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3 years ago

Select a counter-example that makes the conclusion false.

Mathematics

1 answer:

Softa [21]3 years ago

4 0

A counter-example could be

There are more than 3 marbles in the bag, and the other ones are red.

Hope this helps!

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ANSWER QUICKLY PLZ :)

AfilCa [17]

The answer is (-1,1)
The solution is the point where the two lines cross each other
Hope this helps

5 0

3 years ago

Adam put $100 in a savings account. After 10 years, he had $1649 in the account. What rate of interest did he earn? Use the form

Rina8888 [55]

Answer:

Step-by-step explanation: C. 28%

$A = Pe^{rt}$

$1649 = 100 \cdot e^{10r}\\16.49 = e^{10r}\\\ln{16.49} = 10r\\r = \frac{\ln{16.49}}{10} = 0.28\\$

7 0

2 years ago

Which set of side lengths will NOT form a triangle?

Georgia [21]

Answer:

Its D

Step-by-step explanation:

7 0

3 years ago

What is 8 3/5 + 4 4/5?

dangina [55]

Answer:

67/5 = 13 2/5

Step-by-step explanation:

Step 1: <u>Define/explain.</u>

An easier way to solve this is by changing the mixed fractions to improper fractions.

To do this, multiply the whole number by the denominator, then add the product to the numerator; the denominator remains the same.

Mixed fraction - a fraction with a whole number.

Improper fraction - a fraction with a numerator larger than the denominator.

Step 2: <u>Solve.</u>

$8\frac{3}{5} =\frac{43}{5}$

$4\frac{4}{5} =\frac{24}{5}$

From here, add as usual.

$\frac{43}{5} +\frac{24}{5} =\frac{67}{5}$

Step 3: <u>Conclude.</u>

You can change the improper fraction to a mixed fraction if you'd like.

To do this, divide the numerator by the denominator.

The amount of times the numerator evenly goes into the denominator is the whole number.

The amount of remaining numbers in the denominator.

The numerator remains the same.

$\frac{67}{5} =13\frac{2}{5}$

I, therefore, believe the answer to this is 13 2/5.

5 0

2 years ago

Find the angle between u =the square root of 5i-8j and v =the square root of 5i+j.

fenix001 [56]

Answer:

The angle between vector $\vec{u} = 5\, \vec{i} - 8\, \vec{j}$ and $\vec{v} = 5\, \vec{i} + \, \vec{j}$ is approximately $1.21$ radians, which is equivalent to approximately $69.3^\circ$ .

Step-by-step explanation:

The angle between two vectors can be found from the ratio between:

their dot products, and
the product of their lengths.

To be precise, if $\theta$ denotes the angle between $\vec{u}$ and $\vec{v}$ (assume that $0^\circ \le \theta < 180^\circ$ or equivalently $0 \le \theta < \pi$ ,) then:

$\displaystyle \cos(\theta) = \frac{\vec{u} \cdot \vec{v}}{\| u \| \cdot \| v \|}$ .

<h3>Dot product of the two vectors</h3>

The first component of $\vec{u}$ is $5$ and the first component of $\vec{v}$ is also

The second component of $\vec{u}$ is $(-8)$ while the second component of $\vec{v}$ is $1$ . The product of these two second components is $(-8) \times 1= (-8)$ .

The dot product of $\vec{u}$ and $\vec{v}$ will thus be:

$\begin{aligned} \vec{u} \cdot \vec{v} = 5 \times 5 + (-8) \times1 = 17 \end{aligned}$ .

<h3>Lengths of the two vectors</h3>

Apply the Pythagorean Theorem to both $\vec{u}$ and $\vec{v}$ :

$\| u \| = \sqrt{5^2 + (-8)^2} = \sqrt{89}$ .
$\| v \| = \sqrt{5^2 + 1^2} = \sqrt{26}$ .

<h3>Angle between the two vectors</h3>

Let $\theta$ represent the angle between $\vec{u}$ and $\vec{v}$ . Apply the formula $\displaystyle \cos(\theta) = \frac{\vec{u} \cdot \vec{v}}{\| u \| \cdot \| v \|}$ to find the cosine of this angle:

$\begin{aligned} \cos(\theta)&= \frac{\vec{u} \cdot \vec{v}}{\| u \| \cdot \| v \|} = \frac{17}{\sqrt{89}\cdot \sqrt{26}}\end{aligned}$ .

Since $\theta$ is the angle between two vectors, its value should be between $0\; \rm radians$ and $\pi \; \rm radians$ ( $0^\circ$ and $180^\circ$ .) That is: $0 \le \theta < \pi$ and $0^\circ \le \theta < 180^\circ$ . Apply the arccosine function (the inverse of the cosine function) to find the value of $\theta$ :

$\displaystyle \cos^{-1}\left(\frac{17}{\sqrt{89}\cdot \sqrt{26}}\right) \approx 1.21 \;\rm radians \approx 69.3^\circ$ .

3 0

2 years ago