A quadratic polynomial does not cross the x axis at any point since it has no zeros.
An expression that consists of variables, constants, and exponents that is combined using mathematical operations like addition, subtraction, multiplication, and division is referred to as a polynomial (No division operation by a variable).
x^2 - 2x + 5 when compared with the standard form of the quadratic equation, a = 1, b=- 2, c=5
Value of the discriminant =b^2 - 4 ac
= (-2)2 - 4(1) (5)= 4 - 20
= - 15
The value of the discriminant is negative i.e less than zero.
Hence, the quadratic equation x^2 - 2x + 5 has no real zeroes.
Since a quadratic polynomial may only have two real roots, the number of times the graph will cross the x-axis at most is two, and at least zero when there are no roots in the equation.
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The shelf life of a dairy product is normally distributed with a mean of 5 days and a standard deviation of 4 days. What is the probability that the product has a shelf life of at least 1 week and at most 2 weeks
The probability that the product will last for at least 1 wee and at most 2 week is 0.30.
What does the probability rule for products mean?This independent transmission of characteristics phenomenon can be explained by the product rule of probability. It claims that multiplying the odds of each event occurring alone will yield the probability of two independent events occurring together.
How do you calculate a product's probability?P(E F) = P(E) P(F) is the product rule, where E and F are independent events. Explain that independence means that the likelihood of one event occurring has no bearing on the likelihood of the other.
The probability that the product will last for at least 1 wee and at most 2 week is 0.30.
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List the key features of the quadratic function y = -x^(2) + 4x - 3
A) x-intercepts: (1,0) and (3,0), y-intercept: (0,3), vertex: (2,–1)
B) x-intercepts: (–1,0) and (–3,0), y-intercept: (0,–3), vertex: (2,–1)
C) x-intercepts: (1,0) and (3,0), y-intercept: (0,–3), vertex: (–1,2)
D) x-intercepts: (1,0) and (3,0), y-intercept: (0,–3), vertex: (2,1)
The key features of the quadratic function y = -x² + 4x - 3 include the following: D) x-intercepts: (1, 0) and (3, 0), y-intercept: (0, –3), vertex: (2, 1).
What is y-intercept?In Mathematics, the y-intercept of any graph such as a quadratic function, generally occur at the point where the value of "x" is equal to zero (x = 0).
When x = 0, the y-intercept is given by;
y = -x² + 4x - 3
y = -0² + 4(0) - 3
y = -3
Therefore, the y-intercept of this quadratic function y = -x² + 4x - 3 is given by the ordered pair (0, -3).
What is the x-intercept?In Mathematics, the x-intercept can be defined as the point at which the graph of a quadratic function crosses the x-coordinate and the value of "y" is equal to zero (0).
By critically observing the graph of this quadratic function y = -x² + 4x - 3, the x-intercept include the following:
Ordered pair = (1, 0).Ordered pair = (3, 0).In conclusion, the vertex of this quadratic function y = -x² + 4x - 3 is (2, 1).
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What is the slope and y-intercept of this linear equation y 3x 5?
The slope of the line is 3 and the y-intercept is -5.
The slope of a line is the coefficient of the x term (in this case, 3). To calculate the y-intercept, we can plug in x = 0 and solve for y. Doing this, we get y = 0 + 3(0) + 5 = -5. Therefore, the slope is 3 and the y-intercept is -5.
The slope of a linear equation is found by looking at the coefficient of the x term. In this case, the coefficient of the x term is 3, so the slope of the line is 3. To find the y-intercept, we can plug in x = 0 into the equation and solve for y. Doing this, we get y = 0 + 3(0) + 5 = -5, so the y-intercept is -5. Therefore, the slope of the line is 3 and the y-intercept is -5. This equation is therefore a linear equation with a slope of 3 and a y-intercept of -5.
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HELPPP!!!!
Option A: You are given $100 on the first day and then receive $10 each day for the month of February.
Option B: You are given one cent on the first day and that amount will double each consecutive day for the month of February.
Write a function rule to represent the total amount earned with Option A.
Write a function rule to represent the amount of money you will have earned with Option B.
Answer:
For Option A, the function rule would be:
totalAmountEarned(days) = 100 + 10*days
For Option B, the function rule would be:
totalAmountEarned(days) = 2^days
Step-by-step explanation:
If θ is an angle in standard position and its terminal side passes through the point (12,-5), find the exact value of \sec\thetasecθ in simplest radical form.
The exact value of secθ in simplest radical for is 1.083
What are trigonometric identities?Trigonometric identities are the functions that include trigonometric functions such as sine, cosine, tangents, secant, and, cot.
We are Given θ is an angle in standard position.
Its terminal side passes through the point (12, -5).
To find the exact value of secθ in simplest radical form.
When θ is an angle in standard position and its terminal side passes through the point (x,y), then the exact value of secθ is:
So, we have x = 12 and y = -5 which is in the first quadrant.
Therefore,
r² = x² + y²
r² = ( 12 )² + ( -5 )²
r² = 144 + 25
r² = 169
r = 13
Then,
sec θ = 1/cosθ
sec θ = [ 1/(x/r) ]
sec θ = r/x
sec θ = 13/12
sec θ = 1.083
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What is the domain of the function f/x )= √ 4 X²?
The domain and range of function Y = 4x² are:
Domain: (-∞, ∞) {x | x ∈ R}
Range: [0, ∞) {y | y ≥ 0}
Now, According to the question:
What are the domain and range?
The range of values that we are permitted to enter into our function is known as the domain of a function. The x values for a function like f make up this set (x). A function's range is the collection of values it can take as input. After we enter an x value, the function outputs this sequence of values.
We have,
Y = 4x²
The domain of the expression is all real numbers except where the expression is undefined. In this case, there is no real number that makes the expression undefined.
Interval Notation: (-∞, ∞)
Set-Builder Notation: {x | x ∈ R}
The range is the set of all valid y values: [0, ∞)
Set-Builder Notation: {y | y ≥ 0}
Hence, the domain and range of function Y = 4x² are:
Domain: (-∞, ∞) {x | x ∈ R}
Range: [0, ∞) {y | y ≥ 0}
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The complete question is this:
What is the domain of the function Y = 4x²
If 7/8 is multiplied by 4/5, will the product be greater than wait her of the two factors Explain.
Answer:
[tex] \frac{7}{8} \times \frac{4}{5} = \frac{7 \times 1}{2 \times 5} \\ = \frac{7}{10} [/tex]
How do I solve e less than 5?
Answer:
e-5
Pretty simple
Find three additional points on the parabola that has vertex (1, -2) and passes through (0,– 5). Select all that apply. A. (2,-3) B. (-1,-14) C. (3,2) D. (2,-5) E. (3,-14) F. (-2,7)
Answer: The vertex form of a parabola is:
y = a(x - h)^2 + k
Where (h, k) is the vertex of the parabola.
In this case, we are given that the vertex is (1, -2), so the equation of the parabola will be:
y = a(x - 1)^2 - 2
We know that the parabola passes through (0, -5), and it is given by the equation.
-5 = a(0 - 1)^2 - 2
so,
a = 1/3
The final equation of the parabola is :
y = 1/3(x-1)^2 - 2
so, the points that are on the parabola are:
A. (2,-3)
B. (-1,-14) is not true,
y = 1/3 (-1 -1)^2 - 2 = -1/3 + 2 = 1/3 ≠ -14
C. (3,2)
D. (2,-5)
E. (3,-14) is not true
y = 1/3 (3-1)^2 - 2 = -4/3 ≠ -14
F. (-2,7) is not true
y = 1/3 (-2-1)^2 - 2 = -7/3 + 2 = -1/3 ≠ 7
Therefore A, C and D are the correct answers.
Step-by-step explanation:
Select the correct answer.
Which expression is in simplest form?
A. 4x√2xy
B. 3a^2 √4b
C. c^3d √3d^3
D. 14s √st^2
Suzy randomly picks marbles from a bag containing 13 identical marbles. How many possible outcomes are there if she selects 9 marbles
Suzy randomly picks marbles from a bag containing 13 identical marbles. The possible outcomes of the given probability if she selects 9 marbles is:
259,459,200.
What is random?Randomness is commonly used to refer to an event's apparent or actual lack of pattern or predictability. Random events, symbols, or steps frequently occur in no particular order and do not adhere to any recognizable pattern or combination.
Germanic in origin, Randon is a name for boys. With a name that means "wolf shield," you can inspire baby Randon to embrace their sense of adventure. something or someone that is suspiciously out of the ordinary, unidentified, or unknown. a peculiar or erratic individual or thing. Something that is random lacks structure, direction, or intent. Like the random selection of lottery numbers or unplanned random events, it occurs entirely by chance.
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When a positive number is multiplied by the sum of twice the number and half the number, the result is the original number. What is the number
By setting up the equation and solving we get the positive number is 2/5.
What is positive number?A positive number is a number greater than zero. In mathematical terms, it is a number that is greater than zero on the number line. Positive numbers are often represented with a "+" sign in front of them, but this is not always necessary as the positive sign is the default and is usually omitted.
What is equations?An equation is a mathematical statement that asserts the equality of two expressions. It is a statement that asserts that the two expressions on either side of the "=" sign are equal and have the same value. The expressions on either side of the "=" sign are called the left-hand side (LHS) and the right-hand side (RHS) of the equation.
For example:
2x + 3 = 7
x(2x+x/2)=x
2x^2+x^2/2=x
5x^2/2=x
5x^2=2x
5x=2
x=2/5
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Simplify the following using law of indices. a) 12x⁷ ÷ 4x³
b) (2x)² × (2x)³ × (2x)⁵
Answer:
a) 3[tex]x^{4}[/tex]
b) 1024[tex]x^{10}[/tex]
Step-by-step explanation:
[tex]\frac{12x^{7} }{4x^{3} }[/tex]
[tex]\frac{3(4)xxxxxxx}{4xxx}[/tex] We can cancel out a 4 and 3 x's. That leaves
3xxxx
or 3[tex]x^{4}[/tex]
[tex](2x)^{2}[/tex] x [tex](2x)^{3}[/tex] x [tex](2x)^{5}[/tex] can be written in expanded form
[(2)(2)xx] x [(2)(2)(2)xxx] x [(2)(2)(2)(2)(2)xxxxx]
(2)(2)(2)(2)(2)(2)(2)(2)(2)(2)xxxxxxxxxx
1024[tex]x^{10}[/tex]
How to convert log2 to log10?
To convert the log2 to log10, we can use the convert of base formula for logarithms. The change of base formula for logarithms is as written:
log b(x)=logc(x) / logc(b)
By Using this formula, we can convert or find log base 2 to log base 10, where log base 10 is called the common logarithm, and we denote log10 (x) as log(x). The change of base formula gives the following:
log2(x)=log10(x)/log10(2) = log(x)/log (2)
This gives us the formula we can use to convert a logarithm with base 2 to a common logarithm with base 10.
The log function of e to the base 10 is denoted as “log 10 e”. Where the value of e is 2.7182818. The natural log function of e is presented as “log e e”.
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The experimental calculation of the specific heat of aluminum was found to be. 156 cal/g °C, but the actual value was given as. 185 cal/g °C. What is the percent error?
The percentage error is 16%
We know that the formula for the percentage error.
E = (absolute error / actual value) × 100
The formula for the absolute error is:
A = |actual value - experimental value|
A = |V1 - V2|
where V1 is the actual value
V2 is the experimental value
E is the percentage error
A is the absolute error
In this question, the experimental calculation of the specific heat of aluminum = 156 cal/g °C
And the actual specific heat of aluminum = 185 cal/g °C
Using above formula of absolute error,
A = |185 - 156|
A = 29 cal/g °C
And the percent error would be,
E = (absolute error / actual value) × 100
E = (29 / 185) × 100
E = 0.16 × 100
E = 16%
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How do you know if a triangle is 30-60-90?
To know if a triangle is a 30-60-90 triangle, you must check if the triangle's angles measure 30°, 60°, and 90°. Additionally, the sides of a 30-60-90 triangle will have a specific ratio. The longest side of the triangle is always double the length of the shortest side, and the side opposite the 60° angle is always the square root of 3 times the shortest side.
1. Measure the angles of the triangle.
2. Check if the angles measure 30°, 60° and 90°.
3. Measure the sides of the triangle.
4. Check if the longest side is double the length of the shortest side and if the side opposite the 60° angle is the square root of 3 times the shortest side.
To know if a triangle is a 30-60-90 triangle, you must check if the triangle's angles measure 30°, 60°, and 90°. Additionally, the sides of a 30-60-90 triangle will have a specific ratio. The longest side of the triangle is always double the length of the shortest side, and the side opposite the 60° angle is always the square root of 3 times the shortest side.
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Benjamin invested $66,000 in an account paying an interest rate of 63%
compounded annually. Christian invested $66,000 in an account paying an interest
rate of 5% compounded continuously. After 19 years, how much more money would
Benjamin have in his account than Christian, to the nearest dollar?
Answer:
$16,755
Step-by-step explanation:
You want the difference in interest earned on $66,000 after 19 years between an account earning 6 3/8% compounded annually, and one earning 5 3/4% compounded continuously.
Interest formulasThe formula for the account value multiplier when interest is compounded annually is ...
k = (1 +r)^t . . . . . . compounded annually at rate r for t years
When interest is compounded continuously, the multiplier is ...
k = e^(rt)
ApplicationThe difference in account values between the two rates is ...
∆value = $66,000·(1 +0.06375)^19 -e^(0.0575·19))
∆value ≈ $16,754.70
Benjamin will have about $16,755 more than Christian after 19 years.
The price of a computer is reduced by 17.5%
The reduced is £264
By how much is the price reduced
Answer:
To find out by how much the price was reduced, we can use the following equation:
price reduction = original price * reduction percentage
We know that the price reduction is £264 and the reduction percentage is 17.5%, so we can plug those values into the equation to get:
price reduction = £264 / 17.5%
To solve this equation, we need to express the percentage as a decimal. We can do this by dividing the percentage by 100:
price reduction = £264 / (17.5 / 100)
This simplifies to:
price reduction = £264 / 0.175
Solving this equation gives us a price reduction of £1512.
So, the original price was reduced by £1512.
Step-by-step explanation:
Simplify the expression. (-3+ 4n²) - (5 - 2n²)
Answer:
2(3n^2-4) and 6n^2-8
Step-by-step explanation:
There are two different answers but try at least both of them.
The population of HaleyValley, Alabama was 4,403 in 2010. Haleyville has been experiencing a population decline of 0. 6% per year since 2000. What will be the projected population of HaleyValley in 2020?
The projected Population in 2020 is given by 4146.
What is compounding ?Compounding is the method through which interest is added to both the principle balance already in place and the interest that has previously been paid. Thus, compounding may be thought of as interest on interest, with the result that returns on interest are magnified over time, or the so-called "magic of compounding."
Compound interest is when an amount receives interest on top of it each time interest is paid on the original amount. The main (initial) sum and the interest that has previously accrued over the course of prior periods are used to compute compound interest.
Number of years to compound is 10 years from 2010 to 2020.
The population deplition is 0.6 % = next year population is 99.4% of present.
So population after 10 years = 4403 * [tex].994\x^{10}[/tex] = 4145.84 =4146
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find value of m
[tex] {m}^{2} + 35 = 240 \div (12 \div 3)[/tex]
Answer:
5 ( or ) - 5
Step-by-step explanation:
12/3 = 4
240/4 = 60
m² + 35 = 60
m² = 60 - 35
m² = 25
m = - 5 ( or ) 5
Because,
( - 5 )² = - 5 * - 5 = 25
5² = 5 * 5 = 25
Find the measure of the indicated angle to the nearest degree.
Answer:
? ≈ 20°
Step-by-step explanation:
using the cosine ratio in the right triangle
cos ? = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{16}{17}[/tex] , then
? = [tex]cos^{-1}[/tex] ( [tex]\frac{16}{17}[/tex] ) ≈ 20° ( to the nearest degree )
18 9/10 + 8 3/10 ?????.....
27 2/10
or
27 1/5
----------------------------------
Solve the Equation.
6x−3(x+8)=9
x=?
Answer:
[tex]x=11[/tex]
Step-by-step explanation:
[tex]6x-3(x+8)=9\\6x-3x-24=9\\3x-24=9\\3x=33\\x=11[/tex]
Answer:
X=11
Step by step:
6x-3(x+8)=9
=6x-3x-24=9
=3x-24=9
+24 +24
=3x=33
=3x/3=33/3
X=11
Find the value of x and y so that the quadrilateral is a parallelogram.
(4x - 35° (y + 15)
(2y-5) (3x + 10)
X=
y =
Therefore, for x = 45 and y = 20, the quadrilateral is a parallelogram.
Define quadrilateral.In geometry a quadrilateral is a four-sided polygon, having four edges and four corners.
What is a polygon?A polygon is a closed polygonal chain made up of a limited number of straight-line segments and is a type of planar figure in geometry. A polygon is an area that is bordered by a bounding circuit, a bounding plane, or both.
We know opposite sides of a parallelogram are equal in length and parallel. Given opposite sides of a parallelogram are:
(4x - 35) and (3x + 10)
(y + 15) and (2y - 5)
Now, setting those opposite sides equal to each other:
4x - 35 = 3x + 10 = >x = 45
y + 15 = 2y - 5 => y = 20
Therefore, x = 45 and y = 20, the quadrilateral is a parallelogram.
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Select the correct answer from each drop-down menu.
The boundary of a park is shaped like a circle. The park has a rectangular playground in the center and 2 square flower beds, one on each side
of the playground. The length of the playground is /and its width is w. The length of each side of the flower beds is a. Which two equivalent
expressions represent the total fencing material required to surround the playground and flower beds? Assume that the playground and beds
do not overlap
2(l+w) + 4a and 2l+2w + 2(2a) are two equivalent expressions which represent the total fencing material required to surround the playground and flower beds.
What are mathematical expressions?Mathematical expressions are a way of representing mathematical ideas, concepts, and operations using symbols and notation. They can take many forms, including numbers, variables, and operators. They can also be combined to create more complex expressions, equations, and formulas.
Explain:
The total fencing material required to surround the playground and flower beds would be the sum of the fencing material for the playground and the fencing material for the flower beds.
So, one possible expression for the total fencing material required to surround the playground and flower beds would be: 2(l+w) + 4a
Another possible expression for the total fencing material required to surround the playground and flower beds would be: 2l+2w + 2(2a)
Please note that these expressions are based on the information provided, and the actual total fencing material required will depend on the specific dimensions of the park and playground, and may differ from these expressions.
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find x pah lease and thank you
Answer: x=4
Step-by-step explanation: x+3=2x-1, then you do simple algebra
To serve 1 person at a restaurant it takes 10 minutes. To serve 5 people at a restaurant it takes 18 minutes. How many minutes will it take to serve 8 people
What is the value of the expression 4x 3 x )+ 5x x 2 for x 3?
The value of the given expression 4x(3-x)+5x(x-2) when x = -3 is 3.
What are expressions?A phrase is considered a mathematical expression if it contains at least two numbers or variables and one or more mathematical operations.
A number is 6 more than half of the other number, which is x.
This statement is represented by the mathematical equation x/2 + 6.
So, we have the expression:
4x(3-x)+5x(x-2)
Now, the value of the expression when x = -3.
Insert values and calculate as follows:
4x(3-x)+5x(x-2)
4(-3)(3-(-3))+5(-3)((-3)-2)
-12(6)-15(-5)
-72 + 75
3
Therefore, the value of the given expression 4x(3-x)+5x(x-2) when x = -3 is 3.
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Correct question:
What is the value of the expression 4x(3-x)+5x(x-2) for x=(-3)?
EKA MATH²
6 M2 TD Lesson
▸
A trainer at a gym earns $2,456.75 every month. She earns an extra $4.75 every time she sells
a gym membership. Last month, the trainer sold 32 gym memberships. What is the total amount
of money the trainer earned last month?
Answer: We know that the trainer earns $2,456.75 every month, and she earns an extra $4.75 every time she sells a gym membership.
And last month she sold 32 gym memberships
We can calculate the total amount of money the trainer earned from selling gym memberships by multiplying the number of memberships sold by the amount earned per membership:
32 memberships * $4.75 per membership = $152.00
To find the total amount of money the trainer earned last month, we can add the amount earned from selling gym memberships to the amount earned from her salary:
$2,456.75 + $152.00 = $2,608.75
So, the total amount of money the trainer earned last month is $2,608.75
Step-by-step explanation: