Answer: -1 < x < 3
Step-by-step explanation:
[tex]\dfrac{5}{(x+2)(4-x)}<1[/tex]
Step 1 The denominator cannot equal zero:
x + 2 ≠ 0 and 4 - x ≠ 0
x ≠ -2 4 ≠ x
Place these restrictive values on the number line with an OPEN dot:
<----------o-------------------o--------->
-2 4
Step 2 Find the zeros (subtract 1 from both sides and set equal to zero):
[tex]\dfrac{5}{(x+2)(4-x)}-1=0\\\\\\\dfrac{5}{(x+2)(4-x)}-\dfrac{(x+2)(4-x)}{(x+2)(4-x)}=0\\\\\\\dfrac{5-(-x^2+2x+8)}{(x+2)(4-x)}=0\\\\\\\dfrac{5+x^2-2x-8}{(x+2)(4-x)}=0\\\\\\\dfrac{x^2-2x-3}{(x+2)(4-x)}=0\\\\\\\text{Multiply both sides by (x+2)(4-x) to eliminate the denominator:}\\x^2-2x-3=0\\(x-3)(x+1)=0\\x-3=0\quad x+1=0\\x=3\quad x=-1[/tex]
Add the zeros to the number line with an OPEN dot (since it is <):
<----------o-----o----------o----o--------->
-2 -1 3 4
Step 3 Choose test points to the left, between, and to the right of the points plotted on the graph. Plug those values into (x - 3)(x + 1) to determine its sign (+ or -):
Left of -2: Test point x = -3: (-3 - 3)(-3 + 1) = Positive
Between -2 and -1: Test point x = -1.5: (-1.5 - 3)(-1.5 + 1) = Positive
Between -1 and 3: Test point x = 0: (0 - 3)(0 + 1) = Negative
Between 3 and 4: Test point x = 3.5: (3.5 - 3)(3.5 + 1) = Positive
Right of 4: Test point x = 5: (5 - 3)(5 + 1) = Positive
+ + - + +
<----------o-----o----------o----o--------->
-2 -1 3 4
Step 4 Determine the solution(s) based on the inequality symbol. Since the original inequality was LESS THAN, we want the solutions that are NEGATIVE.
Negative values only occur between -1 and 3
So the solution is: -1 < x < 3
Convert the improper fraction 17⁄5 into a mixed number The denominator is 5 So the denominator of the ______number will be 5 This is from Seneca Learning:
Answer:
3 wholes 2/5
I hope this helps you!
Which expressions are equivalent to 2(4f+2g)2(4f+2g)2, left parenthesis, 4, f, plus, 2, g, right parenthesis ? Choose 3 answers: Choose 3 answers: (Choice A, Checked) A 8f+2g8f+2g8, f, plus, 2, g (Choice B) B 2f(4 + 2g)2f(4+2g)2, f, left parenthesis, 4, plus, 2, g, right parenthesis (Choice C) C 8f+4g8f+4g8, f, plus, 4, g (Choice D, Checked) D 4(2f+g)4(2f+g)4, left parenthesis, 2, f, plus, g, right parenthesis (Choice E) E 4f+4f+4g4f+4f+4g
Answer:
8f + 4g
Step-by-step explanation:
Given
2(4f + 2g)
Required
Determine the equivalent expression
2(4f + 2g)
Open the bracket
2 * 4f + 2 * 2g
Perform right operations on the above
8f + 4g
The expression cannot be further simplified; Hence the result of 2(4f + 2g) when simplified is 8f + 4g
Answer: 8f + 4g also 4(2f + g) and 4f + 4f+ 4g
Step-by-step explanation:
The number of patients treated at Dr. Jason's dentist office each day was recorded for seven days: 3, 8, 11, 22, 17, 5, 4. Using the given data, find the mean, median, and mode for this sample. A. mean: 10, median: 8, mode: none B. mean: none, median: 8, mode: 10 C. mean: 8, median: 10, mode: none D. mean: 14, median: 10, mode: 8
Answer: A. mean: 10, median: 8, mode: none
Step-by-step explanation:
Given : The number of patients treated at Dr. Jason's dentist office each day was recorded for seven days: 3, 8, 11, 22, 17, 5, 4.
First we arrange it order.
3, 4, 5, 8, 11, 17, 22
Mean = (Sum of observations) ÷ (Number of observations)
Number of observations = 7
Sum of observations = 3+4+5+8+11+17+22 =70
Mean = 70 ÷7 = 10
Median = Middle-most value
= 8
Mode = Most repeatted value
= none
Hence, the mean, median, and mode for this sample = A. mean: 10, median: 8, mode: none
Please please please help
Answer:
[tex]\boxed{s=3}[/tex]
Step-by-step explanation:
Use a proportion to solve for the missing side length - a/c = b/d.
AB = XYBC = YZ4/2 = 6/s cross-multiply
4s = 12 divide by 4
[tex]\boxed{s=3}[/tex]
Answer:
Step-by-step explanation:
Because these triangles are similar, their sides exist in proportion to one another. Their angles are exactly the same. but their sides are proprtionate IF they are similar. We are told they are so setting up the proportion:
[tex]\frac{4}{2}=\frac{6}{s}[/tex] and cross multiply:
4s = 12 so
s = 3
You could also look at the fact that the height of the larger triangle is 4 and the height of the smaller is 2, so the larger is twice as big as the smaller; likewise, the smaller is half the size of the larger (that means the same thing). So if the larger side is 6, half of that is 3.
Population data from three towns is displayed in the tables below. Which
town has growth that follows an exponential model?
Answer:
Rushmont
Step-by-step explanation:
Trenton can be ruled out due to its constant increase rate of 1.5. Rushmont can be ruled out because it goes from an increase rate of ~1.8 to an increase rate of 1.4 to an increase rate of 1.3 (exponential decay, not growth, so possibly...). Springville has a rate of ~1.9, then 1.475, then 1.3, also exponential decay. However, y\ =\ x\frac{38}{10}-185 goes through all of springville's points (or close to it), so Rushmont must be the answer.
The town that has growth that follows an exponential model is Town B, Rushmont where the population increases or decreases at a consistent rate over time.
In this case, analyze the population data from the three towns to determine which one exhibits exponential growth.
Let's go through each option briefly:
A. Springville:
The population of Springville in 1960 is 42, and in 1990 it is 156.The difference in population over 30 years is 156 - 42 = 114.The average increase per year is 114 / 30 = 3.8.The growth in Springville does not follow a consistent exponential pattern, as the average increase is not constant over time.B. Rushmont:
The population of Rushmont in 1960 is 38, and in 1990 it is 131.The difference in population over 30 years is 131 - 38 = 93.The average increase per year is 93 / 30 = 3.1.The growth in Rushmont exhibits a consistent increase of approximately 3.1 per year, indicating a possible exponential model.C. Trenton:
The population of Trenton in 1960 is 32, and in 1990 it is 108.The difference in population over 30 years is 108 - 32 = 76.The average increase per year is 76 / 30 = 2.5.The growth in Trenton does not follow a consistent exponential pattern, as the average increase is not constant over time.Based on the analysis above, the town that shows growth following an exponential model is Rushmont (B). It exhibits a consistent increase in population over time, suggesting exponential growth.
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1.
The Springfield Meteorological Center wanted to determine the accuracy of their weather forecasts. They
searched their records for those days when the forecaster had reported a 70% chance of rain. They
compared these forecasts to records of whether or not it actually rained on those particular days. The
forecast of 70% chance of rain can be considered very accurate if it rained on:
A. 95% to 100% of those days.
B. 85% to 94% of those days.
C. 75% to 84% of those days.
D. 65% to 74% of those days.
E
55% to 64% of those days.
Answer:
The correct option is;
D. 65% to 74%
Step-by-step explanation:
The accuracy of a forecast given based on a percentage or proportion or likelihood is determined by the based on the prevalence of the forecast in a similar proportion over the range of data points in which the forecast is made
Therefore, if it actually rained on 70% of those days for which the forecast was made, the forecast can be said to be very accurate.
Which is to say that the forecast of 70% chance of rain can be considered very accurate if it rained on 65 to 74% of those days which is in the range of the forecasted 70%.
Intersecting chords form a pair of supplementary, vertical angles. True or false.
Answer:
its false
Step-by-step explanation:
Answer:
The answer is false
Step-by-step explanation:
I need help with 3 and 4
Answer:
Step-by-step explanation:
3) G
Step-by-step explanation:
Q(-1,-1) R(3,1) S(2,-4)
x+2 y+3 translation then rotation 180 (x,y) be (-x,-y)
Q -1+2 -1+3 (1,2) (-1,-2)
R 3+2 1+3 (5,4) (-5,-4)
S 2+2 -4+3 (4,-1)
The cost of a daily rental car is as follows: The initial fee is $59.99 for the car, and it costs $0.30 per mile. If Joan's bill was $200.00 before taxes, how many miles did she drive? Please help!
Answer:
466.7 or 42.003 miles
Step-by-step explanation:
subtract 59.99 from 200.00. Then you have 140.01 and divide or multiply it by 0.30.
Find the value of x. Your answer must be exact.
X
12.
600
X=
Answer:
x = 6√3Step-by-step explanation:
Since the figure above is a right angled triangle we can use trigonometric ratios to find x
To find x we use sine
sin ∅ = opposite / hypotenuse
From the question
The hypotenuse is 12
The opposite is x
Substitute the values into the above formula and solve for x
That's
[tex] \sin(60) = \frac{x}{12} [/tex]
[tex] \sin(60) = \frac{ \sqrt{3} }{2} [/tex]
[tex]x = \frac{ \sqrt{3} }{2} \times 12[/tex]
We have the final answer as
x = 6√3Hope this helps you
Given quadrilateral ABCD, where the diagonals AC and BD intersect at point E. AE≅EC and BE≅DE Can you prove can you prove that the figure is a parallelogram? Explain. A. Yes; two opposite sides are both parallel and congruent. B. Yes; diagonals of a parallelogram bisect each other. C. Yes; opposite sides are congruent. D. No; you cannot determine that the quadrilateral is a parallelogram.
Answer:
B. Yes; diagonals of a parallelogram bisect each other.
Step-by-step explanation:
The diagonals of a parallelogram bisect each other. If the diagonals of a quadrilateral bisect each other, the quadrilateral is a parallelogram.
Answer: B. Yes; diagonals of a parallelogram bisect each other.
If AE=EC and BE=DE then quadrilateral ABCD is a parallelogram because diagonals of parallelogram bisect each other.
What is parallelogram?A parallelogram is a 2 dimensional figure whose opposite sides are equal to each other and parallel to each other. Area of parallelogram is base*height.
How to prove quadrilateral a parallelogram?To be parallelogram ΔAEB and ΔEDC should be congruent.
Angle AEB= Angle DEC
AE=EC
DE=EB
so both triangles are congruent by side, side, angle.
Similarly AE=EC , DE=EB and vertical angles AED= Vertical angle BEC.
Therefore triangle AED and BEC are congruent and that makes all their corresponding sides are also congruent.
And AB=DC.
Hence both pairs of opposite sides of a quadrilateral are congruent ,then the quadrilateral is a parallelogram.
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A certain forest covers an area of 2600 km^2. Suppose that each year this area decreases by 4.75%. What will the area be after 11 years? Use the calculator provided and round your answer to the nearest square kilometer.
Answer:
1522km^2
Step-by-step explanation:
To solve this, first convert the percentage to a decimal. That would be .0475.
Now subtract that from 1.0 to get the factor it decreases by. This would be 1-.0475 = .9525
Multiply 2600 x (.9525)^11 = 1522.258 which rounds to 1522 km^2
Answer:
The area will be 1292.98 km² after 11 years.
Step-by-step explanation:
To find what decreases by 4.57% each year in kilometers:
2600 × 4.57/100 = 26 × 4.57
= 118.82 km²
To find the area after 11 years:
118.82 × 11 = 1307.02
2600 - 1307.02 = 1292.98 km²
1292.98 km² is the answer.
Write the equation of the line that is parallel to the line y=−14x−3 through the point (4,4). A. y=x+5 B. y=−14x+5 C. y=5x+1 D. y=5x−14
Answer:
None of the answers seem to be correct.
Step-by-step explanation:
The given equation is of the form y = mx + b where m is the slope and b is the y-intercept.
Here, m = -14
Two parallel lines have the same slope. So, the slope of the new line will be -14.
To calculate the y-intercept substitute x=4 and y=4 in the equation.
4 = (-14)(4) + b
Solving for b, we get b = 60.
So, the new equation will be y = -14x + 60
The equation of the line parallel to the given line is y =-14x+60, none of the given options is correct.
What is the equation of a straight line ?The equation of the straight line is given by y = mx +c , Where m is the slope of the line and c is the y-intercept.
The equation of the line is y = -14x -3
The slope of the line parallel to this will be the same as the given line.
m = -14 for both the lines
The line equation parallel to the given line is
y = -14x +c
The line passes through the points (4,4)
4 = -14 * 4 + c
c = 60
y = -14x +60
Therefore, the equation of the line parallel to the given line is y =-14x+60.
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Calculate the volume and surface area of a cone with the base of 20cm, the vertical hieght of 34cm and 35.6cm leaning height.
Answer:
Step-by-step explanation:
Volume = 1/3πr²h
Surface Area = πr(r+√(h²+r²))
V = 1/3π(10)²(34) = 3560 .5 cm³
SA = π(10)(10 + √(34²+10²)) = 1427.5 cm²
A point is randomly chosen on a map of North America. Describe the probability of the point being in each location: North America: New York City: Europe:
Answer:
We know that the map is of North America:
The probabilities are:
1) North America:
As the map is a map of North America, you can point at any part of the map and you will be pointing at North America, so the probability is p = 1
or 100% in percentage form.
2) New York City.
Here we can think this as:
The map of North America is an extension of area, and New Yorck City has a given area.
As larger is the area of the city, more probable to being randomly choosen, so to find the exact probability we need to find the quotient between the area of New York City and the total area of North America:
New York City = 730km^2
North America = 24,709,000 km^2
So the probability of randomly pointing at New York City is:
P = ( 730km^2)/(24,709,000 km^2) = 3x10^-5 or 0.003%
3) Europe:
As this is a map of Noth America, you can not randomly point at Europe in it (Europe is other continent).
So the probaility is 0 or 0%.
Answer:
North America: certain
New York City: unlikely
Europe: impossible
Step-by-step explanation:
simply
2x - 3y = -5
5x - 22 = -4y
Solve In Multiplication Method
Answer:
(2, 3 )
Step-by-step explanation:
Given the 2 equations
2x - 3y = - 5 → (1)
5x + 4y = 22 → (2) [ rearranged equation ]
Multiplying (1) by 4 and (2) by 3 and adding will eliminate the term in y
8x - 12y = - 20 → (3)
15x + 12y = 66 → (4)
Add (3) and (4) term by term to eliminate y, that is
23x = 46 ( divide both sides by 23 )
x = 2
Substitute x = 2 in either of the 2 equations and evaluate for y
Substituting into (2)
5)2) + 4y = 22
10 + 4y = 22 ( subtract 10 from both sides )
4y = 12 ( divide both sides by 4 )
y = 3
Solution is (2, 3 )
Find all complex numbers $z$ such that $z^4 = -4.$
Note: All solutions should be expressed in the form $a+bi$, where $a$ and $b$ are real numbers.
Converting -4 to polar form gives [tex]-4=4\exp(i\pi)[/tex].
Then the 4th roots of -4 would be the numbers
[tex]4^{1/4}\exp\left(i\dfrac{\pi+2k\pi}4\right)[/tex]
where k is taken from {0, 1, 2, 3}.
So we have
[tex]z_1=4^{1/4}\exp\left(\dfrac{i\pi}4\right)=\sqrt2\left(\cos\dfrac\pi4+i\sin\dfrac\pi4\right)=1+i[/tex]
[tex]z_2=\sqrt2\left(\cos\dfrac{3\pi}4+i\sin\dfrac{3\pi}4\right)=-1+i[/tex]
[tex]z_3=\sqrt2\left(\cos\dfrac{5\pi}4+i\sin\dfrac{5\pi}4\right)=-1-i[/tex]
[tex]z_4=\sqrt2\left(\cos\dfrac{7\pi}4+i\sin\dfrac{7\pi}4\right)=1-i[/tex]
20 POINTS!!! Please Help! No nonsense answers please!
Answer:
[tex](2-\sqrt{7}, 2+\sqrt{7})[/tex]
Step-by-step explanation:
it is 4km from Martina house to the nearest mailbox. how far is it in meters?
Answer:
4,000
Step-by-step explanation:
1 kilo = 1,000 meters.
in the equation x=c-b/a, find the value of x when c=10, b=2, and a=2
Answer:
9
Step-by-step explanation:
x = c - b/a
x = 10 - 2/2
x = 10 - 1
x = 9
Answer:
x = c - b (divided by) a
Step-by-step explanation:
x = 10 - 2over2
x = 10 - 1
x = 9
try 18/2 since that part is a fraction.
Initial Knowledge Check
Question 2
Suppose that $4000 is placed in an account that pays 11% interest compounded each year.
Assume that no withdrawals are made from the account.
Follow the instructions below. Do not do any rounding.
(a) Find the amount in the account at the end of 1 year
sc
(b) Find the amount in the account at the end of 2 years.
?
Answer:
Step-by-step explanation:
We first need to figure out what the equation is for this set of circumstances before we can answer any questions. We will use the equation
[tex]A(t)=P(1+r)^t[/tex] which is just another form of an exponential equation where
(1 + r) is the growth rate, P is the initial investment, and t is the time in years. We will fill in the values we know first to create the equation:
[tex]A(t)=4000(1+.11)^t[/tex] which simplifies to
[tex]A(t)=4000(1.11)^t[/tex]
Now we'll just sub in a 1 for t and solve, then a 2 for t and solve.
When t = 1:
A(t) = 4000(1.11) so
A(t) = 4440
When t = 2:
[tex]A(t)=4000(1.11)^2[/tex] which simplifies to
A(t) = 4000(1.2321) so
A(t) = 4928.40
Christine, Dale, and Michael sent a total of 71 messages during the weekend. Dale sent 9 fewer messages than Christine. Michael sent 2 times as many messages as Christine. How many messages did they each send?
Answer:
Micheal sent 40 messages, Christine sent 20, and Dave sent 11.
Step-by-step explanation:
Christine, Dale, and Michael sent a total of 71 messages
C + D + M = 71
Dale sent 9 fewer messages than Christine
D = C - 9
Michael sent 2 times as many messages as Christine
M = 2C
Plug-in the numbers.
C + C - 9 + 2C = 71
4C - 9 = 71
4C = 80
C = 20
Now, plug in to other equations for other results.
D = (20) - 9
D = 11
M = 2(20)
M = 40
Micheal sent 40 messages, Christine sent 20, and Dave sent 11.
Verify?
40 + 20 + 11 = 71.
A will states that 4/5 of estate is to be divided among relatives. Of the remaining estate1/4 goes to the American cancer society. What fraction of the estate goes to the American cancer Society
Answer:
1/9 of the estate is for American cancer societyStep-by-step explanation:
In this problem we are expected to calculate the fraction of a whole that belongs to a part. that is the fraction of the estate the belongs to American cancer society.
let us state as given that the total estate is 5
and 4 is to be divided among relatives, remaining 1
out of the remaining 1 estate,
1/4 belongs to American cancer society
Therefore the fraction of the 5 estates that belongs to American cancer society is = 1/4 of 1/5= 1/9
Point E is on line segment DF. Given DE=9 and DF=11, determine the length EF.
Answer:
EF = 2 units
Step-by-step explanation:
Given:
Line segment DF and point E on it.
DF = 11 unit
DE = 9 Unit
Find:
EF
Computation:
We know that,
DF = DE + EF
11 = 9 + EF
EF = 11-9
EF = 2 units
The table shows ordered pairs of the function. What is the value of y when? A 2-column table with 6 rows. The first column is labeled x with entries negative 3, negative 1, 1, 4, 8, 10. The second column is labeled y with entries 14, 10, 6, 0, question mark, negative 12. –20 –8 8 48
I need this quick;-;
Answer:
-8
Step-by-step explanation:
i checked it out on ... and it was negative eight
Answer:
B: -8
Step-by-step explanation:
edg2021
Just plug 8 into the equation.
determine the equation for the quadratic relationship graphed below.
Answer:
[tex]\large \boxed{\sf \bf \ \ y=3x^2-6x-1 \ \ }[/tex]
Step-by-step explanation:
Hello, please consider the following.
We can read from the graph that the vertex is (1,-4) , it means that the equation is, a being a real number.
[tex]y=a(x-1)^2-4[/tex]
And the point (0,-1) is on the graph so we can write.
[tex]a\cdot 1^2-4=-1 \\\\a-4+4=-1+4\\\\a = 3[/tex]
So the equation is.
[tex]y=3(x-1)^2-4\\\\=3(x^2-2x+1)-4\\\\=3x^2-6x+3-4\\\\=3x^2-6x-1\\\\=\boxed{3}x^2\boxed{-6}x\boxed{-1}[/tex]
Hope this helps.
Do not hesitate if you need further explanation.
Thank you
Answer:
[tex]y=3x^{2} -6x-1[/tex]
Step-by-step explanation:
Pls help me... Need proper working .. Answer all questions and explain a bit, a bit..... OK?if anything that you don't understand.... Ask me.
Step-by-step explanation:
for no .5.no.6...you must understand that if u want to get speed,distance must multiple with time
Drag each tile to the correct box.
Arrange the functions in increasing order of their periods.
y=-3tan(x+2pi)
y = 2/3csc(x/4)+6
y=-1/2cos(5x/6+pi)
y=5sec(3x) +6
y =-1/3sin(x/3)
y=-10cot(x/2-2pi)
Answer:
y=5sec(3x) +6
y=-3tan(x+2pi)
y=-10cot(x/2-2pi)
y=-1/2cos(5x/6+pi)
y =-1/3sin(x/3)
y = 2/3csc(x/4)+6
The functions in increasing order of their periods are given below.
y=5sec(3x) +6
y=-3tan(x+2pi)
y=-10cot(x/2-2pi)
y=-1/2cos(5x/6+pi)
y =-1/3sin(x/3)
y = 2/3csc(x/4)+6
As y = 2/3csc(x/4)+6 gives a high value than the other, it is considered the highest.
What are increasing order and decreasing order?Ascending order way going up from small value to excessive cost and textual content from A to Z. Descending order manner arranging the numbers from largest to smallest and textual content from Z to A. while the names are arranged for a list, then it is usually arranged in A to Z order, alphabetically.
Steps to find the Period of a Function
If a function repeats over a constant period we say that is a periodic function.It is represented like f(x) = f(x + p), p is the real number and this is the period of the function.Period means the time interval between the two occurrences of the wave.Learn more about functions here: https://brainly.com/question/2833285
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A beach is 7.3 miles wide and 30 miles long. If one inch of rain falls on this beach, how many cubic feet of rain fell in this area? Hint: convert units to feet first.
Answer:
Step-by-step explanation:
volume=7.3×1760×3×30×1760×3×1/12=73×176×90×440=508780800 ft³
Answer:
508,780,800 ft³ of rain
Step-by-step explanation:
In order to do the computation, we need to express all the given lengths in feet.
recall that 1 mile = 5280 feet
hence,
width = 7.3 miles = 7.3 x 5280 = 38,544 feet
length = 30 miles = 30 x 5280 = 158,400 feet
also recall that 1 inch = 1/12 feet
hence,
depth of rainfall = 1 inch = 1/12 feet
Volume of rain = width of beach x length of beach x depth of rainfall
= 38,544 x 158,400 x (1/12)
= 508,780,800 ft³ of rain
Factor completely, then place the answer in the proper location on the grid. 6x2 - 3x - 30
Answer:
3(2x-5)(x+2)
Step-by-step explanation:
Factor out the 3.
3(2x²-x-10)
Factor the remaining.
3(2x-5)(x+2)
(I don‘t know what grid they’re talking about.)
