Given the following graphs of f(x) and g(x), find the value of lim x->7 f(g(x)) in simplest form.
Answers
The limit of the composite function is given as follows:
lim x->7 f(g(x)) = 2.
What is a limit?A limit is given by the value of function f(x) as x tends to a value.
From the graph of g(x), we have that the lateral limits at x = 7 are given as follows:
[tex]\lim_{x \rightarrow 7^-} = \lim_{x \rightarrow 7^+} = -2[/tex]
Hence:
lim x->7 f(g(x)) = f(lim x->7 g(x)) = f(-2).
Looking at the graph of f(x), we have that:
f(-2) = 2.
Hence:
lim x->7 f(g(x)) = 2.
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Related Questions
Find the solutions of the quadratic equation –9x2 + 49 = 0.
Question 8 options:
A)
x = 9∕7, – 9∕7
B)
x = 3∕7, –7∕3
C)
x = 7∕3, –7∕3
D)
x = 7∕9, –7∕9
Answers
The solutions to the quadratic equation, -9x² + 49 = 0, are: C. x = 7∕3, –7∕3.
How to Find the Solutions to a Quadratic Equation?Given the quadratic equation, -9x² + 49 = 0, we can factorize to find the roots (the values of x) as shown below:
-9x² + 49 = 0
-(9x² - 49) = 0
Divide both sides by -1
-(9x² - 49)/-1 = 0/-1
9x² - 49 = 0
9x² - 49 + 49 = 0 + 49
9x² = 49
Divide both sides by 9
9x²/9 = 49/9
x² = 49/9
Take the square root of both sides
√x² = √(49/9)
x = ±7/3
Therefore, the solutions to the quadratic equation, -9x² + 49 = 0, are: C. x = 7∕3, –7∕3.
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Find the equation of the line given the following conditions.
-Passing through (2, -3) and perpendicular to the line whose equation is y=1/5x+6
-Passing through (5, -9) and perpendicular to the line whose equation is x + 7y – 12 = 0
Answers
Considering the definition of perpendicular line, you obtain:
1) the equation of perpendicular line is y= -5x + 7.
2) the equation of perpendicular line is y= 7x + 54.
Linear equationA linear equation o line can be expressed in the form y = mx + b
where
x and y are coordinates of a point.m is the slope.b is the ordinate to the origin and represents the coordinate of the point where the line crosses the y axis.Perpendicular linePerpendicular lines are lines that intersect at right angles or 90° angles. If you multiply the slopes of two perpendicular lines, you get –1.
Equation of perpendicular line of y=1/5x +6If you multiply the slopes of two perpendicular lines, you get –1. In this case, the line has a slope of 1/5. So:
1/5× slope perpendicular line= -1
slope perpendicular line= (-1)÷ (1/5)
slope perpendicular line= -5
So, the perpendicular line has a form of: y= -5x + b
The line passes through the point (2,-3). Replacing in the expression for perpendicular line:
-3= -5× (2) + b
-3= -10 + b
-3 +10 = b
7= b
Finally, the equation of perpendicular line is y= -5x + 7.
Equation of perpendicular line of x +7y -12= 0In this case, the line is x +7y -12= 0. Expressed in the form y = mx + b, you get:
7y= -x +12
y= (-x + 12)÷ 7
y= -1/7x +12/7
If you multiply the slopes of two perpendicular lines, you get –1. In this case, the line has a slope of -1/7. So:
-1/7× slope perpendicular line= -1
slope perpendicular line= (-1)÷ (-1/7)
slope perpendicular line= 7
So, the perpendicular line has a form of: y= 7x + b
The line passes through the point (5,-9). Replacing in the expression for perpendicular line:
-9= 7× (-9) + b
-9= -63 + b
-9 + 63 = b
54= b
Finally, the equation of perpendicular line is y= 7x + 54.
Summary
In summary, you obtain:
1) the equation of perpendicular line is y= -5x + 7.
2) the equation of perpendicular line is y= 7x + 54.
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Chika's uncle makes perfect brownies. Chika noted how much sugar he uses based on how many batches
he makes:
Answers
Answer:
7.5 batches
Step-by-step explanation:
if he uses 0.6kg of sugar per 2 batches, it's 0.3kg per batch.
2.25kg would let us make
2.25kg / 0.3kg = 2.25 / 0.3 = 7.5 batches
a 3 gallon bottle of bleach costs 15.84. what is the price per cup
Answers
Answer: $0.33 per cup
15.84/3 to find the price per 1 gallon.
15.84/3 = 5.28 per gallon
There are 16 cups in a gallon, so divide the price of a single gallon by 16.
5.28/16 = price per cup
5.28/16 = .33
The price for each cup of bleach is $0.33.
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On a number line, the coordinates of X, Y, Z, and W are -8, -4, 3, and 9, respectively.
Find the lengths of thetwo segments below. Then tell wethwr they are congruent.
___ ___
XY and ZW
___
The length of XY is ___
___
The length of ZW is ___
Answers
The length of XY is 4, the length of ZW is 6 and the lengths are not congruent
How to find the lengths of the two segments?The coordinates of the points are given as:
X, Y, Z, and W = -8, -4, 3, and 9,
The above means that
XY = |Y - X|
ZW = |W - Z|
So, we have
XY = |-4 + 8| = 4
ZW = |9 - 3| = 6
Hence, the length of XY is 4, the length of ZW is 6 and the lengths are not congruent
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In a sample of 10,000 observations from a normal population, how many would you expect to lie beyond three standard deviations of the mean? Group of answer choices About 100 About 127 None of them About 27
Answers
Around 27 of the observations are expected to lie beyond this interval.
Given data values of 10000 observations, 0.27 percent of 10000 is 0.27∗10000100=27. 0.27 ∗ 10000 100 = 27.
A set of real numbers known as an interval in mathematics contains all real numbers falling inside any two of the set's numbers. For instance, the interval containing 0, 1, and all integers in between is the set of values x satisfying 0 x 1.
The numbers in between any two particular provided numbers are referred to as an interval. For instance, the interval containing 0, 5, and all values between 0 and 5 is the set of numbers x satisfying 0 x 5.
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Can someone help ????:)
Answers
Answer:
Step-by-step explanation:
1. 65,700. 65,740 65,743 65,743.2 65,743.18
2. 0 20 20. 19.7 19.74
3. 8,500. 8,460. 8,456 8,456.2 8,456.19
4. 300. 320. 318 318.3 318.28
Simplify the expression. (2+1)×42÷2
Answers
Answer:
63
Step-by-step explanation:
Simplifying the expression,
→ (2+1) × 42 ÷ 2
→ 3 × 42 ÷ 2
→ 126 ÷ 2 = 63
Hence, the answer is 63.
ALGEBRA 1 HW!! PLEASE HELP I WILL GIVE BRAINLYEST also pls explain what the heck an explicit formula is..
Answers
Answer:y=10n+15
Step-by-step explanation:
four boys hiked a distance of 2.53 km from manila south cemetery to washington sycip park. round the distance to the nearesr tenths
Answers
Answer:
2.5
Step-by-step explanation:
Mu choices are 2.5 or 2.6 .
2.53 would be closer to 2.5 than to 2.6
The distances would be
2.50, 2.51. 2.52, 2.53, 254. 2.55, 2.56, 2.57, 2.58, 2.59, 2.60
Another name for 2.5 would be2.50 and another name for 2.6 would be 2.60. Do you see from the list above that 2.53 would be closer to 2.50 than 2.60
please help
maths geometry
(you can’t use congruency)
Answers
Step-by-step explanation:
ok, let's try this again. we need to explain congruence then in its details as an implicit part of the proof, as everything boils down to that.
due to AE = FC we also know that ED = BF.
because as ABCD is a parallelogram, it means AD = BC (and AB = DC).
and AD || BC, AB || DC.
as AD = AE + ED and BC = BF + FC, it means that
AE + ED = BF + FC
with AE = FC we can then simplify to
ED = BF.
as AD || BC, so is also ED || BF.
since the distance from E to D is the same as for B to F, it means that EB and DF must be equidistant to each other, and that means they are parallel.
and because ED || BF, that also means that both line segments are equidistant from each other, and that means that the connections between their end points (EB and DF) must have the same lengths.
therefore, the shape is a quadrilateral with 2 pairs of parallel and equally long line segments. and that is the definition of a parallelogram.
so, BEDF is a parallelogram.
The relationship between the 8’s in 0.088
Answers
Hundred(ths)
Answer:
It's in the Hundredths place uwu
Use properties to find the product. 25x8x4
Answers
The line of reflection is the y-axis.
True
False
Answers
Answer: True :)
Step-by-step explanation:
You want to put a 2 inch thick layer of topsoil for a new 25 ft by 34 ft garden. The dirt store sells by the cubic yards. How many cubic yards will you need to order? The store only sells in increments of 1/4 cubic yards.
Answers
the answer is d just did it
the area of a sector is 5.024cm2 and the angle is 36°. what's the radius
Answers
Answer:
mark me brainlest
Step-by-step explanation:
The area of sector is = pi* r^2*β\360 …. . . .(1
Where
Pi=3.14
r = radius
β= angle=36
So. Put value in equation 1
5.024=3.14 * r^2*36/360
5.024*360/(3.14*36)= r^2
16=r^2
r=4
Given the recursive formula shown, what are the first 4 terms of the sequence?
f(n)=
f(1) = 3
(f(n)=f(n-1)+4 if n>1
OA) 3, 7, 11, 15
B) 4, 7, 10, 13
C) 3, 9, 11, 13
D) 3, 8, 10, 12
Answers
Answer:
Option A: 3, 7, 11, 15
Step-by-step explanation:
f(2) = f(1) + 4 = 3 + 4 = 7
f(3) = f(2) + 4 = 7 + 4 = 11
f(4) = f(3) + 4 = 11 + 4 = 15
f(5) = f(4) + 4 = 15 + 4 = 19
Find a pair of real number whose sum and product are both 12
Answers
The real number whose sum and product are both 12 area 1.101 and 11.899
A quadratic formula that provides the solutions of the final equation ax2 + bx + c = zero which is typically written within the form x = (-b ± √(b2 − 4ac))/(2a) ...(1)Let first number be " x "
Let other number be " 12 - x "
According to the question the product of two numbers is 12 which is given by x(12 - x) = 12
12x - x² = 12
x²- 12x + 12 = 0
Using quadratic formula , we get
Put a = 1 , b = -12 , c = 12 in equation (1) , we get
[tex]\frac{-(-12)\pm\sqrt{(-12)^2-4(1)(12)} }{2(1)} \\\\\frac{12\pm\sqrt{144-48} }{2} \\\\\frac{12\pm\sqrt{96} }{2} \\\\\frac{12\pm9.79 }{2} \\\\[/tex]
Two numbers are 12 + 9.79 / 2 = 1.10 and 12 - 9.79/2 = 10.89
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A cyclist his bike at a speed of 40 kilometers per hour what is this speed in miles? How many miles will the cyclist travel in 5 hours ? In your computations assume that 1 mile is equal to 1.6 kilometers. do not round your answers.
Answers
The cyclist cover 200 kilometer in 5 hours and his speed in miles are 25 miles per hour.
According to the statement
We have to find that the speed of the cyclist.
So, For this purpose, we know that the
Speed is the time rate at which an object is moving along a path
From the given information:
A cyclist his bike at a speed of 40 kilometers per hour
Then
The distance he covered in 5 hours = 40*5
The distance he covered in 5 hours = 200.
And then
The speed in miles :
We have given that the 1 mile is equal to 1.6 kilometers
Then
If he covers a 40 kilometers in a hour then
in miles it becomes = 40/1.6
In other words,
Speed in miles = 40/1.6
Speed in miles = 25 miles per hour.
So, The cyclist cover 200 kilometer in 5 hours and his speed in miles are 25 miles per hour.
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Sam had 233 dollars to spend on 7 books. How much did each book cost ?
Answers
Answer:
0
3
3
7
2
3
3
-
0
2
3
-
2
1
2
3
-
2
1
2
Step-by-step explanation:
SOOOOOOOOOO THE ANSWER 33 with the reamder of 2
Find the slope of (8,9) and (23,9)
Answers
Step-by-step explanation:
you mean the slope of the line between (8, 9) and (23, 9).
we can see that right away, as the y value does not change. it means it is a flat line, and that means the slope is 0.
now, formally :
the slope of a line is (y coordinate change / x coordinate change) when going from one point on the line to another.
the direction does not matter, but once we pick one for the comparison of one coordinate, we have to use the same direction also for the other.
I prefer to go from left to right.
so, from (8, 9) to (23, 9).
x changes by +15 (from 8 to 23).
y changes by 0 (from 9 to 9).
the slope is therefore 0/+15 = 0.
True or False:
______1. The number of decimal numbers in the product is based on the number of decimal numbers of the factors.
______2. In multiplying with 0.001, move the decimal point to the right 3 times.
______3. Multiplying decimal is almost the same as multiplying whole numbers.
______4. In 3.41 x 1,000, the product is 3,410.
______5. The product of 16.23 and 17.4 is 282.402.
Answers
Answer:
Step-by-step explanation:
2 plus the cube of a number.
Answers
Answer:
2+[tex]x^{2}[/tex]
Step-by-step explanation:
Converted from word to standard form.
Please solve this. it is due TODAY. no explain needed.
Answers
a = 18t + 5 4) Leo made an initial deposit to a savings account. Each week thereafter, he deposited a fixed amount into the account. The equation above models the amount, a, in dollars, that Leo has deposited after t weekly deposits. According to the model, how many dollars was Leo's initial deposit? (Disregard the $ sign when gridding your answer.) 5 6 8 9
Answers
According to the model, Leo's initial deposit was $0
According to the model, how many dollars was Leo's initial deposit?The model is given as
a = 18t + 5
When he makes his initial deposit, the value of t is
t = 0
i.e. this represents his balance before he starts saving on a weekly basis
Substitute 0 for t in the equation a = 18t + 5
So, we have
a = 18 * 0 + 5
Evaluate
a = 5
Hence, Leo's initial deposit was $0
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A plastic page designed to hold trading cards will hold up to 8 cards. How many pages will be needed to store 583 cards? Give an appropriate counting number answer to the question. (Find the least counting number that will work.)
The number of pages that would be needed to store 583 cards is (blank).
Answers
Answer:
73 pages
Step-by-step explanation:
You want the number of pages required to hold 583 cards when each page will hold 8.
Least integerThe number of pages required is ...
(583 cards)/(8 cards/page) = 72 7/8 pages
The least integer greater than this number is 73
The number of pages needed to store 583 cards is 73.
Please help need to turn in by tomorrow I really need help I don’t even get how to do it could someone explained
Answers
Step-by-step explanation:
Technically what you have to do is find what changed in the table charts
find the difference between the output values
find the difference between the input values
then calculate the ratio between the change in the Y and X values
Convert 50°F to degrees Celsius.
If necessary, round your answer to the nearest tenth of a degree.
Here are the formulas.
C=5/9(F-32)
F=9/5C+32
Answers
Answer:
10°C
Step-by-step explanation:
F = 50
C = 5/9 * (F - 32) = 5/9 * (50 - 32) = 5/9 * 18 = 5 * 2 = 10
What's the current temperature? 5 + (-12) = ?
Answers
Answer:
-7
Step-by-step explanation:
To add a positive number, 5, and a negative number, -12, take the absolute value of both numbers.
You get 5 and 12.
Subtract the smaller absolute value from the larger absolute value.
12 - 5 = 7
The sign of the answer is the same sign as the number that has the larger absolute value. The absolute of 5 is 5. The absolute value of -12 is 12. -12 has the larger absolute value, and -12 is negative, so the answer is negative.
5 + (-12) = -7
Can the cube of an integer be a negative number? Explain.
Answers
Answer: yes only if the number is negative itself.
Step-by-step explanation: [tex]-3^{3}[/tex] = -27
explanation: -3 x -3 x -3 = 9 x -3 = -27
