The given 4th order polynomial equation only has real solutions, x = √7 and x = –√7
The given equation is x⁴-14 x²+49 = 0.
This is a 4th degree polynomial equation.
Let p = x².
Then we can write x⁴-14 x²+49 = 0 as:
p²- 14p +49 = 0
This is a quadratic equation.
There are three ways to find the solutions of a quadratic equation:
By factoringBy completing the squareBy applying the quadratic formulaNotice that p²- 14p +49 = 0 can be written as a perfect square:
(p - 7)² = 0
Hence, it has only single real solution:
p - 7 = 0
p = 7
Substitute p = 7 into p = x², we get:
x² = 7
x = ± √7
The solutions are, therefore, x = √7 and x = –√7
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Dan's has a current credit card statement of $785. his credit card apr is 24.42%. what would be his finance charge if he does not pay the balance in full?
A loan fee is an amount a consumer pays for a loan. This includes taking out a car loan, credit card, or mortgage. Common loan fees include interest rates, origination fees, service fees, late fees, etc. Gross Loan Fees are typically associated with your credit card and consist of any outstanding balance plus any other fees incurred if you carry overdue amounts to your credit card.
If you know three numbers related to your credit card account: credit card (or loan) balance, APR, and billing cycle length, you can calculate your loan fees.
Current Balanced Owned =$785
APR = 24.42%
Let’s suppose the billing cycle is 30 days, then
Finance charge = $15.76
The new balance you owe = $800.76.
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Round this number to the
nearest hundredth.
1.2983
Answer: 1.3
Step-by-step explanation:
Answer:
1.3
Step-by-step explanation:
9 is the hundredth and we round up with 8 so we’d round up 1 and we get 1.3
SOMEONE PLEASE HELP 100 points
Answer:
A) No solution
B) No solution
Step-by-step explanation:
[tex]A)[/tex] [tex]\mathrm {If}\:|u|\: < \:a,\:a > 0\:\mathrm{then}\:-a\: < \:u\: < \:a[/tex] (Which in this case leads to no solution because c cannot be less than 0 logically)
[tex]B)[/tex] [tex]\mathrm {If}\:|u|\: < \:a,\:a > 0\:\mathrm{then}\:-a\: < \:u\: < \:a[/tex] (Whether you change the </> sign or not, c cannot be any less than 0 or it will lead to no solution.)
Answer:
All real numbers im pretty sure
Step-by-step explanation:
Psychologists use an exponential model of the learning process, f(t)= c(1-e -kt) , where c is the total number of tasks to be learned, k is the rate of learning, t is time, and f(t) is the number of tasks learned.
c. Open-Ended Does this function seem to describe your own learning rate? If not, how could you adapt it to reflect your learning rate?
We will know 8 complete names after 2 days and 20 complete names after 8 days. Whether or not this function represents your learning rate will vary from person to person.
Here, we are given an exponential function: f(t)= c{1- e^(-kt)}
where
f(t) = number of tasks learned.
c = total number of tasks to be learned
k = rate of learning
t = time
Now, when we move to a new school, number of names we need to learn ⇒ c = 25
learning rate for new tasks = 20%
⇒ k = 0.2
and time = 2 days
⇒ t = 2
Substituting these values in the function we get-
f(2) = 25{1- [tex]e^{-0.2 * 2}[/tex]}
= 25{1- [tex]e^{-0.4}[/tex]} [tex]e^{-0.4}[/tex]
= 0.67
Thus, f(2) = 25( 1-0.67 )
f(2) = 25(0.33)
f(2) = 8.25
Thus, we will be able to learn 8 complete names in 2 days.
If t = 8f(8) = 25{1- [tex]e^{-0.2*8}[/tex]}
= 25{1- [tex]e^{-1.6}[/tex]}
= 25(1- 0.20)
= 25(0.80)
= 20
Thus, we will be able to learn 20 complete names in 8 days. Whether of not this function describes your own learning rate will vary from person to person. Some people are fast learners whereas others take their time. A fast learner will have a higher learning rate whereas a slow learner will have a lower learning rate as depicted by k. You can change the value of k to adjust the function as per your learning abilities.
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Your question was incomplete, check for full content below-
Psychologists use an exponential model of the learning process, f(t)= c(1-e -kt) , where c is the total number of tasks to be learned, k is the rate of learning, t is time, and f(t) is the number of tasks learned.
a. Suppose you move to a new school, and you want to learn the names of 25 classmates in your homeroom. If your learning rate for new tasks is 20 % per day, how many complete names will you know after 2 days?
b. After 8 days?
c. Does this function seem to describe your own learning rate? If not, how could you adapt it to reflect your learning rate?
i need help with this
Based on the information, it should be noted that the appropriate fraction for 8.33 will be 8 1/3.
How to illustrate the information?It should be noted that a decimal simply means the numbers that is represented as a whole number and a fraction.
In this case, it should be noted that the 8.33 consist of a whole number as well as a fraction.
Therefore, it should be noted that 8.33 will be:
= 8 + 1/3
It should be noted that 1/3 is a repeating decimal as it will always give 0.3333...
Therefore, the appropriate fraction for 8.33 will be 8 1/3.
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r(x)=-x-7 when x=-2,0, and 5
The output values of x = -2, 0, and 5 in the given function are -5, -7 and -12 respectively.
What are the output values when x = -2, 0, and 5?Given the data in the question;
r(x) = -x - 7r(-2) = ?r(0) = ?r(5) = ?When x = -2. replace all the occurrence of x with -2 in the function and simplify to determine the output value.
r(x) = -x - 7
r(-2) = -(-2) - 7
r(-2) = 2 - 7
r(-2) = -5
When x = 0. replace all the occurrence of x with 0 in the function and simplify to determine the output value.
r(x) = -x - 7
r(0) = -(0) - 7
r(0) = 0 - 7
r(0) = -7
When x = 5. replace all the occurrence of x with 5 in the function and simplify to determine the output value.
r(x) = -x - 7
r(5) = -(5) - 7
r(5) = -5 - 7
r(5) = -12
Therefore the output values of x = -2, 0, and 5 in the given function are -5, -7 and -12 respectively.
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An arrow is modeled on the coordinate plane as shown. What is the area of the arrow? Round your answer to the nearest tenth, if necessary.
y
(0,3)
(0, 1)
O
(4,4)
(4.5,3)
(4.5,1)
(4,0)
(8, 2)
square units:
X
l o o k i t u p o n g a u t h m a t h c o p y u r q e s t i o n t h e r e
Step-by-step explanation: You're welcome
Using the division properties, how can the expression 2/5÷(−5/5) be simplified? Drag and drop your answers into the boxes to complete the statement.
The required solution of the given expression is -2/5 as a simplified form.
What is expression?
An expression is a set of terms combined using the operations +, – , x or ÷. An expression is a number, a variable, or a combination of numbers and variables and operation symbols. An expression is in simplest form when no terms can be combined
Given:
The given expression is
2/5÷(−5/5)
According to given question we have
The expression is
2/5÷(−5/5)
=2/5÷(-1)
=2*(-1)/5
=-2/5
Therefore, the required solution of the given expression is -2/5 as a simplified form.
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Use the graph to answer the following question.
If ∆ PQR is translated left 2 and down 6, what would be the coordinates of R' ?
The coordinate of the point R' after translation will be (0, - 4).
What is a transformation of a point?A spatial transformation is each mapping of feature space to itself and it maintains some spatial correlation between figures.
If ∆PQR is translated left 2 and down 6. Then the translation rule is given as,
(x', y') → (x - 2, y - 6)
From the graph, the coordinate of point R will be at (2, 2). Then the coordinate of the point R' after translation will be
(x', y') → (2 - 2, 2 - 6)
(x', y') → (0, - 4)
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f(x)= x; translation 2 units right followed by a horizontal stretch by a factor of 2
Answer: f(x) = | x |
Step-by-step explanation:
when transforming and translating a function, you use the form a | x - h | + k
a= vertical shrink/stretch factor
h = horizontal movement ( right or left)
k = vertical movement ( up or down )
So a = 1/2 h = 0 and k =2
g(x) = 1/2 | x-0 | + 2
g(x) = 1/2 | x | + 2 [which means vert shrink of 1/2 and up 2 units ]
A holiday company offer a 12% discount if you book before 31st March. How much
would you pay today for a holiday to France if the full price is £1,245?
Please Help! Determine the range of the following graph:
the range of the function in the graph is:
-4 ≤ y ≤ 2
How to determine the range of a given graph?For a function y = f(x), we define the range as the set of the outputs. This is, the set of the possible values of y.
Now, remember that the values of y are on the vertical axis. So if we want to know the range, we just need to look at the vertical axis and see which ones are the allowed values.
If we look at the graph, we can see that the minimum value of y is:
y = -4
And we can see that the maximum value of y is:
y = 2
Then the range of the function in the graph is:
-4 ≤ y ≤ 2
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Expand each binomial.
(2 x-3)⁷
Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. (2x - 3)⁷ is expanded as 128x⁷ − 1344x⁶ + 6048x⁵ − 15120x⁴ + 22680x³ − 20412x² + 10206x − 2187.
What is meant by binomial expansion theorem?The Binomial theorem tells us how to expand expressions of the form (a + b)ⁿ, for example, (x + y)⁷. The larger the power is, the harder it is to expand expressions like this directly.
The total number of terms in the expansion of (x+y)ⁿ are (n+1).
The sum of exponents of x and y is always n.
nC₀, nC₁, nC₂, … .., nCₙ are called binomial coefficients and also represented by C₀, C₁, C₂, ….., Cₙ
The binomial coefficients which are equidistant from the beginning and from the ending are equal.
i.e. nC₀ = nCₙ, nC₁ = nCₙ₋₁ , nC₂ = nCₙ₋₂ ,….. etc.
Let the function be (2x - y)⁴
By using binomial expansion theorem, we get
(2x - 3)⁷ = 128x⁷ − 1344x⁶ + 6048x⁵ − 15120x⁴ + 22680x³ − 20412x² + 10206x − 2187
(2x - 3)⁷ is expanded as 128x⁷ − 1344x⁶ + 6048x⁵ − 15120x⁴ + 22680x³ − 20412x² + 10206x − 2187.
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GSE Geometry
Unit 3
Check For Understanding!!
Parallel Lines cut by a Transversal
1. Given and m/8 = 119, find the measures of all the
numbered angles in the figure.
m<1=_
m<2=_
m<3=_
m<4 = _
m<5 =_
m<6 =_
m<7=_
The measure of all the angles are :
∠1 = 119°, ∠2 = 61°, ∠3 = 61° , ∠4 = 119° , ∠5 = 119° , ∠6 = 61° and ∠7 = 61°
According to the question we have been given two parallel lines which is cut by a transversal line. There total 8 angles and given is the measure of
∠8 = 119°.
We need to find the measure of all other 7 angles.
Note that when two parallel lines are cut by a transversal then
i) corresponding angles are equal that is
∠1 = ∠5, ∠2 = ∠6, ∠3 = ∠7, and ∠4 = ∠8
ii) alternate interior angles are equal that is
∠3 = ∠6, and ∠4 = ∠5
iii) alternate exterior angles are equal that is
∠1 = ∠8, and ∠2 = ∠7
iv) Consecutive interior angle sum is 180°
∠4 + ∠6 = 180°, and ∠3 + ∠5 = 180°.
So according to the rules given above the measure of all the angles are:
∠1 = 119°, ∠2 = 61°, ∠3 = 61° , ∠4 = 119° , ∠5 = 119° , ∠6 = 61° and ∠7 = 61°
Hence measure of all the angles is given above
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PRACTICAL APPLICATIONS: DO YOU ADD, SUBTRACT, MULTIPLY, OR DIVIDE
36. ELECTRICAL TRADES: From a roll of no. 12 wire an electrician cut the following lengths:
9, 13, 42, and 12 feet. How many feet of wire did he use?
Using addition, Total length of wire used by the electrician is 76 feet.
What would you say about addition?Through addition, items are combined and counted as a single large group. The process of adding two or more numbers together is known as addition in mathematics. The terms addends and total both refer to the numbers that are added and the result of the operation.
What does addition serve as?One of the four fundamental operations of mathematics is addition, which is typically denoted by the plus sign (+). The other three are subtraction, multiplication, and division. The entire amount or sum of the two whole numbers is obtained by adding them.
We will use simple addition here,
Total length used by electrician is
(9 + 13 + 42 + 12) feet.
= 76 feet
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Riya is applying mulch to her garden. she applies it at a rate of 250{,}000\text{ cm}^3250,000 cm 3 250, comma, 000, start text, space, c, m, end text, cubed of mulch for every \text{ m}^2 m 2 start text, space, m, end text, squared of garden space.
The area of her garden where Riya is applying Mulch is 0.25m³.
To understand this answer, we will analyze the information in the question statement. So, we know that Riya is applying Mulch to her Garden. The application of Mulch is at the rate of 250 000 cm^3 for every m^2. Now to find the rate for every m^3, we will use the basic conversion formula for converting cm to m:
we know that,
100 cm = 1m
Now we can write this formula as follows,
1 cm = 1 / 100 m
1 cm = 0.01 m
We will use the same relation for the values given to us in the question:
250, 000 cm^3 = 250, 000 x 1 cm x 1cm x 1cm
1 cm^3 = 1 cm x 1cm x 1cm
250, 000 cm^3 = 250, 000 x 0.1 x 0.1 x 0.1
From, 1 cm = 0.01 m
250, 000 cm^3 = 250, 000 x 0.000001
250, 000 cm^3 = 0.25 m^3
Hence Riya is applying at 0.25 m^3 per m^2 (meter square).
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The 3rd term of (a-b)4 is
The third term of the expansion is 6a^2b^2
How to determine the third term of the expansion?The binomial term is given as
(a - b)^4
The r-th term of the expansion is calculated using
r-th term = C(n, r - 1) * x^(n - r + 1) * y^(r - 1)
So, we have
3rd term = C(4, 3 - 1) * (a)^(4 - 3 + 1) * (-b)^(3-1)
Evaluate the sum and the difference
3rd term = C(4, 2) * (a)^2 * (-b)^2
Evaluate the exponents
3rd term = C(4, 2) * a^2b^2
Evaluate the combination expression
3rd term = 6 * a^2b^2
Evaluate the product
3rd term = 6a^2b^2
Hence, the third term of the expansion is 6a^2b^2
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A man travelled a distance of 8km in an hour. How long
will it take him to cover a distance of 12km, travelling at
the same speed?
Answer:1 hour 30 minutes
Step-by-step explanation:8 kilometres are compete in an hour, plus another 4 kilometres (to make 12 total) is half of that, so adds another half an hour
The time it will take the man 1.5 hours to cover a distance of 12 km, travelling at the same speed.
What is the relation of speed and distance?
Speed describes how accelerated something or somebody is moving. If you know the distance traveled and the time it took, we can calculate the average speed of an object.
The speed formula is speed = distance / time.
We are given that;
Distance = 12 km
Speed = 8 km/h
Now,
Plugging these values into the formula for time, you get:
time = 12 / 8
time = 1.5 hours
Therefore, by the given speed the answer will be 1.5 hours.
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Simplify and write each expression
Fully. Show
(a) (3x²y-¹)(2³x³y).
The simplified form of the expression (3[tex]x^{2}[/tex][tex]y^{-1}[/tex])([tex]2^3 x^{3}[/tex] y) is (24)([tex]x^{5}[/tex]).
What is an algebraic expression?An algebraic expression (or variable expression) is a term that has been combined with operations like addition, subtraction, multiplication, and division.
To simplify an algebraic expression, we simply combine like terms. As a result, variables that are similar will be combined. The same abilities will now be combined from the similar variables.
The given expression is (3[tex]x^{2}[/tex][tex]y^{-1}[/tex])([tex]2^3 x^{3}[/tex] y).
As we know [tex]x^{a}[/tex] + [tex]x^{b}[/tex] = [tex]x^{a+b}[/tex]
So, (3[tex]x^{2}[/tex][tex]y^{-1}[/tex])([tex]2^3 x^{3}[/tex] y) = (3×[tex]2^{3}[/tex])([tex]x^{2}[/tex]×[tex]x^{3}[/tex])([tex]y^{-1}[/tex]×y)
(3[tex]x^{2}[/tex][tex]y^{-1}[/tex])([tex]2^3 x^{3}[/tex] y) = (24)([tex]x^{5}[/tex])([tex]y^{0}[/tex])
(3[tex]x^{2}[/tex][tex]y^{-1}[/tex])([tex]2^3 x^{3}[/tex] y) = (24)([tex]x^{5}[/tex])
As a result, the abbreviated form of the expression (3[tex]x^{2}[/tex][tex]y^{-1}[/tex])([tex]2^3 x^{3}[/tex] y) is (24)([tex]x^{5}[/tex]).
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Evaluate the determinant of each matrix.
[4 -1 8 2]
For the matrix:
[tex]\left[\begin{array}{ccc}4&-1\\8&2\\\end{array}\right][/tex]
The determinant is equal to 16.
How to find the determinant of the given matrix?Remember that for a general 2 by 2 matrix:
[tex]\left[\begin{array}{ccc}a_1&b_1\\a_2&b_2\\\end{array}\right][/tex]
The determinant is given by the simple formula:
D = a₁*b₂ - b₁*a₂
This is the only thing we need to use in this problem, we will use this formula to find the determinant of the given 2 by 2 matrix.
In this case we have the matrix:
[tex]\left[\begin{array}{ccc}4&-1\\8&2\\\end{array}\right][/tex]
Then we can just use the given formula for the determinant, we will get
D = 4*2 - (-1)*8
We just need to solve that expression, we will get:
D = 8 - (-8) = 8 + 8 = 16
We can see that the determinant of the given matrix is equal to 16.
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T is known that 3% of people whose luggage is screened at an airport have questionable objects in their luggage. what is the probability that a string of 15 people pass through screening successfully before an individual is caught with a questionable object? what is the expected number of people to pass through be- fore an individual is stopped?
The probability that a string of 15 people passes through screening successfully before an individual is caught with a questionable object is 0.3040 and the expected number of people to pass through be- fore an individual is stopped 49
3% of people whose luggage is screened at an airport have questionable objects in their luggage i.e
P(x)=3/100=0.03
The probability of people whose luggage is screened at an airport and have no questionable object in their luggage is
〖P(x)〗^1=1-P(x)
〖P(x)〗^1=1-0.03
〖P(x)〗^1=0.97
Using Binomial probability which states that
P(x)=(nCx) (p)^x (q)^(n-x)
N= 16 total number in consideration
p= probability with no questionable luggage
q= probability with questionable luggage
P(15)=(16C15) (p)^15 (q)^(16-15)
P(15)=(16C15) (0.97)^15 (0.03)^(16-15)
16C15=16!/((16-15)!(15!))
15C15=15!/((1)!(15!))
16C15=20922789888000/((1)(1307674368000))
16C15=20922789888000/1307674368000
16C15=16
P(15)=(16) (0.97)^15 (0.03)^1
P(15)=(16)(0.63325)(0.03)
P(15)=0.3040
P(x) =(Required outcome)/(Total outcome)
0.3040 =15/(Total outcome)
Total outcome=15/0.3040
Total outcome=49.34
Total outcome=49
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check attached images
PLSS HELP :((
will mark brianlist if its the correct answer ty
The step 2 should be m∠p + m∠o = 180 degrees(supplementary angles)
How to find the angles of a triangle?The external angle theorem states that the measure of each exterior angle of a triangle is equal to the sum of the opposite and non-adjacent interior angles(remote interior angles) .
Therefore,
Step 1
m∠m + m∠n + m∠o = 180°(sum of angles of a triangle)
It's very correct
Step 2
m∠p - m∠o = 90 degrees(Alternate angles)
This is incorrect.
It should be m∠p + m∠o = 180 degrees(supplementary angles)
The angles m∠p and m∠o are supplementary angles. This simply implies the angles add up to 180 degrees.
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If a polygon has 5 sides, then it is a pentagon.
Write the inverse of the conditional statement and determine whether it is true or false.
If a polygon does not have 5 sides, then it is not a pentagon.; FALSE
If a polygon is a pentagon, then it has 5 sides.: TRUE
If a polygon is a pentagon, then it has 5 sides; FALSE
If a polygon does not have 5 sides, then it is not a pentagon.: TRUE
Answer:
Step-by-step explanation:
If a polygon does not have 5 sides, then it is not a pentagon.: TRUE
Which function represents the equation of the line?
Answer:
A linear function is of the form f(x)= mx+b
2.) Which represents the part of the 10-by-
10 grid that is shaded?
A
B
C
D
10
3
1-
20
Scott borrowed $985 for a new TV and game system. He made 6 monthly payments to repay the loan. He paid $155 interest. What is his simple interest rate?
Based on the amount that Scott borrowed for the new TV and game system, and the interest paid, the simple interest rate is 15.7%
What is the simple interest rate?The simple interest rate can be found by the formula:
= Interest paid by Scott on the loan / Amount Scott borrowed x 100%
Solving for the simple interest rate gives:
= 155 / 985 x 100%
= 0.1573604060913705583756345177665 x 100%
= 0.157 x 100%
= 15.7%
This means that Scott paid 15.7% on the loan he borrowed.
In conclusion, Scott's simple interest rate is 15.7%.
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Find the sum of (7.3 × 106) and (4.6 × 105). write the final answer in scientific notation. 11.9 × 1011 1.19 × 1010 7.76 × 106 7.76 × 105
The sum in scientific notation will give:
7.76*10⁶
How to find the sum in scientific notation?
Here we want to find the sum between the numbers (7.3*10⁶) and (4.6*10⁵).
To sum these numbers, we need to have the same exponent in the "10", then we can rewrite:
7.3*10⁶ = 73*10⁵
Now the sum will be:
73*10⁵ + 4.6*10⁵
Taking a common factor we get:
73*10⁵ + 4.6*10⁵ = (73 + 4.6)*10⁵ = 77.6*10⁵
Now we want to go back to scientific notation, so we need to move the decimal point one time to the left, we will get:
77.6*10⁵ = 7.76*10⁶
That is the outcome of the sum.
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In this figure, AB∥CD and m∠6=75° . What is m∠3 ?
115°
75°
15°
105°
The measure of angle <3 is 105 degrees
How to use the diagram to find the measure of angle 3?The diagram that completes the question is added as an attachment
The angle is given as
<6 = 75
From the diagram, we have
<3 + <6 = 180 degrees
The above is true by the sum of internal angles between parallel lines
So, we have
<3 + 75 = 180
Subtract 75 from both sides of the equation
So, we have
<3 + 75 - 75 = 180 - 75
Evaluate the like terms
So, we have
<3 = 105
Hence, the measure of angle <3 is 105 degrees
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What is the highest common factor of 39375 and 779625?
Answer:
To get the Greates Common Factor (GCF) of 39375 and 779625 we need to factor each value first and then we choose all the copies of factors and multiply them:
39375: 3 3 5 5 5 5 7
779625: 3 3 3 3 5 5 5 7 11
GCF: 3 3 5 5 5 7
The Greates Common Factor (GCF) is: 3 x 3 x 5 x 5 x 5 x 7 = 7875
Step-by-step explanation: