3. The value of a car in relation to the number of miles driven is given by the linear
function y = -9x + 55000.
a. Interpret the meaning of the rate of change and initial value for the linear function.
Answers
Answer:
General form of a linear equation: [tex]y=mx+b[/tex]
(where m is the slope and b is the y-intercept)
A linear equation has a constant rate of change which is represented by the slope (m). It is the rate at which one quantity is changing with respect to another quantity.
Question 3Part (a)
Given equation: [tex]y=-9x+55000[/tex]
where:
y = value of car (in dollars)x = number of miles drivenThe rate of change (slope) is -9 and represents that for every 1 mile driven, the value of the car decreases by $9.
The initial value is the y-intercept (b) as this is the value when x = 0.
Therefore, the initial value of car is $55,000.
Part (b)
To find the number of miles at which the car be valued at $35,002, set the equation to $35,002 and solve for x:
[tex]\implies -9x+55000=35002[/tex]
[tex]\implies -9x=35002-55000[/tex]
[tex]\implies -9x=-19998[/tex]
[tex]\implies x=\dfrac{-19998}{-9}[/tex]
[tex]\implies x=2222[/tex]
Therefore, the car will be valued at $35,002 after 2,222 miles.
Question 4Given equation: [tex]y=0.39x+2.55[/tex]
where:
y = price of carrots (in dollars)x = weight (in oz)The rate of change (slope) is 0.39 and represents that for every increase of 1 oz of weight in carrots, the price of the carrots increases by $0.39
The initial value is the y-intercept (b) as this is the value when x = 0.
Therefore, the initial cost of the carrots is $2.55.
Part (b)
To find the weight of carrots you can buy for $6.06, set the equation to $6.06 and solve for x:
[tex]\implies 0.39x+2.55=6.06[/tex]
[tex]\implies 0.39x=6.06-2.55[/tex]
[tex]\implies 0.39x=3.51[/tex]
[tex]\implies x=\dfrac{3.51}{0.39}[/tex]
[tex]\implies x=9[/tex]
Therefore, you can buy 9 oz of carrots for $6.06
Part (c)
To find out how much it costs to buy 21 oz of carrots, substitute x = 21 into the equation and solve for y:
[tex]\implies y=0.39(21)+2.55[/tex]
[tex]\implies y=10.74[/tex]
Therefore, it costs $10.74 to buy 21 oz of carrots.
Related Questions
The combined volume of two identical cubes is 250 cubic centimeters what is the measure of one cubes edge
Answers
Answer:
5 cubic centimeters
Step-by-step explanation:
250 divided by 2 = 125
To get to 125 you can do 5 x 5 x 5.
Since it is a cube you have to do Length x Width x Height which is why you do _ x _ x _.
Find the vertex of the parabola.
y = 2x2 + 8x+12
Answers
[tex]\textit{vertex of a vertical parabola, using coefficients} \\\\ y=\stackrel{\stackrel{a}{\downarrow }}{2}x^2\stackrel{\stackrel{b}{\downarrow }}{+8}x\stackrel{\stackrel{c}{\downarrow }}{+12} \qquad \qquad \left(-\cfrac{ b}{2 a}~~~~ ,~~~~ c-\cfrac{ b^2}{4 a}\right) \\\\\\ \left(-\cfrac{ 8}{2(2)}~~~~ ,~~~~ 12-\cfrac{ (8)^2}{4(2)}\right)\implies \left( -\cfrac{8}{4}~~,~~12-\cfrac{64}{8} \right) \\\\\\ (-2~~,~~12-8)\implies (-2~~,~~4)[/tex]
There are two unit rates for every rate, true or false?
Answers
Answer:
True
Step-by-step explanation:
A rate is a special ratio in which the two terms are in different units. For example, if a 12-ounce can of corn costs 69¢, the rate is 69¢ for 12 ounces. This is not a ratio of two like units, such as shirts. This is a ratio of two unlike units: cents and ounces
it should be true. Let me know if I'm incorrect.
Does the federal government have enough power to carry out its constitutional responsibilities? Explain.
Answers
Answer:
The federal government's "enumerated powers" are listed in Article I, Section 8 of the Constitution. Among other things, they include: the power to levy taxes, regulate commerce, create federal courts (underneath the Supreme Court), set up and maintain a military, and declare war. It is their job to carry out constitutional responsibilities for society.
Step-by-step explanation:
Can someone explain how I need to do this please?
Answers
Answer: do what?
Step-by-step explanation:
A store sold 250 shirts last week. The sales increased by 15% this week.
Find the sales volume for this week.
Answers
Answer:
288
Step-by-step explanation:
quick calculator use
15% of 250 is 37.5
add that to 250 to get 287.5
can't sell half a shirt so the answer is 288
solve:
i)x+y=5
ii)x-y=3
iii)2x+y=7
iv)3x-2y=0
Answers
Answer:
I) X+Y
when X=0
0+y=5
Y=5
When Y=0
X+0=5
X=5
(X,y)=(5,5)
(ii) X-Y=3
When X=0
0-Y=3
Y=-3
When Y=0
X-0=3
X=3
(X,Y)=(3,3(
(III) 2x+Y=7
when X=0
0+Y=7
Y=7
when Y=0
2x+0=7
2x=7
X=7/2 or 3.5
(X,Y)=(3.5,7)
(Iv)
3X-2Y=0
when X=0
0-2Y=0
-2Y=0
Y=0
When Y=0
3x-0=0
3X=0
X=0
(X,Y)=(0,0)
What is a possible value for the missing term of the geometric sequence?
43, ___, 688, ...
Answers
We have the first term, 43, as well as 3 terms so far, with the third term being 688.
3 - 1 = 2
Set up the following formula for the ratio:
43 * ratio^2 = 688
Ratio^2 = 16
ratio = 4
43 * 4 = 172 is the second term.
Hope this helps
What is the area of 6 and 12 obtuse triangle
Answers
Answer:
A
Step-by-step explanation:
if it's not I'm sorry but that is the most logical answer:)
36 sq. units
[tex]\bold{EXPLANATIONS:}[/tex]
Identify coordinate point D.
(1, 5)
(0, 2)
(6, 7)
(7, 3)
Answers
Point d 7,3 point c 6,7 point b 1,5 point a 0,2 I took this quiz got 100Answer:
Step-by-step explanation:
D) (7, 3)
Step-by-step explanation on coordinates:
The coordinates indicate the position of a point in the 2D coordinate plane relative to the origin. The x-coordinate of a point is its perpendicular distance from the y-axis measured along the x-axis. The y-coordinate of a point is its perpendicular distance from the x-axis measured along the y-axis.
Coordinates are two numbers (Cartesian coordinates), or sometimes a letter and a number, that locate a specific point on a grid, known as a coordinate plane. A coordinate plane has four quadrants and two axes: the x axis (horizontal) and y axis (vertical).
Coordinates are written as (x, y) meaning the point on the x axis is written first, followed by the point on the y axis.
Therefore, the veracious answer (7, 3).
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________________________________________________
Answers
Answer:
( 50, 30 )
Step-by-step explanation:
Equal distance
Joseph needs to buy insulation for the inside of a truck container. The container is a rectangular prism 12 feet long, 7 feet wide, and 6.5 feet high. How much insulation should Joseph buy if all surfaces except the floor are to insulated?
Answers
Answer:
Joesph needs to be 331 feet of flooring to cover all sides except the floor.
Step-by-step explanation:
To answer this question, you need to find the areas of the sides and the roof.
Side (left and right): 12 feet long multipled by 6.5 feet high. 12*6.5=78 ft^2. Multiply this by 2 to get the combined areas of both the left and right side. 156 ft ^2
Side (back and front): 7 feet wide by 6.5 feet high. 7*6.5=45.5 ft^2. Multiply this by two to get the combined areas of the back and the front sides. 91 ft^2
Roof: 7 feet wide multiplied by 12 feet long. 7*12=84 ft^2
84+91+156=331 ft^2
Answer:
331 ft²
Step-by-step explanation:
Area of a rectangle = width × height
Given:
base width = 7 ftbase length = 12 ftheight = 6.5 ftSurface area (minus the floor):
= 2(7 × 6.5) + 2(12 × 6.5) + (7 × 12)
= 91 + 156 + 84
= 331 ft²
In order for the function to be linear, what must a be and why?
a = 22 because the rate of change is 1.
a = 20 because the rate of change is 3.
a = 22 because the rate of change is –1.
a = 20 because the rate of change is –3.
Answers
For the function to be a linear, D. a = 20 because the rate of change is –3.
What is the Rate of Change of a Function?The rate of change = change in y / change in x.
Therefore, for the function to be linear, the rate of change must be the same across the table of values.
Using, (4, 26) and (5, 23):
Rate of change = (26 - 23)/(4 - 5)
Rate of change = (3)/(1) = -3
Using (5, 23) and (6, a), we have:
(23 - a)/(5 - 6) = -3
(23 - a)/(-1) = -3
23 - a = (-3)(-1)
23 - a = 3
-a = 3 - 23
-a = -20
a = 20
Therefore, the answer is: D. a = 20 because the rate of change is –3.
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The formula for the area of a square is A = sa, where s is the length of a side.
If the area of a square is 400 m², what is the length of a side of the square?
Answers
Answer:
[tex]\sqrt{400} = 20[/tex]
Step-by-step explanation:
Since the sides of a square are equal, A = s x s so taking the square root of the square provides the length of each side
put y+-6=5(x-4) to where x is by itself
Answers
Answer:
x=y/5+14/5
Step-by-step explanation:
please asap correct answer gets brainliest
Answers
Answer:
54 square units
Step-by-step explanation:
Edgar has taken out a $6,250 unsubsidized Stafford loan to fund his four-year undergraduate degree. The loan has a duration of 10 years and an interest rate of 6.1%, compounded monthly. How much interest capitalization will have accrued by the time Edgar graduates? Round all dollar values to the nearest cent.
a.
$1,670.30
b.
$1,722.22
c.
$664.35
d.
$1,524.96
Please select the best answer from the choices provided.
A
B
C
D
Answers
Answer:
the answer is B. 1,722.22
come get a brainliest
Answers
The schools is loacted at (1, -8) and the park is loacted at (-6,-8)
If the radius of a circle is 8 ft, what is the length of the diameter? 8 ft 24 ft 4 ft 16 ft
Answers
[tex]\large\boxed{\bold{d= r ×2}}[/tex]
In this question all the required values are given so we'll simply have to solve.
Let's substitute the values according to the formula.
[tex]\bold{d= 8×2}[/tex]
[tex]\large\boxed{\bold{d= 16 \ ft}}[/tex]
Therefore, the diameter of the given circle is 16 ft.
Answer= Option D
The length of a rectangle is 6 yd longer than its width. If the perimeter of the rectangle is 60 yd, find its length and width.
Answers
Answer:
Length: 18 yards Width: 12 yards
Step-by-step explanation:
Perimeter = (L+W) x 2
L = W + 6
60 yd = (W+W+6) x 2
30 yd = 2W + 6
24 yd = 2W
W = 12
L = 12 + 6 = 18
please I need help. YOU BE THE TEACHER Your friend finds the difference. 7-(-12) = 7+ 12 = 19 Is your friend correct? yes or no Explain your reasoning
Answers
Answer:
Yes.
Step-by-step explanation:
Yes it is correct.
When any bracket is opened by "-" sign then the sign inside the bracket changes.
Here,
→7-(-12)
→7+12
→19
In the above question the bracket is opened by "-' and the sign of 12 is also negative. So, -×- changes into +.
Point M is the midpoint of AB¯¯¯¯¯. AM=3x+3, and AB=8x−6.
What is the length of AM¯¯¯¯¯¯?
Enter your answer in the box.
units
Answers
Answer: the answer is 21 units
Step-by-step explanation:
I took the test
Answer: the correct answer is 21 units
Step-by-step explanation: hope this helps :)
I rlly thought I understood this but I really don't PLEASE help. You are planning a pizza party for your class. There are 42 students in the class. If a medium pizza has 8 slices, a large pizza has 10 slices and an extra large pizza has 12 slices. What fraction of the class will each pizza serve. Show Working.
Answers
Hope this helps!
PLSS HELP. ALGEBRA 1. 9TH GRADE..ASAP PLSSS
Answers
Answer:
y = - 4
Step-by-step explanation:
[tex]\cfrac{2}{5}\left(10y-5\right)-2y=-10[/tex] (Multiply)
[tex]\cfrac{2\left(10y-5\right)}{5}-2y=-10[/tex]
[tex]\cfrac{2\left(10y-5\right)}{5}\times \:5-2y\times \:5=-10\times \:5[/tex]
[tex]2\left(10y-5\right)-10y=-50[/tex] (Expand)
[tex]10y-10=-50[/tex]
[tex]10y-10+10=-50+10[/tex] ( Add 10)
[tex]10y=-40[/tex] (Simplify)
[tex]\cfrac{10y}{10}=\cfrac{-40}{10}[/tex] (Divide by 10)
[tex]y=-4[/tex]
Answer:
[tex]y=-4[/tex]
Step-by-step explanation:
Given equation:
[tex]\dfrac{2}{5}(10y-5)-2y=-10[/tex]
Expand the brackets:
[tex]\implies \dfrac{2}{5}(10y)-\dfrac{2}{5}(5)-2y=-10[/tex]
[tex]\implies \dfrac{2 \cdot 10}{5}y-\dfrac{2 \cdot 5}{5}-2y=-10[/tex]
[tex]\implies \dfrac{20}{5}y-\dfrac{10}{5}-2y=-10[/tex]
[tex]\implies 4y-2-2y=-10[/tex]
Collect like terms:
[tex]\implies 4y-2y-2=-10[/tex]
Combine like terms:
[tex]\implies 2y-2=-10[/tex]
Add 2 to both sides:
[tex]\implies 2y-2+2=-10+2[/tex]
[tex]\implies 2y=-8[/tex]
Divide both sides by 2:
[tex]\implies \dfrac{2y}{2}=\dfrac{-8}{2}[/tex]
[tex]\implies y=-4[/tex]
Question 36 Choose the expression that is the largest value. cos 30° O tan 30° sin 45 tan 45°
Answers
Answer:
Step-by-step explanation:
Remark
The moment you put Tan(45) in the choices, non of the other choices can compete.
Tan(45) = 1
Sin(a) or cos(a) are all less then one except when a = 0 or 90. Even then they can only have a value of 1. Since none of the angles = 0 or 90 then the largest value is Tan(45) = 1.
What is the area of the arrow?
Answers
Answer:
C. 192 1/2 in^2.
Step-by-step explanation:
Split this up anto 1 triangle and one rectangle
Area of the triangle = 1/2 * base * height
Its height = 36 - 25 = 11, and the base = 2 1/4 + 2 1/4 + 5 1/2= 10.
So it's area = 1/2 * 10 * 11 = 55.
Area of rectangle = 25 * 5 1/2 = 137 1/2.
Total area of the arrow = 55 + 137 1/2 = 192 1/2 in^2.
Hiro ran 5 1/8 miles each day for a week how far did he run in all?
Answers
Answer: 35 7/8 miles
Step-by-step explanation:
5*7 + 1/8*7 = 35 7/8 miles
The magnitude, m, of an earthquake is defined to be m = log startfraction i over s endfraction, where i is the intensity of the earthquake (measured by the amplitude of the seismograph wave) and s is the intensity of a "standard" earthquake, which is barely detectable. what is the magnitude of an earthquake that is 35 times more intense than a standard earthquake? use a calculator. round your answer to the nearest tenth.
Answers
The magnitude of an earthquake that is 35 times more intense than a standard earthquake is 1.5
What is an equation?An equation is an expression that shows the relationship between two or more variables and numbers.
The magnitude, m, of an earthquake is:
m = log (I/S)
Where I is the intensity of the earthquake and S is the intensity of a "standard" earthquake. Hence, for an earthquake that is 35 times more intense than a standard earthquake:
m = log (35S / S) = log (35) = 1.5
The magnitude of an earthquake that is 35 times more intense than a standard earthquake is 1.5
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Zoe supplies costumes to a number of theatre companies. She recently provided 20 different hats, including 4 fedoras. Considering this data, how many of the next 15 hats requested from Zoe’s inventory will be fedoras?
Answers
Answer:
3.
Step-by-step explanation:
If there were 20 hats, and 4 of them were fedoras, we can conclude that 1/5 of the sent hats are going to be fedoras.
If there are 15 hats, we multiply 15 by 1/5 to get 3.
Hope this helps!
How do you solve this URGENT (50pts)
Answers
Explanation:
x + 3y = 2
Converting it to slope intercept form:
y = mx + b [where m is slope, b is y-intercept]
Make y the subject:
[tex]\sf \rightarrow 3y = 2 - x[/tex]
[tex]\sf \rightarrow 3y = -x + 2[/tex]
[tex]\sf \rightarrow y = -\dfrac{x}{3} + \dfrac{2}{3}[/tex]
[tex]\sf \rightarrow y = -\dfrac{1}{3} x+ \dfrac{2}{3}[/tex]
which reveals slope:
[tex]\star \ slope: \sf - \dfrac{1}{3}[/tex]
Answer:
slope = - [tex]\frac{1}{3}[/tex]
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
given
x + 3y = 2 ( subtract x from both sides )
3y = - x + 2 ( divide all terms by 3 )
y = - [tex]\frac{1}{3}[/tex] x + [tex]\frac{2}{3}[/tex] ← in slope- intercept form
with slope m = - [tex]\frac{1}{3}[/tex]