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3 years ago

Which of the following diagrams includes a centroid? In order: A, B, C, D

Mathematics

2 answers:

Ivanshal [37]3 years ago

5 0

The answer is A.......

Musya8 [376]3 years ago

5 0

Answer:

Figure A

Step-by-step explanation:

First let's see what a centroid of a triangle is.

In a triangle there are three vertices. We draw a line segment from each vertices to the median of the opposite sides. The median of each vertices intersect in a point inside the triangle. That point is called the centroid of the triangle.

That is also called the center of gravity of the triangle.

By looking at the given figures,

The figure A is the correct answer.

There each line segments drawn from the vertices intersect the opposite side at the median. The point E is the centroid of the triangle.

Therefore, the answer is figure A.

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Rick drove for 45 minutes on Wednesday for a distance of 34.5 miles. On Thursday, he increased his speed by 3 miles per hour, an

riadik2000 [5.3K]

Answer:

is d and a

Step-by-step explanation:

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2 years ago

Name the shortest segment from Point A to Line CD. Write and Solve an inequality for X.

Misha Larkins [42]

Attached the solution with work shown.

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3 years ago

There are 29235 marbles and 371 jacks. If you want to know the percentage of jacks, do you divide the first number by the second

garik1379 [7]

Answer:

Correct answer: Two decimal places to the right

Step-by-step explanation:

We will set the classic proportion:

29,235 - 100%

371 - x%

29,235 : 371 = 100 : x ⇒ 29,235 · x = 371 · 100

x = (371/ 29,235) · 100 = 0.0127 · 100 = 1.27%

x = 1.27%

You divide first number by the second and then multiply with 100,

which is the same as moving the decimal point two places to the right.

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3 years ago

What is the equation of the quadratic graph with a focus of (3, 1) and a directrix of y = 5?

lbvjy [14]

Answer:

The equation of the quadratic graph is f(x)= - (1/8) (x-3)^2 + 3 (second option)

Step-by-step explanation:

Focus: F=(3,1)=(xf, yf)→xf=3, yf=1

Directrix: y=5 (horizontal line), then the axis of the parabola is vertical, and the equation has the form:

f(x)=[1 / (4p)] (x-h)^2+k

where Vertex: V=(h,k)

The directix y=5 must intercept the axis of the parabola at the point (3,5), and the vertex is the midpoint between this point and the focus:

Vertex is the midpoint between (3,5) and (3,1):

h=(3+3)/2→h=6/2→h=3

k=(5+1)/2→k=6/2→k=3

Vertex: V=(h,k)→V=(3,3)

p=yf-k→p=1-3→p=-2

Replacing the values in the equation:

f(x)= [ 1 / (4(-2)) ] (x-3)^2 + 3

f(x)=[ 1 / (-8) ] (x-3)^2 + 3

f(x)= - (1/8) (x-3)^2 + 3

4 0

3 years ago

6. Let f and g be differentiable functions

Julli [10]

Answer:

(b) 1

Step-by-step explanation:

To differentiate $h(x)=f(x)g(x)$ we will need the product rule:

$h'(x)=f'(x)g(x)+f(x)g'(x)$ .

We have $h'(x)=f(x)g'(x)$ , so the following equation is true by the transitive property:

$f'(x)g(x)+f(x)g'(x)=f(x)g'(x)$

By subtraction property we have:

$f'(x)g(x)=0$

Since $g(x) \neq 0$ , then we can divide both sides by $g(x)$ :

$f'(x)=\frac{0}{g(x)}$

$f'(x)=0$

This implies $f(x)$ is constant.

So we have that $f(x)=c$ where $c$ is a real number.

Since $f(0)=1$ and $f(0)=c$ , then by transitive property $1=c$ .

So $f(x)=1$ .

Checking:

$h(x)=1 \cdot g(x)$

$h'(x)=g'(x)=1 \cdot g'(x)$

So the following conditions were met.

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3 years ago