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3 years ago

What is the vertex of the absolute value function defined by ƒ(x) = |x - 2| - 7?

Mathematics

1 answer:

inn [45]3 years ago

8 0

<h3><u>Explanation</u></h3>

Modulus Function

$y = a |x - h| + k$

The structure or equation is similar to a quadratic function.

The value of a determines the slope of graph.

Tthe value of h determines the horizontal shift of graph.

The value of k determines the vertical shift of the graph.

From the given equation,

$f(x) = |x - 2| - 7$

We can say that the graph shifts to the right 2 units and shifts down 7 units. Hence the vertex would be at x = 2 and y = -7. It can be written in coordinate form as (2,-7).

<h3><u>Answer</u></h3>

<u> $\large{(2,-7)}$ </u>

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The two triangles are similar.

Neko [114]

Given that the triangles are similar.

When triangles are similar, all three pairs of corresponding sides are in the same ratio.

Similarly in the given triangles, the ratio of the corresponding sides are equal.

$\frac{8}{2x-2}= \frac{8+6}{3x}$

$\frac{8}{2x-2}= \frac{14}{3x}$

Cross multiplying, we get

$8 \times 3x = 14 \times (2x-2)$

$24x = 28x-28$

$-4x = -28$

Dividing both sides of the equation by -4.

So, we get

x = 7.

7 0

3 years ago

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jeka57 [31]

Answer:

x=30°

2x=60°

Step-by-step explanation:

Value of x°=x°/(2x°+x°)×90°

= 1/3×90°

=30°

Value of 2x°=30°×2

=60°

4 0

3 years ago

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The object below was made by placing a cone on top of a cylinder. The base of the cone is congruent to the base of the cylinder.

Ber [7]

Answer:

Part 1) The volume of the object is $32\pi\ cm^{3}$ or $100.48\ cm^{3}$

Part 2) see the procedure

Step-by-step explanation:

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

Part 1) What is the volume, in cubic centimeters, of the object?

we know that

The volume of the object is equal to the volume of the cylinder plus the volume of the cone

Find the volume of the cone

The volume of the cone is equal to

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

we have

$r=4/2=2\ cm$ -----> the radius is half the diameter

$h=3\ cm$

substitute the values

$V=\frac{1}{3}\pi (2^{2})(3)=4\pi\ cm^{3}$

Find the volume of the cylinder

The volume of the cylinder is equal to

$V=\pi r^{2} h$

we have

$r=4/2=2\ cm$ -----> the radius is half the diameter

$h=(10-3)=7\ cm$

substitute the values

$V=\pi (2^{2})(7)=28\pi\ cm^{3}$

Part 2) Then explain how you found the volume of the total shape

The volume of the total shape is equal to the volume of the cylinder plus the volume of the cone

$4\pi\ cm^{3}+28\pi\ cm^{3}=32\pi\ cm^{3}$ ------> exact value

Find the approximate value of the volume

assume

$\pi=3.14$

$32(3.14)=100.48\ cm^{3}$

7 0

3 years ago

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Find the Slope:

AveGali [126]

Answer:

4) slope= 0

5) $slope = - \frac{1}{7}$

Step-by-step explanation:

$\boxed{ slope = \frac{y _{2} - y_1 }{x_2 - x_1} }$

4) Slope

$= \frac{10 - 10}{ - 10 - 3}$

$= \frac{0}{ - 13}$

= 0

The slope is zero as the line is a horizontal line (since both points have the same y-coordinate of 10).

5) Slope

$= \frac{5 - 4}{2 - 9}$

$= \frac{1}{ - 7}$

$= - \frac{1}{7}$

Since you have taken (x₁, y₁) to be (9, 4), the value of x₁ should be 9 instead of 2.

6 0

3 years ago

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The equation of a circle is given below. x ^2 +(y-2.25)^2 =196/169. What is the center? What is the radius?

yuradex [85]

Answer:

center : (0, 2.25)

radius: 14/13

Step-by-step explanation:

x^2+(y-2.25)^2=196/169

Rewrite x^2+(y-2.25)^2=196/169

(x-0)^2+(y-2.25)^2=(14/13)^2

c=(0,2.25),r= (14/13)

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3 years ago