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2 years ago

The measure of angle X is 18 more than three times the measure of its complement. Find the measure of angle X.

1 answer:

6 0

The complement of an angle is 90 minus the angle, or

90 - x = complement angle

if x is 18 more than 3 times it's complement, then

x = 3(complement angle) + 18

We can substitute "90 - x" for the "complement angle" in the second equation:

x = 3(90 - x) + 18

distribute the 3 to the 90 and the x

x = 270 - 3x + 18

add 3x to both sides

4x = 270 - 18
4x = 252
x = 63

the measure of angle x is 63 degrees

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1) f(x)=(x - 3)(x - 5)

NemiM [27]

Answer:

Step-by-step explanation:

f(x)= (x - 3)(x - 5)

f(x) = x^2 - 5x - 3x + 15

f(x) = x^2 - 8x + 15

Answer is A

7 0

2 years ago

A cup of coffee at 93 degrees Celsius is placed in a room at 23 degrees Celsius. Suppose that the coffee cools at a rate of 1 de

Alinara [238K]

Answer:

Step-by-step explanation:

The rate of change of temperature of the coffee with respect to time is expressed by the differential equation

dT/dt=k(T−A) when k = -1 and A = 23. The equation will become:

dT/dt = -(T-23)

If the coffee cools at the rate of 1°C per minute, then dT/dt = -1 and T = 70

Substituting into the equation:

-1 = k(70-23)

-1 = 47k

k = -1/47

k = -0.0213

Substituting k = -0.0213 into the original equation, the differential equation will be:

dT/dt=k(T−A)

dT/dt = -0.0213(T-23)

dT/dt = -0.0213T+0.489

To get the value of T, we will use variable separable method

dt = dT/-0.0213T+0.489

Integrate both sides

t = -0.0213ln(-0.0213T+0.489)

At t = 1 minute

1 = -0.0213ln(-0.0213T+0.489)

1/-0.0213 = ln(-0.0213T+0.489)

-46.95 = ln(-0.0213T+0.489)

Apply exp to both sides

e^-46.95 = e^ln(-0.0213T+0.489)

4.073×10^-21= -0.0213T+0.489

-0.0213T = 4.073×10^-21-0.489

-0.0213T = -0.489

T = 0.489/0.0213

T = 22.96°C

5 0

3 years ago

What is the unit rate of $4.20 for 6 muffins

Sergio [31]

Well, you would divide 4.20/6 to find the price of just 1 muffin. 4.20/6 is 0.7, meaning that the price for one muffin is 70 cents.

7 0

3 years ago

Joan has 1/2 yard of felt. She will use 1/3 of it to make place cards. How much felt will she will use for place cards?

-Dominant- [34]

ANSWER

$\frac{1}{6} \: yards$

EXPLANATION

It was given that, Joan has

$\frac{1}{2} \: yard \: of \: felt$

and she will use

$\frac{1}{3}$
of it to make place cards.

We want to find how felt she will use for place cards.

We just have to find,

$= \frac{1}{3} \: of \: \frac{1}{2}$

$= \frac{1}{3} \times \frac{1}{2}$

$= \frac{1}{6}$

Therefore Joan will use

$\frac{1}{6}$

yards of felt for the place cards.

7 0

2 years ago

Andrew is about to leave for school. If he walks at a speed of 50 meters per minute, he will arrive 3 minutes after the bell rin

Mariana [72]

Answer:

The answer is: 13 minutes

Step-by-step explanation:

First Let us form equations with the statements in the two scenario

$time=\frac{distance}{speed}$