Answer:
103.23 square feet
Step-by-step explanation:
Area of the largest room = length × width
Each centimeter was equal to 1.5 feet
7.4 cm = 1.5 × 7.4 = 11.1 feet
6.2 cm = 1.5 × 6.2 = 9.3 feet
Length = 11.1 feet
Width = 9.3 feet
Area of the largest room = length × width
= 11.1 feet × 9.3 feet
= 103.23 square feet
(a) Determine a cubic polynomial with integer coefficients which has $\sqrt[3]{2} + \sqrt[3]{4}$ as a root.
(b) Prove that $\sqrt[3]{2} + \sqrt[3]{4}$ is irrational.
Answer:
(a) [tex]x\³ - 6x - 6[/tex]
(b) Proved
Step-by-step explanation:
Given
[tex]r = $\sqrt[3]{2} + \sqrt[3]{4}$[/tex] --- the root
Solving (a): The polynomial
A cubic function is represented as:
[tex]f = (a + b)^3[/tex]
Expand
[tex]f = a^3 + 3a^2b + 3ab^2 + b^3[/tex]
Rewrite as:
[tex]f = a^3 + 3ab(a + b) + b^3[/tex]
The root is represented as:
[tex]r=a+b[/tex]
By comparison:
[tex]a = $\sqrt[3]{2}[/tex]
[tex]b = \sqrt[3]{4}$[/tex]
So, we have:
[tex]f = ($\sqrt[3]{2})^3 + 3*$\sqrt[3]{2}*\sqrt[3]{4}$*($\sqrt[3]{2} + \sqrt[3]{4}$) + (\sqrt[3]{4}$)^3[/tex]
Expand
[tex]f = 2 + 3*$\sqrt[3]{2*4}*($\sqrt[3]{2} + \sqrt[3]{4}$) + 4[/tex]
[tex]f = 2 + 3*$\sqrt[3]{8}*($\sqrt[3]{2} + \sqrt[3]{4}$) + 4[/tex]
[tex]f = 2 + 3*2*($\sqrt[3]{2} + \sqrt[3]{4}$) + 4[/tex]
[tex]f = 2 + 6($\sqrt[3]{2} + \sqrt[3]{4}$) + 4[/tex]
Evaluate like terms
[tex]f = 6 + 6($\sqrt[3]{2} + \sqrt[3]{4}$)[/tex]
Recall that: [tex]r = $\sqrt[3]{2} + \sqrt[3]{4}$[/tex]
So, we have:
[tex]f = 6 + 6r[/tex]
Equate to 0
[tex]f - 6 - 6r = 0[/tex]
Rewrite as:
[tex]f - 6r - 6 = 0[/tex]
Express as a cubic function
[tex]x^3 - 6x - 6 = 0[/tex]
Hence, the cubic polynomial is:
[tex]f(x) = x^3 - 6x - 6[/tex]
Solving (b): Prove that r is irrational
The constant term of [tex]x^3 - 6x - 6 = 0[/tex] is -6
The divisors of -6 are: -6,-3,-2,-1,1,2,3,6
Calculate f(x) for each of the above values to calculate the remainder when f(x) is divided by any of the above values
[tex]f(-6) = (-6)^3 - 6*-6 - 6 = -186[/tex]
[tex]f(-3) = (-3)^3 - 6*-3 - 6 = -15[/tex]
[tex]f(-2) = (-2)^3 - 6*-2 - 6 = -2[/tex]
[tex]f(-1) = (-1)^3 - 6*-1 - 6 = -1[/tex]
[tex]f(1) = (1)^3 - 6*1 - 6 = -11[/tex]
[tex]f(2) = (2)^3 - 6*2 - 6 = -10[/tex]
[tex]f(3) = (3)^3 - 6*3 - 6 = 3[/tex]
[tex]f(6) = (6)^3 - 6*6 - 6 = 174[/tex]
For r to be rational;
The divisors of -6 must divide f(x) without remainder
i.e. Any of the above values must equal 0
Since none equals 0, then r is irrational
simplify (-9)×5×6(-3)
[tex]\bf \large \hookrightarrow \:( - 9) \: \times \: 5 \: \times \: 6 \: \times \: ( - 3) \\ \\ \bf \Large \hookrightarrow \: \: \: - 45 \: \times \: ( - 18) \\ \\ \bf \Large \hookrightarrow \: \: 810[/tex]
1. In a board game, you must roll two 6-sided number cubes. You can only start the game if you roll a 3 on at least one of the number cubes.
(a) Make a list of all the different possible outcomes when two number cubes are rolled.
(b) What fraction of the possible outcomes is favorable?
(c) Suppose you rolled the two number cubes 100 times, would you expect at least one 3 more or less than 34 times? Explain. Answer:
Answer:
34
Step-by-step explanation:
You should not expect more than 34 times to be favorable, because favorable outcomes are about 28% of outcomes, and 28% of 100 is 28, which is less than 34.
6/21 outcomes will be favorable.
Here is a list of all possible :
1 - 1
1 - 2
1 - 3
1 - 4
1 - 5
1 - 6
2 - 2
2 - 3
2 - 4
2 - 5
2 - 6
3 - 3
3 - 4
3 - 5
3 - 6
4 - 4
4 - 5
4 - 6
5 - 5
5 - 6outcomes29 out of every 100 outcomes will likely
6 - 6
One or two of the underlined outcomes have a three. The total number of outcomes is 21, and six of them include 3's. Therefore, when we multiply 6/21 by .286, we get 28.6%. be favorable.
Hope this helps! : )
Which of the following is a composite number?
A. 1
B. 63
C.O
D. 19
B. 63
some simple googling would've been able to help you with this. but 0 isn't prime or composite, not sure about 1, 19 is prime, 63 is a definite composite
(17)^ 3 *(289)^ -6 =(17)^ 2m - 1
Answer:
m = -4
Step-by-step explanation:
The given expression is :
[tex](17)^{3}\cdot(289)^{-6}=(17)^{2m-1}[/tex]
We need to find the value of m
We know that, 17² = 289
So,
[tex](17)^{3}\cdot(17^2)^{-6}=(17)^{2m-1}\\\\(17)^{3}\cdot(17)^{-12}=(17)^{2m-1}[/tex]
Also,[tex]x^ax^b=x^{a+b}[/tex]
So,
[tex]17^{3-12}=17^{2m-1}\\\\17^{-9}=17^{2m-1}\\\\\implies -9=2m-1\\\\-9+1=2m\\\\-8=2m\\\\m=-4[/tex]
So, the value of m is equal to -4.
What is the inverse of the function f(x) = x +3?
O h(x) = 5x + 3
O h(x) =
1x-3
Oh(x) = x-3
Oh(x) = x + 3
The value of the inverse of the function f(x) = x +3 is,
⇒ h (x) = x - 3
What is mean by Function?A relation between a set of inputs having one output each is called a function. and an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).
Given that;
Function is,
f (x) = x + 3
Now, We can find the inverse of the function f(x) = x +3 as,
f (x) = x + 3
y = x + 3
x = y - 3
h (x) = x - 3
Thus, The value of the inverse of the function f(x) = x +3 is,
⇒ h (x) = x - 3
Learn more about the function visit:
https://brainly.com/question/11624077
#SPJ7
You buy a 1:10000 scale model of the One World Trade Center during a trip to New York City. The height of the model is 5.41 centimeters. Find the actual height x (in meters) of the One World Trade Center.
Answer:
541m
Step-by-step explanation:
The scale given 1 represents the height of the model and 10000 represents the actual height,place the 5.41 in line with the one and an unknown letter in line with the 10000 inorder to calculate the actual height
1:10000
5.41:x
cross multiply and solve for x,which will be 54100cm
but since the answer has to be in meters convert the 54100cm to a meter by dividing it by 100..
Three exterior angles of a pentagon measures 60,80and 90.Find the measure of other two exterior angle, assuming them equally Thanks!
Given:
The three exterior angles of a pentagon measures 60,80 and 90.
To find:
The measure of other two exterior angle, assuming them equally.
Solution:
Let x be the measure of two other exterior angles of the pentagon.
We know that the sum of all exterior angles of a pentagon is 360 degrees.
[tex]60^\circ+80^\circ+90^\circ+x+x=360^\circ[/tex]
[tex]230^\circ+2x=360^\circ[/tex]
[tex]2x=360^\circ-230^\circ[/tex]
[tex]2x=130^\circ[/tex]
Divide both sides by 2.
[tex]\dfrac{2x}{2}=\dfrac{130^\circ}{2}[/tex]
[tex]x=65^\circ[/tex]
Therefore, the measures of both exterior angles are 65 degrees.
How to find the frequency in a histogram
Answer:Para preparar la tabla de frecuencia para un histograma, es necesario primero establecer el número de intervalos que se desea tener.
Luego, se debe determinar el ancho común de los intervalos (interval width). Para esto, se calcula la diferencia del dato mayor y el dato menor, y se divide entre el número de intervalos deseados. Este resultado se redondea al entero mayor más cercano.
Por ejemplo, si se desea tener 10 intervalos y encontramos que el dato mayor es 35 y el menor es 12,
Step-by-step explanation:
Can someone help me with this math homework please!
Answer:
x = 12.5
Step-by-step explanation:
Explanation in progress ;-)
x/3 + 8 = 23 . Find the value of x
Answer:
45
Step-by-step explanation:
x/3 + 8 =23
=> x/3 = 23-8
=> x/3 = 15
=> x = 15 x 3
x = 45
Answer:
x=45
Step-by-step explanation:
To find x isolate the variables by using the properties of equality. First, subtract 8 from both sides, [tex]\frac{x}{3} = 15[/tex]. Then multiply both sides by 3, [tex]x=45[/tex]. Finally, to check you can plug 45 back into the equation, [tex]\frac{45}{3} +8=23[/tex]. Next, solve this equation and get 23=23, since this is a true statement 45 is correct.
Given: ABCD is a parallelogram.
Prove: ∠A and ∠D are supplementary.
Parallelogram A B C D is shown.
By the definition of a parallelogram, AB∥DC. AD is a transversal between these sides, so ∠A and ∠D are
angles. Because AB and DC are
, the same-side interior angles must be
by the same-side interior angles theorem. Therefore, ∠A and ∠D are supplementary.
Answer:
AB = DC So ∠A and ∠D are bigger then 90%
Answer:
E2020
Step-by-step explanation:
please help!!
The length of side AC is | 3,4,5,6 | units.
The area of triangle ABC is | 5,10,15,20 | square units.
Look at ∠A, the angle which resides on (1, 3). If we count 5 units down, you find the other endpoint on side AC. Hence, the length of side AC is 5 units. This figure is equal to the height of the graphed triangle.
If we mirror this process with the figure representing the triangle's length, side BC, we get 4 units.
The formula for calculating a triangle's area is [tex]\frac{1}{2}bh[/tex]. In this context, the base of the triangle is the same as the length. Now, let's plug in the base and the height.
[tex]\frac{1}{2}(4)[/tex] × [tex](5) = 10[/tex]
The area of triangle ABC is 10 squared units.
Answer:
first box: 5 second box: 10
Step-by-step explanation:
Using trial and improvement, find the solution between 5 and 6 for the following equation:
x
2
=
27
Give your answer rounded to 1 DP.
Answer:
2
Step-by-step explanation:
that is √ 14 which is 27 ×>44.2177
Three less than 3 times a number, n, is
19 more than twice the number. What
is the number?
А
17
B
19
21
D 22
The equation is:
3n - 3 = 2n + 19
=> 3n - 2n = 19 + 3
=> n = 22
So, the answer is 22.
can someone help me with this please
Answer:
for question B
2A 3C = 70
70-15 = 55/5 = 11.
so each child is 11
while adult 11 + 7.50 = 18.50
Find the product: 3/4 x 2/3. What's the product? 5/7, 6/12, 5/12, 6/7. What is it please help me!!!!
Answer:
1/2
Step-by-step explanation:
3/4 x 2/3
= 1/2
Aubrey tiene un nuevo estuche de arte con forma de prisma rectangular. El estuche es de 12 cm por 20 cm por 5cm. Lo único dentro del estuche es un nuevo borrador rosa con las dimensiones que se muestran a continuación.
¿Cual es el volumen del estuche que no ocupa por el borrador?
Respuesta:
720 cm³
Explicación paso a paso:
El volumen de un prisma rectangular viene dado por:
V = largo * ancho * alto
Dimensión de la caja de arte = 12 por 20 por 5
Dimensión del borrador = largo * ancho * alto
Volumen del borrador = 2 por 4 por 0,5
Dimensión del estuche de arte que no contiene borrador:
(12 por 20 por 5) - (2 por 4 por 0,5)
(10 por 16 por 4,5)
Volumen de la caja que no contiene borrador:
10 * 16 * 4,5 = 720 cm³
Write the equation of the line (in y = ax+b form) in the
graph below. do not use any spaces when typing your
answer
Answer:
y=3x-8
Step-by-step explanation:
Use a trigonometric ratio to find the value of x. Round your answer to the nearest tenth.
2/5x - 1/5y = 98
2/7x - 1/14y = 55
If the ordered pair (x, y) satisfies the system of
equations shown above, what is the value of x?
Answer:
x = 140
Step-by-step explanation:
Given the equations
[tex]\frac{2}{5}[/tex] x - [tex]\frac{1}{5}[/tex] y = 98 ( multiply through by 5 to clear the fractions )
2x - y = 490 → (1)
[tex]\frac{2}{7}[/tex] x - [tex]\frac{1}{14}[/tex] y = 55 ( multiply through by 14 to clear the fractions )
4x - y = 770 → (2)
Subtract (1) from (2) term by term to eliminate y
2x + 0 = 280
2x = 280 ( divide both sides by 2 )
x = 140
what is the answer to the problem
pls help and explain answer!!
At a certain point in time, a physicist measures the
speed of a falling object to be 17.6 feet per second.
What is the equivalent speed in miles per hour?
(5280 feet = 1 mile)
Answer:
0.003 miles per hour
Step-by-step explanation:
Well since 5280 feet gives 1 mile den convert 17.6 feet per sec to miles per hr
The following list shows how many brothers and sisters some students have: 3, 4, 4, 5, 5, 3, 2, 4, 6, 3, 6, 4, 2 State the mode.
Answer:
mode is 4
it has the highest occurrence
Answer:
The mode is 4
Step-by-step explanation:
The mode is a value that appears most frequently in a data set.
By looking at all the numbers, the number 4 appears the most: a total of four times.
Hope it helps (●'◡'●)
Please help me with 1-6 (means) ASAPPPPP
I will give brainiest
Answer:
Geometric mean of [8,18] = 12Geometric mean of [3,7] = 4.58Geometric mean of [5,8] = 6.32Geometric mean of [8,4] = 5.65Geometric mean of [6,3] = 4.24Geometric mean of [2,8] = 4Step-by-step explanation:
Given:
Geometric mean of two digit = √ab
Answer 1;
Geometric mean of [8,18] = √(8)(18)
Geometric mean of [8,18] = √144
Geometric mean of [8,18] = 12
Answer 2;
Geometric mean of [3,7] = √(3)(7)
Geometric mean of [3,7] = √21
Geometric mean of [3,7] = 4.58
Answer 3;
Geometric mean of [5,8] = √(5)(8)
Geometric mean of [5,8] = √40
Geometric mean of [5,8] = 6.32
Answer 4;
Geometric mean of [8,4] = √(8)(4)
Geometric mean of [8,4] = √32
Geometric mean of [8,4] = 5.65
Answer 5;
Geometric mean of [6,3] = √(3)(6)
Geometric mean of [6,3] = √18
Geometric mean of [6,3] = 4.24
Answer 6;
Geometric mean of [2,8] = √(2)(8)
Geometric mean of [2,8] = √16
Geometric mean of [2,8] = 4
What is the midpoint of the segment shown below?
Step-by-step explanation:
simply take the average of the x and y coordinates
Eva created a coffee blend for her restaurant by mixing Kenya and French Roast coffee beans. The Kenya beans cost $15 per pound and the French Roast costs $8 per pound. She bought a total of 10 pounds of coffee for a total of $97.50. Please help ASAP!!!!
Answer:
what is the question you are only telling us the fact
Step-by-step explanation:
Solve for x. Round to the nearest tenth of a degree, if necessary
Answer:
31.80°
Step-by-step explanation:
In ∆ ABC :-
sin x = BC / AC sin x = 39/74 x = sin -¹ ( 39/74) x = 31.80 °A stereo was originally priced at 75.50. it was marked down 24%. a store had a big sale of 60% off the lowest marked price. what was the final price of the stereo
Answer:
We can calculate the price with both sales by multiplying the 75.5 units of money by both percentages (to multiply them, we divide them by 100 first):
75.5 * 0.24 * 0.6 [tex]\approx.[/tex] 10.8
Examine the linear functions that represent Abel and Neal's mountain biking scenario. Abel: d = 14t, Neal: d = 11t + 6 How will you inspect the equations to determine the number of solutions? Compare the slopes. If they are the same, there will be one solution. Compare the slopes. If they are different, there will be one solution. Compare the y-intercepts. If they are the same, there will be one solution. Compare the y-intercepts. If they are different, there will be one solution.
Answer:
B: Compare the slopes. If they are different, there will be one solution.
Step-by-step explanation:
I gottchu guys :)
Answer:
Step-by-step explanation:
