Answer:
m = -2 and n = 10
Step-by-step explanation:
If the polynomial mx^3 - 3x^2 + nx + 2 is divided by x + 3, the remainder is -1. Then;
x+ 3 = 0
x = -3
Substitute x =-3 into the polynomial and equate to -1
-1 = m(-3)³-3(-3)²+n(-3) + 2
-1 = -27m - 27 - 3n + 2
27m + 3n = -25 + 1
27m + 3n = -24 ... 1
Similarly, if it is divided by x - 2, the remainder is -4, then;
-4 = m(2)³-3(2)²+n(2) + 2
-4 = 8m - 12- 2n + 2
8m -2n = -4 + 10
8m + 2n = 6 ... 2
Solve 1 and 2 simultaneously
27m + 3n = -24 ... 1 * 2
8m + 2n = 6 ... 2 * 3
______________________
54m + 6n = -48
24m + 6n = 12
54m - 24m = -48 - 12
30m = -60
m = -60/30
m = -2
Get n by substituting m = -2 into 1
From 1: 27m + 3n = -24
27(-2) + 3n = -24
-54 + 3n = -24
3n = -24 +54
3n = 30
n = 30/3
n = 10
Hence m = -2 and n = 10
Most pets age at a different rate than their human companions. For example, a 3-year-old dog is often considered to be 21 in human years. Assume that the age of a dog varies directly as its equivalent age in human years. What is the human-year age of a dog that is 6-years-old?
The human-year age of a dog that is 6 years old is 42.
What is an expression?The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
Given that most pets age at a different rate than their human companions. For example, a 3-year-old dog is often considered to be 21 in human years.
The human-year age of a dog that is 6 years old will be,
3 years old dog = 21 human gae
6 year old dog = 21 x 2 = 42 human age
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Need help with this question it’s my first time on here !
Answer:
We conclude that the statement 'To host a wedding with 104 people, 13 tables will be needed'.
Hence, option C is correct.
Step-by-step explanation:
We know that when 'y' varies directly with 'x', we get the equation
y ∝ x
y = kx
where 'k' is termed as the 'constant of variation'.
Given that a wedding reception seats 8 people at each table.
Given that the relationship between the number of people 'p' and the number of tables 't'.
p = 8t
CHECKING OPTION A
substitute t = 22 in the given equation
p = 8 × 22 = 176 people
It means to host 176 people, 22 tables will be needed.
Hence, OPTION A is INCORRECT!
CHECKING OPTION B
substitute t = 8 in the given equation
p = 8 × 8 = 64 people
It means to host 64 people, 8 tables will be needed.
Hence, OPTION B is INCORRECT!
CHECKING OPTION C
substitute t = 13 in the given equation
p = 8 × 13 = 104 people
It means to host 104 people, 13 tables will be needed.
Hence, OPTION C is CORRECT!
CHECKING OPTION D
substitute t = 6 in the given equation
p = 8 × 6 = 48 people
It means to host 48 people, 6 tables will be needed.
Hence, OPTION C is INCORRECT!
Thus, we conclude that the statement 'To host a wedding with 104 people, 13 tables will be needed'.
Hence, option C is correct.
The cost of admission to the Baytown Zoo is $10.50 for each senior citizen, $15.75 for each adult, and $8.25 for each child. What if 2 more tickets for admission are purchased? If the two additional tickets cost $16.50, determine what type of tickets the family purchases. Explain how you can determine the answer without calculating.
Answer:
Child ticket
Step-by-step explanation:
Cost per senior citizen = $10.50
Cost per adult = $15.75
Cost per child = $8.25
Since the cost of the 2 additional ticket is $16.50
Then the only ticket of which two can be purchased with that amount is :
$16.50 / 2
= $8.25
Cost of children ticket.
the value pi/12 is the solution for the equation 2 cos^2 (4x) - 1 = 0 : true or false
Answer:
[tex]2 \cos ^{2} (4x) - 1 = 0 \\ \cos ^{2} (4x) = \frac{1}{2} \\ \cos(4x) = \sqrt{ \frac{1}{2} } \\ 4x = { \cos }^{ - 1} ( \sqrt{ \frac{1}{2} } ) \\ x = \frac{ { \cos}^{ - 1} ( \sqrt{ \frac{1}{2} } )}{4} \\ x \isnt \: \frac{\pi}{2} [/tex]
Evaluate -7 1/3 - (-2/5)=
Answer:
-6 14/15
Step-by-step explanation:
8. Write the missing symbol (+,-, or =) to
make the equation true. Use precise math
language to explain how you chose the symbol.
16 = 4 + 8 ⚪️ 4
What is the solution to the equation 1/4x+2=-5/8x-5?
O X=-8
O X=-7
O X=7
O X=8
Answer:
The solution to the equation [tex]\frac{1}{4}x+2=\frac{-5}{8}x-5[/tex] is [tex]\mathbf{x=-8}[/tex]
Option A is correct option.
Step-by-step explanation:
What is the solution to the equation [tex]\frac{1}{4}x+2=\frac{-5}{8}x-5[/tex]
Solving the equation
[tex]\frac{1}{4}x+2=\frac{-5}{8}x-5[/tex]
Subtracting 2 on both sides
[tex]\frac{1}{4}x+2-2=\frac{-5}{8}x-5-2\\\frac{1}{4}x=\frac{-5}{8}x-7[/tex]
Adding 5/8x on both sides
[tex]\frac{1}{4}x+\frac{5}{8}x=\frac{-5}{8}x-7+\frac{5}{8}x\\\frac{2x+5x}{8}=-7 \\\frac{7x}{8}=-7[/tex]
Multiply both sides by 8/7
[tex]\frac{7x}{8}\times \frac{8}{7}=-7 \times \frac{8}{7}\\x=-8[/tex]
So, we get x = -8
The solution to the equation [tex]\frac{1}{4}x+2=\frac{-5}{8}x-5[/tex] is [tex]\mathbf{x=-8}[/tex]
Option A is correct option.
Write the equation in standard form
using factoring.
f(x) = (2x
+
1)(x – 4)
Answer:
2x^2-7x-4
Step-by-step explanation:
=2x^2-8x+x-4
=2x^2-7x-4
What is the midpoint for CD given the coordinates C (-4,8) and D (8,-4).
A. (0,0)
B. (2,2)
C. (4,4)
D. (6,6)
Graph the system below and write its solution.
y = -x+2
-2x-2y=-6
Note that you can also answer "No solution" or "Infinitely
Answer:
No solution.
General Formulas and Concepts:
Algebra I
Solving systems of equations by graphingStep-by-step explanation:
Where the 2 lines intersect is the solution set to the systems of equations.
If the 2 lines are parallel, then they will have no solution.
If the 2 lines are the same, then they will have infinite amount of solutions.
According to the graph, our lines are parallel. Therefore, we have no solution.
1/3 2/7 Common
Denominator: ________
Answer:
21
Step-by-step explanation:
btw is it LDC or GCD?
Please help this is timed!!!!
Answer:
C and D
89 _> 12.50t -14
+14 +14
103 _> 12.5t
/12.5 /12.5
8.24 _> t
Write this in expanded form and find the sum.
9514 1404 393
Answer:
(c) 5 +15/4 +45/16 +135/64 +...; 20
Step-by-step explanation:
The first term of this geometric series is 5. The common ratio (r) is 3/4. The sum of the infinite series is ...
5(1/(1 -r)) = 5/(1 -3/4) = 5/(1/4) = 20 . . . series sum
Of course, the terms are ...
5 + 5(3/4) +5(3/4)² + 5(3/4)³ + ...
= 5 + 15/4 + 45/16 +135/64 + ... . . . series
Together, these observations match choice C.
Develop an estimate for each of the following situations.(at) The cost of a 500-mile automobile trip, if gaso-line is $4 per gallon, vehicle wear and tear is$0.65 per mile, and our vehicle gets 25 miles pergallon.(b) The total number of hours in the average humanlife, if the average life is 75 years.(c) The number of days it takes to travel around the equator using a hot air balloon, if the balloon
Answer:
The answer is below
Step-by-step explanation:
develop an estimate for each of the following situations.
(a) The cost of a 500- mile automobile trip, if gasoline is $4.00 per gallon, vehicle wear and tear is $0.65 per mile, and our vehicle gets 25 miles per gallon.
(b) The total number of hours in the average human life, if the average life is 75 years.
(c) The number of days it takes to travel around the equator using a hot air balloon, if the balloon averages 100 miles per day, the diameter of the earth is ~4,000 miles.
Solution:
a) The total trip = 500 mile
Cost of wear and tear = $0.65 per mile = $0.65 * 500 mile = $325
25 miles takes 1 gallon of gasoline at a cost of $4 per gallon
Cost of gasoline = $4 per gallon * 500 miles / 25 miles per gallon = $80
cost of a 500-mile automobile trip = Cost of wear and tear + Cost of gasoline = $325 + $80 = $405
b) Average life of human = 75 years.
1 year = 365 days, 1 day = 24 hours
Average life of human in hours = 75 years * 365 days * 24 hours =657000 hours
c) Diameter of earth = 4000 miles
Distance of equator = diameter of earth = 4000 miles
100 mile per day
number of days for the balloon to travel round the earth = 4000 miles / (100 mile per day) = 40 days
Can someone help me please.
Step-by-step explanation:
Realistic domain: t >= 0 (as time is non-negative)
When t = 0,
v(0) = -3(0)² + 73(0) + 50 = 50.
Hence Jennifer started with $5000.
Vertex = -b/2a = -(73)/2(-3) = 73/6.
When t = 73/6
v(73/6) = -3(73/6)² + 73(73/6) + 50 = 494.08.
The maximum value is $49,408.
Find the x- and y-intercepts of the equation x – 5y = –15. Question 16 options: A) x-intercept: (0,3), y-intercept: (–15,0) B) x-intercept: (0,–15), y-intercept: (3,0) C) x-intercept: (–15,0), y-intercept: (0,3) D) x-intercept: (3,0), y-intercept: (0,–15)
Answer:
y-intercept: (3,0) C) x-intercept: (–15,0)Step-by-step explanation:
Given the expression x - 5y = -15
x intercept occurs at y = 0
Substituting y = 0 into the expression
x - 5(0) = -15
x - 0 = -15
x = -15
Hence the x-intercept occurs at (-15, 0)
y intercept occurs at x = 0
Substituting x = 0 into the expression
0 - 5y = -15
-5y = -15
y = -15/-5
y = 3
Hence the y-intercept is at (0, 3)
guys pls help me I need to know which one is composite!!!
Which is a composite number?
33
43
19
3
Answer:
33 is a composite number ;)
I need help on this question please!! Look at image :)
Answer:
(x, y) ––> (x – 2, y – 1)
Step-by-step explanation:
Two units left would make it (x – 2, y).
Then two units down would make it (x – 2, y – 2)
Then one unit up would make it (x – 2, y – 1)
Help Me fast please
2[3(4²+1)]-2³
Answer:
94
Step-by-step explanation:
Answer:
94
Step-by-step explanation:
Find the equivalent expression.
3+5x−4y+2y−8x
Answer:
-3x - 2y + 3
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightAlgebra I
Terms/CoefficientsStep-by-step explanation:
Step 1: Define
3 + 5x - 4y + 2y - 8x
Step 2: Simplify
Combine like terms (x): -3x - 4y + 2y + 3Combine like terms (y): -3x - 2y + 3Answer:
3+5x−4y+2y−8x is the equivalent ti 3-3x-2y
Step-by-step explanation:
3+5x−4y+2y−8x
3+5x-8x-4y+2y
3-3x-2y
6/7x - 2/5y + 5/7(y+x)
Answer:
[tex] \frac{6}{7} x - \frac{2}{5} y + \frac{5}{7} (y + x) \\ = ( \frac{6}{7} + \frac{5}{7} )x + ( \frac{5}{7} - \frac{2}{5} )y \\ = \frac{11}{7} x + \frac{15}{35} y \\ = \frac{11}{7} x + \frac{3}{7} y \\ = \frac{1}{7} (11x + 3y)[/tex]
Pls help grades close today I’ll brainlest for the right answer
Answer:
decrease 40%
Step-by-step explanation:
20/50 * 100 = 40
how do you write 4.41*
[tex] {10}^{1} [/tex]
PLS HELP BRAINLIEST ND EXTRA POINTS !
From the trade fairs in France, Germany, and Holland, river and land trade routes carried goods such as wool, wheat, and precious metals into the region. The widespread trade that stretched from Egypt to the Baltic created large financial surpluses that allowed big investments in mining and agriculture. What region is being described in this passage? A. northern Italy B. sub-Saharan Africa C. northern England D. southern Spain
Step-by-step explanation:
i think is the answer is d
Northern Italy is described in the passage of trade fairs in France.
Option A is the correct answer.
What are trade fairs?Trade fairs, also known as trade shows or exhibitions, are events where companies showcase their products or services to potential customers, partners, and investors.
We have,
The region described in the passage is not mentioned directly, but it can be inferred that the trade fairs in France, Germany, and Holland were part of a larger trading network that extended from Egypt to the Baltic.
Based on this information, we can eliminate options B, C, and D.
Northern Italy was also an important region for trade and finance during this time period, but it is not explicitly mentioned in the passage.
Therefore,
The most likely answer is Northern Italy.
Thus,
Northern Italy is described in the passage of trade fairs in France.
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Find the distance between the two points and simplest rational form (3,-4) (6,-7))
Answer:
[tex]D = 3\sqrt{2}[/tex]
Step-by-step explanation:
Given
[tex](x_1,y_1) = (3,-4)[/tex]
[tex](x_2,y_2) = (6,-7)[/tex]
Required
Determine the distance between the two points
Distance (D) is calculated as:
[tex]D = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}[/tex]
Substitute values for x's and y's
[tex]D = \sqrt{(6 - 3)^2 + (-7 - (-4))^2}[/tex]
[tex]D = \sqrt{(6 - 3)^2 + (-7 +4)^2}[/tex]
[tex]D = \sqrt{(3)^2 + (-3)^2}[/tex]
[tex]D = \sqrt{9+9}[/tex]
[tex]D = \sqrt{18}[/tex]
Express as 9 * 2
[tex]D = \sqrt{9*2}[/tex]
Split:
[tex]D = \sqrt{9}*\sqrt{2}[/tex]
[tex]D = 3*\sqrt{2}[/tex]
[tex]D = 3\sqrt{2}[/tex]
tomatoes are $2.75 per pound, or you can buy a 5 pound box for $11. what is the better value option?
Answer:
The better value is 5pounds for $11
Step-by-step explanation:
2.75×5= $13.75
so the 5 pounds for $11 would be better because the other option would cost $13.75 for the same amount
Answer:
buying the box for $11 is the better option
2.75×5=13.75
so 5 pounds separately would be $13.75
prove the given identity
Step-by-step explanation:
tan(2x) = sin(2x)/cos(2x) = 2sinxcosx/(cos^2x - sin^2x).
Dividing the num- and denominator by sinxcosx, we get
2/(cosx/sinx - sinx/cosx) = 2/(cotx - tanx)
cotA + cotB = cosA/sinA + cosB/sinB
We just add them like fractions, with a common denominator of sinAsinB
(cosAsinB + sinAcosB)/sinAsinB
Note that sinAcosB + sinBcosA = sin(A+B)
Therefore we have
sin(A+B)/sinAsinB
10 snails is to be chosen from this population. Find the probability that the percentage of streaked-shelled snails in the sample will be (a) 50%. (b) 60%. (c) 70%.
Here is the full question:
[tex]The \ shell \ of \ the \ land \ snail \ Limocolaria \ martensiana \ has \ two \ possible \ color[/tex][tex]forms: \ streaked \ and \ pallid. \ In \ a \ certain \ population \ of \ these \ snails, \ 60\% \ o f \ the[/tex][tex]individuals \ have \ streaked \ s hells.\ 16 \ Suppose \ that \ a \ random \ sample \ of \ 10 \ snails[/tex][tex]is \ to \ be \ chosen \ from \ this \ population. \ F ind \ the \ probabilit y \ that \ the \ percentage \ of[/tex]
[tex]streaked-shelled \ snails \ in \ t he \ sample \ will \ be[/tex]
[tex](a) 50\%. \ (b) 60\%. \ (c) 70\%.[/tex]
Answer:
(a) 0.2007
(b) 0.2510
(c) 0.2150
Step-by-step explanation:
Given that:
The sample size = 10
Sample proportion= 60% 0.6
Let X represents the no of streaked-shell snails.
[tex]X \sim Binom (n =1 0, p = 0.60)[/tex]
The Probability mass function (X) is:
[tex]P(X =x)= (^n_x) p^x(1-p)^{n-x}; x = 0,1,2,3...[/tex]
The Binomial probability with mean μ = np
= 10 * 0.6
= 6
Standard deviation σ = [tex]\sqrt{np(1-p)}[/tex]
= [tex]\sqrt{10*0.6*(1-0.6)}[/tex]
= 1.55
The probability that the percentage of the streaked-shelled snails in the sample will be:
a)
[tex]P(X = 0.5) = ^nC_x p^x (1 -p) ^{(n-x)}[/tex]
[tex]= ^{10}^C_5 * (0.6)^5(1-0.6)^{10-5}[/tex]
[tex]= \dfrac{10!}{5!(10-5)!} * (0.6)^5(1-0.6)^{10-5}[/tex]
= 0.2007
b)
[tex]P(X = 0.6) = ^nC_x p^x (1 -p) ^{(n-x)}[/tex]
[tex]= ^{10}^C_6 * (0.6)^6(1-0.6)^{10-6}[/tex]
[tex]= \dfrac{10!}{6!(10-6)!} * (0.6)^6(1-0.6)^{10-6}[/tex]
= 0.2510
c)
[tex]P(X = 0.7) = ^nC_x p^x (1 -p) ^{(n-x)}[/tex]
[tex]= ^{10}^C_7 * (0.6)^7(1-0.6)^{10-7}[/tex]
[tex]= \dfrac{10!}{7!(10-7)!} * (0.6)^7(1-0.6)^{10-7}[/tex]
= 0.2150
The equation c=0.09sc=0.09s gives the amount cc (in dollars) of commission a salesperson receives for making a sale of ss dollars.
What’s the independent and Dependent variable
Answer:
independent variable is s and the dependent variable is c
Step-by-step explanation:
Answer:
is not the top it is this
Step-by-step explanation:
The equation c=0.09s represents the amount c (in dollars) of commission a salesperson receives for making a sale of s dollars.
The independent variable is s
.
The dependent variable is c
.
The store is selling lemons at $0.33 each. Each lemon yields about 2 tablespoons of juice. How much will it cost to buy enough lemons to make four 9-inch lemon pies, each requiring half a cup of lemon juice?
Answer:
$5.28
Step-by-step explanation:
There are 16 table spoons in a cup, and since the entire recipe calls for 2 cups, 32 table spoons would be needed. If each lemon yields about 2 tablespoons, then that means 16 lemons would be needed. To get the price, we multiply 0.33 x 16, and get 5.28.