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3 years ago

Use the Substitution Method, what is the point of intersection for the following system:

Mathematics

1 answer:

Wittaler [7]3 years ago

8 0

Answer:

$2x + 2(x - 3) = 18 \\ 2x + 2x - 6 = 18 \\ 4x = 24 \\ x = 24 \div 4 = 6 \\ y = x - 3 = 6 - 3 = 3$

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Classify the following polynomials according to the number of terms. Combine any like terms first.

11Alexandr11 [23.1K]

1) Combining like terms, we get x^2 + 5x, which is a binomial.

2) Combining like terms, we get x^3 + 3x^2, which is a binomial.

3) Combining like terms, we get 4x^3 + x^2 - x, which is a trinomial.

4) I can't answer this because there's an asterisk in place of the exponent.

3 0

3 years ago

The value of k so that the sequence k-1, k+3, 3k-1 forms an arithmetic progression is?

VashaNatasha [74]

Answer:

k = 4.

Step-by-step explanation:

An arithmetic sequence has a common difference.

So for this to be arithmetic:

k + 3 - (k - 1) = 3k - 1 - (k + 3)

k + 3 - k + 1 = 3k - 1 - k - 3

3 + 1 = 2k - 4

4 + 4 = 2k

k = 4.

The sequence is 3, 7, 11.

3 0

4 years ago

Senior classes high school A and high school B planned separate trips to New York City. The senior class at high school A rented

ICE Princess25 [194]

Let van =v and bus=b
V+6B=324
9V+3B=264×2 this will become
18V+6B=528 minus equ 1 from equ 2
-17V=-204 divide both side by -17
V=-204/-17=12
if V is 12 put it in equ 1
12+6B=324,6B=324-12=312 divide both side by 6
B=312/6=52
therefore the van and bus will take 12 and 52 persons respectively

3 0

4 years ago

Two pillars support the archway entrance of a castle. The archway can be modelled by the relation h=-0.025d^2 +d

BartSMP [9]

For this case we have the following function:
$h = -0.025d ^ 2 + d
$
To find the distance between the pillars, we must match the equation to zero:
$-0.025d ^ 2 + d = 0
$
From here, we clear the value of d:
$d (-0.025d + 1) = 0
$
The roots are:
Root 1:
$d = 0
$
Root 2:
$-0.025d + 1 = 0

 0.025d = 1

 d = 1 / 0.025

 d = 40$
Thus, the pillars are 40 units away.

The maximum height, we obtain it by deriving:
$h = -0.025d ^ 2 + d

 h '= - 0.050d + 1$
We equal zero and clear d:
$-0.050d + 1 = 0

 0.050d = 1

 d = 1 / 0.050

 d = 20
$
Then, we substitute the value of d = 20 in the equation for the height:
$h = -0.025 * (20) ^ 2 + (20)

 h = 10$
The maximum height is 10 units of distance

8 0

4 years ago

PLZ HELP ASAP CIRCLES

Nana76 [90]

For this case the ABC arc is given by:
ABC = AB + 41
The arc AB is a straight line, therefore:
AB = 180
Substituting values:
ABC = 180 + 41
ABC = 221 degrees
Answer:
The measure of the ABC arc is given by:
ABC = 221 degrees

5 0

3 years ago

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