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Paladinen [302]
3 years ago
6

Solve the exponential equation for x. 625 = 5 (7x-3)

Mathematics
1 answer:
posledela3 years ago
7 0

Answer:

<h2>A. x = 1</h2>

Step-by-step explanation:

5^{7x-3}=625\\\\5^{7x-3}=5^4\iff7x-3=4\qquad\text{add 3 to both sides}\\\\7x=7\qquad\text{divide both sides by 7}\\\\x=1

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Why does the sum of -4 and 3 complain more than the sum of -3 and 5?
Katyanochek1 [597]

Answer:

Negative

Step-by-step explanation:

-4 + 3 = -1

-3 + 5 = 2

if you scramble the leters, you get negative, and -1 is a negative number

8 0
2 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
With sales tax, it costs $29.58 to buy a $29 volleyball net. What is the sales tax percentage?
zubka84 [21]
2% is the correct answer...
4 0
3 years ago
Read 2 more answers
The rangers at two park stations spot a signal flare at the same time. Based on the measurements shown in the diagram, what is t
kykrilka [37]

The distance between park station 1 and the point where the flare was set off is 73.9 km.

<h3>What is distance?</h3>

Distance is the length between two points expressed in meters or kilometers.

To calculate the distance between park station 1 and the point where the flare was set off can be calculated using Sine Rule

Formula:

  • a/sinA = b/sinB....................... Equation 1

Where:

  • a = Distance between park station 1 and the point where the flare was set off.

Make a the subject of the equation

  • a = bsinA/sinB............ Equation 2

From the diagram,

Given:

  • A = 59°
  • B = (180-59-75) = 46°
  • b = 6.2 km

Substitute these values into equation 2

  • a = 6.2(sin59°)/(sin46°)
  • a = 73.9 km

Hence, the distance between park station 1 and the point where the flare was set off is 73.9 km.

Learn more about distance here: brainly.com/question/17273444

#SPJ1

5 0
2 years ago
Help me plzzzz<br><br>Graph y = -3x + 7.​
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Answer:

This is the graph. Hope the pic loads.

4 0
2 years ago
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