Answer:
2 1/8
Step-by-step explanation:
I counted from 29 to 31 and then saw that for 29 it was 3/8 and for 31 it was 2/8 so i knew that the answer would be 2 1/8
How many and of which kind of roots does the equation f(x)=x^3+2x^2+4x+8 have?
The cubic equation f(x) = x³ + 2 · x² + 4 · x + 8 has one real root and two complex roots.
What kind of roots does have a cubic equation?
In this problem we have a cubic equation and the nature of their roots must be inferred according to a algebraic method.
Cubic equations are polynomials of the form y = a · x³ + b · x² + c · x + d, there is a method to infer the nature of the roots of such polynomials: The discriminant from Cardano's method, an analytical method used to solve polynomials of the form a · x³ + b · x² + c · x + d = 0.
The discriminant is described below:
Δ = 18 · a · b · c · d - 4 · b³ · d + b² · c² - 4 · a · c³ - 27 · a² · d² (1)
Where:
There are three distinct real roots for Δ > 0.Real roots with multiplicity greater than 1 for Δ = 0.A real root and two complex roots for Δ < 0.If we know that a = 1, b = 2, c = 4 and d = 8, then the nature of the roots is:
Δ = 18 · 1 · 2 · 4 · 8 - 4 · 2³ · 8 + 2² · 4² - 4 · 1 · 4³ - 27 · 1² · 8²
Δ = - 1024
The cubic equation f(x) = x³ + 2 · x² + 4 · x + 8 has one real root and two complex roots.
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Describe all x-values within a distance of 9 from the number 9
The value |x−9|≤9 is equivalent to [18,0] in interval notation.
According to the statement
We have given that the distance of 9 from the number 9. and we have to find the all value of x between it.
So, For find all x value we use absolute value inequalities.
distance of 9 from number 9.
So, when we draw the number line
we see that the number will become
The distance from x to 9 can be represented using an absolute value symbol, |x−9|.
Write the values of x that satisfy the condition as an absolute value inequality.
So, it become
|x−9|≤9
Now write two inequalities then it become
x−9≤9 and x−9≥−9
x≤18 and x≥0
So, The solution set is x≤18 and x≥0,
then the solution set is an interval including all real numbers between and including 18 and 0.
So |x−9|≤9 is equivalent to [18,0] in interval notation.
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Add: 5/7 + 9/11 + 21/77
Answer:
Step-by-step explanation:
You want to begin by making each fraction have the same common denominator. The LCF (least common factor) is 77. So, knowing this, we can now multiply the fractions that need to have a denominator of 77.
1. 5/7*11/11=55/77
2. 9/11 * 7/7 =63/77
Now we can add
55/77 + 63/77 + 21/77 = 139/77 or 1.805194805
Find the value of x
[tex] \qquad \qquad \bf \huge\star \: \: \large{ \underline{Answer} } \huge \: \: \star[/tex]
x = 12°[tex]\textsf{ \underline{\underline{Steps to solve the problem} }:}[/tex]
[tex]\qquad❖ \: \sf \:2x + 6 + 5x + 90 = 180[/tex]
[ by linear pair ]
[tex]\qquad❖ \: \sf \:7x + 6 = 180 - 90[/tex]
[tex]\qquad❖ \: \sf \:7x + 6 = 90[/tex]
[tex]\qquad❖ \: \sf \:7x = 90 - 6[/tex]
[tex]\qquad❖ \: \sf \:7x = 84[/tex]
[tex]\qquad❖ \: \sf \:x = 84 \div 7[/tex]
[tex]\qquad❖ \: \sf \:x = 12[/tex]
[tex] \qquad \large \sf {Conclusion} : [/tex]
[tex]\qquad❖ \: \sf \:x = 12 \degree[/tex]
Heyy i just need some help with questions 5,7,9 if anyone could help me and show the work that would be amazing thank you!!
Step-by-step explanation:
5)f(g(8))
from the table g(8)=4
f(4) =4 from the table
7)g(f(5))
from the table f(5)=0
g(0)=9 from the table
9)f(f(4))
from the table f(4)=4
f(4)=4 from the table
A line with slope
-1/3
passes through the point (-4, 4).
Find the coordinates of another point on the line.
Answer:
(0, 8/3) = y-intercept
Step-by-step explanation:
I chose to find the y-intercept since it is easy to find with the given information.
The equation for a line is y = mx + b
To find the y-intercept, we must plug in the info we have and solve for b:
4 = -1/3 (-4) + b
4 = -4/3 + b
8/3 = b
To find a point on the line, you also could have added -1 to 4 and 3 to -4 since slope means rise/run or change in y/change in x:
(y - 1) / (x + 3) = (4 - 1) / (-4 + 3) = (3, -1) (flip since it's the y and x coordinate) = (-1, 3)
a tree 20 feet tall with a circumference of 3 ft has a vine wound around 7 times how long is the vine?
The length of the vine wounded to the tree is 21 feet.
How to solve circumference?Circumference is the perimeter of a circular object. Therefore,
circumference = 2πr
where
r = radiusThe circumference of the tree is 3 feet. A vine was wound around 7 times .
The length of the vine can be calculated as follows:
Therefore,
circumference = 3 ft
length of the vine = 7 × 3
length of the vine = 21 feet
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Underwood Company is preparing its annual profit plan. As part of its analysis of the profitability of individual products, the controller estimates the amount of manufacturing overhead that should be assigned to each of the two product lines from the information given below. Wall Mirrors Specialty Windows Total units produced 30 30 Total number of material moves 7 18 Direct labor hours per unit 145 145 Budgeted material-handling costs are $30,000. The material-handling cost per wall mirror under activity-based costing is:
The material-handling cost per wall mirror under activity-based costing is $280
What is activity-based costing?
Activity-based costing involves absorbing overheads based on cost drivers which directly impact the incurrence of the overhead, in this case, material moves determine the amount of material-handling costs to be incurred, hence, material-handing overheads would be absorbed into the two products based on material moves, which is the appropriate cost driver.
There 25 materials move in both divisions (i.e. 7+18=25)
Material-handling cost per material move=Budgeted material-handling costs /total material moves
Budgeted material-handling costs =$30,000
Material-handling cost per material move=$30,000/25
Material-handling cost per material move=$1,200
Total material-handing costs for wall mirror=number of material moves for wall mirror*Material-handling cost per material move
Total material-handing costs for wall mirror=7*$120
Total material-handing costs for wall mirror=$8,400
material-handling cost per wall mirror=Total material-handing costs for wall mirror/number of wall mirrors
material-handling cost per wall mirror=$8,400/30
material-handling cost per wall mirror=$280
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Find the value of x.
The value of x from the given circle is 4
What is intersecting chord theorem?The intersecting chords theorem is a statement in geometry that describes a relation of the four line segments created by two intersecting chords within a circle.
It states that the products of the lengths of the line segments on each chord are equal.
According to the theorem;
x * 3 = 2 * (4 + 2)
3x = 2(6)
3x = 12
Divide both sides by 3
3x/3 = 12/3
x =4
Hence the value of x from the given circle is 4
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A father's age now is three times the age that his son was four years ago. In 12 years, the father will be twice as old as his son. Find their ages.
Answer:
Now, the father is 60, and the son is 24.
Step-by-step explanation:
Now:
Father's age = f
Son's age = s
4 years ago:
Father's age = f - 4
Son's age = s - 4
In 12 years:
Father's age = f + 12
Son's age = s + 12
Now:
f = 3(s - 4)
In 12 years:
f + 12 = 2(s + 12)
We have 2 equations that we can solve in a system of equations.
f = 3(s - 4)
f + 12 = 2(s + 12)
f = 3s - 12
f + 12 = 2s + 24
f = 3s - 12
f = 2s + 12
Since above both equations are in terms of f, set the right sides equal and solve for s.
3s - 12 = 2s + 12
s = 24
f = 3(s - 4)
f = 3(24 - 4)
f = 3(20)
f = 60
Now, the father is 60, and the son is 24.
find the square roots by division method of
210,681
Answer: square of 459 is 210681
find the positive square roots by division method of 151,321 please tell me fast
Answer:
389 is the answer
Hope you like it!
Some banks charge a fee on savings accounts that are left inactive for an extended period of time.
The equation `y=5000\left(0.98\right)^{x}` represents the value, y, of one account that was left inactive for a period of x years.
According to the equation, is the balance in this account increasing or decreasing?
Since the value 0.98 is less than 1, we can therefore say that balance in this account is decreasing.
How to recognize Exponential Function.Exponential Function can be used for increase rate and also for decay rate. The difference between the two are the plus and minus signs. To put it in another perspective, If Y = P(M)³
If M is less than one, that means it is decaying or decreasing. And if M is greater than one, that means it is increasing.
Given that Some banks charge a fee on savings accounts that are left inactive for an extended period of time. And the equation
y = 5000(0.98)^x represents the value, y, of one account that was left inactive for a period of x years.
According to the equation, to know if the balance in this account is increasing or decreasing, we will analyze the value 0.98.
Since the value 0.98 is less than 1, we can therefore say that balance in this account is decreasing.
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Ivanna knit a scarf for each of her 9 friends. Altogether, the scarves had a total length of 41.4 ft. If each scarf was the same length, how long was each scarf? Write your answer in inches. Use the table of conversion facts as necessary, and do not round your answer. Conversion facts for length 12 inches (in) = 1 foot (ft) 3 feet (ft) = 1 yard (yd) 36 inches (in) = 1 yard (yd) 5280 feet (ft) = 1 mile (mi) 1760 yards (yd) = 1 mile (mi)
Answer: 55.2 in
Step-by-step explanation:
1ft = 12 in
41.4/9 = 4.6 ft
4.6 x 12 = 55.2 in
If BC= 48 cm and sin
Using relations in a right triangle, it is found that the length of AC is of 14 cm.
What are the relations in a right triangle?The relations in a right triangle are given as follows:
The sine of an angle is given by the length of the opposite side to the angle divided by the length of the hypotenuse.The cosine of an angle is given by the length of the adjacent side to the angle divided by the length of the hypotenuse.The tangent of an angle is given by the length of the opposite side to the angle divided by the length of the adjacent side to the angle.Researching this problem on the internet, we have that:
The opposite leg to angle A is of 48 cm.sin(A) = 0.96.Hence the hypotenuse is found as follows:
sin(A) = 48/h
0.96 = 48/h
h = 48/0.96
h = 50 cm.
The length of side AC is the other leg of the triangle, found using the Pythagorean Theorem, hence:
[tex]x^2 + 48^2 = 50^2[/tex]
[tex]x^2 = \sqrt{50^2 - 48^2}[/tex]
x = 14 cm.
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prove 1-cot23 = 2/ ( 1- cot22)
From all the steps below, we have been able to prove that; 1 - cot23° = 2/(1 - cot22°).
How to prove trigonometric functions?We want to prove that 1 - cot23° = 2/(1 - cot22°).
We will prove it using the trigonometric expression
cot(22° + 23°) = cot45°
Using trigonometric identities, we can rewrite as;
(cot22° cot23° - 1)/(cot22° + cot23°) = 1
Cross multiply to get;
cot22° cot23° - 1 = cot22° + cot23°
Rearrange to get;
cot22° cot23° - 1 - cot22° - cot23° =0
⇒ cot22° cot23° - 1 - cot22° - cot23° + 2 =2
⇒ cot22° cot23° + 1 - cot22° - cot23° =2
⇒ cot22° cot23° - cot22° - cot23° + 1 = 2
⇒ cot22° (cot23° - 1) - 1 (cot23° - 1) = 2
⇒ (cot22° - 1) (cot23° - 1) = 2
Divide both sides by (cot23° - 1) to get;
cot23° - 1 = 2/(cot22° - 1)
⇒ 1 - cot23° = 2/(1 - cot22°).
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please help me im begging you help me i beg u :(
In order to finance furniture for an office in a new retail store, Tools for Schools signs a 80-day simple discount note with a maturity value of $7700. Find the proceeds if the discount rate is 6%.
Based on the number of periods for the simple discount note to reach maturity and the discount rate, the proceeds are $7,598.74.
What are the proceeds?You can solve for the discounted price as:
= Maturity value x discount rate x number of periods
Solving gives:
= 7,700 x (6% / 365) x 80
= $101.26
The proceeds can then be found by subtracting the discounted price from the maturity price.
Solving for the proceeds gives:
= 7,700 - 101.26
= $7,598.74
Based on the simple discount note period, the maturity value, and the discount rate, the proceeds can be found to be $7,598.74.
In conclusion, the proceeds are $7,598.74.
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ALOT KF POINTS PLEASE HELP The measures of two exterior angles are given in the figure below.
Choose an equation that could be used to represent one of the exterior
angles and a logical conjecture about the exterior angles of a triangle.
An exterior angle is equal to the sum of two non-adjacent interior angle of the triangle. Option B
What is a triangle?The term triangle refers to a figure that has three sides. There are several types of triangles such as the;
Isosceles triangleScalene triangleRight angled triangleDespite all these types of triangle, the basic geometric properties of triangles can be applied to all types of triangle that we have mentioned above.
Considering the question, an equation that could be used to represent one of the exterior angles and a logical conjecture about the exterior angles of a triangle is that; m<4 = m<1 + m<2. An exterior angle is equal to the sum of two non-adjacent interior angle of the triangle. Option B
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6/(v+4) + 2/(v-6)
What is the answer?
Answer:
8v-28/v^2-2v-24
Step-by-step explanation:
1. Find common denominator
2. Combine fractions with common denominator
3. Re-order terms so constants are on the left
evaluate 2n-1, where N -7
The value of the expression 2n - 1 when n = 7 is 13.
Equation2n - 1
when n = 7
Substitute n = 7 into the equation2n - 1
= 2(7) - 1
= 14 - 1
= 13
What is mathematical expression?Mathematical expression is an expression which involves the combination of numbers and variables in a valid way, in a function of addition, subtraction, multiplication, division and exponentiation
Therefore, the value of the expression 2n - 1 when n = 7 is 13.
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Please help solve this equation?
[tex]{ \red{ \bold{cos \: y \: }}}[/tex]
Step-by-step explanation:
[tex]{ \green{ \tt{ \frac{1 \: + \: \cos \: y \: }{1 \: + \: \sec \: y \: }}}} \: → {eq}^{n} (1)[/tex]
But, as you know that
[tex]{ \blue{ \tt{sec \: y \:}}} = { \green{ \tt{\frac{1}{ \ \cos \: y }}}} [/tex]
Then the equation (1) becomes
[tex]{ \green{ \tt{ \frac{1 \: + \: cos \: y }{1 \: + \: \frac{1}{cos \: y} }}}} \: [/tex]
Multiply Numerator and Denominator by [tex] \frac{cos \: y}{cos \: y} [/tex]
then,
[tex]{ \green{ \tt{( \frac{cos \: y}{cos \: y})}}} \: { \green{ \tt{ \frac{1 \: + \: cos \: y}{1 \: + \: \frac{1}{cos \: y}}}}} [/tex]
[tex] = { \green{ \tt{ \frac{cos \: y \: + \: {cos}^{2} \: y }{cos \: y \: + \: 1 }}}}[/tex]
take cos y as common, then
[tex]{ \green{ \tt{cos \: y}}} \: { \green{ \tt( \frac{1 \: + \: cos \: y}{cos \: y \: + \: 1} )}}[/tex]
Here, (1+cos y/cos y + 1) gets cancelled.
Then the remaining answer is cos y.
Write expressions for the length and width of a rectangle that has an area equal to 3x2-5x+2.
Answer:
x - 2, x - 3
Step-by-step explanation:
3x² - 5x + 2
x² - 5x + 6
(x - 3)(x - 2)
length = x - 2
width = x - 3
What index of m will equal to 1/m^2 ?
Answer:
index of m is -2
Step-by-step explanation:
any number or letter to the negatIve power(index) is the same as 1 divided by that number or letter to the positive index.
for example, 10^-2 = 1/10^2 and X^-4 is the same as 1/X^4.
Find the mean for the scores 3,820, 5,500, 8,560, 4,400, 5,350
Answer:
5,526
Step-by-step explanation:
Mean of scores = Total Value of Scores / Number of Values
= [tex]\frac{3820+5500+8560+4400+5350}{5} \\[/tex]
= 5,526
Answer:5526
Step-by-step explanation: Add everything up and divide by 5 because there are 5 numbers
Item3 4.28 points eBookReferencesCheck my workCheck My Work button is now enabledItem 3 Yarra Fabrication estimates that its manufacturing overhead will be $2,342,400 in year 1. It further estimates that direct material costs will amount to $1,464,000. During July, Yarra worked on four jobs with actual direct materials costs of $76,000 for Job 0701, $104,000 for Job 0702, $135,000 for Job 0703, and $67,000 for Job 0704. Actual manufacturing overhead costs for the year were $2,480,000. Actual direct materials costs were $1,630,000. Manufacturing overhead is applied to jobs based on direct materials cost using predetermined rates. Required: a. How much overhead was applied to each of the four jobs, 0701, 0702, 0703, and 0704? b. What was the over- or underapplied manufacturing overhead for year 1?
First of all, we would calculate the predetermined overhead rate by using this formula:
Predetermined overhead rate = Manufacturing overhead/Direct material costs
Predetermined overhead rate = $2,342,400/$1,464,000
Predetermined overhead rate = 1.6 per DM $.
Next, we would calculate the overhead applied by using this formula:
Overhead applied = Job × DM cost
For job 0701, we have:
Overhead applied = 76,000 × 1.6
Overhead applied = $121,600.
For job 0702, we have:
Overhead applied = 104,000 × 1.6
Overhead applied = $166,400.
For job 0703, we have:
Overhead applied = 135,000 × 1.6
Overhead applied = $216,000.
For job 0704, we have:
Overhead applied = 67,000 × 1.6
Overhead applied = $107,200.
Part B.For the overapplied manufacturing overhead for year 1:
Less applied overhead = $1,630,000 × 1.6
Less applied overhead = $2,608,000.
Overapplied manufacturing overhead = Actual overhead cost - Less applied overhead
Overapplied manufacturing overhead = $2,480,000 - $2,608,000
Overapplied manufacturing overhead = $128,000.
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3. Joyce had a 10.00am appointment 60Km from her house. She averaged 80Km/h for the trip
but arrived 20 minutes late for the appointment. At what time did she leave her home that
morning?
A) 9.40
C) 9.15
B) 9.35
D) 9.20
E) None of these
Answer:
B) 9:35
Step-by-step explanation:
the travel time we get by dividing the distance by the speed
distance / distance/time = time
so,
60 / 80 = 6/8 = 3/4 = 0.75 hours or 45 minutes.
since she arrived 20 minutes late, that means at 10:20 am, she left home 45 - 20 = 25 minutes before 10:00am.
and that is 9:35 am.
i need help this is effecting my grade please help it would make my day
Answer:
8
Step-by-step explanation:
-32/-4 the minus takes out the second minus then we are left with 32/4which makes the answer a positive 8
Given that mLa = 36° and m
Answer:
mLx = 144
mLy=154
Step-by-step explanation:
180-36=144
x=144
180-62=118
36+118=154
180-154=26
180-26=154
y=154
Answer:
154 degrees
Step-by-step explanation:
you can find measure of angle y, since it is the supplement of angle a, so
measure of angle y = 180 - measure of angle a, which is 144 degrees
you can find the measure of angle x, by finding its complement.
Looking at the center triangle, we see that it is formed from angle a, the supplement of angle b, and the supplement of angle x, so the equation is 180 = 36 + 180 - 62 + supplement of angle x
so, the supplement of angle x is 26 degrees, so x is 154 degrees
The graph of the function f(x) = –(x + 6)(x + 2) is shown below.
On a coordinate plane, a parabola opens down. It goes through (negative 6, 0), has a vertex at (negative 4, 4), and goes through (negative 2, 0).
Which statement about the function is true?
The function is increasing for all real values of x where
x < –4.
The function is increasing for all real values of x where
–6 < x < –2.
The function is decreasing for all real values of x where
x < –6 and where x > –2.
The function is decreasing for all real values of x where
x < –4.
Answer:
c,d
Step-by-step explanation: