Given that
[tex]\displaystyle \lim_{x\to0} f(x) = 4[/tex]
we can use the properties of limits to show
[tex]\displaystyle \lim_{x\to0} \frac14 f(x)^4 = \frac14 \lim_{x\to0} f(x)^4 = \frac14 \left(\lim_{x\to0} f(x)\right)^4 = \frac14 \times 4^4 = 4^3 = \boxed{64}[/tex]
Let's see
[tex]\\ \rm\Rrightarrow \lim_{x\to 0}\dfrac{1}{4}f(x)^4[/tex]
[tex]\\ \rm\Rrightarrow \dfrac{1}{4}\lim_{x\to 0}f(x)^4[/tex]
[tex]\\ \rm\Rrightarrow \dfrac{1}{4}\times 4^4[/tex]
[tex]\\ \rm\Rrightarrow \dfrac{256}{4}[/tex]
[tex]\\ \rm\Rrightarrow 64[/tex]
Can someone please help me with this?
Answer:
Answer Option C
Step-by-step explanation:
They make a big plus sign, PLUS=PERPENDICULAR
do these ratios form a proportion?
Answer:
No, because both of them will never be able to match; become equivalent. You would have to multiply 2 different numbers to make them match, meaning they would not be proportional. For a comparison to be proportional, the ratio you are trying to simplify to must be achieved by multiplying 2 numbers from the previous ratio by one LCD.
[tex]\frac{3\cdot 4}{7 \cdot 3} = \frac{12}{21}[/tex]
They are able to make 12/21, but that does not mean they are proportional.
Find the volume of pyramid
Answer:
V=lwh
3
Step-by-step explanation:
please answer!!
Use the parabola tool to graph the quadratic function.
f(x)=3x^2+6x−24
Graph the parabola by first plotting its vertex and then plotting a second point on the parabola.
Answer:
See below
Step-by-step explanation:
[tex]f(x)=3x^2+6x-24\\\\f(x)=3(x^2+2x-8)\\\\f(x)+3(9)=3(x^2+2x-8+9)\\\\f(x)+27=3(x^2+2x+1)\\\\f(x)=3(x+1)^2-27[/tex]
Here, we can see that the vertex of the parabola is [tex](-1,-27)[/tex] when we compare to the equation [tex]y=(x-h)^2+k[/tex] with vertex [tex](h,k)[/tex].
A second point you could plot is the y-intercept, when [tex]x=0[/tex]:
[tex]f(0)=3(0+1)^2-27\\\\f(0)=3-27\\\\f(0)=-24[/tex]
So, your y-intercept is [tex](0,-24)[/tex].
( 4 , 1 2/3 ) ( 2 , − 2/3 ) find the slop
Answer:
7/6
Step-by-step explanation:
To find the slope you divide the difference of the y-coordinates of 2 points on a line by the difference of the x-coordinates of those same 2 points.
so doing that i get 7/6
Hope This Helped
Please help it’s easy, I just need help on the state the problem questions. Make sure to put the number by the answer.
The property of the questions are correctly stated below.
Properties of the various given equations Commutative property of addition: This is represented by equation 7Commutative property of multiplication: This is represented by equation 5.Associative property of addition: This is represented by equation 4.Associative property of multiplication: Not represented with any equation.Additive identity property: This is represented by equation 10.Multiplicative identity property: This is represented by equation 1.Multiplicative property of zero: This is represented by equation 8.Multiplicative inverse property: Not represented with any equation.Distribution property: This is represented by equation 2.Reflexive property: This is represented by equation 3.Symmetric property: Not represented with any equation.Transitive property: This is represented by equation 2.Substitution property: This is represented by equation 2.Learn more about equations here:
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Solve the inequality for x and identify the graph of its solution (picture added)
The inequality that is correctly graphed is the one in option B.
Which graph correctly describes the inequality?Remember that if we have symbols like ≤ or ≥, we graph a solid circle, while if we use symbols like > or <, we need to use an open circle.
If we write:
x < -3
Then we must have an orange line to the left of x < -3
Finally, the option that you marked is wrong.
Why?
There it says that:
"x < -3 and x > 1"
The "and" means that x meets both properties at the same time, which is impossible.
The correct option is the one that says:
"x < -3 or x > 1".
The "or" means that x needs to meet only one of the two conditions, not both at the same time.
Then the correct option is B.
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Which number is rational?
Ο Α. π
Ο Β. εξ
Ο c. 0.777...
Ο D. 0.36458121...
Step-by-step explanation:
0.777... is rational since it can be put in fraction form which is 7/9
note: if something can be put as an integer/integer its rational
what is 29/5 is equal to
Answer:
5 4/5 or 5.8
Step-by-step explanation:
convert 29/5 to 5 4/5
or
divide 29/5 is 5.8
solve 5x^2=180 algebraically
Answer:
x = ± 6
Step-by-step explanation:
Hello!
Solve[tex]5x^2 = 180[/tex][tex]x^2 = 180/5[/tex][tex]x^2 = 36[/tex][tex]\sqrt{x^2} = \sqrt{36}[/tex][tex]x = \pm 6[/tex]The value of x is 6 or -6.
Hi...
Given:
[tex]\texttt{5x}[/tex]² [tex]\texttt{= 180}[/tex]
Solution:[tex]\texttt{5x}[/tex]² [tex]\texttt{= 180}[/tex]
Explanation:Divide both sides by 5
[tex]\hookrightarrow{\mathtt{\frac{5x^2}{5}} = {\mathtt{\frac{180}{5}}[/tex]
Simplify:
[tex]\hookrightarrow{\mathtt{x^2 = 36}[/tex]
[tex]\hookrightarrow{\mathtt{For \: x^2 \: = f(a) \: the \: solutions \: are \: x = \sqrt{f(a)}}[/tex] , [tex]\mathtt{- \sqrt{f(a)}}[/tex]
[tex]\hookrightarrow{\mathtt{x = \sqrt{36}}[/tex] , [tex]\mathtt{x = -\sqrt{36}}[/tex]
Factor the number: 36 = 6²
[tex]\mathtt{= \sqrt{6^2}}[/tex]
Apply radical rule: [tex]\mathtt{\sqrt[n]{a^n} \: = a}[/tex]
[tex]\mathtt{\sqrt{6^2} = 6} \\\mathtt{= 6}[/tex]
- [tex]\sqrt{36} = -6[/tex]
[tex]\boxed{\fbox{\bf{x = 6 , x = -6}}}[/tex]
Hope It Helps You...
what is the volume of a rectangular prism 8 inches long, 3 inches wide,and 5 inches high?
120 cubic inches
220 cubic inches
16 cubic inches
or 158 cubic inches
Answer:
V=whl=3·5·8=120
Step-by-step explanation:
Just use l x w x h and there you go.
3x^2-8=5x solve using quadratic equation
Answer:
x = -1 or x = 8/3
Step-by-step explanation:
3x² - 8 = 5x
3x² - 5x - 8 = 0
3x² - 8x + 3x - 8 = 0
(Here you find two numbers which have a sum of -5 and a product of 3×-8= -24. These two numbers are -8 and 3. -8 + 3 = -5 and -8 × 3 = -24.)
(3x² - 8x) (3x - 8) = 0
x(3x - 8) +1(3x - 8) = 0
(x + 1) (3x - 8) = 0
x + 1 = 0 OR 3x - 8 = 0
x = -1 3x = 8
x = [tex]\frac{8}{3}[/tex]
Simplify the expression. Write your answer as a power.
The simplified expression is
What number can be used to complete the volume statement for the cone?
a cone with height 4 meters and diameter 3 meters.
volume =
Answer: 9.42 cu. meters
Step-by-step explanation:
V= 1/3 x TT x r^2 x height
TT (pi) = 3.14
r^2 is 1/2 diameter = 1.5
height = 4
V = 1/3 x 3.14 x 1.5^2 x 4
V= 1/3 x 3.14 x 2.25 x 4
V = 9.42 cu. meters
Use the graph to find the value of f(x) when x = 9 for the function f (x) =
1
3
x − 3.
Step-by-step explanation:
this looks totally like
f(x) = 1/3 x - 3
to me.
because
f(0) = -3
f(3) = -2
f(6) = -1
so, f(9) = 1/3 × 9 - 3 = 3 - 3 = 0
f(9) = 0
you did not list that as answer option, but that is the correct answer.
the area of the triangle below is 1/4 square meters. what is the length of the base. express your answer in simplest form
Answer:
4/5
Step-by-step explanation:
Given,
Area of the triangle = 1/4 square meters
From the diagram,
Height = 2/5 m
To find : Length of the base
Formula : -
A = bh/2
Here,
A denotes Area
b denotes Base
h denotes Height
A = 1/4
h = 2/5
A = bh/2
Cross multiply,
A * 2 = bh
2A = bh
2 * (1/4) = b * (2/5)
(1 * 2)/4 = (b * 2)/5
2/4 = 2b/5
1/2 = 2b/5
Cross multiply,
1 * 5 = 2 * 2b
5 = 4b
b = 4/5 meters
Hence,
The length of the base is 4/5 meters.
The length of the base of the triangle is 5/4 meters.
What is Triangle?A triangle is a two dimensional figure which consist of three vertices, three edges and three angles.
Sum of the interior angles of a triangle is 180 degrees.
The formula to find the area of the triangle is,
Area = [tex]\frac{1}{2}[/tex] × base × height
Given,
Area of the given triangle = 1/4 square meters
Height = 2/5 meters
Substituting in to the formula,
[tex]\frac{1}{2}[/tex] × base × 2/5 = 1/4
1/5 × base = 1/4
Base = 5/4 meters
Hence the base of the triangle is 5/4 meters.
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-10 + 2t = -20 16t + 17t
t=2/61
1 Rearrange terms
2
Multiply the numbers
3
Combine like terms
4
Add
10
to both sides
5
Simplify
6
Add
303t
to both sides
7
Simplify
8
Divide both sides by the same factor
9
Simplify
What is the missing probability from the line?
Give your answer as a decimal.
The missing probability from the line in the diagram attached is 0.5.
What is a missing probability from the number line?The number line is a graduated straight line system showing the value of each real number from (-∞, +∞).
The probability of a number line in the diagram below is halfway (middle) between the impossible event and a certain event.
Thus,
Probability from the line = 1/2Probability from the line = 0.5 (decimal)Learn more about missing probability here:
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What is the area of the parallelogram?
A parallelogram with a base of 9 centimeters and a height of 4 centimeters.
18 cm2
28 cm2
36 cm2
45 cm2
Answer:
Step 1: area is base × height
Step 2: 36cm2
Step-by-step explanation:
Base × height is 9 and 4 and 9×4 = 36cm2
Hope this helps :)
You are preparing a chemical hazard label for a new product. you know that the product is flammable. what pictogram should be on the label
A graphic logo that depicts the meaning of any warning or sign through pictorial illustrations is called a pictogram. It can be used in chemicals, laboratories, geography or tourism. The label should have: Flammable and Health Hazard!
What is a pictogram?The pictogram can be explained as: According to the above description, the label sign should have a warning sign of flammable as it can catch and cause fire, a health hazard as it can cause corrosion, carcinogenic and irritation followed by an exclamation mark.
The flammable sign depicts that the substance can cause and catch fires also it can contain pyrophoric. It is cancer-causing, respiratory irritant and toxic hence is hazardous to health.
The exclamation mark is used at the end of the sentence for showing awareness and to convey the meaning of the sign.
Therefore, Flammable and Health Hazard! the sign should be used.
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What compass heading represents 20° north of west? PLS HELP
Answer:
West North West
Step-by-step explanation:
West North West would be the bottom half of North West after you split the compass heading into 2 again.
Answer:
north of west = 290 degrees
north of east = 70
Step-by-step explanation:
Starting with blue balls, in each of sequential rounds, we remove a random ball and replace it with a new red ball. for example, after the first round we have 9 blue balls and one red ball, after the second round, with probability we have 8 blue balls and 2 red balls, and with probability we have 9 blue balls and one red ball, etc. what is the probability that the ball we remove at the 11th round is blue
The probability that the ball we remove at the 11th round is blue will be 0.6.
How to calculate probability?From the information given, we remove a random ball and replace it with a new red ball. for example, after the first round we have 9 blue balls and one red ball.
Since we have 9 blue balls and remove one every round. Let's assume that the number of blue and red balls will be 6 and 4 respectively in the 11 the round
Therefore, the probability that the ball we remove at the 11th round is blue will be:
= 6/(6 + 4)
= 6/10
= 0.6
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Despite control measures, the pigeon population in Winchester is increasing by 10% each year. If there are currently 9,520 pigeons, how many pigeons will there be in 13 years?
If necessary, round your answer to the nearest whole number.
Using an exponential function, it is found that there will be 32,866 pigeons in 13 years.
What is an exponential function?An increasing exponential function is modeled by:
[tex]A(t) = A(0)(1 + r)^t[/tex]
In which:
A(0) is the initial value.r is the decay rate, as a decimal.The initial value and the growth rate are given by:
A(0) = 9520, r = 0.1.
Hence the function is given by:
[tex]A(t) = 9520(1.1)^t[/tex]
Hence in 13 years, the amount of pigeons will be of:
[tex]A(13) = 9520(1.1)^{13} = 32866[/tex]
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Jasper buys ten bagels with a listed price of $2 each. Which of these coupons will deduct the most from Jasper's purchase price?
A. Free bagel
B. Save 10%
C. $5 off
D. Buy 8, Get 2 free
Answer:
c. $5 off
Step-by-step explanation:
If jasper buys 10 bagels $2 each then it'll cost $20. With a free bagel it'll deduct $2. With 10% off it'll deduct $2. Buy 8, get 2 free deducts $4. Therefore $5 off is the most
Select the correct answer.
Which of the following represents a function?
A.
A value negative 7 in x corresponds to 45 in y. A value negative 4 in x corresponds to 52 in y. A value negative 1 corresponds to negative 2 in y. A value 2 in x corresponds to 45 in y.
B.
{(-7,-9), (-4,-9), (5,15), (7,19)}
C.
x 5 -5 10 5 -10
y 13 -7 23 17 -17
D.
A graph plots the points (negative 3, 1), (negative 3, negative 1), (negative 1, negative 3), (1, 5), (3, negative 3), and (4, negative 5) on the x y coordinate plane.
Answer:
A and B
Step-by-step explanation:
In both of these relations, each input corresponds to one and only output.
5. x = 5,- ²/3, √2
help pls
Answer: 2. 5. f(x)=x²-5; vertically stretched by a factor of 4, followed by a translation 3 units to the right. 4(x²-5). 4((x-3)²-5) g(x)= 4(x-3)²-20.
Step-by-step explanation:
Please help me quick !!
Will mark whoever is first brainliest
Answer:
c
Step-by-step explanation:
y goes up by 4, so the each step is by 4, so that is the slope, which is the number before x, and then you subtract 4 to find the y-intercept, and 3-4=-1
i need to fine the value of x
please help bro
i needa get my grade up and i don’t understand any of this … if you can explain how u got the answer that would be helpful but if not, then it’s fine i guess.
Answer:
7. 630
8. I'm not sure on this one-
9. 1331
Step-by-step explanation:
So for a rectangular prism the formula is l x w x h (length times width times height) Which would be 14 * 5 * 9 which equals 630
For the triangular prism, I forgot the formula
For the cube, you are given 1 number, 11, since it's a cube all lengths are the same so you do 11 to the power of 3 = 1331
100- 1/2 x=92
HELP ME OUT PEPS
Answer:
Hi! The answer is x=16