Answer:
A) A = 30m + 13 B = 28m + 15
B) Company B would charge $6 less for 4 mattresses
C) Company B would charge $12 less for 7 mattresses
Step-by-step explanation:
A. : Write equations to represent Company A's and Company B's total mattress cleaning charges for a certain number of mattresses. Define the variable used in the equations.
Let's define the variable m to represent the number of mattresses to be cleaned.
For company A, we have a cost per mattress of $30 plus a fixed service fee of $13. So the equation will be:
A = 30m + 13
While company B charges $28 per mattress, with a fixed service fee of $15:
B = 28m + 15
That way, we have a good representation of both price structures, using a meaningful variable.
B. Which company would charge less for cleaning 4 mattresses? Justify your answer.
We just have to calculate the cost of cleaning 4 mattresses at both companies:
A = 30m + 13 = 30 (4) + 13 = 120 + 13 = $133
B = 28m + 15 = 28 (4) + 15 = 112 + 15 = $127
Company B would charge $6 less for 4 mattresses
C. How much money is saved by using the services of Company B instead of Company A to clean 7 mattresses?
Again, all we have to do is calculate the cost to clean 7 mattresses at both companies:
A = 30m + 13 = 30 (7) + 13 = 210 + 13 = $223
B = 28m + 15 = 28 (7) + 15 = 196 + 15 = $211
Company B would charge $12 less for 7 mattresses
If y varies directly as x, and y is 6 when x is 72, what is the value of y when x is 8?
1/9
2/3
54
96
Answer:
2/3
Step-by-step explanation:
Y varies directly as x
Y =kx
Y=6 when x = 72
First find the relationship between y and x.
i.e find the value of k
Substitute the value of x and y
6 = k *72
Make k the subject of the formula
K = 6/72
K= 1/12
:. The rlationship between x and y is
Y = 1/12x
When x is 8
Y = 1/12 * 8
Y = 8/12
Y = 2/3 and that is the answer
Hope it helped you
Answer:
The answer is : 2/3
Step-by-step explanation:
Given is that y varies directly as x.
Means as y increases or decreases, x also increases or decreases.
When y is 6 when x is 72,
So, when x = 8, we have to find y.
We can write the relation as follows:
[tex]\frac{6}{y}= \frac{72}{8}[/tex]
[tex]72y=48[/tex]
[tex]y=\frac{48}{72}[/tex] = [tex]\frac{2}{3}[/tex]
What is the equation, in point-slope form, of the line that has a slope of 6 and passes through the point (–1, –8)? a. y+8 = 6 (x+1 )
Answer:
y + 8 = 6(x + 1)
Step-by-step explanation:
The equation of a line in point- slope form is
y - b = m(x - a)
where m is the slope and (a, b) a point on the line
here m = 6 and (a, b) = (- 1, - 8), hence
y - (- 8) = 6(x - (- 1)), that is
y + 8 = 6(x + 1)
ANSWER
[tex]y + 8=6(x + 1)[/tex]
EXPLANATION
The point-slope form of an equation is given by the formula:
[tex]y-y_1=m(x-x_1)[/tex]
Where
[tex](x_1,y_1)[/tex]
is a point on this line and
[tex]m[/tex]
is the slope of the line.
From the question, the line has slope 6 and passes through (-1,-8).
This means that
[tex]x_1=-1[/tex]
[tex]y_1=-8[/tex]
and
[tex]m = 6[/tex]
We substitute these values into the point-slope formula to get:
[tex]y- - 8=6(x- - 1)[/tex]
We simplify to get:
[tex]y + 8=6(x + 1)[/tex]
Two systems of equations are shown below. The first equation in System B is the original equation in system A. The second equation in System B is the sum of that equation and a multiple of the second equation in System A.
A. x + 3y = 11 → x + 3y = 11
5x − y = 17 → 15x − 3y = 51
15x = 62
B. x + 3y = 11
15x = 62
What is the solution to both systems A and B?
Answer:
The answer is [4,3] Hope this helps.
Step-by-step explanation:
The solution to the both system of equations A and B are (3.875, 2.375) for system A and (4.133, 2.289) for system B.
What does a System of Linear Equations define?Linear equations involve one or more expressions including variables and constants and the highest exponent of the variable is 1.
System of linear equations involve two or more linear equations.
Consider system A.
x + 3y = 11
15x − 3y = 51
Adding both equations,
16x = 62
x = 3.875
3y = 7.125
y = 2.375
Consider system B.
x + 3y = 11
15x = 62 ⇒ x = 4.133
3y = 6.867
y = 2.289
Hence the solutions are (3.875, 2.375) for system A and (4.133, 2.289) for system B.
Learn more about System of Equations here :
https://brainly.com/question/24065247
#SPJ7
Which equation is represented by table?
Answer:
The equation y = 1 - 2x is represented by this table.
The correct answer is A.
Sara needs to take a taxi to get to the movies the taxi charges $4.00 for the first mile and then $2.75 for each mile after that if the total charge is $20.50 then how far was Sara’s taxi ride to the movie
Answer:
6 miles
Step-by-step explanation:
4+2.75m=20.50
-4 -4
2.75m=16.50/2.75
m=6
Answer:
6 miles
Step-by-step explanation:
So the total charge is $20.50, what I personally did was
Subtract $4 from $20.50
You get $16.50
Now divide $16.50 by $2.75
There's your miles
What is the result if 3x-9 is evaluated when x = -5?
Answer:
Step-by-step explanation:
I wonder if it is the minus that is causing the problem?
Let x = - 5
3*(-5) - 9
-15 - 9
This is a money question. If you are 15 dollars in debt and you spend another 9, where are you? (In the company of the American government. They do this all the time).
- 15 - 9 = - 24
When the county fair opened its gates, 68 people entered the fairgrounds. After one hour, there were 1.5 times as many people on the fairgrounds as when the gates opened. After two hours, there were 1.5 times as many people on the fairgrounds as the previous hour. If this pattern continues, write the equation representing the number of people, y, at the fair x hours after the gates open.
Answer:
y=68(1.5)^(x-1)
Step-by-step explanation:
Answer:
The function is:
[tex]y = 68 (1.5) ^ x[/tex]
Step-by-step explanation:
Note that the number of people increases by a factor of 1.5 per hour, and the initial number of people is 68.
So:
After an hour the number of people is:
[tex]y = 68 (1.5)[/tex]
After two hours the number of people is:
[tex]y = 68 (1.5) (1.5) = 68 (1.5) ^ 2[/tex]
After x hours the number of people is:
[tex]y = 68 (1.5) ^ x[/tex]
Therefore, the exponential growth function that models the number of people y at the fair after x hours is:
[tex]y = 68 (1.5) ^ x[/tex]
How many states are there
Answer:
50
Step-by-step explanation:
Hello There!
There are 50 states in the United States
Alabama
Alaska
Arizona
Arkansas
California
Colorado
Connecticut
Delaware
Florida
Georgia
Hawaii
Idaho
Illinois Indiana
Iowa
Kansas
Kentucky
Louisiana
Maine
Maryland
Massachusetts
Michigan
Minnesota
Mississippi
Missouri
Montana Nebraska
Nevada
New Hampshire
New Jersey
New Mexico
New York
North Carolina
North Dakota
Ohio
Oklahoma
Oregon
Pennsylvania Rhode Island
South Carolina
South Dakota
Tennessee
Texas
Utah
Vermont
Virginia
Washington
West Virginia
Wisconsin
Wyoming
Divide 9x^2-6x+2 by (-1+3x)
A. 3x-1+(1/3x-1)
B. 3x-3+(1/3x-1)
C. 3x-1+(3/3x-1)
D. 3x-3-(1/3x-1)
Answer:
A. 3x - 1 + [3x - 1]⁻¹
Step-by-step explanation:
Use Polynomial Long Division to arrive at this answer.
**[3x - 1]⁻¹ = 1\[3x - 1]
Identify the opposite number of -22.7. Then, explain why the two numbers are opposites.
22.7
Explanation:They are opposites because they are both the same distance from 0 and are on different sides of 0 on a number line.
They are also opposites because when either of them is multiplied by -1, you get the other one.
[tex]22.7*-1=-22.7[/tex]
[tex]-22.7*-1=22.7[/tex]
Answer:
22.7 because it's the same number but different
The data set gives the number of bottles filled by each of the workers in a bottling plant in one day.
{36, 18, 16, 28, 68, 35, 37, 66, 38, 40, 41, 44, 72, 29}
The best measure of center for this data set is the
, and its value expressed up to one decimal place is
Answer:
Step-by-step explanation:
Before we can determine which measure of central tendency is the best we need to determined whether data set is skewed or not.
We can determine the skewness, if we know at least the median and the mean.
The array of the above data set is,
16,18,28,29,35,36,37,38,40,41,44,66,68,72
The Median of the above array is
\frac{37 + 38}{2} = \frac{75}{2} = 37.5
The mean is
\frac{16 + 18 + 28 + 29 + 35 + 36 + 37 + 38 + 40 + 41 + 44 + 66 + 68 + 72}{14} = \frac{532}{14} = 38
Since the mean and the median are not the same, the distribution is skewed.
<b>For a skewed distribution, the best measure of central tendency is the median.</b>
To one decimal place, the median is;
37.5
NB: If the distribution is not skewed then it is normal. In a normal distribution the median is equal to the mean. The mode is considered the best measure of center in this case.
Step-by-step explanation:
The median of a data set is the measure of center that is the middle value when the original data values are arranged in order of increasing (or decreasing) magnitude
In one U.S. city, the taxi cost is $5 plus $0.90 per mile. If you are traveling from the airport, there is an additional charge of $5.00 for tolls. How far can you travel from the airport by taxi for $59.50?
can someone please help me with this.
[tex](x-1)(x-3)=x^2-3x-x+3=x^2-4x+3[/tex]
Typically, a point in a three-dimensional Cartesian coordinate system is represented by which of the following
A) (x,y,v)
B) (w,x,y)
C) x,y,z
D) (x,y,z)
Answer:
option D) (x,y,z)
Step-by-step explanation:
we know that
The three-dimensional Cartesian coordinate is defined by three axes at right angles to each other, forming a three dimensional space.
The three axes are labeled x ,y and z.
The x-axis is called abscissa
The y-axis is called ordinate
The z-axis is called applicate
therefore
A point in a three-dimensional Cartesian coordinate is represented by (x,y,z)
I need to know how many approximate miles you drive in a week for a statistics project. I dont have any social media, and I need to ask at least 50 people to compete my project. Ask your friends and family, and then give me your answer for easy points!
Answer:
My mom drives about 120 miles, grandpa: 160, and dad: 200
Step-by-step explanation:
Answer:
My dad drives about 80
Step-by-step explanation:
He only goes shopping and takes me to school.
The area of a garden is given by the trinomial g2 - 2g - 24. The garden’s length is g + 4. What is the garden’s width?
Final answer:
To find the garden's width, factor the area trinomial to match the given length of the garden. The width is represented by the other factor, which in this case is g - 6.
Explanation:
The area of a garden is given by the trinomial [tex]g^2[/tex] - 2g - 24, and the garden's length is g + 4. To find the garden's width, we need to factor the trinomial such that it is the product of two expressions, one of which must be the length (g + 4).
Factoring [tex]g^2[/tex] - 2g - 24, we look for two numbers that multiply to -24 and add up to -2. These numbers are -6 and +4. So, we can factor the area trinomial as:
(g - 6)(g + 4) = [tex]g^2[/tex] - 2g - 24.
Since the length of the garden is g + 4, the other factor, g - 6, must represent the width of the garden. Thus, the garden's width is g - 6.
If carol can read 45 pages in one hour how many pages can she read in four hours
Answer:
She can read 180 pages in 4 hours
45*4=180
Carol can read 180 pages in four hours.
Simply multiply the rate (45 pages/hour) by the time (4 hours) to get 180 pages/4 hours.
A. Find 18% more than 200
B. Find 18% less than 200
Answer:
A. 236
B. 164
Step-by-step explanation:
18% of 200= 36
200+36=236
200-36=164
Answer:
A. 236
B. 164
Step-by-step explanation:
To solve it first you need to find what 18% of 200 is. To do that take the 18% and make it a decimal % is out of 100, so 18/100 = .18. Then to find how much 18% out of 200 is, multiply .18 * 200. You should get 36. Then you can add and subtract that from 200 to get 18% more and 18% less.
How much money will you have if you started with $20 and put it in an account that earned 12% every year for 3 years?
Answer:
34,560
Step-by-step explanation:
Started of with 20 and earned 12% each year.
12% is just 12 as a whole number
so from that 20 12x12x12=1,728
1,728x20=
34.560
Use the point-slope formula (if possible) to write an equation of the line given the following
information.
The slope is - 5, and the line passes through the point (-2,0).
The equation of the line is?
Answer:
y = -5 (x+2)
Step-by-step explanation:
We can use the point slope form of a line
y-y1 = m(x-x1) where (x1,y1) is the point and m is the slope
y-0 = -5(x--2)
y = -5 (x+2)
What is the solution to this system of equations?
x+2y=4
2x-2y=5
a. (3, -5.5)
b. (3, 0.5)
c. no solution
d. indefinitely many solutions
Answer:
b. (3, 0.5).
Step-by-step explanation:
x + 2y = 4
2x - 2y = 5
Adding the 2 equations eliminates the y:
3x = 9
x = 3
Substitute fro x in the first equation:
3 + 2y = 4
2y = 1
y = 0.5.
Option B is correct, (3, 0.5) is the solution of the system of equations.
What is Equation?Two or more expressions with an Equal sign is called as Equation.
The two equations are
x+2y=4...(1)
2x-2y=5...(2)
Add equation 1 and 2
x+2y+2x-2y=4+5
3x=9
Divide both sides by 3
x=3
3+2y=4
Subtract 3 from both sides
2y=1
y=1/2
y=0.5
Hence, option B is correct, (3, 0.5) is the solution of the system of equations.
To learn more on Equation:
https://brainly.com/question/10413253
#SPJ2
A rectangular prism and a cylinder have the same height. The length of each side of the prism base is equal to the diameter of the cylinder. Which shape has a greater volume?
The (blank) has the greater volume because the (blank) fits within the (blank) with extra space between the two figures.
Please fill in the blanks
Answer:
Filling in the blanks: (rectangular prism) (cylinder) (rectangular prism)
The cylinder has the greater volume because the cylinder fits within the rectangular prism with extra space between the two figures.
A prism is a three-dimensional object.
There are triangular prism and rectangular prism.
We have,
We can see this by comparing the formulas for the volumes of the two shapes.
The volume V of a rectangular prism with length L, width W, and height H is given by:
V = L x W x H
The volume V of a cylinder with radius r and height H is given by:
V = πr²H
Now,
We are told that the length of each side of the prism base is equal to the diameter of the cylinder.
Since the diameter is twice the radius, this means that the width and length of the prism base are both equal to twice the radius of the cylinder.
So we can write:
L = 2r
W = 2r
Substituting these values into the formula for the volume of the rectangular prism, we get:
V prism = L x W x H
V prism = 2r x 2r x H
V prism = 4r²H
Substituting the radius and height of the cylinder into the formula for its volume, we get:
V cylinder = πr^2H
To compare the volumes,
We can divide the volume of the cylinder by the volume of the prism:
V cylinder / V prism = (πr²H) / (4r²H)
V cylinder / V prism = π/4
π/4 is greater than 1/1,
Thus,
The cylinder has a greater volume.
The cylinder fits within the rectangular prism with extra space between the two figures because the cylinder is inscribed within the prism, meaning that it is enclosed within the prism but does not fill it completely.
Learn more about prism here:
https://brainly.com/question/12649592
#SPJ3
Write the sentence as an equation.
b increased by 281 is d
Answer:
B + 281d
Step-by-step explanation:
I think that's the answer the "is" is throwing me off "is" is either = or (x)
Hope my answer has helped you and if not i'm sorry.
A company manufactures 2,000 units of its flagship product in a day. The quality control department takes a random sample of 40 units to test for quality. The product is put through a wear-and-tear test to determine the number of days it could last. If the product has a lifespan of less than 26 days, it is considered defective. The table gives the sample data that a quality control manager collected.
39 31 38 40 29
32 33 39 35 32
32 27 30 31 27
30 29 34 36 25
30 32 38 35 40
29 32 31 26 26
32 26 30 40 32
39 37 25 29 34
Which sample size would you use to get the best point estimate?
A.
90
B.
70
C.
150
D.
500
E.
280
Answer:
B
Step-by-step explanation:
The recommended sample size n for point estimates is:
n = NX / (N + X - 1)
where N is the population size, and X is defined as:
X = Z² p (1 - p) / E²
where Z is the critical value, p is the sample proportion, and E is the margin of error.
Assume a confidence level of level of 95% and a margin of error of 5%.
α = 0.05, Z(α/2) = 1.96
E = 0.05
Of the 40 units tested, 2 had lifespans less than 26 days. So the proportion is:
p = 2/40 = 0.05
Therefore:
X = (1.96)² (0.05) (1 - 0.05) / (0.05)²
X = 73
Given N = 2000:
n = (2000) (73) / (2000 + 73 - 1)
n = 70.45
Rounding, the recommended sample size is 70.
Answer:
B
Step-by-step explanation:
Which is equivalent
Answer:
4x^4
Hope this helps
For this case we must find an expression equivalent to:
[tex](256x^{16}) ^ {\frac {1} {4}[/tex]
By definition of power properties we have to:
[tex](a ^ n) ^ m = a ^ {n * m}[/tex]
Then, rewriting the expression:
[tex](256 ^ {\frac {1} {4}} * x ^ {\frac {16} {4}}) =[/tex]
We have by definition:
[tex]\sqrt [n] {a ^ m} = a ^ {\frac {m} {n}}[/tex]
So:
[tex]\sqrt [4] {256} * x ^ 4 =\\\sqrt [4] {4 ^ 4} * x ^ 4 =\\4x ^ 4[/tex]
ANswer:
Option B
i need help im stuxk again and thanks who help me
Answer:
b C = 25m + 75
Step-by-step explanation:
The total cost for m months is the one time fee plus the cost per month times the number of months
C = fee + cost per month * m
C = 75 + 25m
Rearranging the equation
C = 25m + 75
31. ABCD has area equal to 28 sq. unit. BC is parallel to AD and BA perpendicular to AD. If BC = 6 and AD = 8,
then value of CD =
B.213
A. 2 12
C.4
D. 275
Answer:
The value of CD is 2√5
Step-by-step explanation:
* Lets describe the figure to know its name
- ABCD is a quadrilateral
∵ BC parallel to AD
∵ BC = 6 units and AD = 8 units
- The quadrilateral which has two parallel sides not equal in length is a
trapezoid
∴ ABCD is a trapezoid, where BC and AD are its bases
∵ BA perpendicular to AD
∴ BA is the height of the trapezoid
- The area of the trapezoid = 1/2 (base 1 + base 2) × its height
∵ The bases of the trapezoid are BC and AD
∵ BC = 6 and AD = 8
∵ Its area = 28 units²
∴ 1/2 (6 + 8) × height = 28
∴ 1/2 (14) × height = 28
∴ 7 × height = 28 ⇒ divide both sides by 7
∴ height = 4
∵ The height is BA
∴ BA = 4 unit
- To find the length of CD draw a perpendicular line from C to AD and
meet it at E
∵ BA and CE are perpendicular to AD
∴ BA // CE
∵ BC // AD
- Perpendicular lines between parallel lines are equal in lengths
∴ BA = CE and BC = AE
∵ BA = 4 and BC = 6
∴ CE = 4 and AE = 6
∵ AD = 8 units
∵ AD = AE + ED
∴ 8 = 6 + ED ⇒ subtract 6 from both sides
∴ ED = 2 units
- In ΔCED
∵ m∠CED = 90°
∴ CD = √[(CE)² + (ED)²] ⇒ Pythagoras theorem
∵ CE = 4 and ED = 2
∴ CD = √[(4)² + (2)²] = √[16 + 4] = √20 = 2√5
* The value of CD is 2√5
Final answer:
The value of the unknown side CD in quadrilateral ABCD can be found using the area of a trapezoid formula and the Pythagorean theorem. Given the area, and the lengths of BC and AD, we calculated that CD equals 8 units.
Explanation:
The student has asked to find the value of CD in a quadrilateral ABCD, where BC is parallel to AD, BA is perpendicular to AD, the area of quadrilateral ABCD is 28 square units, BC is 6 units, and AD is 8 units.
Since BA is perpendicular to AD and BC is parallel to AD, we can determine that ABCD is a trapezoid with AB and CD as the non-parallel sides. The area of a trapezoid is given by the formula Area = ½ × (sum of parallel sides) × height. So we have:
½ × (AD + BC) × height = 28
½ × (8 + 6) × height = 28
½ × 14 × height = 28
7 × height = 28
height = 4 units
Since BA is perpendicular to AD, and given BA is the height of the trapezoid, this means that AB = 4 units. Now, because ABCD has right angles at A and B, triangles ABD and ABC are right triangles and we can use the Pythagorean theorem to calculate CD.
In triangle ABD:
AB² + BD² = AD²4² + BD² = 8²BD = √(8² - 4²) = √(64 - 16) = √48 = 4√3Since CD is the hypotenuse of triangle ABD:
CD² = AB² + BD²CD² = 4² + (4√3)²CD² = 16 + 48CD = √64CD = 8 unitsTherefore, the correct answer is CD = 8 units.
If f(x)=5x-1, then f^-1(x)=
Answer:
f^-1(x) = (x+1)/5
Step-by-step explanation:
f(x)=5x-1
y = 5x-1
Exchange x and y
x = 5y-1
Solve for y
Add 1 to each side
x+1 = 5y-1+1
x+1 = 5y
Divide by 5
(x+1)/5 = 5y/5
(x+1)/5 = y
The inverse is (x+1)/5
f^-1(x) = (x+1)/5
or what value of x does 4x=(1/8)^x+5?
–15
–3
3
15
Answer:
x = -3Step-by-step explanation:
[tex]4^x=\left(\dfrac{1}{8}\right)^{x+5}\qquad\text{use}\ a^{-1}=\dfrac{1}{a}\\\\4^x=(8^{-1})^{x+5}\\\\(2^2)^x=\bigg((2^3)^{-1}\bigg)^{x+5}\qquad\text{use}\ (a^n)^m=a^{nm}\\\\2^{2x}=2^{-3(x+5)}\iff2x=-3(x+5)\qquad\text{use the distributive property}\\\\2x=-3x-15\qquad\text{add}\ 3x\ \text{to both sides}\\\\5x=-15\qquad\text{divide both sides by 5}\\\\x=-3[/tex]
Answer:
B, -3
Step-by-step explanation:
What is the factorization of the polynomial below?
9x^2-16
The factorized form of the given polynomial is (3x + 4)(3x - 4). Using one of the factorization methods of polynomial, the result is obtained.
What is the factorization of a polynomial?Writing a polynomial as the product of its factors (monomial, binomial or and so on) is called the factorization of the polynomial.
There are different methods of factorization. Some of them are the grouping method, GCF method, the difference of squares method, etc.
Factorizing the given polynomial:The given polynomial is [tex]9x^2-16[/tex]
Using the difference of squares method we can write the given polynomial as
[tex]9x^2-16 = (3x)^2-(4)^2[/tex]
We know that difference between any two squares is
[tex]a^2-b^2=(a+b)(a-b)[/tex]
So,
[tex]9x^2-16[/tex] = (3x + 4) (3x - 4)
Therefore, the factors of the given polynomial are (3x + 4) and (3x - 4).
Learn more about the factorization of polynomials here:
https://brainly.com/question/11434122
#SPJ2