Given:
Consider the given function is:
[tex]f(x)=5^x+1[/tex]
To find:
The average rate of change between x = 0 and x = 4.
Solution:
The average rate of change of a function f(x) over the interval [a,b] is:
[tex]m=\dfrac{f(b)-f(a)}{b-a}[/tex]
We have,
[tex]f(x)=5^x+1[/tex]
At [tex]x=0[/tex],
[tex]f(0)=5^0+1[/tex]
[tex]f(0)=1+1[/tex]
[tex]f(0)=2[/tex]
At [tex]x=0[/tex],
[tex]f(4)=5^4+1[/tex]
[tex]f(4)=625+1[/tex]
[tex]f(4)=626[/tex]
Now, the average rate of change between x = 0 and x = 4 is:
[tex]m=\dfrac{f(4)-f(0)}{4-0}[/tex]
[tex]m=\dfrac{626-2}{4}[/tex]
[tex]m=\dfrac{624}{4}[/tex]
[tex]m=156[/tex]
Hence, the average rate of change between x = 0 and x = 4 is 156.
A manufacturer determines that the cost of making a computer component is $4.131313. Write the repeating decimal cost as a fraction and as a mixed number. The cost written as a fraction is
Answer:
The cost written as a fraction is --> 4 13/99
Step-by-step explanation:
Let x = 4.131313
100x = 413.1313
So, 100x - x = 99x
100(4.131313) - 4.131313 = 408.99, or 409 when rounded
x = 409/99
x = 4 13/99
1. What is the perimeter of the rectangle?
Answer:
32
Step-by-step explanation:
A = l*w
55 = 5*w
55 /5 = 5w/5
11 = w
The perimeter is
P =2(l+w)
P = 2(5+11)
=2(16)
= 32
Answer:
32Units
Step-by-step explanation:
We know Area of rectangle=LENGTH×BREADTH
Here, breadth and Area given
55=5×L
L=11(value of length=11)
Perimeter=2(L+B)
32=2(5+11).
A pet shop owner buys large bags of dry cat food that contain 10kg. He wants to make up bags that contain 200g of cat food. How many 200g bags of cat food can he make from one large bag?
Answer:
50 bags
Step-by-step explanation:
1 kg = 1000 grams
10 kg * 1000g/ 1kg = 10000 g
Divide 10000 grams by 200 g
10000g / 200g = 50
Round off all these
1) 378811,
2) 267988,
3) 250260,
4) 196596,
5) 193171
to the nearest ten thousand
Answer:
1. 380,0002. 270,0003. 250,0004. 200,0005. 190,000[tex]\tt{ \green{P} \orange{s} \red{y} \blue{x} \pink{c} \purple{h} \green{i} e}[/tex]
What is the area of a rectangle whose length is (5x + 2)cm and whose width is (3x + 1)cm?
Answer:
[tex]\displaystyle A = 15x^2 + 11x + 2\text{ cm}^2[/tex]
Step-by-step explanation:
We are given that the length and width of a rectangle is given by:
[tex]\ell = (5x + 2)\text{ cm} \text{ and } w = (3x+1)\text{ cm}[/tex]
And we want to find the area of the rectangle.
Recall that the area of a rectangle is given by:
[tex]\displaystyle A = w\ell[/tex]
Substitute:
[tex]A = (3x+1)(5x+2)[/tex]
Expand and simplify:
[tex]\displaystyle \begin{aligned}A &= 5x(3x+1) + 2(3x+1) \\ &= (15x^2+5x)+(6x+2) \\ &= (15x^2)+(5x+6x)+(2) \\ &= 15x^2 + 11x +2 \end{aligned}[/tex]
Hence, the area of the rectangle is:
[tex]\displaystyle A = 15x^2 + 11x + 2\text{ cm}^2[/tex]
If there are:
6 red marbles
10 yellow marbles
5 green marbles
and 1 blue marble What is the probability of picking 1 blue marble and 1 green marble?
(Once a marble is chosen it is NOT put back into the box).
(Write your answer in the form of a decimal, round to 2 places).
Answer:
total number of marble=22
probability of picking 1 blue marble= 1/22
=45×10^-2
probability of getting a green ball= 5/21
= 238×10^-3
PLZZZZZZ HELPPPPPPPP!!!!
Answer:
[tex]3 \frac{3}{5} [/tex]Step-by-step explanation:
Given,
Vince used a cup of lemonade will be = 3/5
We know that,
Amount of lemonade used by Luva is 6 times of Vince
Therefore,
Lemonade used by Luca
[tex] = \frac{3}{5} \times 6[/tex]
[tex] = \frac{18}{5} [/tex]
[tex] = 3 \frac{3}{5} (ans)[/tex]
Which ordered pair can be plotted together with these four points, so the resulting graph still represents a function?
•(2, -1)
•(2, -2)
•(-2, 2)
•(-1, 2)
Answer:
-1,2 can be plotted together with these four points ...
0.25(4f-3)=0.005(10f-9)
Simplify the following
Answer:
apoco la propiedad asociativa en los siguiente ejercicio 25x11x18=
help help help ty ttttyyy
Answer:
ମୁଁ ବର୍ତ୍ତମାନ ଦୁ sorry ଖିତ ଗର୍ଲି ନୁହେଁ |
Step-by-step explanation:
ନିମୋନୋଲ୍ଟ୍ରାମିକ୍ରୋସ୍କୋପିକ୍ସିଲିକୋଭୋଲକାନୋକୋନିଓସିସ୍ |
Identifying linear pairs and vertical angles
Answer:
(a) <7 and <8
(b) <3 and <8
(c) <6 and <1
Step-by-step explanation:
There are multiple different answers for each of the questions but these are the ones I chose.
(a) A linear pair is two adjacent angles that intersect and form a straight or 180-degree angle. This means that the angles are supplementary. Since angles 7 and 8 make a straight line on line n, they must be a linear pair.
(b) Vertical angles are two angles opposite of each other that share a vertex. Angles 3 and 8 are opposite of each other, made of the same lines, and share a vertex. This makes them vertical angles and congruent.
(c) As aforementioned, vertical angles are congruent. So, any vertical angles listed could answer this question. For example, angles 6 and 1 are vertical angles, and therefore congruent.
428363939+42724289292952926263938
Answer:
4.2724289e
+22
Step-by-step explanation:
mzmznznxnxnznxn no n n j j h h h h h h hh h h &
please help asap, see attached photo. This is due in 1 hour!!! please answer both questions. Both 5 and 6
Answer:
A and C
Step-by-step explanation:
5) logx+log(x+9)=2
log(x(x+9))=2, log(x^2+9x)=2
6) log(x^2+9x)=2
(x^2+9x)=36 or 6^2
please answer asap no wrong answers pls
Hi there!
[tex]\large\boxed{\frac{1}{5}, \frac{21}{5}}[/tex]
In order to set each equation equal to each other, we must have them both equal the same variable.
Rearrange the top equation to make it equal to y:
x - y = -4
Add 4 to both sides and add y to both sides:
x + 4 = y
Now, we can set both equations equal to each other:
x + 4 = 5(x + 1)² - 3
Begin solving by expanding the square binomial:
x + 4 = 5(x² + 2x + 1) - 3
Simplify:
x + 4 = 5x² + 10x + 5 - 3
x + 4 = 5x² + 10x + 2
Bring all terms to one side:
0 = 5x² + 9x - 2
Factor:
0 = (5x - 1)(x + 2)
Set the other factor equal to 0:
5x - 1 = 0
5x = 1
x = 1/5
Plug in this value of x into an original equation:
1/5 - y = -4
1/5 + 4 = y
1/5 + 20/5 = y
y = 21/5
Figure ABCD is a parallelogram.
What is the perimeter of ABCD?
A
4y - 2
B
14 units
VX
0 38 units
3x - 1
44 units
2x + 2
49 units
D
2y + 6
С
Answer:
3rd option, 44 units
Step-by-step explanation:
3x-1 = 2x+2
or, x = 3
so each side, 3×3-1 = 8
4y-2 = 2y+6
or, y = 4
so each side, 4×4-2 = 14
so perimeter
= 2(8+14)
= 44 units
Answered by GAUTHMATH
James wants to tile his floor using tiles in the shape of a trapezoid. To make the pattern a little more interesting he has decided to cut the tiles in half along the median. The top base of each tile is 12 inches in length and the bottom base is 16 inches. How long of a cut will John need to make so that he cuts the tiles along the median? O A. 2 inches B. 4 inches O C. 14 inches O D. 28 inches
Answer:
Choice C. 14 inches
Step-by-step explanation:
Middle between 12 and 16 inches.
please help asap don't give me the wrong answers.
Answer: 340cm^
Step-by-step explanation:
you have to multiply them to find out
Help please asap :(......
3(y+11) y=12
3(12+11)=?
12+11=23
3x23=69
Answer = 69
I hope this helps :)
Alice stand at point A and looks at the top of a 17.8 m tree TB, such that her line of sight makes an angle 38° with the horizontal. The height of her eye level is 1.5 m. Find the horizontal distance AB between Alice and the tree.
Answer:
Step-by-step explanation:
let the horizontal distance be x
(17.8-1.5)/x = tan 38
or x = 16.3/tan38
or x = 20.863
Will Mark Brainlest helpppp plssss
Answer:
C = [tex]\left[\begin{array}{ccc}-2&-4\\-1&1\\\end{array}\right][/tex]
Step-by-step explanation:
A = B+ C then
C = A - B
C = [tex]\left[\begin{array}{ccc}2&-5\\-1&4\\\end{array}\right][/tex] - [tex]\left[\begin{array}{ccc}4&-1\\0&3\\\end{array}\right][/tex] (subtract corresponding elements )
= [tex]\left[\begin{array}{ccc}2-4&-5-(-1)\\-1-0&4-3\\\end{array}\right][/tex]
= [tex]\left[\begin{array}{ccc}-2&-4\\-1&1\\\end{array}\right][/tex]
Hi! i need some help with this question, you don't need to help with the 2 parts, just any 1. Thank you!!
y varies is directly as 3x – 4, and y = 33 when x = 5
Find:
a) y when x = 2
b) x when y = 15
Answer:
See explanation
Step-by-step explanation:
y = k * (3x - 5)
Where,
k = constant of proportionality
y = 33 when x = 5
y = k * (3x - 5)
33 = k * (3 * 5 - 5)
33 = k * (15 - 5)
33 = 15k - 5k
33 = 10k
k = 33/10
k = 3.3
a) y when x = 2
y = k * (3x - 5)
y = 3.3(3 * 2 - 5)
= 3.3(6 - 5)
= 3.3(1)
y = 3.3
b) x when y = 15
y = k * (3x - 5)
15 = 3.3(3x - 5)
15 = 9.9x - 16.5
15 + 16.5 = 9.9x
31.5 = 9.9x
x = 31.5/9.9
x = 3.18
Please help me.
List the sides of MNP in ascending order:
m< M = 15, m < N= 75
Answer:
Take a look at this: https://brainly.com/question/14269575?referrer=searchResults
Step-by-step explanation:
a 9-ft roll of wrapping paper costs $6.48, what is the price per inch?
Answer: $0.06 per inch
Concept:
When encountering questions that ask for unit price, follow the statements to get the answer. For example, this question asks the price per inch. Therefore, in the actual answer, use the total price given divided by the number of inches.
Solve:
Price = $6.48
Inch = 9 × 12 = 108 in
1 ft = 12 inchPrice / Inch = 6.48 / 108 = $0.06 per inch
Hope this helps!! :)
Please let me know if you have any questions
"A parabola has the equation y=3x^2+ 6x- 12 . What are the coordinates of the vertex? (You must solve by factoring)!!!!!" I NEED THE ANSWER TO THIS FAST WITH STEPS I'm a grade 10 academic student by the way
y = 3x ^ 2 + 6x- 12
(a=3; b=6; c= -12)
• Ta có Δ=b^2 -4ac
= 6^2 -4*3*( -12)
=180
• X= (-b+√Δ)/2a
≈ 3.2
• X= (-b-√Δ)/2a
≈ -3.2
Khi đó: y= 948/25
Và: y= -12/25
Vậy : A(3.2: 948/25)
B(-3.2; -12/25)
Step-by-step explanat bion :
What is 200% of 20? Thanks!
Answer:
40
Step-by-step explanation:
200% x 20
200/100 x 20
(200 ÷ 100) x 20
200 x 20 ÷ 100
4,000 ÷ 100 = 40
find the missing length indicated
Answer:
240
Step-by-step explanation:
We are given a right triangle. Based on the leg rule, the following equation shows how the length of a leg in a right triangle relates with the segments connected to the hypotenuse:
Hypotenuse/leg = leg/part
Where,
Hypo = 400
Leg = x
Part = 144
Substitute
400/x = x/144
Cross multiply
400*144 = x*x
57,600 = x²
√57,600 = x
240 = x
x = 240
If d= the number of dogs ,which variable expression represents the phase below? The sun of the number of dogs and the 6 cats
Answer:
d + 6
Step-by-step explanation:
Given that :
Number of dogs = d
The sum of the number of the number of dogs and 6 cats is :
This is a straightforward question :
We take the sum of d and 6
Hence, we have
d + 6
The midpoint of a segment is (6,−4) and one endpoint is (13,−2). Find the coordinates of the other endpoint.
A. (20, -6)
B. (-1, 0)
C. (-1, -6)
D. (20, 0)
Answer:
(-1,-6)
Step-by-step explanation:
(13 + x)/2 = 6
13+x= 12
x = -1
~~~~~~~~~~~~~~~
(-2 + y ) / 2 = -4
-2 + y = -8
y = -6
The coordinates of the other endpoint will be (-1,-6). The correct option is C.
What is the midpoint of the line?Divide the measurement of the distance between the two end locations by 2. The middle of that line is located at this separation from either end.
A coordinate plane is a 2D plane that is formed by the intersection of two perpendicular lines known as the x-axis and y-axis.
Given that the midpoint of a segment is (6,−4) and one endpoint is (13,−2).
The x- coordinate will be calculated as:-
(13 + x)/2 = 6
13+x= 12
x = -1
The y-coordinate will be calculated as:-
(-2 + y ) / 2 = -4
-2 + y = -8
y = -6
Therefore, the coordinates of the other endpoint will be (-1,-6). The correct option is C.
To know more about midpoints of the line follow
https://brainly.com/question/24431553
#SPJ2
Describe the pattern in the following sequence and list the next three terms:
4, 8, 16, 32, ...
I’ll mark brainliest! Please help me
[tex]x + 0.25 = -0.25[/tex]
Answer:
x = -0.5
Step-by-step explanation:
x + 0.25 = -0.25
x = -0.25 - 0.25
x = -0.5