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2 years ago

If you can mow 90 lawns in 45 hours, how long will it take to mow 12?

Mathematics

1 answer:

Alex777 [14]2 years ago

5 0

<h3>Answer: 6 hours</h3>

Work Shown:

(90 lawns)/(45 hours) = (12 lawns)/(x hours)

90/45 = 12/x

2 = 12/x

2x = 12

x = 12/2

x = 6

It takes 6 hours to mow 12 lawns.

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Please help thank you.

nikklg [1K]

I believe that through deductive reasoning angle O is 64 degrees. The reason is it's bigger than angle R so that rules out 32 and 16 degrees, but it's not obtuse, so that rules out 128 degrees, thereby leaving you with 64. Hope this helps :)

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3 years ago

2. The Soccer Club is selling T-shirts and washing cars to raise money for a summer trip. Last week, the club raised $292.50 by

Rudik [331]

15x = 292.50
Divide 15 from both sides
X= 5.85
1 T-shirt = $5.85

45x = 747.50
Divide 45 from both sides
X= 16.61

1 T-shirt = $ 16.61

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3 years ago

A student is attempting to factor a polynomial. Sample mathematical work is shown below. Which statement best applies to the sam

Vladimir [108]

The choices are:

<span>A. The student identified the greatest common factor incorrectly.
B. The student incorrectly divided each term by the greatest common factor.
C. The student failed to simplify the expression.
D. The mathematical work shown is correct.</span>

I think the correct answer from the choices is option D. The mathematical work shown is correct. Hope this answers the question. Have a nice day.

4 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

Write the rate as a unit rate. 44 points in 4 quarters

Margaret [11]

Answer:

44 p points in 4 quarters = llets per Qtr.

3 0

3 years ago