Answer:
The answer is below
Step-by-step explanation:
The equation for a linear function is given as:
y = mx + b
where m is the slope of the function (that is the rate of change), b is the initial value of y when x is 0.
Given that the function where x represent the number of years since 1960 and y is the cost in dollar as:
[tex]f(x)=\frac{2.14}{55}x+0.31[/tex]
a) In the year 1960, that is x = 0, the cost of a gallon of gas is given as:
[tex]f(0)=\frac{2.14}{55}(0)+0.31\\\\f(0)=\$0.31[/tex]
b) From the function [tex]f(x)=\frac{2.14}{55}x+0.31[/tex], we can see that the rate of change is 2.14/55. Therefore, the cost increase each year by 4 cents per year.
[tex]\lim_{h \to \116} x-16/\sqrt{x} -4[/tex]
What is the limit?
Answer:
[tex] \displaystyle 8[/tex]
Step-by-step explanation:
we would like to compute the following limit
[tex] \displaystyle \lim_{x \to 16} \left( \frac{x - 16}{ \sqrt{x} - 4} \right) [/tex]
if we substitute 16 directly we'd end up
[tex] \displaystyle = \frac{16 - 16}{ \sqrt{16} - 4} [/tex]
[tex] \displaystyle = \frac{0}{ 0} [/tex]
which isn't a good answer now notice that we have a square root on the denominator so we can rationalise the denominator to do so multiply the expression by √x+4/√x+4 which yields:
[tex] \displaystyle \lim_{x \to 16} \left( \frac{x - 16}{ \sqrt{x} - 4} \times \frac{ \sqrt{x} + 4 }{ \sqrt{x} + 4 } \right) [/tex]
simplify which yields:
[tex] \displaystyle \lim_{x \to 16} \left( \frac{(x - 16)( \sqrt{x} + 4)}{ x - 16} \right) [/tex]
we can reduce fraction so that yields:
[tex] \displaystyle \lim_{x \to 16} \left( \frac{ \cancel{(x - 16)}( \sqrt{x} + 4)}{ \cancel{x - 16} } \right) [/tex]
[tex] \displaystyle \lim _{x \to 16} \left( \sqrt{x } + 4\right) [/tex]
now it's safe enough to substitute 16 thus
substitute:
[tex] \displaystyle = \sqrt{16} + 4[/tex]
simplify square root:
[tex] \displaystyle = 4 + 4[/tex]
simplify addition:
[tex] \displaystyle = 8[/tex]
hence,
[tex] \displaystyle \lim_{x \to 16} \left( \frac{x - 16}{ \sqrt{x} - 4} \right) = 8[/tex]
if f(x)=3x+10, find f(4)?
a. f(4)=17
b. f(4)=22
c. 22
d. f(4)=12
Answer:
f(4) =22
Step-by-step explanation:
f(x)=3x+10
Let x=4
f(4)=3*4+10
Multiply
f(4) =12+10
Add
f(4) =22
Answer:
[tex]f(4 )= 22[/tex]
Step-by-step explanation:
[tex]f(x) = 3x + 10[/tex]
[tex]f(4) = 3(4) + 10[/tex]
[tex]f(4) = 3 \times 4 + 10[/tex]
[tex]f(4) = 12 + 10[/tex]
[tex]f(4 )= 22[/tex]
Hope it is helpful...please help me and thank you.
Answer:
[tex]482.5\:\mathrm{in^2}[/tex]
Step-by-step explanation:
The area of the figure consists of a rectangle with a triangle removed from the corner of it. Therefore, the area of the composite of the figure can be found by subtracting the area of the triangle from the area of the rectangle.
Area of the rectangle: [tex]25\cdot 20=500\:\mathrm{in^2}[/tex]
Area of the triangle: [tex]\frac{1}{2}\cdot 5\cdot 7=17.5\:\mathrm{in^2}[/tex]
Thus, the area of the figure is [tex]500-17.5=\boxed{482.5\:\mathrm{in^2}}[/tex]
What is the ratio of the people who prefer vanilla to the people who prefer strawberry?
-5/4
-4/5
-3/2
-2/3
Answer:
4/5
Step-by-step explanation:
From the above question, we are given the number of people who like a particular flavor.
The number of people who like:
Vanilla = 36
Strawberry = 45
Therefore, the ratio of the people who prefer vanilla to the people who prefer strawberry is written as
Vanilla : Strawberry
= 36:45
= 4:5
= 4/5
Therefore, option B = 4/5 is the correct option
What are the zeros and x-intercepts of this quadratic function?
y
Select two answers: one for the zeros and one for the x-intercepts.
A. x-Intercepts: (-3,0) and (2.0)
B. X-Intercepts: (0, -3) and (0,2)
C. Zeros: -3 and 2
The answer is ⇒C. Zeros: -3 and 2
A. x-intercepts: (-3,0) and (2,0).
What are zeros & x-intercepts of quadratic function?The zero of the function is where the y-value is zero.
The x-intercept is where the graph crosses the x-axis.
Here, in graph we have,
at (-3,0) and ( 2,0) the quadratic crosses the x-axis.
And, at -3 & 2 the value of y is zero.
Hence, the answer is ⇒C. Zeros: -3 and 2
A. x-intercepts: (-3,0) and (2,0).
To learn more on zeros & x-intercepts of quadratic function click:
https://brainly.com/question/28822774
#SPJ2
Help plzzz..........
Answer:
39
Step-by-step explanation:
Sufure area of cylinder
Answer:
1733.28 Square inches
Step-by-step explanation:
2(3.14)(6^2)+2(3.14)(6)(40)= 1733.28
r = radius (which is 6 in. Because radius is half of circumference and the circumference is 12 in.)
h = height of cylinder (which is 40 in. Shown in the diagram)
Answer:
1733.28 square inches
Step-by-step explanation:
Hi there!
What we know:
The diameter of the base (12 in.)The height of the cylinder (40 in.)The formula for the surface area of a cylinder: [tex]SA=2\pi r^2+2\pi rh[/tex]1) Determine the radius of the base (r)
The radius is equal to half the diameter. Given the diameter 12 in., we know that the radius would be 6 in.
Radius = 6
2) Plug all values into the SA equation and solve
[tex]SA=2\pi r^2+2\pi rh\\SA=2\pi (6)^2+2\pi (6)(40)\\SA=2\pi (36)+2\pi (240)\\SA=72\pi+480\pi\\SA=552\pi\\SA=552(3.14)\\SA=552(3.14)\\SA=1733.28[/tex]
Therefore, the surface area of the cylinder is 1733.28 square inches.
I hope this helps!
can someone please help me with question 1? I will give brainliest to first answer! Thank you so much! I really appreciate anyone who helps
Answer:
49 in the first box and 7 in the second one
25 in the 3rd box and 5 in the 4th
if GJ = 11a and IJ = a + 10, find the value of a that makes quadrilateral FGHI a parallelogram
Note: Consider J is the intersection point of diagonals of quadrilateral FGHI.
Given:
[tex]GJ=11a[/tex]
[tex]IJ=a+10[/tex]
To find:
The value of a that makes quadrilateral FGHI a parallelogram.
Solution:
We know that the diagonals of a parallelogram bisect each other.
If FGHI is a parallelogram and J is the intersection point of diagonals, then
[tex]GJ=IJ[/tex]
[tex]11a=a+10[/tex]
[tex]11a-a=10[/tex]
[tex]10a=10[/tex]
Divide both sides by 10.
[tex]a=\dfrac{10}{10}[/tex]
[tex]a=1[/tex]
Therefore, the required value of a is 1 units.
How much total money will Kiara have to pay back at the end of the 9 years?
Answer:
a= $29,505. it. is useful answer
I need help with this problem pls help!
Evaluate expressions- if r=45 and t=9 what is the value of the following expression?
A.36
B.75
C.80
D.66
Answer:
[tex]d. \: \: 66[/tex]
Step-by-step explanation:
[tex]r + 63 \div t \times 3[/tex]
[tex]45+63÷9 \times 3[/tex]
[tex]45+7 \times 3[/tex]
[tex]45 + 21[/tex]
[tex]66[/tex]
Hope it is helpful...80 POINTS HURRY ILL GIVE BRANLIEIST!!!
A landscape architect built a square playground. The outside edges of the playground measure 3x meters. The playground has an area of 8100 m^2. How much fencing is needed to fully enclose the playground?
Answer:
360 meters
Step-by-step explanation:
[tex]\sqrt{8100}[/tex] = 90
one edge = 90 meters
90 x 4 = 360
360 meters
gabby volunteers at an animal shelter. Last month she volunteered 1 3/4 hours on each of 3 Saturday. She also volunteered 3/4 hour on 4 Wednesday evenings. How many hours of volunteer work did Gabby put in last month.
Answer:
8 1/4 hoursStep-by-step explanation:
Total hours:
3(1 3/4) + 4(3/4) = 3 + 3*3/4 + 3 = 6 + 9/4 = 6 + 2 1/4 = 8 1/4 hoursHelp ASAP. I will give branliest.
Answer:
( 1, 3)
Step-by-step explanation:
4x+y=7 * 2 = 8x + 2y = 14
8x + 2y = 14
- 3x + 2y = 9
--------------------
5x = 5
x = 1
Now substitute x into the equation for 1
8*(1) + 2y = 14
8 + 2y = 14
2y = 6
y = 3
Sunaina had three pizzas. She shared the pizzas with her friends. Each of them ate
many friends ate 3/7 of a pizza. How many friends ate the pizza
Answer:
6 friends
Step-by-step explanation:
Take 1/7 multiply by 5/6
9514 1404 393
Answer:
7 friends
Step-by-step explanation:
3 pizzas will give 3/7 of a pizza to each of ...
3/(3/7) = 3 · 7/3 = 7 . . . friends
7 friends ate the pizza.
_____
We assume that Sunaina and her 6 friends constitute 7 friends.
1) Find 5 points on the line y = 3/5 x - 4 by picking 5 x values, plugging in, and getting 5 y values. You must pick x
values that result in INTEGER values for y. Show every step of the process, working vertically.
2) Graph the line from problem 1. You must use a straightedge on axes and line. Each line on the graph paper is one
unit. Put arrowheads on the line. Do NOT put numbers or hash marks on your graph. Show your 5 points clearly
3) Using the formula and working vertically, firid the slope between the points (-2,5) and (6,-7).
4) Identify the slope and y-intercept of the line y = -4/3 x + 4
5) Graph the line from problem #4 by plotting the y-intercept, and then using the slope to get a second point. All rules
from problem 2 apply here as well.
Find the area of the rhombus.
48 cm2
14 cm2
96 cm2
24 cm2
Answer:
96 cm^2
Step-by-step explanation:
the diagonal bisect in the point of intersection, so their length is 12 cm and 16 cm
Area = (12 * 16)/2 = 96 cm^2
Answer:
24 cm^2
Step-by-step explanation:
rhombus -.-
Our school is selling t-shirts and sweatshirts as a fundraiser . One student buys 2 t-shirts and 2 sweatshirts for $26 . Another student buys 1 t-shirt and 3 sweatshirts for $33 . This situation can be modeled by the system of equations below .
Answer:
The value of each T-shirt is $ 3 and the value of each sweatshirt is $ 10.
Step-by-step explanation:
Given that our school is selling T-shirts and sweatshirts as a fundraiser, and one student buys 2 Tt-shirts and 2 sweatshirts for $ 26, while another student buys 1 T-shirt and 3 sweatshirts for $ 33, to determine the value of the T-shirts and sweatshirts the following calculation must be made:
2X + 2Y = 26
X + 3Y = 33
Y - X = 7
2 x 3 + 2 x 10 = X
6 + 20 = X
26 = X
Therefore, the value of each T-shirt is $ 3 and the value of each sweatshirt is $ 10.
Express the location of the point on the number line as both a fraction and a decimal. A number line that has moving left to right, a starting mark at 0, nine unlabeled tick marks, a tick mark labeled one-tenth, nine unlabeled tick marks, a tick mark labeled two-tenths, nine unlabeled tick marks, and an ending tick mark at three-tenths. There is a dot at the ninth tick mark to the right of one-tenth.
Answer:
9 / 100 ; 0.09
Step-by-step explanation:
From the line plot given :
The number of unlabeled ticks marks between any two labeled tick marks can be obtained by :
(Difference between any two successive labeled tick marks / number of tick marks)
Picking the labeled tick marks, 0 and 1/10
(1/10 - 0) / 10
1 / 10 ÷ 10
1/ 10 * 1 / 10 = 1 / 100
To find the marked point : (this is tick mark 9 from 0) ;
Number of ticks * distance between ticks
Location of marked tick = 1 / 100 * 9 = 9 / 100
Decimal equivalent = 9/100 = 0.09
What is m ZPHJ?
L
0 100°
140°
0 120°
M
200
K
H
O 140°
0 160°
Р
Answer:
o 140. age125 M so that you answer
Stefan sells Jin a bicycle for $149 and a helmet for $19. The total cost for Jin is 140% of what Stefan spent originally to buy the bike and helmet. How much did Stefan spend originally? How much money did he make by selling the bicycle and helmet to Jin?
Answer:
$120
$48
Step-by-step explanation:
total amount Jin spent = cost of bicycle + cost of helmet
$149 + $19 = $168
This equation can be derived from the question :
1.4 x t = 168
where t = total cost Stephan spent on the helmet and bicycle
t = 168/1.4 = $120
Profit = selling price - cost price
$168 - $120 = $48
pls help pls pls pls
Answer:
12/4 i really hope this helps i took the test and got a 100
Step-by-step explanation:
PLEASE HELP! Pam bought 6.5 pounds of apples for $16.19. If the equation 6.5x=16.19 models the situation, what does the variable stand for?
A. The weight of one apple
B. The cost of 1 pound of apples
C. The number of pounds of apples
D. The total cost of the apples
A scale drawing of a school playground in the shape of a rectangle is shown. What is the area in square meters of the playground
Answer:
b
Step-by-step explanation:
8×19= 152
1 : 4.5
152×4.5=684
How many fl oz are in 4 table spoons
Answer:
2 fl oz
Step-by-step explanation:
2 tbsp = 1 fl oz. Simply double.
Can someone please help with this ? Thanks
What is the volume of this Sphere?
8 pi cm3
16 pi cm3
27 pi cm2
36 pi cm2
Answer:
V = 36 pi cm^3
Step-by-step explanation:
The volume of a sphere is given by
V = 4/3 pi r^3 where 4 is the radius
V = 4/3 pi(3)^3
V = 36 pi cm^3
which graph is a function of x?
Answer:the one to the left
Step-by-step explanation:
helppppppppppppppppppppppp
Answer:
gotta be answer A
Step-by-step explanation:
you can search up f(x) = square root of x