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3 years ago

Identify the vertex of the parabola given by f(x) = (x + 2)^2 – 4

Mathematics

1 answer:

kicyunya [14]3 years ago

8 0

Answer:

The vertex is ( -2, -4)

Step-by-step explanation:

The vertex form is

y = a( x-h) ^2 +k

where ( h,k) is the vertex

f(x) = (x + 2)^2 – 4

Rewriting

f(x) = (x - -2)^2 – 4

The vertex is ( -2, -4)

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The figures below are made out of circles, semicircles, quarter circles, and a square. Find the area and the perimeter of each f

WITCHER [35]

Answer:

Part 1) $A=36(\pi-2)\ cm^2$

Part 2) $P=6(\pi+2\sqrt{2})\ cm$

Step-by-step explanation:

<u><em>The picture of the question in the attached figure</em></u>

Part 1) Find the area

we know that

The area of the shape is equal to the area of a quarter of circle minus the area of an isosceles right triangle

$A=\frac{1}{4}\pi r^{2}-\frac{1}{2}(b)(h)$

we have that the base and the height of triangle is equal to the radius of the circle

$r=12\ cm\\b=12\ cm\\h=12\ cm$

substitute

$A=\frac{1}{4}\pi (12)^{2}-\frac{1}{2}(12)(12)\\A=(36\pi-72)\ cm^2$

simplify

Factor 36

$A=36(\pi-2)\ cm^2$

Part 2) Find the perimeter

The perimeter of the figure is equal to the circumference of a quarter of circle plus the hypotenuse of the right triangle

The circumference of a quarter of circle is equal to

$C=\frac{1}{4}(2\pi r)=\frac{1}{2}\pi r$

substitute the given values

$C=\frac{1}{2}\pi (12)\\C=6\pi\ cm$

Applying the Pythagorean Theorem

The hypotenuse of right triangle is equal to

$AC=\sqrt{12^2+12^2}\\AC=\sqrt{288}\ cm$

simplify

$AC=12\sqrt{2}\ cm$

Find the perimeter

$P=(6\pi+12\sqrt{2})\ cm$

simplify

Factor 6

$P=6(\pi+2\sqrt{2})\ cm$

4 0

3 years ago

The sum of the cost of a veterinarian exam v and a $50 x-ray tip divided equally between 2 people.

JulijaS [17]

If you're just asking for how that'd look in algebraic form then the answer would be v+50/2

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3 years ago

Solve the equation <br><br> 3(x+2) = 2(2 - x)

RideAnS [48]

Answer:

x=-2/5

Step-by-step explanation:

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3 years ago

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Paul drinks 6 cups of coffee each day. Each cup contains 275 milliliters of coffee. How

scZoUnD [109]

<h3>Answer: 11.55 liters</h3>

=================================================

Work Shown:

275 mL = 275/1000 = 0.275 L

1 cup = 0.275 L

6 cups = 6*0.275 L = 1.65 L

He drinks 1.65 L per day, so over 7 days he drinks a total of 7*1.65 = 11.55 liters.

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2 years ago

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How do you draw a line for this

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I'd do a little more than 77minutes for the 6and 7for if you could have it on 77and but you could have it in your head

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