Width = 27 units
The perimeter of the rectangle is:
= Length + Width + Length + Width
= 17 + 27 + 17 + 27
= 88 units
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asmine is filling a small fish tank with water. The fish tank is in the shape of a right circular cylinder with a radius of 3 in and a height of 10 in. What is the volume of this fish tank
The volume of the fish tank in the shape of a right circular cylinder with a radius of 3 in and a height of 10 in is 90π cubic inches.
Therefore the answer is 90π in³.
Recognize that the fish tank is in the shape of a right circular cylinder.
Remember that the formula for the volume of a cylinder is
V = πr^2h
where r is the radius and h is the height.
Plug in the given values for the radius (r = 3 inches) and the height (h = 10 inches) into the formula.
Perform the calculation:
πr^2h
= π(3^2)(10)
= π×9×10
= 90π cubic inches
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What is:
(7*8) + (42-8) / 4
Answer:
5.5
Step-by-step explanation:
7*8=56
42-8=34
56-34=22
22/4=5.5
Write the terms in standard form. Then state the degree of the polynomial and the leading coefficient (LC).
On solving the provided question, we can say that - the answer of the following sequence 1.9, 3x , 8x will be 13.78x
what is a sequence?A sequence is a collection of numerals (referred to as "terms"), for example, 2, 5, 8. A specific pattern that some sequences follow may be leveraged to make them infinitely long. To continue the series, add 3 and use the example of 2,5,8. Formulas that show where to look for words inside a sequence can be found there. Informally, a sequence in mathematics is a collection of items that are in some order (or events). It has components, much like a set (also called elements or terms). The length of the sequence refers to the total, potentially unlimited number of ordered items. arranging two or more objects in a logical sequence. Chronological.
sequence 1.9, 3x , 8x
answer is = 13.78x
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d minus 2 = 4.6 please help meeee im not good at mathhh
[tex]d-2=4.6[/tex]
Add 2 to both sides:
[tex]d-2+2=4.6+2[/tex]
[tex]\fbox{d = 6.6}[/tex]
h(a) = a^2 + 4 when a = -3
Answer:
[tex] \sf \: h(-3) = 13[/tex]
Step-by-step explanation:
Given information,
→ h(a) = a² + 4
The value of h(a) when a is -3,
→ h(a) = a² + 4
→ h(-3) = (-3)² + 4
→ h(-3) = 9 + 4
→ [ h(-3) = 13 ]
Hence, required answer is 13.
A mountain on a tropical island experiences changes in its height due to volcanic activity. Its current height is 2,827 meters, which is 10% taller than it was when the mountain was last measured. How tall was it then?
Answer:
2,570 meters
Step-by-step explanation:
110% of what number is 2827
1.1x = 2827 Divide both sides by 1.1
[tex]\frac{1.1x}{1.1}[/tex] = [tex]\frac{2827}{1.1}[/tex]
x = 2570
0.7 times square root of 300
The value of the expression 0.7 x √300 is 12.124.
What is an expression?An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
Example: 2 + 3x + 4y = 7 is an expression.
We have,
0.7 x √300
This can be written as,
= 0.7 x √3 x √100
= 0.7 x 1.732 x 10
= 12.124
Thus,
The value is 12.124.
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The Key Club has a goal to raise $1,700, which they need for new equipment, by conducting various fundraisers. First, they did a baked of their goal 2/5amount. Next, they did a goods sale and earned 3/8 BINGO night and earned of their goal amount. How much more money does the Key Club still need to earn in order to reach their goal?
The amount of money more that Key Club still need to earn in order to have reached their target is $ 382. 50
How to find the money needed ?To find the amount of money needed by Kay Club to get to their target, first, find the amount of money earned from the bake sale :
= 2 / 5 x Target amount
= 2 / 5 x 1, 700
= $ 680
Then, they did a good sale and earned 3 / 8 of the amount :
= 3 / 8 x 1, 700
= $ 637. 50
The amount of money that Key Club still needs is:
= Total amount - amount raised
= 1, 700 - 680 - 637. 50
= $ 382. 50
In conclusion. Key Club would still need to engage in other activities to be able to reach their goal of $ 1, 700 as they have to raise $ 382. 50.
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a shopper purchased 8 t-shirts and 5 pairs of pants for $220. the next day, he purchased 5 t-shirts and 1 pair of pants for $112.How much does each t shirt and each pair of pants cost?
Answer:
Step-by-step explanation:
Let the costs of 1 t - shirt and 1 pair of pants be 'x' and 'y' respectively then:
Case 1 --> 8x + 5y = 220 ----------(1)
Case 2 --> 5x + y = 112 ----------(2)
Multiplying equation (2) by 5:
8x + 5y = 220
25x + 5y = 560 ------(3)
Subtracting equation (1) from equation (3) we get :
17x = 340
x = 20
Putting x in (2):
5 x 20 + y = 112
y = 12
therefore, cost of each t-shirt is 20 rupees and the cost of each pair of pants is 12 rupees
In the diagram below, \overline{MN}
MN
is parallel to \overline{JK}
JK
. If MNMN is 1212 more than LNLN, LK=33LK=33, and JK=55JK=55, find the length of \overline{LN}
LN
. Figures are not necessarily drawn to scale. State your answer in simplest radical form, if necessary.
The value of the missing length LN of the similar triangles is; LN = 18
How to solve Similar Triangles?Similar triangles are defined as triangles that have the same shape, but their sizes may vary. This means therefore that, if two triangles are similar, then we can say that their corresponding angles are congruent and also their corresponding sides are in equal proportion.
In the given triangle attached, we can say that if we apply the concept of similar triangles, we will get;
LN/LK = MN/JK
We are told that;
MN is 12 more than LN. Thus; MN = 12 + LN
LK = 33
JK = 55
Thus;
LN/33 = (12 + LN)/55
55LN = 33(12 + LN)
55LN = 396 + 33LN
22LN = 396
LN = 396/22
LN = 18
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Find the 6th term of the geometric sequence whose common ratio is 3/2 and whose first term is 4
6th terms of given geometric progression whose common ratio is 3/2 and first term is 4 is 243/8 using the farmula ar^(n-1).
What is a geometric sequence?
A mathematical sequence known as a geometric progression (GP) is one in which each following phrase is generated by multiplying each preceding term by a fixed integer, or "common ratio." This progression is sometimes referred to as a pattern-following geometric sequence of numbers. Learn development in mathematics here as well. Here, each phrase is multiplied by the common ratio to generate the subsequent term, which is a non-zero value. A geometric series with a common ratio of 2 is 2, 4, 8, 16, 32, 64, etc.
Geometric Progression takes the following general form: a, ar, ar^2, ar^3, ar^4,..., ar^(n-1).
a = First term where
The common Ratio is r.
nth term = ar^(n-1)
6th terms ar^(6-1) = ar^5.
given is that r =3/2. a = 4.
6th term = 4 * (3/2)^5
= 4 * 3^5/2^5
=4*243/4*8
=243/8.
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Write A=C+Kx in words variation
In word variation, we can write as;
⇒ In the equation, A = C + Kx, if K is a nonzero constant and C = 0, then you have the function A = Kx, which is called a direct variation.
What is Equation of line?The equation of line in point-slope form passing through the points
(x₁ , y₁) and (x₂, y₂) with slope m is defined as;
⇒ y - y₁ = m (x - x₁)
Where, m = (y₂ - y₁) / (x₂ - x₁)
We have to given that;
The equation is,
⇒ A = C + Kx
Now, We know that;
The direct variation is of the form of y = kx.
Here, The equation is,
⇒ A = C + Kx
Hence, Its words variation is written as;
In the equation, A = C + Kx,
if K is a nonzero constant and C = 0, then you have the function A = Kx, which is called a direct variation.
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How do you find the slope of a logarithmic function?
By taking derivative, slope of the logarithmic function can be found.
The slope of a logarithmic function can be found by taking the derivative of the function with respect to x using the rules of logarithmic differentiation. The general form of the derivative of a logarithmic function is:
d/dx(log(f(x))) = (1/f(x))*(df/dx)
The slope means change in Y with respect to change in X. The slope is the ratio of the rise to run and it shows the steepness of the plane.
The slope is denoted by m.
Example:
Find the slope of y = log(x^2+1)
d/dx(log(x^2+1)) = (1/(x^2+1))*(2x) = 2x/(x^2+1)
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I need to know the steps to solve this.
The Constraints of the inequality are
x ≤ 2y + 500
22500 < √ 35x + 50y
What is Inequality?Mathematical expressions with inequalities are those in which the two sides are not equal. Contrary to equations, we compare two values in inequality. Less than (or less than or equal to), greater than (or greater than or equal to), or not equal to signs are used in place of the equal sign.
Given:
The Company A (x) at most 500 more than twice then unit by B(y).
So, x ≤ 2y + 500
Now, the square of Company Profit will be equal to 35x + 50y
Then, the constraints will be
1. x ≤ 2y + 500
2. Company Profit² < 35x + 50y
Company Profit < √ 35x + 50y
22500 < √ 35x + 50y
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Is 2x³ a polynomial?
[tex]2xA^{3}[/tex] is a polynomial as a result. Constants, variables, and exponents can all be included in a polynomial, but variable division is never permitted.
what is a polynomial ?In mathematics, a polynomial is an expression made up of variables (also known as indeterminates) and coefficients that exclusively uses the operations of addition, subtraction, multiplication, and non-negative integer exponentiation of variables. A polynomial is an equation made up of variables, constants, and exponents that are mixed using mathematical operations including addition, subtraction, multiplication, and division (No division operation by a variable).
given
[tex]2xA^{3}[/tex] is a polynomial as a result. Constants, variables, and exponents can all be included in a polynomial, but variable division is never permitted.
It is impossible to classify an expression as a polynomial if it contains a variable with exponents that are negative or fractional, divides by a variable, or is included inside a radical.
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7(3n + 2) - 3n - 5 i need to factor it tysvm!!
The answer to the Linear expression 7(3n + 2) - 3n - 5 is 18n + 11
What is a linear expression?A linear expression is an algebraic statement where each term is either a constant or a variable raised to the first power. In other words, none of the exponents can be greater than 1.
From the expression 7(3n + 2) - 3n - 5
By expanding the bracket, we have
21n + 14 - 3n - 5
By collecting like terms, we have
21n - 3n + 14 - 3
18n + 11
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