Completing the square first gets brainliest maths Question plus 30 points.
Answer:
Hello,
Step-by-step explanation:
a)
[tex]x^2-2x-6=x^2-2x+1-1-6\\\\=(x-1)^2-7\\[/tex]
b)
[tex]x^2-2x-6=(x-1)^2-7\\\\=(x-1-\sqrt{7} )(x-1+\sqrt{7} )\\\\\\\boxed{x=1-\sqrt{7} \ or\ x=1+\sqrt{7} }\\[/tex]
What of the following is not a vertical asymptote of the function
f(x)= tan(pi x/4) / x^2-8x+15?
2
3
4
5
6
Rewrite the function as
[tex]f(x) = \dfrac{\tan(\left(\frac{\pi x}4\right)}{x^2 - 8x + 15} = \dfrac{\sin\left(\frac{\pi x}4\right)}{\cos\left(\frac{\pi x}4\right) (x-3) (x-5)}[/tex]
Vertical asymptotes occur wherever the denominator is zero (but not necessarily when the numerator is also zero).
We have
[tex]\cos\left(\dfrac{\pi x}4\right) (x-3) (x-5) = 0[/tex]
[tex]\implies \cos\left(\dfrac{\pi x}4\right) = 0 \text{ or } x - 3 = 0 \text{ or } x - 5 = 0[/tex]
In the first case, we have
[tex]\cos\left(\dfrac{\pi x}4\right) = 0 \implies \dfrac{\pi x}4 = \pm\dfrac\pi2 + 2n\pi \implies x = \pm 2 + 8n[/tex]
where [tex]n[/tex] is an integer. That is, any of [tex]x\in\{\ldots,-10,-2,\boxed{6},14,\ldots\}[/tex] and [tex]x\in\{\ldots,-6,\boxed{2},10,18,\ldots\}[/tex] are asymptotes.
In the latter two cases, we get [tex]x=\boxed{3}[/tex] or [tex]x=\boxed{5}[/tex]. The numerator is finite at these values [tex]\left(\sin\left(\frac{3\pi}4\right)=\frac1{\sqrt2}\text{ and } \sin\left(\frac{5\pi}4\right)=-\frac1{\sqrt2}\right)[/tex].
This means [tex]x=4[/tex] is not an asymptote. (C)
9x7/9-6+13 order of Operations
((9×7)÷9−6)+13
(63÷9−6)+13
(7−6)+13
1+13
14
Answer:
9 X 7 / 9 - 6 + 13
we can cut 9
=7-6 + 13
=1+13
=14
What unit would I use in this equation for science
Answer:
I think Dessicant
Step-by-step explanation:
i hope it helped you if I'm right :D
Ms. Francis is planning a birthday party for her daughter. There will be 22 children at the party, and in order to seat them all she needs to rent square card tables. Only 1 child can sit at each side of a card table.
Ms. Francis wants to arrange the tables in a rectangular shape so they look like one large table. The room is large enough that
the rectangle can be made with more than one row of tables.
Part A: How many different arrangements can Ms. Francis make to seat all 22 children?
Part B: What is the smallest number of tables that Ms. Francis needs to rent?
DIRECTIONS: To solve the problem, apply the steps of the Mathematical Problem-Solving Routine.
Understand
1. Try to visualize the situation. Consider drawing a diagram
2. State the problem in your own words.
3. What is the important information in the problem?
Plan
4. What strategy will you use to solve the problem? Why?
There are 5 possible arrangements to make seat all 22 children.
The smallest number of tables Ms. Francis is 10 tables.
Total number of children at the party = 22
When we picturize the scenario, each child need to get a side of the table.
So at least 22 sides should be there after arranging it into rectangles. Also the square card tables are arranged side to side to get rectangle rows.
It is also said that there can be multiple rows. So combining all these points, we can consider a row of 10 tables. Then the the squares on the ends contribute a total of 6 sides and the remaining 16 seats can be arranged by 8 square tables in between the end square tables. So a total of 10 square table is required to make a rectangle in one row.
For making 22 seats in 2 rows, the 4 square tables on the ends contribute 8 seats. For the remaining 12 seats add 7 square tables in each row, that is a total of 14 square tables. That is, for 2 rows, the square tables required is 14 + 4 = 18.
Similarly, for 3 rows, a total of 24 square tables are required.
For 4 rows, a total of 28 tables and for 5 rows, a total of 30 tables are needed.
We cannot make a 6 row because it will be same as a 5 row.
So 5 different arrangements can be made to seat all 22 children.
They are:
1 row → 1 x 10 = 10 tables
2 rows → 2 x 9 = 18 tables
3 rows → 3 x 8 = 24 tables
4 rows → 4 x 7 = 28 tables
5 rows → 5 x 6 = 30 tables
The smallest number of tables that Ms. Francis needs to rent is, therefore, 10 tables.
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1. What information can be seen most easily in the dot plot?
a dot plot can easily show all the data.
Step-by-step explanation:
In this example, a dot plot can easily show all the data. If the data set is very large (more than 100 values, for example) or if there are many different values that are not exactly the same, it may be hard to see all of the dots on a dot plot.
A store has clearance items that have been marked down by 25%. They are having a sale, advertising an additional 45% off clearance items. What percent of the original price do you end up paying?
we end up paying 41.25 % of the original price after the addition sale on the clearance.
Let the original price of the good be x
Now, there is a sale of 25 %.
So the price will become
Price = x - 25 % of x
Price = x - 25 / 100 x
Price = x - 0.25 x
Price = 0.75 x
Now, there is an addition 45 % sale on the price.
so the price become:
New price = P = 0.75 x - 45 % of 0.75 x
P = 0.75 x - 45 / 100 (0.75 x)
P = 0.75 x - 0.45( 0.75 x)
P = 0.75 x - 0.3375 x
P = 0.4125 x
percentage of original price is:
P = 41.25 % of x
Therefore, we get that, we end up paying 41.25 % of the original price after the addition sale on the clearance.
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Elroy's Balloon Emporium sells boxes of balloons. There are 500 balloons in a box. In January, they sell 3 boxes.In February they sell 6 boxes .If they started with 10 boxes, how many balloons do they have left to sell?
Answer:
500
Step-by-step explanation:
3+6=9
10-9=1
They sell 9 out of the 10 boxes. if each box has 500 balloons, then they have 500 left
Answer: 500 balloons
Step-by-step explanation: if you do 500 x 10 you get 5000 and then you do 3 x 500 + 6 x 500 then you get 4500 then subtract that from 5000
nth term of -9, -5, -1, 3, 7
The nth term of the given sequence is 4n - 1.
What do we mean by the nth term?The nth term is a formula that allows us to locate any term in a series. The 'n' represents the term number. By substituting different values for the term number, we can create a sequence using the nth term ( n ).So,
-9 + 4 = -5-5 + 4 = -1-1 + 4 = 33 + 4 = 7As, (4 × 2) - 1 = 7Then, the nth term is 4n - 1Therefore, the nth term of the given sequence is 4n - 1.
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The length of a rectangle is 5 times the width. If the perimeter of the rectangle is 108 feet, find the length
and the width.
Answers:
Length = 45 feet
Width = 9 feet
=========================================================
Work Shown:
x = width
5x = five times the width = length
P = perimeter of the rectangle
P = 2*(length + width)
P = 2*(5x+x)
P = 2*(6x)
P = 12x
Set this equal to the stated perimeter (108) and solve for x.
12x = 108
x = 108/12
x = 9 feet is the width
5x = 5*9 = 45 feet is the length
-------------
Check:
P = 2*(9+45) = 108
or you could add up the four sides like this
P = 9+45+9+45 = 108
Either way the answers are confirmed.
She begins at sea level, which is an elevation of o feet.
She travels down 27.2 feet.
She then ascends 2.1 feet.
Next, she descends a second time, 19.6 feet.
How many feet must she now rise to get back to sea level?
Answer:
She will need to rise 55.4 feet.
Step-by-step explanation:
-27.2 feet + 2.1 feet = -25.1
-25.1 + -19.6 = 44.6
100- 44.6 = 55.4 feet
The term containing b^6 in the expansion of (a + b2)10
The term containing b^6 is -210 a^6 b^6
The given expansion can be solved by using the Binomial expansion
The binomial expansion for two terms (a + b) raised to the power n is given by
(a+b)^n = Σ[tex]a^{n-k} * b^k[/tex] * n!/k!(n-k)!
To find term contain b^6 we use the formula
Use the formula T r+1 =(−1) ⁿCr [tex]a^{n-r} * b^r[/tex]
Putting n=10,
we get 10-r=6
r=4
Therefore,
it is the fourth term ,
T = (-1)^3 10!/4!6! [tex]a^{10-6} * (b^2)^4[/tex]
= -1 x 10x9x8x7/4x3x2=-210 [tex]a^6 b^6[/tex]
Hence the term containing b^6 is -210 a^6 b^6
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Karen worked her 40 regular hours last week, plus 6 hours at the time-and-a-half rate. Her gross pay was $650. What was her hourly rate?
As Karen worked for 40 regular hours and 6hours overtime at the rate of 1.5 regular hours and her gross pay was $650 then her hourly rate is $13.27 (approximately).
As given,
Regular working hours =40 hours
Overtime at the rate of (1.5 of regular hours) = 6 hours
Gross pay =$650
Let 'h' be the hourly rate
Required equation
40h + 6(1.5h) =650
⇒ 40h +9h=650
⇒49h=650
⇒h=$13.27(approximately)
Therefore, as Karen worked for 40 regular hours and 6hours overtime at the rate of 1.5 regular hours and her gross pay was $650 then her hourly rate is $13.27 (approximately).
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Find an expression which represents the difference when (- x - 3y) is subtracted
from (8a - 9y) in simplest terms.
Answer:
hello
Step-by-step explanation:
hi
MSA
my milkshake brings all the boys to the yard yeah right its better than yours yeah right its better than yours
A person is putting oranges into a box. The dimensions of the box
are 13 inches by 16 inches by 13 inches. Assuming oranges are
spherical with a 2.8-inch diameter, how many oranges should fit in
the box? (Hint: Packing spheres in a rectangular prism usually takes
up 190% of the volume of the spheres using random packaging.)
Answer:
oranges
The number of oranges that will fit in the box is 235 oranges.
How to find the number of oranges that will fit in the box using volume?The dimensions of the box are 13 inches by 16 inches by 13 inches.
Therefore,
volume of the box = lwh
where
l = lengthw = widthh = heightHence,
volume of the box = 13 × 16 × 13
volume of the box = 2704 inches³
volume of the spherical orange = 4 / 3 πr³
where
r = radius of the sphere = 2.8 / 2 = 1.4 inchesvolume of the spherical orange = 4 / 3 × 3.14 × 1.4³
volume of the spherical orange = 34.46464 / 3
volume of the spherical orange = 11.4882133333 inches cube = 11.5 inches³
number of oranges in the box = 2704 / 11.5
number of oranges in the box = 235.130434783
number of oranges in the box = 235 oranges
Therefore, the number of oranges that will fit in the box is 235 oranges.
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Write three different expressions that equivalent to 8 to the power 2 x 4 to the power of 2
Answer:
One could be: 8*8 times 4*4
Another could be: 8 to the second power times 4 to the second power
A third way to write this could also be: 8*4*8*4
Step-by-step explanation:
Hope its helpful
Consider a data set with at least three data values suppose the highest value is increased by 10 and the lowest is decreased by five
plss give your self a answer
Find the probability that there are no T when a fair coin is flipped three times.
The probability that no Tails is achieved on flipping a fair coin for three consecutive times is [tex](\frac{1}{8})[/tex].
As per the question statement, we are to flip or toss a fair coin thrice consecutively.
We are required to calculate the probability that no Tails is achieved during the above mentioned event.
To solve this question, first let us calculate all the possible outcomes of flipping a fair coin thrice consecutively. [We will denote a Heads outcome as "H" and a Tails outcome as "T"]
The total number of outcomes can be given by the formula [tex](2^{n})[/tex], where "n" is the number of times, the coin is tossed.
Here, (n = 3), therefore, total number of outcomes in our case [tex]=(2^{3})=8[/tex].
These 8 outcomes can be listed as [tex][{(H, H, H), (H, H, T), (H, T, H), (H, T, T), (T, H, H), (T, H, T), (T, T, H), (T, T, T)}][/tex]
And among the above listed 8, our favorable outcome is (H, H, H), i.e., 1 favorable outcome of 8.
Hence, probability that no Tails is achieved on flipping a fair coin thrice consecutively = [tex]\frac{1}{8}[/tex].
Probability: In Mathematics, probability is the chance to of the occurrence of a specific event among the occurrence of all possible events, and is measured by the ratio of the favorable cases to the whole number of cases possible.To learn more about Probability, click on the link below.
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b. The cardinal number of (2, 4, 6, ..., 106) is
The cardinal number of (2, 4, 6, ..., 106) is 53.
The cardinal number of a set is the number of elements in the particular set.
We are given the set (2, 4, 6, ..., 106). As we can can clearly see, it is forming an Arithmetic Progression (AP).
Hence, let the number of elements or the cardinal number of the set be n.
Hence, according to the formula of AP, we can write,
2 + (n-1)(2) = 106
2(n-1) = 106 - 2
2(n-1) = 104
n - 1 = 104/2
n - 1 = 52
n = 52 + 1
n = 53
Hence, the cardinal number of the set is 53.
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Lily's book has 468 pages. Joe's book is 2 2/3 as long as Lily's book. How many pages is Joe's book?
Answer: Joe's book has 1248 Pages.
Step-by-step explanation:
468 * 2 2/3
Multiply 2 and 3 to get 6.
468×( 6+2/3)
Add 6 and 2 to get 8.
468x(8/3)
Express 468×(8/3) as a single fraction
468x8/3
Multiply 468 and 8 to get 3744.
3722/3
Divide 3744 by 3 to get 1248.
1248
So Joe's Book has 1248 pages
NEED ANSWER PLS HURRY !!
Answer:it's the second option
Step-by-step explanation:
-x is already -1 so why would factoring it make it -1 again
a pebble dropped into a calm pond causing ripples in the form of concentric
Answer:
A pebble is dropped into a calm pond, causing ripples in the form of concentric circles. The radius (in feet) of the outer ripple is given by r ( t ) = 0.6 t r(t) = 0.6t r(t)=0.6t, where t is the time in seconds after the pebble strikes the water.
Step-by-step explanation:
Answer:
well dude it's because of the law of gravity
6. Find the product: 6.45 x 19.3
Identify the Property of Operation that is being used.
3(a – 2) = 3a – 6
Question 1 options:
Distributive Property
Commutative Property
Identity Property
Associative Property
-------------------------------
(5 x 4) x 2 = 5 x (4 x 2)
Question 2 options:
Commutative Property
Distributive Property
Associative Property
Identity Property
-------------------------------
Simplify the expression.
9y + 6 – 7y - 3
Question 3 options:
-2y - 3
2y + 3
2y + 9
-2y + 9
-------------------------------
9y + 6 – 7y - 3
Question 3 options:
-2y - 3
2y + 3
2y + 9
-2y + 9
-------------------------------
a + b + 2a + 2b + 5 − b
Question 5 options:
3a + 2b + 5
3a + 4b + 5
2a + 4b + 5
2a + 2b + 5
Answer:
3×a-3×2=3a-6
3a-6=3a-6 proved
Find the slope of the line.
The total cost of a jacket and a pair of pants was $52.37. If the price of the jacket was $4.87 less than the pair of pants, what was the price of the jacket? Express your answer as a simplified fraction or a decimal rounded to two places.
The price of the jacket is $23.75
Let m be the price of a jacket and n be the price of pair of pants.
The total cost of a jacket and a pair of pants was $52.37
So, we get an equation,
m + n = 52.37 ................(1)
Also, the price of the jacket was $4.87 less than the pair of pants
So, we get an equation,
m = n - 4.87 .............(2)
Substitute above value of m in equation (1)
⇒ (n - 4.87) + n = 52.37
⇒ 2n - 4.87 = 52.37
⇒ 2n = 52.37 + 4.87
⇒ 2n = 57.24
⇒ n = 28.62
This means, the cost of a pair of pants is $28.62
Substitute above value of n in equation (2)
⇒ m = n - 4.87
⇒ m = 28.62 - 4.87
⇒ m = 23.75
This means, the cost of a jacket is $23.75
Therefore, the price of the jacket is $23.75
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I'm really confused about this equation. I'm trying to figure it out, but I'm lost and think I'm overthinking it
Jet A Travels at 417 mph and gets halfway to its destination in two hours. Jet B makes the same journey but makes it to the destination in 5 minutes. How fast is Jet B in MPH, or how much faster is Jet B than Jet A As A Multiplier?
Example: 417 * 48 = 20016 Or Jet B = X MPH
I think the answer is 417 * 48 = 20016 and Jet B= 20016
But I just need reassurance, or a definitive answer
Answer:
Jet B speed: 20,016 mphspeed multiplier: 48Step-by-step explanation:
You want the speed and speed multiplier for Jet B given that it makes a journey in 5 minutes that takes Jet A 2 hours for half the journey.
Speed multiplierFor the same distance, speed is inversely proportional to time.
speed multiplier = (speed B)/(speed A) = (time A)/(time B)
speed multiplier = ((2 h)/(1/2))/(5 min)
speed multiplier = (240 min)/(5 min) = 48
SpeedThe speed of Jet B is 48 times that of Jet A:
48(417 mph) = 20016 mph . . . . speed of Jet B
__
Additional comment
The time for the full trip by Jet A can be found using the proportion ...
partial time/partial distance = total time/total distance
If the total distance is "1 unit", then this proportion is ...
(2 h)/(1/2) = t/1 . . . . . where t/1 = t is the time for the full trip by Jet A
You will recognize the value (2 h)/(1/2) as the time value we used for Jet A in the above solution.
-7=
n-10
3
2 step eq
3(n-10)=-7
Solve the equation in 2 step equation.
n=18.5
Given that 3(n-10)=7
step1: multiplication
Adding a number to itself as many times as the value of the other number is equivalent to multiplying two numbers by their sum.
3n-30=7
step2: adding 30 on both sides of the equation.
When objects are collected together, addition, a mathematical operation, describes how many total items there are in the collection.
2n-30+30=7+30
2n=37
step3: divide the equation by 2.
Basically, dividing is the act of dividing anything into equal sections or groups.
[tex]\frac{2n}{2} =\frac{37}{2}\\ n=\frac{37}{2} or 18.5[/tex]
Therefore, n=18.5
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Showing each step... use the product rule to simplify the following monomial.
INCLUDE ANY STEP THAT SHOWS HOW EXPONENTS ARE CHANGING (for example,
exponents adding, subtracting, multiplying, etc.).
Show Your Work
3a4 . 5a³
PLS HELP! LAST QUESTION! The scatter plot shows prize money, in thousands of dollars, for a contest over eight consecutive years.
Predict the amount of prize money in year 10 of the contest.
$11,790
$20,340
$35,200
$45,900
From the given scatter plot, finding a line of best fit, the estimate of the amount of prize money in year 10 of the contest is of $11,790.
How to find the equation of the line of best fit using a calculator?To find the equation of the line of best fit, we need to insert the points (x,y) from the scatter plot in the calculator.
From the scatter plot, the points are given as follows:
(1, 9.5), (2,9), (3,7), (4,10), (5,11), (6, 10), (7, 10.5).
Inserting these points into a calculator, the line of best fit for the prize in year x is given as follows:
P(x) = 0.32143x + 8.28571
For year 10, we have that x = 10, hence:
P(10) = 0.32143(10) + 8.28571 = $11,500.
The closest option is $11,790, and the difference is due to rounding of coefficients or points in the table.
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