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3 years ago

Is a line having no slope the same as it having a slope of 0?

Mathematics

2 answers:

andrew-mc [135]3 years ago

8 0

They are the same if they have the same y values

Zanzabum3 years ago

4 0

Yes it is the same as having no slope.

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Find the number of possible ways one can choose marbles from a bag containing three marbles: a) if the order is important b) if

vladimir1956 [14]

Answer:

There are 3 marbles, that we assume are different.

Let's define them as marble 1, marble 2, and marble 3.

a) If the order is important, and we select the 3 marbles, then:

for the first marble, we have 3 options.

For the second marble, we have 2 options (because one is already taken)

for the third marble is only one option.

The total number of combinations is equal to the product between the numbers of options, so in this case, we have:

C = 3*2*1 = 6 combinations.

Now, if we only select 2 marbles from the bag, we have:

for the first marble, we have 3 options.

For the second marble, we have 2 options

Here the number of different combinations is:

C = 3*2 = 6 combinations.

And if we select only one marble from the bag, we have:

for the first marble, we have 3 options.

Then here are only 3 combinations.

the total number of combinations is:

C' = 6 + 6 + 3 = 15 different combinations.

b) If the order is not important, then there is only one combination when we draw the 3 marbles.

When we draw one marble there are 3 combinations (one for each marble)

When we draw two marbles, again there are 3 combinations (one for each marble that we do not draw)

then the total number of combinations in this case is:

C = 1 + 3 + 3 = 7

3 0

3 years ago

You create 15 centerpieces for a party in 5 hours.

barxatty [35]

A) 3 centerpieces per hour because 15/5 = 3
b) 14 hours, because 3 goes into 42 14 times exactly.
Hope this helps!

7 0

3 years ago

Please help I don’t understand this.

tresset_1 [31]

The average rate of change of g(x) over the interval [2, 8] is given by

(g (8) - g (2)) / (8 - 2)

In other words, it's the slope of the line through the points (2, g (2)) and (8, g (8)).

Use the definition of the function to evaluate it at the points in the numerator:

• 8 ≥ 4, so using the second piece, g (8) = -0.5(8) + 8 = 4

• 2 < 4, so g (2) = 5(2) + 1 = 11

Then the average rate of change is

(g (8) - g (2)) / (8 - 2) = (4 - 11) / 6 = -7/6

3 0

3 years ago

to estimate the height of the jin mao tower in shanghai , a tourist sights the top of the tower form a mirror that is 86.7 meter

Ray Of Light [21]

Answer:

The height of the tower = 420.48 meters

Step-by-step explanation:

For better understanding of the solution, see the figure attached below :

Let the height of the tower be x meters

Now, using the laws of reflection : angle of reflection = angle of incidence

Also, both the tower and the tourist are standing parallel to each other

⇒ ∠A = ∠i ( Alternate interior angles are equal)

Similarly, ∠D = ∠r ( Alternate interior angles)

But, ∠i = ∠r

⇒ ∠A = ∠D

Also, the tourist and the tower is perpendicular to the ground surface.

⇒ m∠B = m∠E = 90°

Now, in ΔABC and ΔDEC

∠A = ∠D (Proved above)

m∠B = m∠E = 90°

So, by AA postulate of similarity of triangles, ΔABC ~ ΔDEC

As the sides of similar triangles are proportional to each other

$\frac{AB}{DE}=\frac{BC}{EC}\\\\\implies\frac{1.92}{x}=\frac{0.4}{87.6}\\\\\implies x=\frac{87.6\times 1.92}{0.4}\\\\\bf\implies x = 420.48\textbf{ meters}$

Hence, The height of the tower = 420.48 meters

5 0

4 years ago

Solve the system of equations. y = 2x y = x 2 – 15

inn [45]

Answer:

D. (–3, –6) and (5, 10)

Step-by-step explanation:

The system has equations:

$y=2x$ ...(1)

and

$y=x^2-15$ ...(2)

Equate both equations;

$x^2-15=2x$

Rewrite in standard form:

$x^2-2x-15=0$

We factor to obtain:

$(x+3)(x-5)=0$

By the zero product principle;

$(x+3)=0,(x-5)=0$

$\implies x=-3,x=5$

When x=-3, y=2(-3)=-6

This yields the ordered pair (-3,-6).

When x=5, y=2(5)=10

This yields the ordered pair (5,10).

The correct choice is D.

8 0

3 years ago