Answer:
[tex]\pm i\sqrt{2}\text{ and } \pm i[/tex]
Step-by-step explanation:
[tex]\text{let u = } x^2[/tex] so then [tex]u^2=x^4[/tex].
This gives you the equation: [tex]u^2+3u+2=0[/tex].
Now factor the equation by looking for factors of 2 that add up to 3, which is just 2 and 1. Use these to rewrite the equation: [tex](u+2)(u+1)[/tex]. So now just set each factor equal to 0:
[tex]u+2=0\\u=-2[/tex]
Now substitute x^2 back in as u
[tex]x^2=-2[/tex]
Take the square root of both sides
[tex]x=\pm \sqrt{-2}[/tex]
Separate the radical into sqrt(-1) * sqrt(2)
[tex]x=\pm \sqrt{-1}*\sqrt{2}[/tex]
Rewrite using i
[tex]x=\pm i\sqrt{2}[/tex]
Now set the other factor equal to 0
[tex]u+1=0\\u=-1[/tex]
substitute x^2 back in as u
[tex]x^2=-1[/tex]
Take the square root of both sides
[tex]x=\pm\sqrt{-1}[/tex]
rewrite using i
[tex]x=\pm i[/tex]
Find a formula for the general term an of the sequence, assuming that the pattern of the first few terms continues. (Assume that n begins with 1.)
{2, 6, 10, 14, 18, . . . }
The formula for the general term of the sequence is Tn = 4n - 2
How to determine the formula?The sequence is given as:
{2, 6, 10, 14, 18, . . . }
The above sequence is an arithmetic sequence with the following features:
First term, a = 2Common difference, d = 4 i.e. 6 - 2The formula for the general term is calculated using:
Tn = a + (n - 1) * d
This gives
Tn= 2 + (n - 1) * 4
Expand
Tn = 2 + 4n - 4
Evaluate the like terms
Tn = 4n - 2
Hence, the formula for the general term of the sequence is Tn = 4n - 2
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[tex]212 \times 5 + 5222 \div 45 + 63 - 34[/tex]
this question i want
Find k. ..................
Answer:
k = -10
Explanation:
f(x) = 4x³ - 3kx² + 44x - 30
The divisor is:
(x - 2)Set divisor to zero:
(x - 2) = 0x = 2Insert this into equation.
⇒ 4(2)³ - 3k(2)² + 44(2) - 30 = 210
⇒ 32 - 12k + 88 - 30 = 210
⇒ -12k + 90 = 210
⇒ -12k = 210 - 90
⇒ -12k = 120
⇒ k = 120/-12
⇒ k = -10
Answer:
k = -10
Step-by-step explanation:
From the remainder theorem, we know that the remainder, 210, is equal to f(2).
∵ [tex]f(2) = 210[/tex] ,
⇒ [tex]4(2)^3 - 3 k(2)^2+44(2) - 30 = 210[/tex]
⇒ [tex]32 -12k + 88 - 30 = 210[/tex]
⇒ [tex]90 - 12k = 210[/tex]
⇒ [tex]-12k = 120[/tex]
⇒ [tex]k = -10[/tex]
Given: f(x) = 4x+1 and g(x)= x2+1, find (f g)x.
Answer:
given
fx = 4x+1
gx= 2x+1
Step-by-step explanation:
fg x = ?
we know ,
f g x = (4x+1) ( 2x+1)
= 4x ( 2x+1) +1 (2x+1)
= 8x² +4x +2x+1
= 8x² + 6x +1
Which choice is equivalent to the quotient below?
-/100/-/25
the answer to this equation is 4
8. determine the shape:
Melissa: Does your shape have exactly one right angle?
Keya: Yes
Melissa: Does your shape have opposite congruent sides?
Keya: No
Melissa: Does your shape have any parallel sides?
Keya: Yes
Melissa: The shape is a _____________________
How did you rule out other shapes?
b) Michelle: Does your shape have 2 pairs of congruent opposite sides?
Olga: Yes
Michelle: Does your shape have right angles?
Olga: No
Michelle: Does your shape have 2 pairs of opposite parallel sides?
Olga: Yes
What is the shape?
Is there an additional question Michelle should ask to be sure? If so, what should she ask?
Quadrilaterals are plane shapes with four sides. Thus, the required answers are:
a) The first shape is a right trapezoid.
b) The second shape is a parallelogram.
The given properties are that of a quadrilateral, thus both shape is a quadrilateral. A quadrilateral is a family of shapes that have four straight sides. Examples include squares, rhombus, kites, etc.
A. Given that the shape has one right angle and parallel sides. Then considering the given properties, the most likely shape is a right trapezoid.
A right trapezoid is a type of trapezium that has one right angle, and a pair of parallel sides. Thus the shape here is a right trapezoid.
Other shapes could be ruled out by comparing their properties with the properties of the shape given in the question.
B. The properties of the required shape as given are: it has two pairs of congruent opposite sides, and 2 pairs of opposite parallel sides. Thus the most likely shape required here is a parallelogram. A parallelogram is a shape with parallel and congruent opposite sides, and no right angle.
Other shapes could be ruled out by comparing their properties with the properties of the shape given in the question.
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Kindly contact a 1-on-1 tutor if more explanations are required.
The sum of 8 times a number and 10 is 34. Find the number.
Answer: 3
8x+10=34
sub 10
8x=24 divide by 8
x=3
Step-by-step explanation:
2b^3+5=2(3)^3+5
I will mark u brainliest if u get the question right
ALSO I NEED THE ANSWER AS SOON AS POSSIBLE
Answer:
B=3
Solution in photo
I hope this helped :)
Which of these is the quadratic parent function?
A. f(x) = (1/4 x)²
B. f(x)=x²-3
C. f(x) = x² +5
D. f(x) = x²
Answer:
[tex]f(x)=x^2[/tex]
Step-by-step explanation:
The quadratic parent function, has no transformations, and has the vertex at (0, 0). Which is the function: [tex]f(x)=x^2[/tex]. Any other quadratic function, has some form of transformation, whether it be a reflection, translation, compression/stretch, etc...
What’s the formula for the geometric mean of three numbers?
Answer:
Geometric mean is most commonly represented as:
[tex]\sqrt{abc}[/tex]
Geometric mean formula is represented by [tex]\sqrt[n]{\sf x_1 \cdot x_2 \cdot x_3 \cdot ... x_n}[/tex] where n resembles term position and x₁, x₂, x₃ are numbers and they continue.
The formula for geometric mean of three numbers [n = 3]:
Solution: [tex]\sqrt[3]{\sf x_1 \cdot x_2 \cdot x_3 }[/tex]
Example's:
Geometric mean of 5 numbers [n = 5] : [tex]\sqrt[5]{\sf x_1 \cdot x_2 \cdot x_3 \cdot x_4 \cdot x_5 }[/tex]
Geometric mean of 2 numbers [n = 2] : [tex]\sqrt[2]{\sf x_1 \cdot x_2 }[/tex]
1. What is the remainder when x³+4x2-2x+1 is divided by x+2 1. What is the remainder when x³ + 4x2-2x + 1 is divided by x + 2
Answer:
Remainder is 13
Step-by-step explanation:
You can apply the remainder theorem here. You just equate the divisor to 0, then substitute the x-value in the expression.
[tex]x^3 + 4x^2 - 2x + 1 \\[/tex] then, [tex]x+2=0\\x=-2[/tex]
substitute:
[tex]-2^3 + 4(-2)^2-2(-2) + 1 =13[/tex]
Therefore, the remainder is 13
Which is the equation in slope-intercept form for the line that passes through (−2, 15) and is perpendicular to 2x + 3y = 4?
y=−32x+18
y=32x−12
y=23x+18
y=32x+18
The linear equation that respects the given conditions is:
[tex]y = \frac{3}{2}x + [/tex]
What is a linear function?A linear function is modeled by:
y = mx + b
In which:
m is the slope, which is the rate of change, that is, by how much y changes when x changes by 1.b is the y-intercept, which is the value of y when x = 0, and can also be interpreted as the initial value of the function.When two lines are perpendicular, the multiplication of their slopes is of -1. Hence, considering it is perpendicular to 2x + 3y = 4.
[tex]2x + 3y = 4[/tex]
[tex]3y = -2x + 4[/tex]
[tex]y = -\frac{2x}{3} + \frac{4}{3}[/tex]
Then:
[tex]-\frac{2}{3}m = -1[/tex]
[tex]m = \frac{3}{2}[/tex]
Hence:
[tex]y = \frac{3}{2}x + b[/tex]
It passes through (−2, 15), that is, when x = -2, y = 15, hence:
[tex]y = \frac{3}{2}x + b[/tex]
[tex]15 = \frac{3}{2}(-2) + b[/tex]
15 = -3 + b
b = 18.
So the equation is:
[tex]y = \frac{3}{2}x + [/tex]
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Use the equations to find the perimeter equation
The perimeter of the park is 3x^2 + 37x - 4
How to determine the perimeter?The side lengths of the triangular park are:
10x + 3x^2 - 8, 12x and 15x + 4
Add these sides to determine the perimeter
P = 10x + 3x^2 - 8 + 12x + 15x + 4
Collect the like terms
P = 3x^2 + 10x + 12x + 15x - 8 + 4
Evaluate the sum
P = 3x^2 + 37x - 4
Hence, the perimeter of the park is 3x^2 + 37x - 4
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Please help me. NO LINKS!!
The domain (input values) of the cosine function is all negative and positive angle measures.
Let the function be f(x) = cos(x)
The domain of cos(x) is -∞ < x < ∞
The range is -1 ≤ f(x) ≤ 1
Hence, domain of cos(x) is all (+) and (-) angle measures.
Same goes with sine function as well
For function f(x) = sin(x)
The domain is -∞ < x < ∞ and range -1 ≤ f(x) ≤ 1
However for f(x) = tan(x) the same is not applicable.
Answer:
A. all negative and positive angle measures.
Step-by-step explanation:
The domain of a function is the set of input values (x-values).
The cosine function is a continuous function, and therefore has no restrictions throughout its domain.
Therefore, its domain is all real numbers.
Set notation: { x | x ∈ R }
Interval notation: (-∞, ∞)
h(t)=t^4+3t^2-t+3
h'?
Answer: [tex]h'(t)=4t^3 + 6t-1[/tex]
Step-by-step explanation:
Use the power rule for differentiation.
4(4 - x) - 8(-2 + 4x)
If you want the answer simplified, its
-36x + 32
Brian has earned 65%, 80% and 92% on his three pre-final exams. These exams are not weighed equally: the lowest counts for only 20% of his overall grade, while the other two count for 25% each. If the final exam is the remainder of the overall grade and there are no opportunities for extra credit, what is the highest grade Brian can earn in the class? Express your answer to the nearest whole percent.
Answer:
89.25%
Step-by-step explanation:
65 is the lowest so it only counts for 20% of the grade
65*0.2=16.25
80*0.25=20
92*0.25=23
There is 30% left and 100% is the highest score
100*0.3=30
16.25+20+23+30=89.25
Answer:
86%
Step-by-step explanation:
From the information give:
Exam 1
Exam result = 65%
Overall grade weighting = 20%
⇒ Credit = 65% of 20% = 0.65 × 0.2 = 0.13 = 13%
Exam 2
Exam result = 80%
Overall grade weighting = 25%
⇒ Credit = 80% of 25% = 0.8 × 0.25 = 0.2 = 20%
Exam 3
Exam result = 92%
Overall grade weighting = 25%
⇒ Credit = 92% of 25% = 0.92 × 0.25 = 0.23 = 23%
Final Exam
The highest grade Brian can earn = 100%
Overall grade weighting = 100% - 20% - 25% - 25% = 30%
⇒ Credit = 100% of 30% = 1 × 30% = 30%
Highest potential class grade
Sum of each exam credit:
⇒ 13% + 20% + 23% + 30% = 86%
Therefore, the highest grade possible that Brian can earn in the class is 86%.
Problem
(a) Find x given that [tex]4x^2=2[/tex]
(b) Let x = 1.1609... be the positive real number such that [tex]4^x=5[/tex]. Prove that x is irrational.
The value of x is ±0.7071 and x is an irrational number
How to solve for x?The equation is given as:
[tex]4x^2 = 2[/tex]
Divide by 4
[tex]x^2 = 0.5[/tex]
Take the square roots
[tex]x = \pm 0.7071[/tex]
Hence, the value of x is ±0.7071
How to prove that x is irrational?The equation is given as:
[tex]4^x = 5[/tex]
Take the logarithm of both sides
[tex]x\log(4) = \log(5)[/tex]
Divide both sides by log(4)
x = 1.16096....
The above number is a non-terminating decimal.
Non-terminating decimals cannot be represented as fractions of two integers
Hence, x is an irrational number
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Can someone answer this
We can see that the unit rate of y = 6.5*x is larger than the unit rate on the graph.
How to get the unit rate of the line?
The unit rate is the equal to the slope of the line.
In the written line, y = 6.5*x, the unit rate is 6.5
On the graphed line we can see that it passes through the points (0, 0) and (1, 3), so the unit rate is:
[tex]r = \frac{3 - 0}{1 - 0} = 3[/tex]
Then we can see that the unit rate of y = 6.5*x is larger than the unit rate on the graph.
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A data set is summarized in the frequency table below. Using the table, determine the number of values less than or equal to 6.
Based on the data set given in the frequency table, the number of values that are less than or equal to 6 is 18.
How many values are less than or equal to 6?The value that will be less than or equal to 6 are those that are valued at 6 or below.
The sum of these values are:
= 2 + 3 + 6 + 4 + 3
= 18
In conclusion, 18 values are less than or equal to 6.
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How many sides does a nonagon have
Cost of a CD: $17.50
Markup: 45%
Answer:
25.375
Step-by-step explanation:
17.50×45%=7.875
17.50+7.875=25.375 new price
I need to know The value of f(1/2)
[tex]\huge\boxed{\textsf{a.)}\ 10}[/tex]
Substitute [tex]\frac{1}{2}[/tex] for [tex]x[/tex].
[tex]f\left(\frac{1}{2}\right)=5\cdot4^\frac{1}{2}[/tex]
Use [tex]a^\frac{m}{n}=\sqrt[n]{a^m}[/tex].
[tex]\begin{aligned}f\left(\frac{1}{2}\right)&=5\cdot\sqrt[2]{4^1}\\&=5\cdot\sqrt[2]{4}\\&=5\cdot2\\&=\boxed{10}\end{aligned}[/tex]
A survey found that 10 out of 15 students like pizza. If four students are chosen at random, what is the probability that all the four students like pizza?
Using the hypergeometric distribution, it is found that there is a 0.1539 = 15.39% probability that all the four students like pizza.
What is the hypergeometric distribution formula?The formula is:
[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}C_{N-k,n-x}}{C_{N,n}}[/tex]
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
The parameters are:
x is the number of successes.N is the size of the population.n is the size of the sample.k is the total number of desired outcomes.For this problem, the values of the parameters are given as follows:
N = 15, n = 4, k = 10.
The probability that all the four students like pizza is P(X = 4), hence:
[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}C_{N-k,n-x}}{C_{N,n}}[/tex]
[tex]P(X = 4) = h(4,15,4,10) = \frac{C_{10,4}C_{5,0}}{C_{15,4}} = 0.1539[/tex]
0.1539 = 15.39% probability that all the four students like pizza.
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This is from Khan academy I have to attach a PNG if you can help me solve it! Thank you!
Answer:
Step-by-step explanation:
Question
64^m
--------
4^2m
Solution
(64)^m = (4^3)^m = 4^3m
4^3m/4^2m = 4^(3m - 2m) = 4^m
Answer
2^2m = (2^2)^m = 4^m Equivalent
16^0.5m = (16^0.4) ^m = 4^m Equivalent
4^m Equivalent
All three of these are equivalent. The catch is in splitting the powers apart. In this top one (2^2m) you move the brackets so that the right bracket is after the two which gives (2^2)^m = 4m
You do the same thing with (16^0.5)^m. 16^0.5 = 4 So the answer is 4^m
The last one is 4^m which is the answer you got from the division.
Given expression: [tex]64^{m} /{4^{2m} }[/tex]
We can rewrite the expression (in the numerator and the denominator) as the product of multiple fours. Then, we can apply the exponent rule to simplify the expression to its simplest form. The simplest form will be the required simplified expression (solution to the provided expression).
[tex]\implies (4^{3}) ^{m} /{4^{2m} } \\[/tex][tex]\implies 4^{3m} /{4^{2m} }[/tex]We can apply the following exponent rule to simplify the expression:
[tex]\boxed{\text{Exponent rule:} \ 4^{m} /4^{n} = 4^{m - n}}[/tex]
The exponent rule states that the "base" must be the same when subtracting exponents. If we divide a term with same bases, we can reduce work time by subtracting the exponent to simplify the expression.
[tex]\implies 4^{3m} /{4^{2m} }[/tex][tex]\implies 4^{3m - 2m} = 4^{m}[/tex]Step-2) Equivalent or Non-equivalent?Now, let us look at all the options to verify which term matches our simplified term, and which expressions do not match our simplified term.
First option:Given term: [tex]2^{2m} \\[/tex]
Can be re-written as:
[tex]=2^{2m} \\[/tex][tex]= [2^{(2)}]^{m}[/tex]Simplifying the expression inside the long brackets:
[tex]\\= [4]^{m}[/tex][tex]\\= 4^{m} \ ( \text{matches})[/tex]Therefore, the first option is equivalent to our simplified term.
Second option:Given term: [tex]16^{0.5m}[/tex]
Can be re-written as:
[tex]= 16^{0.5m}[/tex][tex]\\= (4^{2}) ^{0.5m}[/tex]Exponent Rule: (xᵃ)ᵇ = xᵃᵇ
[tex]= (4^{1}) ^m[/tex][tex]= (4^{1m})[/tex][tex]= 4^m[/tex]Therefore, the second option is equivalent to our simplified term.
Third option:Given term: [tex]4^{m}[/tex]
This term already matches our simplified term.
Therefore, the third option is equivalent to our simplified term.
Step-3) Conclude/verify your answerWe can conclude that all the options provided are equivalent to the given expression. We proved it by applying exponent rules and formulas.
If y is inversely proportional to x and y=−54 when x=38, find y if x=30. (Round off your answer to the nearest hundredth.)
Answer:
-68.4
Step-by-step explanation:
answer explained on the photo !
AADF, AB = 16,
mZB = 59° mZD = [?]
Answer:
59°
Step-by-step explanation:
ABC and ADF are congruent (that is the meaning of that symbol).
that means all their associated angles and side lengths are the same.
it is relatively clear to see that
A corresponds to A.
D corresponds to B.
F corresponds to C.
therefore, the angle D = angle B = 59°.
FYI - it also means that AD = AB = 16. but this information was actually irrelevant for this question.
Two children had 110 marbles between them. After one child had lost half her marbles
and the other had lost 20 they had an equal number. How many marbles did each child
start with and how many did they finish with?
Answer:
1 child - 60 another child - 50
Step-by-step explanation:
we start from the end. they had a equal number.
child A lost half therefore we give them another half having 2 units as shown in the diagram. child B had 1 unit plus 20 because he lost 20 which total adds up to 110. from there you have
3 units + 20 = 110
3 units = 90
1 unit = 30
since A has 2 units,
30 × 2 = 60
child A has 60.
since B has 1 unit plus 20
30 + 20 = 50
Solve for x in the diagram below.
Answer:
x=40
Step-by-step explanation:
total sum of angle in a triangle =180
180-100=80
x+x =2x
x= 80/2
x=40
simplify the expression -2v+15d
Answer:
isn't this already fully simplified?
Step-by-step explanation: