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
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Carol's Phone Service charges $17.62 for an activation fee plus $3 for every gigabyte (g) used. Which of the following graphs models the situation?
Answer:
a
Step-by-step explanation:
17.62 y intercept
slope 1/3
There is an array under. what is the last number?
1 2 4 7 13 24 ?
Answer:
Here's one possible solution
Step-by-step explanation:
Double the number and subtract the corresponding value from the sequence
0, 0, 1, 1, 2, 2, 3, 3, 4, 4, 5, 5...
1 + 1 - 0 = 2
2 + 2 - 0 = 4
4 + 4 - 1 = 7
7 + 7 - 1 = 13
13 + 13 - 2 = 24
24 + 24 - 2 = 46 ←←←
46 + 46 - 3 = 89
89 + 89 - 3 = 175
175 + 175 - 4 = 346
Layla missed 38 questions on her multiple choice math final that had a total of 200 problems. What percentage of questions did Layla answer correctly?
Answer:
81%
Step-by-step explanation:
200-38= 162
162/200= 81/100
81%
(15 points) Critique Reasoning Jamie says that the
expressions 6x - 2x + 4 and 4(x + 1) are not
equivalent because one expression has a term
that is subtracted and the other does not. Do
you agree? Explain.
a
Answer:
they are the same
Step-by-step explanation:
6x - 2x + 4 ← collect like terms
= 4x + 4
and
4(x + 1) ← distribute parenthesis by 4
= 4x + 4
The 2 expressions are equivalent to 4x + 4
Answer:
No, Jamie is incorrect
Step-by-step explanation:
No, because in the expression 4(x+1) you will first need to multiply 4 by x, your result is 4x, and then you multiply 4 by 1, you get 4, so the answer will be 4x+4.
Also in the expression 6x-2x+4 ,you will first need to subtract 2x from 6x, your result is 4x ,and then you add 4 , so the answer will be 4x + 4
Our final answer is:
6x-2x+4 = 4x + 4 and 4(x+1) = 4x + 4
What is the quotient? -4/5 ÷ 2
LAST ATTEMPT IM MARKING AS BRAINLIEST!! (Pythagorean theorem )
Answer:
x = √7km
Step-by-step explanation:
Answer:
21
Step-by-step explanation:
You take a right triangle and find the lengths of the two sides that are vertical and horizontal. Then, using the formula a^2 + b^2 = c^2, find the length of C
(aka: Hypotenuse)
hope this helps!
Find the equation of a line that passes through the points (1,-2) and (3,-4). Express your final answer in slope-intercept form.
[tex]\text{Given that,}\\\\(x_1,y_1) = (1,-2)~~ \text{and}~~ (x_2,y_2) = (3,-4)\\\\\text{Slope,}~ m= \dfrac{y_2-y_1}{x_2 -x_1} = \dfrac{-4+2}{3-1} = -\dfrac 22 = -1\\\\\text{Equation with given points,}\\\\y-y_1 = m(x-x_1)\\\\\implies y +2 = -1(x-1)\\\\\implies y = -x+1 -2\\\\\implies y = -x-1\\\\\text{This is the slope-intercept form(y =mx+b).}[/tex]
Answer:
y=-x-1
Step-by-step explanation:
m=(y2-y1)/(x2-x1)
m=(-4-(-2))/(3-1)
m=(-4+2)/2
m=-2/2
m=-1
y-y1=m(x-x1)
y-(-2)=-1(x-1)
y+2=-x+1
y=-x+1-2
y=-x-1
The constraints of a problem are listed below. What are the vertices of the feasible region?
x+3y<=6
4x+6y>=9
x>=0
y>=0
The vertices of the feasible region of the constraints is (0,2.5)
How to determine the vertices?The constraints are given as:
x + 3y ≤ 6
4x + 6y ≥ 9
x ≥ 0, y ≥ 0
Express the inequalities as equations
x + 3y = 6
4x + 6y = 9
Make x the subject in x + 3y = 6
x = 6 - 3y
Substitute x = 6 - 3y in 4x + 6y = 9
4(6 - 3y) + 6y = 9
Expand
24 - 12y + 6y = 9
Evaluate the like terms
-6y = -15
Divide by 6
y = 2.5
Substitute y = 2.5 in x = 6 - 3y
x = 6 - 3 * 2.5
Evaluate
x = -1.5
So, we have:
(x,y) = (-1.5, 2.5)
Recall that: x ≥ 0, y ≥ 0
This means that the feasible region must have positive coordinates or zero
So, we set x = 0
(x,y) = (0, 2.5)
Hence, the vertices of the feasible region of the constraints is (0,2.5)
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58. What is the equation that best represents the graph (0,5) (3, 3) (6, 1)
3. Vocabulary Suppose △MNP ∼△RST. How can you identify corresponding parts?
4. Reasoning Suppose △ABC ∼△TUV. Determine whether each pair of measures is equal.
a. the measures of ∠A and ∠T
b. the perimeters of the two triangles
c. the ratios of the sides BC/UV and AC/TV
5. Reasoning e scale of a map is 1 in. : 100 mi. Is the actual distance between two towns 100 times the map distance between the two towns? Explain.
Similar triangles may or may not have congruent sides, but the ratio of the corresponding sides will always be congruent.
(3) Corresponding sides of △MNP and △RST
Given that △MNP ∼△RST.
This means that, the corresponding sides are:
MN and RSMP and RTNP and ST(4) The equal measures
Given that △ABC ∼△TUV
This means that, the corresponding angles are equal, but corresponding sides are not.
So, the equal measures are:
(a). the measures of ∠A and ∠T (c). the ratios of the sides BC/UV and AC/TVThe unequal measure is:
(b). the perimeters of the two triangles(c) Scale mapping
The scale mapping is given as:
[tex]Ratio = 1\ in : 100\ mi[/tex]
The above scale means that 1 inches on the scale represents 100 miles of the actual distance.
Take for instance, 5 inches would represent 500 miles.
500 is 5 times 100
Hence, the actual distance between two towns 100 times the map distance between the two towns
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What is the value of x in the equation 8+4 = 2(x-1)2
O 5
11
o
2
끌
o
13
2
O 7
Step-by-step explanation:
→ 8 + 4 = 2(x -1)
→ 12 = 2x - 2
→ 2x - 2 = 12
→ 2x = 12 + 2 = 14
→ x = 14/2 = 7
→ x = 7
hence, option D (7) is correct.
Hope this answer helps you dear ! take care
-2(x-6)=6 help me out
Answer:
x = 9
Step-by-step explanation:
i took the quiz
[tex]\mathfrak{-2(x-6)=6} [/tex]
[tex]\mathfrak{-2x+12=6} [/tex]
[tex]\mathfrak{-2x=6-12} [/tex]
[tex]\mathfrak{-2x=-6} [/tex]
[tex]\boxed{\mathfrak{x=3} }[/tex]
need this soon please
Answer: pretty sure -7
Step-by-step explanation:
Answer:
-7
Step-by-step explanation:
(-80) - (-10) is -79
-70 / (+10) = -7
16,40 and 56 LCM
Solve this problem
Answer:
LCM = 2^4 x 5^1 x 7^1 = 560
Step-by-step explanation:
I hope this helps you !!The component form of vector vec w is vec w =(-25,10); Find- 1 5 vec w
Answer:
Let’s take a point each on the x, y, and z-axis as follows:
A (1, 0, 0) on x-axis
B (0, 1, 0) on y-axis and
C (0, 0, 1) on z-axis
unit vector
So, we have
|OA→| = 1 , |OB→| = 1, and |OC→| = 1
These vectors OA→, OB→, and OC→, each having magnitude 1 are Unit Vectors along the axes OX, OY, and OZ respectively. They are denoted by i⃗ , j⃗ , and k⃗ as shown in Fig. 1 above.
Step-by-step explanation:
W LOOKS LIKE PAIN, DEM
Directions:
Plattbo ondorod patroof obere ca a pregl la tho endor boy
aro Motod conmocilag tbeca with longercato as you plot thom.
Start a new Une after the word "LINE ENDE.
• (1.-20)
(3,-20)
(3.-19)
(4,-10)
(4,-5).
(2,-7)
LINEENDS
(4, 21)
(S24)
(S, 20)
(1, 20)
(0, 19)
(4, 16)
(d, 14)
(3, 14)
(2, 15)
LINZENDS
(-8, 15)
(-8, 14)
(-4, 12)
(-4, 5)
(-5, 3)
(-6, 0)
(-6,-3)
(-5,-6);
(-4,-7)
(-4,-20)
(-5,-21)
(-6,-23)
(-4,-23)
(-4,-22)
(-3,-20)
(-3,-7)
(-1,-7)
(-1,-20)
(0.-22)
(0,-23)
(2,-23)
(1,-21)
(0,-20)
(0,-7)
(1,-6)
LINEENDS
(4,-5)
(5,-)
(9,-18)
(6,-19)
(6;-20)
(8,-20)
(6.-17)
(6.-8)
(3,-1)
(6, 1)
F2, -3)
(8,4).
(9, 7)
(10, 4)
(9, 2)
(8, 2)
LINEENDS
(-2, 5)
(-2. 12)
(2, 14)
(2, 15)
(0, 10)
(-1, 19)
(-1, 20)
(-5, 20)
(-5, 19)
(-6, 10)
(-8, 15)
(-9, 14)
(-10, 14)
(-10, 16)
(-6, 19)
(-7, 20)
(-11, 20)
(-11, 24)
(-10, 21)
(-9, 21)
(-9, 23)
(-8, 21)
(-6, 21)
(-5, 20)
LINEENDS
(-3, 15)
(-3, 16)
(-4, 17)
(-4, 19)
(-5, 18)
(-1, 18)
(-2, 19)
(-2, 17)
(-3, 16)
LINEENDS
(-i, 16)
(0, 16)
(-1, 15)
(-5, 15)
(-6, 16)
(-5, 16)
LINEENDS
(0,-7)
(2,-7)
(3,-8)
(3,-17)
W, 3)
(5, 4)
(3, 4)
(1, 3)
(0, 3)
(-1, 20)
(0, 21)
(2, 21)
(3, 23)
(3, 21)
Mystery Media
29
Answer:
Step-by-step explanation:
S
(4,-5)
(5,-)
(9,-18)
(6,-19)
(6;-20)
(8,-20)
(6.-17)
(6.-8)
(3,-1)
(6, 1)
F2, -3)
(8,4).
(9, 7)
(10, 4)
(9, 2)
(8, 2)
LINEENDS
(-2, 5)
(-2. 12)
(2, 14)
(2, 15)
(0, 10)
(-1, 19)
(-1, 20)
(-5, 20)
(-5, 19)
(-6, 10)
(-8, 15)
(-9, 14)
(-10, 14)
(-10, 16)
(-6, 19)
(-7, 20)
(-11, 20)
(-11, 24)
(-10, 21)
(-9, 21)
(-9, 23)
(-8, 21)
(-6, 21)
(-5, 20)
LINEENDS
(-3, 15)
(-3, 16)
(-4, 17)
(-4, 19)
(-5, 18)
(-1, 18)
(-2, 19)
(-2, 17)
(-3, 16)
LINEENDS
(-i, 16)
(0, 16)
(-1, 15)
(-5, 15)
(-6, 16)
(-5, 16)
LINEENDS
(0,-7)
(2,-7)
(3,-8)
(3,-17)
W, 3)
(5, 4)
(3, 4)
(1, 3)
(0, 3)
(-1, 20)
(0, 21)
(2, 21)
(3, 23)
(3, 21)
Mystery Media
Dave and Kyle are 40 miles apart on a path when they start moving toward each other. Dave runs at a constant speed of 8 miles per hour, while Kyle walks at a constant speed of 5 miles per hour. How long does it take until they meet?
Answer:
About 3 hours
Step-by-step explanation:
together, they go 13 miles in one hour. 40/13 = 3 with remainder 1
I need help on this math question
Answer:
84
Step-by-step explanation:
7 Sizes * 3 Lengths * 4 Colors = 84
f(x)=3x-1 and g(x)=-2x+5
Answer:
Step-by-step explanation:
what is 2 + 2 no one in my class can get it my teacher says its the hardest question I want to look smart please help
Answer:
4
Step-by-step explanation:
use your fingers and count 2 fingers then put 2 more up and count how many u got then. boom u got 4
Ms Lewis is hiring a carpenter to repair her shed the cost of carpenter L is shown in the table
Part a. What is the initial cost and hourly rate of carpenter L?
Part B write an equation to repent the function
Part C. Carpenter n charges 60$ an hour and and additional 195$ for the materials needed what is the difference in cost between carpenter N and carpenter L
Initial cost __
rate per hour __
Equation__
difference in cost__
Based on the information given, it can be deduced that the initial cost will be $187 and the hourly rate is $72 per hour.
From the information given, the initial cost is $187. The cost for 2 hours is $259 and the cost for 3 hours is $331.
Therefore, the rate per hour will be:
= $259 - $187 = $72
The equation will then be:
= 187 + 72h
Lastly, the difference in the costs is $72.
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Subtract:
(3x^3– 10x^2+ 13x) – (5x^3+ 4x² – 9x)
A. 8x^3 + 14x^2 - 22x
B. 8x^3 - 6x^2 + 4x
C. 2x^3 - 6x^2 - 4x
D. -2x^3 - 14x^2 + 22x
Answer:
D. -2x^3 - 14x^2 + 22x
Step-by-step explanation:
1) Remove parentheses.
3x³ - 10x² + 13x - 5x³ - 4x² + 9x
2) Collect like terms.
(3x³ - 5x³) + (-10x² - 4x²) + (13x + 9x)
3) Simplify.
-2x³ - 14x² + 22x
Given the linear equation y = -3x
identify the initial value and rate of change
Hurry timed test!!
Answer:
here you go. hope u past the test
Step-by-step explanation:
I hope it's helpful :)
Area =12
X+2
X+4
X =
Answer:
To find area of the square you'll need to square one side
(3X)^2 = 81
9(X)^2 = 81
(x)^2 = 81/9
x^2 = 9
X = (9)^1/2
X = 3
1038*472 please help
Answer:
443,226
Step-by-step explanation:
Identify the explicit formula for the sequence given by the following recursive formula:
(see picture below)
A) f(n) = 2 – 4(n – 1)
B) f(n) = –4 + 2(n – 1)
C) f(n) = 4 – 2(n – 1)
D) f(n) = –2 + 4(n – 1)
If f(n) = f(n - 1) + 4, then
f(n - 1) = f(n - 2) + 4
and substituting this into the first equation gives
f(n) = f(n - 2) + 2•4
Similarly,
f(n - 2) = f(n - 3) + 4
so that
f(n) = f(n - 3) + 3•4
and so on.
Note the pattern:
f(n) = f(n - k) + k•4
so that when k = n - 1, we have
f(n) = f(n - (n - 1)) + (n - 1)•4
or
f(n) = f(1) + 4 (n - 1)
so that
[D] f(n) = -2 + 4 (n - 1)
Leora is finding the length of a horizontal line segment on a coordinate grid She subtracted the x coordinates and got
-17.5 What is her next step?
Add 17.5
Take the absolute value of -17.5
Add the y.coordinate values.
Round up to -17
Answer:
Take the absolute value of -17.5
Step-by-step explanation:
Answer:
2. Take the absolute value of ' - 17. 5 '
Step by Step Explanation:
The distance/length is always positive, so make sure to take the absolute value of -17.5
Help help math math
Answer:
y = 1/2x + 3
Step-by-step explanation:
Y= mx+b is slope-intercept form, m is for slope, and b is for my y-intercept. Also remember the pitch is the rise over the run or the y-direction over the x-direction.
In our case, they highlight 2 points to calculate the slope; looking at the graph, we can see it rises one and runs two to get to the second highlighted point at (2,4). And my slope is rise over run, so here it 1/2.
My b or y-intercept is simply three because that is where the line passes over or intercepts the Y-axis
Answer: y = 1/2 x + 3
Step-by-step explanation:
a length of top is stretched between the top edge of a building and a stake in the ground the head of the stake is at ground level. the rope also touches a tree that is growing half way between the stake and the building. if the tree is 38 ft tall how tall is the building?
The relationship between the rope, the building, the tree and the ground is an illustration of similar triangles and equivalent ratios.
The building is 76ft tall
The height of the tree is given as:
[tex]Height = 38ft[/tex]
The position of the tree is halfway between the building and the stake.
From the figure, the rope touches the top of the building, and the top of the tree.
This means that: the height of the building is twice the height of the tree.
So, we have:
[tex]Building=2\times 38ft[/tex]
[tex]Building=76ft\\[/tex]
Hence, the building is 76ft tall
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To check out a customer, a grocery store cashier needs 2 seconds to scan each item being purchased, as well as 30 seconds to process payment. If it takes 44 seconds to ring up a particular customer, how many items is the customer purchasing?
Answer:
7
Step-by-step explanation:
Let's say the customer has x items. For each item, we add 2 seconds. For 3 items, we need 2 + 2 + 2 = 2*3 seconds. For x items, we need 2 * x seconds. Then, we add the processing payment time of 30 seconds, so for x items, the total amount of time = 30 + 2 * x
Here, the total amount of time is 44, so we have
44 = 30 + 2x
subtract 30 from both sides to isolate the variable and its coefficient
14 = 2x
divide both sides by 2 to isolate x
x = 7