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jeka57 [31]
3 years ago
14

One quadratic function has the formula h(x) = -x 2 + 4x - 2. Another quadratic function, g(x), has the graph shown below

Mathematics
2 answers:
jeyben [28]3 years ago
7 0
We are comparing maxima.  From the graph we know that the max of one graph is +2 at  x = -2.  What about the other graph?  Need to find the vertex to find the max.

Complete the square of <span>h(x) = -x^2 + 4x - 2:

</span>h(x) = -x^2 + 4x - 2 = -(x^2 - 4x) -2
= -(x^2 - 4x + 4 - 4) - 2
=-(x^2 - 4x + 4)       -2+4
= -(x-2)^2 + 2            The equation describing this parabola is y=-(x-2)^2 + 2, from which we know that the maximum value is 2, reached when x = 2.

The 2 graphs have the same max, one at x = -2 and one at x = + 2.
ale4655 [162]3 years ago
7 0

Answer:

Functions g and h have the same maximum of 2.

Step-by-step explanation:

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1. If a scale factor is applied to a figure and all dimensions are changed proportionally, what is the effect on the perimeter o
tester [92]

Answer:

Part 1) The perimeter of the new figure must be equal to the perimeter of the original figure multiplied by the scale factor (see the explanation)

Part 2) The area of the new figure must be equal to the area of the original figure multiplied by the scale factor squared

Part 3) The new figure and the original figure are not similar figures (see the explanation)

Step-by-step explanation:

Part 1) If a scale factor is applied to a figure and all dimensions are changed proportionally, what is the effect on the perimeter of the figure?

we know that

If all dimensions are changed proportionally, then the new figure and the original figure are similar

When two figures are similar, the ratio of its perimeters is equal to the scale factor

so

The perimeter of the new figure must be equal to the perimeter of the original figure multiplied by the scale factor

Part 2) If a scale factor is applied to a figure and all dimensions are changed proportionally, what is the effect on the area of the figure?

we know that

If all dimensions are changed proportionally, then the new figure and the original figure are similar

When two figures are similar, the ratio of its areas is equal to the scale factor squared

so

The area of the new figure must be equal to the area of the original figure multiplied by the scale factor squared

Part 3) What would happen to the perimeter and area of a figure if the dimensions were changed NON-proportionally? For example, if the length of a rectangle was tripled, but the  width did not change? Or if the length was tripled and the width was decreased by a factor of 1/4?​

we know that

If the dimensions were changed NON-proportionally, then the ratio of the corresponding sides of the new figure and the original figure are not proportional

That means

The new figure and the original figure are not similar figures

therefore

Corresponding sides are not proportional and corresponding angles are not congruent

so

<u><em>A) If the length of a rectangle was tripled, but the  width did not change?</em></u>

Perimeter

The original perimeter is P=2L+2W

The new perimeter would be P=2(3L)+2W ----> P=6L+2W

The perimeter of the new figure is greater than the perimeter of the original figure but are not proportionals

Area

The original area is A=LW

The new area  would be A=(3L)(W) ----> A=3LW

The area of the new figure is three times the area of the original figure but its ratio is not equal to the scale factor squared, because there is no single scale factor

<u><em>B) If the length was tripled and the width was decreased by a factor of 1/4?</em></u>

Perimeter

The original perimeter is P=2L+2W

The new perimeter would be P=2(3L)+2(W/4) ----> P=6L+W/2

The perimeter of the new figure and the perimeter of the original figure are not proportionals

Area

The original area is A=LW

The new area  would be A=(3L)(W/4) ----> A=(3/4)LW

The area of the new figure is three-fourth times the area of the original figure but its ratio is not equal to the scale factor squared, because there is no single scale factor

5 0
3 years ago
1 x 10^7 x 2 x 10^6 is
fomenos

Answer:

2e+13

Step-by-step explanation:

7 0
2 years ago
Find the area of the parallelogram.<br> 6 cm<br> 7.5cm<br> 9cm
lisabon 2012 [21]

Answer: Find the area of the parallelogram. Answer is A=54

6 cm

7.5cm

9cm

Step-by-step explanation: get the base and the height and then multiply

4 0
3 years ago
Read 2 more answers
The formula for the volume of a cone is V = jarh, where V is the volume, r is the radius, and h Is the heightWhat is the volume
olga nikolaevna [1]

Given:

The radius, r=4x

The height,

h=21xy^2

To find the volume of the cone:

The volume of the cone formula is,

V=\frac{1}{3}\pi r^2h

Substitute the values of r and h in the above formula we get,

\begin{gathered} V=\frac{1}{3}\pi\times(4x)^2\times21xy^2 \\ =\frac{1}{3}\pi\times16x^2\times21xy^2 \\ =\pi\times16x^2\times7xy^2 \\ =112\pi x^3y^2 \end{gathered}

Hence, the volume of the cone is

V=112\pi x^3y^2

Thus, the correct option is option D.

7 0
1 year ago
Can someone please answer this question please answer it correctly and please show work please help me I need it
JulsSmile [24]

Answer:

B

Step-by-step explanation:

We'll use Natasha's location as 0 on a number line. To the left of her, 51/20 would be negative and 25/4 would be positive.

To find how far apart the dogs are, we would need to add the absolute value of each number:

|-51/20| + |25/4| however, this can also be rewritten as:

25/4 - (-51/20)

3 0
3 years ago
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