1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
FinnZ [79.3K]
3 years ago
15

Solve the equation for the unknown variable.

Mathematics
2 answers:
Georgia [21]3 years ago
8 0

Answer:

d = -3

Step-by-step explanation:

Given the equation:

d^3 = -27

Solve for d:

Take both sides cube root we have;

d =\sqrt[3]{-27}

We can write 27 as:

27 = 3 \cdot 3 \cdot 3 = 3^3

then;

d = \sqrt[3]{-3^3}

Using the rules:

\sqrt[n]{a^n} = a

\sqrt[3]{-1} = -1

then;

d = -\sqrt[3]{3^3} = -3

therefore, the unknown variable d is, -3

EleoNora [17]3 years ago
4 0

Answer:

-3

Step-by-step explanation:

this is the anwer............ ben solo once said: let the numbers dicrease make them negetive if you have to:D lol

You might be interested in
What is the equation of the line in slope-intercept form?
andreev551 [17]

Answer:

10x + 4y is the correct answer

8 0
3 years ago
A little girl counts using the fingers of her left hand as follows:
Vanyuwa [196]

Answer:

1 to 10 = Pointer Finger

1 to 100 = Ring Finger

1 to 1000 = Ring Finger

Step-by-step explanation:

Every time she counts 10 on her fingers starting from 1 it either lands on her Index Finger or Ring Finger in a pattern of starting first on her index finger for 10 then ending up on her Ring Finger for 20 and 30 the going back to her Index finger for 40 and 50 and so on. Using this you can figure out 100 and 1000.

3 0
3 years ago
The line 5x – 5y = 2 intersects the curve x2y – 5x + y + 2 = 0 at
inna [77]

Answer:

(a) The coordinates of the points of intersection are (-2, -12/5), (2/5, 0), and (2, 8/5)

(b) The gradient of the curve at each point of intersection are;

Gradient at (-2, -12/5) = -0.92

Gradient at (2/5, 0) = 4.3

Gradient at (2, 8/5) = -0.28

Step-by-step explanation:

The equations of the lines are;

5·x - 5·y = 2......(1)

x²·y - 5·x + y + 2 = 0.......(2)

Making y the subject of equation (1) gives;

5·y = 5·x - 2

y = (5·x - 2)/5

Making y the subject of equation (2) gives;

y·(x² + 1) - 5·x + 2 = 0

y = (5·x - 2)/(x² + 1)

Therefore, at the point the two lines intersect their coordinates are equal thus we have;

y = (5·x - 2)/5 = y = (5·x - 2)/(x² + 1)

Which gives;

\dfrac{5 \cdot x - 2}{5} = \dfrac{5 \cdot x - 2}{x^2 + 1}

Therefore, 5 = x² + 1

x² = 5 - 1 = 4

x = √4 = 2

Which is an indication that the x-coordinate is equal to 2

The y-coordinate is therefore;

y = (5·x - 2)/5 = (5 × 2 - 2)/5 = 8/5

The coordinates of the points of intersection = (2, 8/5}

Cross multiplying the following equation

Substituting the value for y in equation (2) with (5·x - 2)/5 gives;

\dfrac{5 \cdot x^3 - 2 \cdot x^2 - 20 \cdot x + 8}{5} = 0

Therefore;

5·x³ - 2·x² - 20·x + 8 = 0

(x - 2)×(5·x² - b·x + c) = 5·x³ - 2·x² - 20·x + 8

Therefore, we have;

x²·b - 2·x·b -x·c + 2·c -5·x³ + 10·x²

5·x³ - 10·x² - x²·b + 2·x·b + x·c - 2·c = 5·x³ - 2·x² - 20·x + 8

∴ c = 8/(-2) = -4

2·b + c = - 20

b = -16/2 = -8

Therefore;

(x - 2)×(5·x² - b·x + c) = (x - 2)×(5·x² + 8·x - 4)

(x - 2)×(5·x² + 8·x - 4) = 0

5·x² + 8·x - 4 = 0

x² + 8/5·x - 4/5  = 0

(x + 4/5)² - (4/5)² - 4/5 = 0

(x + 4/5)² = 36/25

x + 4/5 = ±6/5

x = 6/5 - 4/5 = 2/5 or -6/5 - 4/5 = -2

Hence the three x-coordinates are

x = 2, x = - 2, and x = 2/5

The y-coordinates are derived from y = (5·x - 2)/5 as y = 8/5, y = -12/5, and y = y = 0

The coordinates of the points of intersection are (-2, -12/5), (2/5, 0), and (2, 8/5)

(b) The gradient of the curve, \dfrac{\mathrm{d} y}{\mathrm{d} x}, is given by the differentiation of the equation of the curve, x²·y - 5·x + y + 2 = 0 which is the same as y = (5·x - 2)/(x² + 1)

Therefore, we have;

\dfrac{\mathrm{d} y}{\mathrm{d} x}= \dfrac{\mathrm{d} \left (\dfrac{5 \cdot x - 2}{x^2 + 1}  \right )}{\mathrm{d} x} = \dfrac{5\cdot \left ( x^{2} +1\right )-\left ( 5\cdot x-2 \right )\cdot 2\cdot x}{\left (x^2 + 1 ^{2} \right )}.......(3)

Which gives by plugging in the value of x in the slope equation;

At x = -2, \dfrac{\mathrm{d} y}{\mathrm{d} x} = -0.92

At x = 2/5, \dfrac{\mathrm{d} y}{\mathrm{d} x} = 4.3

At x = 2, \dfrac{\mathrm{d} y}{\mathrm{d} x} = -0.28

Therefore;

Gradient at (-2, -12/5) = -0.92

Gradient at (2/5, 0) = 4.3

Gradient at (2, 8/5) = -0.28.

7 0
3 years ago
Please answer correctly !!!!!!!! Will mark brainliest !!!!!!!!!!!!
FinnZ [79.3K]

Step-by-step explanation:

h(x) = (x-11)(x+3)

= x^2 + 3 - 11x - 33

= x^2 - 11x -30

8 0
3 years ago
A circuit contains three resistors rated at 100 Ω, 200 Ω, and 300 Ω that are connected in parallel. What's the total resistance
jasenka [17]

Answer:

total resistance is 54.54 ohms

Step-by-step explanation:

In parallel circuits, current can take various paths so the resistance are not added simply like that in series circuit, instead the reciprocal of total resistance in parallel circuit is calculated by adding the reciprocals of all the resistors connected parallel in circuit.

Given:

Resistor r1= 100

resistor r2 = 200

resistor r3= 300

The three resistors are connected in parallel  so the total resistance will be calculated by:

1/R= 1/r1 +1/r2 +1/r3

Putting the values of r1, r2, r3 in above we get

1/R= 1/100 + 1/200 +1/300

  = 0.01 + 0.005 + 0.0033

  = 0.0183

Taking reciprocal of both sides:

R=54.54

Hence total resistance is 54.54 ohms!

8 0
3 years ago
Other questions:
  • Without evaluating the expression, explain why your answer is positive or negative.
    7·1 answer
  • KX equals X +4 find a K7
    7·1 answer
  • Definition: This type of factory and mill was common in the American South at the start of the 20th
    9·1 answer
  • MATH!!! I HAVE NO IDEA HOW TO DO THIS PLEASE SHOW ME THE WORK I WANNA KNOW HOW TO DO THIS FOR THE NEXT QUESTION!!!!​
    5·1 answer
  • What is the solution of the following system of equations?<br> 2x + y = -7<br> -3x - 2y = 10
    8·1 answer
  • Help pls!1!1!1!1!!1!1
    6·2 answers
  • Solve: <br><br> -7/2 + (-5 1/2) + 8 3/4
    9·2 answers
  • Please help me with the picture attached I am so confused :(
    10·2 answers
  • What is the sale price of jeans which regularly cost $28, but now are 10% off ?
    5·2 answers
  • A rhombus has a base of 8 centimeters and a height of 4.2 centimeters. What is its area? Do not round your answer.
    13·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!