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Verdich [7]
2 years ago
9

Four times a first number decreased by a second number is - 14. The first

Mathematics
1 answer:
mel-nik [20]2 years ago
3 0

Answer:

f = -5, s = -6

Step-by-step explanation:

F= first number

S= second number

4f - s = -14

f + 3s = -23

3(4f - s = -14)

12f - 3s = -42

+ f + 3s = -23

13f = -65

————

13

f = -5

4f - s = -14

4(-5) - s = -14

-20 - s = -14

+20 +20

-s = 6

———

-1

s = -6

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Answer:

100 boys at the concert

Step-by-step explanation:

When changing the ratio between the number of boys to the number of girls, it always has to be equivalent to the original ratio 2:7

So, convert the ratio 2:7 to a different ratio, but it still has to be equivalent to the ratio 2:7. By doing that, multiply both sides of the 2:7 ratio by 50:

  2   :   7

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To get:

100:350  ⇒  This ratio means that the ratio between the number of boys to the number of girls is now 100:350, but that’s okay to have because it’s still equivalent to the original 2:7 ratio.

So, using the new ratio 100:350, this means that there are 100 boys at the concert and 350 girls at the concert, and 350 is 250 more than 100 which proves what the question is asking. So there are 100 boys at the concert.

<u>Answer:</u> 100 boys at the concert

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2 years ago
(1/1+sintheta)=sec^2theta-secthetatantheta pls help me verify this
Xelga [282]

Answer:

See Below.

Step-by-step explanation:

We want to verify the equation:

\displaystyle \frac{1}{1+\sin\theta} = \sec^2\theta - \sec\theta \tan\theta

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\displaystyle \frac{1}{1+\sin\theta}\left(\frac{1-\sin\theta}{1-\sin\theta}\right) = \sec^2\theta - \sec\theta \tan\theta

Simplify. The denominator uses the difference of two squares pattern:

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Recall that sin²(θ) + cos²(θ) = 1. Hence, cos²(θ) = 1 - sin²(θ). Substitute:

\displaystyle \displaystyle \frac{1-\sin\theta}{\cos^2\theta} = \sec^2\theta - \sec\theta \tan\theta

Split into two separate fractions:

\displaystyle \frac{1}{\cos^2\theta} -\frac{\sin\theta}{\cos^2\theta} = \sec^2\theta - \sec\theta\tan\theta

Rewrite the two fractions:

\displaystyle \left(\frac{1}{\cos\theta}\right)^2-\frac{\sin\theta}{\cos\theta}\cdot \frac{1}{\cos\theta}=\sec^2\theta - \sec\theta \tan\theta

By definition, 1 / cos(θ) = sec(θ) and sin(θ)/cos(θ) = tan(θ). Hence:

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2 years ago
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4 0
3 years ago
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cricket20 [7]

Answer:

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Step 2: Divide both sides by -6.

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