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3 years ago

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What is the exact quotient of 434 divided by 7

1 answer:

liberstina [14]3 years ago

7 0

434 divided by 7 equals 62.

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1. Write the equation in standard form. Identify the important features of the graph:

NeTakaya

Answer:

(x-4.5)^2 +(y +5)^2 = 30.25
x = (1/8)y^2 +(1/2)y +(1/2)
y^2/36 -x^2/64 = 1
x^2/16 +y^2/25 = 1

Step-by-step explanation:

1. Complete the square for both x and y by adding a constant equal to the square of half the linear term coefficient. Subtract 15, and rearrange to standard form.

(x^2 -9x +4.5^2) +(y^2 +10y +5^2) = 4.5^2 +5^2 -15

(x -4.5)^2 +(y +5)^2 = 30.25 . . . . . write in standard form

Important features: center = (4.5, -5); radius = 5.5.

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2. To put this in the form x=f(y), we need to add 8x, then divide by 8.

x = (1/8)y^2 +(1/2)y +(1/2)

Important features: vertex = (0, -2); focus = (2, -2); horizontal compression factor = 1/8.

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3. We want y^2/a^2 -x^2/b^2 = 1 with a=36 and b=(36/(3/4)^2) = 64:

y^2/36 -x^2/64 = 1

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4. In the form below, "a" is the semi-axis in the x-direction. Here, that is 8/2 = 4. "b" is the semi-axis in the y-direction, which is 5 in this case. We want x^2/a^2 +y^2/b^2 = 1 with a=4 and b=5.

x^2/16 +b^2/25 = 1

_____

The first attachment shows the circle and parabola; the second shows the hyperbola and ellipse.

6 0

2 years ago

A positive real number is 2 less than another. When 4 times the larger is added to the square of the smaller, the result is 49.

Kobotan [32]

Answer:

The numbers are

$-2+3\sqrt{5}$ and $3\sqrt{5}$

Step-by-step explanation:

Let

x -----> the smaller positive real number

y -----> the larger positive real number

we know that

A positive real number is 2 less than another

so

$x=y-2$

$y=x+2$ ----> equation A

When 4 times the larger is added to the square of the smaller, the result is 49

so

$4y+x^2=49$ ----> equation B

substitute equation A in equation B

$4(x+2)+x^2=49$

solve for x

$x^2+4x-41=0$

The formula to solve a quadratic equation of the form

$ax^{2} +bx+c=0$

is equal to

$x=\frac{-b\pm\sqrt{b^{2}-4ac}} {2a}$

in this problem we have

$x^2+4x-41=0$

so

$a=1\\b=4\\c=-41$

substitute in the formula

$x=\frac{-4\pm\sqrt{4^{2}-4(1)(-41)}} {2(1)}$

$x=\frac{-4\pm\sqrt{180}} {2}$

$x=\frac{-4\pm6\sqrt{5}} {2}$

$x=-2\pm3\sqrt{5}$

so

The positive real number is

$x=-2+3\sqrt{5}$

Find the value of y

$y=x+2$

$y=-2+3\sqrt{5}+2$

$y=3\sqrt{5}$

6 0

3 years ago

I wasn’t at school when we learned this. Could someone he

Ksenya-84 [330]

Answer:

a= (1,4)

b=(4,2)

c=(2,6)

d=(2,-1)

Step-by-step explanation:

All I did was looked at the regions the points began and ended. I'm not 100% this is correct but I hope I helped!

6 0

2 years ago

What is the area surface of a cylinder 11x8

maxonik [38]

Answer:

400.7 cm^3

Step-by-step explanation:

8 0

2 years ago

Graph f(x) = 4[x] + 5

Elena L [17]

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6 0

2 years ago