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Lunna [17]
3 years ago
7

00:00

Mathematics
1 answer:
Aleks04 [339]3 years ago
7 0

Answer:

Figure A is a  translation of Figure 1

hope it helps...

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A quadrilateral has congruent diagonals. It is probably a( n) ______.
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<span>A quadrilateral has congruent diagonals. It is probably a <u>Square</u></span>
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-infinity, positive infinity
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Annie is framing a photo with a length of 6 inches and a width of 4 inches. The distance from the edge of the photo to the edge
Ede4ka [16]

Answer:

Part a) The quadratic function is 4x^{2} +20x-39=0

Part b) The value of x is 1.5\ in

Part c) The photo and frame together are 7\ in wide

Step-by-step explanation:

Part a) Write a quadratic function to find the distance from the edge of the photo to the edge of the frame

Let

x----> the distance from the edge of the photo to the edge of the frame

we know that

(6+2x)(4+2x)=63\\24+12x+8x+4x^{2}=63\\ 4x^{2} +20x+24-63=0\\4x^{2} +20x-39=0

Part b) What is the value of x?

Solve the quadratic equation 4x^{2} +20x-39=0

The formula to solve a quadratic equation of the form

ax^{2} +bx+c=0

is equal to

x=\frac{-b(+/-)\sqrt{b^{2}-4ac}} {2a}

in this problem

we have

4x^{2} +20x-39=0

so

a=4\\b=20\\c=-39

substitute in the formula

x=\frac{-20(+/-)\sqrt{20^{2}-4(4)(-39)}} {2(4)}

x=\frac{-20(+/-)\sqrt{1,024}} {8}

x=\frac{-20(+/-)32} {8}

x=\frac{-20(+)32} {8}=1.5\ in  -----> the solution

x=\frac{-20(-)32} {8}=-6.5\ in

Part c) How wide are the photo and frame together?

(4+2x)=4+2(1.5)=7\ in

5 0
3 years ago
The quotient of 24 and a number is 6.
Flauer [41]

The answer will be: 4

24 / 6 = 4

6 0
3 years ago
Read 2 more answers
Given the parabola below, find the endpoints of the latus rectum. (x-2)^2=-20(y+2)
Shtirlitz [24]

Answer:

The endpoints of the latus rectum are (12, -7) and (-8, -7).

Step-by-step explanation:

A parabola with vertex at point C(x, y) = (h,k) and whose axis of symmetry is parallel to the y-axis is defined by the following formula:

(x-h)^{2} = 4\cdot p \cdot (y-k) (1)

Where:

y - Independent variable.

x - Dependent variable.

p - Distance from vertex to the focus.

h, k - Coordinates of the vertex.

The coordinates of the focus are represented by:

F(x,y) = (h, k+p) (2)

The <em>latus rectum</em> is a line segment parallel to the x-axis which contains the focus. If we know that h = 2, k = -2 and p = -5, then the latus rectum is between the following endpoints:

By (2):

F(x,y) = (2, -2-5)

F(x,y) = (2,-7)

By (1):

(x-2)^{2} = -20\cdot (-7+2)

(x-2)^{2} = 100

x - 2 = \pm 10

There are two solutions:

x_{1} = 2 + 10

x_{1} = 12

x_{2} = 2-10

x_{2} = -8

Hence, the endpoints of the latus rectum are (12, -7) and (-8, -7).

4 0
2 years ago
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