The rationalization the denominator of the fraction (6)/(4+\sqrt(5)) is [tex]\dfrac{6(4-\sqrt(5))}{11}[/tex].
How to rationalize a fraction?Suppose the given fraction is [tex]\dfrac{a}{b+c}[/tex]
Then the conjugate of the denominator is given by b - c
Thus, rationalizing the fraction will give us
[tex]\dfrac{a}{b+c} \times \dfrac{b-c}{b-c} = \dfrac{a(b-c)}{b^2 - c^2}[/tex]
The given expression is
[tex]\dfrac{6}{4+\sqrt(5)}\\\\[/tex]
By rationalizing the denominator of the fraction
[tex]\dfrac{6}{4+\sqrt(5)}\times \dfrac{4-\sqrt(5)}{4-\sqrt(5)} \\\\\\\dfrac{6(4-\sqrt(5))}{4^2-(5)}\\\\\\\dfrac{6(4-\sqrt(5))}{11}[/tex]
Thus, the rationalization the denominator of the fraction (6)/(4+\sqrt(5)) is [tex]\dfrac{6(4-\sqrt(5))}{11}[/tex].
Learn more about rationalization here;
https://brainly.com/question/14261303
#SPJ1
What is the area of this triangle?
Answer:
A = 26.35 mm²
Step-by-step explanation:
the area (A) of the triangle is calculated as
A = [tex]\frac{1}{2}[/tex] bh ( b is the base and h the perpendicular height )
here b = 8.5 and h = 6.2 , then
A = 0.5 × 8.5 × 6.2 = 26.35 mm²
Step-by-step explanation:
1/2 ×bh
1/2×8.5×6.2
=26.35mm
Find the slope rise/run
Answer:
m = -1/3
Step-by-step explanation:
Find two points in order to calculate slope:
(0, 2) (3, 1)Slope (m) =
ΔY /ΔX= -1/ 3= -0.33333333333333
( ΔX = 3 – 0 = 3ΔY = 1 – 2 = -1 )Slope intercept:
y = -0.33333333333333x + 2
Answer:
Slope = - 1/3
Step-by-step explanation:
Choose the point on the right and move upwards. How many times did you move upwards until you were at the same level as the point on the left? You moved once, which means your rise is 1.
Now from the point where you are at now, move right or left depending on where the point is. In this case, it's on the left which means our run will be negative. Now move left until you reach that point on the left. How many times did you move left? You moved three times, which means your run is 3.
Rise/Run = -1/3
Slope = Rise/Run
Slope: - 1/3
hope this helps!! p.s. i really need brainliest :)
X - 4.5y=20.5 - X + 4.7y= -21.5
The value of x and y is -0.0434 and -4.5652.
What is equation?equation, statement of equality between two expressions consisting of variables and/or numbers.
given:
x - 4.5y=20.5
x + 4.7y= -21.5
Solving above two equation we have:
20.5+4.5y=-21.5-4.7y
42= -9.2y
y= -42/9.2
y= -4.5652
x=-0.0434
Hence, the value of x and y is -0.0434 and -4.5652.
Learn more about equation here:
https://brainly.com/question/2263981
#SPJ1
The graphs of f(x) and g(x) are shown below:
If f(x) = (x + 7)2, which of the following is g(x), based on the translation?
Hint: How many units is g(x) shifting down of f(x)?
a
g(x) = (x + 9)2
b
g(x) = (x + 5)2
c
g(x) = (x + 7)2 + 2
d
g(x) = (x + 7)2 − 2
Answer:
d
Step-by-step explanation:
Comparing the graphs we understand :
⇒ g(x) is equal to f(x) when shifted down 2 units
===========================================================
Hence :
⇒ g(x) = f(x) - 2
⇒ g(x) = (x + 7)² - 2
For what value of x will the line passing through the following pairs of points be
vertical?
F(3-2x, 12) and G(x +9, 7)
The radius of a circle is 9 inches. What is the circle's circumference?
Use 3.14 for
Answer:
56.52
Step-by-step explanation:
The formula for circumference is C=2πr
So, C=2(3.14)(9)
C=56.52 answer
Each of the s swimmers on the relay team swam an equal number of the 8 laps in a race. Write an expression that shows how many laps each swimmer swam.
The number of laps that Swimmer A swam was 50 laps.
How to form mathematical expression from the given description?You can represent the unknown amounts by the use of variables. Follow whatever the description is and convert it one by one mathematically. For example if it is asked to increase some item by 4 , then you can add 4 in that item to increase it by 4. If something is for example, doubled, then you can multiply that thing by 2 and so on methods can be used to convert description to mathematical expressions.
Let we suppose that:
Swimmer A swam x laps
Swimmer B swam y laps.
Then, according to the given data, we have:
x + y = 175 laps
y = 25 + 2x
(25 more than twice of laps of A is the number of laps of B).
Thus, we get a system of two equations:
x + 25 + 2x = 175
3x + 25 = 175
3x = 175 - 25 = 150
x = 50
As x is the number of laps Swimmer A swam, thus, the number of laps that Swimmer A swam was 50 laps.
To know more about equations follow
https://brainly.com/question/2972832
#SPJ1
A cone will be inscribed in a sphere of radius 11 in.
Part A: Find the exact dimensions of the cone of largest volume that will fit inside the sphere. (20 points)
Part B: Find the maximum volume cone to the nearest tenth. (20 points)
The exact dimensions of the cone of largest volume that will fit inside the sphere will be 14.67 inches and 22✓2/3 inches.
How to calculate the dimensions?From the information given, the height of the cone will be:
h = 11 + x
h = 11 + 3 2/3
h = 14 2/3 inches
The radius of the base of the cone will be:
= ✓121 - ✓121/9
= 2✓2(11)/3
= 22✓2/3
Therefore, the dimensions of the cone aren't 14.67 inches and 22✓2/3 inches.
Learn more about cone on:
https://brainly.com/question/1082469
#SPJ1
Select all of the true statements below.
• Circles always contain arcs.
• Line segments always contain lines.
• Lines always contain line segments.
• Angles always form perpendicular lines.
Answer:
Circles always contain arcs.Lines always contain line segments.According to the graph of the rational function y equals 2 over the quantity x squared minus 1 end quantity which of the following statements is/are true?
The function is odd.
The function is decreasing for all values in the domain.
There is a horizontal asymptote along the x-axis.
The given function y = 2(x² - 1) is decreasing for all values in the domain and it has a horizontal asymptote along the x-axis so options (B) and (C) will be correct.
What is a function?A certain kind of relationship called a function binds inputs to essentially one output.
The nature of the relationship between the variables that makes up a function, such as y = sinx and y = x +6, defines the function.
Given the function,
y = 2(x² - 1)
If we increase the value of x to positive then the denominator x² - 1 will go to increase and thus y will decrease.
If we increase the value of x in negative then denominator x² - 1 will go to increase and thus y will decrease.
Therefore it is decreasing for all values in the domain.
Now,
Lim at x tends to ∞ of function is 2/∞ = 0 so y = 0 means there is a horizontal asymptote along the x-axis.
Hence "The given function y = 2(x² - 1) is decreasing for all values in the domain and it has a horizontal asymptote along the x-axis".
For more about the function,
brainly.com/question/23712366
#SPJ2
x^2 + 8x +7
Explain answer
Step-by-step explanation:
[tex] {x}^{2} + 8x + 7 \\ [/tex]
express as a mixed fraction 5¼×6
I need method
And answer should be 31½
Answer:
express as a mixed fraction 5¼×6
I need method
And answer should be 31½
If the cost of 3 notebooks is 30.30, then find the cost of 15 such notebooks.
Answer:
If the cost of 3 notebooks is 30.30, we can infer the cost of one notebook is 10.10.
Step-by-step explanation:
[tex]10.10 * 15 = x[/tex]
[tex]10.10 * 15 = 151.5[/tex]
Hi student, let me help you out! :)
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
We are asked to find the cost of 15 notebooks, given that the cost of 3 notebooks is 30.30.
[tex]\triangle~\fbox{\bf{KEY:}}[/tex]
First of all, we need to find the cost of 1 notebook.So we divide the cost of three notebooks (30.30) by 3:
[tex]\star~\large\pmb{30.30\div3}[/tex]
[tex]\star~\large\pmb{10.10}[/tex]
That's the cost of 1 notebook. Now, multiply that times 15 (we're asked to find the cost of 15 notebooks).
[tex]\star~\large\pmb{10.10\times15}[/tex]
This gives us:
[tex]\star~\large\pmb{151.5}[/tex]
That's the cost of 15 notebooks if the cost of one notebook is 10.10.
Hope it helps you out! :D
Ask in comments if any queries arise.
#StudyWithBrainly
~Just a smiley person helping students out :)
What is the value of e^in7x?
1
7e
7x
7
Answer:
[tex]7x[/tex]
Step-by-step explanation:
[tex]\text{Let,}~~\\\\~~~~~~~y = e^{\ln 7x}\\\\\implies \ln y = \ln \left(e^{\ln 7x} \right)\\\\\implies \ln y = \ln (7x) \ln e\\\\\implies \ln y = \ln (7x)\\\\\implies y = 7x\\\\\implies e^{\ln 7x} = 7x[/tex]
An angle measure 20 more than the measure of its supplementary angle.What is the measure of each angle?
Based on the definition of supplementary angles, the measure of both angles are: 80° and 100°.
What are Supplementary Angles?The sum of angles that are supplementary to each other equals 180 degrees.
Let the measure of the supplementary angle be x.
The other angle will be: x + 20.
(x + 20) + x = 180
x + 20 + x = 180
2x + 20 = 180
2x = 180 - 20
2x = 160
x = 160/2
x = 80°
The other angle will be x + 20 = 80 + 20 = 100°.
The measure of the angles are: 80° and 100°.
Learn more about supplementary angles on:
https://brainly.com/question/8992900
#SPJ1
please help asap
3/2
3
7/2
Answer:
[tex] \frac{7}{2} [/tex]
Step-by-step explanation:
[tex] \frac{3! + 0!}{2! \times1! } = \frac{(3 \times 2 \times 1) + 1}{(2 \times 1) \times 1} = \frac{6 + 1}{2} = \frac{7}{2} [/tex]
Expresar en la forma más simple: (3x² + 4x - 8) - (-2x² + 4x + 2)
The simplest form of the given expression (3x² + 4x - 8) - (-2x² + 4x + 2) will be 5x² - 10.
What is a quadratic equation?A quadratic equation is the second-order degree algebraic expression in a variable.
The standard form of this expression is ax² + bx + c = 0 where a. b are coefficients and x is the variable and c is a constant.
We have been given an expression
(3x² + 4x - 8) - (-2x² + 4x + 2)
(3x² + 4x - 8 + 2x² - 4x - 2)
Solving like terms
5x² + 4x - 4x - 10
5x² - 10
Learn more about quadratic equations;
brainly.com/question/13197897
#SPJ1
A line that passes through the point (x,y) with a y-intercept of b and a slope of m can be represented by the equation y = mx + b.
Natasha drew a line on the coordinate plane that passes through the point (15,13) and has a y-intercept of -8. What is the slope, m, of the line?
A slope is also known as the gradient of a line. The slope of the line is 1.4.
What is Slope?A slope also known as the gradient of a line is a number that helps to know both the direction and the steepness of the line.
Natasha drew a line on the coordinate plane that passes through the point (15,13) and has a y-intercept of -8. Since the coordinate of a point on the line is known the value of the y-intercept is known, therefore, we can write,
13 = m15 - 8
13 + 8 = 15m
21 = 15m
m = 7/5 = 1.4
Hence, the slope of the line is 1.4.
Learn more about Slope of Line:
https://brainly.com/question/14511992
#SPJ1
can you please help me? 2.1.3
[tex]~~(2I_2)A\\\\\\=2\begin{bmatrix} 1&0\\0&1 \end{bmatrix}\begin{bmatrix} 4&2\\3&-3 \end{bmatrix}\\\\\\=\begin{bmatrix} 2&0\\0&2 \end{bmatrix}\begin{bmatrix} 4&2\\3&-3 \end{bmatrix}\\\\\\=\begin{bmatrix} 8+0&4+0\\0+6&0-6 \end{bmatrix}\\\\\\=\begin{bmatrix} 8&4\\6&-6 \end{bmatrix}[/tex]
Use this tax table to find how much tax you need to pay on a taxable income of $40,000.
If taxable
But not
The tax is:
income is over--
over-
$0
$7,825
10 percent of the
amount over $0
$7,825
$31,850
$782.50 plus 15 percent
of the amount over
7,825
$31,850
$77,100
$4,386.25 plus 25
percent of the amount
over 31,850
$77,100
$160,850 $15,698.75 plus 28
percent of the amount
over 77,100
$160,850
$349,700 $39,148.75 plus 33
percent of the amount
over 160,850
$349,700
no limit
$101,469.25 plus 35
percent of the amount
over 349,700
OA $6,423.75
OB. $8,150.50
OC. $12,536.25
Answer:
b
Step-by-step explanation:
Amount of tax you need to pay on a taxable income of $40,000 is,
= $6423.75
What is compound interest?It is defined as the interest on the principal value or deposit and the interest which is gained on the principal value in the previous year.
According to table, $40,000 falls in the 3rd category between $31,850 and $77,100
And, The tax is "$4,386.25 + 25% of amount over 31,850"
Hence, we have:
= $4,386.25 + 25% of (40,000 - 31,850).
= $4,386.25 + 0.25 x 8150
= $6423.75
Thus, Amount of tax you need to pay on a taxable income of $40,000 is,
= $6423.75
Learn more about the compound interest here:
brainly.com/question/26457073
#SPJ5
ow is the product of 3 and –2 shown using integer tiles?
3 positive tiles and 2 negative tiles.
3 negative tiles and 2 positive tiles.
3 sets of 2 negative tiles.
3 sets of 2 positive tiles.
The correct answer is option C which is 3 sets of 2 negative tiles.
What is multiplication?Multiplication is the process of determining the product of two or more numbers in mathematics.
We have the product of 3 and -2. We can represent this as 3 is equivalent to -2 negative tiles.
When we add -2 three times -2 - 2 -2 = -6 we will get -6 that is 3 sets of 2 negative tiles.
So when we multiply it by 3, we end with 3 sets of 2 negative tiles. This is because the order of the factors does not change the product.
Therefore the correct answer is option C which is 3 sets of 2 negative tiles.
To know more about multiplication follow
https://brainly.com/question/10873737
#SPJ1
HELP PLEASE Can someone at lest help me with the 2nd question a) b) and c) PLEASE AND THANKYOU
Answer:
a
Step-by-step explanation:
I say you need to get mays age to even get lilacs age
A 6 foot shadow is cast by a 10 foot lamp post. What is the angle of elevation of the sun?
Let that be theta
tanØ=Perpendicular/BaseHere perpendicular is lamp post and base is the shadow
tanØ=10/6tanØ=5/3tanØ=1.67Ø=59°Answer:
59.0° (nearest tenth)
Step-by-step explanation:
This can be modeled as a right triangle (see attachment).
To find the angle of elevation (marked as [tex]x[/tex] on the attached diagram), use the tan trig ratio:
Tan trigonometric ratio
[tex]\sf\tan(\theta)=\dfrac{O}{A}[/tex]
where:
[tex]\theta[/tex] is the angleO is the side opposite the angleA is the side adjacent the angleGiven:
[tex]\theta = x[/tex]O = 10A = 6Substitute the given values into the formula and solve for x:
[tex]\implies \sf\tan(\theta)=\dfrac{10}{6}[/tex]
[tex]\implies \sf\theta=\tan^{-1}\left(\dfrac{10}{6}\right)[/tex]
[tex]\implies \theta = \sf 59.03624...^{\circ}[/tex]
[tex]\implies \theta = \sf 59.0^{\circ}\:(nearest\:tenth)[/tex]
The diagram shows 3 identical circles inside a rectangle.
Each circle touches the other two circles and the sides of a rectan
as shown in the diagram.
The radius of each circle is 2 mm.
Work out the exact area of the rectangle.
Give your answer in the form a√3 + b
where a and b are integers.
Based on the calculations, the exact area of this rectangle is equal to 16√3 + 32 mm².
How to calculate the area of a rectangle?Mathematically, the area of a rectangle can be calculated by using this formula:
Area = Length × Width
Note: Radius (R) is equal to 2 mm.
Joining the center of the circles would form an equilateral triangle with side length of 2R. Also, the height of the equilateral triangle is given by:
Height = √2R² - R²
Height = √3R
For the length and width of this rectangle, we have:
Length = R + 2R + R
Length = 4R
Width = 2R + height of equilateral triangle
Width = 2R + √3R
Width = (2 + √3)R
Therefore, the area of a rectangle becomes:
Area = 4R × (2 + √3)R
Area = 4(2 + √3) × R²
Area = 4(2 + √3) × 2²
Area = (8 + 4√3) × 4
Area = 16√3 + 32 mm² ≡ a√3 + b
In conclusion, a = 16 and b = 32.
Read more on rectangle here: https://brainly.com/question/25292087
#SPJ1
Given that a = 10 cm and b = 13 cm, work out the height of the triangle.
The Pythagorean theorem is also known as the Pythagoras' theorem. The height of the triangle is 12cm.
What is Pythagoras theorem?The Pythagorean theorem, sometimes known as Pythagoras' theorem, is a basic relationship between the three sides of a right triangle in Euclidean geometry. The size of the square whose side is the hypotenuse is equal to the sum of the areas of the squares on the other two sides, according to this rule.
Given a=10cm and b=13cm, therefore, the height of the triangle can be found using the Pythagoras theorem, therefore,
AB² = AD² + BD²
13² = AD² + 5²
169 = AD² + 25
AD = 12cm
Hence, the height of the triangle is 12cm.
Learn more about Pythagoras theorem:
https://brainly.com/question/12105522
#SPJ1
A geologist in South America discovers a bird skeleton that contains 43% of its original amount of C-14. K value
of C-14 is 0.0001
Find the age of the bird skeleton to the nearest year.
The age of the bird skeleton is 6539.
What is Exponent Function?An exponential function is a function of form f (x) = aˣ, where “x” is a variable and “a” is a constant which is called the base of the function and it should be greater than 0.
Here, N =[tex]N_{0}.e^{-0.0001t}[/tex]
= 52% N₀
[tex]e^{-0.0001t}[/tex] = 0.52
-0.0001 t = ln 0.52
t = -10000 ln 0.52
t = 6539
Thus, the age of the bird skeleton is 6539.
Learn more about Exponent Function from:
https://brainly.com/question/4250446
#SPJ1
Answer:
Step-by-step explanation:
NO LINKS!!!
14. Write the converse of each statement and then determine whether or not the converse is true.
Part A
Converse = "If corresponding angles are equal, then two lines are parallel"Result = TrueExplanation:
Refer to the converse of the corresponding angles theorem. The original version is stated as part A, and the converse is marked in bold above.
Conditional statements are of the form "if this, then that". Symbolically we can use the template "If P, then Q". The P and Q are placeholders for logical statements.
The converse of "if P, then Q" is "If Q, then P". We swap the positions of P and Q. Do not negate either piece.
========================================================
Part B
Converse = "If angle C is 70 degrees, then the sum of angles A and B is 110 degrees"Result = TrueExplanation:
Recall that for any triangle, the three interior or inside angles always add to 180 degrees. In short: A+B+C = 180. If C = 70, then A+B = 180-C leads to A+B = 180-70 and A+B = 110. This process can be reversed.
========================================================
Part C
Converse = "If two lines are not parallel, then alternate interior angles k and s are not equal"Result = TrueExplanation:
For more information, check out the converse of the alternate interior angles theorem. The regular version of the theorem is "If two lines are parallel, then the alternate interior angles are congruent".
The converse of this theorem flips things to say: "If alternate interior angles are congruent, then the lines are parallel".
========================================================
Part D
Converse = "If John loses his money, then he throws coins in the fountain"Result = FalseExplanation:
Throwing coins in a fountain is one way to lose money, but there are other ways. He could drop a coin somewhere, or leave the coin somewhere he forgot.
In other words, just because he lost his money does not mean he threw a coin in the fountain.
A rectangle has a height of m+8m+8m, plus, 8 and a width of
2m^3+m^2+3m2m 3 +m 2 +3m2, m, cubed, plus, m, squared, plus, 3, m. Express the area of the entire rectangle.
Your answer should be a polynomial in standard form.
Answer:
it is 18
Step-by-step explanation:
Find y. Give your answer in the simplest form.
Step-by-step explanation:
you use Sin60 to find y because Sin60=
[tex] \frac{y}{8} [/tex]
A line connecting the points (-3,0) and (x, -6)has slope -1. Determine x.
Answer:
x=3
Step-by-step explanation:
We can use the slope formula to help complete this question
m = (y2-y1)/(x2-x1)
-1 = ( -6-0)/(x- -3)
-1 = -6/ (x+3)
Multiply each side by (x+3)
-x-3 = -6
Add 3 to each side
-x -3+3 = -6+3
-x =-3
Multiply each side by -1
x = 3
Answer:
x = 3
Step-by-step explanation:
The given slope and point can be used to write the equation of the line using the point-slope form. To find x for a given y, we can solve that equation.
__
setupThe point-slope form of the equation for a line is ...
y -k = m(x -h) . . . . . . line with slope m through point (h, k)
For (h, k) = (-3, 0), and m = -1, the equation is ...
y -0 = -1(x -(-3))
y = -x -3
We want x when y = -6, so this becomes ...
-6 = -x -3
solutionAdding x+6 to both sides of the equation, we get ...
(x +6) -6 = -x -3 +(x +6)
x = 3 . . . . . . . simplify