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2 years ago

Plot the vertex and the axis of symmetry of this function on the provided graph. f(x) = (x + 2)2 − 6

Mathematics

1 answer:

Nookie1986 [14]2 years ago

3 0

Answer:

See attached image

Step-by-step explanation:

This equation for a parabola is given in vertex form, so it is very simple to extract the coordinates of its vertex, by using the opposite of the number that accompanies the variable "x" in the squared expression (opposite of 2) for the vertex's x-value, and the value of the constant (-6) for the vertex's y-value.

The vertex coordinates are therefore: (-2,-6)

The equation of the axis of symmetry of the parabola is a vertical line passing through the vertex. Since all vertical lines have the shape x = constant in our case, in order to pass through (-2,-6) the vertical line is defined by the equation: x = -2.

See image attached to find the vertex drawn as a red point, and the axis of symmetry as an orange vertical line passing through it.

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Right the slope intercept form for the line that travels through (4,-1) and is parallel to y=1/4x

ololo11 [35]

Answer:

Step-by-step explanation:

The slope is given to you by the line y = 1/4 x

The slope is just read as the number in front of x providing that the coefficient of y is 1. If that is not so, then you must divide by the coefficient in front of y. So far what you have is y = 1/4 x + b.

The second part of the question is to use the given point to find b.

x = 4

y = -1

b = ? substitute x and y to find b

y = 1/4 * 4 + b

- 1 = 1/4 * 4 + b

-1 = 1 + b

-2 = b

The equation of the line is y = 1/4 x - 2 Just to confirm this, I'm going to include the graph with the point 4,-1 on it.

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2 years ago

The figure shows ∆ABC with m∠ABC = 90°.

notsponge [240]

Answer:

Hello,

Please, see the attached file.

Thanks.

Step-by-step explanation:

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2 years ago

Read 2 more answers

Bill has two fat cats. He feeds each cat 150 grams of dry food each, twice a day. If he buys a 5 kilogram bag of dry food, about

Alinara [238K]

Answer: 4 days (I think)

Step-by-step explanation:

One cat = 150*2 = 300g

Two cats = 600g

600*2 = 1200 (this is the total amount of food they both eat in a day)

5kg = 5000g

1200g/5000g = 4.17

The bag will last 4 days.

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2 years ago

Explain why segments connecting any pair of corresponding vertices of congruent pentagons are congruent. make a sketch to suppor

Veronika [31]

Answer:

Congruence between pentagons

Step-by-step explanation:

The relationship occurs because having two congruent Pentagons and generating a segment within them (or outside), congruence is extrapolated to the triangles generated within them. Thus, if there is congruence among the pentagons, it will exist between the formed triangles. In other words since the two pentagons are congruent, the corresponding angle pair is congruent. also the two corresponding side pairs are also congruent.

In the attached image for example, the ABCDE and KLMNO pentagons are congruent, so all of their internal division lines are also congruent (AC and KM)

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2 years ago

Jesse uses this expression to determine how much to pay, including tax and tip, when he goes out to a restaurant:

lana66690 [7]

Answer:

x is the price of the meal

(1+0.0825 + 0.18) is the total percentage on top of the price he pays with sales tax and tip.

Step-by-step explanation:

The factor x is the price of the meal. The factor (1 + 0.0825 + 0.18) is the 100% of the price, the sales tax on that price and the tip on the total. 1 + 0.0825 + 0.18 = 1.2625 is the total percentage he pays on the price. He pays 26.25% in addition of the price of the meal to cover tax and tip.

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2 years ago