Answer:
[tex]\displaystyle \lim_{x \to 5} \frac{x^2 - 25}{x + 5} = 0[/tex]
General Formulas and Concepts:
Algebra I
Terms/Coefficients
FactoringCalculus
Limits
Limit Rule [Variable Direct Substitution]: [tex]\displaystyle \lim_{x \to c} x = c[/tex]
Step-by-step explanation:
Step 1: Define
Identify
[tex]\displaystyle \lim_{x \to 5} \frac{x^2 - 25}{x + 5}[/tex]
Step 2: Evaluate
Factor: [tex]\displaystyle \lim_{x \to 5} \frac{x^2 - 25}{x + 5} = \lim_{x \to 5} \frac{(x - 5)(x + 5)}{x + 5}[/tex]Simplify: [tex]\displaystyle \lim_{x \to 5} \frac{x^2 - 25}{x + 5} = \lim_{x \to 5} x - 5[/tex]Limit Rule [Variable Direct Substitution]: [tex]\displaystyle \lim_{x \to 5} \frac{x^2 - 25}{x + 5} = 5 - 5[/tex]Simplify: [tex]\displaystyle \lim_{x \to 5} \frac{x^2 - 25}{x + 5} = 0[/tex]Topic: AP Calculus AB/BC (Calculus I/I + II)
Unit: Limits
27 exponent x divided by 3 is equal to one divided by 81.
27 exponent x/3 = 1/81
we can say exponent as power also
(27 power x) × (3 power -1) = 81 power -1
(3 power 3x) × ( 3 power -1) = 3 power -4
IN MULTIPLICATION WHEN BASES ARE SAME THEN POWERS ARE ADDED
3 power 3x + (-1) = 3 power -4
IN AN EQUATION WHEN BASES ARE EQUAL POWERS ALSO EQUAL
3x +(-1) = -4
3x - 1 = -4
3x = -4 + 1
3x = -3
x = -3/3
x = -1
Answer:
x = -1
Step-by-step explanation:
27 exponent x = [tex]27^x[/tex]
Divided by 3 = [tex]\frac{27^x}{3}[/tex]
Is equal to : [tex]\frac{1}{81}[/tex]
Therefore,
[tex]\frac{27^x}{3} = \frac{1}{81}[/tex]
Cross multiplying :
[tex]27^x \times 81 = 1 \times 3[/tex]
[tex]27^x = \frac{3}{81}[/tex]
[tex]27^x = \frac{1}{27}[/tex]
[tex]27^x = 27^{-1}[/tex]
[tex]x = -1[/tex] [tex][a^x = a^y => x = y][/tex]
Write the numbers in a standard form:
57,900,000
227,900,000
1,427,000,000
Answer:
madarchud
bhag loudeye bsdk
Write 5/14 with denominator 28
Answer:
10
Step-by-step explanation:
if you multiply 14 by 2 you get 28, therefore you have to multiply the numerator by 2 also, which gives you 10
Answer:
10/28
Step-by-step explanation:
5/14 = x/28
See that 28 is 14*2
So multiply 14*2 to get 28, and 5 * 2 to get 10
5 / 14 * 2/2 = 10 / 28
If my answer is incorrect, pls correct me!
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-Chetan K
What transformation(s) were made to the original f(x) = x3 graph?
The function was shifted to the right 3 units.
The function was shifted to the left 2 units.
The function was stretched by a factor of 2.
The function was shifted to the right 2 units.
The function was shifted upward 2 units.
The function was stretched by a factor of 0.5.
Answer: it is c which is the function was stretched by all the factor of 2
hope this help
What is the length of the diagonal of a rectangle that is 12 inches long and 6 inches wide?
A poll is given, showing 60% are in favor of a new building project.
If 7 people are chosen at random, what is the probability that exactly 5 of them favor the new building project?
Round this value however you need to.
==================================================
Explanation:
n = 7 = sample sizep = 0.60 = probability of someone being in favork = 5 = number of people in favorWe use the binomial distribution here. The formula for that is
P(k) = (n C k)*(p)^k*(1-p)^(n-k)
where the n C k refers to the nCr combination formula
[tex]_n C _r = \frac{n!}{r!*(n-r)!}[/tex]
simply replace r with k.
------------------------------
So,
P(k) = (n C k)*(p)^k*(1-p)^(n-k)
P(5) = (7 C 5)*(0.6)^5*(1-0.6)^(7-5)
P(5) = 21*(0.6)^5*(0.4)^(2)
P(5) = 21*0.07776*0.16
P(5) = 0.2612736
This decimal value is exact (meaning there aren't any other digits after that last '6'). Round this value however you need to.
There's roughly a 26.1% chance of getting exactly 5 people to be in favor of the project.
Give an example of a composite number written as a product of primes.
Choose the correct answer below.
A. 60 = 2 x 2 x 15 or 60 = 22 x 15
B. 41 = 1x41
C. 28 = 2x2x7 or 28 = 22x7
Trapezoid A B C D is shifted down and to the left to form trapezoid A prime B prime C prime D prime. Trapezoid A prime B prime C prime D prime is rotated 270 degrees about point B.
What is the final transformation in the composition of transformations that maps pre-image ABCD to image A"B'C"D"?
a translation down and to the right
a translation up and to the right
a 270° rotation about point B'
a 180° rotation about point B'
Answer:
a 270° rotation about point B'
Answer:
C is correct 270°
Step-by-step explanation:
yuh
ᴘʟs ʜᴇʟᴘᴘᴘᴘ ᴍᴇᴇᴇᴇᴇᴇ!!
ɴᴏɴsᴇɴsᴇ = ʀᴇᴘᴏʀᴛ
216 in²
Step-by-step explanation:
The above diagram is a rectangular prism, a three-dimensional shape, having six faces, where all the faces (top, bottom, and lateral faces) of the prism are rectangles such that every two opposite side faces are identical.
Hence we can calculate the surface area of the diagram by multiplying the surface areas of the three faces by 2, and adding them together.
= 2(5 x 4.5) + 2(5 x 9) + 2(4.5 x 9)
= 45 + 90 + 81
= 216 in²
What is the approximate surface area of the figure?
A. 101.3 in²
B. 108 in²
C. 202.5 in²
D. 216 in²
Solution:-Since the base of the prism is a rectangle, the perimeter P of the base is 2(9+4.5) or 27 inches. The area of the base is 9•4.5 or 40.5 square inches. The height is 5 cinches.
[tex]\sf{S=Ph+2B}[/tex]
[tex]\sf{ \: \: \: \: =(27•5)+2(4.5)}[/tex]
[tex]\sf{ \: \: \: \: =135+81}[/tex]
[tex]\sf{ \: \: \: \: =\:}{\color{magenta}{216}}[/tex]
Answers:-The surface area of the figure is 216 square inches. So, the correct option is D.
========================#Hope it helps!
(ノ^_^)ノ
Write an equation of a line that is parallel to 6x - 2y = -3 and passes through the point (1, 3).
Answer:
Step-by-step explanation:
hope this video link be helpfull to you
use the diagram below to find all the missing angles
Answer: M<1=135 M<2=45 M<3=135 M<4=45
Step-by-step explanation:
A baseball is "popped" straight up by a batter with an initial velocity of 32 ft/sec. The height of the ball above ground is given by a function where t is time in seconds after the ball leaves the bat and h(t) is the height in feet above the ground. The batter hit the ball at an original height of 4 feet off of the ground, and the acceleration due to gravity is -16ft/se2
Answer:
The ball reaches the maximum height after 1 seconds
Step-by-step explanation:
Given
[tex]y = -16t^2 + 32t + 4[/tex] --- the function missing from the question
Required
Time to reach maximum height
The time (t) to reach maximum height is calculated using:
[tex]t = -\frac{b}{2a}[/tex]
Where
[tex]y =at^2 + bx + c[/tex]
So, by comparison:
[tex]a = -16[/tex]
[tex]b = 32[/tex]
[tex]c = 4[/tex]
So, we have:
[tex]t = -\frac{b}{2a}[/tex]
[tex]t = -\frac{32}{2*-16}[/tex]
[tex]t = -\frac{32}{-32}[/tex]
[tex]t = \frac{32}{32}[/tex]
[tex]t = 1[/tex]
Every spring the grade four students play the grade five students in softball. The graph shows their scores.
Softball Scores
5
4
Score
2
1
grade 4
grade 5
year 1 year 2 year 3
Year
year 4 year 5
In which year was the difference between the grade four score and the grade five score the greatest?
O A year 1
O B. year 2
Oc. year 3
D. year 4
O E years
Answer:
B
Step-by-step explanation:
answer please answer
Answer:
4 liters
Step-by-step explanation:
8/2 8 divided by 2 is 4 how do I know this, because if its per apple juice then we have to find out what can get me per apple juice, you just basically had to divde it by its own number
Can y’all help me?! :)
Option C.88ft².
Answer:
Solution given:
side 1=19ft
side 2=25ft
height=4ft
now
area =½height (side 1+side 2)
=½*4*(19+25)=88ft²
Answer:
The area of trapezoid is 88 ft ² .
Step-by-step explanation:
The, area of trapezoid is given by
= 1 / 2 ( Base ¹ + Base ² ) × Height
Where,
Base ¹ and Base ² are the length of parrallel side and Height is the perpendicular distance between them.
1 / 2 ( Base ¹ + Base ² ) × Height
Where, given that
Base ¹ = 19 ftBase ² = 25 ft Height = 4 ftSubstitute the values
Area = 1 / 2 × ( 19 ft + 25 ft ) × 4 ft
add the both parallel sides of trapezoid
Area = 1 / 2 × 44 ft × 4 ft
multiply the values , we get
Area = 176 ft ²/ 2
Divide and we get
Area of trapezoid = 88 ft ²
Therefore, the area of trapezoid is 88 ft ².
If f(x) = 2x – 6 and g(x) = 3x + 9, find (f+ g)(x).
Answer:
(f + g)(x) = 5x + 3
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightAlgebra I
Terms/CoefficientsFunctionsFunction NotationStep-by-step explanation:
Step 1: Define
Identify
f(x) = 2x - 6
g(x) = 3x + 9
(f + g)(x) is f(x) + g(x)
Step 2: Find
Substitute in function values: (f + g)(x) = 2x - 6 + 3x + 9Combine like terms: (f + g)(x) = 5x + 3what happens when you divide by 0? i did this problem in my calculator and it broke.
69 + 420 divided by 0
Answer:
ans is 0
Step-by-step explanation:
69 + 420 ÷ 0
489 ÷ 0
0
Answer:
Undefined
Step-by-step explanation:
When you try to divide by 0, your calculator will yield an error because any number (including zero) divided by zero is undefined.
You can think of it like this: if you divide any number by zero, how many times does zero go into that number? An undefined amount of times. If you had zero divided by zero, you'd still run into the issue that any number works:[tex]k\cdot 0=0, k\in \mathbb{R}[/tex]. Because [tex]k[/tex] can be any real number, it is still undefined.
There is an argument for infinity because for function [tex]f(x)=\frac{k}{x}, k\in \mathbb{R}[/tex], as [tex]x[/tex] approaches 0, [tex]f(x)[/tex] approaches infinity:
[tex]\lim_{x\rightarrow 0}f(x)=\infty[/tex]
However, infinity is not a number and should not be treated as such. Undefined is a more precise answer.
Please help, show work! Limits and functions! 85 points!
Answer:
Ok I might misunderstand this but this is what I got ( in order )
the data below shows the number of car thefts in a city for a period of 20 days. complete parts (a) and (b) below.
51, 64, 71, 56, 53, 68, 53, 49, 70, 33
64, 53, 79, 65, 55, 46, 80, 76, 73, 74
a. Draw an ordered stem and leaf plot for the data.
Answer:
Kindly check explanation
Step-by-step explanation:
The oederd data :
33, 46, 49, 51, 53, 53, 53, 55, 56, 64, 64, 65, 68, 70, 71, 73, 74, 76, 79, 80
Stem Leaf
3 | 3
4 | 6 9
5 | 1 3 3 3 5 6
6 | 4 4 5 8
7 | 0 1 3 4 6 9
8 | 0
Key :
3 | 3 = 33
witch value of x makes this eqation true -12x-2(x+9)=5(x+4)
Answer:
x = -2
Step-by-step explanation:
HELLLLLLLPPPPPPPPPPPP
Answer:
250
5:15
true
i already helped you
Answer:
9- 4 hours 30 minutes
10- 250
11- False
The average daily balance of a credit card for the month of November was $700, and the unpaid balance at the end of the month was $1400. If the monthly interest rate is 1.3% of the average daily balance, what is the total balance on the next billing date December 1? Round your answer to the nearest cent. Do not use commas to separate numbers or dollar signs. For example, $5,678.00 should be entered as 5678.00.
9514 1404 393
Answer:
$1409.10
Step-by-step explanation:
The interest is added to the unpaid balance to obtain the total balance.
$700×1.3% + 1400 = $9.10 +1400 = $1409.10
aman şego şego...... ....
sego........ ... sego segó
HELPP PLEASEE!!! FIRST ONE TO ANSWER GETS BRAINLEST!!!!
A square pyramid is shown. What is the surface area of the pyramid? Enter your answer in the box.
4 cm
3 cm
3 cm
cm2
Answer:
33cm squared
Step-by-step explanation:
Answer:
33cm
Step-by-step explanation:
Sherrie travels 120 miles in 3 hours. Find the unit rate of speed missing number.
Answer:
The unit rate of speed is 40 miles per hour.
Step-by-step explanation:
Since Sherrie travels 120 miles in 3 hours, to find the unit rate of speed the following calculation must be performed:
3 = 120
1 = X
(1 x 120) / 3 = X
120/3 = X
40 = X
Therefore, the unit rate of speed is 40 miles per hour.
PLZ HELP ASAP!!!!!!!!!!!!!!
Answer:
AB = 5√55
Step-by-step explanation:
Part 1 = AD = 25
Hypotenuse = AC = 55
Leg 1 = AB = x
To find AB, apply the leg rule which is:
Hypotenuse/leg 1 = leg 1/part 1
Plug in the values
55/x = x/25
Cross multiply
x*x = 55*25
x² = 1,375
x = √1,375
x = 5√55
AB = 5√55
Question
The angles in
triangle are such that one angle is 100 degrees more than the smallest angle, while the third angle is 2 times
as large as the smallest angle. Find the measures of all three angles.
9514 1404 393
Answer:
20°, 120°, 40°
Step-by-step explanation:
Let s represent the smallest angle. Then the largest is (100+s) and the third angle is (2s). The sum of angles in a triangle is 180 degrees, so we have ...
s + (100+s) +(2s) = 180
4s = 80 . . . . . . . . . . subtract 100
s = 20 . . . the smallest angle
100+s = 120 . . . the largest angle
2s = 40 . . . the third angle
The angle measures are 20°, 120°, and 40°.
who is the president of Uganda
Answer: Yoweri Museveni
☆彡HannaWhich statement is true?
Answer:
second 1
Step-by-step explanation:
i literally just had that question
If 14 people are shorter than Alice, 12 people are taller than Bob, and 4 people are shorter than Alice and taller than Bob, how many people are there?
Answer:
THERE IS A LOT OF PEOPLE