Given:
The sum of the cubic powers of three rational numbers is -1009.
The ratio between the first number and the second number is [tex]\dfrac{2}{3}[/tex].
The ratio between the first number and the third number is [tex]\dfrac{4}{9}[/tex].
To find:
The three numbers.
Solution:
Let [tex]x,y,z[/tex] be the three numbers, then
[tex]x^3+y^3+z^3=-1009[/tex] ...(i)
[tex]\dfrac{x}{y}=\dfrac{2}{3}[/tex]
[tex]3x=2y[/tex]
[tex]\dfrac{3}{2}x=y[/tex] ...(ii)
[tex]\dfrac{x}{z}=\dfrac{4}{9}[/tex]
[tex]9x=4z[/tex]
[tex]\dfrac{9}{4}x=z[/tex] ...(iii)
Using (i), (ii) and (iii), we get
[tex]x^3+\left(\dfrac{3}{2}x\right)^3+\left(\dfrac{9}{4}x\right)^3=-1009[/tex]
[tex]x^3+\dfrac{27}{8}x^3+\dfrac{729}{64}x^3=-1009[/tex]
[tex]\dfrac{64+216+729}{64}x^3=-1009[/tex]
[tex]\dfrac{1009}{64}x^3=-1009[/tex]
[tex]x^3=\dfrac{-1009\times 64}{1009}[/tex]
On simplification, we get
[tex]x^3=-64[/tex]
[tex]x^3=-4^3[/tex]
[tex]x=-4[/tex]
Substituting [tex]x=-4[/tex] in (ii), we get
[tex]\dfrac{3}{2}(-4)=y[/tex]
[tex]-6=y[/tex]
Substituting [tex]x=-4[/tex] in (iii), we get
[tex]\dfrac{9}{4}(-4)=z[/tex]
[tex]-9=z[/tex]
Therefore, the three numbers are -4, -6 and -9 respectively.
Determine the slope of the line that passes through pair of points: (-4, 11) and (1,-9)
Answer:
rise/run= -20/5= -4/1=-4 slope
or you sound use the slope formula (y2-y1)/(x2-x1)
(-9-11)/(1+4)
-20/5
-4
Hope this helps
Simplify the expression.
53 + (- 12) + (- 4t)
Answer:
8
Step-by-step explanation:
41-4t
Hope this helps ^^
Hi! im not sure if my answer is correct or not can someone check me :)
What is the equation to find the slope
m=
Answer:
[tex]m=\frac{y2-y1}{x2-x1}[/tex]
Step-by-step explanation:
Answer:
[tex]\huge\boxed{m=\frac{y_2-y_1}{x_2-x_1} }[/tex]
Step-by-step explanation:
The equation for slope is [tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex], when given two points,
[tex](x_1,y_1), and (x_2,y_2)[/tex].
Hope it helps :) and let me know if you want me to elaborate.
X, Y, and Z are collinear and Y is between X and Z. If XY = 3x – 1, YZ = 5, and XZ = 5x – 8,
what is the value of x?
a. 6
b. 4
c. 10
d. 8
Answer:
6
Step-by-step explanation:
XY = 3x – 1, YZ = 5, and XZ = 5x – 8,
We know that XY + YZ = XZ, so
3x - 1 + 5 = 5x - 8
3x + 4 = 5x - 8
3x + 12 = 5x
12 = 2x
6 = x
The value of x from the given line segment XZ is 6. Therefore, the correct answer is option A.
Given that, X, Y, and Z are collinear and Y is between X and Z.
Collinear points are those that are on the same straight line or in the same plane. In Euclidean geometry, two or more points on a line that are close to or far from each other are said to be collinear.
So, here [tex]XZ=XY+YZ[/tex]
[tex]5x-8=3x-1+5[/tex]
[tex]5x-8=3x+4[/tex]
[tex]5x-3x=4+8[/tex]
[tex]2x=12[/tex]
[tex]x=6[/tex]
Therefore, the correct answer is option A.
To learn more about an collinear points visit;
https://brainly.com/question/5191807.
#SPJ3
Can someone help me please
Answer:
D
Step-by-step explanation:
Plot the value(s) on the number line where this function is equal to zero: fx) = (x + 5)(x - 1).
Answer:
x = - 5, x = 1
Step-by-step explanation:
let f(x) = 0 , that is
(x + 5)(x - 1) = 0
Equate each factor to zero and solve for x
x + 5 = 0 ⇒ x = - 5
x - 1 = 0 ⇒ x = 1
Plot the points - 5 and 1 on the number line
Plz answer rn nmmmm ASAP!!
Answer:
C
Step-by-step explanation:
Students majoring in engineering make up 21% of the students at a university. There are 6,600 total students enrolled at the university, How
many students are majoring in engineering?
Answer:
Step-by-step explanation:
21 percent of 6600 is 1386.
I'm sorry if I'm wrong.
Pythagorean Theorem Question! Please help
Answer:
It is the fourth one.
Step-by-step explanation: You use it to find it to see if it is a right triangle.
A park is rectangular with a length of 12 miles. If the area of the park is 68 square miles, what is its width? Input your answer as a fraction.
Answer:
17/3
Step-by-step explanation:
to find out the width, we need to divide the area by the length.
68/12=5.666666667
fraction form: 17/3 (5 2/3)
Can someone pleasee answer this
Solve for x.
2x + 20=2x - 4
+
x = [?]
Enter
Answer:
x=24
Step-by-step explanation:
2x+20=2x-4+x
Subtract 2x from both sides
2x+20-2x=2x-4+x-2x
Simplify
20=-4+x
Add 4 to both sides
24=x
Switch sides
x=24
WHAT IS 12+23+67+10+19+60=
Answer:
The answer is 191.
Hope that helps. x
Answer:
191
Step-by-step explanation:
12+23=35
67+10=77
19+60=79
Now let's add all three numbers
35+77+79=191
Hope this helps!
If the radius is 18 cm and the angle at centre of circle is 120° then the
area of sector is? Use pi as 3.142 *
The area of a sector is 339.336 cm²
The area of a sector is defined to be as the region of space bounded by a boundary from the center of the circle.
It can be determined by using the formula:
[tex]\mathbf{A = \dfrac{\theta }{360}\times \pi r^2 }[/tex]
Given that;
Radius r = 18 cmAngle θ = 120°Then. the area of the sector can be calculated as:
[tex]\mathbf{A = \dfrac{120}{360}\times \pi (18)^2 }[/tex]
[tex]\mathbf{A = \dfrac{1}{3}\times 3.142 \times 324 }[/tex]
A = 339.336 cm²
Learn more about the area of a sector here:
https://brainly.com/question/7512468?referrer=searchResults
what is the slope of the line
Answer:
The slope is 0.8 or 4/5.
Step-by-step explanation:
Let's take two points on a line. (-2,0) and (3,4).
Now, determine the rise and run.
Rise: 4Run: 5Slope = Rise/Run
=> 4/5Conclusion:
Therefore, the slope is 0.8 or 4/5.
Hoped this helped.
[tex]BrainiacUser1357[/tex]
Answer:
The answer is rise over run
Step-by-step explanation:
You divide the rise coordinate on the Y axis of the X coordinate
someone pls pls help
Answer:
4√2 cm
Step-by-step explanation:
ABCD is a square.
Each side measures 8 cm.
So,
AB = BC = CD = AD = 8 cm
P, Q, R, and S are mid - points of ABCD.
P is the mid - point of AB.
So,
AP = PB
AP + PB = AB
AP + AP = AB
2AP = 8
AP = 8 / 2
AP = 4 cm
S id the mid - point of AD.
So,
DS = SA
DS + SA = AD
SA + SA = AD
2SA = 8
SA = 8 / 2
SA = 4 cm
Property of a square : The angle between two sides is 90°.
So,
The angle between side SA and AP is 90°.
So,
SA, AP and SP forms a right angled triangles.
By Pythagoras theorem,
( SP)² = ( SA )² + ( AP )²
( SP )² = 4² + 4²
= 16 + 16
( SP )² = 32
SP = √32
SP = 4√2 cm
Since PQRS is also a square.
In square, all sides are equal.
So,
PQ = QR = RS = SP
Since SP = 4√2 cm
Hence,
PQ = 4√2 cm
Therefore,
the length of PQ is 4√2 cm.
Answer: 5.7
Step-by-step explanation:
Midpoint means the middle of line. So to find the middle of the line I just need to divide the line by 2.
So the midpoint of AB is:
8/2=4 = BP
Since Q is also a midpoint so BQ is equal to 4.
We know BP=BQ=4. Looking at the diagram we can tell PBQ is a triangle.
The hypotenuse of the triangle is PQ.
Pythagoras's theorem helps us to find the hypotenuse. So we just plug in the values to find PQ.
P's Theorem : a²+b²=c²
basically in the case of this question it means:
(BP)²+(BQ)²=(PQ)²
now we just subsiture the values and solve for PQ:
4²+4²=(PQ)²
16+16=(PQ)²
32=(PQ)²
PQ=5.65...
= 5.7(rounded to one decimal place)
Describe fully the single transformation which takes shape A to shape B
Answer:
Translation down by 1 then reflection over Y axis.
Step-by-step explanation:
Hard work problem please help me find the sum
-3 + -2 + -4 = -9
the total is -9
my Christmas present to you
Answer:
i can help u if u need help
Step-by-step explanation:
Answer:
it's not Christmas but OK.
Step-by-step explanation:
btw thx!!
12. Name the angle included between AB and AD.
Answer fast
Answer: Either angle DAB or angle BAD
Explanation:
The segments AB and AD have the point A in common. So this common point is the middle letter of the angle name. We could go for angle DAB or angle BAD as they both name the same exact angle. The order doesn't matter as long as the middle letter is fixed like this.
Simplify the variable expression below as much as possible.
6x + 1 + 7- 3
Answer:
6X+5
Step-by-step explanation:
Answer:
6x+5
Step-by-step explanation:
6x+1+7-3
6x+(1+7)-3
6x+8-3
6x+5
Xavier's pet turtle laid eggs! So far, only 2 eggs have hatched for every 5 that are unhatched. If Xavier's turtle laid 35 eggs in all, how many eggs have hatched?
Answer: 21
Step-by-step explanation:
At 7 P.M., a burning candle is 16 inches tall. At 9:30 P.M., the candle is only 3.5 inches tall. At what rate is the height of the candle decreasing?
Answer: 5 inches per hour or 2.5 inches per half an hour
Step-by-step explanation:
Amount of Time Passed: 2 hours 30 minutes
Difference in Candle Height: 12.5 inches
12.5 / 2.5 = 5 inches
5 inches per hour or 2.5 inches per half an hour
If it is incorrect, please let me know.
The population of the bacteria triples each hour. Initially, there are 20 bacteria in the lab. Find the number of bacteria at the end of 5th hour
1620
4500
4860
5000
Answer:
4860
Step-by-step explanation:
Get the product of twenty and three, then multiply that to three again, repeat this for three more times.
Lee's Leather Store marked down leather jackets 10 percent. What is the sale price of a
leather jacket regularly priced at $130?
O $103
O $113
O $123
O $117
What is 0.02349 written in standard form to 3 significant figures
Answer: The answer is (B)
Explanation: The answer is (B) because, there are 2 zeros so that means that there would have to be a 2 behind the 10 and then there is 2,3,4,and 9. We take out the 9 and use the other numbers, bring over the decimal and now you have [tex]2.34 x 10^{2}[/tex] .
Let's cancel out from left to right
[tex]\\ \sf\Rrightarrow 0.02349[/tex]
[tex]\\ \sf\Rrightarrow 0.0235\times 10^{-1}[/tex]
[tex]\\ \sf\Rrightarrow 2.35\times 10^{-3}[/tex]
Option C is correct
Taylor left to walk the dog at
4:25. She got back at 5:00. How
long was the dog's walk?
Answer:
Taylor walked 35 minutes
Step-by-step explanation:
4:25
+:35
=5:00.
once a clock hits 60 it's automatically turned to the next hour so since 25 + 35 = 50 it's automatically turned to 5:00
What is the area of the square?
32 square units
64 square units
24 square units
16 square units
Answer:
64 square units
Step-by-step explanation:
All you have to do is multiply 8 by 8 to get 64.
What is the reciprocal of A if A doesn't equal 0?
Answer:
1/a
Step-by-step explanation:
