⇒x (x+2) + x + 2
⇒x² + 2x + x + 2
⇒x² + 3x + 2
✯ Now factorising☛ By Splitting the middle term method
⇒x² + 3x + 2
⇒x² + 2x + x + 2
⇒ x(x+2)+1(x+2)
⇒ (x+1) (x+2)
if √x-5 varies directly as y and x=30 when y= 2, find the value of x when y=8.
Answer:
let,
√x-5=ky
x=30 when y=2
√30-5=2k
or, k=(√30-5)/2
now, when y=8
√x-5=8×(√30-5)/2
or, √x-5=4√30-20
or, √x=4√30-15
or, x=(4√30-15)²
or, x=47.73..
The divisibility rule for 7 says 10a + b is a multiple of 7 if only and only if a - 2b is a multiple of 7
Explain.
Answer:
Step-by-step explanation:
Well I can show you by example. Try 28
a = 2
b = 8
2 - 2*8 = 2 - 16 = -14
- 14 is divisible by 7. You get - 2.
That means that 28 is also divisible by 8
We'll try one more. Try 56
a = 5
b = 6
5 - 2*6 = 5 - 12 = - 7
- 7 is divisible by 7 so 56 must be as well. What I'm wondering is if the rule in some form works for 735 and if it does how?
a = 73
b = 5
73 - 10 = 63
63 is divisible by 7 (giving 9)
so 10*73 + b is divisible by 7.
Try something a bit harder.
115444
a = 11544
b = 4
a - 2*4
11544 - 8
11536 / 7
1648 which works perfectly.
115444 is divisible by 28 which is a multiple of 7
Really amazing! Thanks for posting.
In January Mr.Tan's students read 20 books. In February, they read 15 books. What is the percent increase or decrease in the number of books the read?
Answer:
there is a 25% decrease in books being read
what is the bionomial expansion of (x-1y)^2
Answer:
[tex] {(x - y)}^{2} \\ = (x - y)(x - y)[/tex]
open the brackets:
[tex] = ( {x}^{2} - xy - xy + {y}^{2} ) \\ = {x}^{2} - 2xy + {y}^{2} [/tex]
which is odd one out 4:10 12:25 20:50 8:20
Answer:
All of them except 12:25 simply to 2:5. So 12:25 is the odd one out.
PLEASE HELP QWQ AsAp with these 4 questions
Answer:
Step-by-step explanation:
I can't believe I'm doing this for 5 points, but ok!
For the first 3, we are going to multiply to find the value of that 3 x 3 matrix by picking up the first 2 columns and plopping them down at the end and then multiplying through using the rules for multiplying matrices:
[tex]\left[\begin{array}{ccccc}7&4&6&7&4\\-4&8&9&-4&8\\1&8&7&1&8\end{array}\right][/tex] and from there find the sum of the products of the main axes minus the sum of the products of the minor axes, as follows (I'm not going to state the process in the next 2 problems, so make sure you follow it here. This is called the determinate. The determinate is what you get when you evaluate or find the value of a matrix. Just so you know):
[tex](7*8*7)+(4*9*1)+(6*-4*8)-[(1*8*6)+(8*9*7)+(7*-4*4)][/tex] which gives us:
392 + 36 - 192 - [48 + 504 - 112] which simplifies to
236 - 440 which is -204
On to the second one:
[tex]\left[\begin{array}{ccccc}-8&-4&-1&-8&-4\\1&7&-3&1&7\\8&9&9&8&9\end{array}\right][/tex] and multiplying gives us
[tex](-8*7*9)+(-4*-3*8)+(-1*1*9)-[(8*7*-1)+(9*-3*-8)+(9*1*-4)][/tex] which gives us:
-504 + 96 - 9 - [-56 + 216 - 36] which simplifies to
-417 - 124 which is -541, choice c.
Now for the third one:
[tex]\left[\begin{array}{ccccc}-2&-2&-5&-2&-2\\2&7&-3&2&7\\8&9&9&8&9\end{array}\right][/tex] and multiplying gives us
[tex](-2*7*9)+(-2*-3*8)+(-5*2*9)-[(8*7*-5)+(9*-3*-2)+(9*2*-2)][/tex] which gives us:
[tex]-126+48-90-[-280+54-36][/tex] which simplifies to
-168 - (-262) which is 94, choice c again.
Now for the last one. I'll show you the set up for the matrix equation; I solved it using the inverse matrix. So I'll also show you the inverse and how I found it.
[tex]\left[\begin{array}{cc}-4&-5&\\-6&-8\\\end{array}\right][/tex] [tex]\left[\begin{array}{c}x\\y\\\end{array}\right][/tex] = [tex]\left[\begin{array}{c}-5\\-2\\\end{array}\right][/tex] and I found the inverse of the 2 x 2 matrix on the left.
Find the inverse by:
* finding the determinate
* putting the determinate under a 1
* multiply that by the "mixed up matrix (you'll see...)
First things first, the determinate:
|A| = (-4*-8) - (-6*-5) which simplifies to
|A| = 32 - 30 so
|A| = 2; now put that under a 1 and multiply it by the mixed up matrix. The mixed up matrix is shown in the next step:
[tex]\frac{1}{2}\left[\begin{array}{cc}-8&5\\6&-4\end{array}\right][/tex] (to get the mixed up matrix, swap the positions of the numbers on the main axis and then change the signs of the numbers on the minor axis). Now we multiply in the 1/2 to get the inverse:
[tex]\left[\begin{array}{cc}-4&\frac{5}{2}\\3&-2\\\end{array}\right][/tex] Multiply that inverse by both sides of the equation. This inverse "undoes" the matrix that's already there (like dividing the matrix that's already there by itself) which leaves us with just the matrix of x and y. Multiply the inverse matrix by the solution matrix:
[tex]\left[\begin{array}{c}x&y\end{array}\right] =\left[\begin{array}{cc}-4&\frac{5}{2} \\3&-2\end{array}\right] *\left[\begin{array}{c}-5&-2\\\end{array}\right][/tex] and that right side multiplies out to
x = 20 - 5 which is
x = 15 and
y = -15 + 4 which is
y = -11
(It works, I checked it)
WILL GIVE BRAINLIEST PLS HELP
Answer:
Hello
Step-by-step explanation:
[tex]y=2x^2-12x+19\\=2(x^2-6x)+19\\=2(x^2-2*3*x+9)+19-18\\=2(x-3)^2+1\\\\Vertex\ is\ (3,1)\\\\Axis\ of\ symmetry\ is\ x=3\\\\y-intercept\ is \\\\y=2(0-3)^2+1=19\\[/tex]
Christa needs to make a painting for art class.
She can only choose two of the eight colors listed
in the table above. What is the probability the two
colors she chooses are green and purple?
A lemonade recipe calls for 1/4 cups of lemon juice for every cup of water.
Plot the pairs in the table in a coordinate plane
Answer:
they are in order cross x with the y across from it
Step-by-step explanation:
A circle has a radius of 8cm. An angle of 1.4 radians is subtended at the center by an arc. Calculate the length of the arc
Answer:
11.2 cm
Step-by-step explanation:
Given that;
Arc Length Formula (if θ is in radians): l = ϴ × r
ϴ = angle subtended in radians
r= radius of the circle
l = 8cm × 1.4 radians
l= 11.2 cm
A set of composite number less than 12.Express it in listing and set-builder methods
composite numbers less than 12={1,3,4,6,8,9,10}
Miguel can use all or part of his $25 gift card to make a music purchase. Each song costs $1.50, and there is a $1.00 per account activation fee.
Which inequalities can represent this situation if m is the number of songs he can buy? Select two options.
1 + 1.5 m less-than-or-equal-to 25
Answer:
A, E or 1, 5
Step-by-step explanation:
Its not A, D
A shopkeeper marked the price of an article a certain percent above the cost price and he allowed 16% discount to make 5% profit. If a customer paid Rs 9,492 with 13% VAT to buy the article, by what percent is the marked price above the cost price of the article?
Plz solve this problem
Answer:
25%
Step-by-step explanation:
let the MP be x
sp without vat =x-16%of x
= 21x/25
sp with VAT = 21x/25 +13% of 21x/25
rs 9492 = 2373x/2500
( 9492*2500)/2373=x
x = 10000
cp = ((21x/25 )*100)/100+5 ( 5= profit percent )
=8000
(10000-8000)×100%/8000
=25%
HELPPP HELP PLS PRONTO ASAP
Ahmed is working at a restaurant. His boss pays him $16.00 per hour and
promises a raise of $1.25 per hour every 6 months. Which sequence
describes Ahmed's expected hourly wages, in dollars, starting with his current
wage?
Answer:
B
Step-by-step explanation:
each of the numbers is just adding 1.25 on to it
Answer: Choice B
16.00, 17.25, 18.50, 19.75, ...
==========================================================
Explanation:
We start with $16.00 as the first term, as this is the amount the boss pays him initially. Then we add on 1.25 to get 16+1.25 = 17.25 to represent the next wage after that first raise.
Then after the second raise he gets, he'll then earn 17.25+1.25 = 18.50 an hour. This process theoretically can go on forever, but realistically the boss will likely set some kind of limit.
We say that this sequence { 16.00, 17.25, 18.50, 19.75, ... } is arithmetic with the first term of 16.00 and common difference 1.25
The common difference is the gap width between any two neighboring terms, and it's the amount the wage goes up each time he gets a raise.
Write an equation of a circle given the center (-4,4) and radius r=5
Answer:
Step-by-step explanation:
Equation of circle: (x - h)² + (y - k)² = r² where (h,k) is the center.
Center( -4 , 4) and r = 5
(x -[-4])² + (y - 4)²= 5²
(x + 4)² + (y-4)² = 25
x² + 2*4*x +4² + y² - 2*y*4 + 4² = 25
x² +8x + 16 + y² - 8y + 16 = 25
x² + 8x + y² - 8y + 16 + 16 -25 = 0
x² + 8x + y² - 8y +7 = 0
We have that the an equation of a circle given the center (-4,4) and radius r=5 is mathematically given as
(x-4)^2+(y-4)^2=5^2
Equation of a circle
Question Parameters:
Given the center (-4,4) and radius r=5
Generally the equation for the Equation of a circle is mathematically given as
(x-x')^2+(y-y')^2=r^2
Therefore, The resultant equation will be
(x-x')^2+(y-y')^2=r^2
(x-4)^2+(y-4)^2=5^2
Hence,an equation of a circle given the center (-4,4) and radius r=5 is
(x-4)^2+(y-4)^2=5^2
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On the first day of travel, a driver was going at a speed of 40 mph. The next day, he increased the speed to 60 mph. If he drove 2 more hours on the first day and traveled 20 more miles, find the total distance traveled in the two days.
Answer:
380
Step-by-step explanation:
This is a bit nasty. It depends on how you read the 20 miles more and what you do with it. The best and most careful way to do it is do it a long way setting up the two equations carefully.
Second day
Let the time travelled = t
Let the speed travelled = 60 mph
d2 = 60*t
First Day
40*(t + 2) = d1
but d1 = d2 + 20 because he travelled 20 miles further on d1
40 * (t + 2) = d2 + 20
d2 however = 60*t
40*(t+2 ) = 60*t + 20 Remove the brackets
40t + 80 = 60t + 20 Subtract 20 from both sides
40t + 60 = 60t Subtract 40t from both sides
60 = 20*t Divide by 20
t = 60/20
t = 3 hours.
Day 2 = 60 + t = 180
Day 1 = 40*5 = 200
Total distance = 380
Where did that 20 miles go? It was just an observation about the difference in distance travelled between the 2 days.
The total distance the driver traveled in the two days is 260 miles
From the question, on the first day, the driver was going as a speed of 40 mph.
Let s be speed
∴ [tex]s_{1}= 40mph[/tex]
On the second day, he increased the speed to 60 mph
∴ [tex]s_{2}= 60mph[/tex]
From the statement- If he drove 2 more hours on the first day
Let time be t
Then
[tex]t_{1}= t_{2} + 2[/tex] hrs
and traveled 20 more miles
Let d be distance
Then,
[tex]d_{1}= d_{2} + 20[/tex] miles
From the formula
Distance = Speed × Time
Then,
[tex]d = s \times t[/tex]
∴ [tex]d_{1} = s_{1} \times t_{1}[/tex]
From above,
[tex]d_{1}= d_{2}+20[/tex] miles
[tex]s_{1}= 40mph[/tex]
[tex]t_{1}= t_{2} + 2[/tex] hrs
Putting these into
[tex]d_{1} = s_{1} \times t_{1}[/tex]
[tex]d_{2} + 20 = 40\times (t_{2}+2)[/tex] ...... (1)
But,
[tex]Time = \frac{Distance}{Speed}[/tex]
∴ [tex]t_{2}= \frac{d_{2} }{s_{2} }[/tex]
From above, [tex]s_{2}= 60mph[/tex]
∴ [tex]t_{2}= \frac{d_{2} }{60}[/tex]
Put this into equation (1)
[tex]d_{2} + 20 = 40\times (t_{2}+2)[/tex]
[tex]d_{2} + 20 = 40\times (\frac{d_{2}}{60} +2)[/tex]
[tex]d_{2} + 20 = \frac{2}{3}d_{2} +80\\d_{2} = \frac{2}{3}d_{2} +80-20\\d_{2} = \frac{2}{3}d_{2} +60[/tex]
Multiply through by 3
[tex]3\times d_{2} = 3\times \frac{2}{3}d_{2} +3 \times 60\\3d_{2} = 2d_{2} + 120\\3d_{2} -2d_{2} = 120[/tex]
∴ [tex]d_{2} = 120[/tex] miles
∴The distance traveled on the second day is 120 miles
For the distance traveled on the first day,
Substitute [tex]d_{2}[/tex] into the equation
[tex]d_{1}= d_{2}+20[/tex] miles
∴ [tex]d_{1}= 120+20[/tex]
[tex]d_{1}= 140[/tex] miles
∴ The distance traveled on the first day is 140 miles
The total distance traveled in the two days = [tex]d_{1} + d_{2}[/tex]
The total distance traveled in the two days = 120 miles + 140 miles
The total distance traveled in the two days = 260 miles
Hence, the total distance the driver traveled in the two days is 260 miles
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Wendy went to the salon and had 2 1/6 inches of hair cut off. The next day she went back
and asked for another 2 1/6 inches to be cut off. How much hair did she have cut off in all?
Write your answer as a fraction or as a whole or mixed number.
inches.
Answer:
4 1/3 of her hair
Step-by-step explanation:
Just add 2 1/6 + 2 1/6 and there you go
There is the total amount of her hair she cut
What is the solution to the system of equations graphed below?
Answer:
the third option=C -2,3
Step-by-step explanation:
solve simultaneously
Answer:
(-2,3)
Step-by-step explanation:
The solution to the system is where the two lines cross
x= -2
y = 3
(-2,3)
Find the volume of this cylinder please..
Answer: 825
Step-by-step explanation:
Plug in the values for v = π*r²*h
So, your new equation is v = π*5²*11 (I got 5 because 10 is the diameter, the radius is half the diameter, therefore r = 5.)
The question is also telling us to replace π with 3.
now we solve, after gathering all of our information.
v = 3*5²*11
v=3*25*11
v=75*11
v=825
SOMEONE PLEASE ANSWER THIS ASAP!!
The population of Arlington High School can be modeled using the equation P(t) = 3,500(1.027)^t , where t represents the number of years since 2010
Is the population of Arlington High increasing or decreasing? Explain how you can tell using the equation.
How do you interpret the statement that P(6)= 4,107
SOMEONE PLEASE ANSWER THIS
Step-by-step explanation:
Arlington is increasing because it has 1.027, if it was 0.27 it would be decreasing
If p(6)= 4107 that means after 6 years there would be a total population of 4107
If you could answer them all It would really be helpful PLEASE marking brainliest
Answer:
1. the area of the triangle minus the area of the small, inner rectangle. what did you not understand there ?
the standard formula (hi, internet !) for the area of a triangle is baseline×height/2.
the standard formula (hi, first grade !) for the area of a rectangle is length×width.
that's it.
1.a.
the volume of an object regularity shaped like a silo is always ground area times height.
for this object we only need to imagine to stand the object up sideways on the triangle side.
and don't forget - an area is always a square unit (like cm²,m², ft², ...). and a volume is always a cubic unit (like cm³, m³, ft³, ...).
so then, the triangle area is the ground area. and the original long side line of the object is is height.
as we said in 1. above, the area of a triangle is baseline×height (of the triangle, not of the overall object) divided by 2.
so, we have here 6×4/2 = 6×2 = 12 m²
and now the ground area × object height = 12×8=96 m³
b.
the standard formula for the volume of a ball (hi, internet !) is pi×r³.
so, we have here pi×9³. can you calculate that with your calculator ? that is pi×729 = 2290.221 cm³
2a.
the height of the cone is (as the drawing already suggests) determined via the right-angled triangle of the radius (half of the diameter) of the ground circle, the height of the cone and the length of the sideline on the outside mantle of the cone. this sideline is the Hypotenuse (the baseline of the triangle opposite of the 90 degree angle).
so, we use Pythagoras
c² = a² + b² (c being the Hypotenuse, a and b being the sides).
11² = 8² + h²
121 = 64 + h²
h² = 57
h = 7.55 cm
2b.
the standard formula for the volume of a cone (hi, internet !) is
pi×r²×h/3
pi×8²×7.55/3 = pi×64×7.55/3 = 506 cm³
Step-by-step explanation:
all of that you could easily search on the internet and since it yourself way faster than putting things in here and waiting for responses.
as there is really nothing to explain but just to use the standard formulas with the given numbers.
What is the name of an investment that pools money from many investors in
order to acquire a large variety of stocks, bonds, and other investments?
A. Derivative
B. Mutual fund
C. Annuity
Answer:
Mutal fund because its a formerly greatest instruments
The name of an investment that pools money from many investors in order to acquire a large variety of stocks, bonds, and other investments is Mutual fund.
What is investment?Investment is traditionally defined as the "commitment of resources to achieve later benefits
A mutual fund is a type of investment vehicle that pools money from multiple investors to invest in a diversified portfolio of stocks, bonds, and other securities.
Mutual funds are managed by professional fund managers who use the pooled funds to purchase a range of investments, with the goal of generating a return for the investors.
Investors in mutual funds own shares in the fund, and the value of their investment is based on the performance of the underlying securities held by the fund.
Mutual funds offer investors the benefits of diversification, professional management, and ease of investment, as well as the ability to invest in a variety of asset classes with relatively low minimum investment requirements.
Hence, the name of an investment that pools money from many investors in order to acquire a large variety of stocks, bonds, and other investments is Mutual fund.
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If f(x) = 3x^2-2x+4 and g(x) = 5x^2+6x-8, find (f-g)(x)
Answer:
-2x^2-8x+12
Step-by-step explanation:
f(x) = 3x^2-2x+4
g(x) = 5x^2+6x-8
(f-g)(x)= 3x^2-2x+4 -(5x^2+6x-8)
Distribute the minus sign
(f-g)(x)= 3x^2-2x+4 -5x^2-6x+8
Combine like terms
=-2x^2-8x+12
Answer: (f+g)(x)=8x^2+4x-4
Step-by-step explanation:
solve for the measure of a
Answer:
Step-by-step explanation:
The supplement of the exterior angle is 180 - 75 = 105
In a cyclic quadrilateral (a four sides figure where all the vertices touch the circumference of a circle), the opposite angles are supplementary. Therefore <a = 180 - 105 = 75
But I think you already knew that.
In the figure below j ll h find the values of x and y
Answer:
26
Step-by-step explanation:
Given: Lines J and H are parallel lines. O intersects both lines equally.
Since two angles equal 180, that will be what (4y + 12) and 64 will be equal to.
(4y + 12) + 64 = 180
76 + 4y = 180
-76 -76
-------------------
4y = 104
y = 26
x and y is both 26 because they are vertical angles.
Hope this helped.
what must be added to a + b to get a
Answer:
we have to add (-b) to get (a)
Step-by-step explanation:
a+b+(-b)=a
a+b-b=a
a=a
Hence verified.
Hope this helps you. Have a nice day^_^
Justin is saving money to buy a stereo. He has $25 saved in the bank right now. He earns $40 each week delivering newspapers.
Let y = the total amount of money Justin has, and x is in weeks.
(6 1/4)^4
Answer fast or i will report you
Answer:6
Step-by-step explanation: The rules of exponential says (a^x)^y=a^xy.
Therefore you will multiply 1/4 with 4 to get an exponent of 1. So the answer is 6^1 which is also written as 6
Help fast!
Describe at least two ways to find or
estimate the year the population of the town
will be 40 thousand. (You don't have to
actually find the value.)
In XYZ, what is the cosine ratio of X?
Answer:
c) 12/15 = 4/5
Step-by-step explanation:
imagine we mirror the triangle up, so that Z is on top.
then you can clearly see that 6 is cos(X) times r (and r is then 7.5).
XY is sin(X)×7.5
and again, 7.5 is r (the line making the X angle).
so, the cosine ratio of X is
6 = cos(X)×7.5
cos(X) = 6/7.5 or then 12/15. or simplified 4/5.
