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3 years ago

If a square has an area of 225 square feet what is the length of each side

1 answer:

3 0

The area of the square: $A=a^2$

where "a" is a length of side.

Therefore:
$A=225\ ft^2\ and\ A=a^2\Rightarrow a^2=225\Rightarrow a=\sqrt{225}\Rightarrow \boxed{a=15\ (ft)}$

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an aquarium has a ratio of 5 rays for every 3 sharks. What percent of this grouping of animals are rays

sashaice [31]

Answer:

62.5%

Step-by-step explanation:

Total number of animals in a group= 5+3=8 animals

Number of rays=5

Since we only have 5 rays out of the total 8, to express the number of rays as a percentage of the total animals, we divide the number of rays by the total animals then multiply by 100 to express in percentage as needed in the question

Percentage of rays= $\frac {5}{8}\times 100=62.5$

Therefore, the percentage is 62.5%

6 0

3 years ago

I need help with 10,11,12,13 plz it's due tomorrow

tangare [24]

10. GCF is 3

11. GCF is 4

12. GCF is 16

13. That the numbers are prime

4 0

3 years ago

Which statement is false?

wariber [46]

All integers are whole numbers is false Whole numbers are non-negative while integers are negative, positive or zeros. D

6 0

3 years ago

g Use this to find the equation of the tangent line to the parabola y = 2 x 2 − 7 x + 6 at the point ( 4 , 10 ) . The equation o

natali 33 [55]

Answer:

The tangent line to the given curve at the given point is $y=9x-26$ .

Step-by-step explanation:

To find the slope of the tangent line we to compute the derivative of $y=2x^2-7x+6$ and then evaluate it for $x=4$ .

$(y=2x^2-7x+6)'$ Differentiate the equation.

$(y)'=(2x^2-7x+6)'$ Differentiate both sides.

$y'=(2x^2)'-(7x)'+(6)'$ Sum/Difference rule applied: $(f(x)\pmg(x))'=f'(x)\pm g'(x)$

$y'=2(x^2)'-7(x)'+(6)'$ Constant multiple rule applied: $(cf)'=c(f)'$

$y'2(2x)-7(1)+(6)'$ Applied power rule: $(x^n)'=nx^{n-1}$

$y'=4x-7+0$ Simplifying and apply constant rule: $(c)'=0$

$y'=4x-7$ Simplify.

Evaluate y' for x=4:

$y'=4(4)-7$

$y'=16-7$

$y'=9$ is the slope of the tangent line.

Point slope form of a line is:

$y-y_1=m(x-x_1)$

where $m$ is the slope and $(x_1,y_1)$ is a point on the line.

Insert 9 for $m$ and (4,10) for $(x_1,y_1)$ :

$y-10=9(x-4)$

The intended form is $y=mx+b$ which means we are going need to distribute and solve for $y$ .

Distribute:

$y-10=9x-36$

Add 10 on both sides:

$y=9x-26$

The tangent line to the given curve at the given point is $y=9x-26$ .

------------Formal Definition of Derivative----------------

The following limit will give us the derivative of the function $f(x)=2x^2-7x+6$ at $x=4$ (the slope of the tangent line at $x=4$ ):

$\lim_{x \rightarrow 4}\frac{f(x)-f(4)}{x-4}$

$\lim_{x \rightarrow 4}\frac{2x^2-7x+6-10}{x-4}$ We are given f(4)=10.

$\lim_{x \rightarrow 4}\frac{2x^2-7x-4}{x-4}$

Let's see if we can factor the top so we can cancel a pair of common factors from top and bottom to get rid of the x-4 on bottom:

$2x^2-7x-4=(x-4)(2x+1)$

Let's check this with FOIL:

First: $x(2x)=2x^2$

Outer: $x(1)=x$

Inner: $(-4)(2x)=-8x$

Last: $-4(1)=-4$

---------------------------------Add!

$2x^2-7x-4$

So the numerator and the denominator do contain a common factor.

This means we have this so far in the simplifying of the above limit:

$\lim_{x \rightarrow 4}\frac{2x^2-7x-4}{x-4}$

$\lim_{x \rightarrow 4}\frac{(x-4)(2x+1)}{x-4}$

$\lim_{x \rightarrow 4}(2x+1)$

Now we get to replace x with 4 since we have no division by 0 to worry about:

2(4)+1=8+1=9.

6 0

3 years ago

18 ➗ (-4 1/2) with explanation

slamgirl [31]

Answer:

-4

Step-by-step explanation:

If anything the first thing you would want to do is covert your fraction so a decimal. (-4 1/2) as a decimal is -4.50. From there it would be easier to divide. to get an answer of -4

8 0

2 years ago