Answer:
Hello,
3842
Step-by-step explanation:
[tex]a=4-\sqrt{15} \\\\\dfrac{1}{a} =\dfrac{1}{4-\sqrt{15}} \\\\=\dfrac{4+\sqrt{15}}{(4-\sqrt{15})*(4+\sqrt{15})}\\\\=\dfrac{4+\sqrt{15}}{16-15} \\\\=4+\sqrt{15}\\\\[/tex]
[tex]a+\dfrac{1}{a} =4-\sqrt{15}+4+\sqrt{15}=8\\\\[/tex]
[tex](a+\dfrac{1}{a} )^2=a^2+\dfrac{1}{a^2} +2\\\\a^2+\dfrac{1}{a^2} =8^2-2=62\\[/tex]
[tex](a+\dfrac{1}{a} )^3=a^3+\dfrac{1}{a^3} +3*\dfrac{a^2}{a} +3*\dfrac{a}{a^2} \\\\8^3=a^3+\dfrac{1}{a^3} +3(a+\dfrac{1}{a} )\\\\a^3+\dfrac{1}{a^3} =8^3-3*8=488\\[/tex]
[tex](a+\dfrac{1}{a} )^4=a^4+\dfrac{1}{a^4} +4*\dfrac{a^3}{a} +6*\dfrac{a^2}{a^2} +4*\dfrac{a}{a^3}\\\\a^4+\dfrac{1}{a^4}=(a+\dfrac{1}{a} )^4-4*a^2-4*\dfrac{1}{a^2} -6\\a^4+\dfrac{1}{a^4} =8^4-4*62-6\\\\=4096-248-6\\\\=3842\\\boxed{a^4+\dfrac{1}{a^4} =3842}\\[/tex]
Using a calculator:
[tex]a=4-\sqrt{15}=0,1270166537925831148207346002176....\\\\a^4= 2,6028112122495108436170792979303e-4\\\\\dfrac{1}{a} =4+\sqrt{15} =7,8729833462074168851792653997824...\\\\\dfrac{1}{a^4}=3841,9997397188787750489156382921....\\\\a^4+\dfrac{1}{a^4} \\\\= 2,6028112122495108436170792979303e-4+3841,9997397188787750489156382921....\\\\=3842\\[/tex]
Select the correct statement which describes the multiplicative relationship between two equivalent ratios.
A The ratios
5
16
and
32
10
are equivalent. Each term in
32
10
is two times the corresponding term in
5
16
.
B The ratios
16
5
and
10
32
are equivalent. Each term in
10
32
is four times the corresponding term in
16
5
.
C The ratios
16
5
and
32
10
are equivalent. Each term in
32
10
is two times the corresponding term in
16
5
.
D The ratios
16
5
and
32
15
are equivalent. Each term in
32
15
is four times the corresponding term in
16
5
.
Answer:
A
Step-by-step explanation:
If f(x) = 6/x-1
for what value of x does f(x) = 5 ?
Answer:
11/5
Step-by-step explanation:
f(x) = 6/x-1
f(x) = 5
6/x-1 = 5
=> 6 = 5(x-1)
=> 6 = 5x - 5
=> 11 = 5x
=> 5x = 11
=> x = 11/5
Help please, area of a triangle
Answer:
84 ft^2.
Step-by-step explanation:
Use Pythagoras to find the value of h:
25^2 = h^2 + 7^2
h^2 = (25-7)(25+7)
h^2 = 576
h = √576 = 24
Area = 1/2 * 7 * 24
= 84.
HELPPP plzzzzz due soon
find the distance between (3,3) and (3,4)
Answer:
1
Step-by-step explanation:
√(4-3²+(3-3)²
√1¹+0
√1
1
Answer:
1 unitStep-by-step explanation:
Since x- coordinates are same, the distance is the difference of the y-coordinates:
4 - 3 = 1You are taking a survey on the heights of all your classmates. This is an example of categorical data.
True or false
The given statement is false as taking a survey on the heights of all your classmates is an example of quantitative data.
Quantitative data is data that can be measured and expressed as numbers,
such as height, weight, age, etc. Categorical data, on the other hand, consists of distinct categories or groups, such as eye color, gender, favorite color, etc.
Data can be classified into two main types: quantitative data and categorical data.
Quantitative data:
Quantitative data is numerical data that represents measurements or quantities.
It deals with things that can be measured and expressed as numbers.
For example, the heights of people, the weights of objects, the ages of individuals, and the temperatures in degrees are all examples of quantitative data.
Quantitative data can be further divided into two subtypes: discrete and continuous data.
Discrete data: Discrete data consists of whole numbers that cannot be further divided into smaller parts.
For example, the number of students in a class, the number of cars in a parking lot, and the number of books on a shelf are all examples of discrete data.
Continuous data: Continuous data consists of real numbers that can take on any value within a specific range.
For example, the height of a person can be measured as 165.5 cm, 170.2 cm, 178.9 cm, etc. These are all examples of continuous data.
Categorical data:
Categorical data, also known as qualitative data, involves the grouping of items into categories or classes.
It represents characteristics or attributes and is not numerical in nature. Categorical data is further divided into two subtypes: nominal and ordinal data.
Nominal data: Nominal data consists of categories with no intrinsic order or ranking.
For example, eye color ( blue, brown, green) and types of fruits (e.g., apple, banana, orange) are examples of nominal data.
Ordinal data: Ordinal data consists of categories with a meaningful order or ranking.
However, the differences between the categories are not quantifiable.
For instance, educational levels (elementary, middle, high school) and satisfaction levels (very satisfied, satisfied, neutral, dissatisfied, very dissatisfied) are examples of ordinal data.
The height survey of classmates, the data collected would be numerical values representing the heights of each individual.
Since heights are measured and expressed as numbers, this falls under quantitative data, not categorical data.
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Which situation is best represented using a negative integer?
Answer:
a
Step-by-step explanation:
The total cost of 2 bracelets and 3 necklaces is $15.50. The total cost of 4 bracelets and 1 necklace is $13.50. Let b represent the cost of each bracelet and n represent the cost of each necklace. This situation can be represented by the following system of equations.
{2b+3n=15.504b+n=13.50
What is the cost of one bracelet?
A
$2.50
B
$7.75
C
$5.00
D
$3.50
Answer:
A
$2.50
Step-by-step explanation:
b = cost of bracelet
n = cost of necklace
2b+3n = 15.50
4b+1n = 13.50
Multiply the first equation by -2
-4b -6n = -31
4b +n = 13.50
---------------------------
-5n = -17.50
Divide each side by -5
-5n/-5 = -17.5/-5
n = 3.50
Now we can find b
4b+n = 13.50
4b+3.50 = 13.50
4b+3.50-3.50 = 13.50 -3.50
4b = 10
Divide by 4
4b/4 = 10/4
b = 2.50
A) 60° B) 85° C) 96° D) 40°
Answer:
A)60°
Step-by-step explanation:
a straight line is 180° then
if a line bisect it in to a half it become 90°
then
the exterior angle of a triangle is equal to the sum of two interior angles
this means 150°-90°=60°
Answer: A) 60
Step-by-step explanation:
The line at the top signifies 180 degrees, as does any straight line. The 150° that intersects with P tells you that P must be 30 degrees, as 180 - 150 = 30.
The three angles of a triangle must always equal 180°. Angle R tells you that it’s 90°, shown by the square instead of a curve. If you subtract the value of P we found before, and the value of R we just found, you get your answer.
180 - 30 - 90 = 60.
Find the volume of a cone with a
radius of 10 and a height of 7. Use 3.14 for n and
round the answer to the nearest whole number.
Answer:
Step-by-step explanation:
Volume of a cone formula is
[tex]V=\frac{1}{3}\pi r^2h[/tex] where r is radius and h is height. Filling in:
[tex]V=\frac{1}{3}(3.14)(10)^2(7)[/tex] and doing all the math on that and rounding gives us
V = 733 units cubed
(x − 5)∙ 3 = 2∙ 10 + 8
Answer:
x=17
Step-by-step explanation:
3x-15=20+16
3x-15=36
3x=36+15
3x=51
x=17
A marina is in the shape of a coordinate grid. Boat A is docked at (2.4, -3) and Boat B is docked at (-3.4, -3). The boats are ___ units apart.
A 5.8
B 6.4
C 8.8
D 9.4
pls answer this its a question from wootube
Answer:
Its -34 cuhcuhcuchuchcuh
Step-by-step explanation:
cuhcuhcuchucuhcuhcuhcuhcuchcuh
Before soccer practice, Laura warms up by jogging around the outside of the entire soccer field. The field measures 80 meters by 120 meters.
(y+2)(y^2-2y+4) ..........................
You can use the distributive property to multiply:
( y )( y² - 2y + 4 ) + ( 2 )( y² - 2y + 4) =
y³ - 2y² + 4y + 2y² - 4y + 8 =
y³ + 8
The -2y² and the 2y² cancel each other, and the 4y and -4y cancel each other out!
The vertex is 2,-4 what is the parabola equation
Answer:
y + 4 = (x - 2)^2
Step-by-step explanation:
The vertex form of the equation of a vertical parabola is
y - k = a(x - h)^2, where (h, k) represents the vertex and a is a scaling factor which stretches or compresses the parabola vertically. If all we know is the vertex (2, -4), then the desired equation is:
y + 4 = a(x - 2)^2
If there is no vertical stretching or compression, then the equation becomes:
y + 4 = (x - 2)^2
Answer:
y = x² - 4x
Step-by-step explanation:
The equation of a parabola in vertex form is
y = a(x - h)² + k
where (h, k ) are the coordinates of the vertex and a is a multiplier
Here (h, k ) = (2, - 4) , with a = 1 , the equation is
y = (x - 2)² - 4 ← expand using FOIL
= x² - 4x + 4 - 4
y = x² - 4x ← equation of parabola
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What is the value of p in the equation of the line px + 2y + 8 = 0, so that the x-intercept is 4?
Answer:
p = -2
Step-by-step explanation:
px + 2y + 8 = 0
px + 2y = -8
p(4) = -8
p = -2
complete by using the distributive property (y+3)(y+3)(y+3)
Answer:
y^3+9y^2+27y+27
Step-by-step explanation:
Step 1: Start by understanding FOIL. First. Outer. Inner. Last.
Step 2: In this case we have three sets of parenthesis not 2. So we have to do the same thing but multiply 2 (y+3) sets by y and 3 instead of only multiplying y and 3 by one set.
Step 3: So we get y^3+6y^2+9y+3y^2+18y+27.
This simplifies to y^3+9y^2+27y+27
Find the length of the arc.
We know
Length if arc=L[tex]\boxed{\sf L=\dfrac{\theta}{360}\times 2πr}[/tex]
[tex]\\ \sf\longmapsto L=\dfrac{135}{360}\times2π(7)[/tex]
[tex]\\ \sf\longmapsto L=\dfrac{27}{72}\times 14π[/tex]
[tex]\\ \sf\longmapsto L=\dfrac{27}{36}\times 14π[/tex]
[tex]\\ \sf\longmapsto L=\dfrac{9}{12}\times 7π[/tex]
[tex]\\ \sf\longmapsto L=\dfrac{63π}{12}[/tex]
[tex]\\ \sf\longmapsto L=\dfrac{21π}{4}in[/tex]
What is the value of the expression 53.5-5? please explain
Answer:
48.5
Step-by-step explanation:
53.5
- 5.0
48.5
5 tenths - 0 tenths = 5 tenths (.5)
3 minus 5, three smaller than 5 so BORROW 10 13 -5 = 8 (8)
the 5 in the tens position becomes a four because one got "borrowed"
4 - 0 = 4 (4)
48.5 is the result
On a survey, 6 students reported how many minutes it takes them to travel to school. Here are their responses.
Find the mean travel time for these students.
4, 11, 14, 9, 4, 8
PLZ HELP ASAP ITS KHAN WILL GIVE 5 STARS AND HEART AND 10 POINTS AND BRAINLIST
Answer:
14.4
Step-by-step explanation:
Cross multiply.
5x = 8 * 9
5x = 72
x = 14.4
Answer:
x= 14.4
Step-by-step explanation:
1. cross multiply
5*x and 8*9
5x=72
2. divide 72 by 5
x= 14.4
A pizza parlor offers 4 different pizza toppings. How many different kinds of 2-topping pizzas are available?
Answer:
you need to be more specific.
Step-by-step explanation:
Luke is swimming in still water at a constant speed of 3 meters/second.
If you graph this relationship with time along the x-axis and distance along the y-axis, the slope of the line representing this relationship is
.
A point on this line that corresponds to the distance Luke swam in 45 seconds is
Answer:
1. velocity
Step-by-step explanation:
that is the answer above
How are a desert and a tundra similar?
A. They both have high levels of precipitation.
B. They have many trees and a lot of vegetation.
C. They have high average temperatures.
D. They have low humidity and low levels of precipitation.
Answer:
D is right option
Step-by-step explanation:
Similarities:
Both the biomes experience less precipitation due to this they have a less diversity of flora and fauna as compared to other biomes like savanna, grasslands, chaparral etc. Let us see how they differ from each other!
Low rain fall _ annual rainfal of lessthan 20cm in deserts, 15-20cm in tundra
Minimal life_ only small shurbs can survive in both kind of environments
Poor drainage.. In deserts, though sandy soil may seem much porous, these are most flood prone areas of world. The tundra is characterised by permafrost soils ie, under the thin layer of soil, a thick ice sheet is present and hence is no seepage.
High range of temperatures: In tundra, the maximum temperatures are recorded in summer (abt 10^C) and minimum during winter(-20 to -30^C). While, in desert too, the temperature range is high but diurnally ie, nights are too cold and day time is scorching.
express 40% of a right angle into radian measure
40% of a right angle into radian measure will be π/5.
What is an angle?The angle is the distance between the intersecting lines or surfaces. The angle is also expressed in degrees. The angle is 360 degrees for one complete spin.
40% of a right angle.
We know that the right angle given in the form of radian will be as π / 2.
Then the 40% of the right angle will be given as,
⇒ 40% of π/2
⇒ 0.40 × π/2
⇒ 2/5 × π/2
⇒ π/5
40% of a right angle into radian measure will be π/5.
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The sequence shown below is defined using a recursion formula. Write the first four terms of the sequence.
a1=10 and an-1+3 for n is greater than and equal to 2
Explanation:
The notation [tex]a_1 = 10[/tex] says that the first term is 10.
The notation [tex]a_n = a_{n-1}+3[/tex] is the recursive rule that says "to find the nth term, we add 3 to the previous term". So we add 3 to each term to get the next one.
first = 10second = first+3 = 10+3 = 13third = second+3 = 13+3 = 16fourth = third + 3 = 16+3 = 19This sequence is arithmetic due to the common difference d = 3.
Answer:
Step-by-step explanation:
a1=10
a_{n}=a_{n-1}+3
n=2
[tex]a_{2}=a_{1}+3=10+3=13\\n=3\\a_{3}=a_{2}+3=13+3=16\\n=4\\a_{4}=a_{3}+3=16+3=19\\first~four~terms~are\\10,13,16,19[/tex]
An ice-making machine needs to be switched on
for 10 minutes before the production of ice begins.
The mass, in tờnnes, of ice produced is directly
proportional to the number of hours of production.
Given that 20 tonnes ofâce are produced when the
machine runs for half an hour, find the mass of ice
manufactured when the machine runs for
1.75 hours
Since the question explicitly stated that ice production is proportional to time, we're going to have to use proportion fractions. Remember to convert hours into minutes as well.
3. Which word phrase can be used to represent the algebraic expression 4(21+ n)? (2 point) 4 plus the sumn of 21 and a number » O4 times the product of 21 and a number » ne the sum of 21 and a number x 4 less than the sum of 21 and a number : O4 timeſ the
Answer:
4 times the sum of 21 and a number
Step-by-step explanation:
4(21+ n)
The four is being multiplied by the sum of 21 and n
What is the solution to this equation?
6(x - 3) = 3x + 9
OA.X-1
OB.X=9
OC.X=3
OD X=-3
NO WRONG ANSWERS ILL REPORT YOUR ANSWER
6(x-3)=3x+9
6x-18=3x+9
6x-3x=18+9
3x=27
x=27 ÷3
x=9
Hope this will help you
The solution is x = 9, which is an option (B).
What is algebraic Expression?Any mathematical statement that includes numbers, variables, and an arithmetic operation between them is known as an expression or algebraic expression. In the phrase 4m + 5, for instance, the terms 4m and 5 are separated from the variable m by the arithmetic sign +.
Let's simplify the equation by distributing 6 on the left-hand side:
6x - 18 = 3x + 9
Now, let's isolate the x terms on one side and the constant terms on the other side:
6x - 3x = 9 + 18
3x = 27
x = 9
Therefore, the solution to the equation 6(x - 3) = 3x + 9 is x = 9, which is option B.
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