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4 years ago

Write an equation of the line with the given characteristics: passes through (-6,5) and has slope m= -5/2

1 answer:

4 0

The equation is y= -5/2x + (-10)
To find the y-intercept you use the equation.
y= -5/2x + b
You substitute y with the y value which is 5 and x with the x value which is -6. You multiply -5/2 by -6 which gives us 30/2 which equals to 15. Then you subtract 15.
5= -5/2(-6) + b
5-15 = 15 - 15
b= -10
The slope is -5/2 and the y-intercept is -10

So the equation of the line is y= -5/2x + (-10)
Hope this helps, please mark brainliest!

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What's 12 4/5 rounded to the nearest whole

borishaifa [10]

4/5= 0.8
12 4/5= 12.8

Number in ones place: 2
Number in tenths place: 8
Since 8>5, the number rounds up.

Final answer: 13

5 0

4 years ago

Which is the greatest to least, 12 3/4, 12 3/5 and 12.7

Ne4ueva [31]

Answer:

12 3/4, 12.7, 12/5

Step-by-step explanation:

12 3/4 = 12.75

12 3/5 = 12.6

4 0

3 years ago

Read 2 more answers

Find a solution to the initial value problem, y′′+18x=0,y(0)=5,y′(0)=1.

Serga [27]

We want to find a solution to the initial value problem:

$y'' + 18x = 0 \qquad,\qquad y(0) = 5 \qquad,\qquad y'(0)=1.$

We can start by integrating the equation once:

$\dfrac{\textrm{d}^2 y}{\textrm{d}x^2} + 18 x = 0 \iff \dfrac{\textrm{d}^2 y}{\textrm{d}x^2} = -18 x \iff\\\\\iff \dfrac{\textrm{d}y}{\textrm{d}x} = -18\displaystyle\int x\textrm{ d}x \iff \dfrac{\textrm{d}y}{\textrm{d}x}=-18\dfrac{x^2}{2} + C \iff\\\\\iff \dfrac{\textrm{d}y}{\textrm{d}x} = -9x^2 + C.$

Using the initial condition $y'(0) = 1$ , we can determine the integration constant $C$ :

$\dfrac{\textrm{d}y}{\textrm{d}x}\Big\vert_{x= 0} = 1 \iff -9 \times 0^2 + C = 1 \iff C = 1.$

Therefore, we have:

$\dfrac{\textrm{d}y}{\textrm{d}x} = -9x^2 + 1$

We can now integrate again:

$y(x) = \displaystyle\int\dfrac{\textrm{d}y}{\textrm{d}x}\textrm{ d}x = \int\left(-9x^2+1\right)\textrm{d}x = -9\int x^2\textrm{ d}x + \int\textrm{d}x =\\\\= -9\dfrac{x^3}{3} + x + K = -3x^3 + x + K.$

The integration constant $K$ is determined by using $y(0) = 5$ :

$y(0) = 5 \iff -3 \times 0^3 + 0 + K = 5 \iff K = 5.$

Finally, the solution is:

$\boxed{y(x) = -3x^3 + x + 5}.$

7 0

3 years ago

If U = {x: X € N, 1 < × < 15)

Inessa05 [86]

Answer:

Step-by-step explanation:

Given:

U = {x: X € N, 1 < × < 15) = {1,2,3,4,5,6,7,8,9,10,11,12,13,14,15}

A = {2,4,6,8,10,12,14}

B = {3,6,9,12,15}

C = {5,10,15}

(a) Verify A(BnB)=(AUB)(AUB)

A U (B n B)

= {2,4,6,8,10,12,14} U ( {3,6,9,12,15} n {3,6,9,12,15} )

= {2,4,6,8,10,12,14} U {3,6,9,12,15}

= {2,3,4,6,8,9,10,12,14,15}

( A U B) n (A U B)

= {2,3,4,6,8,9,10,12,14,15} n {2,3,4,6,8,9,10,12,14,15}

= {2,3,4,6,8,9,10,12,14,15}

Therefore

A U (B n B) = ( A U B) n (A U B)

verifies

(b) Verify An(BUC)=(AnB)u(AnC)

A n ( B U C)

= {2,4,6,8,10,12,14} n ( {3,6,9,12,15} U {5,10,15} )

= {2,4,6,8,10,12,14} n {3,5,6,9,10,12,15}

= {6,10,12}

( A n B ) U ( A n C )

= ( {2,4,6,8,10,12,14} n {3,6,9,12,15} ) U ( {2,4,6,8,10,12,14} n {5,10,15} )

= {6,12} U {10}

= {6,10,12}

Therefore

A n ( B U C) = ( A n B ) U ( A n C )

verifies

AU(BUC)

= {2,4,6,8,10,12,14}U{3,6,9,12,15}U{5,10,15}

= {2,3,4,5,6,8,9,10,12,14,15}

(AUB)U(AUC)

= ({2,4,6,8,10,12,14}{3,6,9,12,15})U({2,4,6,8,10,12,14}U{5,10,15})

= {2,3,4,6,8,9,10,12,14,15}U{2,4,5,6,8,10,12,14,15}

= {2,3,4,5,6,8,9,10,12,14,15}

Therefore

AU(BUC)=(AUB)U(AUC)

verifies

5 0

3 years ago

The Rogers Park cafeteria sells veggie pizza and cheese pizza. Today they sold 25 pizzas at lunch. They sold seven more cheese p

MA_775_DIABLO [31]

Let the number sold of veggie pizza be a
The number sold of cheese pizza be b
a+b=25…1
A+7=b…2

Sub 2 into 1
a + a+7 = 25
2a+7=25
2a=18
a=9

Sub a=9 into 2
9+7=b
b=16

They sold 9 veggie pizza and 16 cheese pizza

8 0

4 years ago