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Marizza181 [45]

2 years ago

7

Which of the following are the coordinates of a rectangle with a length of 4 units and a width of 3 units in the coordinate plan

e?
A- (−2, 1), (−2, −2), (2, 1), (2, −2)
B- (4, 3), (0, 3), (4, 7), (0, 7)
C- (1, −4), (−1, −4), (1, 0), (−1, 0)
D- (5, 6), (−3, 6), (5, 1), (−3, 1)

1 answer:

jekas [21]2 years ago

5 0

A!!
-2 and 2 are the x values of the coordinates which are 4 units apart, being 4 units in LENGTH
1 and -2 are 3 units apart and them being in the y part of the coordinate it’s 3 units wide

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The space allowed for the mascot on a school's Web page is 75 pixels wide by 60 pixels high. Its digital image is 500 pixels wi

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Answer:

It will be 60 pixels high and 75 pixels wide

Step-by-step explanation:

$\frac{400}{60}=\frac{500}{x}$

As

The space allowed for the mascot on a school's Web page is 75 pixels wide by 60 pixels high
Its digital image is 500 pixels wide by 400 pixels high

So, the expression becomes

$\frac{400}{60}=\frac{500}{x}$

$\mathrm{Apply\:fraction\:cross\:multiply:\:if\:}\frac{a}{b}=\frac{c}{d}\mathrm{\:then\:}a\cdot \:d=b\cdot \:c$

$400x=60\cdot \:500$

$400x=30000$

$\mathrm{Divide\:both\:sides\:by\:}400$

$\frac{400x}{400}=\frac{30000}{400}$

$\mathrm{Simplify}$

$x=75$

Therefore, it will be 60 pixels high and 75 pixels wide

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Answer:

The factorization of $729x^{15} +1000$ is $(9x^{5} +10)(81x^{10} -90x^{5} +100)$

Step-by-step explanation:

This is a case of factorization by <em>sum and difference of cubes</em>, this type of factorization applies only in binomials of the form $(a^{3} +b^{3} )$ or $(a^{3} -b^{3})$ . It is easy to recognize because the coefficients of the terms are <u><em>perfect cube numbers</em></u> (which means numbers that have exact cubic root, such as 1, 8, 27, 64, 125, 216, 343, 512, 729, 1000, etc.) and the exponents of the letters a and b are multiples of three (such as 3, 6, 9, 12, 15, 18, etc.).

Let's solve the factorization of $729x^{15} +1000$ by using the <em>sum and difference of cubes </em>factorization.

1.) We calculate the cubic root of each term in the equation $729x^{15} +1000$ , and the exponent of the letter x is divided by 3.

$\sqrt[3]{729x^{15}} =9x^{5}$

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So, we got that

$729x^{15} +1000=(9x^{5})^{3} + (10)^{3}$ which has the form of $(a^{3} +b^{3} )$ which means is a <em>sum of cubes.</em>

<em>Sum of cubes</em>

$(a^{3} +b^{3} )=(a+b)(a^{2} -ab+b^{2})$

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2.) Solving the sum of cubes.

$(9x^{5})^{3} + (10)^{3}=(9x^{5} +10)((9x^{5})^{2}-(9x^{5})(10)+10^{2} )$

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