By answering the above question, we may state that by equation Once more, we can observe that the two conjugates' product is an integer.
What is equation?Using the equals notation (=) to indicate equivalence, a math equation links two statements. Algebraic equations prove the equality of three mathematical expressions by a mathematical assertion.
The equal sign, for example, provides a gap between the numbers 3x + 5 and 14 in the equation 3x + 5 = 14. You can use a mathematical formula to understand the connection between the two phrases that are inscribed on opposite sides of a letter. Most of the time, the symbol and the particular software match. e.g., 2x - 4 = 2 is an example.
An integer is always obtained when a radical expression is multiplied by its conjugate since the product has the form[tex]a^2 -b^2[/tex], where a and b are rational numbers. This is so that we may obtain the difference of the squares of the two terms within the radical when we multiply the two conjugates.
Consider the radical expression [tex]\sqrt3 - \sqrt2[/tex] and its conjugate, [tex]\sqrt3 - \sqrt2[/tex] , to understand this. These two expressions can be multiplied as follows:
[tex]\sqrt{\sqrt3 - \sqrt2\\[/tex]
[tex]\sqrt{(\sqrt3 - \sqrt2) ((\sqrt(3 + \sqrt(2)))} = 3 - \sqrt(2 ) = 1$$[/tex]
As a result, we can observe that the two conjugates' product is an integer.
The radical phrase [tex]\sqrt5 - \sqrt3[/tex] and its conjugate, [tex]\sqrt5 +\sqrt3[/tex] , serve as another illustration.
[tex](\sqrt5 -\sqrt3)[/tex]
[tex](\sqrt(5) + \sqrt(3)) = \sqrt(5) \times \sqrt(5) + \sqrt(5) \times \sqrt(3) - \sqrt(3) \times \sqrt(3)[/tex]
[tex](\sqrt5 - \sqrt3)( \sqrt 5+ \sqrt3) = 5 - 3 = 2[/tex]
Once more, we can observe that the two conjugates' product is an integer.
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each dance class in 3/4 hours it takes 7 1/2 hours to learn a dance routine which statement is true ?
Step-by-step explanation:
Answer:
10 dance class
Step-by-step explanation:
The correct option is (d) a student needs to take 10 dance classes to learn the routine. Step-by-step explanation: Given that each dance class is hour and a student takes hours to learn a dance routine. We are to select the TRUE statement. Thus, a student needs 10 dance classes to learn the dance routine.
Which of the following equations has a positive slope and a negative y intercept A.y=3.5x
B.y=1/4x+7
C.y=7.5x-2
D.y=-5x-8
Answer:
C
Step-by-step explanation:
Because 7.5 is a positive and that is the slope and -2 is a negative and that is the y intercept.
PLEASE HELP I will mark brainliest if you explain what you got and how you got it
Answer:
m=-2 b=0
Step-by-step explanation:
first, in order to understand anything, you gotta know what y=mx+b means :)
first, m is just there so you can substitute it for a number. x represents the slope, and b represents the y-intercept, which you also substitute for a number.
so in y= -2x, there's no y intercept, because there is no number that represents the y intercept.
so if we use y=mx+b, we can just substitute the numbers.
which would be, y= -2.
PLEASE HELP ME WITH THIS GUYS!!
Answer:
C
Step-by-step explanation:
So they bought 2 sneakers. A pair of sneakers cost $6.49. Multiply that by 2, and you get $12.98.
Then they bought a pair of flip flops. So one pair is $0.99. Add that to the $12.98 you got and now you have $13.97.
They also got a pair of flats. One pair is $7.19, so add that to your $13.97 and you now have $21.16.
They also have to pay $1.75 tax, meaning you add that to the $21.16 you have which makes $22.91 total.
But they said how much change they would get from $30 so we're not done yet. So subtract $22.91 from $30 and your answer will be $7.09 which is C.
Hey please help, I'm pretty sure it's C, but I'm not sure if it's a also
Answer:
It is only C
Step-by-step explanation:
The only answer for this is C
The correct option is option C i.e. "If the ratio of the arc length to r is 1, then the measure of θ is 1 radians".
What is Arc length?The arc length is defined as the interspace between the two points along a section of a curve.
Here, we know that,
angle = arc length / radius ............(i)
If arc length / radius = 1 ............(ii)
then from eq. (i) and (ii), we get
angle = 1
θ = 1
Thus, The correct option is option C i.e. "If the ratio of the arc length to r is 1, then the measure of θ is 1 radians".
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(20x^2 – 3x – 9)/(4x – 3)
Answer:
5x+3
Step-by-step explanation:
Rewrite the expression to 20x^2-3x-9/4x-3
Factor 20x^2+12x-15x-9/4x-3
Factor 4x*5x+3-3(5x+3)/4x-3
Factor (5x+3)*(4x-3)/4x-3
Solution then becomes 5x+3 as stated above
5(2x+1)-2x
How to solve
Answer:
8x + 5
Step-by-step explanation:
5 * (2x+1) = 10x +5
10x + 5 -2x
8x + 5
What can u multiply by 8.6
then divide by two to get
32.25
Answer:
umm
Step-by-step explanation:
32.25*2=64.50
64.50/8.6=7.5
so the answer is yes
HELP ME PLEASEEEEE I NEEED HELP AGAIN HELP
Answer:
a. w<1
Step-by-step explanation:
divide by -11 from both sides, when you divide by a negative number, flip the sign
What is the equation of this line?
Answer:
A
Step-by-step explanation:
plz brainliest :)
do you want an explanation?
PLEASEEE HELP!!!!!!!!!!
solve the equation 24 = y + 19
y=
Answer: y = 6/5
Step-by-step explanation:
what mixed numbers divide to 12
work out( 10-3 times 2)^2
Answer:
16
Step-by-step explanation:
The answer is 16
Gabrielle read 53 pages of her book in the morning,
She read 26 fewer pages in the afternoon"
How many pages did Gabrielle read in the afternoon?
Solve on paper. Then, check your work on Zearn. )
Gabrielle read 1 pages in the afternoon. 1)
Answer:
27 pages
Step-by-step explanation:
This is a subtraction problem
26 fewer so you subtract 26
53 - 26 = 27
If r(x) = 2x^2 – 5x + 1, find r(x + 2)
Step-by-step explanation:
1 Expand by distributing terms.
rx+r×2
2 Regroup terms.
rx+2r
Find the Shaded Area:
10 m
10 m
Answer:
100-25pi m
Step-by-step explanation:
Let us subtract the circles area from the square
First, let us find the area of the square:
Base x height =
10m x 10m = 100m
Now, the circle:
pi x radius ^2 =
pi x (10/2)^2 =
pi x 5^2=
25 pi
Therefore, the shaded area is 100-25pi m. You can also simplify it further by plugging in the 3.14... value into pi.
I hope this helps! :)
Divide £48 in the following ratios.
a 2:1 b) 1:3
Answer:
a) £32 and £16
b) £12 and £36
Step-by-step explanation:
It is given that:
Amount to divide = £ 48
a) 2 : 1
Let,
x be the times of share.
2x + x = 48
3x = 48
Dividing both sides by 3
[tex]\frac{3x}{3}=\frac{48}{3}\\x=16[/tex]
Thus,
2x = 2(16) = £32
x = £16
b) 1 : 3
x+3x=48
4x=48
Dividing both sides by 4
[tex]\frac{4x}{4}=\frac{48}{4}\\x=12[/tex]
x = £12
3x = 3(12) = £36
Therefore,
a) £32 and £16
b) £12 and £36
Someone! I need help.
Answer:
With?
Step-by-step explanation:
During his lunch break, Leon sent 6 texts in 3/4
of a minute. What was his rate of texting?
Answer:
His rate was 8 text per minute... Please brainliest?
Answer: 8
Step-by-step explanation: trust me
URGENT!!!! THIS IS DUE TODAY!!
Answer:
Unless I am an idiot here (think I am) it is AE s the length between A and E, so it is 8
Step-by-step explanation:
Every side of the square is 16.
A to E is half of a side of the square, not a full side.
So you divide 16 by 2, getting 8.
Hope this helps, and sorry if this seems sloppy, I am new to brainly :)
Find the sum.
(3x - 4) + (12x + 10)
Answer:
15x+6
Step-by-step explanation:
Answer:
hiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiii
What is the domain and range of the inverse of: f (x)= (x + 2)² - 1
Answer:
The inverse of this function is a parabola that has been rotated 90 degrees clockwise, with it's vertex at point 1, 0.
So it's domain is x ≥ 1
And it's range is y ≥ -2
Step-by-step explanation:
Given:
f(x) = (x + 2)² - 1
First we find the inverse:
x = (f(x) + 2)² - 1
x - 1 = (f(x) + 2)²
√(x - 1) = f(x) + 2
f(x) = -2 ± √(x - 1)
If 2000 is placed into a bank account that pays 3% compond interest per year, how much will be in the account after 2 years
Answer:
Interest =(Principle ×Rate×Time)/100
=(2000×3×2)/100
=$120
Total money in the account=$120+$2000
=$2120
Step-by-step explanation:
WHICH STAMENT IS TRUE ABOUT THE GRAPH SHOWN
A school band is buying new jackets and hats. A jacket costs $100 and a hat costs $40. The expression 100/+40h represents the cost of /jackets and h hats. How much will 5 new jackets and 8 new hats cost?
Answer:
820
Step-by-step explanation:
100j+40h
100(5)+40(8)
500+320
820!
Calculate the perimeter of the shape to the nearest whole number
Answer:
Option B
Step-by-step explanation:
Perimeter of the given figure = Sum of measures of all sides
= AB + BC + CA
Since, AB = BC = 9 cm (Radii)
CA = Length of arc CA which is the quarter of the circumference of a circle with radius 9 cm
CA = [tex]\frac{1}{4}(\text{Circumference of the circle})[/tex]
= [tex]\frac{1}{4}(2\pi r)[/tex]
= [tex]\frac{1}{2}(\pi )(9)[/tex]
= 14.14 cm
Now perimeter of the shape = 9 + 9 + 14.14
= 32.14 cm
≈ 32 cm
Therefore, Option B will be the correct option.
Need a bit of help here. :/
Answer:
A or B
Step-by-step explanation:
Which is the corresponding angle
Answer:
4 and 8Step-by-step explanation:
4 and 8 are corresponding angles as they form at parallel lines cut by a transversal.
4 and 3 are supplementary angles (they both add up to 180°).
4 and 1 are vertically opposite angles and are equal to each other.
From the above explanations, only 4 and 8 are corresponding angles.
I hope this helps! I would really appreciate it if you would please mark me brainliest! Have a blessed day!
How do i solve this??
Answer:
x = 25
Step-by-step explanation:
It's a square, so:
[tex]4(4x-10)=360\\16x-40=360\\16x=400\\x=25[/tex]