Answers
An expression to represent the perimeter of the rectangle with 10/(x² + 11x +24) and (x+1)/(x+3) would be (x+12)(x+6)//(x+8)/(x+3).
What is the perimeter?
A closed path that covers, encircles, or outlines a one-dimensional length or a two-dimensional shape is called a perimeter. A circle's or an ellipse's circumference is referred to as its perimeter. There are numerous uses in real life for perimeter calculations.
Here, we have
Given: Sides = 10/(x² + 11x +24) and (x+1)/(x+3)
The perimeter is when you add all the sides of a shape.
In a rectangle, two sides are the same, and so are the other two. therefore, if the two sides are 10/(x² + 11x +24) and (x+1)/(x+3) the expression will be:
= 2(10/(x² + 11x +24)) + 2(x+1)/(x+3)
= 20/(x² + 11x +24) + 2(x+1)/(x+3)
= 20/(x+8)/(x+3) + 2(x+1)/(x+3)
= {20 + 2(x+1)(x+8)}/(x+8)/(x+3)
= {20 + 2(x² + 9x + 8)}/(x+8)/(x+3)
= { 20 + 2x² + 18x + 16}/(x+8)/(x+3)
= {2x² + 18x + 36}/(x+8)/(x+3)
= (x+12)(x+6)//(x+8)/(x+3)
Hence, an expression to represent the perimeter of the rectangle with 10/(x² + 11x +24) and (x+1)/(x+3) would be (x+12)(x+6)//(x+8)/(x+3).
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Related Questions
Does The slopes of parallel lines have a product of -1.
Answers
Answer:
No. The slopes of parallel lines are equal.
Step-by-step explanation:
If you have two lines and their slopes are the same, then the lines are parallel.
If the two lines have slopes that are negative reciprocals (opposite signs and flipped over) then when you multiply the slopes together, you get -1... THOSE lines are perpendicular (they make right angles or make 90° angles or square angles).
Lines in the same plane that have different slopes will intersect at one point.
A fashion designer wants to know how many new dresses women buy each year. A sample of 523 women was taken to study their purchasing habits. Construct the 95% confidence interval for the mean number of dresses purchased each year if the sample mean was found to be 7.3. Assume that the population standard deviation is 1.4. Round your answers to one decimal place.
Answers
The confidence interval for the meannumber of dresses purchased each year is (7.2,7.4).
Given sample mean of 7.3 and sample standard deviation of 1.4 and confidence interval of 95%.
We have to find confidence interval for the mean number of dresses purchased each year.
Because the sample size is more than 30 so z test test will be used.
Margin of error is the difference in real values and calculated values.
Margin of error=z*σ/[tex]\sqrt{n}[/tex]
where zis the criticalvalue of confidence level.
σ is sample standard deviation,
n is sample size.
z value for 95% confidence level=1.96
Margin of error=1.96*1.4/[tex]\sqrt{523}[/tex]
=2.744/22.869
=0.12
Upper level= Mean + margin of error
=7.3+0.12
=7.42
Rounding off
=7.4
Lower level=Mean - margin of error
=7.3-0.12
=7.18
Rounding
=7.1
Hence the confidence interval is (7.1,7.4).
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F(x) = 3* + 10xand g(x) = 5x - 3, find (f - g) (x)
Answers
Answer:
(f-g)(x)= (3x + 10) - (5x -3)
f-g = 3x + 10 - 5x + 3
f-g = -2x + 13
10. A shopkeeper bought 5 sets of sofa from a factory for $ 15800 (inclusive of a 10% value-added
tax). He then sold each set of sofa for $6794.
(a) Calculate the percentage profit made by the shopkeeper. [3]
(b) How much was the value-added tax for the 5 sets of sofa? [2]
Answers
Percentage profit made by the shopkeeper
= (5(6794)-15800)/15800 x 100
= (33970-15800)/15800 x 100
= 1.15 x 100
= 115 %
(b).
Value-added tax
= 10/100 x 15800
= $1580
Hope it helps : )
There are 20 teachers and 705 students in cory's school. what is the ratio of teachers and students
Answers
We know that ratios can be shown with both fractions and colons.
20:705
or
[tex]\frac{20}{705}[/tex]
It also looks like we can simplify this by dividing by 5.
20/5 = 4
705/5 = 141.
This means that for every 4 teachers, there are 141 students.
The ratio for teachers to students is:
4 : 141
HELPP A PERSON OUT PLSS! i dont really understand how to do ittt!!
giving you all my points so help pleaseeee
Answers
(1) 14^2+y^2=Z^2
(2) 6^2+y^2=x^2 and (3) x^2+z^2=20^2
The next step is to solve them simultaneously e.g you can rearrange (2) to give you y^2=x^2-6^2 and then input that into (1) to get 14^2+x^2-6^2=Z^2 and again you rearrange (3) to get z^2=20^2-x^2 and input that in and solve for x. Then you will have to repeat that solving for y and only y as the question doesn’t originally ask for z but only for the values of x and y I assume. Using this idea, from glancing at the other questions you should be able to apply this concept to those other questions, if not then make another post outlining any specific questions
A balloon is falling. it falls 200 feet each minute. how far will it in 3 minutes?
Answers
Answer:
600ft
Step-by-step explanation:
The balloon falls 200 feet in one minute and we need the amount it fell in 3 minutes: 200feet*3minutes = 600 ft
A saleslady is paid a commission of 3% on goods worth 100,000.she is also paid a salary of 11000.in a certain month she sold 360 shoes at460 each.the following month she had a salary increase of 20%.her total earnings were 22,200 calculate total amount of money received from sales of shoes that month
Answers
The total amount of money received from sales of shoes that month = $4968
Calculating sales commissionSalary = $11000
Number of shoes sold = 360
Cost of 1 shoe = $460
Total cost of shoes sold = 360 x 460
Total cost of shoes sold = $165600
Since $165600 is greater than $100000, she will earn a commission of 3%
Commission = (3/100) x $165600
Commission = $4968
The commission is the amount of money received from sales of shoes. Other earnings are salary or increment
Therefore, the total amount of money received from sales of shoes that month = $4968
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Scenario: Kevin is baking cupcakes for a fundraiser at his school. Yesterday, he prepared 30 cupcakes in 45 minutes. Today, he prepared 20 cupcakes in 30 minutes.
A) Does the scenario represent a direct variation?
B) If yes, explain the meaning of the constant of proportionality in the scenario.
take your time if you want :)
Answers
a) As the constants are equal, the situation represents a proportional relationship.
b) The constant of 2/3 cupcakes per minute means that in a minute, 2/3 of a cupcake is made.
What is a proportional relationship?A proportional relationship is a function in which the output variable is given by the input variable multiplied by a constant of proportionality, that is:
y = kx
In which k is the constant of proportionality.
In this problem, the constants for each situation are:
k = 30/45 = (30/15)/(45/15) = 2/3 = 20/30.
Since the constants are equal, the situation represents a proportional relationship.
The constant of 2/3 cupcakes per minute means that in a minute, 2/3 of a cupcake is made.
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Margo spends a quarter of her paycheck on a new dress, one-eighthof her paycheck on shoes, and $24 on a birthday present. if she spent $60 altogether, how much was margo’s paycheck? $96 $160 $216 $504
Answers
So 0.375x + 24=60
0.375x = 60-24
0.375x= 36
X=36/0.375
X=$96
Answer:
$96
Step-by-step explanation:
how many positive odd factors of 48 are greater than 2 and less than 10
Answers
Answer:
Just 1 positive, odd factor
Step-by-step explanation:
48 has many factors. But not many odd factors. Only 3 is odd and bigger than 2 and less than 10.
So, just one odd, positive factor.
in a school of 40 students, 14 liked English language only, 7 students like both English and French language and 12 also like French language only
a. how many students like English but not French?
b. many students did not like any of the two languages?
c. how many students like at least one of the language?
d. if a student is chosen at random what is the probability that he likes only French
Answers
Answer:
A. 14, because it says that only 14 liked English language ONLY
B. It’s 7.
14 liked only English, 7 liked both languages, 12 liked only French.
Add those them together.
14 + 7 + 12
21 + 12
33
33 - 40 = 7
( 33 is the number of students that liked a language and 40 is ALL the students in total )
So it would be 7.
C. 26 liked one language.
7 liked both languages and 7 didn’t like neither. You could add them together.
7 + 7 = 14
40 - 14 = 26
OR
14 + 12 = 26
( just English + just French )
D. The probability of a student chosen at random that ONLY likes French would be 12/40.
Since only 12 of the 40 students liked ONLY French, it would be 12/40 or 12 : 40
Step-by-step explanation:
I hope it helps! Have a great day!
Pan~
Answer:
a) 14
b) 7
c) 33
d) P = 12/40 = 3/10 (In decimal P=0.3)
Step-by-step explanation:
Hope this helps
The more novel a new product or service design is, the more forecasters have to rely on:_______
a) smoothed variation.
b) historical data.
c) seasonality.
d) cyclicality.
e) subjective estimates.
Answers
The more on these factors forecasters must rely, the more innovative a new product or service design is: Subjective Estimates.
Option (e) is correct.
A subjective estimate is a specific type of estimate that is founded on a person's subjective evaluation or in-depth comprehension of the possibility of a specific outcome.
A subjective estimate only takes into account the subject's ideas and prior experiences rather than employing data or exact calculations.
Individual subjective evaluations are highly biased and differ from person to person.
Contrarily, a subjective estimate is incredibly prone to revision, even when only one person's viewpoint is taken into account.
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Tara has read 95%, percent of the books she owns. if tara owns 160 books, how many of her books has she not read?
Answers
Answer:
8 books have not been read.
Step-by-step explanation:
Let X be the number of books Tara owns.
We learn that she has read 95%, which would mean (0.95)*(X) have already been read.
5% have not been read. 5% 0f 160 books equals (0.05)*(160) = 8 books have not been read. Impressive.
In a two-tailed hypothesis test comparing the means of independent samples, the test statistic is 3.06 and the critical values are /-2.086. True or false: the null hypothesis is not rejected.
Answers
In a two-tailed hypothesis test the null hypothesis is rejected.
According to the statement
The test statistic is 3.06 and the critical values are /-2.086.
If we find the value of t by using the formula the then it comes with Negative sign and it lies under the critical region.
That's why In a two-tailed hypothesis test the null hypothesis is rejected.
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bestbroi
If light travels at 10,000 km in 3.0 x 10² seconds,
how long will it take light to travel one meter?
(1 km = 1 x 10³m)
Answers
Answer:
0.03 seconds
Step-by-step explanation:
10,000km = 300secs
1km = x seconds
Cross multiply the equation
10,000x = 300
Divide both sides by 10,000
10,000x = 300
10,000 10,000
x = 0.03 seconds
SOLVE FOR X AND THEN SOLVE FOR A
Answers
Answer:
Step-by-step explanation:
A + B= 180°
(5x+20)+(9x-92)=180°
14x-72=180°
14x=252
x=18
A=5(18)+20
A=110
Answer:
x = 18 , ∠ A = 110°
Step-by-step explanation:
∠ A and ∠ B are same- side interior angles and sum to 180° , that is
5x + 20 + 9x - 92 = 180
14x - 72 = 180 ( add 72 to both sides )
14x = 252 ( divide both sides by 14 )
x = 18
Then
∠ A = 5x + 20 = 5(18) + 20 = 90 + 20 = 110°
Find the seventh term of the sequence which has a first term of 1/2 and has a common ratio of three
Answers
The seventh term of the sequence is 364.5
Geometric progressionFrom the question, we are to determine the seventh term of the sequence
Using the formula,
[tex]a_{n} = ar^{n-1}[/tex]
Where [tex]a_{n}[/tex] is the nth term
a is the first term
and r is the common ratio
From the given information,
a = 1/2
r = 3
Thus,
[tex]a_{7} = (\frac{1}{2}) 3^{7-1}[/tex]
[tex]a_{7} = (\frac{1}{2}) 3^{6}[/tex]
[tex]a_{7} = \frac{1}{2} \times 729[/tex]
[tex]a_{7} = 364\frac{1}{2} \ OR \ 364.5[/tex]
Hence, the seventh term of the sequence is 364.5
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Calculate the (modeled) probability P(E) using the given information, assuming that all outcomes are equally likely.
S = {1, 3, 5, 7, 9}, E = {1, 5, 7}
Answers
The probability P(E) is 13/15.
According to the statement
we have given that the S = {1, 3, 5, 7, 9}, E = {1, 5, 7}
And we have to find the probability P(E).
So, For this purpose
Recall the formula for the probability of an event E in case when all outcomes are equally likely:
P(E)= n(E) /n(S)
in which S is the sample space.
But we have the S = {1, 3, 5, 7, 9},
so, n(S) = Sum of all outcomes / number of outcomes
n(S) = 1+3+5+7+9 /5
n(S) = 25 /5
n(S) = 5 and
For n(E) = Sum of all outcomes / number of outcomes
n(E) = 1+5+7 /3
n(E) = 13 /3
n(E) = 13 /3
Substitute these values in the above written formula then
P(E)= n(E) /n(S)
P(E)= (13/3)/ 5
P(E)= 13 /15
So, The probability P(E) is 13/15.
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HELP HELP HELP HELP
HELP HELP HELP HELP
Answers
I didn't quite get what u meant by exponential form of the function but here
A circle has a central angle measuring startfraction 7 pi over 6 endfraction radians that intersects an arc of length 18 cm. what is the length of the radius of the circle? round your answer to the nearest tenth. use 3.14 for pi.
Answers
The radius of this circle is (B) 4.9 cm.
To find the radius of the circle:To solve this problem, we need to, first of all, convert the angle from radians to degrees.
data;
length of an arc = 18cmangle = 7/6π radsπ= 3.14[tex]\frac{7\pi }{6rads} =210^{0}[/tex]
Length of an Arc:
The formula for the length of an arc is given:
[tex]l_{arc} =[/tex] θ/360 × [tex]2\pi r[/tex]
Let's substitute the values and solve:
[tex]18=\frac{210}{360} *2\pi r\\18=3.663r\\r=\frac{18}{3.663} \\r=4.9cm[/tex]
From the calculations above, the radius of this circle is 4.9cm.
Therefore, the radius of this circle is (B) 4.9 cm.
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Complete question
A circle has a central angle measuring 7pi/6 radians that intersects an arc of length 18 cm. What is the length of the radius of the circle? Round your answer to the nearest tenth. Use 3.14 for pi.
(A) 3.7 cm
(B) 4.9 cm
(C) 14.3 cm
(D) 15.4 cm
What is the solution of startfraction 1 over c minus 3 endfraction minus startfraction 1 over c endfraction = startfraction 3 over c (c minus 3) endfraction?
Answers
The solution of the given equation can be all real numbers, except c = 0 and c = 3.
Lets simplify the given problem,
1/c-3 - 1/c = 3/ (c-3)
As the denominators cannot be equal to zero (0) because a division by zero (0) is undefined.
Next, we would multiply both sides of the given by the lowest common multiple (LCM).
The lowest common multiple (LCM) is c(c - 3).
c-[c-3] = 3
c-c+3 = 3
0 = 3-3
0=0
Therefore, the solution of the given equation can be all real numbers, except c = 0 and c = 3.
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the ecentricity of the conic section below is
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Hi! ❄
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The eccentricity of the conic section below is 1, since the conic section given is a parabola.
The eccentricity of a parabola is 1.
Hope that made sense !!
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[tex]\star\tiny\pmb{_{calligraphy}}\star[/tex]
Hi!
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The eccentricity of the conic section below is 1, since the conic section given is a parabola.
What is parabola?
a parabola is a plane curve which is mirror-symmetrical and is approximately U-shaped. The name "parabola" is due to Apollonius, who discovered many properties of conic sections. conic section produced by the intersection of a right circular cone and a plane parallel to an element of the cone.
#CarryOnLearning
What are the three coordinates that need to be plotted?
Answers
Answer:
Step-by-step explanation:
y=2*|x-3|+2
y=|2*x-2*3|+2
y=|2x-6|+2
1)
y=2x-6
x | 2 | 3 |
y | -2| 0 |
2)
y=|2x-6|
3)
y=|2x-6|+2
y=2*|x-3|+2.
Can someone help me on this pls? It’s urgent, so ASAP (it’s geometry)
Write formal proofs using LL Theorem.
Answers
Question 6
1) [tex]\overline{AB} \cong \overline{BD}[/tex], [tex]\overline{CD} \perp \overline{BD}[/tex], O is the midpoint of [tex]\overline{BD}[/tex], [tex]\overline{AB} \cong \overline{CD}[/tex] (given)
2) [tex]\angle ABO, \angle ODC[/tex] are right angles (perpendicular lines form right angles)
3) [tex]\triangle ABO, \triangle CDO[/tex] are right triangles (a triangle with a right angle is a right triangle)
4) [tex]\overline{BO} \cong \overline{OD}[/tex] (a midpoint splits a segment into two congruent parts)
5) [tex]\triangle ABO \cong \triangle CDO[/tex] (LL)
Question 7
1) [tex]\angle ADC, \angle BDC[/tex] are right angles), [tex]\overline{AD} \cong \overline{BD}[/tex]
2) [tex]\overline{CD} \cong \overline{CD}[/tex] (reflexive property)
3) [tex]\triangle CDA, \triangle CDB[/tex] are right triangles (a triangle with a right angle is a right triangle)
4) [tex]\triangle ADC \cong \triangle BDC[/tex] (LL)
5) [tex]\overline{AC} \cong \overline{BC}[/tex] (CPCTC)
Question 8
1) [tex]\overline{CD} \perp \overline{AB}[/tex], point D bisects [tex]\overline{AB}[/tex] (given)
2) [tex]\angle CDA, \angle CDB[/tex] are right angles (perpendicular lines form right angles)
3) [tex]\triangle CDA, \triangle CDB[/tex] are right triangles (a triangle with a right angle is a right triangle)
4) [tex]\overline{AD} \cong \overline{DB}[/tex] (definition of a bisector)
5) [tex]\overline{CD} \cong \overline{CD}[/tex] (reflexive property)
6) [tex]\triangle ADC \cong \triangle BDC[/tex] (LL)
7) [tex]\angle ACD \cong \angle BCD[/tex] (CPCTC)
Evaluate if m= 14.
m
2 + m =
Answers
Answer:
16
Step-by-step explanation:
You replace m with 14. 2 + 14 = 16.
[tex]\huge\text{Hey there!}[/tex]
[tex]\huge\textsf{Assuming equation:}[/tex]
[tex]\mathsf{\dfrac{m}{2} + m}[/tex]
[tex]\huge\textsf{If so, let's solve for your equation:}[/tex]
[tex]\mathsf{\dfrac{m}{2} + m}[/tex]
[tex]\mathsf{= \dfrac{14}{2} + 14}[/tex]
[tex]\mathsf{= 7 + 14}[/tex]
[tex]\mathsf{= 21}[/tex]
[tex]\huge\textsf{Therefore, your answer should be:}[/tex]
[tex]\huge\boxed{\frak{21}}\huge\checkmark[/tex]
[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]
~[tex]\frak{Amphitrite1040:)}[/tex]
The graph represents the cost of catering a dinner as a function of the number of guests. On a coordinate plane, a graph titled Dinner Catering Cost shows Guests Served on the x-axis and Total cost in dollars on the y-axis. A piecewise function has 3 lines. The first line has an open circle at (0, 100) and goes up to a closed circle at (40, 600). The second line has an open circle at (40, 700) and goes up to a closed circle at (80, 1300). The third line has an open circle at (80, 1600) and goes up to (100, 2000). What is the catering cost for a dinner with 40 guests? $400 $600 $700 $800
Answers
Considering the piece-wise function described, the catering cost for a dinner with 40 guests is of $600.
What is a piece-wise function?A piece-wise function is a function that has different definitions, depending on the input.
In this problem, considering between 0 and 40 guests, the definition is the open circle at (0, 100) and goes up to a closed circle at (40, 600), hence the catering cost for a dinner with 40 guests is of $600.
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Answer:
600
Step-by-step explanation:
edge
Need help w this problem
Answers
Answer:
9, 18Step-by-step explanation:
The key word "product" tells us to multiply.
And, you probably know, but "integer" just means "number".
The question is, essentially:
A × B = 162 where A is half of B.
As someone who was never gifted in math, my best suggestion for something like this is to grab a calculator and start dividing 162 by all the numbers below 10. You will know you've got your answer when the calculator gives you a number that is twice the number you divided by.
In this case, I divided 162 by 9 and got 18. Since 9 is half of 18, and multiplied they make 162, we know this is the correct answer.
Hope this helps
a^4 b^2÷4a^3 b^-2
[tex] {a}^{4} {b}^{2} \div 4 {a}^{3} {b}^{ - 2} [/tex]
Answers
That is the simplification
Can someone help me please?
A.0.36
B.0.55
C.0.18
D.0.45
Answers
Answer:
B
Step-by-step explanation:
44/77
=0.55