100 POINTS PLEASE ANSWER FULLY!!

What is the product of 8/15 and 2 3/4?

Black_prince [1.1K]

The correct answer is 1 7/15.

4 0

3 years ago

I really need help pls. Its about 3d shapes

Svet_ta [14]

The image is blurry

Step-by-step explanation:

3 0

3 years ago

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The graph of the equation below is a circle. What is the length of the radius of the circle? (x - 4)^2 + (y + 12)^2 = 17^2

djverab [1.8K]

The correct answer is: [D]: "17" .
______________________________________________________
The radius is: " 17" .
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Note:
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The formula/equation for the graph of a circle is:
______________________________________________________
(x − h)² + (y − k)² = r² ;

in which:

" (h, k) " ; are the coordinate of the point of the center of the circle;

"r" is the length of the "radius" ; for which we want to determine;
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We are given the following equation of the graph of a particular circle:
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→ (x − 4)² + (y + 12)² = 17² ;

which is in the correct form:

→ " (x − h)² + (y − k)² = r² " ;

in which: " h = 4 " ;

" k = -12" ;

"r = 17 " ; which is the "radius" ; which is our answer.

→ { Note that: "k = NEGATIVE 12" } ;

→ Since the equation for this particular circle contains the expression: _________________________________________________________
→ "...(y + k)² ..." ;

[as opposed to the standard form: "...(y − k)² ..." ] ;
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→ And since the coordinates of the center of a circle are represented by:
" (h, k) " ;

→ which are: " (4, -12) " ; (for this particular circle) ;
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→ And since: " k = -12 " ; (for this particular circle) ;
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then:

" [y − k ] ² = [ y − (k) ] ² = " [ y − (-12) ] ² " ;

= " ( y + 12)² " ;

{NOTE: Since: "subtracting a negative" is the same as "adding a positive" ;

→ So; " [ y − (-12 ] " = " [ y + (⁺ 12) ] " = " (y + 12) "
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Note: The above explanation is relevant to confirm that the equation is, in fact, in "proper form"; to ensure that the: radius, "r" ; is: "17" .
___________________________________________________
→ Since: "r = 17 " ;

→ The radius is: " 17 " ;

which is: Answer choice: [D]: "17" .
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8 0

3 years ago

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Find a value for y for which the expression (1-y)(3-y)(6-y) has each given value

erik [133]

$\\ \tt\Rrightarrow (1-y)(3-y)(6-y)=-70$

$\\ \tt\Rrightarrow -y(1+1)(3+1)(6+1)=-70$

$\\ \tt\Rrightarrow y(2)(4)(7)=70$

$\\ \tt\Rrightarrow y(56)=70$

$\\ \tt\Rrightarrow y=\dfrac{70}{56}$

$\\ \tt\Rrightarrow y=\dfrac{5}{4}$

#2

$\\ \tt\Rrightarrow (1-y)(3-y)(6-y)=120$

$\\ \tt\Rrightarrow -y(1+1)(3+1)(6+1)=120$

$\\ \tt\Rrightarrow -y(2)(4)(7)=120$

$\\ \tt\Rrightarrow 56y=-120$

$\\ \tt\Rrightarrow y=\dfrac{-120}{56}$

$\\ \tt\Rrightarrow y=\dfrac{-15}{7}$

7 0

3 years ago

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What is the equation of the following graph in vertex form? parabolic function going down from the left through the point negati

Anestetic [448]

A parabolic function's key characteristic is either having 2 x-intercepts or 2 y-intercepts. That is the reason why the standard form of parabolic functions are:

(x-h)^2 = +/- 4a(y-k) or (y-k)^2 = +/- 4a(x-h), where

(h,k) is the coordinates of the vertex
4a is the lactus rectum
a is the distance from the focus to the vertex

This is also called vertex form because the vertex (h,k) is grouped according to their variable.

Since we don't know any of those parameters, we'll just have to graph the data points given as shown in the picture. From this data alone, we can see that the parabola has two x-intercepts, x=-4 and x=-2. Since it has 2 roots, the parabola is a quadratic equation. Its equation should be

y = (x+4)(x+2)
Expanding the right side
y = x²+4x+2x+8
y = x²+6x+8
Rearrange the equation such that all x terms are on one side of the equation
x²+6x+___=y-8+___
The blank is designated for the missing terms to complete the square. Through completing the squares method, you can express the left side of the equation into (x-h)² form. This is done by taking the middle term, dividing it by two, and squaring it. So, (6/2)²=9. Therefore, you put 9 to the 2 blanks. The equation is unchanged because you add 9 to both sides of the equation.

The final equation is
x²+6x+9=y-8+9
(x+3)²=y+1

6 0

4 years ago