Jamie and Hudson took a road trip to the beach. Their total distance traveled after getting on the highway can be found using the function d(h)=55h+10, where h is the number of hours they have been driving on the highway.
1) Explain why the relationship between total distance and hours is a function.
2) Is this function continuous or discrete? Explain how you know.
3) If the girls can drive a maximum of 8 hours, what is the domain for the function? Explain your answer.
4) If the girls can drive a maximum of 8 hours, what is the range for the function? Explain your answer.
5) Create a graph that models this function. Be sure to include a title and to label your x- and y-axis with the variable names, but just x and y.
6) What is the slope of the function? What does it represent?
7) What is the y-intercept? What does it represent?
The total distance is an illustration of a linear function.
(1) Why the relationship is a function
The relationship is a function because all input values of h, have exactly one corresponding output value of d
(2) The function type
The function is a discrete function, because the number of hours is an integer, and it cannot take decimal values (in this case)
(3) The domain for a drive of 8 hours
The domain is the set of time the girls drive.
So, the domain is: [0,8]
(4) The range
The function is given as:
[tex]d = 55h +10[/tex]
When h = 0,
[tex]d = 55(0) +10 = 10[/tex]
When h = 8,
[tex]d = 55(8) +10 = 450[/tex]
So, the range is: [10,450]
(5) The graph
See attachment
(6) The slope
A linear function is represented as:
[tex]y = mx + c[/tex]
Where:
m represents the slope.
So, by comparison:
[tex]Slope = 55[/tex]
The slope in this case represents the distance travelled per hour
(7) The y-intercept
In (6) above, c represents the y-intercept.
So, by comparison:
[tex]c = 10[/tex]
The y-intercept in this case represents the initial distance
Read more about linear functions at
https://brainly.com/question/15602982
Find the value of x.
6x+3(-3x+4)=13
Answer
Well I’d distribute first
So if simplified you’d get
6x-9x+12=13
-3x+12=13
-3x=1
x= 1/-3
X is - 1/3
write 2³ in simplified form
Answer:
8
Step-by-step explanation:
2^1 = 2×1 = 2
2^2= 2×2= 4
2^3= 2×2×2= 8
solve 7e^(2x)-5>58. Round to the nearest hundredth.
Answer:
[tex]x\gtrapprox1.1[/tex]
Step-by-step explanation:
[tex]7e^{2x}-5>58[/tex]
[tex]7e^{2x}>63[/tex]
[tex]e^{2x}>9[/tex]
[tex]2x>ln(9)[/tex]
[tex]x>\frac{ln(9)}{2}[/tex]
[tex]x\gtrapprox1.1[/tex]
Can someone please take the time out of They’re day and help me with this
Answer:
a. 3x = 2x + 10, b. x = 10, c. 30 degrees
Step-by-step explanation:
Angle 4 and angle 6 = 180 degrees, so
3x = 2x + 10
x = 10
Angle 7 is congruent to angle 6, so it is also 2x + 10, x = 10, so it is 30 degrees.
Answer:
see explanation
Step-by-step explanation:
∠ 4 and ∠ 6 are same- side interior angles and sum to 180° , that is
(a)
3x + 2x + 20 = 180 , simplifying
(b)
5x + 20 = 180 ( subtract 20 from both sides )
5x = 160 ( divide both sides by 5 )
x = 32
(c)
∠ 6 and ∠ 7 are vertically opposite angles and are congruent , then
∠ 7 = 2x + 20 = 2(32) + 20 = 64 + 20 = 84°
Simplify (45)-(+14). Pls guys explain it to me
Answer:
Answer: 31
Step-by-step explanation:
[tex]{ \rm{45 - ( {}^{ + } 14)}} \\ \\ = { \rm{45 - 14}} \\ \\ = { \rm{31}}[/tex]
Answer:
31
Step-by-step explanation:
(45)-(+14)
This is asking us to take 45 [(45)] and subtract 14 [-(+14)]
That is 45 - 14 = 31
The expression "-(+14)" is a deliberate attempt to confuse. It says "subtract a positive 14." There was no need to add the "+" sign in the parentheses, since a positive value is always assumed. But it was added here to promote heartburn and the sale of TUMS. When I see something like "-(+10000)," I immediately change it to "-10000" and move on, adding one demerit to the author of the problem.
the sum of six and two times a number is one
Answer:
Equation: 6+2x=1
Step-by-step explanation:
Sum means addition and just add an x for the 2 times a number and set it equal to 1.
I need help on this, thank you in advance
Answer:
65
50
Step-by-step explanation:
yeah-ya........ right?
Two ships leave a harbor together traveling
on courses that have an angle of 128°
between them. If they each travel 543 miles,
how far apart are they (to the nearest mile)?
A) 976 mi
B) 476 mi
C) 42 mi
D) 1952 mi
Answer:
use cosine law
x^2 = 543^2 + 543^2 - 2(543)(543cos 128°
solve for x
Step-by-step explanation:
The original qauntity is 10 and the new quantity is 13. What is the percent change?
The probability of event A is 0.53 and the probability of event B is 0.17. The probability of A and B occurring is 0.901. Which statement accurately describes these two events?
Explanation:
We're given that
P(A) = 0.53P(B) = 0.17P(A and B) = 0.901Note that P(A)*P(B) = 0.53*0.17 = 0.0901 which is somewhat similar to 0.901 but not entirely the same. We have an extra zero between the decimal point and the nine. So this indicates that [tex]P(A)*P(B) \ne P(\text{A and B})[/tex]. Therefore, events A and B are not independent. We consider them dependent.
please help with this
Answer:
v = 32
Step-by step explanation:
Step-1: Subtract 15 both sides
⇒ v/4 + 15 = 23
⇒ v/4 + 15 - 15 = 23 - 15
⇒ v/4 = 8
Step-2: Use cross multiplication
⇒ v/4 = 8
⇒ v = 8 × 4 = 32
what is the speed of a skater who travels a distance of 210 m in a time of 10 secands
solve (2x + 5)= (2x + 3)(2x - 1)
[tex](2x + 5)= (2x + 3)(2x - 1)\\<=>2x+5=4x^2-2x+6x-3\\<=>4x^2-2x+6x-3-2x-5=0\\<=>4x^2+2x-8=0\\<=>(4x+1-\sqrt{33})( 4x+1+\sqrt{33})=0 \\<=> x=\frac{-1+\sqrt{33} }{4} /or/x=\frac{-1-\sqrt{33} }{4}[/tex]
Answer:
x = -1± sqrt( 33)
----------------------------
4
Step-by-step explanation:
(2x + 5)= (2x + 3)(2x - 1)
Distribute
2x+5 = 4x^2 +6x-2x-3
Combine like terms
2x+5 = 4x^2 +4x -3
Subtract 2x +5 from each side
0 = 4x^2 +4x-3-2x-5
Combine like terms
0 =4x^2 +2x -8
Using the quadratic formula
a=4 b=2 c=-8
x = -b± sqrt( b^2-4ac)
----------------------------
2a
x = -2± sqrt( 2^2-4(4)(-8))
----------------------------
2(4)
x = -2± sqrt( 4+128)
----------------------------
8
x = -2± sqrt( 132)
----------------------------
8
x = -2± 2sqrt( 33)
----------------------------
8
x = -1± sqrt( 33)
----------------------------
4
CAN SOMEONE HELP ME PLEASE ASAP!?
Answer:
last option
Step-by-step explanation:
b) 1/6 = 16.7 to 1dp
c) 45% = 45/100 = 9/20
d) 7/9 = 77.8% to 1dp
Find the unit rate.
289 miles on 10 gallons
The unit rate is( )miles per gallon
Answer:
28.9 mpg
Step-by-step explanation:
Divide the miles by the gallons. 289 / 10 = 28.9
Can someone please help !!
PLZ HELP
If a triangle has one interior angle measuring 102°, what is a possible pair of measurements for the other two
interior angles?
Answer:
39
Step-by-step explanation:
There is a possibility that this triangle is isosceles. Angles in triangles add up to 180. 102-180=78. Since we are assuming this triangle is isosceles, we can just divide 78 by 2 and get 39 which might be the other two angles. They might both be 39 degrees.
Since triangle angles must add up to 180 degrees, the other angles must add up to 78 degrees. One possible pair could be if you divided 78 in half, which is 39. There could also be tons of more I can provide a list of below:
39,39
40,38
35,43
Name the perpendicular bisector….
Answer:
B and C
Step-by-step explanation:
I chose these bisector angles because they both are at a 90 degree angle
If f (x)= 3x - 5 and g(x) = x^2, find (f•g)(3).
Answer:
do it got a picture
on the edge2020
Step-by-step explanation:
7. A shopkeeper sold a pen set for 180 at a profit of 30. To make a profit of 26%, what should be the selling price of the pen set? 1otor
[tex]\huge\color{pink}\boxed{\colorbox{black}{Answer♡}}[/tex]
[tex]selling \: price \: of \: pen = 180 \: rs \\ profit = 30 \: rs \\ cost \: price = selling \: price - profit \\ = > 180 - 30 \\ = > 150 \: rs[/tex]———————————required profit = 26%so ,
[tex]new \: selling \: price = 150 + \frac{26}{100} \times 150 \\ = > 150 + 39 \\ = > 189 \: rs[/tex]
———————————thuѕ, thє nєw ѕєllíng prícє σf pєn ѕєt wíll вє rѕ. 189hσpє hєlpful~
Based on the information given the selling price of the pen set is $189.
Using this formula
Selling price=Selling price of pen+(Profit percentage× Selling price of pen)
Let plug in the formula
Selling Price=$150 +( 26% ×$150)
Selling Price=$150 +$39
Selling Price=$189
Inconclusion the selling price of the pen set is $189.
Learn more about selling price here:https://brainly.com/question/1153322
What is the degree of 3x^4-4x^2?
Answer:
the degree is 4
Step-by-step explanation:
the largest exponent of x
PLZZ HELP
Order these numbers from least to greatest.
1. Write the equation of the line in slope-intercept with a slope of 1 and passing through the (0,-1)2. Write the equation of the line in slope-intercept with a slope of 4 passing through the (-2,1)please help with atleast one problem i need help asap
Answer:
Write the equation of the line in slope-intercept with a slope of 1 and passing through the (0,-1)
y = x - 1
Write the equation of the line in slope-intercept with a slope of 4 passing through the (-2,1)
y = 4x + 9
Step-by-step explanation:
Write the equation of the line in slope-intercept with a slope of 1 and passing through the (0,-1)
y = mx + b
if slope is 1, m= 1
y = x + b
if passing through (0,-1), then y = -1, x = 0
-1 = (0) + b
b = -1
then
y = x - 1
Write the equation of the line in slope-intercept with a slope of 4 passing through the (-2,1)
y = mx + b
if slope is 4, m= 4
y = 4x + b
if passing through (0,-1), then y = 1, x = -2
1 = 4(-2) + b
b = 9
then
y = 4x + 9
Convert 112 degrees Fahrenheit to degrees Celsius
Equation
C = (F - 32) ÷ 1.8
Solution
C = (112 - 32) ÷ 1.8
=44.4 (44.4444444444)
Answer may vary depending on how your teacher wants you to do it and whether they want a exact answer.
A gold chain with an original price of $150 is on sale for $87 what is the percent of the discount
Answer:
i believe its 58%
Step-by-step explanation:
I need 3 more brainiest can anyone help a girl out plz
Answer:
:/
Step-by-step explanation:
Answer:
Sure
Step-by-step explanation:
3. A rock is lying on a rock ledge that is 3 m high. The rock as 120 J of potential energy.
What is the mass of the rock?
Answer:
For the gravitational force the formula is P.E. = mgh, where m is the mass in kilograms, g is the acceleration due to gravity (9.8 m / s2 at the surface of the earth) and h is the height in meters. Notice that gravitational potential energy has the same units as kinetic energy, kg m2 / s2.
Step-by-step explanation:
Angel plans to get his new product into Walmart. If he plans to sell 10,000 units to Walmart at $45 each, but Walmart negotiates a 20% discount, how much revenue has Angel lost compared to his original plan?
Answer:
90,000
Step-by-step explanation:
First you want to know how much money Angel plans to earn so you multiply 10,000 * 45 and that is 450,000. Then you find the 20% discount that Walmart negotiated so you turn 20% into a decimal. 20% as a decimal is 0.20 or 0.2. You then multiply 0.2 * 450,000 to get 90,000 which is the amount Walmart is discounting off. And if you need to find how much Angel is getting after the discount, subtract 90,000 from 450,000! :D I hope this helps!!
Explain how to use the distributive property to find an expression that is equivalent to 20+16.
Answer:
Explain how to use the distributive property to find an expression that is equivalent to 20 + 16. First, I would find that the GCF of 20 and 16 is 4. Then, I would divide both 20 and 16 by 4. Last, I would use the distributive property to write the sum as 4(5 + 4).