Answer:
x = 3 ± 5[tex]\sqrt{2}[/tex]
Step-by-step explanation:
x² - 6x - 41 = 0 ( add 41 to both sides )
x² - 6x = 41
to complete the square
add ( half the coefficient of the x- term )² to both sides
x² + 2(- 3)x + 9 = 41 + 9
(x - 3)² = 50 ( take square root of both sides )
x - 3 = ± [tex]\sqrt{50}[/tex] = ± 5[tex]\sqrt{2}[/tex] ( add 3 to both sides )
x = 3 ± 5[tex]\sqrt{2}[/tex]
Match the vocab word with the definition:
Question 1 options:
Order of Operations
Operator
Equation
Constant
Numerical Expression
Exponent (Power)
Evaluate
Variable Expression
Variable
Open Sentence
Term
Coefficient
Grouping Symbol
Inequality
1.
Devices, such as parentheses, brackets, and fraction bars, used to set apart an expression that should be simplified before other operations are performed
2.
An expression that consists of numbers, operations, and sometimes grouping symbol.
3.
The order in which operations must be computed when more than one operation is involve.
4.
A number representing how many times the base number should be multiplied by itself.
5.
A Symbol that represents a value that can change.
6.
A single number or variable, or numbers and variables multiplied together.
7.
The numerical factor in a term. A number being multiplied by a variable.
8.
A number on its own, it has a fixed value.
9.
A combination of variables, numbers, and operations.
10.
You replace, or substitute, all the variables with numbers and then simplify.
11.
A statement that the values of two math expressions are equal (indicated by the sign =).
12.
The relation between two expressions that are not equal, employing a sign such as ≠ “not equal to,” > “greater than,” or < “less than.”.
13.
The symbol of a math operation.
plus, minus, times, divided by, equals
14.
An equation or inequality containing one or more variable.
Answer:
1 : Grouping Symbol
2 : Operator
3 : Order of Operations
4 : Exponent
5 : Variable
6 : Term
7 : Coefficient
8 : Constant
9 : Numerical Expression
10 : Variable Expression
11 : Equation
12 : Inequality
13 : Evaluate
14 : Open Sentence
what is 40 divided by 50
Answer:
See below
Step-by-step explanation:
40 ÷ 50 = 40/50 = 4/5 = .8
Evaluate the following function for the given value.
f(x)=-x-2; find f(-7).
Answer: f(-7)=-9
Step-by-step explanation:
Jenny put all her shoeboxes in a row. The width of each shoebox is 12.02 cm. What is the total width of all 14 shoeboxes?
Answer:
168.28
Step-by-step explanation:
A population forms a normal distribution with a mean of μ = 55 and a standard deviation of σ = 12. For each of the following samples, compute the z-score for the sample mean. a. M = 58 for n = 4 scores b. M = 58 for n = 16 scores c. M = 58 for n = 36 scores
It should be noted that the z-score for the sample mean that's given is 0.5.
What is the z score!A Z-score is a metric that quantifies how closely a value relates to the mean of a set of values. Standard deviations from the mean are used to measure Z-score. A Z-score of zero means the data point's score is the same as the mean score.
The following can be seen from the information illustrated:
Mean ( u ) =55
Standard Deviation ( sd )=12
Number ( n ) = 4
Normal Distribution = Z= X- u / (sd/Sqrt(n) ~ N(0,1)
Z = (58-55)/12/ Sqrt ( 4 )
Z = 3/6= 0.5
Therefore, the z score is 0.5.
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Adam has 18 counters.
He gives 10 of the counters to Lesley.
a) What fraction of the 18 counters does Lesley get?
Give your answer in its simplest form.
b) What fraction of the 18 counters does Adam have now?
Give your answer in its simplest form.
The fraction of counters Lesley get if Adam gives 10 counters out of 18 counters is 5/9.
The fraction of counters Adam have now is 4/9.
FractionThis is an expression which consists of a numerator and a denominator
A numerator is the upper of top value of a fraction
A denominator is the lower or bottom value of a fraction
Number of counters Adam has = 18Number of counters Adam gave to Lesley = 10Number of counters Adam has left = Number of counters Adam has - Number of counters Adam gave to Lesley
= 18 - 10
= 8
Fraction of the 18 counters Lesley get = Number of counters Adam gave to Lesley / Number of counters Adam has
= 10/18
= 5/9
Fraction of the 18 counters Adam have now = Number of counters Adam has left / Number of counters Adam has
= 8 / 18
= 4/9
In conclusion, the fraction of counters Adam have now after giving out 10 counters to Lesley is 4/9
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A student claimed that 0.045 m and 0.0045 m have the same number of significant digits. Do you agree or disagree?
Agree
Disagree
3^x-3^y=234,find the value of x and y
Value of x =5 and value of y =2
The exponent of a number indicates how many times a number has been multiplied by itself. For instance, 3^4 indicates that we have multiplied 3 four times. Its full form is 3 3 3 3. Exponent is another name for a number's power. It could be an integer, a fraction, a negative integer, or a decimal. Exponents are necessary since, without them, it is highly challenging to express the product when a number is repeated several times by itself. For instance, it is much simpler to write 5^7 than it is to write 5 5 5 5 5 5.
[tex]3^{x}-3^{y}=234\\ 3^{x-y}.3^{y}-3^{y}=234\\ 3^{y}(3^{x-y}-1)=234\\ 3^{y}(3^{x-y}-1)=3^{2}.26\\[/tex]
Now, by comparison, we get:
[tex]3^{y}=3^{2}\\ y=2\\ Also, \\3^{x-y} -1=26\\ 3^{x-y}=27\\ 3^{x-y}=3^{3}\\ x-y=3\\ x-2=3\\x=5[/tex]
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The revenue for selling x units of a product is R = 113.95 x. The cost of producing x units is C = 93 x + 750. In order to obtain a profit, the revenue must be greater than the cost. For what values of x will this product produce a profit? (Enter a number. Round your answer up to the nearest whole unit.)
For profit with the revenue of R=113.95x and cost of C=93x + 750 the value of x is 36units.
As given in the question,
Revenue for selling x units of a product is R = 113.95 x
Cost of producing x units is C = 93 x + 750
For profit, the revenue must be greater than the cost.
R > C
113.95x > 93x +750
Subtract 93x from both the sides
113.95x -93x >93x-93x +750
⇒20.95x > 750
Divide by 20.95
⇒x > 750/20.95
⇒x>35.7995
Nearest whole number is 36.
Value of x to produce a profit is 36units
Therefore, to make a profit with the revenue of R=113.95x and cost of
C =93x + 750 the value of x is 36units.
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how many groups of 1/2 are in 8
i think 16? 1/2+1/2=1 so 8*2=16
Explain how -6 2/5 + 7/3
Answer is -4.0
Answer:
Answer is - 4 1/15
Step-by-step explanation:
-6 2/5 = -32/5
-32/5 + 7/3 to add fractions they must have the same denominator
- 96/15 + 35/15 = ( -96 + 35) / 15 = - 61/15 = - 4 1/15
HELP! ALgebra 2!
A rectangular swimming pool is twice as long as it is wide. The pool has an area of 450 feet. What are the dimensions of the pool?
======================================================
Explanation:
x = width
2x = length, since it is twice as long as it is wide
area = length*width = 2x*x = 2x^2
Set this equal to the area of 450 sq ft and solve for x
2x^2 = 450
x^2 = 450/2
x^2 = 225
x = sqrt(225)
x = 15 feet is the width
2x = 2*15 = 30 feet is the length
Check:
area = length*width = 30*15 = 450
The answers are confirmed.
Write the equation of the line described.
through
(−1, 2)
and perpendicular to
5x + 3y = 15
Answer:
[tex]y = \frac{3}{5} x + \frac{13}{5} [/tex]
Step-by-step explanation:
The equation of a line can be written in the slope-intercept form y= mx +c, where m is the slope and c is the y-intercept.
Let's rewrite the given equation into the slope-intercept form, so that we can identify its slope.
5x +3y= 15
3y= -5x +15
Divide both sides by 3:
[tex]y = - \frac{ 5}{3} x + 5[/tex]
Thus, the slope of the given line is [tex] - \frac{5}{3} [/tex]
The slope of a perpendicular line is the negative reciprocal of the given line. In simpler terms, the slope of the perpendicular line can be found by flipping the denominator and numerator, and by multiplying -1 afterwards.
Slope of perpendicular line= [tex] \frac{3}{5} [/tex]
Substitute the value of the slope into the equation:
[tex]y = \frac{3}{5} x + c[/tex]
To find the value of c, substitute a pair of coordinates the line passes through.
When x= -1, y= 2,
[tex]2 = \frac{3}{5} ( - 1) + c[/tex]
Solve for c:
[tex]c = 2 + \frac{3}{5} [/tex]
[tex]c = \frac{13}{5} [/tex]
Thus, the equation of the line described is [tex]y = \frac{3}{5} x + \frac{13}{5} [/tex].
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Examine angle ABC below.
Which of the following equations correctly represent the relationships between the segments?
A) AG= 2GD
B) GC= 1/2FG
C) BE= 2BG
D) GA= 1/2AD
Answer:
A
Step-by-step explanation:
The centroid cuts the median in a 2:1 ratio from vertex to side.
help me
look at the picture
The zeros of the quadratic are (1 and 3), the vertex is (2, -1). Draw the parabola with a "solid" line. Shade the "interior" of the parabola.
What is defined as the inequality?Inequalities are mathematical representations in which neither side is equal. Unlike equations, we consider the two values in inequality.When inequalities are connected together, it is possible to jump so over middle inequality.If, p < q and q < d, then p < dIf, p > q and q > d, then p > dFor the given question;
The inequality of the function is given as;
= x² - 4x + 3
Find the factors;
(x - 3)(x - 1) = 0
x = 1 and x = 3 are the zeros of the equation.
Now, to graph the equation find the point;
Put x = 0; y = 3
Put x = 1; y = 0
Put x = 2, y = -1
Plot the points on the graph and join the points with solid line.
The vertex of the parabola is found at (2, -1).
Thus, the graph of the parabola is plotted.
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PLEASE HELP I GIVE BRAINLYS TO THE FIRST ONE THAT GETS IT RIGHT
Answer: 6 blue, 6 yellow, 6 red
Step-by-step explanation:
A fair stack of cards is an equal amount of cards.
3 colors, 18 total
18 / 3 = 6
Therefore 6 of each
NEED HELP.... Tom is planning a trip to three different cities this summer. When looking at amap, Tom has drawn in two of the distances between these cities. Which of youranswer choices is the correct way to represent the potential range for how manymiles City B is away from City C?- 3
we have that
the distance city B to city C is equal to
405+401=806 miles4
therefore
the answer is
3 < x < 807 -----> because is a potential range (Its not exact)You want to open an account with $2,000. You can earn 4% interest each year, and you plan to leave this account for 6 years. How much more would the account be worth after 6 years by calculating interest compounded daily versus calculating simple interest? (Assume 365 days in a year.) Do not round until the final answer. Round to the nearest cent.
The account would be worth more after 6 years if calculating interest compounded daily versus calculating simple interest by $62.46
How to calculate compound interest and simple interest?Principal, p = $2,000Interest rate, r = 4% = 0.04Time, t = 6 yearsNumber of periods, n = 365 daysCompound interest:
A = P(1 + r/n)^nt
= 2,000(1 + 0.04/365)^(365×6)
= 2,000.00(1 + 0.000109589041095)^(2190)
= 2000(1.0.000109589041095)^2190
= 2000 (0.00010958904109589)
= $2,542.46 to the nearest cent
Simple interest:
S.I = principal × rate × time
= 2,000 × 0.04 × 6
= $480
Total = Principal + simple interest
= $2,000 + $480
= $2,480
To find the amount more would the account would be worth after 6 years by calculating interest compounded daily versus calculating simple interest
= Compound interest - Simple interest
= $2,542.46 - $2,480
= $62.46
In conclusion, the account would be worth $62.46 more if compounded daily than simple interest.
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Find the quotient of (+22)÷(+2)
Please help I’ll mark you as brainliest if correct!!
Answer:
1 hour, 28 minutes, 15 seconds
Step-by-step explanation:
How can you use the Power of a Quotient, Quotient of Powers, Zero Exponent Laws Identity Exponent and to evaluate numerical expressions with whole-number exponents?
The powers can be used in the following manner using multiplicative identity.
Powers are mathematical expressions of the kind where x is the base and n is the exponent. In powers, the exponent specifies how many times to multiply the base by itself whereas the base is the integer or variable that is continuously multiplied.
The quotient rule states that exponents should be subtracted when dividing powers by the same base. For instance, h(6-2) Equals h when h(6) is divided by h(2) (4). Subtracting the exponents is a quick and easy way to simplify the issue.
When separating similar words with exponents, using the Quotient of Powers Rule to minimize the number of terms. This rule states that when dividing words with the same base, the exponents should be removed in order to find the result. When separating similar words with exponents, using the Quotient of Powers Rule to minimize the number of terms. This rule states that when dividing words with the same base, the exponents should be removed in order to find the result. The trick is to eliminate only exponents with compatible bases.
Since the multiplicative identity, or one, is the simple outcome of no numbers at all, it follows that every integer raised to the power of zero equals one.
Thus, we came to the logical conclusions.
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what is the geometric mean of 14 and 6 (just need answer)
9.16
1) Considering 14, and 6 the data. Let's calculate the Geometric Mean of it
[tex]X_G=\sqrt[]{14\cdot6}\Rightarrow X_G\approx9.16[/tex]2) To do that we just need to multiply those numbers, and since there are two of them take the square root of that product, between those 2 numbers
3) So the Geometric mean is 9.16 (approximately).
what are the transformations of this functions compared to the parent function
The technique of altering an existing graph or graphed equation to create a different version of the following graph is known as graph transformation.
Numerous different coordinate systems can be used to describe geometrical figures.
The connection between several systems is defined by coordinate transformations, which offer formulas for the coordinates in one system in terms of the coordinates in another system. The coordinate transformation from polar to Cartesian coordinates is given by the formulas x = r cos and y = r sin, for example, if the polar axis is the positive x axis on the plane and the origins of the Cartesian coordinates (x, y) and polar coordinates (r) are the same.Every bijection from the space to itself can be related to two coordinate transformations.The formulas for the new coordinates of each point's image are constructed in a way that the old coordinates of the original point's image are maintained.In particular, the change of algebraic equations, it is a typical kind of algebraic problem.To learn more about transformation visit:
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Given that AABC ADEF. Find the scale factor from AABC to ADEF.A2x24B20CDX-2E5
1) To find the scale factor for these triangles, we need to write a pair of ratios and then solve for x:
[tex]\begin{gathered} \frac{2x}{4}=\frac{20}{5} \\ \\ 10x=80 \\ \\ \frac{10x}{10}=\frac{80}{10} \\ \\ x=8 \\ \\ \end{gathered}[/tex]Now, we can plug x=8 into those:
[tex][/tex]Please help me with that. Thank you
The logarithms in terms of a and b are:
a) log 72 = 3a + 2b
b) log √27 = [tex]\frac{3}{2} b[/tex]
c) log 360 = 3a + 2b + log 5
What are logarithms?The use of a logarithm can be utilized to solve problems that cannot be resolved using the concept of exponents alone. A logarithm is simply another way to describe exponents. It can be represented as:nˣ = a ⇔ logₙ a = x , log stands for logarithm here.
Where,
Two positive real numbers are a and n. x is a real number.
The "argument" is defined as a and is located inside the log.The "base," is denoted by the letter n at the bottom of the log.The rules of logs can be used to expand a logarithm, compress a collection of logarithms into a single one, or simplify a logarithm.Given:
log 2 = a
log 3 = b
a) log 72
= log (2³ × 3²)
= log 2³ + log 3² [ By product rule of logarithms, log mn = log m + log n]
= 3log 2 + 2log 3 [By power rule of logarithms, log mⁿ = nlog m]
Replacing with the values of log 2 and log 3.
= 3a + 2b
b) log √27
= [tex]\frac{1}{2}[/tex] log 27 [By power rule of logarithms, log mⁿ = nlog m]
= [tex]\frac{1}{2}[/tex] log 3³
= [tex]\frac{1}{2} *3 log3[/tex]
= [tex]\frac{3}{2} log 3[/tex]
= [tex]\frac{3}{2} b[/tex]
c) log 360
= log (2³ × 3² × 5)
= log 2³ + log 3² + log 5 [By product rule of logarithms,log mn = log m + log n]
= 3log 2 + 2log 3 + log 5 [By power rule of logarithms, log mⁿ = nlog m]
= 3a + 2b + log 5
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Write an equation of the line that passes through (-5,4) and is perpendicular to the line that is defined by x-2y=-4
By using the equation of the line and properties of perpendicular lines, we find that the equation of the line is equal to y = - 2 · x - 6.
How to determine the equation of a line
Herein we need to find a line that passes through point (- 5, 4) and is perpendicular to a given line in implicit form: x - 2 · y = - 4. The complete procedure is shown below. First, rewrite the equation of the perpendicular line into explicit form:
x - 2 · y = - 4
2 · y = x + 4
y = (1 / 2) · x + 2
Second, determine the slope of the new line:
m · m' = - 1
(1 / 2) · m' = - 1
m' = - 2
Third, calculate the intercept of the new line:
b = y - m · x
b = 4 - (- 2) · (- 5)
b = 4 - 10
b = - 6
Fourth, complete the new equation of the line:
y = - 2 · x - 6
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A large pepperoni pizza from Papa Johns costs $14.75. After tax, the pizza is $15.93. What is the sales tax rate?
Answer:
8%
Step-by-step explanation:
divide the after tax price by the before tax price
15.93/14.75=1.08
then subtract 1 from 1.08 (the 1 is the base price of the pizza) and convert the difference to percent to get the answer of 8% tax rate
−8+n3=6, what does the n equal?
Answer:
n=2.4
Step-by-step explanation:
The value of n is ∛14.
What is Equation?An equation is a mathematical statement that asserts the equality of two expressions. It consists of two sides, known as the left-hand side (LHS) and the right-hand side (RHS), connected by an equal sign (=).
To solve the equation −8 + n³= 6
Add 8 to both sides of the equation to isolate the term with n:
−8 + n³ + 8 = 6 + 8.
Simplifying the equation gives: n³ = 14.
Take the cube root of both sides to solve for n.
Taking the cube root of n³ = 14
∛(n^3) = ∛14.
Therefore, n = ∛14.
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a. 161b.16c. -16116d.e.5
64 ^ (-2/3)
Rewrite 64 as 4^3
(4^3) ^ (-2/3)
Using the power rule a^b^c = a^(b*c)
4 ^(3*-2/3)
4^ -2
We know that a^ -b = 1/ a^b
1 / 4^2
1/16
help me!!! Write an equation of the line passing through the point (2, 8) that is perpendicular to the line 2x - 3y = 7
Answer:
y = -3/2x +11
Step-by-step explanation:
First you have to change the equation from standard form to slope form.
y = mx + b
2x-3y=7 --> subtract 2x from both sides
-3y = -2x + 7 --> now divide both sides by -3 to get y by itself
y = 2/3x - 7/3 --> the reason 2/3x is positive is because when there are two negatives it turns to a positive.
now you have to use point slope form y - y1 = m (x - x1)
x1 and y1 would be your point. 2 is x1 and 8 is y1
y - 8 = -3/2 (x - 2) --> the reason that m is -3/2 is because a perpendicular equation is the opposite reciprocal of the original slope
next distribute the -3/2
y-8 = -3/2x + 3 --> and now add 8 to 3 to get why by it self
now you have y = -3/2x + 11