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Anton [14]
1 year ago
10

Madeline drove 180 miles in 4 hours. If she drove at a constant rate, how far did shetravel in one hour?On the double number lin

e below, fill in the given values, then use multiplication ordivision to find the missing value.

Mathematics
1 answer:
Tcecarenko [31]1 year ago
8 0

We have a question on motion with the elements of distance, time taken and speed.

This question in particular is asking us for distance per unit time (in this case, hours).

We are required to find out how much distnace is covered in on hour and our approach will be as follows:

\text{Speed= }\frac{\text{Distance}}{\text{time}}=\frac{180\text{miles}}{4\text{hours}}=\frac{45\text{ miles}}{1\text{ hour}}

This right here just tells us that 4 hours, Madeline covered 180 miles and since her rate was constant (equal distances in equal times), then she also covered 45 miles in an hour.

Now we plot our number line.

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Brian has reduced his cholesterol level by 18% after his last check up. If his original level was 220, what is his approximate
Drupady [299]

Answer:

B

Step-by-step explanation:

multiply 18% and 220 which is 39.6

subtract 39.6 from 220 which is 180.4

simplify

3 0
3 years ago
Read 2 more answers
Eliminate the parameter. x = 1/2t, y = 3t^3 - 1
Elis [28]
X = t/2. t = 2x
y = 3t^3 - 1
y = 3(2x)^3 -1

y = 24x^3 -1
4 0
3 years ago
Use​ l'Hôpital's Rule to find the following limit. ModifyingBelow lim With x right arrow 0StartFraction 3 sine (x )minus 3 x Ove
steposvetlana [31]

Answer:

\lim_{x \to 0} \frac{3sinx-3x}{7x^3}=-\frac{1}{14}

Step-by-step explanation:

The limit is:

\lim_{x \to 0} \frac{3sinx-3x}{7x^3}=\frac{0}{0}

so, you have an indeterminate result. By using the l'Hôpital's rule you have:

\lim_{x \to 0} \frac{a(x)}{b(x)}= \lim_{x \to 0} \frac{a'(x)}{b'(x)}

by replacing, and applying repeatedly you obtain:

\lim_{x \to 0} \frac{3sinx-3x}{7x^3}= \lim_{x \to 0}\frac{3cosx-3}{21x^2}= \lim_{x \to 0}\frac{-3sinx}{42x}= \lim_{x \to 0}\frac{-3cosx}{42}\\\\ \lim_{x \to 0} \frac{3sinx-3x}{7x^3}=\frac{-3cos0}{42}=-\frac{1}{14}

hence, the limit of the function is -1/14

8 0
3 years ago
Molly has $45 in her wallet, which is 3 times as much money as her brother has. Write an equation to represent this situation, w
Lisa [10]

Answer:

the equation for this answer is 45(3)=a

5 0
3 years ago
Read 2 more answers
The Oxy coordinate plane for two parallel lines a and a' has the equations 2x - 3y-1 = 0 and 2x - 3y + 5 = 0. respectively. Whic
Andru [333]

Answer:

Remember that a vector translation can be written as:

T(a, b)

And if we apply this to a random point, (x, y), the translation gives:

T(a, b)(x, y) = (x + a, y + b)

now, remember that a general line can be written as:

y = m*x + s

Then a point of that line can be written as: (x, m*x + s)

Then if we apply the translation to a point in the line, we get:

T(a, b)(x, m*x + s) = (x + a, m*x + s + b)

Here we have two lines:

2x - 3y - 1 = 0

2x - 3y + 5 = 0

First, let's rewrite both of these in the slope-intercept form:

y = (2/3)*x - 1/3

y = (2/3)*x + 5/3

Now let's assume that we apply a translation to the first line, that has points of the form (x,  (2/3)*x - 1/3), such that we want to get points of the form:

(x, (2/3)*x + 5/3).

Then we must have:

T(a, b)(x,  (2/3)*x - 1/3) = (x + a,  (2/3)*x - 1/3 + b) = (x, (2/3)*x + 5/3).

Then we need to solve:

(x + a,  (2/3)*x - 1/3 + b) = (x, (2/3)*x + 5/3).

This means that:

x + a = x

(2/3)*x - 1/3 + b = (2/3)*x + 5/3

From the first equation, we can see that a = 0

Now we can solve the second one to find the value of b.

(2/3)*x - 1/3 + b = (2/3)*x + 5/3

subtracting (2/3)*x in both sides, we get:

-1/3 + b = 5/3

b = 5/3 + 1/3

b = 6/3 = 2

b = 2

Then the vector translation is:

T(0, 2)

So it moves the whole line 2 units upwards.

7 0
3 years ago
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