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2 years ago

Tom determines the system of equations below has two solutions, one of which is located at the vertex of the parabola.

Mathematics

1 answer:

Rus_ich [418]2 years ago

5 0

Answer:

b must equal 7 and a second solution to the system must be located at (2, 5).

Step-by-step explanation:

Rearranging the first equation:

y = (x - 3)^2 + 4

From this we see that the vertex is at the point (3,4).

So one solution of equation 2 is (3 ,4).

Substituting in equation 2:

4 = -3 + b

b = 7.

So equation 2 is y = - x + 7.

Now we check if (2, 5) is on this line:

5 = -2 + 7 = 5 , therefore (2, 5) is on this line.

Verifying if (2, 5) is also on y = (x - 3)^2 + 4:

5 = (2 - 3)^2 + 4 = 1 + 4 = 5

- so it is. and a second solution to the system is (2, 5).

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A cell phone provider will allow you to buy a phone over time. They require a $50 initial payment and then charge $25 per month.

kumpel [21]

Answer:

Step-by-step explanation:

Given that:

Initial payment done for buying the phone = $50

Charges per month for the phone = $25 per month

To find:

The equation to represent the situation and its slope.

Solution:

First of all, let us assume that $m$ represents the number of months for which monthly is to be made.

Charges paid for one month = $25

Charges paid for $m$ months = $25 $m$

Total cost of the phone = Initial payment + Charges paid for $m$ months

$C = 25m + 50$

It is a linear equation between two variables $C$ and $m$ .

This equation can be compared with slope intercept form of a line.

Slope intercept form of a line is represented by:

$y=Mx+c$

$M$ is the slope.

On Comparing, we get:

$y = C, M = 25, x = m, c = 50$

Therefore, the slope is <em>25</em>.

5 0

2 years ago

Kareem wrote the values shown below.

grandymaker [24]

Answer:

Option D is correct.

$\lfloor 4.8 \rfloor$ and $\lceil 3.2 \rceil$

Step-by-step explanation:

Floor function states that the greatest integer that is less than or equal to x.

It is represented by: $\lfloor x \rfloor$

Ceiling function states that the least integer that is greater than or equal to x.

It is represented by: $\lceil x \rceil$

As per the statement:-

Kareem wrote the values show below:

$\lceil 3.2 \rceil$ , $\lfloor 2.7 \rfloor$ , $\lceil 2.9 \rceil$ and $\lfloor 4.8 \rfloor$ .

by definition:

$\lceil 3.2 \rceil$ = 4

$\lfloor 2.7 \rfloor$ = 2

$\lceil 2.9 \rceil$ =3

$\lfloor 4.8 \rfloor$ = 4

From the given options only pair which is equivalent is:

$\lfloor 4.8 \rfloor$ and $\lceil 3.2 \rceil$

7 0

3 years ago

How many pounds is 5,888 oz??

lubasha [3.4K]

Answer:

368 lbs

Step-by-step explanation:

divide the mass value by 16

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3 years ago

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A ladder is 6 m long.

IRISSAK [1]

Answer:

5.8 m

Step-by-step explanation:

Using the Pythagorean Theorem (a² + b² = c²) you get the equation a² + 1.5² = 6² (or 1.5² + b² = 6²). Then you solve from there and rounding to the first decimal place you get 5.8

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2 years ago

Unit rate for 490 in 3 1/2 hour

k0ka [10]

490 / 3.5 = 140 per hr

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3 years ago

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