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3 years ago

A square has a side length of 3x3y5. What is the area of the square?

Mathematics

1 answer:

kotykmax [81]3 years ago

8 0

Answer:

9x^3 y^5

Step-by-step explanation:

Since the formula to finding area is (L*W = A), we first have to find the width.

Width: 3x^3 y^5 times 2 = 6x^3 y^5

Then we add them. So, 3x^3 y^5 + 6x^3 y^5 = 9x^3 y^5

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A science class has a ratio of 3 boys and 2 girls. Can there be 24 students in the class?

guajiro [1.7K]

Answer:

Let 3x be the number of boys

Let 2x be the number of girls

3x + 2x = 24

5x = 24

x = 4.8

3(4.8) = 14.4 boys

2(4.8) = 9.6 girls

There can't be 24 students for a ratio of 3 boys and 2 girls, because there can't be 14.4 boys and 9.6 girls, it has to be an exact number, otherwise it wouldn't make any sense.

For example, you and I are both 1 person, we can't be half a person or 0.6 of a person, only 1.

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3 years ago

Read 2 more answers

Determine the projection of vector w onto vector u. u=9i-6j, v=-3i-2j, w=19i+15j

Naily [24]

Answer:

$proj_uw=6.2i-4.2j$

Step-by-step explanation:

The projection of a vector $v$ onto a vector $u$ is defined as the projection of the vector $v$ on the line that contains the vector $u$ . It can be calculated using the following formula:

$proj_uv=\frac{u\cdot v}{||u||^2} u$

Where:

$u\cdot v$

Is the dot product between $u$ and $v$ which is given by:

$u\cdot v= $$\sum_{i=1}^{n} u_iv_i= u_1v_1+u_2v_2+...+u_nv_n$$$

and:

$||u||$

Is the magnitude of vector which can be calculated as follows:

$||u||=\sqrt{u_1^2+u_2^2+...+u_n^2}$

In this sense, the projection of vector w onto vector u is:

$proj_uw=\frac{u\cdot w}{||u||^2} u$

Where the dot product between $u$ and $w$ is:

$u\cdot w =(9*19)+(-6*15)=171-90=81$

And the magnitude of $u$ is:

$||u||=\sqrt{9^2+(-6)^2} = 3 \sqrt{13}$

Thus:

$proj_uw=\frac{u\cdot w}{||u||^2} u=\frac{81}{117} \langle9,-6\rangle=\langle6.23,-4.15\rangle\approx6.2i-4.2j$

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3 years ago

Kinleigh makes gift baskets to sell. The first day she made 3 baskets. Each day she plans on making 2 more baskets than the prev

nata0808 [166]

Answer:

168 baskets

Step-by-step explanation:

i did it the dumb way and just did 3+5+7+9+11+13+15+17+19+21+23+25 = 168

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3 years ago

An isosceles triangle has two sides of equal length, a, and a base, b. The perimeter of the triangle is 15.7 inches, so the equa

Marrrta [24]

Answer:

2 inches and 7.9 inches

Step-by-step explanation:

triangle sides can't be negative or 0.

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3 years ago

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Help with algebra question?

Charra [1.4K]

The system is

i) $\displaystyle{ \frac{-12+4y}{2x}-\frac{5x-6}{x}=-1$

ii) $\displaystyle{ 8^{5y-4}=8^{10x-4}$

In the second equation, the bases are equal, so we make the exponents equal to set the equation:

5y-4=10x-4. This means that 5y=10x, that is y=2x.

So, we can substitute y with 2x in the first equation:

$\displaystyle{ \frac{-12+8x}{2x}-\frac{5x-6}{x}=-1$ .

Multiplying the second fraction by 2/2 and -1 by 2x/2x, we have:

$\displaystyle{ \frac{-12+8x}{2x}-\frac{2(5x-6)}{2x}=-\frac{2x}{2x}$ .

Since the denominators are all equal, we can only work with the numerators, setting the equation:

-12+8x-10x+12=-2x,

simplifying we get 0-2x=-2x, that is -2x=-2x, which is always true. (Here remember that x cannot be 0 since x was in the denominator).

This means that for any (x, y) such that y=2x, the system is satisfied.

We can check that the correct statements are:

3) The point (1, 2) is a solution. (Since we have y=2x).

6) The system has infinitely many solutions. (Since any pair (x, 2x) is a solution, except when x=0)

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3 years ago

A square has a side length of 3x3y5. What is the area of the square?​

A square has a side length of 3x3y5. What is the area of the square?