Answers
Using the continuity concept, as the value of the function has to be equal to the limit, it is found that the value of k is of k = -4.
When a function is continuous?A function is said to be continuous at x = a if, and only if:
[tex]\lim_{x \rightarrow a} f(x) = f(a)[/tex]
In this problem, we have to check at x = -2, hence:
[tex]\lim_{x \rightarrow -2} f(x) = f(-2)[/tex]
[tex]k = \lim_{x \rightarrow -2} f(x)[/tex]
For the limit, we have to check the lateral conditions, hence:
[tex]\lim_{x \rightarrow -2} f(x) = \lim_{x \rightarrow -2} \frac{x^2 - 4}{x + 2} = \lim_{x \rightarrow -2} \frac{(x - 2)(x + 2)}{x + 2} = \lim_{x \rightarrow -2} x - 2 = -2 -2 = -4[/tex]
Hence, from the continuity condition, k = -4.
More can be learned about the continuity concept at https://brainly.com/question/24637240
#SPJ1
Related Questions
Solve using substitution method:
X= y/3 +2
7x − 5y = 10
Solve for (x,y)
Answers
[tex]\quad \huge \quad \quad \boxed{ \tt \:Answer }[/tex]
[tex]\qquad \tt \rightarrow \:x = 5/2 [/tex]
[tex] \qquad \tt \rightarrow \: y = 3/2[/tex]
____________________________________
[tex] \large \tt Solution \: : [/tex]
[tex]\qquad \tt \rightarrow \: x = \cfrac{y}{3} + 2 \: \: \: \: \: \: \: \: - (1)[/tex]
[tex]\qquad \tt \rightarrow \: 7x -5 y = 10 \: \: - (2)[/tex]
[tex] \textsf{put value of x in equation 2} [/tex]
[tex]\qquad \tt \rightarrow \: 7 \bigg( \cfrac{y}{3} + 2 \bigg) - 5y = 10 [/tex]
[tex]\qquad \tt \rightarrow \: \cfrac{7y}{3} + 14 - 5y = 10 [/tex]
[tex]\qquad \tt \rightarrow \: \cfrac{7y}{3} - 5y = 10 - 14[/tex]
[tex]\qquad \tt \rightarrow \: \cfrac{7y - 15y}{3} = - 4[/tex]
[tex]\qquad \tt \rightarrow \: - 8y = - 4(3)[/tex]
[tex]\qquad \tt \rightarrow \: y = \cfrac{ - 12}{ - 8} [/tex]
[tex]\qquad \tt \rightarrow \: y = \cfrac{ 3}{ 2} [/tex]
[tex] \textsf{put value of y in equation 1 } [/tex]
[tex]\qquad \tt \rightarrow \: x = \cfrac{y}{3} + 2[/tex]
[tex]\qquad \tt \rightarrow \: x = \bigg (\cfrac{3}{2} \sdot\cfrac{1}{3} \bigg) + 2[/tex]
[tex]\qquad \tt \rightarrow \: x = \cfrac{1}{2} + 2[/tex]
[tex]\qquad \tt \rightarrow \: x = \cfrac{1 + 4}{2} [/tex]
[tex]\qquad \tt \rightarrow \: x = \cfrac{5}{2} [/tex]
The perimeter of a rectangle is 34 cm. The length is 1 cm longer than the width. What is the length of the longest side of the rectangle?
Answers
Answer: 9 cm
Step-by-step explanation:
The formula for the perimeter of a rectangle is [tex]2l+2w=P[/tex]
Where
l is the length
w is the width
and P is the perimeter (34)
Because the length is 1 cm longer than the width instead of representing the length is l we can use w+1
Sub in the known values and solve
Step 1: Simplify both sides of the equation with the Distributive Property
[tex]2(w+1)+2w=34\\(2)(w)+(2)(1)+2w=34\\2w+2+2w=34\\(2w+2w)+(2)=34\\4w+2=34\\[/tex]
Step 2: Subtract 2 from both sides.
[tex]4w+2-2=34-2\\4w=32[/tex]
Step 3: Divide both sides by 4.
[tex]\frac{4w}{4}=\frac{32}{4} \\w=8[/tex]
Step 4: Add 1 to w to find the length of the longer side
[tex]w+1\\8+1\\9[/tex]
Directions: Find the inverse of each number.
Additive
-3 =
14 =
-28 =
-1/5 =
Multiplicative
2/3 =
6/18 =
5 =
11 =
Answers
Answer:
Step-by-step explanation:
Additive inverse:
-3=3
14=-14
-28=28
-1/5=1/5
Multiplicative Inverse:
2/3=3/2
6/18=18/6
5=1/5
11=1/11
Answer:
inverse of -3 is +3
inverse of 14 is -14
inverse of -28 is 28
inverse of -1/5 is 1/5
inverse of 2/3 is 3/2
inverse of 6/18 is 18/6
inverse of 5 is 1/5
inverse of 11 is 1/11
Step-by-step explanation:
Because inverse mean switch it. or opposite of digit
if plus digit then negative digit .
evaluate the following expression when x=-4 and y=4
x³-x /4y[tex]\frac{x}{y}[/tex]
Answers
Answer: - 60
Step-by-step explanation:
[tex]\frac{(-4)^3 - (-4)}{4(4)^-4/4} \\\\= -60[/tex]
find the value of x
a) 5
b) 35
c) 3
d) 7
Answers
Answer:
x=3
Step-by-step explanation:
due to its same angle of the graphic. it has to be +6 as well
23-29-35
35=11.×+2
35-2=33
33=11.×
x=3
{x + 8y = -16
{x-3y = -5
Answers
Answer: y= -1 and x=-8
x+8y=-16
x=-8y-16
so x-3y=-5
-8-16-3y=-5
-11y-16=-5
-11y=-5+16
-11y=11
y=-1
x-3y=-5
x+3=-5
x=-8
Step-by-Step Solution:
=> x + 8y = -16 (Eq. 1)
=> x - 3y = -5 (Eq. 2)
Subtracting Eq. 2 from 1, we get :-
8y + 3y = -16 + 5
11y = -11
y = -11/11
=> y = -1
Therefore, y = -1
Substitute value of ‘y’ in Eq. 2 :-
x - 3y = -5
x - 3(-1) = -5
x - -3 = -5
x + 3 = -5
x = -5 - 3
x = -5 + -3
=> x = -8
Therefore, x = -8
Hence, x = -8 and y = -1 (-8, -1)
HEPPPPPPPPPP PLEASEEEEEEEE
Answers
Answer:
x-int=(2,0)
y-int=(0,4)
Step-by-step explanation:
What is the answer?????
Answers
Answer:
36.7075 Hz is the answer
On a coordinate plane, a parabola opens up. It goes through (negative 8, negative 2), has a vertex at (negative 5, negative 6.5), goes through (negative 2, negative 2), and has a y-intercept at (0, 6).
Over which interval is the graph of f(x) = one-halfx2 + 5x + 6 increasing?
Answers
The graph is increasing for x > -5
12 identically sized pieces of timber are
x
cm long when put together. How long is each individual piece?
Answers
Answer:
[tex]\frac{x}{12}[/tex] (x/12)
Step-by-step explanation:
if 12 pieces combine to make x, [we know they are identical], each piece must be 1/12 of x [1/12·x = x/12]
(think of it like this: "x" length must be divided amongst 12 pieces, so, we divide x/ 12)
Answer:
Timber=x/12
Step-by-step explanation:
12 pieces long is x, if the length of each one is same, so the length of each one is x/12.
what is the sum of first 6 terms
Answers
Answer:
182
Step-by-step explanation:
Sum = a(r^n -1) ÷ r - 1
1(-3^6 - 1) ÷ -3 -1
= 182
r = t2 ÷ t1 * since they stated that it is geometric
Use the accompanying table to answer the questions regarding money ratios.
(a) What is the capital a 40-year-old should have with an income of $32,000?
(b) How much should a 35-year-old be saving for retirement with an income of $86,000?
(c) How much in education debt should a 30-year-old have with an income of $59,000?
The 40-year-old should have $___in capital.
(Simplify your answer)
(b) The 35-year-old should be saving $ for retirement.
(Simplify your answer)
(c) The 30-year-old should have $___ in education debt.
(Simplify your answer)
.
Answers
The 40-year-old should have $76800 in capital. The 35-year-old should be saving $$10,320 for retirement.
How to solve for the amountsThe capital that a 40 year old has to have with an income of 32000 is
capital income at age 40 * income
= 2.4 * 32000
Capital = $76800
b. At 35 the savings income has to be
percentage of savings income * income
= 12% * $86000
= $10,320
c. There is no specified value for education earnings.
Read more money ratios here:
https://brainly.com/question/16812427
We have two fractions, 1/6 3/8 and we want to rewrite them so that they have a common denominator (and whole number numerators). What numbers could we use for the denominator? Choose 2 answers:
Answers
Answer:
See below
Step-by-step explanation:
The denominator has to be divisible by 6 and 8
you could choose 24 48 72 96 etc
Question 29 of 40
Find f(-2) for f(x) = 5.3*.
Answers
Answer:
A. [tex]\frac{5}{9}[/tex]
Step-by-step explanation:
To find f(-2) in f(x)=5*3^x, plug in -2 into all the x values.
f(-2)=5*3^-2, you can use calculator to calculate 3^-2 which equals 0.1, forever 1's.
f(-2)=5*0.1=0.5 Forever 5's.
f(-2)=0.5 or [tex]\frac{5}{9}[/tex]
Hope this helps!
If not, I am sorry.
what is the value of k such that 5x-2y=9 and 6x+ky=4 are perpendicular?
Answers
15
5x-2y=9......(1)
6x+ky=4......(2)
slope of eqn i= -5/-2
=5/2
slope of eqn ii = -6/k
since the line are perpendicular
5/2 * -6/k = -1
-30= -2k
k=15
What is the difference between normal definition of set and contors definition of set
Answers
Step-by-step explanation:
The collection of well defined object is called set
find the average rate of change
Answers
Answer:
3rd option
Step-by-step explanation:
the average rate of change of f(x) in the closed interval [ a, b ] is
[tex]\frac{f(b)-f(a)}{b-a}[/tex]
here [ a, b ] = [ 1, 4 ] , then
f(b) = f(4) = 3³ + 2 = 27 + 2 = 29
f(a) = f(1) = [tex]3^{0}[/tex] + 2 = 1 + 2 = 3 , then
average rate of change = [tex]\frac{29-3}{4-1}[/tex] = [tex]\frac{26}{3}[/tex]
6 less than a number is less than the quotient of the number and 3.
Answers
Answer:
x<9
Step-by-step explanation:
x-6<x/3
3(x-6)<x
3x-18<x
3x-x<18
2x<18
X<18/2
X<9
Solve the inequality and express your answer in interval notation.
Answers
The correct answer is option B which is (-4-√11) and (-4+√11).
What is inequality?
Inequality is the relationship between two expressions that are not equal, employing a sign such as ≠ “not equal to,” > “greater than,” or < “less than.”.
The inequality is given as x² + 8x + 5 < 0 for we will draw a graph of the inequality and find the range of x which ranges from ( -7.31,- 0.68) So these points in the options will be equal to (-4-√11) and (-4+√11).
(-4 - √11) = -4 -3.31 =-7.31
(-4 + √11) = -4 +3.31 = -0.68
Therefore the correct answer is option B which is (-4-√11) and (-4+√11).
To know more about inequality follow
https://brainly.com/question/24372553
#SPJ1
Harry used 0.75 liters of gasoline on the first day of his trip, 1.5
liters on the second, 2.25 liters on the third, and 3 liters on the
fourth. Write a function to describe the sequence, and then use
the function to predict the amount of gasoline used on the
eighth day of his trip.
Oy=0.5n; 4 L
O y = 0.75n; 6 L
Oy=n; 8L
Oy=1.5m; 12 L
Answers
The function is to describe the sequence and the amount of gasoline used on the eighth day of his trip will be y = 0.75n and 6 L respectively. Option B is correct.
What is an arithmetic sequence's sum of terms?Each consecutive term in an arithmetic sequence has a common constant difference.
The sequence of the liters of gasoline on each day is;
0.75,1.5,2.25,3
The given series is an arithmetic series with a common difference of 0.75
Common difference,d=0.75
First-term,a=0.75
The amount of gasoline used on the eighth day of his trip.
The nth term of the arithmetic sequence is;
[tex]\rm a_n = a+(n-1)d \\\\ \rm a_8 = 0.75+(8-1)0.75 \\\\ a_8 = 6[/tex]
The 8th term of the arithmetic sequence is 6L.
The function is to describe the sequence and the amount of gasoline used on the eighth day of his trip will be y = 0.75n and 6 L.
Hence, option B is correct.
To learn more about the arithmetic sequence refer;
https://brainly.com/question/15412619
#SPJ1
Evaluate the expression for the given values of the variables:
2a³-7b²+ 3c - (d + e) a = 3, b = 2, c = 4, d = 11, and e = 7
Answers
Answer:
yes
Step-by-step explanation:
it's hard but you'll figure it out so don't worry
Jane and David had identical chocolate bars.
David ate 78 of his chocolate bar.
Jane ate more of her chocolate bar than David.
What fraction of her chocolate bar could Jane have eaten?
Answers
Answer:
Step-by-step explanation:
I'm assuming you meant "David at 78% of his chocolate bar" which means he at 78/100 of his chocolate bar. So if Jane ate more she could've eaten n/100 of her chocolate bar where [tex]78 < n \leq 100[/tex]. Greater than 78 since David at 78/100 and less than or equal to 100 since 100/100 means Jane at the entire thing at 101/100 wouldn't make any sense.
A green gold bracelet weighs 56g. The bracelet is made from 75% gold, 20% silver and 5% copper.
(a) What is the mass of the gold in the bracelet?
(b) What is the mass of the copper in the bracelet?
Answers
Answer:
a. 42 g
b. 2.8 g
Step-by-step explanation:
a. Since the entire thing weighs 56g and gold is 75% of the mass you simply find 75% of the mass. This is done by converting the 75% into decimal form by dividing it by 100 to get 0.75 and then multiply it by the 56 g to get (0.75 * 56 g) = 42 g
b. same thing here as the previous answer. 5%/100 = 0.05. (0.05 * 56 g) = 2.8 g
Use the figure below to find the answer.
X
Find y.
y=
45
III
7
T
234567890
Answers
Answer: [tex]\frac{7\sqrt{2}}{2}[/tex]
Step-by-step explanation:
[tex]\sin 45^{\circ}=\frac{7}{y}\\\\\frac{1}{\sqrt{2}}=\frac{7}{y}\\\\y=\frac{7}{\sqrt{2}}=\boxed{\frac{7\sqrt{2}}{2}}[/tex]
Peter uses the equation y = StartFraction 13 over 4 EndFraction x to model the number of miles that he has walked in x hours. Which statement is true about the proportional relationship that is modeled by Peter’s equation?
Answers
The statement C is true about the proportional relationship that is modeled by Peter’s equation. Peter walks at a rate of 13/4 miles per hour.
What is the equation?A mathematical statement consisting of an equal symbol between two algebraic expressions with the same value is known as an equation.
The complete question is
"Peter uses the equation Y=13/4x to model the number of miles that he has walked in x hours. Which statement is true about the proportional relationship that is modeled by the peat there's the equation?
A: Peter walks a rate of 4/13 miles per hour.
B: Peter walks at a rate of 4 miles per hour.
C: Peter walks at a rate of 13/4 miles per hour.
D: Peter walks at a rate of 13 miles per hour."
Given equation;
Y=13/4x
Where,
y represents the number of miles
x is the time period
The equation shows Peter walks at a rate of 13/4 miles per hour.
Hence statement C is true about the proportional relationship that is modeled by Peter’s equation.
To learn more, about equations, refer;
https://brainly.com/question/10413253
#SPJ1
There are 10 marbles in a bag. are red and the others are blue. 5 What is the ratio of red marbles to blue marbles? Question 11 * 1 There are 10 marbles in a bag . are red and the others are blue . 5 What is the ratio of red marbles to blue marbles ?
Answers
Answer:
%50 1÷2
if there is missing information. if there is 10 total marbels 5 would be red, 5would be blue.
batman wants to wrap a perestn in a box for robin. the top and the bottom of the box is 10 cm. by 5 cm. the sides are both 3 cm by 2 cm. and the front and back are 8 cm. by 2 cm. hhow muvh wrapping papper will atman need to wrap the present?
Answers
Answer:
15
Step-by-step explanation:
A part of a line that starts at one endpoint and extends forever in one direction is a(n)
A. angle
B.point
C.line
D.ray
Answers
Answer:
[tex]\fbox {D. ray}[/tex]
Step-by-step explanation:
A part of a line that starts at one endpoint and extends forever in one direction is a ray.
Answer: D. Ray
Step-by-step explanation:
Let's do the process of elimination.
It's not A because there is only one line.
It is not B because a point is only a dot.
It is not C because a line extends forever from BOTH ends.
The correct answer is D because a ray starts on one endpoint and extends forever in one direction.
I hope this helps!! Pls mark brainliest!! :)
how many feet? help me please
Answers
Answer:
[tex]\fbox {400.41 feet}[/tex]
Step-by-step explanation:
Here we need to take the tan ratio of the angle.
⇒ tan 4° = 28/x = 0.0699268119
⇒ x = 28/0.0699268119
⇒ x = 400.41 feet
1/5 divided by 4 equals to what
Answers
Answer:
1/5 divided by 4 equals to 0.05
