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3 years ago

If possible could you explain how to get the answer if not it is ok.

Mathematics

1 answer:

Softa [21]3 years ago

3 0

Rules of exponents come in hand here.

Multiplication rule: a^m x a^n = a^ m+n

Division rule: a^m / a^n = a^m-n

Negative exponent: a^-m = 1/a^m; 1a^-m =a^m

So it would be (-3)^7+5 / (-3)^-2; (-3)^12 / (-3)^-2; (-3)^12 x (-3)^2; (-3)^14

The answer is (-3)^14. If you multiply it out it is 4,782,969.

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Roselyn wants to drive her car at a speed of 60 miles per hour for 1.25 hours. Her car has a fuel efficiency of 15 miles per gal

EleoNora [17]

Hence, there is 5 gallons of fuel Roselyn needed for her journey.

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3 years ago

The vertices of a triangle are p(3,7) Q(7,-6) R(-8,7). Name the vertices of the image reflected across the x axis

pantera1 [17]

Answer:

P'(3,-7) Q'(7,6) R'(-8,-7).

Step-by-step explanation:

Reflection across the x-axis

Given a point P(x,y), its reflection across the x-axis will map to point P'(x,-y), i.e., the y-coordinate gets inverted.

We are given the vertices of a triangle P(3,7) Q(7,-6) R(-8,7). The vertices of the image reflected across the x-axis are:

P'(3,-7) Q'(7,6) R'(-8,-7).

The new triangle has vertices P'Q'R'.

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2 years ago

Given that cot θ = 1/√5, what is the value of (sec²θ - cosec²θ)/(sec²θ + cosec²θ) ?

Bogdan [553]

Step-by-step explanation:

$\mathsf{Given :\;\dfrac{{sec}^2\theta - co{sec}^2\theta}{{sec}^2\theta + co{sec}^2\theta}}$

$\bigstar\;\;\textsf{We know that : \large\boxed{\mathsf{{sec}\theta = \dfrac{1}{cos\theta}}}}$

$\bigstar\;\;\textsf{We know that : \large\boxed{\mathsf{co{sec}\theta = \dfrac{1}{sin\theta}}}}$

$\mathsf{\implies \dfrac{\dfrac{1}{cos^2\theta} - \dfrac{1}{sin^2\theta}}{\dfrac{1}{cos^2\theta} + \dfrac{1}{sin^2\theta}}}$

$\mathsf{\implies \dfrac{\dfrac{sin^2\theta - cos^2\theta}{sin^2\theta.cos^2\theta}}{\dfrac{sin^2\theta + cos^2\theta}{sin^2\theta.cos^2\theta}}}$

$\mathsf{\implies \dfrac{sin^2\theta - cos^2\theta}{sin^2\theta + cos^2\theta}}$

Taking sin²θ common in both numerator & denominator, We get :

$\mathsf{\implies \dfrac{sin^2\theta\left(1 - \dfrac{cos^2\theta}{sin^2\theta}\right)}{sin^2\theta\left(1 + \dfrac{cos^2\theta}{sin^2\theta}\right)}}$

$\bigstar\;\;\textsf{We know that : \large\boxed{\mathsf{cot\theta = \dfrac{cos\theta}{sin\theta}}}}$

$\mathsf{\implies \dfrac{1 -cot^2\theta}{1 + cot^2\theta}}$

$\mathsf{Given :\;cot\theta = \dfrac{1}{\sqrt{5}}}$

$\mathsf{\implies \dfrac{1 - \left(\dfrac{1}{\sqrt{5}}\right)^2}{1 + \left(\dfrac{1}{\sqrt{5}}\right)^2}}$

$\mathsf{\implies \dfrac{1 - \dfrac{1}{5}}{1 + \dfrac{1}{5}}}$

$\mathsf{\implies \dfrac{\dfrac{5 - 1}{5}}{\dfrac{5 + 1}{5}}}$

$\mathsf{\implies \dfrac{5 - 1}{5 + 1}}$

$\mathsf{\implies \dfrac{4}{6}}$

$\mathsf{\implies \dfrac{2}{3}}$

Hence, option (a) 2/3 is your correct answer.

3 0

2 years ago

FREE POINTS!!!!!!!!!! 10 POINTS Len's recipe for blueberry muffins calls for 110.25 grams of brown sugar for the muffin batter a

RSB [31]

Wow.... My brother Said that it took him a while to figure it out... but

add 110.25 and 55.45

you would get 165.70

multiply 165.70 by 4.5

then you would get 745.65

745.65 is your answer

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3 years ago

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3 years ago