The result after rationalizing is [tex]\frac{9\sqrt{x+3} }{x+3}[/tex].
What is Rationalization?Rationalization can be considered as the process used to eliminate a radical or an imaginary number from the denominator of an algebraic fraction.
Here, given fraction
[tex]\frac{9}{\sqrt{x+3} }[/tex]
Multiply and divide by [tex]\sqrt{x+3}[/tex], we get
[tex]\frac{9}{\sqrt{x+3} } \frac{\sqrt{x+3} }{\sqrt{x+3} }[/tex] = [tex]\frac{9\sqrt{x+3} }{x+3}[/tex]
Thus, the result after rationalizing is [tex]\frac{9\sqrt{x+3} }{x+3}[/tex].
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Rasberry Crazy Ants, a species found in wall sockets, cellphones, and television sets are
slowly spreading across Texas and are poised to spread across the entire South. Named for
Texas exterminator Tom Rasberry, who spotted ants moving in an erratic swarm in 2002,
the destructive ants are now in 23 counties in Texas, the Austin American-Statesman
recently reported. Although their march in impossible to stop, it is also quite slow. They travel at an average speed of 1.8 feet per day.
a. At that rate, how long will the swarm that is presently centered in Austin, Texas, take to reach your home? Express your answer in the timeframe that is most appropriate.
b. Do you need to be worried about these ants infesting your cellphone or television? Do you need to worry for your children? For your grandchildren? Explain why or why
not.
The average time taken to travel to Toronto by the swarm of Rasberry Crazy Ants is 12,947 Years
What is the calculation for the above Solution?To arrive at the solution above, we need to look at the information given and the information assumed.
Step 1 - Information given:
Step 2 - Information assumed:
The swarm are travelling to the location of the student which is assumed to be Toronto.
Hence,
Time taken for the swam to get to Toronto (TTS) =
Distance between Austin, Texas and Toronto (DBTT) / Average distance covered per day by the Rasberry Ants. (ADC)
Estimated distance between Austin Texas and Toronto = 2592.6 Kilometers
Time travelled per day by the ants (In Km) = 0.00054864
Thus,
TTS = DBTT/ADC
= 2592.6 /0.00054864
≈ 4,725,503.06 days or
≈ 12,947 Years
Do I need to be worried about these ants infesting your cellphone or television? Do you need to worry for your children? For your grandchildren?The answer to both questions is NO.
The average life expectancy in Toronto (as at 2022) is 80 years. Assuming I was born today, it is expected that the time between now and when my last grand child will die is about:
80 x 3 = 240 years.
Given that the ants have to travel 12,947 to get to Toronto, the possibility of my grand children seeing them is zero.
Besides, even if they by chance got to Toronto and infested my grandchildren's residence, they would have nothing to worry about because Rasberry Crazy Ants are 100% harmless.
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In ΔABC, m < C = 50* , a = 14 and b = 15. Find the length of side c, to the nearest integer.
The length of the side c, to the nearest integer is 12.
What is a cosine law?Cosine law is a formula relating the length of the sides of a triangle to the cosine of one angle of the triangle.
u² = s² + t² - 2(s)(t)·cos U
In ΔABC, m < C = 50* , a = 14 and b = 15.
We can solve for the length of side a to the nearest whole number using the Laws of Cosines
c² = b² + a²- 2ba CosC
Solving for the value of a, we have:
c² = 15² + 14²- 2(15)(14)cos50°
c² = 225 + 196 - 269.97
c² = 151.029
c = 12.28
Hence, The length of the side c, to the nearest integer is 12.
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Can u help me with this I don’t understand
Answer:
D -6, 15
Step-by-step explanation:
Because 3,11 is the middle, and 12,7 is the other end, you can do
12 - 3 = 9
3 - 9 = 6
then
11 - 7 = 4
11 + 4 = 15
so
6 is you x and 15 is your y
what is the mid point of 3,2 and -3,4?
Answer
(0,3)
Step-by-step explanation:
from mid point (x+x)/2, (y+y)/2((3+-3)/2,(2+4)/2)(0/2, 6/2)(0, 3)Using the Empirical Rule, it is found that:
Scores between 80% and 96% are within 2 standard deviations of the mean.
68 scores are within one standard deviation of the mean.
It states that, for a normally distributed random variable:
Approximately 68% of the measures are within 1 standard deviation of the mean.
Approximately 95% of the measures are within 2 standard deviations of the mean.
Approximately 99.7% of the measures are within 3 standard deviations of the mean.
Considering the mean of 88% and the standard deviation of 4%, the scores that are within 2 standard deviations of the mean are:
88 - 2 x 4 = 80%.
88 + 2 x 4 = 96%.
68% are within 1 standard deviation of the mean, hence, out of 100:
0.68 x 100% = 68 scores.
What is the median of the above answer? Pls help fast.
Considering that the mean of the normal distribution is the same as the median, the median is of 88%.
What does the Empirical Rule state?It states that, for a normally distributed random variable:
Approximately 68% of the measures are within 1 standard deviation of the mean.Approximately 95% of the measures are within 2 standard deviations of the mean.Approximately 99.7% of the measures are within 3 standard deviations of the mean.For the normal distribution, the median is the same of the mean, that is, the median is of 88%.
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The May bank statement for Rental shows a balance of $6,000, but the balance per books shows a cash balance of $8,000. Other information includes: 1. A check for $190 to pay the electric bill was recorded on the books as $10. 2. Included on the bank statement was a note collected by the bank for $450 plus interest of $30. 3. Checks outstanding totaled $270. 4. Bank service charges were $60. 5. Deposits in transit were $2,510.
The adjusted cash Balance is $8060 .
What is Bank Balance ?The amount of money in a person's account at any given time is the Bank Balance of that person's account.
Unadjusted bank balance 6000
Difference in the electricity bill -180
Add: Deposit in transit 2510
Less: Outstanding Checks -270
Adjusted cash balance 8060
So answer is a) $8060
Therefore the adjusted cash Balance is $8060 .
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An empty rectangular tank was 25 cm long, 23 cm wide and 18 cm high. Ravi filled 5 identical bottles with water to the brim. Then he poured all the water from the 5 bottles into the empty tank and the tank became What was the capacity of each bottle? height of water, = = 1/2 X 18 3 23 cm Co 25 cm 3 full. 18 cm 2 An empty rectangular tank was 25 cm long , 23 cm wide and 18 cm high . Ravi filled 5 identical bottles with water to the brim . Then he poured all the water from the 5 bottles into the empty tank and the tank became What was the capacity of each bottle ? height of water , = = 1/2 X 18 3 23 cm Co 25 cm 3 full . 18 cm
NS,
Word problem on unit rates associated with ratios of whole...
Answer each part. If necessary, round your answers to the nearest hundredth.
(a) Greg bought 16 pounds of sugar for $8.
C
How many dollars did he pay per pound of sugar?
dollars per pound
(b) It takes 76 pounds of seed to completely plant a 12-acre field.
How many pounds of seed are needed per acre?
pounds per acre
|||
Answer:
Define different tipes of discontuinity of a function .also,write the condition for increasing, decreasing and concave of function
Which explicit formula models this situation
Answer:
The formula is: y = y•e^(-k•x)
In this specific case the function is: 512•e^(-x/1.44)
The number of players in the round 7 is 4
Needa line segment has endpoints P(-8,7) and Q(6,-3). What is the midpoint of the segment?
Answer:
1/2(6-8), 1/2(-3+7)=-1,2
Answer: C - (-1, 2)
Step-by-step explanation:
Please help
Follow the steps to find the area of the shaded region.
First use the formula below to find the area of the whole sector.
Sector Area= ( angle of sector/360). R2
Sector Area = ? Cm^2
Round to four decimal places.
14 cm
46°
14 cm
The area of the sector, to 4 decimal places, is: 78.6794 cm².
How to Find the Area of a Sector of a Circle?Area of sector = ∅/360 × πr².
Given the following:
∅ = 46°Radius (r) = 14 cmArea of sector = 46/360 × π(14²)
Area of sector ≈ 78.6794 cm²
The area of the sector is approximately 78.6794 cm².
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If x is a positive integer, what is the value of x for the equation (x!-(x-3)!)\23=1?
I think the first step is knowing (x!-(x-3)!) equals to 23, but after that i'm stuck, can someone help me?
[tex]\dfrac{x!-(x-3)!}{23}=1\\x!-(x-3)!=23\\(x-3)!((x-2)(x-1)x-1)=23\\(x-3)!((x^3-x^2-2x^2+2x)-1)=23\\(x-3)!((x^3-3x^2+2x)-1)=23[/tex]
23 is a prime number, therefore there are two possibilities:
[tex]\text{I.}\, (x-3)!=1 \wedge x^3-3x^2+2x-1=23[/tex]
or
[tex]\text{II.}\, (x-3)!=23 \wedge x^3-3x^2+2x-1=1[/tex]
[tex]\text{I.}\\(x-3)!=1\\x-3=0 \vee x-3=1\\x=3 \vee x=4[/tex]
Now, we check if any of these solutions is also a solution to the second equation:
[tex]3^3-3\cdot3^2+2\cdot3-1=23\\27-27+6-1-23=0\\ -18=0[/tex]
Therefore, 3 is not a solution.
[tex]4^3-3\cdot4^2+2\cdot4-1=23\\64-48+8-1-23=0\\0=0[/tex]
Therefore, 4 is a solution.
[tex]\text{II.}[/tex]
[tex](x-3)!=23[/tex]
We know that [tex]3!=6[/tex] and [tex]4!=24[/tex], therefore there isn't any [tex]n\in\mathbb{N}[/tex], for which [tex]n!=23[/tex], so there's no solution.
So, the only solution is [tex]x=4[/tex].
Sianna bought 3 pens, 4 notebooks, and a calculator. The calculator cost $25. If x represents the cost of each pen and y represents the cost of each notebook, which expression represents the amount of change Sianna should receive from $50?
3x + 4y +25
50 – (3x + 4y)
50 – (3x + 4y + 25)
3x + 4y + 25 + 50
Answer:
50 – (3x + 4y + 25)
Step-by-step explanation:
To see how much change she is gonna receive we need to find how much she spent on the items and add them all up:
The calculator was $25
The price of pens and notebooks are unknown so they are represented with x and y respectively.
With given information we can write the following equation to see the change she will receive:
50 – (3x + 4y + 25)
Please help!!
Write an equation in slope-intercept form for the line that passes through the given point and is perpendicular to the graph of the equation
(-4,5) y=1/3x +6
Answer:
The Equation of the line is y = [tex]\frac{-1}{3}[/tex]x + [tex]\frac{11}{3}[/tex]
Step-by-step explanation:
Multiplication of slope of two perpendicular lines is = -1
first line is y= [tex]\frac{1}{3}[/tex]x +6
slope of this line is [tex]\frac{1}{3}[/tex]
So the slope of the second line is : [tex]\frac{-1}{3}[/tex]
Equation of line would be written by using :
(y - y1) = m(x - x1)
here the line passing through (-4,5)
put the values in equation
y -5 =[tex]\frac{-1}{3}[/tex][x - (-4)]
3y - 15 = -x -4
3y = -x +11
y = [tex]\frac{-1}{3}[/tex]x + [tex]\frac{11}{3}[/tex]
So The Equation of the line is y = [tex]\frac{-1}{3}[/tex]x + [tex]\frac{11}{3}[/tex]
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Find the equation of the line with slope 43 and y-intercept (0,−3).
[tex]\triangleright[/tex]Hii! [tex]\triangleleft[/tex]
_ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _
[tex]\stackrel\star{\rightsquigarrow\circ\boldsymbol{\underbrace{Answer}}}\circ\leftharpoonup[/tex] Equation: [tex]\bullet[/tex] y=43x-3 ✅
[tex]\stackrel\star{\rightsquigarrow\circ\boldsymbol{\underbrace{Explanation}}}\circ\leftharpoonup[/tex]
Do you need to know the equation of the line with a slope of -43 and a y-intercept of (0,-3)? No problem! Luckily, there's a formula to find it! (:
The Slope Intercept FormulaThe slope intercept formula, [tex]\boldsymbol{y=mx+c}[/tex], comes in handy when we need to find the equation of a line!
In this formula,
"m" denotes the slope"c" denotes the y intercept-- ↩
This particular question provides us both "m" and "c."
m=43c=-3 (It's the second co-ordinate, the y co-ordinate, in the point "(0,-3)"Stickin the values
[tex]\boldsymbol{y=43x+(-3)}[/tex]
Simplify!
[tex]\boldsymbol{y=43x-3}[/tex]
--
Hope that this helped! Best wishes.
[tex]\textsl{Reach far. Aim high. \: Dream big. }[/tex]
--
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Describe a scenario where the function value exists at x=c, but the limit does not exist.
The scenario can be described using a piecewise function like:
f(x) = 1/x if x < c.
f(x) = x if x = c
f(x) = 1/(x + 73) if x > c.
When the value exists but the limit does not?
Remember that the limit only exists if the limit from left and the limit from the right give the same value.
Then, we can just define a piecewise function of the form:
f(x) = 1/x if x < c.
f(x) = x if x = c
f(x) = 1/(x + 73) if x > c.
Clearly, this is not a continuous function.
Notice that:
[tex]f(c) = c.\\\\ \lim_{x \to c^{-}} f(x) = 1/c\\\\ \lim_{x \to c^{+}} f(x) = 1/(c + 73)[/tex]
So the limits from left and right are different, then:
[tex]\lim_{x \to c^{}} f(x)[/tex]
Does not exist.
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You started this year with $413 saved and you continue to save $21 per month.
Write an equation to model this situation (use m for months and s for savings)
Answer:
y = 21x + 413
Step-by-step explanation:
Use y = mx + b
m represents the slope which in this case is 21.
b represents the y - intercept which in this case is 413.
Now, just fill in the variables.
y = 21x + 413
Hope this helps!
1. Draw an appropriate Venn diagram to depict each of the following sets. U = The set of integers. A = The set of even integers. B = The set of odd integers. C = The set of multiples of 3. D= The set of prime numbers. 1. Draw an appropriate Venn diagram to depict each of the following sets . U = The set of integers . A = The set of even integers . B = The set of odd integers . C = The set of multiples of 3 . D= The set of prime numbers .
The attached diagram represents the Venn diagram of the sets
How to draw the Venn diagram?The sets are given as:
The universal set, U = The set of integers. A = The set of even integers. B = The set of odd integers. C = The set of multiples of 3. D= The set of prime numbersFrom the above representation, we have the following highlights:
Set A and set B will not intersect, because no number can be even and oddSet C and set D will intersect set A because they have common elements 6 and 2, respectivelySet C and set D will intersect set B because they have common elements 3 and 3, respectivelyUsing the above highlights, we can now draw the Venn diagram
See attachment for the Venn diagram
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Use the Change of Base Formula to solve each equation.
3x = 27.3
Answer:
9.1
Step-by-step explanation:
3(9.1)=27.3
27.3÷3=×
×=9.1
What is the inverse of p>q
Inequalities help us to compare two unequal expressions. The inverse of p>q is p<q.
What are inequalities?Inequalities help us to compare two unequal expressions. Also, it helps us to compare the non-equal expressions so that an equation can be formed.
It is mostly denoted by the symbol <, >, ≤, and ≥.
Given the inequality that p is greater than q, therefore, the inverse of it will be p smaller than q. Thus, The inverse of p>q is p<q.
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Find the domain and range of the relation graphed below. Write your answers in interval notation.
Answer:
Domain: [tex][-1, 3][/tex]Range: [tex][0, 4][/tex]Step-by-step explanation:
The domain is the set of x-values and the range is the set of y-values.
A tower on a college campus was built with a faulty foundation and is starting to lean. A student climbs to the tilted top and drops a rope down to the ground. The
end of the rope lands 3 feet from the base of the tower and measures 57 feet from
the top of the building to the ground. What is the angle that the tower is leaning?
Round your answer to the nearest degree, and enter the number only
Answer:
leaning at 3 degrees off of normal (to the nearest whole degree)
Step-by-step explanation:
To visualize, let's assume the tower is leaning to the right, (as viewed by us).
If the rope is dropped from the top to the ground, the tower, the rope and the ground (between the rope and the tower) form a right triangle.
The height and base of the triangle are given
Often we're looking for the angle near the ground, but here, we're looking for the angle between the rope and the tower because the angle is congruent to the angle that the tower forms with it's original vertical position (alternate interior angles). If the tower was standing straight up and hadn't been leaning at all, we wouldn't say that the tower was leaning 90°... we would say it was leaning 0°. Whereas if the tower fell over and was laying flat on the ground, we would say it was leaning at 90°. So, we're not measuring the angle between the tower and the ground, but rather the angle between the tower where it should be, and where it is... which is the same angle as the rope forms with the tower.
Recall that [tex]tan(\theta)=\dfrac {opp}{hyp}[/tex]
Since we know the two legs of the right triangle, one can setup a tangent relationship with the two legs, but remember that the "opposite" side is going to be the ground, and the "adjacent side" will be the rope.
[tex]tan(\theta)=\dfrac {ground}{rope}\\tan(\theta)=\dfrac {3ft}{57ft}\\tan(\theta)=\frac {3}{57}\\\theta=tan^{-1}(\frac {3}{57})\\\theta=3.012787504^o\\\theta \approx 3^o\\[/tex]
There are 192 pencils in 8 Super Saver packs. If there are the same number of pencils in each Super Saver pack, how many pencils are in 5 packs?
There are two boxes of cereal in the shape of rectangular prisms on a shelf. The
dimensions of each box of cereal are listed below.
. Box B has a height of 25 centimeters, a length of 19 centimeters,
and a width of 6 centimeters.
• Box A has a height of 25 centimeters, a length of 20 centimeters,
and a width of 9 centimeters.
What is the difference in volume, in cubic centimeters, between the two boxes of cereal?
A 1,650
B 3,900
C 4,500
D 7,350
Answer:
1650 Cubic Centimeters
Step-by-step explanation:
To get the volume of the cereal boxes, you must multiply their 3 dimensions together.
Box A:
25×20=500
500×9=4500
Box B:
25×19=475
475×6=2850
Now, to find the difference of these volumes, you want to subtract the smaller volume from the larger volume.
4500-2850=1650
The answer is 1650 cubic centimeters.
In what table does y vary directly with x?
Answer:
The phrase “ y varies directly as x” or “ y is directly proportional to x” means that as x gets bigger, so does y, and as x gets smaller, so does y. That concept can be translated in two ways. for some constant k. The k is called the constant of proportionality. Therefore a chance of probability is a binary table.
Step-by-step explanation:
Find the quotient: (9mn2)(−3m6n)33m10n3
The quotient is -27m/ 55.
What is Algebra?Algebra is a branch of mathematics dealing with symbols and the rules for manipulating those symbols.
Given:
(9mn²)(−3m*6n)÷33m*10n³
=9mn² *(-18mn) / 330mn³
= -162m²n³/ 330mn³
= -27m/ 55
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a.- Representa el cálculo del porcentaje de cada par de artículos y marca el que es más conveniente comprar.
1 el par de zapatos cuesta $90.Por la compra de dos pares , tienes el 25% del descuento total
2 el par de zapatos cuesta $90.El segundo par de zapatos esta con el 40% de descuento
El costo en la opción uno es menor que el de la opción dos, asi que la primera es la más conveniente.
¿Cual opción es más conveniente?
En la primera opción, el par de zapatos cuesta $90, y el segundo par tiene un descuento del 25%.
Entonces el costo por 2 pares es:
C = ($90 + $90)*(1 - 25%/100%)
Donde le aplicamos un descuento del 25% al total del costo de los dos zapatos, resolviendo esto obtenemos:
C = ($180)*(0.75) = $135.
En la segunda opcion tenemos que los pares cuestan $90, pero esta vez le aplicamos un descuento del 40% al segundo par.
C = $90 + $90*(1 - 40%/100%) =
C = $90 + $90*(0.6) = $144
Así, vemos que en la primera opción el costo es menor, entonces esa es la mejor opción.
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!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
[tex]\quad \huge \quad \quad \boxed{ \tt \:Answer }[/tex]
[tex]\qquad \tt \rightarrow \: [ - 10,- 8] \cup[ - 2,0] \cup[2,5][/tex]
____________________________________
[tex] \large \tt Solution \: : [/tex]
The intervals in which a function is decreasing has a negative slope. and for given graph, the required intervals are :
[tex]\qquad \tt \rightarrow \: [ - 10,- 8] \cup[ - 2,0] \cup[2,5][/tex]
Answered by : ❝ AǫᴜᴀWɪᴢ ❞
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
[tex]\quad \huge \quad \quad \boxed{ \tt \:Answer }[/tex]
[tex]\texttt{Yes, there's a local maximum at -9,} [/tex] [tex] \texttt{and it is 9} [/tex]
____________________________________
[tex] \large \tt Solution \: : [/tex]
By Observing the graph, we can easily conclude that there's a local maxima at -9
[tex] \textsf{And f(-9) = 9} [/tex]
Answered by : ❝ AǫᴜᴀWɪᴢ ❞
write a quadratic function in standard form with zeros -5 and 0
Answer:
(x^2+5x)
Step-by-step explanation:
