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3 years ago

Write the equation of a line that is parallel to y = 1/2 x + 5

Mathematics

1 answer:

kumpel [21]3 years ago

3 0

Answer:

y = 1/2x + 5

Step-by-step explanation:

Slope-Intercept Form: y = mx + b

When 2 lines are parallel, they have the same slope.

Step 1: Define variables

Random point (2, 6)

<em>m</em> = 1/2

y = 1/2x + b

Step 2: Find <em>b</em>

6 = 1/2(2) + b

6 = 1 + b

5 = b

Step 3: Rewrite parallel linear equation

y = 1/2x + 5

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The area of the rectangle is 5 times the triangle

nirvana33 [79]

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3 years ago

At 7:00 A.M., Alicia pours a cup of tea whose temperature is 200°F. The tea starts to cool to room temperature (72°F). At 7:02 A

alexgriva [62]

Answer: A) Option B

B) 22.3 minutes.

Step-by-step explanation:

The temperature decreases in an exponential decrease, this means that we can write the equation as:

T(x) = A*r^x + B

Where A is the difference between the initial temperature and the room temperature, B is the room temperature, and r is a positive number smaller than 1, that says "how fast" the temperature decreases (and x is the variable, in units of time)

We know that the initial temperature

A = 200° - 72° = 128°

B = 72°

T(x) = 128°r^x + 72°

The only option with those two values is option B.

T(x) = 128(0.989)^x + 72

We should check that when x = 2m, the temperature must be 197°

T(2m) = 128*(0.989)^2 + 72 = 197.2° (that we can round down to 197°)

So this equation is correct

Now we want to find the time such the temperature is 172°F

then:

172° = 128°(0.989)^x + 72°

100° = 128°(0.989)^x

100/128 = (0.989)^x

x = ln(100/128)/ln(0.989) = 22.3 minutes.

Let's check in our equation:

T(22.3) = 128°(0.989)^22.3 + 72 = 172°

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3 years ago

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Elanso [62]

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3 years ago

What is the degree of x^5-4x+2

8090 [49]

Answer:

degree 5

Step-by-step explanation:

the degree of a polynomial is determined by the term with the largest exponent and is the value of the exponent.

$x^{5}$ is the term with the largest exponent of 5

degree of polynomial is 5

8 0

3 years ago

The sum of two numbers is 18. One number is 2 more that for times the other. Find the numbers.

seropon [69]

Hi there!

Let the first number be represented by X.
The second number (which is 2 more than four times the other), can be represented by 4X + 2.

We can now find the sum of this expression.
X + 4X + 2

Collect terms
5X + 2

The sum of the numbers is 18. Therefore we can set up the following equation.
5X + 2 = 18

Subtract 2.
5X = 16

Divide both sides by 5.
X = 16/5 = 3 1/5.

Therefore, the first number is 3 1/5. To find the second number we must plug in X = 3 1/5 into the expression 4X + 2

4 * (3 1/5) + 2 = 12 4/5 + 2 = 14 4/5
The two numbers are
$3 \frac{1}{5} \: \: and \: \: 14 \frac{4}{5}$

~ Hope this helps you!

3 0

3 years ago