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DedPeter [7]
3 years ago
12

Y=x​2​​−6x+10​ y=4−x​​ How do I substitute?

Mathematics
1 answer:
Shtirlitz [24]3 years ago
7 0

Answer:

(2,2) and (3,1)

Step-by-step explanation:

Since we're given the value of y in the second equation, we can replace the y on the left side of the first equation with 4-x, giving us

4-x=x^2-6x+10\\0=x^2-5x+6

We can factor the expression on the right to get us

0=x^2-5x+6\\0=x^2-3x-2x+6\\0=x(x-3)-2(x-3)\\0=(x-2)(x-3)

Solving x-2=0 and x-3=0 gets us the solutions x=2,3, which we can plug into the second equation to get us

y=4-2=2\\y=4-3=1

So, our solution set is the pair of points (2,2) and (3,1)

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A curve passes through the point (0,7) and has the property that the slope of the curve at every point P is five times the y-coo
iren [92.7K]

Answer:

y(x) = 7e^(5x)

Step-by-step explanation:

The question says that the slope of the curve at every point P is five times the y-coordinate of P. This means that

dy/dx = 5y

Refer to solutions of differential equations, dy/dt = ky, being in the form of y(t) = y(0) e^(kt)

Using the above stated law now, we can relate to our equation, saying that

y(x) = y(0) e^(5x)

The point given from the question is, (0, 7). This also means that y(0) = 7. So finally, we can have

y(x) = 7e^(5x)

And that is our needed equation of the curve

8 0
3 years ago
In circle pp, ad¯¯¯¯¯ad¯ is a diameter and bc¯¯¯¯¯bc¯ is perpendicular to ad¯¯¯¯¯ad¯ at ee. if pd=7pd=7 and ae=4ae=4, find cece.
kvv77 [185]
See the attached figure.

<span>ad is a diameter of the circle with center p
</span>
∵ pd = radius = 7 ⇒⇒⇒ ∴ ad = 2 * radius  = 2 * 7 = 14
∵ ae = 4 ⇒⇒⇒ ∴ ed = ad - ae = 14 - 4 = 10
∵ ad is a diameter
Δ acd is a triangle drawn in a half circle
∴ Δ acd is a right triangle at c
∵ bc ⊥ ad at point e
By applying euclid's theorem inside Δ acd
∴ ce² = ae * ed
∴ ce² = 4 * 10 = 40
∴ ce = √40 = 2√10 ≈ 6.325


3 0
3 years ago
What does four over five take away two over three eqall
BartSMP [9]
The answe to this question is 0.133333333
5 0
3 years ago
Read 2 more answers
Use the Distributive Property to solve the equation.
aliya0001 [1]

Answer:

x = -6

Step-by-step explanation:

-5(x + 3) = 15

Distribute the -5

-5x -15 =15

Add 15 to each side

-5x-15+15 =15+15

-5x = 30

Divide each side by -5

-5x/-5 = 30/-5

x =-6

8 0
3 years ago
The Muffin Man’s shop on Drury Lane charges 8% sales tax. Prince Charming’s purchases at the shop rang up at $34, and the tax wa
Gemiola [76]

Answer:

he multiplied by 0.8 not .08

Step-by-step explanation:

when doing 8% you go back 2 places so 0.08

34×0.08= 2.72

34+2.72= 36.72

7 0
2 years ago
Read 2 more answers
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