Answer:
11/20
Step-by-step explanation:
55% = 55/100
by simplifying this fraction (divide top and bottom by 5), you get 11/20
Which of the following is a solution of 3x² 5x 2 0?
The solution of the given equation 3x²+ 5x +2= 0 is given by :
option c. x = -2 / 3 or x = -1.
As given in the question,
Given equation is equal to :
3x²+ 5x +2= 0
Solve the given equation by splitting the middle term of the quadratic equation we have,
3x²+ 5x +2= 0
⇒ 3x²+ 3x + 2x + 2 = 0
⇒ 3x ( x + 1 ) + 2 ( x + 1 ) = 0
⇒ ( 3x + 2 ) ( x + 1 ) = 0
⇒ ( 3x + 2 ) = 0 or ( x + 1 ) = 0
⇒ x = -2 / 3 or x = -1
From the given options :
option c. x = -2 / 3 or x = -1 is the solution.
Therefore, the solution of the given equation 3x²+ 5x +2= 0 is equal to :
option c. x = -2 / 3 or x = -1 .
The above question is incomplete, the complete question is:
Which of the following is a solution of the equation 3x²+ 5x +2= 0?
a. x = 2/3 or x = 1
b. x = -2/3 or x = 1
c. x = -2/3 or x = -1
d. x = 2/3 or x = -1
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A cross-section of a parabolic reflector is shown in the figure. The bulb is located at the focus and the opening at the focus is 10 cm.
(a) Find an equation of the parabola.
(b) Find the diameter of the opening CD, 11 cm from the vertex.
The equation and diameter CD of the parabola are x=1/10 y^2and 2√110
How to determine the standard equation of the parabola?In this question we have four case of parabolas with vertical axes of reference, whose standard formula is:
a(x – h)2 + k
Where:(h, k) - The vertex of the parabola.
a - Least distance between the vertex and the focus of the parabola.
Please notice that p < 0 when the directrix is above the focus, otherwise p < 0. The vertex is the midpoint of line segment between the directrix and the focus.
Given;
Vertex is at origins (0,0) and latus rectum = 10 and the graph open right so a is positive and the equation is:
x=a (y-k)^2+h.
To write the equation we need to find a using the latus rectum equation.
We substitute the values.Then inverse place of a with 10
Latus rectum=|1/a|
10=|1/a|
a=1/10
The equation:
x=a (y-k)^2+h
x=1/10(y-0)^2+0
x=1/10 y^2
-Assume the distance between C and the center is EC. If E is (11,0) and C is (11, y).
-EC=y
-The equation of the parabola is x=1/10 y^2
Now, Substitute the value of C coordinate, which
x=1/10 y^2
Substitute the value of C coordinate, which is (11, y).
11×10=1/(10×10) y^2
√(y^2 )=√110
y=EC=√110
Because the distance of EC = ED
CD=EC×2
CD=√110×2
CD=2√110
Therefore, the equation of parabola and CD will be x=1/10 y^2 and 2√110
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What is the 4 basic rule in solving equation?
One-step equations can be solved in four different ways: by adding, subtracting, multiplying, and dividing. Both sides of an equation will remain equal if we add the same amount to each side.
What are the four fundamental rules for solving equations?Addition:
In math, addition is the process of adding two or more numbers together. The numbers being added are known as addends, and the outcome of the addition process, or the answer we ultimately get, is known as the sum.Subtraction:
The process of determining a difference between two numbers is called that. The letter "-" (for "minus") is used. In this method, we take a number and divide it by a smaller number.Multiplication:
The result of two numbers being multiplied is known as the product. The multiplier is the quantity that multiplies the number of such equal groups by the multiplicand, the quantity of objects in each group.Division:
In mathematics, division is the process of dividing a number into equal parts and determining how many equal parts can be made. For instance, breaking 15 into 3 equal groups of 5 is equivalent to dividing 15 by 3. The symbol for division, "," or occasionally "/," is used.To know more about the equations, here
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what are 2 numbers that can multiply to 14 and add up to sum -9
Answer: -2, -7
Step-by-step explanation:
blueprints Ezra redrawing the blue paint shown of a stage he is planning to build for his band. By what percentage should he multiply the dimension of the stage so that the dimensions of the image are 1/2 the size of the original blueprint? what will be the perimeter of the updated blueprint?
The percentage by which Ezra should multiply the dimension of the stage so that the dimensions of the image are 1/2 the size of the original blueprint is of:
50%.
The perimeter of the updated blueprint will be 50% of the perimeter of the original blueprint.
What is a dilation?A dilation happens when the coordinates of the vertices of an image are multiplied by the scale factor, changing the side lengths of a figure.
For this problem, we want for the dimensions of the updated stage to be half the dimensions of the original stage, hence the scale factor of the dilation is given as follows:
k = 1/2.
The percentage equivalent to a fraction of 1/2 is of 50%, and the perimeter of the updated stage will be 1/2 the perimeter of the original stage, as both the perimeter and the side lengths have the same unit.
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If the marble has a volume of 18,000 cubic centimeters, what are the dimensions of the marble?
The dimensions of the marble is thus 10∛18 cm when the volume is 18000 cm³.
What is volume?An object's capacity is the amount of material it can hold inside, while an object's volume is the amount of space it takes up. Here, the cubic unit is used to measure either of the two.
Cubic units are used to measure volume. The quantity of cubes needed to completely fill any given figure, such as blocks in a box, is its volume.
As there is no definite shape is given we can assume that the shape is cube.
Volume of cube = a³
given the volume 18000cm³
dimensions of the marble,
a × a × a = 18000
a³ = 18000
a = ∛18000
a = 10∛18
a = 26.21
Hence, the dimensions of the marble is thus 10∛18 cm when the volume is 18000 cm³.
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What is a residual and how is it used in finding the line of best fit?
Residual is the difference between the expected and actual y values, so r I = y I y i. A negative residual indicates that the anticipated value is excessively high, whereas a positive residual indicates that the projected value was excessively low. The goal of a regression line is to reduce the total amount of residuals.
What is Mcq, or salvage value?
When an item reaches the end of its useful life, its salvage value—or potential market value—is estimated. It can also be described as the asset's book value after depreciation has been taken into account.
What does the depreciation formula's residual value mean?
The asset's final worth is its residual value. To obtain the entire amount, it is therefore deducted from the starting value. Consequently, we are given the depreciation figure. This sum is divided by the usable years of the asset using the straight-line depreciation technique.
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A shop offers the following conversions between pounds (£) and US dollars ($) : £1=$1.28 $1= £0.74 if Niamh converts £150 into US dollars and then back into pounds, what percentage of her money will she lose? Give your answer to 1 d.p.
Answer:5.3%
Step-by-step explanation:
we say 150/1 multiplied by 0.74/1=$111
then when we convert it back to pounds, we say 111/1 multiplied by 1.28/1 =142.08
150.00-142.08=7.92
7.92/150.00 multiplied by 100=5.28 to 1 decimal place is 5.3%
hope you understand
$9, 100 is invested in an account earning
3% interest (APR), compounded quarterly.
Write a function showing the value of the
account after t years, where the annual
growth rate can be found from a constant
in the function. Round all coefficients in
the function to four decimal places. Also,
determine the percentage of growth per
year (APY), to the nearest hundredth of a
percent.
Answer: A = P(1 + r/n)^(nt)
Where
A is the future value of the account
P is the initial principal amount, which is $9,100
r is the annual interest rate, which is 3%
n is the number of times the interest is compounded per year, which is 4 (quarters)
t is the number of years
So the function for the value of the account after t years is:
A = 9100(1 + 0.03/4)^(4t)
To determine the percentage of growth per year (APY), we can use the formula:
APY = ( (A/P)^(1/t) - 1) * n
In this case,
APY = ( (A/9100)^(1/t) - 1) * 4
APY represents the annual percentage yield, which is the interest rate taking compounding into account.
Please note that in the above expression the coefficient 0.03 is rounded to four decimal places as instructed.
Step-by-step explanation:
A tortilla chip is shaped like an equilateral triangle.
If an exterior angle on this tortilla chip measures(2x-80), which equation can you solve to calculate the value of x?
HINT: The interior angles of an equilateral triangle all measure 60.
Step-by-step explanation:
Two interior opposite angles of a triangle are equal to the exterior angel
[tex]60 + 60 = 2x - 80 \\ 120 = 2x - 80 \\ 2x = 120 + 80 \\ 2x = 200 \\ x = \frac{200}{2} \\ x = 100[/tex]
Lamont earns an annual salary of $58,000. He has to pay a 4.5% income tax on his earnings. How much does Lamont pay in income tax?
Answer:If you make ₱ 58,000 you will be taxed ₱ 4,711. That means that your net pay will be ₱ 53,289 per year, or ₱ 4,441 per month.
What is 7 to the 3rd power and evaluate
Answer: 343
Step-by-step explanation:
7 to the 3rd power
⇒7³
⇒7 × 7 × 7
⇒343 ... answer
hope that helps...
A ray , and an angle is two . The measure of an angle related to the length of its sides. So, the measure of an angle the same at all distances from its vertex.
The combination of two rays with the same terminal is called an angle. The vertex of the angle is the common terminal of the rays, which are referred to as the sides of the angle.
What is the relation between angle and rays?A ray is a segment of a line with one endpoint and an endlessly extending end. Two rays can be linked at their starting points to create an angle, and their other ends can stretch indefinitely.
According to the question,
the proportion of an angle's measurement to the width of its sides.
Therefore, an angle's measure is constant regardless of how far it is from its vertex.
Due to the fact that adjacent angles are two angles with a shared vertex, and side, but not interior points.
Therefore,
The combination of two rays with the same terminal is called an angle.
The vertex of the angle is the common terminal of the rays, which are referred to as the sides of the angle.
Hence the measure of an angle is the same at all distances from its vertex.
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Answer:
Step-by-step explanation:
The first three terms of a sequence are given. Round to the nearest thousandth (if necessary). 13, 19,25,... Find the 48th term.
The given sequence is 13, 19, 25, ...
What comprises an arithmetic series?
An ordered group of numbers with a shared difference between each succeeding word is known as an arithmetic sequence. For instance, the common difference in the arithmetic series 3, 9, 15, 21, and 27 is 6. An arithmetic progression is another name for an arithmetic sequence.
This sequence appears to be increasing by 6 each time, so it is an arithmetic sequence. The common difference is 6. The nth term of an arithmetic sequence is given by the formula:
an = a1 + (n-1)d
where a1 is the first term, d is the common difference and n is the position of the term in the sequence.
We can use this formula to find the 48th term of the sequence:
a48 = a1 + (48-1)d
a48 = 13 + (48-1)6
a48 = 13 + 47*6
a48 = 13 + 282
a48 = 295
So, the 48th term of the sequence is 295.
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Can a triangle be formed with side lengths 7/10 20?
It is not possible to construct a triangle with lengths of its sides 7cm, 10cm and 20cm because the sum of two sides of a triangle is greater than the third side.
Now, According to the question:
We know that:
What is triangle inequality rule?
The triangle inequality theorem states that for any given triangle, the sum of the two sides is always greater than the third side. The Triangle is a polygon with three line segments as its boundaries.
Suppose A, B and C are three sides of a triangle, then by using triangle inequality rule, A + B > C then A, B and C make a triangle.
We have the sides:
7, 10 and 20
7 + 10 > 20
It is not possible to construct a triangle with lengths of its sides 7cm, 10cm and 20cm because the sum of two sides of a triangle is greater than the third side.
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Holly needs to buy some cloth to make masks. The following deals are available at various stores. Choose the best deal
A.
$11.04 per 4 yd
B.
$16.26 per 6 yd
C.
$19.11 per 7 yd
D.
$13.85 per 5 yd
Answer: B, $16.26 per 6 yards
Step-by-step explanation:
$11.04/ 4 yd is $2.76 a yd
$16.26/ 6 yd is $2.71 a yd
$19.11/ 7 yd is $2.73 a yd
$13.85/ 5 yd is $2.77 a yd
F(x) = x^2 - x - 1 Over which interval doe f have an average rate of change of zero
The interval over which f(x) = x² - x - 1 has an average rate of change of zero is (1/2, 1/2) as it is the only point at which the average rate of change is zero.
An average rate of change of zero means that the function is not increasing or decreasing over the interval in question. To find the interval over which f(x) has an average rate of change of zero, we need to find the critical points of the function. A critical point is a point at which the function's derivative is equal to zero or is undefined.
The derivative of f(x) = x² - x - 1 is:
f'(x) = 2x - 1
Setting f'(x) = 0, we get:
2x - 1 = 0
Solving for x, we get:
x = 1/2
Since this is the only critical point of the function, it is the point where the function has an average rate of change of zero. To determine the interval, we need to check the sign of the function's derivative on either side of the critical point.
f''(x) = 2 > 0
So x = 1/2 is the minima of the function
f'(x) = 2(1/2) - 1 = 0, at x = 1/2
so f'(x) > 0 for x < 1/2 and f'(x) < 0 for x > 1/2
Therefore the interval over which f(x) has an average rate of change of zero is (1/2, 1/2) or {1/2}.
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what 1\3 of a full rotation
Answer:
120°
Step-by-step explanation:
what 1\3 of a full rotation?
one full rotation = 360°so
360° x 1/3 =
360° : 3 =
120°
How do you convert base 10 to base 2?
Steps To Convert From Base 10 to Base 2
Divide the given number (in base 10) with 2 until the result finally left is less than 2.Traverse the remainders from bottom to top to get the required number in base 2.Number system conversionThe number system is a way of representing the quantity of a physical item.
For example, the number system that is widely used by humans is the decimal number system, which is a number system that uses 10 kinds of symbols. In everyday life, the number system that is widely used by humans is the decimal number system, which is a number system that uses 10 kinds of symbols. if it is associated with Computer Logic it is represented by two-state elements, namely off and on which is the concept used in the binary number system which only uses 2 kinds of values to represent value quantities.
In addition, the Number System uses a certain number of bases or bases (base / radix). There are 4 types of number systems that have to do with computers, which include:
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Simplify: (8^ 2/3)^4
Answer: 256
Step-by-step explanation:
Remove any grouping symbol such as brackets and parentheses by multiplying factors.Use the exponent rule to remove grouping if the terms are containing exponents.Combine the like terms by addition or subtraction.Combine the constants.
please please please help me
Answer:
For the first one, the answer would be:
2/3 * 3/8 = 6/24 because, all you have to do is multiply straight across.
2 * 3 = 6 and 3 * 8 = 24
6/24 can be simplified to 1/4 because 6 with go into the denominator 4 times, so the simplified fraction will be 1/4.
(Im not so sure what to do about the second one, so I would need to see what the options look like)
For the third:
The answer would be 3/3, because:
2 * 3 = 6
5 * 3 = 15
And the result fraction is 6/15, which matches what the image shows!
Step-by-step explanation:
Hope it helps! =D
What do you mean by method of factorization in method of substitution?
Method of factorization in method of substitution is a technique used to solve systems of linear equations. In this method, one of the equations is multiplied by a factor to make the coefficient of one of the variables the same. This allows the equations to be combined and solved for the remaining variables.
Solving Linear Equations Using Method of Factorization in Method of SubstitutionMethod of factorization in method of substitution is a useful technique for solving systems of linear equations. It allows one to isolate a single variable and make use of substitution to solve the system. The first step is to multiply one of the equations by a factor to make the coefficient of one of the variables the same in both equations. This allows the equations to be combined and solved for the remaining variables. Once the values of the variables have been found, they can be substituted into the other equation to find the solution of the system. This technique is beneficial because it allows one to avoid tedious calculations that are often required when solving linear equations.
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Choose the correct simplification of the expression (3x^3 y^4 z^4) (2x^3 y^4 z^2).
5x^9 y^16 z^8
6x^9 y^16 z^8
5x^6 y^8 z^6
6x^6 y^8 z^6
So, the correct simplification for the expression (3x^3 y^4 z^4) (2x^3 y^4 z^2) is option d: 6x^6 y^8 z^6.
What is simplification?
To simplify simply means to make anything easier. In mathematics, simplifying an equation, fraction, or problem means taking it and making it simpler. Calculations and problem-solving techniques simplify the issue.
The given equation is -
(3x^3 y^4 z^4) (2x^3 y^4 z^2)
On simplification -
=[3·2(x^3+3)(y^4+4)(z^4+2)]
=6x^6y^8z^6
Therefore, the value obtained is 6x^6y^8z^6.
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ITS COMPOUND INTERSERT ITS URGENTT
Mike's car will be worth £4116 at the start of 2017 as the car decreases in value by 30% every year
How to evaluate for the decreased value of the carAt the start of 2014, Mike's car is worth £12000,
we shall calculate the decreased worth of the same car to the start of 2017 as follows:
At the end of 2014, 30% of £12000 is calculated as;
£12000 × 30/100 = £3600
At the start of 2015, the car will be worth
£12000 - £3600 = £8400
At the end of 2015, 30% of £8400 is calculated as;
£8400 × 30/100 = £25200
At the start of 2016, the car will be worth
£8400 - £2520 = £5880
At the end of 2016, 30% of £5880 is calculated as;
£5880 × 30/100 = £1764
At the start of 2017, the car will be worth
£5880 - £1764 = £4116
Therefore, Mike's car will decrease in value to worth £4116 at the start of 2017.
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1. What guides the end behavior of a function
2. What is the line that a graph approaches
3. What does the variable K represent
Answer:
1The degree and the leading coefficient of a polynomial function determine the end behavior of the graph. The leading coefficient is significant compared to the other coefficients in the function for the very large or very small numbers.
2An asymptote is a line that a graph approaches but never touches. That line can be vertical, horizontal, or even slanted, and graphs can have multiple types of asymptotes.
3constant of variation (k) is a ratio that represents the relationship between the independent variable (x) and the dependent variable (y). It can be found by dividing y by x, if both of those variables have known values.
You have an isosceles triangle where the two legs form a 90 degree angle. One of these legs is 2cm. What is the hypotenuse of the triangle? Express
your answer using two decimal places only.
Answer:
2.83 cm
Step-by-step explanation:
The other leg is also 2cm
Pythagorean Theorem
hypot ^2 = 2^2 + 2^2
Hypot = sqrt 8 =~ 2.83 cm
Answer:
Step-by-step explanation:
an isosceles triangle where the two legs form a 90-degree angle is an isosceles right triangle. So, the hypotenuse of the triangle is 2√2
Find the sum of following infinite series
Infinite series, the total of an infinite number of numbers connected in a specific method and listed in a specific order.
What is meant by infinite series?Infinite series, the total of an infinite number of numbers connected in a specific method and listed in a specific order. In addition to being valuable in mathematics, infinite series are also useful in the sciences of physics, chemistry, biology, and engineering. Sigma notation can be used to depict an infinite series. An infinite series, for instance, is ∞∑n=110(12)n−1. The series is endless, as indicated by the infinity symbol above the sigma notation.Infinite series are useful for discovering approximations to complex problems and for highlighting minute details of mathematical precision. A finite series is the accumulation of all of its terms. An infinite series has an infinitely large term count and an infinitely high upper bound.We get,
a) [tex]$\sum_{n=0}^{\infty}$[/tex]
Infinity
b) [tex]$\sum_{n=1}^{\infty}\left(\frac{4}{2^n}\right)$[/tex]
[tex]\sum_{n=1}^{\infty} \frac{4}{2^n}[/tex]
[tex]& =4 \cdot \sum_{n=1}^{\infty} \frac{1}{2^n} \\[/tex]
[tex]& \sum_{n=k}^{\infty}\left(a_n\right)=\sum_{n=0}^{\infty}\left(a_n\right)-a_0-a_1- \\[/tex]
[tex]& =4\left(\sum_{n=0}^{\infty} \frac{1}{2^n}-\frac{1}{2^0}\right)[/tex]
[tex]& \sum_{n=0}^{\infty} \frac{1}{2^n}=2 \\[/tex]
[tex]& =4\left(2-\frac{1}{2^0}\right)[/tex]
Then we get,
=4
c) [tex]$\sum_{n=1}^{\infty}\left(\frac{7}{10^n}\right)$[/tex]
[tex]$\sum_{n=1}^{\infty} \frac{7}{10^n}[/tex]
[tex]& =7 \cdot \sum_{n=1}^{\infty} \frac{1}{10^n} \\[/tex]
[tex]& \sum_{n=k}^{\infty}\left(a_n\right)=\sum_{n=0}^{\infty}\left(a_n\right)-a_0-a_1- \\[/tex]
[tex]& =7\left(\sum_{n=0}^{\infty} \frac{1}{10^n}-\frac{1}{10^0}\right)[/tex]
[tex]& \sum_{n=0}^{\infty} \frac{1}{10^n}=\frac{10}{9} \\[/tex]
[tex]& =7\left(\frac{10}{9}-\frac{1}{10^0}\right)[/tex]
Simplify
[tex]$7\left(\frac{10}{9}-\frac{1}{10^0}\right): \quad \frac{7}{9}$[/tex]
= 7/9
Therefore,
a) infinity, b) =4, and c) = 7/9
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The simple interest on a sum of money invested at 3% per annum for 2 years was $39.75.
Calculate the sum of money invested
Answer:
$37.50
Step-by-step explanation:
[tex]P+Prt=39.75 \\ \\ P+P(2)(0.03)=39.75 \\ \\ 1.06P=39.75 \\ \\ P=\$37.50[/tex]
y=1.7952 × 2.0657^x
find x when y=1000
The value of x when y = 1000 is 8.59.
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,
y = 1.7952 x [tex]2.0657^x[/tex]
Substitute y = 1000
1000 = 1.7952 x [tex]2.0657^x[/tex]
10³ = 1.7952 x [tex]2.0657^x[/tex]
Taking logs on both sides.
log 10³ = log (1.7952 x [tex]2.0657^x[/tex])
3 log 10 = log 1.7952 + x log 2.0657
3 x 1 = 0.25 + 0.32x
3 = 0.25 + 0.32x
0.32x = 3 - 0.25
x = 2.75/0.32
x = 8.59
Thus,
The value of x is 8.59.
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help! this needs to be done ASAP and I don't understand any of these!
Answer:
Step-by-step explanation: