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3 years ago

In the diagram, −→− bisects ∠ .

Mathematics

1 answer:

11111nata11111 [884]3 years ago

4 0

Answer:

x = 9 and ∠ JKM = 59°.

Step-by-step explanation:

See the attached diagram with this question.

∠ JKL is bisected by line KM.

Therefore, angle JKM = angle MKL

Now, ∠ JKM is given to be ( x² - 22 ) and ∠ LKM = ( 6x + 5 ).

So, x² - 22 = 6x + 5

⇒ x² - 6x -27 = 0

⇒ ( x - 9 ) ( x + 3 ) = 0

Therefore, x = 9 or - 3.

∠ JKM = x² - 22 = 59° for x = 9 and ∠ JKM = x² - 22 = - 13° for x = - 3

Since angle JKM can not be negative, so, x = 9 and ∠ JKM = 59°. (Answer)

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How many different 4-digit numerals can be made from the digits of 56987 if a digit can appear just once in a numeral?

In-s [12.5K]

Answer: 120

Step-by-step explanation:

Given : the total number of digits : 5

The number of permutations of n things taken r at a time is given by :-

$\dfrac{n!}{(n-r)!}$

By using permutation, the number of different 4-digit numerals can be made from the digits of 56987 is given by :-

$^5P_4=\dfrac{5!}{(5-4)!}=5!=120$

Hence, the number of different 4-digit numerals can be made from the digits of 56987 is 120 .

8 0

4 years ago

In the figure, m< DBE = 50. Find m< BED

patriot [66]

Could you please put the picture? what type of angle are we talking bout or figure please and thank you!

6 0

4 years ago

Could someone help me bc idkk how this works

dmitriy555 [2]

Answer:

the answer is 2.

Step-by-step explanation:

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5 0

4 years ago

at a baseball game, a vender sold a combined total of 221 sodas and hot dogs. the number of hot dogs sold was 59 less than the n

marishachu [46]

Let h be hot dogs and s be sodas

h+s=221
h=s-59
s=s

s+s-59=221
2s-59=-221
2s=280
s=140
h=140-59=81
140+81=221

Answer: there were 81 hotdogs and 140 sodas sold

7 0

4 years ago

Could someone please assist...it would really help alot...thank you:)

Wittaler [7]

Problem 4.2

We're told that y = 2x is the equation of the tangent line through point Q.

Plug this into the equation of the circle (that was given at the very top of the page). Solve for x.

x^2 + y^2 - 18x - 6y + 45 = 0

x^2 + (2x)^2 - 18x - 6(2x) + 45 = 0 ... every "y" replaced with "2x"

x^2 + 4x^2 - 18x - 12x + 45 = 0

5x^2 - 30x + 45 = 0

5(x^2 - 6x + 9) = 0

5(x-3)^2 = 0

(x-3)^2 = 0

x-3 = 0

x = 3

This then means y = 2x = 2*3 = 6

The coordinates of point Q are (x,y) = (3,6)

----------

<h3>Answer: (3,6)</h3>

===========================================================

Problem 4.3

We first need to find the location of point S. That will involve solving this system of equations

$\begin{cases}x-2y+12=0\\y = 2x\end{cases}$

which represent the equations of lines SR and QS in that exact order.

Like before, we'll apply substitution to solve for x.

x-2y+12 = 0

x-2(2x)+12 = 0

x-4x+12 = 0

-3x+12 = 0

12 = 3x

12/3 = x

4 = x

x = 4

Which leads to y = 2x = 2*4 = 8

Point S is located at (4,8)

Point R is given to be located at (6,9)

Apply the distance formula for these two points to find the length of SR (aka the distance from S to R).

$S = (x_1,y_1) = (4,8)\\\\R = (x_2,y_2) = (6,9)\\\\d = \text{Length of SR, aka distance from S to R}\\\\d = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}\\\\d = \sqrt{(4-6)^2 + (8-9)^2}\\\\d = \sqrt{(-2)^2 + (-1)^2}\\\\d = \sqrt{4 + 1}\\\\d = \sqrt{5}\\\\d \approx 2.236068\\\\$

The exact length is $\sqrt{5}$ and that approximates to roughly 2.236068 units.

----------

<h3>Answer:</h3>

Exact length = $\sqrt{5}$ units

Approximate length = 2.236068 units

8 0

3 years ago