All categories

2 years ago

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

————

f = -5

4f - s = -14

4(-5) - s = -14

-20 - s = -14

+20 +20

-s = 6

———

-1

s = -6

You might be interested in

At a country concert, the ratio of number of boys to the number of girls is 2:7. If there are 250 more girls than boys, how many

Juliette [100K]

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

×50 ×50

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

<em>I hope you understand and that this helps with your question! </em>:)

7 0

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:

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

To start, we can multiply the fraction by (1 - sin(θ)). This yields:

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

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

$\displaystyle \frac{1-\sin\theta}{\underbrace{1-\sin^2\theta}_{(a+b)(a-b)=a^2-b^2}} = \sec^2\theta - \sec\theta \tan\theta$

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:

$\displaystyle \sec^2\theta - \sec\theta\tan\theta \stackrel{\checkmark}{=} \sec^2\theta - \sec\theta\tan\theta$

Hence verified.

8 0

2 years ago

What expression is equivalent to 4 to the power of 4 times 4 to the power of -9

zvonat [6]

Answer:

idk this stuff yet

Step-by-step explanation:

4 0

3 years ago

Read 2 more answers

-6x+4y=-12 in slope intercept form

cricket20 [7]

Answer:

x= 2 /3 y+2

Step-by-step explanation:

Let's solve for x.

−6x+4y=−12

Step 1: Add -4y to both sides.

−6x+4y+−4y=−12+−4y

−6x=−4y−12

Step 2: Divide both sides by -6.

−6x /−6 = −4y−12 /−6 x= 2 /3 y

=x= 2 /3 y+2

<h3><u>brainliest please?</u></h3>

<u />

5 0

3 years ago

Read 2 more answers

Which proportion can be used to find the arc length, s, in units?

Alinara [238K]

Answer:

Option B

Step-by-step explanation:

Formula to be used to calculate the length of an arc,

Length of arc = $\frac{\theta}{360}(2\pi r)$

Here, θ = Angle subtended at the center by the arc

r = radius of the circle

By substituting values in the formula,

s = $\frac{150}{360}(2\pi )(42)$

$\frac{s}{2\times 42\pi }=\frac{150}{360}(\frac{2\times 24\pi }{2\times 24\pi } )$

$\frac{s}{84 \pi }=\frac{150}{360}$

Therefore, Option B will be the answer.

5 0

3 years ago