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10 days ago

The graphs below have the same shape. What is the equation of the blue graph?

Mathematics

2 answers:

AnnZ [3.9K]10 days ago

5 0

Answer: OPTION B

Step-by-step explanation:

The red graph depicts the fundamental form of a quadratic function (the most basic version), with its vertex located at the origin.

The function g(x) results from moving the parent function 2 units to the right and 1 unit upwards.

As a consequence, considering this, the transformation takes the following structure:

$g(x)=(x-h)^2+k$

The horizontal displacement is dictated by the value of h, while the vertical shift is determined by k.

<pThus, the resulting function is:

$g(x)=(x-2)^2+1$

AnnZ [3.9K]10 days ago

5 0

Answer:

B. $g(x)=(x-2)^2+1$

Step-by-step explanation:

The equation for the red graph is $f(x)=x^2$ .

The blue graph features its vertex at (2,1).

<pTherefore, its equation follows this format:

$g(x)=a(x-2)^2+1$

This graph intersects the y-axis at (0,5).

$5=a(0-2)^2+1$

$5-1=a(-2)^2$

$4=4a$

$1=a$

<pThus, the equation for the blue graph is:

$g(x)=(x-2)^2+1$

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The amount of wool required for a sweater was 400 grams.

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A scarf required 75 grams of wool.

Step-by-step explanation:

Let

x ------> grams of wool necessary for a sweater

y -----> grams of wool necessary for a hat

z -----> grams of wool necessary for a scarf

From the information given

x+y+z=555 -----> equation A

y=x/5 ----> x=5y -----> equation B

y=z+5 ---> z=y-5 ----> equation C

By substituting equations B and C into equation A, we can solve for y:

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x=5(80)=400 grams

Next, determine z

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The perimeter of the triangle is 44cm.if it’s sides are in the ratio 9:7:6.find its area

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Answer:

The area calculates to 83.905 cm^3

Step-by-step explanation:

The overall ratio is 9 + 7 + 6 = 22

Thus, the side lengths are computed as follows;

9/22 * 44 = 18 cm

7/22 * 44 = 14 cm

6/22 * 44 = 12 cm

Heron’s formula allows us to determine the area of the triangle

First, we calculate s

s = (a + b + c)/2 = (18+14+12)/2 = 44/2 = 22

Heron’s formula can be expressed as;

A = √s(s-a)(s-b)(s-c)

where a, b, and c are 18, 14, and 12 respectively

Plugging in the values, we obtain;

A = √22(22-18)(22-14)(22-12)

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A = √(7,040)

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