The solution to the limit expression [tex] \lim_{x \to 1} \frac{x^2 - 25}{x - 5} [/tex] is 6
The limit expression is given as:
[tex] \lim_{x \to 1} \frac{x^2 - 25}{x - 5}[/tex]
Express 25 as 5^2
[tex] \lim_{x \to 1} \frac{x^2 - 5^2}{x - 5}[/tex]
Express the numerator as the difference of two squares
[tex] \lim_{x \to 1} \frac{x^2 - 25}{x - 5} = \lim_{x \to 1} \frac{(x - 5)(x +5)}{x - 5}[/tex]
Evaluate the quotient
[tex] \lim_{x \to 1} \frac{x^2 - 25}{x - 5} = \lim_{x \to 1} (x +5)[/tex]
Remove bracket
[tex] \lim_{x \to 1} \frac{x^2 - 25}{x - 5} = \lim_{x \to 1} x +5\\ [/tex]
Substitute 1 for x
[tex] \lim_{x \to 1} \frac{x^2 - 25}{x - 5} = 1 +5[/tex]
[tex] \lim_{x \to 1} \frac{x^2 - 25}{x - 5} = 6[/tex]
Hence, the solution to the limit expression [tex] \lim_{x \to 1} \frac{x^2 - 25}{x - 5} [/tex] is 6
Read more about calculus at:
https://brainly.com/question/15182568
What percent of 111 is 94?
Answer:
I’d say 84.68%
LAST ATTEMPT MARKING AS BRAINLIEST!! ( write a rule to describe each transformation)
Answer:
See below
Step-by-step explanation:
Dilation of 4
Z (0, -1) Z' (0, -4)
X (1, -1) X' (4, -4)
x+3x+3y+3z=21
Find the value of X.
Answer:
[tex] x = \frac{21 - 3y - 3z}{4} [/tex]Step-by-step explanation:
Question:-To find value of xEquation:-x + 3x + 3y + 3z = 21Solution:-=> x + 3x + 3y + 3z = 21
[On adding like terms x and 3x]=> 4x + 3y + 3z = 21
[On subtracting both sides with 3y]=> 4x + 3y + 3z - 3y = 21 - 3y
[On Simplification]=> 4x + 3z = 21 - 3y
[On subtracting both sides with 3z]=> 4x + 3z - 3z = 21 - 3y - 3z
[On Simplification]=> 4x = 21 - 3y - 3z
[On dividing both sides with 4][tex] = > \frac{4x}{4} = \frac{21 - 3y - 3z}{4} [/tex]
[On Simplification][tex] = > x = \frac{21 - 3y - 3z}{4} (ans)[/tex]
Given :
x + 3x + 3y + 3z = 21To Find :
The value of xSolution :
[tex]\qquad { \dashrightarrow \: { \sf{x + 3x + 3y + 3z = 21}}}[/tex]
Adding the like terms :
[tex]\qquad { \dashrightarrow \: { \sf{4x + 3y + 3z = 21}}}[/tex]
Transposing 3y to the other side which then becomes negative :
[tex]\qquad { \dashrightarrow \: { \sf{4x + 3z = 21 - 3y}}}[/tex]
Now, Transposing 3z to the other side which then becomes negative :
[tex]\qquad { \dashrightarrow \: { \sf{4x = 21 - 3y - 3z}}}[/tex]
Dividing both sides by 4 :
[tex]\qquad { \dashrightarrow \: { \sf{ \dfrac{4x}{4} = \dfrac{21 - 3y - 3z}{4} }}}[/tex]
[tex]\qquad { \dashrightarrow \: { \sf{{x} = \dfrac{21 - 3y - 3z}{4} }}}[/tex]
Therefore, the value of x = 21 – 3y – 3z/4
HELP!? ✋
What strategies help prevent cancer?
Select all that apply.
Question 8 options:
using sunscreen
avoiding tobacco
getting enough sleep
eating a healthy diet
30=2y+16 simplify your answer as much as possible
Answer:
y=7
Step-by-step explanation:
PrOblem 1: Find the slope of the line containing the points: (3,-5) and (-1, -2)
Problem 2: Find the x and y intercepts of the line: 2x – 3y = 12
Problem 3: Graph the line x-4y=8
Answer:
1) -3/4
2) (6, 0), (0, -4)
3) connect (0,-2) and (8,0) together
Step-by-step explanation:
1) (-2) - (-5) / (-1) - 3 = -3/4
2) x = 0 -3y=12 y = -4, y= 0 2x = 12 x = 6, x intercept = (6, 0) y intercept = (0, -4)
3) x - 4y = 8 this could be written as y = x/4 - 2 and y intercept is (0, -2) and x intercept is (8, 0) so connect these points together and make a line
#1
m=y2-y1/x2-x1m=-2+5/-1-3m=3/-4#2
Inetercept form x/a+y/b=1
2x-3y=122/12x-3/12y=12/12x/6-y/4=1x inetercept at 6 and y intercect at -4
#3
Graph attached
Please answer the file question.
Answer:
WT = 63
Step-by-step explanation:
Given Δ SDE is similar to Δ SWT then the ratio of corresponding sides are in proportion, that is
[tex]\frac{WT}{DE}[/tex] = [tex]\frac{ST}{SE}[/tex] , substitute values
[tex]\frac{5x+3}{56}[/tex] = [tex]\frac{4x-3}{40}[/tex] ( cross- multiply )
56(4x - 3) = 40(5x + 3) ← distribute parenthesis on both sides
224x - 168 = 200x + 120 ( subtract 200x from both sides )
24x - 168 = 120 ( add 168 to both sides )
24x = 288 ( divide both sides by 24 )
x = 12
Then
WT = 5x + 3 = 5(12) + 3 = 60 + 3 = 63
16. Write an equation for the line that is parallel to the given line and passes through the given
(1 point)
point
y = 3x+7; (2, 10)
A. Y=3x + 11
B. y = 3x + 4
C. y=-3x+4
D. y=(-1/3)x+ 4
Answer:
Step-by-step explanation:
Parallel lines have identical slopes
y = 3x + b
add in the desired point
10 = 3(2) + b
b = 4
B. y = 3x + 4
Suppose that the market price for a bottle of vitamins is $1.61 and that at that price the total market quantity demanded is
255,340,000 bottles. How many firms will there be in this industry?
firm(s)
Answer:
255,340,000(1.61)= $411097400
Step-by-step explanation:
multiply the total amount of bottles by $1.61, since it costs $1.61 per bottle.
Which of the following equations has only one solution? A. x^2 -8 x + 16 = 0 B. x(x - 1) = 8 C. x^2 = 16
[tex]\\\\\\x^2 -8x +16 = 0\\\\\implies x^2 - 2(4) + 4^2 =0\\\\\implies (x-4)^2 =0\\\\\implies x -4 =0\\\\\implies x =4\\\\\text{This equation has only one solution.}[/tex]
more help... please... I'm very stuck
The radius of a circle is 2.5 centimeters (cm).
What is the circumference of the circle?
Answer:
15.7 cm to nearest 10th
Step-by-step explanation:
Circumference = 2 pi r = 2 pi 2.5
= 5 * pi
= 15.708 cm.
Which inequality below is true?
a. -2>4
b. -4< 2
C. -4> 4
d. -4> -2
comparing freezers
Maria compares two freezers.
Freezer A is 8 feet long, 4 feet wide, and 2 feet high.
Freezer B is 6 feet long, 4 feet wide, and 3 feet high.
correctly complete the statement : Freezer _ has _ more cubic feet than Freezer _ .
Answer:
Freezer B has 8 more cubic feet than Freezer A.
Step-by-step explanation:
Volume of Freezer A = 8 * 4 * 2 = 64 ft^3.
Volume of Freezer B = 6 * 4 * 3 = 72 ft^3.
72 - 64 = 8 ft^3.
Answer:
Freezer B has 8 more cubic feet than Freezer A.
Step-by-step explanation:
The set-up cost for a machine that attaches snaps on clothing is $1,100. After set-up,
it costs $0.12 for each snap to be attached. A newer machine has come out that has
a set-up cost of $1,520. With the new machine, it only costs $0.09 for each snap to
be attached. How many snaps would the company have to attach to make the
purchase of the newer machine worthwhile?
Answer:
14,001
Step-by-step explanation:
old machine: 1,100+.12x
new machine: 1,520+.09x
if you plug in 14,000 for x, you get
old machine: 2,780
new machine: 2,780
therefore, you need 1 over 14,000 for it to be worth it because
if you plug in 14,001 for x, you get
old machine: 2,780.12
new machine: 2,780.09
which makes the new machine $.03 cheaper at this point (and the more snaps attached, the more the new machine will be worth it)
hope this helps!
answer pls having problem in this
[tex]\dfrac{\sqrt[3]{343}}{\sqrt[3]{-343}}=\dfrac{\sqrt[3]{343}}{-\sqrt[3]{343}}=-1[/tex]
What is the GCF of 9y and 12y?
Which expression is NOT equivalent to the others?
14^2 x 12^2 x 12^1
14^2 x 12^3
14 x 14 x 12 x 12 x 12
14^1 x 14^1x 12^2 + 12^1
Which equation best matches the scenario below?
The total cost t is proportional to the number n of items purchased at a constant price of $4.
A) 4t = n
B) t = 4n
C) t = n ÷ 4
D) 4t = 4n
Answer:
Definetly t = 4n
How to determine if Triangles are Congruent?
If they are, how do you know if they are SSS or ASA or SAS or AAS?
Essentially, how do I apply the different congruent thermos to the questions attached?
So basically what you have to do is first identify all of the sides or angles that equal eachother then you can see if you did a side side and side in a row etc, like 44 would be SAS because the vertical angles would be inbetween the two sides. 46 would be SSS because after you make the line in the middle for reflexive property you can see that there are three sides in a row. If this didnt help i recommend looking on Khan Academy
50 POINTS FOR EACH PERSON PLSSSSS HELP!!!!!
∫[tex]x^{\frac{3}{2} }[/tex]㏑(x) dx
Answer:
Look at images below ^^
Step-by-step explanation:
I'm not sure if they are correct, since I'm not there yet. But I hope it's correct.
Hassan made a vegetable salad with 2 3/8 pounds of tomatoes, 1 1/4 pounds of asparagus, and 2 7/8 pounds of potatoes. How many pounds of vegetables did he use altogether?
Btw please show work.
Step-by-step explanation:
OK so
Tomatoes = 2 3/8 = 19/8 (turned into improper fraction)
Asparagus = 1 1/4 =5/4
Potatoes = 2 7/8 = 23/8
Total vegetables used =
19/8 + 5/4 + 23/8 = 42/8 + 5/4 = 42+10/8 =52/8
Answer is 52/8 = 6.5
Answer : 52/8 pounds were used altogether
See picture for solution.
Jake has $120 to spend for a party. Juice costs $8. Pizza costs $12. Write the standard equ.
how much juice and pizza Jake can buy?
Answer:
$8x + $12y = $120
Step-by-step explanation:
x = amount of juice
y = amount of pizza
$120 = his total money
please help tysm ill mark brainliest
Answer:
use pemdas(order of the operations)and you'll get the answer 27!!
Step-by-step explanation:
The age melat five times older than the age of hana.In ten years time the ratio of the age of hana to melat is 5:9. find the present age of hana and melat?
Answer:
carbon take x(1)+4(-2)=0
x(1)-8=0
x(1)=8
x=8
Help me plzzzzzzzzzzzzz
Answer: It is D
Step-by-step explanation:
please help
meeeeeeeeeeeeeeee
Answer:
C 43
Step-by-step explanation:
happy holidays
Answer:
Since the two triangles are similar, the two medians AC and FH are in proportion. The proportionality rate is [tex]k=\frac{48}8=6[/tex]. That is the same ratio of the sides., so AD is k times the corresponding side FG, or [tex]\overline {AD} = k\overline{FG} = 6\times 9 = 63[/tex]
Find the area and perimeter of a square whose side length is
2x+3
Answer:
Area = 4x^2 + 12x + 9
Perimeter = 8x + 12
Step-by-step explanation:
if a + b equal to pi by 4 then prove that 1 + cot a into 1 + cot B equal to 2 into cot a into cot b
Answer:
(cotA − 1) (cotB − 1) = 2
Step-by-step explanation:
A+B= π/4 = 180°/4 = 45°
A+B=45°
∴ cot(A+B)=cot45°
∴ cotBcotA−1 / (cotB+cotA) = 1
⇒cotB + cotA = cotBcotA = 1
⇒cotB + cotA − cotBcotA + 1 = 0
⇒cotBcotA − cotB − cotA − 1 = 0
⇒cotBcotA − cotB − cotA − 1 + 2 = 0+2
⇒cotBcotA − cotB − cotA + 1 = 2
⇒cotB(cotA − 1) (cotA − 1) = 2
⇒(cotA − 1) (cotB − 1) = 2
Proved
If x + 2 and x - 3 are factors of the following polynomial, then find the values of a and b. F(x) = x^2 + ax^2- 7x + b
[tex]\text{Given that,}\\\\f(x) = x^3+ax^2-7x+b \\\\\text{Since}~ (x+2)~ \text{and}~ (x-3)~ \text{are factors of f(x),}\\\\f(-2) = 0 ~ \text{and}~ f(3)=0\\\\\\ \text{Now,}\\\\f(-2)=0\\\\\ \implies (-2)^3+a(-2)^2-7(-2)+b =0\\\\\implies -8 +4a +14+b =0\\\\\implies 4a +b +6 =0~~~....(i)\\\\\\f(3) = 0\\\\\implies 3^3+a(3^2) -7(3) +b =0\\\\\implies 27 +9a -21 +b =0\\\\\implies 9a +b +6 =0~~....(ii)\\\\\\(ii)-(i):\\\\9a+b+6 - 4a-b - 6 = 0\\\\\implies 5a =0\\\\\implies a = 0\\[/tex]
[tex]\text{Substitute a=0 in equation (i):}\\\\4(0) +b +6 =0\\\\\implies b+6 =0\\\\\implies b =-6\\\\\text{Hence, a = 0 and}~ b =-6[/tex]