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3 years ago

–9.45 + 5.4d + 9.01 = –0.1d + 0.66

Mathematics

2 answers:

bulgar [2K]3 years ago

7 0

Answer:

1.838181818181818

Step-by-step explanation:

5.4d + 0.1d = 0.66 + 9.45

5.5d = 10.11

d = 10.11 / 5.5

d = 1.838181818181818

Brut [27]3 years ago

7 0

Answer:

d= 0.2

Step-by-step explanation:

–9.45 + 5.4d + 9.01 = –0.1d + 0.66

STEP 1:

Combine Like Terms:

–9.45 + 5.4d + 9.01 = –0.1d + 0.66

–9.45 + 9.01 = -0.44

-0.44+5.4d=-0.1d+0.66

STEP 2:

Add -0.44 from both sides:

-0.44+5.4d=-0.1d+0.66

-0.44+0.44+5.4d=-0.1d+0.66 +0.44

5.4d=-0.1d+0.66+0.44

STEP 3:

Add:

5.4d=-0.1d+0.66+0.44

0.66+0.44= 1.1

5.4d=-0.1d+1.1

STEP 4:

Add 0.1d from both sides:

5.4d=-0.1d+1.1

5.4d=-0.1d+1.1

5.4d+0.1d=-0.1d+0.1d+1.1

5.4d+0.1d=5.5d

5.5d=1.1

STEP 5:

Divide by the coefficient which is 5.5:

5.5d=1.1

d= 0.2

I hope this helps :)

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Consider the graph with four lines below. On a coordinate plane, line a has a positive slope and goes through points (negative 1

yan [13]

Answer:

The correct option is;

line a and line b

Step-by-step explanation:

Lina a passes through (-1, 0) and (1, 2)

Line b passes through (2, 2) and (-1, -1)

Line c passes through (0, 3) and (1, 0)

Line d passes through y = 1

An equation that has no solution

By examination, from the plot of the coordinates using an online tool, the system that would have no solution is the system of line a and line b because they are parallel lines and cannot meet or have a point where there is a common solution, therefore, there are no solutions when the equations of the two lines are combined in one equation

Slope of line a = -2/-2 = 1

Slope of line b = 3/3 = 1

The slopes of lines a and b are equal, therefore, line a and line b are parallel.

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3 years ago

Write 85% as it's fraction, as simply as possible

cricket20 [7]

Hey ! there

Answer:

Simplest fraction form of 85% is 17/20 .

Step-by-step explanation:

Question says that we have to write the simplest form of 85% as it's fraction .

Solution : -

$\quad \longrightarrow \qquad \:85\%$

We know that ,

Percent ( % ) = 1/100

So ,

$\quad \longrightarrow \qquad \: 85 \times \dfrac{1}{100} \:$

or ,

$\quad \longrightarrow \qquad \: \dfrac{85}{100}$

Reducing the fraction by cancelling it by 5 :

$\quad \longrightarrow \qquad \: \dfrac{ \cancel{85}}{ \cancel{100}}$

We get :

$\quad \longrightarrow \qquad \: \pink{\underline{\boxed{\frak{\dfrac{17}{20} }}}} \quad \bigstar$

Now , we can't reduce 17/20 .

Henceforth , 17/20 is the simplest form of 85% .

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2 years ago

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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°

8 0

3 years ago

Suppose that we don't have a formula for g(x) but we know that g(3) = −5 and g'(x) = x2 + 7 for all x. (

True [87]

So it tells us that g(3) = -5 and g'(x) = x^2 + 7.

So g(3) = -5 is the point (3, -5)
Using linear approximation
g(2.99) is the point (2.99, g(3) + g'(3)*(2.99-3))

now we just need to simplify that
(2.99, -5 + (16)*(-.01)) which is (2.99, -5 + -.16) which is (2.99, -5.16)
So g(2.99) = -5.16

Doing the same thing for the other g(3.01)
(3.01, g(3) + g'(3)*(3.01-3))
(3.01, -5 + 16*.01) which is (3.01, -4.84)
So g(3.01) = -4.84

So we have our linear approximation for the two.

If you wanted to, you could check your answer by finding g(x). Since you know g'(x), take the antiderivative and we will get
g(x) = 1/3x^3 + 7x + C
Since we know g(3) = -5, we can use that to solve for C
1/3(3)^3 + 7(3) + C = -5 and we find that C = -35
so that means g(x) = (x^3)/3 + 7x - 35

So just to check our linear approximations use that to find g(2.99) and g(3.01)

g(2.99) = -5.1597
g(3.01) = -4.8397

So as you can see, using the linear approximation we got our answers as
g(2.99) = -5.16
g(3.01) = -4.84
which are both really close to the actual answer. Not a bad method if you ever need to use it.

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3 years ago

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lesya692 [45]

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3 years ago

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