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3 years ago

6. Find the function with x-intercepts (-3,0) and (5,0), which also goes through the point (1,8)

Mathematics

1 answer:

Yakvenalex [24]3 years ago

4 0

Answer:

f(x) = (-1/2)(x^2 + 8x - 15)

Step-by-step explanation:

This function has two roots: -3 and 5. Most likely it is a quadratic (all of which have two roots).

Then f(x) = a(x + 3)(x - 5)

The graph goes through (1. 8): Therefore, y = 8 when x = 1:

f(1) = a(1 + 3)(1 - 5) = 8, or

a(4)(-4) = 8, or

-16a = 8, which leads to a = -1/2.

Thus the quadratic in question is f(x) = (-1/2)(x + 3)(x - 5), or

f(x) = (-1/2)(x^2 + 8x - 15)

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Step-by-step explanation:

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4 years ago

The lines y1 = 2x - 6, y2 = -3x + 4, y3 = -1/2x + 4 intersect to form the sides of a right triangle. Find the perimeter and area

tino4ka555 [31]

The area and perimeter of the triangle is 2/5 square units and (2√10 + 4√5) / 5 units

<h3>Determining the perimeter and area of the triangle giving line equation</h3>

In order to determine the area and perimeter of the lines, we will plot the giving lines, determine the point of intersection and then use the Pythagoras theorem to determine the dimension of the right triangle.

The points of intersection of the line are;

(x₁, y₁) = (- 0.4, 5.2),

(x₂, y₂) = (-0.8, 4.4),

(x₃, y₃) = (0, 4)

Determine the base

b² = c² -a²

b = √(-0.8)² + (4 - 4.4)²

b = 2√5 / 5

Determine the height

h = √((- 0.4) - (- 0.8))² + (5.2 - 4.4)²

height = 2√5 / 5

For the hypotenuse

r = √2 · b

r = 2√10 / 5

<h3>Determine the Perimeter and area</h3>

Perimeter = s1+s2+s3

Perimeter = 2√5 / 5 + 2√5 / 5 + 2√10 / 5

Perimeter = (2√10 + 4√5) / 5 units

area = 1/2* base * height

A = 0.5 · (2√5 / 5) · (2√5 / 5)

A = 2/5 square units

Hence the area and perimeter of the triangle is 2/5 square units and (2√10 + 4√5) / 5 units

Learn more on area and perimeter of triangles here: brainly.com/question/12010318

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1 year ago

HELPPPP What is the volume of the square pyramid? Use Pythagorean’s Theorem to find the height of the pyramid

aalyn [17]

Answer: 4,111.7 mm³

Step-by-step explanation:

You need to use this formula to calculate the volume of the square pyramid:

$V=\frac{s^2h}{3}$

Where "s" is the lenght of any side of the square base and "h" is the height of the pyramid.

Find the height with the Pythagorean Theorem:

$a^2=b^2+c^2$

Where "a" is the hypotenuse and "b" and "c" are the legs of the right triangle. Let be "c" the height of the pyramid.

You can identify in the figure that:

$a=26mm\\\\b=\frac{23mm}{2}=11.5mm\\\\c=h$

Then, you can find the height:

$(26mm)^2=(11.5mm)^2+h^2\\\\h=\sqrt{(26mm)^2-(11.5mm)^2}\\\\h=23.318mm$

Then, knowing that:

$s=23mm\\h=23.318mm$

You can calculate the volume:

$V=\frac{(23mm)^2(23.318mm)}{3}=4,111.7mm^3$

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3 years ago

Use this graph to answer the questions below:

stepladder [879]

the x axis and the yaxis

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3 years ago

Read 2 more answers

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

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

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

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