Answer: The given expression is already in the vertex form:
y = 2(x-3)² - 1
It is the standard form of a parabolic equation with the vertex at (3, -1) and opens upwards.
Step-by-step explanation:
Answer:
[tex]y=2(x-3)^2-2[/tex]
Step-by-step explanation:
[tex]y=2(x-4)(x-2)\\y=2(x^2-6x+8)\\y+2(1)=2(x^2-6x+8+1)\\y+2=2(x^2-6x+9)\\y+2=2(x-3)^2\\y=2(x-3)^2-2[/tex]
Michael needs to pay car insurance premiums of $958 two times per year. He has decided to make deposits from each paycheck to a savings account for “Other Expenses (Predictable)” to cover this expense. How much should Michael deposit from each paycheck if the paycheck is bi-weekly?
Step-by-step explanation:
Michael needs to pay car insurance premiums of $958 two times per year. Since a year has 52 weeks, this means he needs to pay $958 * 2 = $1916 per year.
Since his paycheck is bi-weekly, he needs to make a deposit of $1916 / 26 = $73.54 from each paycheck to cover the expense.
So Michael should deposit $73.54 from each bi-weekly paycheck to a savings account for "Other Expenses (Predictable)" to cover the car insurance premiums.
Simplify the following expression.
m²n³+ 18m³n² + 10m²n
2m²n
A.
B.
C.
O D.
m²n² + 9mn + 5
mn³ + 18m³n² + 8m²n
m²n² + 9mn + 5
2
²² + 16mn + 8
2
The simplification of the expression m²n³+ 18m³n² + 10m²n+2m²n is m²n ( n²+18mn+ 12)
What is simplifying expression?Simplifying an expression is just another way to say solving a math problem. When you simplify an expression, you're basically trying to write it in the simplest way possible. At the end, there shouldn't be any more adding, subtracting, multiplying, or dividing left to do.
m²n³+ 18m³n² + 10m²n+2m²n = m²n³ + 18m³n² +12m²n
Therefore we factorize the common factors out, they are m²n
= m²n ( n²+18mn+ 12)
therefore the simplification of the expression m²n³+ 18m³n² + 10m²n+2m²n is m²n ( n²+18mn+ 12)
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g(x) = x°-27x (a) Determine whether g is even, odd, or neither (b) There is a local minimum of -54 at 3. Determine the local maximum (a) Determine whether g is even, odd, or neither O Neither O Odd O Even (b) There is a local minimum of - 54 at 3. Determine the local maximum.
The local maximum is x = 13.5 with a value of g(13.5) = (13.5)^2 - 27 * 13.5 = g(13.5) = 125.375.
(a) To determine whether a function is even, odd, or neither, we need to check if g(x) = g(-x) for all x (even), g(x) = -g(-x) for all x (odd), or neither.
g(x) = x^2 - 27x is neither even nor odd because it does not satisfy either of the two conditions for even or odd functions.
(b) To determine the local maximum, we need to find the critical points (points where the derivative is equal to zero or undefined) and then determine if they are local maxima, local minima, or neither.
g'(x) = 2x - 27, which has critical points at x = 13.5 and x = 0. Since g'(x) > 0 for x < 0 and g'(x) < 0 for x > 0, x = 0 is a local minimum. Since g'(x) < 0 for x < 13.5 and g'(x) > 0 for x > 13.5, x = 13.5 is a local maximum.
Therefore, the local maximum is x = 13.5 with a value of g(13.5) = (13.5)^2 - 27 * 13.5 = g(13.5) = 125.375.
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A small indoor greenhouse (herbarium) is made entirely of glass panes (including base) held together with tape. It is 30 cm long, 25 cm wide and 25 cm high. (1) What is the area of the glass? (ii) How much of tape is needed for all the 12 edges?
The area of the small indoor greenhouse (herbarium) is equal to 4,250 cm².
The length of tape needed for all the 12 edges is equal to 320 cm.
How to calculate the area of the glass?Mathematically, the total surface area (TSA) of this glass panes (including base) can be calculated by using this mathematical expression:
Total surface area (TSA) = 2[lb + lh + bh]
Where:
l represent the length of the glass panes.b represent the breadth of the glass panes.h represent the height of the glass panes.Total surface area (TSA) = 2[(30 × 25) + (30 × 25) + (25 × 25)]
Total surface area (TSA) = 2[750 + 750 + 625]
Total surface area (TSA) = 2[2,125]
Total surface area (TSA) = 4,250 cm².
Next, we would determine the length of tape needed for all the 12 edges by using this mathematical expression:
Total length = 4(l + b + h)
Total length = 4(30 + 25 + 25)
Total length = 4(80)
Total length = 320 cm.
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Part d
I m really confused
The expressions with powers are ( -7 )³ and [tex]3^{-2}[/tex]
What is an expression?
A mathematical expression is a phrase containing a minimum of two numbers or variables and a minimum of one mathematical operation. It is possible to multiply, divide, add, or subtract in math. An expression has the following structure: (Mathematical Operator, Number/Variable, Expression)
The order of operations is a rule that specifies the right procedure to follow when evaluating a mathematical equation. Using the acronym PEMDAS, we can memorize this order: parentheses, exponents, multiplication, and division (left to right), addition and subtraction (from left to right).
a) -7 is taken 3 times. so raise power as 3
( -7 )³
b) 1/(3²) = [tex]3^{-2}[/tex]
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Geometry
There are 30 students in a class. They were asked if they have a cat or dog as a pet. 10 kids said they have a cat, 12 kids said they have a dog the rest said they don't have either. Of the kids that said they have a cat or dog, 3 kids said they have both pets.
(Please answer in fraction, decimal, and percent form)
a. How many students do not have either pet?
b. If a student is selected at random what is the probability that they have both pets?
c. If a student is selected at random, what is the probability that they have a cat or dog?
Answer:
a. 8
b. 1/10
c. 19/30
Step-by-step explanation:
a. 12 + 10 = 22 30 - 22 = 8
b. 3 students have both, 3/30 simplified is 1/10
not 100% sure about c. but is my best bet
Find the value of x
x + x + (2x + 5) + (2x + 7)
What is the range of the function f(x) = 2x + 4 when the domain is {-2, 0, 3}?
A. {0, 4, 10}
B. All real numbers
O C. {4. 25, 5, 12}
D. {4. 25, 4, 12}
The range of the function is {0, 4, 10}. Option A. {0, 4, 10}
The concept used in finding the range of a function is called functional mapping, which maps the elements in the domain of the function to the corresponding elements in the range.
In this problem, we took a set of values in the domain of the function (which was {-2, 0, 3}) and evaluated the function for each of those values to find the corresponding outputs in the range of the function, which was {0, 4, 10}.
To find the range of the function f(x) = 2x + 4 for the domain {-2, 0, 3}, we need to calculate the output of the function for each of the values in the domain:
For x = -2: f(-2) = 2 * -2 + 4 = -4 + 4 = 0
For x = 0: f(0) = 2 * 0 + 4 = 4
For x = 3: f(3) = 2 * 3 + 4 = 10
Therefore, the range of the function is {0, 4, 10}. Option A. {0, 4, 10}
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The range of the function f(x) = 2x+4 when the domain is {-2,0,3} is {0,4,10} .
The range for this function would be {0,4,10}.
Given, Function f(x) = 2x+4
Domain = {-2,0,3}
After putting the value of x= -2 in the function f(x) =2x+4 ,
f(-2) = 2×-2+4 = -4+4= 0
After putting the value of x= 0 in the function f(x) = 2x+4
f(0)= 2×0+4 =0+4=4
After putting the value of x= 3 in the function f(x) = 2x+4
f(3) =2×3+4= 6+4= 10
Here, after putting values in function the domain will become {0,4,10}.
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i'll pick you as brainily please quick formula for finding the distance between two points
[tex]Let \: the \: two \: points \: be \: \underline{\underline{A( x_{1} ,y_{1})}} \: and \: \underline{\underline{B \: ( x_{2}, y_{2})}}[/tex]
Then ,
[tex]\boxed{d(AB) = \sqrt{ {( x_{2} - x_{1}) }^{2} + {( y_{2} - y_{1}) }^{2} } }\\ [/tex]
where , d(AB) is the distance between the two points A and B.
hope helpful! :)
Answer:
the Distance Between the two points a and b
Step-by-step explanation:
Distance between two points is the length of the line segment that connects the two points in a plane. The formula to find the distance between the two points is usually given by d=√((x2 – x1)² + (y2 – y1)²). This formula is used to find the distance between any two points on a coordinate plane or x-y plane.
Find the point in which the line meets the plane.
x = 1 - t, y = 3t, z = 1 + t; 2x - y + 3z = 6
The point in which the line meets the plane is (3/2, -3/2, 1/2)
The planes is 2x - y + 3z = 6.
The lines are x = 1 - t, y = 3t, z = 1 + t.
We now the value of x, y, z. So we put the value of x, y, z in the plane.
2x - y + 3z = 6
2(1 - t) - 3t + 3(1 + t) = 6
Simplifying
2 - 2t - 3t + 3 + 3t = 6
5 - 2t = 6
Subtract 5 on both side, we get
-2t = 1
Divide by -2 on both side, we get
t = -1/2
Now finding the value of x, y, z by putting the t
x = 1 - t
x = 1 - (-1/2)
x = 1 + 1/2
x = 3/2
y = 3t
y = 3(-1/2)
y = -3/2
z = 1 + t
z = 1 + (-1/2)
z = 1 - 1/2
z = 1/2
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in a hypothesis test, you assume the alternative hypothesis is true. True/ False
[FALSE] In a hypothesis test, you assume the alternative hypothesis is true.
ABOUT ALTERNATIVE HYPOTHESISIf the null hypothesis is rejected, then there is what is called an alternative hypothesis.
the alternative hypothesis states that there is an observed effect between the two variables in the experiment.
That is, the alternative hypothesis opposes the contents of the null hypothesis. Where there are differences and the nature of mutual influence between the two variables studied.
If there are deviations or differences between the two variables, then the null hypothesis is rejected while the alternative hypothesis is accepted. Conversely, if the null hypothesis is accepted, then the alternative hypothesis is rejected.
The alternative hypothesis is symbolized by Ha or also H1. Alternative hypotheses can use symbols not equal to (≠), less than (<), and more than (>).
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Kiran is flying a kite. He gets tired, so he stakes the kite to the ground. The kite is on a string that is 12 feet long and makes a 50 degree angle. What is the height of the kite
The height of the kite is equal to 9.19 feet.
What is the law of sines?In Mathematics, the law of sines is sometimes referred to as sine rule and it can be modeled by this mathematical expression:
[tex]\frac{sinA}{a} =\frac{sinB}{b} =\frac{sinC}{c}[/tex] or Sinθ = opposite/hypotenuse
What is the height of the kite?Since the reference angle lies between the ground and the string of the kite (hypotenuse), the side opposite the reference angle would be denoted by x and calculated as follows;
Sinθ = opposite/hypotenuse
Sin(50) = x/12
x = 12 × sin(50)
x = 12 × 0.7660
x = 9.19 feet.
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Trigonometry Finding side length
Please help!!
The value of x for each given right angled triangle are:
x = 5.6x = 4.52x = 4√3x = 6.26x = 5.87Please remember that these answers are calculated using calculator.
Remember that a triangle has the sum of angles 180°; then since we have a right angled triangle, then the sum of the non-right angles in the triangle should be equal to 90°.
We use Θ as the note for the unknown non-right angle.
1. 36° + Θ = 90°
Θ = 54°
Under the Sinus Law:
x / sin 54 = 7 / sin 90
x / 0.8 = 7 / 1
x = 5.6
2. 41° + Θ = 90°
Θ = 49°
Under the Sinus Law:
x / sin 49 = 6 / sin 90
x / 0.75 = 6 / 1
x = 4.52
3. 30° + Θ = 90°
Θ = 60°
Under the Sinus Law:
x / sin 90 = 6 / sin 60
x / 1 = 6 / (√3/2)
x = 4√3
4. 37° + Θ = 90°
Θ = 53°
Under the Sinus Law:
5 / sin 53 = x / sin 90
x = 5 / 0.79
x = 6.26
5. 33° + Θ = 90°
Θ = 57°
Under the Sinus Law:
7 / sin 90 = x / sin 57
7 / 1 = x / 0.84
x = 5.87
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the sum of 2 and y aleks
The sum of the expression 2 and y is (2+ y).
What is Expression?A mathematical operation such as subtraction, addition, multiplication, or division is used to combine terms into an expression. In a mathematical expression, the following terms are used:
An absolute numerical number is referred to as a constant.Variable: A symbol without a set value is referred to as a variable.Term: A term can be made up of a single constant, a single variable, or a mix of variables and constants multiplied or divided.Coefficient: In an expression, a coefficient is a number that is multiplied by a variable.Given:
The sum of 2 and y.
As, the sum is shows by the addition whose symbol is "+"
So, the sum of 2 and y is
= (2 + y).
Hence, the expression is ( 2+ y).
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How do analogies help readers (1 point)
1. They help readers understand definitions
2. They help readers identify figurative language
3. They help readers analyze the relationship between words
4. They help readers to better comprehend a plot
4. They help readers to better comprehend a plot. An analogy is a comparison of two, otherwise unrelated, things based on similarities in a single feature.
An analogy is what?a comparison of two otherwise disparate objects based on a shared characteristic; similarity; similarity in some specifics between disparate things.
An example of an analogy?To provide an explanation, lets compares one thing to another. "Life is like a box of chocolates—you never know what you're going to get," as an example. When making an analogy, you can utilise metaphors and similes. What Qualifies as a Good Analogy? An effective analogy strikes a balance between the competing objectives of familiarity and representativeness. Good analogies are well-known. They provide words for an abstract concept.
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A telephone line hangs between two poles 14 m apart in the shape of the catenary y = 25 cosh(x/25) − 20, where x and y are measured in meters. (a) Find the slope of this curve where it meets the right pole. (Round your answer to four decimal places. ). 2837 (b) Find the angle θ between the line and the pole. (Round your answer to two decimal places. )
The solutions to both parts of the problem regarding trigonometry have been given below.
Since, the curve traced by the given function is symmetric about vertical axis, is an even function and has minima at x=0, We have to find the slope of this curve at x=+7m, which is the point it meets the pole at the right side.
the derivative of
25cosh(x/25)−20 with respect to x will be
dy/dx = d(25cosh(x/25)−20)/dx
=(25sinh(x/25))/25
=sinh(x/25)
at x=+7 it's value would be ,
=sinh(7/25)=0.2836
Therefore, the slope of curve where it meets the right pole is
0.2836.
The slope of the curve is also given by tangent of the angle subtended by the curve at that point
therefore,
tan θ=0.2836
θ= tan -¹ (0.2836)
but,The expression for angle between right pole and line is
θ'=π/2-θ=π/2-(0.2836)
θ'=1.294 radians
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What is the simplest form of (4x3 + 6x – 7) + (3x3 – 5x2 – 5x)
Answer:
4x-4 that's what I gottt
What is Meant by Proof by Contradiction?
By assuming that the item we wish to prove is false and then demonstrating that the results of this are not feasible, we can prove something by contradiction.
What is meant by contradiction?3a + b = 1 6 . This is contradictory because 3a + b is an integer according to the closure properties, but 1/6 is not. It follows that there aren't any integers a and b for which 18a + 6b = 1. Each of the following claims can be demonstrated using contradiction. The foundation of the evidence by contradiction approach is the contradiction rule. Simple logic dictates that one should assume the falsity of any given premise or assertion. The supplied assertion must be true if this assumption results in a contradiction.When two angles of a triangle are equal, the sides that are on the other side of the equal angles are likewise equal. The evidence moves forward with the presumption that the opposing angles are not equal and creates a contradiction.To learn more about contradiction, refer to:
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The diameter of a circle is 16 meters. What is the radius?
Answer
8meters
Step-by-step explanation:
divide the diameter (16) by 2
=8
Is 6.9meters per second faster than 0.95 meters per second ?
Answer:
Yes
Step-by-step explanation:
Yes, because 6.9 > 0.95
Answer:
Yes
Step-by-step explanation:
Yes....about 7 times faster because 6.9 >> .95 meters
I need this answer TODAY
A triangle has one side that measures x, and the other two sides each measure 4 Inches less than x. The perimeter is 19
Inches.
What is the measure of x?
5
3
9
2
Answer:3
Step-by-step explanation: the closest multiple of for is 16 then reminder 3
Answer:
9
Step-by-step explanation:
one side of a triangle =x
the other two sides measure = (x-4) each
perimeter = 19
therefore :
perimeter of a triangle = x + (x-4) + (x-4)
I.e = x+x+x-4-4=19
= 3x -8=19
= 3x = 19+8
3x=27
divide both sides by 3
x=9
a four-acre lot has front footage of 250 feet. how long is it?
The length of the four-acre lot with front footage of 250 feet is approximately 693.76 feet.
In mathematics, "acre" is a unit of area that is commonly used to measure the size of a piece of land. One acre is equal to 43,560 square feet. To find the length of the lot, we need to know the area of the lot and the front footage.
Here we need to determine the length of a four-acre lot with front footage of 250 feet, we need to use the concept of area and the formula for calculating the area of a rectangle.
In this case, the area of the lot is four acres, or
=> 4 x 43,560 = 173,440 square feet.
In order to find the length of the lot, we can divide the area by the front footage, which is 250 feet.
By using the formula for the area of a rectangle, we can write this as:
=> Area = Length x Front Footage
Therefore, Length is calculated as
=> Area / Front Footage = 173,440 / 250 = 693.76 feet.
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Boubacar is driving on a long road trip. He created the graph below to represent the of gas left in his tank. What is the meaning of the point ? Time ()
of gas in the tank after .
The change in the number of of gas in the tank for every one additional .
How long it takes Boubacar to run out of gas.
The number of of gas initially in the tank.
The meaning of the point (1,10) on the graph of the function is given as follows:
10 gallons of gas in the tank after one hour.
How to interpret the point?All the points in the graph of a function have the format presented as follows:
(x,y).
In which:
x is the input variable.y is the output variable relative to the input variable x.For this problem, the input and output variables are given as follows:
Input: number of hours.Output: number of gallons of gases in the tank.Hence the interpretation of point (1,10) is that there are 10 gallons of gas in the tank after one hour.
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a website requires that passwords only contain alphabetic characters. for each character in checkstr that is not an alphabetic character, replace the character with 'x'.
After the loop has finished executing, the 'newstr' variable should contain 'abcdxxxxxXXXXX'. The newstr variable is set to an empty string and alphabetic, numerical, and symbol characters are replaced with 'x'.
newstr = "abcdxxxxxXXXXXX
1. Initialize a new string variable called 'newstr' set to an empty string.
2. Loop through each character in the 'checkstr' variable.
3. If the character is an alphabetic character, add it to the 'newstr' string.
4. If the character is not an alphabetic character, replace it with 'x' and add it to the 'newstr' string.
5. After the loop has finished executing, the 'newstr' variable should contain 'abcdxxxxxXXXXX'.
The newstr variable is set to an empty string and alphabetic, numerical, and symbol characters are replaced with 'x'.
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PLEASE HELP HELP HELP HELP HELP HELP
Note that one advantage of the given Linear equation over the graph given above is that the whereas from the equation, we can immediately tell what the slope (m)is and what the y-intercept (b) is, this is not given in the above graph.
What is the Y-intercept and the slope as given in the above Linear Equation?Note that every linear equation takes the following form:
y = mx + b
Where:
the variable b denotes the y-intercept of the graph of the line; and variable m denotes the slope of the line.Since we have the given linear equation to be:
y = 6/1x + 100
m here = 6/1 or 6 which is the slope; while
b here = 100, that is the y-intercept.
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he first three terms of a sequence are given. round to the nearest thousandth (if necessary). 2,5,8,...2,5,8,... find the 41st term.find the 41st term.
The first three terms of the sequence are 2, 5, and 8.The 41st term of this sequence is 122.
What is the 41st term of the sequence?To find the 41st term of this sequence, you can use the common difference method.Step 1: Determine the common difference by subtracting the second term from the first term, and then subtracting the third term from the second term.The common difference is:5 - 2 = 3and8 - 5 = 3Step 2: Since the common difference is the same for each pair of consecutive terms, we can conclude that this sequence is an arithmetic sequence.Step 3: To find the 41st term, you can use the formula for the nth term of an arithmetic sequence:an = a1 + (n - 1)dwhere a1 is the first term, n is the term you're looking for, and d is the common difference.Substituting in the values:an = 2 + (41 - 1)3 = 2 + (40)3 = 2 + 120 = 122So the 41st term of this sequence is 122.
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what is fingers and multipliers
Answer: Fingering makes transistors which are connected in series, mulpliers create transistors which are connected in parallel.
Step-by-step explanation:
"Fingers" and "multipliers" are terms used in mathematics and specifically in multiplication to help perform calculations faster and with more accuracy.
"Fingers" is a method of multiplication that uses fingers on one's hand as a visual aid to keep track of numbers being multiplied. The method is often used by children who are learning how to perform basic multiplication, as it provides a concrete way of visualizing the problem. The student would put up a certain number of fingers on one hand to represent one of the numbers being multiplied, and then use the other hand to count the number of times that the first number is being multiplied.
"Multipliers" are a set of pre-memorized values that can be used to perform multiplication more quickly. These values are usually small, and when multiplied by 10, 100, 1000, and so on, give the result of more complex multiplication problems. For example, one common multiplier is 9, which can be used to quickly multiply any number between 90 and 99, such as 93 * 9 = 837. Knowing these multipliers is a key part of mental math and helps to perform calculations faster and with more accuracy.
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Is (1,
–
1) a solution to this system of equations?
y=3x+6
y=
–
8x+7
Answer:
No
Step-by-step explanation:
Is (1, –1) a solution to this system of equations?
-1 = 3(1)+6
-1 = 3 + 6
-1 = 9
This is wrong! (1, -1) is not a solution for this system of equations.
A univerity tudent completed coure were three credit, and ome coure worth four credit. The tudent earned a total of 54 credit after completing 15 coure. How many coure or four credit did the tudent complete?
The student completed 9 courses of four credits each.
Let x = number of four-credit courses the student completed
If the student completed a total of 15 courses, then the expression for the number of three-credit courses the student completed is:
"15 - x"
If the student earned a total of 54 credits after completing 15 courses, then the equation to show this will be:
4x + 3(15 - x) = 54
Simplify the equation and solve for the value of x.
4x + 45 - 3x = 54
x = 9
Hence, the number of four-credit courses the student completed is 9 course.
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The response to a question has three alternatives: A,B , and C. A sample of 120 responses provides 54 A ,24 B, and 42C . Show the frequency and relative frequency distributions (use 2 decimal for the relative frequency column)
Class Frequency Relative Frequency
A
B
C
As a result, we obtain the frequency and relative frequency distributions:
Data Relative Frequency
A 0.5
B 0.19
C 0.31
What is relative frequency?The relative frequency is the ratio of the frequency to the total frequency corresponding to each entry.
Here,
Here we have a total sample as: 120
Also, the frequency corresponding to A is: 60
Corresponding to B is: 23
and corresponding to C is: 37
Hence, the Frequency table is as follows:
Data Frequency
A 60
B 23
C 37
The relative frequency table is given by:
Data Relative Frequency
A 60/120=0.5
B 23/120=0.19
C 37/120=0.31
Hence, we get the frequency and relative frequency distributions:
Data Relative Frequency
A 0.5
B 0.19
C 0.31
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