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Mazyrski [523]
3 years ago
5

write in slope intercept form an equation of the line that passes through the given points (-2,3) (2,7)​

Mathematics
1 answer:
yarga [219]3 years ago
3 0
1. Slope = Yb - Ya / Xb - Xa
= 7-3/2-(-2)
= 7-3/2+2
= 4/4
= 1

2. Y-intercept
Y = mx + b
7 = (1)(2) + b
7 = 2 + b
7 - 2 = 2-2 + b (two’s cancel out and we are just left with our b on the right side)
5 = B

Therefore, the equation is: Y = 1x + 5 which is also the same thing as: Y= X +5.
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Help me please :/// help
gayaneshka [121]
It’s not scaled. You can see it’s not the same shape as image A. 1 is only added to the height. If a shape is scaled, then the shape will remain the same, however it’s size will not. Therefore, the answer is “not a scaled copy of image A because 1 is added to the height”
7 0
2 years ago
Read 2 more answers
can someone show me how to find the general solution of the differential equations? really need to know how to do it for the upc
mariarad [96]
The first equation is linear:

x\dfrac{\mathrm dy}{\mathrm dx}-y=x^2\sin x

Divide through by x^2 to get

\dfrac1x\dfrac{\mathrm dy}{\mathrm dx}-\dfrac1{x^2}y=\sin x

and notice that the left hand side can be consolidated as a derivative of a product. After doing so, you can integrate both sides and solve for y.

\dfrac{\mathrm d}{\mathrm dx}\left[\dfrac1xy\right]=\sin x
\implies\dfrac1xy=\displaystyle\int\sin x\,\mathrm dx=-\cos x+C
\implies y=-x\cos x+Cx

- - -

The second equation is also linear:

x^2y'+x(x+2)y=e^x

Multiply both sides by e^x to get

x^2e^xy'+x(x+2)e^xy=e^{2x}

and recall that (x^2e^x)'=2xe^x+x^2e^x=x(x+2)e^x, so we can write

(x^2e^xy)'=e^{2x}
\implies x^2e^xy=\displaystyle\int e^{2x}\,\mathrm dx=\frac12e^{2x}+C
\implies y=\dfrac{e^x}{2x^2}+\dfrac C{x^2e^x}

- - -

Yet another linear ODE:

\cos x\dfrac{\mathrm dy}{\mathrm dx}+\sin x\,y=1

Divide through by \cos^2x, giving

\dfrac1{\cos x}\dfrac{\mathrm dy}{\mathrm dx}+\dfrac{\sin x}{\cos^2x}y=\dfrac1{\cos^2x}
\sec x\dfrac{\mathrm dy}{\mathrm dx}+\sec x\tan x\,y=\sec^2x
\dfrac{\mathrm d}{\mathrm dx}[\sec x\,y]=\sec^2x
\implies\sec x\,y=\displaystyle\int\sec^2x\,\mathrm dx=\tan x+C
\implies y=\cos x\tan x+C\cos x
y=\sin x+C\cos x

- - -

In case the steps where we multiply or divide through by a certain factor weren't clear enough, those steps follow from the procedure for finding an integrating factor. We start with the linear equation

a(x)y'(x)+b(x)y(x)=c(x)

then rewrite it as

y'(x)=\dfrac{b(x)}{a(x)}y(x)=\dfrac{c(x)}{a(x)}\iff y'(x)+P(x)y(x)=Q(x)

The integrating factor is a function \mu(x) such that

\mu(x)y'(x)+\mu(x)P(x)y(x)=(\mu(x)y(x))'

which requires that

\mu(x)P(x)=\mu'(x)

This is a separable ODE, so solving for \mu we have

\mu(x)P(x)=\dfrac{\mathrm d\mu(x)}{\mathrm dx}\iff\dfrac{\mathrm d\mu(x)}{\mu(x)}=P(x)\,\mathrm dx
\implies\ln|\mu(x)|=\displaystyle\int P(x)\,\mathrm dx
\implies\mu(x)=\exp\left(\displaystyle\int P(x)\,\mathrm dx\right)

and so on.
6 0
3 years ago
Look at the picture. I really need this answer to continue and I just can’t figure it out! I must be doing something wrong
kompoz [17]
Volume of a cone = pir^2h/3
so substitute what you know

1,102.14 = 3.14(r^2)(13/3)
divide by 3.14
351 = r^2(4.3333)
divde by 13/3
81 = r^2
r = 9 inches


6 0
3 years ago
Find the greatest number which divides 6168, 2447 and 3118 leaving the same remainder in each case.
SSSSS [86.1K]

let the greatest number be a and remainder be x. And let the whole number result of the division be b, c and d. So we have

ab + x = 2447............(1)

ac + x = 3118...............(2)

ad + x = 6168.............(3)

Subtracting (2) - (1) gives:-

ac - ab = 671

a(c - b) =671

Now 671 = 61 * 11 so 61 could be the value of a

Checking:- 2447 / 61 = 40 remainder 7 , 3118 / 61 = 51 remainder 7

and 6168 / 61 = 101 remainder 7

Answer 61

5 0
3 years ago
A baby weighs 8 pounds. How many kilograms is it equal to?
timofeeve [1]

Answer:

3.6

Step-by-step explanation:

if 0.45 is 1 pound then you could do 8 x 0.45 because the baby is 8 pounds

3 0
2 years ago
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