Answer:
all of the function values of an absolute value function will be non-negative.
A certain car rental location charges a daily fee as well as a mileage charge. On one trip a businessman rented a car for the day, drove it 150 miles. He was charged $79 (plus taxes). On another occasion when he rented a comparable car for the day, he drove it 65 miles and was charged $63.70 (plus taxes).
How many miles could the car be driven for $100 (without regard for any taxes that might be applied)? Round to a whole number of miles.
Answer:
[tex]x\approx 267\ miles[/tex]
Step-by-step explanation:
Linear Modeling
Some events can be modeled as linear functions. If we are in a situation where a linear model is suitable, then we need two sample points to make the model and predict unknown behaviors.
The linear function can be expressed in the slope-intercept format:
[tex]f(x)=mx+b[/tex]
For the problem at hand, we must pick the adequate variables according to the data provided.
The question states the charge for renting a car is a function of the mileage. It also provides two points from which we can build our model. Let's set the following variables:
c = the charge for renting a car in dollars
x = the distance driven by the businessman in miles
Representing the ordered pair as (x,c), we have the points: (150,79) and (65,63.70). Our model will be expressed as:
[tex]c = mx+b[/tex]
We must find the values of m and b with the data provided. Substituting the first point:
[tex]79 = 150m+b[/tex]
Substituting the second point:
[tex]63.70 = 65m+b[/tex]
Both equations form the following system:
[tex]\left\{\begin{matrix}150m+b=79\\ 65m+b=63.70 \end{matrix}\right.[/tex]
Subtracting both equations:
[tex]150m-65m=79-63.70[/tex]
Note the variable b was canceled out in the operation, leaving only the variable m to solve. Joining like terms:
[tex]85m=15.3[/tex]
Solving:
[tex]m=15.3/85=0.18[/tex]
From the first equation
[tex]79 = 150m+b[/tex]
Solving for b:
[tex]b=79-150m=79-150(0.18) = 52.[/tex]
The model for the problem is:
[tex]c=0.18x+52[/tex]
Now we need to calculate how many miles (x) could be driven for c=$100. From the equation above, substitute c=100
[tex]100=0.18x+52[/tex]
Solve for x:
[tex]0.18x+52=100[/tex]
[tex]0.18x=100-52=48[/tex]
[tex]x=48/0.18=266.67[/tex]
Rounding to the closest integer:
[tex]\boxed{x\approx 267\ miles}[/tex]
-g+2(3+g)=-4(g+1)- Please help !
Hey there! :)
-g + 2(3 + g) = -4(g + 1)
Simplify.
-g + 6 + 2g = -4g - 4
Add like terms.
(-g + 2g) + 6 = -4g - 4
Simplify.
g + 6 = -4g - 4
Add 4g to both sides & subtract 6 from both sides to isolate "g."
g + 4g + 6 - 6 = -4g + 4g - 4 - 6
Simplify.
5g = -10
Divide both sides by 5.
5g/5 = -10/5
Simplify.
g = -2
Hope this helped! :)
Answer: G = -2
Step 1.
Subtract 6 from both sides.
g + 6 - 6 = -4g - 4 - 6
Step 2.
g = -4g - 10
Step 3.
Add 4g to both sides.
g + 4g = -4g - 10 + 4g
Step 4.
Simplify.
5g = -10
Step 5.
Divide both sides by 5.
[tex]\frac{5g}{5}=\frac{-10}{5}[/tex]
Step 6.
Simplify.
1. Divide 5g by 5.
[tex]\frac{5g}{5}=g[/tex]
2. Divide -10 by 5.
[tex]\frac{-10}{5}=-2[/tex]
Hence, -2 is the answer.
What is 1/10 of 9,000
Hello! :)
1/10 of 9000 is 900
9000 divided by 10 is 900
900 times 10 equals 9000
The answer would be 900.
Hope this helped you!
THEDIPER
If Hannah was having 29 apples, and anton takes 9 apples from Hannah,how many apples do Hannah have?
:
A.10
B.9
C.20
Answer:
C.
Step-by-step explanation:
It is C. because 29 - 9 equals 20
Answer:C.20
Step-by-step explanation:it is easy jut subtract 29-9=24 and the are many ways to subtract like visaual take 29 apples and take 9 away and count how many are left or count up from 9 to 29 on your fingers.
George Johnson recently inherited a large sum of money;he wants to use a portion of this money to set up a trust fund for his two children. The trust fund has two investment options: (1) a bond fund and (2) a stock fund. The projected returns over the life of the investments are 6 percent for the bond fund and 10 percent for the stock fund.Whatever portion of the inheritance he finally decides to commit to the trust fund, he wants to invest atleast 30 percent of that amount in the bond fund. In addition he wants to select a mix that will enable him to obtain a total return of atleast 7.5 percent.A) Formulate a linear programming model that can be used to determaine the percentage that should be allocated to each of the possible i nvestment alternativesB) Solve the problem using the graphical solution procedure.
The solution to the given question is "Optimal B = 0.3 and S = 0.7 where 0.088 was its optimal value", and further calculation can be defined as follows:
linear programmingIt is a mathematical formula with something like a system of linear as well as a set of linear programming in which there is a linear optimization problem to the Nonnegative parameters. In this, Let B compensate also for percentages of money held throughout the bond portfolio and S for both the percentage of money held throughout the bond fund.In a fund for stocks.
[tex]Max \ \ 0.06 \ b+0.1 \ S \ \ \ \\\\B \geq 0.3 \ \ \ \ \ \ \ \ \ \ \ \ \text{Bond fund minimum} \\\\0.06 \ B+ 0.1 \ S \geq 0.075 \ \ \ \ \ \ \text{Minimum return} \\\\B+S=1 \ \ \ \ \ \ \ \text{All funds invested}\\\\B,S\geq 0 \\[/tex]
For a maximization problem, just use 5 phases of the visual solution process. Start by measuring the rows which fit the disparities.[tex]B = 0.3 \\ \\0.06 \ B+0.1 \ S = 0.75\\\\ B+s =1[/tex]
It is the very first main principle to use a sign[tex]\geq[/tex], greater than or equal to, that answer is just all points because the third limitation uses an exclamation point, both places on the graph are the answer. Its colored area contains each resolution stage that concurrently fulfills all limitations its Viable Area was named as its location of the approaches to any inequalities. That ideal option exists in which there is limited restriction mostly on bond portfolio and all funds. Making investment constraints converge. Replacement B= 0.3 throughout the restriction invested throughout all resources and settle to S.[tex]B+s=1=10 \\\\0.3+s = 1 \\\\The \ \ s= 0.7 \\[/tex]
Optimal B = 0.3 and S = 0.7 where 0.088 was its optimal value.
please find the attachment:
Find out more about the 'linear programming model' here:
brainly.com/question/15356519
HELP ASAP RIGHT NOW PLEASE
Answer:
X=7
X=2
Step-by-step explanation:
The equations of three lines are given below.
Line 1: -3y = 5x + 6
Line 2: 10x - 6y=-4
3
Line 3: y=-=x+3
5
For each pair of lines, determine whether they are parallel, perpendicular, or neither.
Line 1 and Line 2:
Parallel O Perpendicular ONeither
x
3
?
Line 1 and Line 3:
Parallel Perpendicular
Neither
Line 2 and Line 3: Parallel Perpendicular Neither
I Don't Know
Submit
Submit
2020 M
Answer:
line 1&2 are neither
line 1&3 are also neither
lines 2 and 3 however are perpendicular since they make 90 degree angles when they meet.
Step-by-step explanation:
Step-by-step explanation:
Hey there!
Here, The equations are;
-3y=5x+6
5x+3y+6=0.........(i)
10x-6y+4 =0......(ii)
y= -3/5x+3.......(iii)
From equation (i).
[tex]slope(m1) = \frac{ - coeff. \: ofx}{coeff. \: of \: y} [/tex]
Put all values.
[tex]m1 = \frac{ - 5}{3} [/tex]
Now, from equation (ii).
[tex]m2 = \frac{ - coeff. \: of \: x}{coeff. \: of \: y} [/tex]
Put all values.
[tex]m2 = \frac{ - 10 }{ - 6} [/tex]
[tex]m2 = \frac{5}{3} [/tex]
As m1 is not equal to m2 it is not parallel lines.
For perpendicular lines;
m1×m2= -1.
[tex] \frac{ - 5}{3} \times \frac{5}{3} [/tex]
After simplifying it we get -25/9 which is not equal to-1. So, it is not perpendicular lines.
Therefore, the lines are neither parallel nor perpendicular.
But the lines of equation (ii) and (iii) are perpendicular to eachother.
-3/5×5/3= -1
[ so, the line (ii) and (iii) are perpendicular to eachother but others are neither]
Hope it helps...
. A clinic offers a weight-loss program. A review of is records found the following amounts of weight loss, in pounds, for a random sample of 24 of its clients at the conclusion of a 4-month program.182516111520161928252631454036192825361635201619a) Assume the customer base of this program is very large (>1000). Find a 99% confidence interval for the population mean.b) Without doing the calculations, explain whether a 90% confidence interval for the population mean would be wider than, narrower than, or the same as that found in part a). c) Now assume the total number of customers who have participated in this weight loss program is 400. What is the 99% confidence interval now
Answer:
A) = ( 19.2501, 29.4999 )
B) 90% confidence interval would be narrower than 99% confidence interval
C) ( mean - margin of error , mean + margin of error )
Step-by-step explanation:
customer base > 10000
sample = 24 clients
period ( time ) = 4 months
A) Determine 99% confidence interval for population mean
mean = 24.3750
std = 8.9434
sample size = 24
initial margin of error = 1 - 0.99 = 0.01
99% confidence interval for population mean = ( 19.2501, 29.4999 )
B) 90% confidence interval would be narrower than 99% confidence interval
c) The 99% confidence interval when sample size = 400
we cannot determine the mean value for 400 customers because the values given are for just 24 customers
( mean - margin of error , mean + margin of error )
attached below is the detailed solution
A=bh A=63 b=9 what’s h
solve the inequality: -6+1≤ 3 (-2x)
please answer!
Answer:
7/6...follow me and mark me brainliest....Write the equation of the line in slope-intercept form that passes through the points (2, -2) and (-3, -17)
Answer: y = 3x - 8
Step-by-step explanation: If you’re given two points that lie on a line, and you’re asked to write the equation of the line, your first task will be to find the slope of that line using the slope formula.
The slope formula is m = y₂ - y₁ / x₂ - x₁
Substituting our points in, we have -17 - -2 / -3 - 2 which is -15/-5 or 3.
So the slope of our line is 3 which can be used with either one of our
two points to write the equation of the line in point-slope form.
So let's go with the point (2, -2).
Point-slope form is written y - y₁ = m(x - x₁).
Since we're using the point (2, -2), y - y₁ would be y - -2 or y + 2.
Now, m would be 3 and x - x₁ would be x - 2.
So we have y + 2 = 3(x - 2).
To put this equation into slope-intercept form, we would first distribute
the 3 through the parentheses which gives us y + 2 = 3x - 6.
Move the number to the right side of the equation by
subtracting 2 from both sides and we have y = 3x - 8.
So the equation of the line would be y = 3x - 8.
Find 43 ÷ 6 (as a mixed number).
Answer:
7 1/6
Step-by-step explanation:
43/6 = 7.167
6*7 = 42
7 1/6
What is this answer to the question
Answer:
10/9 or 1.1
Step-by-step explanation:
5/3 divide by 3/2
to divde a fraction, multipby by reciprocal
5/3 * 2/3
Cross Multiply
The answer is 10/9
Answer:
[tex]\frac{10}{9}[/tex] or 1.11
Step-by-step explanation:
[tex]\frac{5}{3}[/tex] × [tex]\frac{2}{3}[/tex]
[tex]\frac{10}{9}[/tex] or 1.11 [tex]Ans[/tex]
PLEASE HELP!!! IT WOULD MEAN SO MUCH IM REALLLLY CONFUSED AND DONT UNDERSTAND, I ALSO PUT A IMAGE OF THE QUESTION, ALSO SORRY FOR USING ALL CAPS I FEEL LIKE IT WOULD GRAB MORE PEOPLES ATTENTION
Find the length of the radius. Write your answer as
simplified radical.
Step-by-step explanation:
[Note] The perpendicular bisects the line segment (property of circles).
Using Pythagorus theorem :
[tex]r = \sqrt{ {12}^{2} + {8}^{2} } = 14.42 \: units[/tex]
math problem
"You want to run in a relay that is coming up. The relay is 1 1/2 miles long and each portion is 1/4 of a mile. A different person will need to run each portion of the relay. How many people will need to be on the relay team?"
pls answer. thanks
12∣x−6∣−9=5∣x−6∣+7
Pls
Answer:
hi there
12x - 5x - 6x + 6x = 9 + 7
7x + x = 16
8x = 16
x = 16/8
Step-by-step explanation:
hope u understand
-4|7 – 6k|= 14 solve for k
Answer:
no solution
Step-by-step explanation:
-4|7 – 6k| = 14
Divide both sides by -4.
|7 - 6k| = -14/4
|7 - 6k| = -7/2
An absolute value can never equal a negative number since an absolute value is always non-negative. Therefore, there is no solution.
Answer: no solution
Is the equation a true statement when x = -3? In the other words, is -3 a
solution to the equation: 6x+5=5x+8+2x?
1. True
2. False
Fill in the table using this function rule.
y= 2 + 3x
Michael received a Grant to make a community garden. He makes a scale drawing of his vision for the garden. Michael's drawing shows the layout of 9 raised garden beds of the same size. The scale from his drawing to the actual garden is 2cm for ever 1ft. What is the actual area of one of the garden beds?
Answer:
32 ft²Step-by-step explanation:
Scale factor
2 cm to 1 ftSize of each garden bed on the drawing
8 cm by 16 cmActual size
8cm = 4*2 cm ⇔ 4 ft16 cm = 8*2m ⇔ 8 ftArea of one garden bed
4 ft * 8 ft = 32 ft²Please help me!
Evaluating PieceWise Function
Answer:
f(0) = 3
Step-by-step explanation:
We will use the first equation, since x = 0
162:53:55
AD and MN are chords that intersect at point B.
A circle is shown. Chords A D and M N intersect at point G. The length of A B is 9, the length of B D is x + 1, the length of M B is x minus 1, and the length of B N is 15.
What is the length of line segment MN?
4 units
6 units
18 units
24 units
Answer:18
Step-by-step explanation:
Answer:
18
Step-by-step explanation:
edg B)
What is the value of the expression 5x + 10 when x=-6?
Answer:
-20
Step-by-step explanation:
5 X -6 =-30
-30 +10=-20
Answer:
-20
Step-by-step explanation:
To find the answer just plug x into the equation.
It should look like 5(-6) + 10 = n
Now just simplify
5(-6) = -30 + 10 = -20
(a positive times a negative always equals a negative)
trevon leah and beth are playing a computer game trevon scored -8 beth score was a 3/4 of trevon score and leah score was 1/4 of beth score what was leah
Answer:
-1.5
Step-by-step explanation:
3/4 of -8 is -6
1/4 of -6 is -1.5
if it is not supposed to be -8 the answer is 1.5
The table below shows the number of Japanese yen that could be exchanged for U.S. dollars on the day
Charlotte came home from her trip to Japan.
Exchange Rate
Number of U.S.
dollars
Number of Japanese
yen
5
600
15
1,800
30
3,600
Which statement could describe the relationship between the number of Japanese yen and the number
of U.S. dollars on this particular day, and does the relationship represent a function?
A.
B.
C.
D.
The number of U.S. dollars is 120 times the number of yen. No, it is not a function.
The number of yen is 120 times the number of U.S. dollars. Yes, it is a function.
The number of U.S. dollars is 595 more than the number of yen. No, it is not a function.
The number of yen is 595 more than the number of U.S. dollars. Yes, it is a function.
А
Answer:
The Answer is B.
Step-by-step explanation:
-8p=40 Solve for P (Algebra)
Step-by-step explanation:
solution
or,-8p=40
or, p=40/-8
or, p=-5
Two numbers total 63 and have a difference of 31. Find the two numbers
Answer: 47 and 16
Step-by-step explanation:
- Make Two Equations
x + y = 63
x - y = 31
- Set one of the equations equal to one of the variables
x + y = 63
x = 31 + y
- Substitute the equation back into the other one
(31 + y) + y = 63
31 + 2y = 63
2y = 32
y = 16
- Substitute the answer back into the equation
x + y = 63
x + 16 = 63
x = 47
Answer:
47 and 16
Step-by-step explanation:
Start by writing this question as two equations, lets call the two numbers x and y.
"Two numbers total 63" we can write that as x+y=63
"...and have a difference of 31" we can write that as x-y=31 or y-x=31 or |x-y| = 31 or |y-x| = 31. There a lot of ways to write that.
So lets use y-x=31 as the second equation, you can ignore the other possible ways since it doesn't matter in this problem to use absolute value
Using subsitution solve for x using x+y = 63, x = -y + 63
Plug that into the other equation, -y+63-y=31
−2y+63=31 (Simplify both sides of the equation)
−2y+63+−63=31+−63 (Add -63 to both sides)
−2y=−32
y=16 (Divide both sides by -2 to get Y by itself)
We solved for Y(of of the numbers), now for X (the other number)
Substitute 16 for y in x= − y + 63:
x=−y+63
x=−16+63
x=47
A recent study claimed that in any given month for every 5 text messages a boy sent or received, a girl sent or received 7 text messages. Is the relationship between the number of text messages sent or received by boys proportional to the number of text messages sent or received by girls? Yes or No
Answer:
i do not think so
Someone plz help me I don’t know how to do these
Answer:
(z+w)y = X
Step-by-step explanation:
first add Z to both sides
w+z = x/y
then multiply both sides by Y
(w+z)y=x
At Teen Tops, a package of 5 T-shirts costs $38. At
Bargain City, a package of 4 T-shirts costs $34. Which
statement is the most accurate?
A Bargain City is the better buy because it sells
T-shirts at $8.50 per T-shirt.
B. Teen Tops is the better buy because the package
has more T-shirts.
C Bargain City is the better buy because $34 is less than $38.
D Teen Tops is the better buy because it sells T-shirts at $7.60 per T shirt
Answer: D is the answer I am also working on this
Step-by-step explanation:
