Identify the vertex of the parabola given by f(x) = 2x
2 – 12x + 7.
Considering the definition of vertex of a quadratic function, the vertex of the quadratic equation y=2x²−12x+7 is (3; -11).
Vertex of a quadratic functionA quadratic function is a variable of a polynomial function defined by f(x)=ax² + bx +c, where a≠0
The graphs of these functions correspond to vertical parabolas (symmetric axis parallel to the ordinate axis), with the particularity that:
when a>0, the parabola opens "up".when a<0, the parabola opens "down".The vertex of a quadratic equation or parabola is the highest or lowest point on the graph corresponding to that function. The vertex is calculated as:
The value of -b÷(2a) indicates the value of x of the vertex.Substituting value of x into the function, you get the value of y of the vertex.Vertex in this caseIn this case, the quadratic equation y=2x²−12x+7, where:
a=2b= -12c= 7The value of x of the vertex is calculated as -(-12)÷(2×2)
Solving: -(-12)÷(4)= 12÷4= 3
The value of y of the vertex of the function is calculated as y=2×3²−12×3+7
Solving y= -11
Finally, the vertex in this case is (3; -11).
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Calvin drew a rectangle with one side greater than 10 but
less than 20. He multiplies to find its area.
Calvin's work: 8x3+8 x 10 = 104
Find the dimensions of Calvin's rectangle.
Explain how you know that your answer is correct.
Please help!!!!
Step-by-step explanation:
LET WIDTH= X
LENGTH= X+5
PERIMETER= 2(L+B)= 170
2(X+X+5)= 170
2X+5= 85
2X= 80
X= 40
WIDTH= 40
LENGTH= 45
The length of a rectangle is five more than the width. The perimeter is 170. What is the length and width? Write the equation and solve.
Sydney wants to make 15 rings, and each ring requires 60 beads. That means you need to multiply 60 beads by 15 rings to see how many beads
Answer:No
Step-by-step explanation:
Sydney wants to make 15 rings, and each ring requires 60 beads. That means you need to multiply 60 beads by 15 rings to see how many beads she needs. 60 times 15 is 900. Sydney only has 852 beads.
Write a system of equations to describe the situation below, solve using substitution, and fill
in the blanks.
Nina is collecting pledges for a walk-a-thon. Her mother has pledged a flat donation of $12,
and her grandmother has pledged $1 per mile. If Nina walks a certain distance, the two
donors will end up owing the same amount. How much will each donor owe? What is that
distance?
Nina's mother and grandmother will each owe $
if she walks
miles.
Nina's mother and grandmother will each owe $12 if she walks 12 miles
What is an equation ?
An equation is a mathematical statement that proves two mathematical expressions are equal in algebra, and this is how it is most commonly used. In the equation 3x + 5 = 14, for instance, the two expressions 3x + 5 and 14 are separated by the symbol "equal."
Standard form, slope-intercept form, and point-slope form are the three main types of linear equations.
According to the question we get to know
mother = 12
Grandmother = x
12 = x
x = 12
$ 12 , she walks 12 miles
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Find the equation (in terms of
x
of the line through the points (-5,-1) and (4,-5)
Answer:
-4/9x - 16.22222
Step-by-step explanation:
Use slope formula
(-5) - (-1) = -4
4 - (-5) = 9
Remember -(-) cancel out to become positive!
The answer is
-4/9x - 16.22222
I can't approximate the 16.222, it is literally that. I did trial and error.
What fraction represents the solution of 4p5 + 3 = 37 + 5p ?
Answer:
Step-by-step explanation:
p = 8
If
log
b
(
8
)
≈
0.8
log
b
(
8
)
≈
0.8
and
log
b
(
5
)
≈
0.6
log
b
(
5
)
≈
0.6
,
log
b
(
200
)
≈
log
b
(
200
)
≈
The answer is [tex]Log_{b}200 = 2[/tex]
What is logarithm?A logarithm is the power to which a number must be raised in order to get some other number.
Given that, [tex]log_{b} 8 = 0.8, log_{b} 5 = 0.6[/tex]
Using formula, [tex]log_{b} a+log_{b} b = log_{b} ab[/tex]
[tex]log_{b} 5 +log_{b} 5 = log_{b} 5*5 = log_{b} 25\\= 0.6+0.6 = 1.2\\\\[/tex]
[tex]log_{b} 200 = log_{b} 25*8\\log_{b} 25*8 = log_{b} 25 + log_{b} 25*8\\ log_{b} 25 + log_{b} 25*8 = 1.2 + 0.8 = 2[/tex]
Hence, The answer is [tex]Log_{b}200 = 2[/tex]
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Given h(x)=4x+2, find h(5)
PLEASE HELP ME
Answer:22
Step-by-step explanation:
Answer: h(5)=22
Step-by-step explanation:
h(5) is saying that x is equal to 5
replace x with 5
h(5)=4(5)+2
h(5)=20+2
h(5)=22
Write an equation that represents the line. Use exact numbers.
What is the common ratio and the general term equation, a, of the geometric sequence?
The common ratio and the general term equation, a, of the geometric sequence is A. r = 1/2 , an = 16(1/2)^(n - 1).
What is a geometric sequence?A geometric sequence simply means the sequence of non zero numbers whereby the term after the first is simony found by multiplying the previous number by a common ratio
Based on the information, the common ratio will be:
= Second term / First term
= -8 / -16
= 1/2
The nth term will then be 16(1/2)^(n - 1).
The correct option is A.
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How many days are in 42 weeks?
294 days
504 days
1,008 days
2,520 days
Answer:
294 days
Step-by-step explanation:
Multiply 42 x 7 and you've got 294 days, which will be your answer.
$1450 is invested at 6.5 % compounded continuously. How long will it take for the balance to reach $2900?
Answer:
Step-by-step explanation:
94.25 days
Which function is best represented by the graph?
The exponential function graphed is the one in option A.
d(x) = (0.45)^x
Which is the function on the graph?On the graph we can see some kind of exponential function, such that it has a vertical asymptote at x = -3
It also decreases as x increases, then the exponential function has a base that is smaller than 1 and larger than zero.
Because the y-intercept must be 1, we can discard option D where:
d(0) =4*(0.5)^0 = 4*1 = 4
Now, the only other option with a base between 0 and 1 is the first option:
d(x) = (0.45)^x
So that is the correct option.
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which figure comes next in a pattern?
Answer:
square
Step-by-step explanation:
need more information
Percent of Sales Method At the end of the current year, Accounts Receivable has a balance of $805,000, Allowance for Doubtful Accounts has a debit balance of $7,000, and sales for the year total $3,620,000. Bad debt expense is estimated at 3/4 of 1% of sales. a. Determine the amount of the adjusting entry for uncollectible accounts.
If Percent of Sales Method At the end of the current year, Accounts Receivable has a balance of $805,000. the amount of the adjusting entry for uncollectible accounts is $27,150.
How to find the amount of bad debts?a. Amount of bad debts
Amount of bad debts = Sales × Bad debts rate
Amount of bad debts = $3,620,000×0.75%
Amount of bad debts= $27,150
b. Adjusted balances
Accounts Receivable $805,000
Allowance for Doubtful Accounts $20,150
( $27,150- $7,000)
Bad Debt Expense $27,150
c. Net realizable value of accounts receivable
Net realizable value of accounts receivable = Balance of accounts receivables - Allowance for Doubtful Accounts
Net realizable value of accounts receivable = $805,000- $20,150
Net realizable value of accounts receivable = $784,850
Therefore the amount of bad debts is $27,150.
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Can you guys please help?
A science fair has 405 projects. The coordinator displays the projects in rows of 42. How many rows have exactly 42 projects?
I really do not understand this. It would really help me if after you have answered the question, you could explain how you got that answer. Thank you!
Answer: x=9
Step-by-step explanation:
To get the answer, just divide, but you must not count in the rows that have less or more than 42 projects. 405/42=xThere are 9 rows that have exactly 42 projects because 42 x 9 = 378, which is the closest we can get to 405.
You have an ace, king, queen, and jack from a deck of cards. After shuffling the cards, you draw one card. Then you replace the card, shuffle again, and again draw a card. What is the probability that you will draw a king and a queen in either order? An ace, king, queen, and jack playing card. CLEARCHECK The total number of possible outcomes is x . The probability of drawing a king and a queen in either order is x
Answer:
[tex]\dfrac{2}{169}[/tex]
Step-by-step explanation:
A standard 52-card deck comprises 4 suits (Spades, Hearts, Diamonds, and Clubs).
Each suit comprises 10 numerical cards (numbered 2 through 10, plus an "ace") and 3 "court" cards (jack, queen and king).
Therefore:
The total number of possible outcomes is 52.There are 4 kings and 4 queens in a standard deck of cards.[tex]\boxed{\sf Probability\:of\:an\:event\:occurring = \dfrac{Number\:of\:ways\:it\:can\:occur}{Total\:number\:of\:possible\:outcomes}}[/tex]
[tex]\implies \sf P(Queen)=\dfrac{4}{52}=\dfrac{1}{13}[/tex]
[tex]\implies \sf P(King)=\dfrac{4}{52}=\dfrac{1}{13}[/tex]
Therefore, the probability of drawing a king, replacing the card, and drawing a queen is:
[tex]\implies \sf P(King)\;and\;P(Queen)=\dfrac{1}{13}\times \dfrac{1}{13}=\dfrac{1}{169}[/tex]
Similarly, the probability of drawing a queen, replacing the card, and drawing a king is:
[tex]\implies \sf P(Queen)\;and\;P(King)=\dfrac{1}{13}\times \dfrac{1}{13}=\dfrac{1}{169}[/tex]
Therefore, the probability of drawing a king then a queen, or a queen then a king is:
[tex]\implies \sf P(King\;and\;Queen)\;or\;P(Queen\;and\;King)=\dfrac{1}{169}+\dfrac{1}{169}=\dfrac{2}{169}[/tex]
Please help I need detailed explication. I will give 100 points and brianliest.
Write a linear equation that represents the trend line that you have drawn. Be sure to use points that are located on your trend line to find the equation. Show your work.
Answer:
[tex]y=53.75x+70[/tex]
Step-by-step explanation:
From inspection of the given graph with added trendline:
y-intercept ≈ (0, 70)another point on the trendline ≈ (8, 500)Find the slope of the trendline by substituting the identified points into the slope formula:
[tex]\implies \textsf{slope}\:(m)=\dfrac{y_2-y_1}{x_2-x_1}=\dfrac{500-70}{8-0}=53.75[/tex]
[tex]\boxed{\begin{minipage}{6.3 cm}\underline{Slope-intercept form of a linear equation}\\\\$y=mx+b$\\\\where:\\ \phantom{ww}$\bullet$ $m$ is the slope. \\ \phantom{ww}$\bullet$ $b$ is the $y$-intercept.\\\end{minipage}}[/tex]
Substitute the found slope and y-intercept into the slope-intercept formula to create an equation for the trendline:
[tex]\implies y=53.75x+70[/tex]
What are the domain and range of h(x) = 3|x|?
Domain: [tex]([/tex] -∝,∝ [tex])[/tex], { [tex]x|x[/tex] ∈ R }
Range: [tex][0,[/tex] ∝ [tex])[/tex], { [tex]y|y\geq 0[/tex] }
Hope this helps!
Do this, for example, 3v x 2t =6vt
Algebraic expressions are mathematical expressions that combine a mathematical constant and variables.
What types of algebraic expressions are used in the multiplication of algebraic expressions?
The four basic mathematical operators are addition (+), subtraction (-), multiplication (), and division. Algebraic expressions are mathematical expressions that combine a mathematical constant and variables connected by one or more of the four basic mathematical operations (). Algebraic expressions include things like 4 x + 8, x - y, etc. The numbers 4 and 8 serve as the expression's given constants in the example 4 x + 8, while the word x serves as the equation's variable.
The process of multiplying two provided expressions made up of variables and constants is known as the multiplication of algebraic expressions. An expression that uses integer constants and variables together is called an algebraic expression.
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if a1 =2 and an= -2an-1 then find the value of a4
describe the transformations from the graph f(x)=|x| to the graph d(x) = -|x-3| + 5
The function d(x) = - |x - 3| + 5 is the result of using an horizontal translation, reflection about the x-axis and vertical translation on the function f(x) = |x|.
What kind of transformations are used to transform of the equation of a given graph?
In this question we have the definition of a function (f(x)) and its image (d(x)), the latter is the result of three rigid transformations:
Horizontal translation
f'(x) = f(x - 3)
Reflection about the x-axis
f''(x) = - f'(x)
Vertical translation
d(x) = f''(x) + 5
If we know that f(x) = |x|, then the series of rigid transformations is shown below:
Horizontal translation
f'(x) = |x - 3|
Reflection about the x-axis
f''(x) = - |x - 3|
Vertical translation
d(x) = - |x - 3| + 5
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Which confidence level would produce the widest interval when estimating
the mean of a population based on the mean and standard deviation of a
sample of that population?
Answer:
99%
Step-by-step explanation:
How do you solve -y +28 +y^2 =2y +2y^2 for y?
We are given the following:
Solve for y.
[tex]-y+28+y^2=2y+2y^2[/tex]
This being said, lets begin.
~~~~~~~~~~~~~~~~~~~~~~~
1. First, move [tex]2y^2[/tex] to the left side.
[tex]-y+28-y^2=2y[/tex]
2. Move [tex]2y[/tex] to the left side.
[tex]-y^2-3y+28=0[/tex]
3. Solve with the quadratic formula.
[tex]y_{1,2} = \frac{-(-3) -+ \sqrt{(-3)^2-4(-1)*28} }{2(-1)}[/tex]
4. [tex]\sqrt{(-3)^2-4(-1)*28}=11[/tex]
[tex]y_{1,2} =\frac{-(3)-+11}{2(-1)}[/tex]
5. Separate the solutions.
[tex]y=\frac{-(-3)+11}{2(-1)} , y_{2} =\frac{-(-3)-11}{2(-1)}[/tex]
6.
[tex]y=\frac{-(-3)+11}{2(-1)}[/tex] [tex]=-7[/tex] ← First Solution
7.
[tex]y=\frac{-(-3)-11}{2(-1)} =4[/tex] ←Second Solution
Final Solution:
[tex]y=-7,y=4[/tex]
Hope this helps!
78x7x54x8 show your work
Answer:
235,872
Step-by-step explanation:
Simplify:
78×7×54×8
78×69
= 235,872
Answer:
235872
Step-by-step explanation:
I hope it's useful to you
Let X be a continuous random variable with the pdf given by f(x)= ax2 for 0 < x ≤ 3. Determine the value of constant 'a' correct to 2 decimal places.
The value of the constant a in f(x) = ax² such that 0 < x ≤ 3 is 0.11
How to determine the value of the constant a?The probability density function is given as
f(x) = ax²
Such that
0 < x ≤ 3
To determine the value of the constant a, we make use of the following equation
[tex]\int\limits^a_b {f(x)} \, dx = 1[/tex]
So, we have:
[tex]\int\limits^3_0 {ax^2} \, dx = 1[/tex]
Factor out the constant
[tex]a\int\limits^3_0 {x^2} \, dx = 1[/tex]
Differentiate the equation
So, we have the following representation
[tex]a\frac{x^3}3 |^3_0 = 1[/tex]
Expand the equation
a[3³ - 0³]/3 = 1
Evaluate the difference
a[3³]/3 = 1
Evaluate the quotient
9a = 1
Divide both sides by 9
a = 0.11
Hence, the variable a is 0.11
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Quadratic Equations and Complex Numbers
please give a clear answer, thank you <3
The result of the given terms is -2/5 as per the given question from complex numbers.
What is a complex number?There is a multiplicative inverse for every nonzero complex number. As a result, complex numbers are a field with real numbers as a subfield. The complex numbers also form a two-dimensional real vector space with 1, I as the standard basis.
Because of this standard basis, the complex numbers form a Cartesian plane known as the complex plane. This allows for a geometric interpretation of complex numbers and operations, as well as the expression of geometric features and constructions in terms of complex numbers. Real numbers, for example, constitute the real line, which corresponds to the complex plane's horizontal axis.
=(((3/5)+(1/5)i)+((4/5)-(2/5)i) -((9/5)-(1/5)i))
=((3/5)+(4/5)-(9/5))-i((1/5)+i((1/5)-(2/5)+(1/5))
=(-2/5)+i(0)
= -2/5
Therefore, the result of the given terms is -2/5
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In parallelogram DEFG if EH=23 find HG.
The length of HG is also equal to 23, which is the length of EH because the line DF bisects EG in the parallelogram DEFG.
Diagonals of a parallelogramA parallelogram is a quadrilateral, and the diagonals always bisect each other. However, diagonals only form right angles if the parallelogram is a rhombus or a square.
For the given parallelogram DEFG; the lines DF and EG are its diagonals, and the both bisect each other, that is the cut each other to form two equal parts.
So EH and HG are equal halves of the line EG
Therefore, since EH = 23 then HG = 23 because they form a diagonal of the parallelogram DEFG bisected by the diagonal DE.
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100 points
Find the maximum value of the objective function and the values of x and y for which it occurs.
f=5x+2y
x+2y[tex]\leq[/tex]=6 x[tex]\geq[/tex]=0 and y[tex]\geq[/tex]=0
2x+y[tex]\leq[/tex]=6
Answer:
Maximum value of the objective function is 15
This occurs at x = 3, y = 0
Step-by-step explanation:
Attached is a plot of the two inequalities. The feasible region is the dark shaded area bounded by the points O, A, B and C
The maximum value of the objective function will occur at one of the corner points
The four corner points are
O (0,0)
A(0,3)
B(2,2)
C(3,0)
Plug in each of these values into the objective function, see which of the corner points will yield the maximum value and those will be the optimal values of x and y
Corner point (x, y) O.F Value (5x + 2y)
(0, 3) 5(0) + 2(3) = 6
(2, 2) 5(2) + 2(2) = 14
(3, 0) 5(3) + 2(0) = 15 (Maximum value)
Tell wether the data in the table can be modeled by a linear equation. Explain.
If possible, write a linear equation that represents y as a function of x. If not possible, leave blank.
Answer:
yes
By dividing the difference between each two corresponding data values, we get a constant rate of change.
y = 0.2x + 1.2
Step-by-step explanation:
1. Find the rate of change between each pair of data values in the table and compare to see if they are equal:
(1.4-1.2)/(1-0) = 0.2/1 = 0.2
(1.6-1.4)/(2-1) = 0.2/1 = 0.2
(2-1.6)/(4-2) = 0.4/2 = 0.2
2. Substitute the numbers found in step 1 for m, and the y-value in the data pair (0,1.2) as b in the equation y = mx + b: y = 0.2x + 1.2