Answer:
180
Step-by-step explanation:
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:
(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
which relation is a function?
The first one because there is only one y value for every x value. The correct option is first.
To determine if a relation is a function, use the vertical line test: If any vertical line intersects the graph of the relation at more than one point, then the relation is not a function. On the other hand, if every vertical line intersects the graph of the relation at most once, then the relation is a function.
In first relation is considered a function, because each input x-value is associated with exactly one output y-value. In other words, for every x-value in the domain of the relation, there can be only one corresponding y-value in the range. Each x-value should not have more than one y-value associated with it.
Therefore, each x-value should not have more than one y-value associated with it. The correct option is first.
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In which section of the number line is 32−−√?
where's the number line?
maybe u can attach it at the comments:)
Answer:
Section B
Step-by-step explanation:
Una torre de 28.2 m de altura esta situada a la orilla de un rio, desde lo alto del edificio el ángulo de depresión a la orilla opuesta es de 25.2°. Calcular el ancho del río
Answer:
El ancho del río es 59.9 metros.
Step-by-step explanation:
El ancho del río lo podemos calcular con la siguiente relación trigonométrica asumiendo que la torre forma un triángulo rectángulo con el río:
[tex]tan(\theta) = \frac{CO}{CA}[/tex]
En donde:
CA: es el cateto adyacente = Altura de la torre = 28.2 m
CO: es el cateto opuesto = ancho del río =?
θ: es el ángulo adyacente a CA
Dado que el ángulo de depresión (25.2°) está ubicado fuera de la parte superior de la hipotenusa del triángulo que forma la torre con la orilla opuesta del río, debemos calcular el ángulo interno (θ) como sigue:
[tex]\theta = (90 - 25.2)^{\circ} = 64.8 ^{\circ}[/tex]
Ahora, el ancho del río es:
[tex]CO = tan(\alpha)*CA = tan(64.8)*28.2 = 59.9 m[/tex]
Por lo tanto, el ancho del río es 59.9 metros.
Espero que te sea de utilidad!
Z Is An Even Integar Greater Than 30 And Less Than Or Equal To 34.
Answer:
32, 34
Step-by-step explanation:
The answer must be grater than 30 so 30 is not an option the integers in the range are 31, 32, 33, and 34 the only even integers in this set are 32, and 34. Hope this helps. :)
is (12, 4), (36, 12), (-6, -2), (21, 7) directly proportional?
Answer:
I think yes
Step-by-step explanation:
12/4=3
36/12=3
-6/-2=3
and so on
Given the roll of paper towels below how much plastic would be needed to cover the role so it can be sold given the diameter of the role is 10 inches and the height is 13 inches
Answer:
Amount of plastic need to cover paper role = 565.2 inches
Step-by-step explanation:
Given:
Diameter of paper role = 10 inch
Height of paper role = 13 inch
Find:
Amount of plastic need to cover paper role
Computation:
Radius of paper role = Diameter of paper role / 2
Radius of paper role = 10 / 2
Radius of paper role = 5 inch
Amount of plastic need to cover paper role = Total surface area of cylinder
Amount of plastic need to cover paper role = 2πr(h+r)
Amount of plastic need to cover paper role = 2(3.14)(5)(13+5)
Amount of plastic need to cover paper role = (3.14)(10)(18)
Amount of plastic need to cover paper role = 565.2 inches
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.
Graph the solution of the inequality 3/7(35x-14)<_ 21x/2+3
Answer:
You'll have a closed circle at x = 2, and shading to the left
See the diagram below
=========================================================
Explanation:
The fractions here are 3/7 and 21/2. The denominators of which are 7 and 2 respectively. The LCD is 7*2 = 14.
If we multiply both sides by 14, then this will clear out the denominators and make the fractions go away.
14*(3/7) = (14*3)/7 = 42/7 = 814*(21/2) = (14*21)/2 = 294/2 = 147So if we multiplied both sides by 14, then we have these steps
[tex]\frac{3}{7}(35x-14) \le \frac{21x}{2}+3\\\\14*\frac{3}{7}(35x-14) \le 14*\left(\frac{21x}{2}+3\right)\\\\14*\frac{3}{7}(35x-14) \le 14*\left(\frac{21x}{2}\right)+14*\left(3\right)\\\\6(35x-14) \le 147x+42\\\\[/tex]
--------------------------
Let's isolate x
[tex]6(35x-14) \le 147x+42\\\\6(35x)+6(-14) \le 147x+42\\\\210x-84 \le 147x+42\\\\210x-147x \le 42+84\\\\63x \le 126\\\\x \le 126/63\\\\x \le 2\\\\[/tex]
The graph of this will consist of a closed or filled in circle at x = 2. We shade to the left to represent numbers smaller than 2.
So either x = 2 or x < 2.
If we used an open hole at 2, then we wouldn't be including 2 (but we want to include this endpoint).
See the diagram below.
i13(12)-2give answer
What is
4
7
as a decimal rounded to 3 decimal places?
Answer:
4/7 as a decimal is 0.57142857142857.
(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.
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.
A farm grew 19.8 tons of wheat in 2013. The farm's wheat output increased by 9.8% from 2013 to 2014 and by 5.1% from 2014 to 2015. Which expression represents a for estimating the total output of wheat, in tons, in 2015?
A. 20 + 10 + 5
B. 20(10)(5)
C. 20 + 1.1 + 1.05
D. 20(1.1)(1.05)
Answer: Choice D
Explanation:
The increase of 9.8% rounds to 10% when rounding to the nearest ten
An increase of 10% would use the multiplier 1.1
Think of it like saying 1 + 0.10 = 100% + 10%
Similarly, the 5.1% rounds to 5% and an increase of this amount will use the multiplier 1.05
So if we started with 20 items, then 20(1.1)(1.05) is the expression that estimates an increase of 10% followed by an increase of 5%. The order doesn't matter (so you could increase by 5% first, then 10% later).
Ardi and Lei are both travelling by train.
Ardi's train travels 70 km in 35 minutes.
Lei's train travels 585 km.
It leaves at 9:05 and arrives at 13:35.
Work out the difference, in km/h, between the average speed of their trains.
Answer:
10 kilometer/hour
Step-by-step explanation:
Average speed = Total distance travelled / Total time taken
Ardi:
Total distance travelled = 70 km
Total time taken = 35 minutes = 35/60 hour
Average speed = Total distance travelled / Total time taken
= 70 km ÷ 35/60 hr
= 70 × 60/35
= 4,200/35
= 120 kilometer/hour
Lei:
Total distance travelled = 585 km Total time taken = 9:05 - 13:35 = 4 hours 30 minutes
= 4.5 hours
Average speed = Total distance travelled / Total time taken
= 585 km / 4.5 hours
= 130 kilometer/hour
Difference, in km/h, between the average speed of their trains = Lei's train - Ardi's train
= 130 kilometer/hour - 120 kilometer/hour
= 10 kilometer/hour
What is the measure of Arc E B C?
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
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(100 points)
1.One of the addends of 17,300 is 11,210. What is the other addend?
a. What are they asking for? __________________
b. identify all the necessary numbers. __________________
c. write the equation or problem in numeric form. ______________
d. solve the math. ______________________________
e.write the answer. ________________________________
2. If one of the factors of 954 is 318 , what is the other factor?
a. What are they asking for? __________________
b. identify all the necessary numbers. __________________
c. write the equation or problem in numeric form. ______________
d. solve the math. ______________________________
e.write the answer. ________________________________
3. HEector bought seven bokes of fruit. Each boc contained 24 fruit. How much fruit did Hector buy?
a. What are they asking for? __________________
b. identify all the necessary numbers. __________________
c. write the equation or problem in numeric form. ______________
d. solve the math. ______________________________
e.write the answer. ________________________________
Answer:
1a. The other addend of 17,300
1b. 17,300 and 11,210
1c. 17,300-11,210
1d. 17,300-11,210= 6090
1e. 6090
2a. The other factor of 954
2b. 954 and 318
2c. 954-318
2d. 954-318= 636
2e. 636
3a. The total amount of fruit Hector bought.
3b. 7 and 24
3c. 7 x 24
3d. 7 x 24 = 168
3e. 168 fruits
help me with this problem please!!!!
Step-by-step explanation:
sorry I wanted to help you but my calculator is take out decimals sorry I don't know what to do
Out of the 30 days in June, you run 13 days and swim 6 days. You lift weights 7 days
and ride a bike 4 days. If you make a pie chart to show this data, how many degrees
of the circle should represent swimming?
9514 1404 393
Answer:
72°
Step-by-step explanation:
In a properly constructed pie chart, the proportion of the circle devoted to each section is the same as the proportion of that section to the the whole.
(6 swim days)/(30 days) = (swim pie angle)/(360°)
Multiply by 360° to find ...
swim pie angle = (360°)(6/30) = 72°
72° of the circle should represent swimming.
Grafico de deportes: fútbol 30%, atletismo 25%, tenis 5%, voleibol 10%, basquetbol 20%. Si 165 jóvenes prefieren el fútbol ¿cuantos prefieren el basquetbol?
Answer:
33 jóvenes prefieren el basquetbol.
Step-by-step explanation:
Hay 165 jóvenes.
De estos, 20% prefieren el basquetbol.
¿cuantos prefieren el basquetbol?
20% de 165, entonces:
[tex]20\% = \frac{20}{100} = 0.2[/tex]
[tex]0.2*165 = 33[/tex]
33 jóvenes prefieren el basquetbol.
what is the answer to the problem
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]
A square has a perimeter of 36 cm.
What is the length of each side?
Answer:
Step-by-step explanation:
The perimeter of a square has a formula P = s + s + s + s or just P = 4s where s is the length of a side. If this perimeter has a number value, we can plug it in and solve for the length of each side, like this:
36 = 4s so
s = 9 cm. And there you go!
Rewrite the expression as a simplified expression containing one term.
Answer:
-(cos α)/(sin α)
= -cot α
Step-by-step explanation:
use trigonometric identities
help I need help with my homework no link please BTW its 9th grade work I need help with number 1 a) I still need help with it
Answer:
you need to learn how to "prime factor" numbers....
primes are 2,3,5,7,11,13,17....
they go on forever. ALL whole numbers can be "broken down" into a bunch of primes multiplied together.
take the fractions (top and bottom) and start dividing them bu the smallest prime, and going up until all the numbers multiplied make the original number...
15 = 3 * 5
24= 2 * 12 = 2 * 2 * 6 = 2* 2* * 2 * 6
thus [tex]\frac{15}{24}[/tex] = [tex]\frac{3 * 5 }{2* 2* 2* 3}[/tex] now just cancel all the SAME numbers from to to bottom
"pair them up" .... in this case only one of the threes in the bottom "takes out" one of the threes in the top
result [tex]\frac{5}{2*2*2 } = \frac{5}{8}[/tex]
~~~~~~~~~~~~~~~~~~~~
[tex]\frac{21}{35}[/tex]
21= 3 * 7
35= 5* 7
[tex]\frac{3*7}{5*7} = \frac{3}{5}[/tex]
Step-by-step explanation:
Find the length of CZ
A. 32
B. 45
C. 9
D. 1
Answer:
c
Step-by-step explanation:
just took it
Answer:
D. 1
Step-by-step explanation:
CA = 17
ZA = 16
CZ + ZA = CA
CZ + 16 = 17
CZ = 1
D. 1
On Monday, 405 students went on a trip to the zoo. All 7 buses were filled and 6 students had to travel in cars. How many students were in each bus
Answer:
57 students
Step-by-step explanation:
Since 6 students count not fit and they had to go in cars, there is a remainder of 6. Subtract that from the total, 405, and you get 399.
Then, divide that by 7, and you get the answer. 57.
Hope it helps!
Answer:
57 students
Step-by-step explanation:
405-6=399
399÷7=57
Solve: [tex]x=4+\left(4x-4\right)\frac{1}{2}[/tex]
x = 2
x = 10
x = 2 or x = 10
no real solution
Answer: x = -2
Step-by-step explanation:
[tex]x=4+(4x-4)\frac{1}{2} \\x=4+\frac{4x}{2}-\frac{4}{2}\\x=4+2x-2\\x=2+2x\\x-2x=2\\-x=2\\x=-2[/tex]
