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3 years ago

Could anyone please help me solve this question?

Mathematics

1 answer:

Sedaia [141]3 years ago

8 0

HL stands for "hypotenuse leg"

The idea is that if we have a pair of congruent hypotenuses and a pair of congruent legs, then we can prove the right triangles to be congruent.

While we have one pair of legs, we do not have one pair of hypotenuses that are known to be congruent. This is shown by the lack of tick marks on the hypotenuse. Recall that the hypotenuse is the longest side of the right triangle. It is opposite the 90 degree angle always.

So Ashley cannot use HL. Ashley can use LL (leg leg) or she can use SAS (side angle side). In fact, LL is a very special case of SAS where the angle is 90 degrees.

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find the slope of the curve y=x^2-2x-5 at the point P(2,5) by finding the limit of secant slopes through point P

Fynjy0 [20]

The point (2, 5) is not on the curve; probably you meant to say (2, -5)?

Consider an arbitrary point Q on the curve to the right of P, $(t,y(t))=(t,t^2-2t-5)$ , where $t>2$ . The slope of the secant line through P and Q is given by the difference quotient,

$\dfrac{(t^2-2t-5)-(-5)}{t-2}=\dfrac{t^2-2t}{t-2}=\dfrac{t(t-2)}{t-2}=t$

where we are allowed to simplify because $t\neq2$ .

Then the equation of the secant line is

$y-(-5)=t(x-2)\implies y=t(x-2)-5$

Taking the limit as $t\to2$ , we have

$\displaystyle\lim_{t\to2}t(x-2)-5=2(x-2)-5=2x-9$

so the slope of the line tangent to the curve at P as slope 2.

- - -

We can verify this with differentiation. Taking the derivative, we get

$\dfrac{\mathrm dy}{\mathrm dx}=2x-2$

and at $x=2$ , we get a slope of $2(2)-2=2$ , as expected.

4 0

3 years ago

Your classmate showed their thought process to the problem below. However, They made a mistake. What mistake did they make? Desc

Aleksandr [31]

Answer:

It's not 5x + 100 = 180,

it's 5x = 180 because they are vertical angles.

x = 36

4 0

3 years ago

Mikayla is training for a half-marathon. At the beginning of her training, she is able to run 2 miles without stopping. Her goal

ivanzaharov [21]

Alright, lets get started.

At the beginning of her training, she is able to run 2 miles without stopping means 2 will be in the addition when we will write the equation for her running miles.

Her goal is to increase her distance by three quarters of a mile each week.

Means in first week, she will add the distance = $\frac{3}{4}$ miles

Suppose she runs x weeks, so shee will add distance = $\frac{3}{4}x$

So, suppose she runs total number of miles = d, then

$d = 2 + \frac{3}{4}x$

Where d is total numer of miles she runs

x is number of weeks : Answer

Hope it will help :)

5 0

3 years ago

A rectangular garden is fenced on all sides with 256 feet of fencing. The garden is 8 feet longer than it is wide. Find the leng

Mekhanik [1.2K]

This is a bit of algebra.. you do not know either side so the width you will label x and the length you will label x +8. we know that if you add all 4 sides, you will have 256 feet. x + x + (x+8) + (x+8)=256 4x+16=256, Subtract 16 from both sides and you have 4x=240. divide by 4 on both sides and you get. x=60.. That makes the width = 60ft and the length = 68ft

3 0

3 years ago

Solve (x + 3 < 5) U (x - 7 > 1).

ale4655 [162]

Answer:

{ x | x < 2 or x > 8}

Step-by-step explanation:

Given the expression

(x + 3 < 5) U (x - 7 > 1).

Solve x+3 < 5

Subtract 3 from both sides

x+3 - 3 < 5-3

x < 2

For x - 7 > 1

Add 7 to both sides

x-7+7 > 1 + 7

x > 8

Hence the union of both is { x | x < 2 or x > 8}

4 0

3 years ago