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dedylja [7]
1 year ago
9

Solve each equation. Round to the nearest ten-thousandth. Check your answers. 25²x⁺¹=144

Mathematics
1 answer:
djverab [1.8K]1 year ago
3 0

25^{2x+1}=144 => x = 0.272, by properties of logarithm.

<h3>What is Logarithm?</h3>
  • The opposite of exponentiation is the logarithm.
  • This indicates that the exponent to which a fixed number, base b, must be raised in order to obtain a specific number x, is represented by the logarithm of that number.
  • A number's natural logarithm is its logarithm to the base of the transcendental and irrational number e, which is roughly equivalent to 2.718281828459.

Given: 25^{2x+1}=144

Taking logarithm on both sides:

log (25^{2x+1}) = log (144)

=> (2x + 1) log (25) = log (144) (As log_b(a)^m = m (log_b(a)))

=> 2x + 1 = \frac{log144}{log25}

=> 2x + 1 = \frac{2.158}{1.397}

=> 2x + 1 = 1.544

=> 2x = 0.544

=> x = 0.272

Hence, 25^{2x+1}=144 => x = 0.272, by properties of logarithm.

To learn more about logarithms, refer to the link: brainly.com/question/25710806

#SPJ4

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3 years ago
X squared+ y squared = 2 y = 2x squared – 3 Which of the following describes the system?
cluponka [151]

Answer:

x=-1,1,-\sqrt{\frac{7}{4} },\sqrt{\frac{7}{4}} and y=-1,\frac{1}{2}

The ordered pair solutions are (-\sqrt{\frac{7}{4}},0.5), (\sqrt{\frac{7}{4}},0.5), (-1,-1), and (1,-1).

Step-by-step explanation:

I'm assuming the system is \left \{ {x^2+y^2=2} \atop {y=2x^2-3}} \right.:

x^2+y^2=2

x^2+(2x^2-3)^2=2

x^2+(4x^4-12x^2+9)=2

x^2+4x^4-12x^2+9=2

4x^4-11x^2+9=2

4x^4-11x^2+7=0

x^4-11x^2+28=0

(x^2-7)(x^2-4)=0

(4x^2-7)(x^2-1)=0

4x^2-7=0

4x^2=7

x^2=\frac{7}{4}

x=\pm\sqrt{\frac{7}{4}}

x^2-1=0

x^2=1

x=\pm1

y=2x^2-3

y=2(\pm\sqrt{\frac{7}{4}})^2-3

y=2({\frac{7}{4}})-3

y=\frac{7}{2}-3

y=\frac{1}{2}

y=2x^2-3

y=2(\pm1)^2-3

y=2(1)-3

y=2-3

y=-1

Therefore, x=-1,1,-\sqrt{\frac{7}{4} },\sqrt{\frac{7}{4}} and y=-1,\frac{1}{2}

The ordered pair solutions are (-\sqrt{\frac{7}{4}},0.5), (\sqrt{\frac{7}{4}},0.5), (-1,-1), and (1,-1).

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Answer:

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Declan draws triangle WXY. He then constructs a perpendicular bisector from vertex W that intersects side XY at point Z. What ca
Ganezh [65]

Answer:

YZ = XZ

Step-by-step explanation:

Perpendicular Bisector:

A perpendicular bisector of a line segment 'l' is a line that is perpendicular to the line segment 'l' and cuts the line segment 'l' into two equal parts.

Given:

1. A triangle WXY.

2. A perpendicular bisector from vertex W that intersects XY at point Z.

Conclusion based on the drawing:

a. Z is the midpoint of the line segment XY because point Z lies on the perpendicular bisector of XY.

b. Hence, XZ = YZ.

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