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2 years ago

Writing a linear equations

Mathematics

1 answer:

Ray Of Light [21]2 years ago

7 0

y = (1/6)x - 3

Step-by-step explanation:

The line goes through (0, -3) and (6, -2) and the slope is given by

m = (y2 - y1)/(x2 - x1)

= (-2 -(-3))/(6 - 0)

= 1/6

so the slope-intercept form of a linear equation is given by

y = mx + b

Using the value of m we just obtained and using the point (0, -3) to find b, we get

(-3) = (1/6)(0) + b ---> b = -3

Therefore, the equation takes the form

y = (1/6)x - 3

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in 1990 Jamaica's population of 2,466,000 was expected to grow exponentially by 1.1% each year. what is the range of the exponen

Misha Larkins [42]

Answer:

Initial population is 2,466,000 ( p0 )

Growth is 1.1% each year ( r=1.1

p(t)=p0(1+r)t

After 30 years, the population of Jamaica should be 3.42 million by that calculation, but it is only 2.95 million, so apparently that growth rate was a little high, or wasn’t sustained.

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2 years ago

I DONT KNOW THESE! HELP!

kkurt [141]

Answer:

20. x = 5, y = -2

21. x = 11, y = 12

22. x = 22, y = 11

23. x = 11, y = 10

Step-by-step explanation:

20. Opposite sides in the parallelogram are congruent, so

$2y+18=3x-1\\ \\6x-3=17-5y$

Solve this system of two equations:

$\left\{\begin{array}{l}2y-3x=-19\\ \\6x+5y=20\end{array}\right.$

Multiply the first equation by 2 and add two equations:

$2(2y-3x)+6x+5y=2\cdot (-19)+20\\ \\4y-6x+6x+5y=-38+20\\ \\9y=-18\\ \\y=-2$

Substitute it into the first equation:

$2\cdot (-2)-3x=-19\\ \\-3x=-19+4\\ \\-3x=-15\\ \\x=5$

21. Opposite angles in the parallelogram are congruent, so

$11x+5=10y+6$

Consecutive angles are supplementary, so

$6x-y+11x+5=180^{\circ}$

Solve this system of two equations:

$\left\{\begin{array}{l}11x-10y=1\\ \\17x-y=175\end{array}\right.$

From the second equation

$y=17x-175$

Substitute it into the first equation:

$11x-10(17x-175)=1\\ \\11x-170x+1750=1\\ \\-159x=-1749\\ \\x=11\\ \\y=17\cdot 11-175=187-175=12$

22. Opposite angles in the parallelogram are congruent, so

$2x-5=3y-12$

Consecutive angles are supplementary, so

$2x-5+7y+x=180^{\circ}$

Solve this system of two equations:

$\left\{\begin{array}{l}2x-3y=-7\\ \\3x+7y=185\end{array}\right.$

From the first equation

$x=-3.5+1.5y$

Substitute it into the second equation:

$3(-3.5+1.5y)+7y=185\\ \\-10.5+4.5y+7y=185\\ \\-105+45y+70y=1,850\\ \\115y=1,850+105\\ \\115y=1,955\\ \\y=17\\ \\x=-3.5+1.5\cdot 17=22$

23. Opposite sides in the parallelogram are congruent, so

$2x+9=4y-9\\ \\3x-5=2y+8$

Solve this system of two equations:

$\left\{\begin{array}{l}2x-4y=-18\\ \\3x-2y=13\end{array}\right.$

Multiply the second equation by 2 and subtract it from the first equation:

$2x-4y-2(3x-2y)=-18-2\cdot 13\\ \\2x-4y-6x+4y=-18-26\\ \\-4x=-44\\ \\x=11$

Substitute it into the first equation:

$2\cdot 11-4y=-18\\ \\-4y=-18-22\\ \\-4y=-40\\ \\y=10$

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3 years ago

write the slope intercept form of the equation of each line given the slope and y intercept. // slope= 1/3 y-intercept= 4 // slo

professor190 [17]

Answer:

Slope: 1/3; Y-iintercept: 4 y=1/3x+4

Slope: -2; Y-intercept: 4 y=-2x

Step-by-step explanation:

Hope this helps :3

if it did pls mark brainliest

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2 years ago

What is the least common multiple of 4 and 12? O 4 O 12 O 24 o ) 48

densk [106]

Answer:

Step-by-step explanation:

Least common multiple means what is the smallest number that both numbers go into

List the prime factors

4= 2*2

12 = 2*2*3

The factors that are in needed to make both are 2 and 3

We need 2 of the 2's and 1 3

2*2*3 = 12

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2 years ago

f(x) = −16x2 + 24x + 16 Part A: What are the x-intercepts of the graph of f(x)? Show your work. (2 points) WILL GIVE BRAINLIEST

castortr0y [4]

Answer:

Step-by-step explanation:

f(x) = −16x2 + 24x + 16 = 0 can be reduced to -2x^2 + 3x + 2 = 0 and then to 2x^2 - 3x - 2 = 0. Solve this for x using the quadratic formula:

The discriminant is b^2 - 4ac = (-3)^2 - 4(2)(-2) = 9 + 16 = 25.

Therefore the roots are:

-(-3) ± √25 3 ± 5

x = ----------------- = ------------ => x = 2 and x = -1/2

2(2) 4

The x-intercepts are points: (2, 0) and (-1/2, 0)

Because the coefficient of the x^2 term is negative, this graph opens down and the vertex represents a maximum.

To graph this function, find and plot the vertex. It is exactly halfway between the x-intercepts, that is, at x = 1 1/4, for which the y value is 21:

vertex and maximum at (5/4, 21)

Finally, find the y-intercept. Let x = 0; we find that y = 16. The y-intercept is 0, 16)

We now have four points on the graph and know where the maximum is. Plot this max (5/4, 21) and the x-intercepts (2, 0) and (-1/2, 0), and finally the y-intercept. Draw a smooth curve through these points, remembering that the graph is symmetrical about the axis of symmetry x = 5/4.

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2 years ago