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3 years ago

Which is equivalent to (negative 2 m + 5 n) squared, and what type of special product is it?

Mathematics

2 answers:

vagabundo [1.1K]3 years ago

8 0

Answer:

4m^2 - 20mn + 25n^2; a perfect square trinomial

Step-by-step explanation:

Have a good one

otez555 [7]3 years ago

4 0

Answer:

4 m squared minus 20 m n + 25 n squared; a perfect square trinomial

Step-by-step explanation:

(-2m+5n)(-2m+5n)

4 $m^{2}$ -20mn+25 $n^{2}$

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f(1)=72 f(n)=f(n−1)+9 Find an explicit formula for f(n)

myrzilka [38]

$a_{n}$ = 9n + 63

generate the first few terms using the recursive equation

f(1) = 72

f(2) = 72 + 9 = 81

f(3) = 81 + 9 = 90

f(4) = 90 + 9 = 99

the sequence is 72, 81, 90, 99, .....

This is an arithmetic sequence whose n th term formula is

$a_{n}$ = $a_{1}$ + (n - 1 )d

where $a_{1}$ is the first term and d the common difference

d = 99 - 90 = 90 - 81 = 81 - 72 = 9 and $a_{1}$ = 72

$a_{n}$ = 72 + 9(n - 1) = 72 + 9n - 9 = 9n + 63 ← explicit formula

8 0

3 years ago

Solve 2x+y=-1 and -x+y=-7 in substitution method

lesantik [10]

Answer:x=2 y=-5

Step-by-step explanation

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3 years ago

Need help with this math. 13 points

densk [106]

Answer:The triangle is dilated by a factor of 1/2

Step-by-step explanation:

5 0

4 years ago

Read 2 more answers

The picture shows a circular clock face.

marysya [2.9K]

Answer:

[C] 25π square inches

Step-by-step explanation:

Given that:

the long hand of the clock is about 5 inches long.

To Find:

What is the approximate area of the clock face?

Solve:

Formula - A =πr²

Note that;

π = 3.14 (about)

Radius - 5 inches

A =πr²

A = 3.14(5)²

A = 3.14(25)

A = 78.5

Now let see the answer choices:

A. 5π square inches ≈ 5(3.14) = 15.7

B. 10 π square inches ≈ 10(3.14) = 31.4

C. 25 π square inches ≈ 25(3.14) = 78.5

D. 100 π square inches ≈ 100(3.14) = 314

Hence, the answer is [C] 25 π square inches

Kavinsky~

6 0

2 years ago

Read 2 more answers

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

3 years ago