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3 years ago

Write an equation in slope-intercept form that describes the line with a slope of 4 and y-intercept of 1

Mathematics

1 answer:

suter [353]3 years ago

4 0

Answer:

Y=4x+1

Step-by-step explanation:

If the y-intercept was negative it would have been y=4x-1

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Working independently, Tina can do a certain job in 12 hours. Working independently, Ann can do the same job in 9 hours. If Tina

Leona [35]

Answer:

Ann would need 3 h to complete the remainder of the Job.

Step-by-step explanation:

Step 1.

The "speed" that each girl has to do the work is determined as:

Tina: $\frac{1}{12h}$ , it means that Tina complete one twelveth of the job each hour.
Ann: $\frac{1}{8h}$ , it means the Ann completes one eighth of the job each hour.

Step 2.

The amount of work done by Tina in 9 hours, is obtain multiplying by the "speed" calculated in step 1:

Amount of work done= $8 h*\frac{1}{12h} = \frac{2}{3}$ . It means that Tina completes two thirds of the work in 9 h.

Step 3.

The remaining job is calculated as $1-\frac{2}{3}=\frac{1}{3}$ . It means that still remains is one third of the job to be completed.

Step 4.

The time required for Ann to complete the job is calculated dividing the remaining of the job by the "speed" of Ann to do the job.

$\frac{\frac{1}{3}}{\frac{1}{9h}}=3h$ . It means that Ann would complete the job in another 3 hours.

3 0

3 years ago

If f(x, y)=xy−x^2, what is the value of f(f(−2, 3), −4)? Explain your reasoning.

hjlf

$\bf f(x,y)=xy-x^2 \\\\[-0.35em] ~\dotfill\\\\ f(\stackrel{x}{-2},\stackrel{y}{3})=(-2)(3)-(-2)^2\implies f(-2,3)=-6-(4)\implies f(-2,3)=-10 \\\\[-0.35em] ~\dotfill\\\\ f(~~\underline{f(-2,3)},~~-4)\implies f(\stackrel{x}{\underline{-10}},\stackrel{y}{-4})=(-10)(-4)-(-10)^2 \\\\\\ f(-10,-4)=40-(100)\implies f(-10,-4)=-60$

3 0

3 years ago

Given cosα = −3/5, 180 < α < 270, and sinβ = 12/13, 90 < β < 180

torisob [31]

I got

$- \frac{6 3}{65}$

What we know

cos a=-3/5.

sin b=12/13

Angle A interval are between 180 and 270 or third quadrant

Angle B quadrant is between 90 and 180 or second quadrant.

What we need to find

Cos(b)

Cos(a)

What we are going to apply

Sum and Difference Formulas

Basics Sine and Cosines Identies.

1. Let write out the cos(a-b) formula.

$\cos(a - b) = \cos(a) \cos(b) + \sin(a) \sin(b)$

2. Use the interval it gave us.

According to the given, Angle B must between in second quadrant.

Since sin is opposite/hypotenuse and we are given a sin b=12/13. We. are going to set up an equation using the pythagorean theorem.

${12}^{2} + {y}^{2} = {13}^{2}$

$144 + {y}^{2} = 169$

$25 = {y}^{2}$

$y = 5$

so our adjacent side is 5.

Cosine is adjacent/hypotenuse so our cos b=5/13.

Using the interval it gave us, Angle a must be in the third quadrant. Since cos is adjacent/hypotenuse and we are given cos a=-3/5. We are going to set up an equation using pythagorean theorem,

$( - 3) {}^{2} + {x}^{2} = {5}^{2}$