For the given equation, [tex](x-7)2=36[/tex] the value for [tex]x=25[/tex].
Calculating the value of the unknown variable while keeping the equation balanced on both sides is the process of solving equations.
A condition on a variable is an equation when it ensures that two expressions in the variable have the same value. The equation's solution is the amount of the variable for which the condition is met.
Initially, the equation [tex](x-7)2=36[/tex] must be made simplified to find [tex]x[/tex].
[tex](x-7)2=36[/tex]
By using distributive law,
⇒ [tex](x-7)2=36[/tex]
⇒ [tex]2x-14=36[/tex]
Now add 14 on both sides,
⇒ [tex]2x-14+14 =36+14[/tex]
⇒ [tex]2x =36+14[/tex]
⇒ [tex]2x =50[/tex]
As the next step, divide both sides by 2,
⇒ [tex]\frac{2x }{2} =\frac{50}{2}[/tex]
⇒ [tex]x=25[/tex]
Therefore, after solving the equation step-by-step, [tex]x=25[/tex].
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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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Write an equation that represents the line. Use exact numbers.
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]
Use the following probabilities to answer the question. It may be helpful to sketch a Venn diagram.
P(A) = 0.37, P(B) = 0.43 and P(AandB) = 0.20.
P(B | not A) =
=
The probability of B | not A i.e. P(B | not A) is 0.3651
How to find P(B | not A)?Probability is defined as the likelihood of a desired event happening.
Given that: P(A) = 0.37, P(B) = 0.43 and P(AandB) = 0.20.
We want to find P(B | not A)
Remember: P(A | B) = P(A n B) / P(B)
Thus, P(B | not A) = P(B and not A) / P(not A)
P(not A) = 1 - P(A) = 1 - 0.37 = 0.63
P(B and not A) = P(B) - P(A and B) = 0.43 - 0.20 = 0.23
Hence,
P(B | not A) = P(B and not A) / P(not A) = 0.23 / 0.63 = 0.3651
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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!
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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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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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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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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What is the value of (2,820/8) / 5?
[The slashes are divided by]
Answer:
70.5
Step-by-step explanation:
2,820/8 equals 352.5.
352.5/5 equals 70.5.
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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evaluate for x=2
12x+8 divided by 4
Answer:
12x + 32
Step-by-step explanation:
Multiply 8 and 4 to get 32.
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.
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:
if a1 =2 and an= -2an-1 then find the value of a4
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.
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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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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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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Which equation accurately represents this statement? Select three options. Negative 3 less than 4.9 times a number, x, is the same as 12.8. Negative 3 minus 4.9 x = 12.8 4.9 x minus (negative 3) = 12.8 3 + 4.9 x = 12.8 (4.9 minus 3) x = 12.8 12.8 = 4.9 x + 3
The value of x in the statement negative 3 less than 4.9 times a number x is the same as 12.8 is 2.
What is a numerical expression?A numerical expression is a mathematical statement written in the form of numbers and unknown variables. We can form numerical expressions from statements.
Given a statement negative 3 less than 4.9 times a number, x, is the same as 12.8 this can be numerically expressed as,
4.9x - (- 3) = 12.8.
4.9x + 3 = 12.8
4.9x = 12.8 - 3.
4.9x = 9.8.
x = 9.8/4.9.
x = 2.
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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!
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.
which figure comes next in a pattern?
Answer:
square
Step-by-step explanation:
need more information
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
The straight line distance between the towns of Martville and Edentown is 120 miles. The straight-line distance between Martville and Newberg is 150 miles.
Which of the following represents a possible straight-line distance between Edentown and Newberg if the three towns form a right triangle on a map?
270 miles
30 miles
90 miles
135 miles
The straight-line distance between Edentown and Newberg is 90 miles. The correct option is the third option 90 miles
Calculating the straight-line distance between two townsFrom the question, we are to determine the possible straight-line distance between Edentown and Newberg if the three towns form a right triangle.
Let the straight-line distance between Edentown and Newberg be x.
Now,
Assume that the straight-line distance between Martville and Newberg is the hypotenuse of the right triangle,
Then,
From the Pythagorean theorem, we can write that
150² = x² + 120²
22500 = x² + 14400
x² = 22500 - 14400
x² = 8100
x = √8100
x = 90 miles
Hence, the straight-line distance is 90 miles
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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
What fraction represents the solution of 4p5 + 3 = 37 + 5p ?
Answer:
Step-by-step explanation:
p = 8
Two ratios that both have values that are equal.
Group of answer choices
Measurement of a Quantity
Rate
Quantity
Equivalent Ratios
Answer:
Equivalent Ratios
Step-by-step explanation:
Two ratios that have the same value are called equivalent ratios. To find an equivalent ratio, multiply or divide both quantities by the same number. It is the same process as finding equivalent fractions.
The equality of two ratios is also known as proportion. The antecedent and consequent values are different.
Equivalent ratios are the same when we compare them. The two quantities of ratio should be of the same kind. To find an equivalent ratio we need to multiply.
Equivalent ratios are just like equivalent fractions. If two ratios have the same value, then they are equivalent, even though they may look very different!
Equivalent ratios or equal ratios are two ratios that express the same relationship between numbers as we covered in our tutorial on scaling up ratios.
Answer:
equivalent ratios
Step-by-step explanation:
write polynomial function in standard form with given zeros, x=-2,0,1
The equation for the polynomial in the standard form is:
P(x) = x^3 + x^2 - 2x
How to find the equation of the polynomial?A polynomial of degree N with the n zeros {x₁, x₂, x₃, ..., xₙ} is written as:
P(x) = (x - x₁)*(x - x₂)*...*(x - xₙ)
That is called the factorized form of the polynomial, and we are assuming that the leading coefficient is equal to 1 just for simplicity.
In this case we have 3 zeros {-2, 0, 1}, so the polynomial is of degree 3, and we can write it as:
P(x) = (x + 2)*(x - 0)*(x - 1)
To write the polynomial in the standard form, we need to expand the product:
P(x) = (x + 2)*(x)*(x - 1)
P(x) = (x^2 + 2x)*(x - 1)
P(x) = (x^3 + 2x^2 - x^2 - 2x)
P(x) = x^3 + x^2 - 2x
That is the polynomial.
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please help i will give brainliest
Explanation:
We want to prove by contradiction that corresponding angles 1 and 5 made by a transversal crossing non-parallel lines are not congruent.
To prove by contradiction, we make an assumption that results in a demonstrably false conclusion. This allows us to conclude the assumption is false.
ProofAssume angles 1 and 5 are congruent.
Then lines m and n are parallel by the converse of the corresponding angles theorem.
Lines m and n are not parallel, hence our assumption must be false.
Angles 1 and 5 are not congruent.