According to the synthetic division below, which of the following statements are true?
Check all that apply.
Answers
A, D and E are correct
given ( x - 4 ) is a factor then x = 4 is a root
the remainder on division by (x - 4 ) = 0 as indicated by the 0 on the right side of the quotient
(x - 4 ) is a factor of 3x² - 13x + 4 → A
the number 4is a root of f(x) = 3x² - 13x + 4 → D ( explained above )
thus 3x² - 13x + 4 ÷ (x - 4 ) = 3x - 1 → E
the quotient line 3 - 1 0
3 and - 1 are the coefficients of the linear quotient and 0 is the remainder
The correct options are [tex]\boxed{{\mathbf{Option A, D and E}}}[/tex].
Further explanation:
In any synthetic division, the dividend polynomial [tex]F\left( x \right) = {a_n}{x^n} + {a_{n - 1}}{x^{n - 1}} + {a_{n - 2}}{x^{n - 2}} + \cdots {a_0}[/tex] and the divisor polynomial [tex]g\left( x \right) = x - b[/tex] can be written as,
[tex]\begin{aligned}b\left){\vphantom{1{\underline {\begin{array}{*{20}{c}}3&{ - 13}&4\\{ }&{12}&{ - 4}\end{array}} }}}\right.\!\!\!\!\overline{\,\,\,\vphantom 1{{\underline {\begin{array}{*{20}{c}}&{a}_n&{ a_{n-1}}&_\cdot_\cdot_\cdot{a_0}\\{ }&{}&{ }\end{array}} }}} \hfill \\\begin{array}{*{20}{c}}{{\text{ }}{c}_n}&_\cdot_\cdot_\cdot{ c_0}&{{\text{ }}0}\end{array} \hfill\\\end{aligned}[/tex]
Here, the monic polynomial is divided by the polynomial that provides the polynomial after division that is also a factor of the polynomial .
Given:
The synthetic division is given below.
[tex]\begin{aligned}4\left){\vphantom{1{\underline {\begin{array}{*{20}{c}}3&{ - 13}&4\\{ }&{12}&{ - 4}\end{array}} }}}\right.\!\!\!\!\overline{\,\,\,\vphantom 1{{\underline {\begin{array}{*{20}{c}}&3&{ - 13}&4\\{ }&{12}&{ - 4}\end{array}} }}} \hfill \\\begin{array}{*{20}{c}}{{\text{ }}3}&{ - 1}&{{\text{ }}0}\end{array} \hfill\\\end{aligned}[/tex]
Step by step explanation:
We have to determine the answer among all the options.
Option A: [tex]\left( {x - 4} \right)[/tex] is a factor of [tex]3{x^2} - 13x + 4[/tex].
It can be observed from the given synthetic division the polynomial is [tex]g\left( x \right) = \left( {x - 4} \right)[/tex] that is divisible by the polynomial [tex]F\left( x \right) = 3{x^2} - 13x + 4[/tex].
Therefore, the polynomial [tex]g\left( x \right) = \left( {x - 4} \right)[/tex] is a factor of the polynomial [tex]F\left( x \right) = 3{x^2} - 13x + 4[/tex].
Therefore, the option A is correct option.
Option B: [tex]\left( {x + 4} \right)[/tex] is a factor of [tex]3{x^2} - 13x + 4[/tex].
From the option A, it has been proved that [tex]g\left( x \right) = \left( {x - 4} \right)[/tex] is a factor of the polynomial
[tex]F\left( x \right) = 3{x^2} - 13x + 4[/tex]
Therefore, [tex](x+4)[/tex] is a not factor of [tex]3{x^2} - 13x + 4[/tex].
Thus, the option B is not correct option.
Option C: The number [tex]-4[/tex] is a root of [tex]F\left( x \right) = 3{x^2} - 13x + 4[/tex].
From the option A, it has been proved that [tex]g\left( x \right) = \left( {x - 4} \right)[/tex] is a factor of the polynomial
[tex]F\left( x \right) = 3{x^2} - 13x + 4[/tex]
Now substitute 0 for [tex]g\left( x \right)[/tex] in the equation [tex]g\left( x \right) = \left( {x - 4} \right)[/tex] to find the root of the polynomial [tex]F\left( x \right) = 3{x^2} - 13x + 4[/tex] as,
[tex]\begin{aligned}0&= \left( {x - 4} \right) \hfill\\x&= 4 \hfill\\\end{aligned}[/tex]
It can be seen that the value of [tex]x[/tex] is 4 it means [tex]-4[/tex] is not a root of the polynomial [tex]F\left( x \right) = 3{x^2} - 13x + 4[/tex].
Therefore, the option C is not correct option.
Option D: The number [tex]4[/tex] is a root of [tex]F\left( x \right) = 3{x^2} - 13x + 4[/tex].
It can be seen that the value of [tex]x[/tex] is 4 in option C it means [tex]4[/tex] is a root of the polynomial [tex]F\left( x \right) = 3{x^2} - 13x + 4[/tex].
Therefore, the option D is correct option.
Option E: [tex]\left( {3{x^2} - 13x + 4} \right) \div \left( {x - 4} \right) = \left( {3x - 1} \right)[/tex]
The option E is also correct as [tex](x-4)[/tex] is the factor of the polynomial [tex]F\left( x \right) = 3{x^2} - 13x + 4[/tex].
Option F: [tex]\left( {3{x^2} - 13x + 4} \right) \div \left( {x + 4} \right) = \left( {3x - 1} \right)[/tex]
The option F is not correct as [tex]\left( {x + 4} \right)[/tex] is not the factor of the polynomial [tex]F\left( x \right) = 3{x^2} - 13x + 4[/tex].
Result:
Therefore, the correct options are [tex]\boxed{{\mathbf{Option A, D and E}}}[/tex].
Learn more:
Learn more about the function is graphed below https://brainly.com/question/9590016 Learn more about the symmetry for a function https://brainly.com/question/1286775 Learn more about midpoint of the segment https://brainly.com/question/3269852Answer details:
Grade: Medium school
Subject: Mathematics
Chapter: Synthetic division
Keywords: Synthetic division, polynomial, monic polynomial, function, factor, real number, root, divisible, addition, remainder, quotient, divisor, dividend.
Related Questions
How many subsets of 100 have exactly 99 elements?
How many subsets of 100 have exactly 98 elements?
How many subsets of 100 have exactly 2 elements?
Answers
The number of k-element subsets of a set of n elements is given by
... C(n, k) = n!/(k!(n-k)!)
a) C(100, 99) = 100!/(99!×1!) = 100
b) C(100, 98) = 100!/(98!×2!) = 100*99/2 = 4950
c) C(100, 2) = 100!/(2!×98!) = 4950 . . . . same as (b)
Solve the problem using the previous balance method.
The account balance on April 1st is $60.15.
On April 15th a payment of $51.00 is made.
On April 25th a purchase of $91.27 is made.
What is the finance charge if the annual rate is 18%?
What is the new account balance?
Finance charge = $ ____
New balance = $ ____
Answers
Annual Percent Rate (APR) = 18%
Rate during the current billing cycle = 18/12 = 1.5%
Balance at the beginning of the billing cycle = 60.15
Payment 51.00
Balance 10.15
Purchase 91.27
Balance - 81.12
Finance Charge 60.15 * 0.015 = 0.90
New Balance - 82.02
P = 215 (1.005)t/3 the equation above can be used to model the population, in thousands, of a certain city t years after 2000. according to the model, the population is predicted to increase by 0.5% every n months. what is the value of n
Answers
As t/3 it means that 0.5% every 3 years.
So n will be 3 years , 36 months
Solution:
The Given model to Predict the population
[tex]P=P_{0}(1.005)^{\frac{t}{3}[/tex]
----------------------------------(1)
The population increases by 0.5 % every n months.
Initial Population = 215
Final Population
[tex]=215+215\times \frac{0.5}{100}\\\\=215+1.075\\\\=216.075[/tex]
Substituting the value of , Initial and final Population in equation 1,
[tex]216.075=215\times (1.005)^{\frac{t}{3}}\\\\ (1.005)^{\frac{t}{3}}=\frac{216.075}{215}\\\\ (1.005)^{\frac{t}{3}}=(1.005)^{1}\\\\ \frac{t}{3}=1\\\\ t=3[/tex]
t=3 years =36 months
The value of n is equal to 36 months.
Stephon has a square brick patio. He wants to reduce the width by 2 feet and increase the length by 2 feet.
Let x represent the length of one side of the square patio. Write expressions for the length and width of the new patio. Then find the area of the new patio if the original patio measures 10 feet by 10 feet.
A. lw = (x + 2)(x – 2); 96 square feet
B. lw = (x – 2)(x – 2); 64 square feet
C. lw = x(x – 2); 80 square feet
D. lw = (x + 2)(x + 2); 144 square feet
Answers
A
reducing one side by 2 is expressed as (x - 2) ← length
increasing the other side by 2 is expressed as (x + 2 ) ← width
the area of new patio = (10 - 2 )(10 + 2) 8 × 12 = 96 ft²
Answer: A. lw = (x + 2)(x – 2); 96 square feet
Step-by-step explanation:
Given: Stephon has a square brick patio. He wants to reduce the width by 2 feet and increase the length by 2 feet.
Let x be the side-length of the patio, then
The length of the patio after change = x+2
The width of the patio after change = x-2
Then the area of the patio is given by :-
[tex]A=lw\\\Rightarrow\ A=(x+2)(x-2)[/tex]
If the original patio measures 10 feet by 10 feet.
Then the area of the patio= [tex](10+2)(10-2)=(12)(8)=96[/tex] square feet.
Hence, A is the right answer.
To get the color dove-white, Ken mixed black paint and white paint in a ratio of 5:3. He used 20 gallons of black paint. How much white paint did he use?
Answers
Because 20 divided by 5 = 4. Meaning that 4 gallons is one part.
4 x 5 = 20
4 x 3 = 12
12 gallons of white paint
divide 20 gallons by 5 to obtain 1 part of the ratio
[tex]\frac{20}{5}[/tex] = 4 gallons ← 1 part
white paint = 3 × 4 = 12 gallons ← 3 parts
when multipling signed numbers how do you know wether the number is positive or neagitive
Answers
If an odd number of minus signs are involved in a product or quotient, the sign of the result is negative. Otherwise, it is positive.
Examples:
(-1)(-1) = 1
(-1)(-1)(-1) = -1
(-1)/(-1) = 1
(-1)(-1)/(-1) = -1
The product of two positive numbers is positive: (+)(+) = (+).
The product of one positive number and one neg number is neg: (+)(-) = (-).
The product of two negative numbers is positive: (-)(-) = (+)
Graph f(x)=12x+2.
Use the line tool and select two points to graph the line.
Answers
Answer:
(0,2) and (1,14)
Graph is attached.
Step-by-step explanation:
Let us find y intercept
When x=0, y = f(x) =2
Hence one point is (0,2)
Other point is let x = 1,
y =12(1)+2 =14
(1,14) (0,2) are plotted and joined.
Graph is attached.
What is the value of the expression (9+15) divided by 3 plus 2
Answers
Hey!
This question is super easy to me. This question is going to be used their order of operations.
Order of operations stands for
↓
P-Parenthesis
E-Exponents
M-Multiply
D-Divide
A-Add
S-Subtract
(9+15)/3+2
24/3+2
8+2
=10
Answer⇒⇒⇒⇒⇒=10
Hope this helps!
Thank you for posting your question at here on Brainly.
-Charlie
Answer:
10
Step-by-step explanation:
(9+15) ÷ 3 + 2 = 10
help please! thanks!
Answers
Answer:
The edge length of the storage cube is 30 centimeters.
Step-by-step explanation:
All sides/edges of a cube has equal length.
Let's take the length of a edge as [tex]a[/tex] centimeters.
The volume a the cube = Height * Width * Length
All height, width and length are equal([tex]a[/tex] centimeters).
Now we can write the equation again as,
The volume a the cube = [tex]a*a*a[/tex]
Volume of the cube is given as 27,000 cubic centimeters.
Therefore,
[tex]a*a*a=27,000[/tex]
[tex]a=\sqrt[3]{27,000}[/tex]
[tex]a=30[/tex]
Therefore, the edge length of the storage cube is 30 centimeters.
Select the functions that have a value of -1. sin180° cos180° tan180° csc180° sec180° cot180°
Answers
We have to break each degree in terms of 90
A) [tex]sin180^\circ=sin(90\times2+0)[/tex]
Which is in third quadrant, therefore sine is negative hence
[tex]sin(90\times2+0)= -sin0 ^\circ = 0[/tex]
B) [tex]cos180^\circ =cos(90\times2+0)[/tex]
Which is in third quadrant, therefore cosine is negative hence
[tex]cos(90\times2+0)= -cos0^\circ = -1 [/tex]
C) [tex] tan180^\circ=tan(90\times2+0)[/tex]
Which is in third quadrant, therefore tangent is positive hence
[tex]tan(90\times2+0)= tan0^\circ = 0[/tex]
D) [tex]csc180^\circ=csc(90\times2+0)[/tex]
Which is in third quadrant, therefore cosec is negative hence
[tex]cosec(90\times2+0)= -csc0^\circ =[/tex]not defined
E)[tex]sec180^\circ=sec(90\times2+0)[/tex]
Which is in third quadrant, therefore secant is negative hence
[tex]sec(90\times2+0)= -sec0^\circ = -1 [/tex]
F) [tex] cot180^\circ=cot(90\times2+0)[/tex]
Which is in third quadrant, therefore tangent is positive hence
[tex]cot(90\times2+0)= cot0^\circ = [/tex] not defined
Hence only [tex] cos 180^\circ [/tex] and
[tex] sec180^\circ [/tex] have value -1
Hope this will help
Answer:
Cos and Sec
Step-by-step explanation:
thats the short of the guy above
Quick!!! I need to do my homework
Solve: x - 1 < 3
Answers
x < 4
given x - 1 < 3 ( add 1 to both sides )
x < 4
or x ∈ ( - ∞, 4 ) ← in interval notation
Evaluate the following
|10| =
|-7| =
Answers
The absolute value of a number is that number with a positive sign.
|10| = 10
|-7| = 7
I need help with this one please help asap thank you
Answers
(b) is the second one. 10 I would say is 96
Please Help ASAP 20 points
Find the slope of the line through the given points.
(−1, 2) and (−5,10)
(1,3) and (0,−9)
(18, 6) and (−7, 7)
(−7, 10 ) and (1, 10)
Answers
2) slope is 12
3) slope is -0.04
4) slope is 0
X+3x-2=6x-12 please help
Answers
[tex]x + 3x - 2 = 6x - 12 \\4x - 2 = 6x - 12 \\ - 4x \: \: \: \: \: \: \: \: - 4x \\ - 2 = 2x - 12 \\ + 12 \: \: \: \: \: \: \: \: \: + 12 \\ 10 = 2x \\ \div 2 \: \: \: \div 2 \\ 5 = x \\ check \\ x + 3x - 2 = 6x - 12 \\ 5 + 15 - 2 = 30 - 12 \\ 18 = 18[/tex]
Which ordered pairs are solutions to the inequality −2x+y≥−4 ?
Select each correct answer.
(0, −5)
(3, −1)
(1, −2)
(0, 1)
(−1, 1)
Answers
Answer:
(0,-5) , (1,-2) , (0,1) and (-1,1)
Step-by-step explanation:
-2x + y ≥ -4
y ≥ 2x - 4
Taking a point (0,-5):
-5 ≥ 0 - 4 , 5 ≥ -4
This situation is true.
Taking a point (3,-1):
-1 ≥ 2(3) - 4 , -1 ≥ 2
This situation is not true.
Taking a situation (1,-2):
-2 ≥ 2(1) - 4 , -2 ≥ -2
This situation is true.
Taking a point (0,1):
1 ≥ 0 - 4 , 1 ≥ -4
This situation is true.
Taking a point (-1,1):
1 ≥ 2(-1) - 4 , 1 ≥ -6
This situation is true.
The correct answers are
(−1, −1)
(5, −12)
(0, 1)
Have a nice day!
I just need help on learning how to do ten and eleven thank you!
Answers
Combine like terms
3x+(x+8)=180
4x+8=180
180-8=172
4x=172
x=43
12.(x-3)+x+(x+8)+(x-5)=360
Combine like terms
4x-3+8-5=360
-3+8=5
5-5=0
4x=360
x=90
there are 200 students in the 7th grade 98% of the students in the greater going on the field trip how many students are going on the field trip show your work and I will mark brainiest
Answers
30 percent
22% of 200 is 44, 44 students play football
12 of 200 is 24, 24 students play baseball
44+24=68
The teams have a total of 68 players
because 8 play both sports you subract 8
68-8=60
The answer is a tolal of 60 students play sports
I think the answer is 60
Use the identity x^3+y^3+z^3−3xyz=(x+y+z)(x^2+y^2+z^2−x^y−y^z−z^x) to determine the value of the sum of three integers given:
the sum of their squares is 110,
the sum of their cubes is 684,
the product of the three integers is 210,
and the sum of any two products (xy+yz+zx) is 107.
Answers
Correctly written, your identity would tell you ...
... (sum of cubes) - 3·(product) = (sum of integers)·((sum of squares) - (sum of any two products))
Filling in the given numbers, you have ...
... 684 - 3·210 = (sum of integers)·(110 -107)
... 54 = (sum of integers)·3 . . . . . simplify
... sum of integers = 54/3 . . . . . . divide by the coefficient of the variable
... sum of integers = 18
_____
Integers 5, 6, and 7 meet these conditions.
please answer this i dont understnad
Answers
Solve each given equation and show your work. Tell whether it has one solution, an infinite number of solutions, or no solutions, and identify each equation as an identity, a contraction or neither.
A) 20-4x=12-x+8-3x
B) 5x+4x-3+24+8x
C) 5x +6+2x+6+3x-15
Confusing please help
Answers
These are three equations and three answers.
Answers:
A) infinite solutions, identityB) one solution, x = 27, neither contradiction nor identiyC) x = no solutions, contradictionExplanation:
Equation A: 20 - 4x = 12 - x + 8 - 3x
The objective is clearing the unknown, which is to isolate it in one side of the equation.
These are the steps and properties that you need to use:
1. Combine like terms on right side:
20 - 4x = 20 - 4x
2. Use addition property of equality (add 4x on each side).
20 = 20 ↔ identity
Conclusion: you have gotten a condition that is always true, no matter the value of x, which means that the equation has infinite solutions and it is an identity.
Equation B: 5x + 4x - 3 = 24 + 8x (note that I placed the equal sign as it was missing)
1. Combine like terms on each side:
9x - 3 = 24 + 8x
2. Subtraction property and addition propertiy of equality (subtract 8x and add + 3 on both sides)
x = 27 ↔ solution (neither contradiction nor identity)
Conclusion: the solution is x = 27.
Equation C: 5x + 6 = 2x + 6 + 3x - 15 (note that I placed the equal signs as it was missing)
1. Comitne like terms on the right side:
5x + 6 = 5x - 9
2. Subtraction property of equality (subtract 5x from each side)
6 = - 9 ↔ contradiction
Conclusion: the equation does not have a solution since the final equality is always false (a condradiction or absurd).
For your information, when the variable (x) dissapears and fhe final equality is always true (for example 0 = 0, or 20 = 20), the equation is an identity.
A) 20-4x=12-x+8-3x
Bring all x values at one side and all numerical values to the other side of the equal sign and solve. Also, do not forget to change the sign when you change the side.
-4x + x + 3x = -20 + 12 + 8
-4x + 4x = -20 + 20
0 =0 No solution
B) 5x+4x-3+24+8x
this expression can only be simplified to 17x + 21 and not solved because there is no equal sign here
C) 5x +6+2x+6+3x-15
this expression can only be simplified to 10x - 3 and not solved because there is no equal sign here
Also, neither of these is an identity or contraction.
A number, n, is multiplied by -3/8. The product is -0.1. What is the value of n?
Answers
Rewriting this symbolically, (-3/8)n = -0.1. Let's solve for n. To do this, multiply both sides of the equation by (-8/3). This results in n = 8/30, or n= 4/15.
72 ÷(11-3²) ÷ 3 but as a fraction
Answers
Let's evaluate the quantity within the parentheses. (11 - 3^2) becomes (2). Then we have:
(72 divided by 2) / 3, or 36/3, or 12.
need help finding the x, y, and z. please and thank you
Answers
The first step in any problem is to look at what you are given. When solving systems of linear equations, it is often helpful to eliminate one or more of the variables by adding or subtracting a multiple of one equation with a multiple of another. It is convenient when at least one of the multipliers is 1.
Here, we can cancel the y-terms in the 2nd and 3rd equations simply by adding them together. This gives
... (5x +y -4z) +(-3x -y +5z) = (41) +(-45)
... 2x +z = -4 . . . . simplified
Likewise, we can add 3 times the second equation to the first to cancel y in that sum.
... 3(5x +y -4z) +(2x -3y +z) = 3(41) + (-1)
...15x +3y -12z +2x -3y +z = 123 -1
...17x -11z = 122 . . . . simplified
Now that we have 2 equations in x and z, we can go through the same process. We observe that the coefficient of z is +1 in the first equation and -11 in the second. The means we can cancel the z terms by adding 11 times the first equation to the second:
... 11(2x +z) +(17x -11z) = 11(-4) +122
...22x +17x = 78 . . . . . . simplify a little bit
... x = 78/39 = 2 . . . . . . divide by 39
From above, we find
... z = -4 -2x = -4 -2·2 = -8
... y = 41 -5x +4z = 41-5(2) +4(-8) = 41 -42 = -1
The solution is (x, y, z) = (2, -1, -8).
_____
The method of elimination used here will vary with the system of equations. If you want to employ a consistent method, you can use Cramer's Rule, Gaussian elimination, or matrix methods. Since you apparently don't mind help from technology, learning to do this on your graphing calculator can also be a good idea.
If i leave my house at 6:52 am and run 1 mile at an easy pace (8:15 per mile), then 3 miles at tempo (7:12 per mile) and 1 mile at easy pace again, what time do i get home for breakfast?
Answers
Running 2 miles at 8:15 per mile takes 16:30 minutes.
Running 3 miles at 7:12 per mile takes 21:36 minutes.
The total running time is 16:30 + 21:36 = 38:06 minutes. That length of time after 6:52 am is 7:30:06 am.
You get home for breakfast at 6 seconds past 7:30 am.
By adding the times spent on each individual run to your start time, you should arrive home at approximately 7:30 am.
Explanation:To begin with, this is a question about time calculation, where you need to know exactly how to calculate time durations. First, you start running at 6:52 am. Your easy pace is 8 minutes 15 seconds, or 8.25 minutes, per mile and you do this once before and once after your tempo run. So, for 2 miles, it's 2*8.25 = 16.5 minutes.
Then you have a tempo pace at 7 minutes 12 seconds, or 7.2 minutes, per mile. You run 3 miles at tempo pace, so that's 3*7.2 = 21.6 minutes.
Adding these two results together, you have a total running time of 38.1 minutes (16.5 minutes easy pace + 21.6 minutes tempo pace). Adding this to your start time of 6:52 am gives you a rough end time of 7:30 am. Please note that this estimation rounds your running time to the nearest minute.
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1000m divided by 100n can be written in the form 10z. Express z in terms of m and n
Answers
Answer:
[tex]10 ^ {3m-2n} = 10 ^ z[/tex]
Where z = 3m-2n
Step-by-step explanation:
An important mathematical property about the powers is that when powers of equal base are divided, the same base is placed and the exponents are subtracted.
Then we can write 1000m and 100n as powers of the same base:
[tex]1000 ^ m = (10 ^ 3) ^ m = 10 ^ {3m}\\ 100 ^ n = (10 ^ 2) ^ n = 10 ^ {2n}[/tex]
Now we perform the division of powers of the same base (10)
[tex]\frac{10 ^ {3m}}{10 ^ {2n}} = 10 ^ {3m-2n}[/tex]
Finally
[tex]10 ^ {3m-2n} = 10 ^ z[/tex]
Where z = 3m-2n
To express z in terms of m and n, rewrite the equation: 1000m / 100n = 10z. Then, simplify to 100m / 10n = z. So, z can be expressed as 10m/n.
Explanation:The given equation is 1000m divided by 100n equals to 10z. To express z in terms of m and n, we need to isolate z. Let's proceed step by step:
First, rewrite the equation: 1000m / 100n = 10z;Then, eliminate the 10 on the right side by dividing both sides by 10, we get: 100m / 10n = z; Then, simplify the left side, we get: 10m/n = z;So, z can be expressed as 10m/n.
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Anyone good with Literal Expressions?
Answers
Answer:
[tex]\boxed{F=\dfrac{9}{5}c+32}[/tex]
Step-by-step explanation:
[tex]\dfrac{5(F-32)}{9}=c\qquad\text{multiply both sides by 9}\\\\5(F-32)=9c\qquad\text{divide both sides by 5}\\\\F-32=\dfrac{9}{5}c\qquad\text{add 32 to both sides}\\\\\boxed{F=\dfrac{9}{5}c+32}[/tex]
A particular style of sunglasses costs the retailer $70 $70 per pair. At what price should the retailer mark them so he can sell them at a 10% 10% discount off the original price and still make 35% 35% profit on his cost?
Answers
After the 10% discount on marked price (P), the selling price is ...
... P×(100% -10%) = 0.90P
After a markup off 35% on cost, the value is
... $70×(100% +35%) = 1.35×$70 = $94.50
The retailer wants these two values to be equal:
... 0.90P = $94.50
... P = $94.50/0.90 = $105.00 . . . . . divide by the coefficient of P
The marked price should be $105.00.
To make a 35% profit on the cost, the retailer should mark the sunglasses at a price of $85.05.
Explanation:To determine the price at which the retailer should mark the sunglasses, we need to calculate the original price and then apply the discount. First, let's find the 35% profit on the cost, which is $70. 35% of $70 is 0.35 * 70 = $24.50.
To make a profit of $24.50, the original price should be $70 + $24.50 = $94.50. To sell the sunglasses at a 10% discount, the marked price will be 90% of $94.50. 90% of $94.50 is 0.90 * 94.50 = $85.05.
Therefore, the retailer should mark the sunglasses at a price of $85.05.
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Suppose the exponential regression equation for some data is y=1.923*3.772^x. When x equals 5, what is the predicted value of y? Round your anser to the nearest whole number. A. 147 B. 99 C. 992 D/ 1468
Answers
Put 5 where x is in the equation and do the arithmetic.
y = 1.923×3.772⁵ ≈ 1468.377444
The most appropriate answer is ...
... D. 1468
Answer:
the value of y when x= 5 is 1468
Step-by-step explanation:
Suppose the exponential regression equation for some data is given by y=1.923*3.772^x
We need to find out the value of y when x= 5
Plug in 5 for x and find out y
y=1.923*3.772^x
y=1.923*3.772^5=1468.37744
So the value of y when x= 5 is 1468
Write the equation of the line parallel to the given line and passing through the given point.
y=2x−8 through (3,10)
Answers
Copy down y = 2x - 8. Note that any line parallel to this will have exactly the same form, although the constant (representing the y-intercept) may be different.
Knowing that this line passes through (3,10), all we have to do is find the value of the constant of this new, parallel line. Substitute 10 for y and 3 for x, obtaining 10 = 2(3) + b. Then 10-6 = b, or b = 4, and:
y =2x + 4 (answer). Again, note how the form of this new equation is exactly the same as the form of the given equation; only the constant (the y-intercept) is different.
Answer:
y=2x+4
Step-by-step explanation:
The equation we have is y=2x-8, so we subsitute the values and 8 is equal to b. After you substitue you solve it. b=4. So, the answer is y=2x+4
Hope this helped :) *also sorry if I spelled some words wrong*