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2 years ago

Find k. Write your answer in simplest radical form.

Mathematics

1 answer:

Airida [17]2 years ago

4 0

Answer:

k = 2 $\sqrt{2}$

Step-by-step explanation:

This is a 45- 45- 90 triangle is isosceles , base angles are congruent

Then legs are congruent , both 2

Using Pythagoras' identity in the right triangle

k² = 2² + 2² = 4 + 4 = 8 ( take square root of both sides )

k = $\sqrt{8}$ = $\sqrt{4(2)}$ = $\sqrt{4}$ × $\sqrt{2}$ = 2 $\sqrt{2}$

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Two students in your class, Tucker and Karly, are disputing a function. Tucker says that for the function, between x = –3 and x

Effectus [21]

The difference between Tucker and Karly's take is that Tucker's solution is analytical while Karly's is graphical. But both are correct either way.

For Tucker's solution, let's say at x=-3 the value for y is 4, and at x=3, the value of y is still 4, then the average rate of change or slope is 0. Note that the slope of the curve is Δy/Δx. Since there is no change for Δy, the slope is zero.

For Karly's solution, even if the curve travels high or low but would have the same elevation of x=-3 and x=3, the average rate of change is still zero. It is actually just same with Tucker's but Karly just verbalizes her solution that was observed visually.

7 0

3 years ago

HALLP QUICKKKK

Rina8888 [55]

To solve this we are going to use the formula for speed: $S= \frac{d}{t}$
where
$S$ is the speed
$d$ is the distance
$t$ is the time

Let $S_{l}$ be the speed of the boat in the lake, $S_{a}$ the speed of the boat in the river, $t_{l}$ the time of the boat in the lake, and $t_{a}$ the time of the boat in the river.

We know for our problem that the current of the river is 2 km/hour, so the speed of the boat in the river will be the speed of the boat in the lake minus 2km/hour:
 $S_{a}=S_{l}-2$
We also know that in the lake the boat sailed for 1 hour longer than it sailed in the river, so:
 $t_{l}=t_{a}+1$

Now, we can set up our equations.
Speed of the boat traveling in the river:
 $S_{a}= \frac{6}{t_{a} }$
But we know that $S_{a}=S_{l}-2$ , so:
$S_{l}-2= \frac{6}{t_{a} }$ equation (1)

Speed of the boat traveling in the lake:
$S_{l}= \frac{15}{t_{l} }$
But we know that $t_{l}=t_{a}+1$ , so:
$S_{l}= \frac{15}{t_{a}+1}$ equation (2)

Solving for $t_{a}$ in equation (1):
$S_{l}-2= \frac{6}{t_{a} }$
$t_{a}= \frac{6}{S_{l}-2}$ equation (3)

Solving for $t_{a}$ in equation (2):
$S_{l}= \frac{15}{t_{a}+1}$
$t_{a}+1= \frac{15}{S_{l}}$
$t_{a}=\frac{15}{S_{l}}-1$
$t_{a}= \frac{15-S_{l}}{S_{l}}$ equation (4)

Replacing equation (4) in equation (3):
$t_{a}= \frac{6}{S_{l}-2}$
$\frac{15-S_{l}}{S_{l}}=\frac{6}{S_{l}-2}$

Solving for $S_{l}$ :
$\frac{15-S_{l}}{S_{l}}=\frac{6}{S_{l}-2}$
$(15-S_{l})(S_{l}-2)=6S_{l}$
$15S_{l}-30-S_{l}^2+2S_{l}=6S_{l}$
$S_{l}^2-11S_{l}+30=0$
$(S_{l}-6)(S_{l}-5)=0$
$S_{l}=6$ or $S_{l}=5$

We can conclude that the speed of the boat traveling in the lake was either 6 km/hour or 5 km/hour.

3 0

4 years ago

Factorise 6x²+x-12 PLEASE HELP!

hichkok12 [17]

6x^2 + x - 12
= (3x - 4) (2x + 3)

Hope this helped and Happy New Year! :)

7 0

4 years ago

Read 2 more answers

Rectangle ABCDABCDA, B, C, D is graphed in the coordinate plane. The following are the vertices of the rectangle: A(2, 0)A(2,0)A

const2013 [10]

9514 1404 393

Answer:

28 square units

Step-by-step explanation:

The rectangle is 7-0 = 7 units high and 6-2 = 4 units wide. Its area is the product of these dimensions:

A = LW

A = (7)(4) = 28 . . . square units

3 0

3 years ago

Read 2 more answers

I need to do all of them.

OLEGan [10]

uh, solve for x? Its simple, but first, since it is a prep for a test, you should study how to solve for x, which is easy. So To solve for x, bring the variable to one side, and bring all the remaining values to the other side by applying arithmetic operations on both sides of the equation. Simplify the values to find the result.

Let’s start with a simple equation as, x + 2 = 7

How do you get x by itself?

Subtract 2 from both sides

⇒ x + 2 - 2 = 7 - 2

⇒ x = 5

Now, check the answer, x = 5 by substituting it back into the equation. We get 5 + 2= 7.

L.H.S = R.H.S

And then for a triangle:

Solve for x" the unknown side or angle in atriangle we can use properties of triangle or thePythagorean theorem.

Let us understand solve for x in a triangle with the help of an example.

△ ABC is right-angled at B with two of its legs measuring 7 units and 24 units. Find the hypotenuse x.

then in △ABC by using the Pythagorean theorem,

we get AC2 = AB2 + BC2

⇒ x2 = 72 + 242

⇒ x2 = 49 + 576

⇒ x2 = 625

⇒ x = √625

⇒ x = 25 units

get it? Good

5 0

3 years ago