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3 years ago

Determine whether the following rates are equal or not using unit rates: 60 units in 3 minutes and 80 units in 4 minutes

Mathematics

2 answers:

vladimir1956 [14]3 years ago

5 0

Answer:

They are equal

1=20

2=40

3=60

4=80

Step-by-step explanation:

alina1380 [7]3 years ago

3 0

Answer:

The rates are equal

Step-by-step explanation:

To see if the rates are equal, divide both of the units by the number of minutes:

60/3

= 20

80/4

= 20

This means both rates are equal, since we got 20 for both of them

This means the rate is 20 units per 1 minute, for both rates.

So, the rates are equal.

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If f(x)=logx, explain the transformation that occurs when f(0.25(x-5))+3

nevsk [136]

Answer:

First, let's explain the transformations in a general way:

Vertical shift.

If we have a function f(x), a vertical shift of N units is written as:

g(x) = f(x) + N

This will move the graph of f(x) up or down a distance of N units.

if N is positive, then the shift is upwards

if N is negative, then the shift is downwards.

Horizontal shift.

If we have a function f(x), a horizontal shift of N units is written as:

g(x) = f(x + N)

This will move the graph of f(x) to the right or left a distance of N units.

if N is positive, then the shift is to the left

if N is negative, then the shift is to the right.

Horizontal dilation/contraction.

For a function f(x), an horizontal contraction dilation is written as:

g(x) = f(k*x)

where:

k is called the "scale factor"

If k < 1, then the graph "dilates" horizontally.

if k > 1, then the graph "contracts" horizontally.

Now, in this problem we have:

f(x) = log(x)

And the transformed function is:

g(x) = f(0.25*(x - 5)) + 3

Then, the transformations that take place here are, in order:

Vertical shift of 3 units up:

g(x) = f(x) + 3.

Horizontal shift of 5 units to the right:

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

Horizontal dilation of scale factor 0.25

g(x) = f( 0.25*(x - 5)) + 3

replacing f(x) by log(x) we have

g(x) = log(0.25*(x - 5)) + 3.

6 0

3 years ago

What are the values of a and b

makvit [3.9K]

Answer:

$\large\boxed{B.\ a=8,\ b=4\sqrt5}$

Step-by-step explanation:

We have three similar triangles:

$\triangle ABC\sim\triangle DBA\sim\triangle DAC$

therefore the sides are in proportion:

$\dfrac{AD}{CD}=\dfrac{BD}{AD}$

We have AD = a, CD = 16 and BD = 4. Substitute:

$\dfrac{a}{16}=\dfrac{4}{a}$ <em>cross multiply</em>

$(a)(a)=(16)(4)\\\\a^2=64\to a=\sqrt{64}\\\\a=8$

and other proportion:

$\dfrac{AB}{BC}=\dfrac{BD}{AB}$

We have AB = b, BC = 16 + 4 = 20 and BD = 4. Substitute:

$\dfrac{b}{20}=\dfrac{4}{b}$ <em>cross multiply</em>

$(b)(b)=(20)(4)\\\\b^2=80\to b=\sqrt{80}\\\\b=\sqrt{16\cdot5}\\\\b=\sqrt{16}\cdot\sqrt{5}\\\\b=4\sqrt{5}$

3 0

3 years ago

Given the arithmetic sequence an=4-4(n-1), what is the domain for n?

m_a_m_a [10]

The domain for n is $-\infty$

Explanation:

The arithmetic sequence is

To determine the domain of the sequence, let us consider $a_n$ as $f(n)$

Thus, the sequence becomes, $f(n)=4-4(n-1)$

The domain of the function is the set of all x-values for which the function is real and well defined.

Since, the function has no domain constraints or undefined points. Therefore, the domain of the function is

Thus, the domain of the arithmetic sequence $a_n=4-4(n-1)$ is $-\infty$

4 0

3 years ago

Genevieve is 3 years older than twice her brother's age. Genevieve is 21 years old. Write an equation to find her brother's age.

vfiekz [6]

Her brother is 9.

Because she is 3 years older than half his age, subtract 3 - 21. This gives 18. Then divide 18 / 2. This gives 9.

3 0

3 years ago

Twice a week a farmer supplies vegetables to 6 stores that she has an agreement with. Experience has shown that there is 20 % ch

olya-2409 [2.1K]

Answer:

Step-by-step explanation:

8 0

3 years ago

Determine whether the following rates are equal or not using unit rates: 60 units in 3 minutes and 80 units in 4 minutes​

Determine whether the following rates are equal or not using unit rates: 60 units in 3 minutes and 80 units in 4 minutes