In right triangle ABC on hypotenuse AB lies points K and M such that AK=AC, BM=BC. Find m∠MCK.

Answers

Answer 1

Answer:

The measure of ∠MCK is 45°

Step-by-step explanation:

The parameters given are;

ΔABC with hypotenuse side AB

Let AB = x

BC = y

AC = z

∴ x² = y² +  z²

∠BCM = ∠CMB  (Base angles of isosceles triangle ΔBMC)

Similarly, ∠ACK = ∠AKC (Base angles of isosceles triangle ΔKAC)

∴ ∠BCM + ∠CMB + ∠CBM = 180° (Sum of interior angles in a triangle)

Hence, 2 × ∠BCM + ∠CBM = 180°........(1)

Similarly, 2 × ∠ACK + ∠CAK = 180°......(2)

Hence, 2 × ∠BCM + ∠CBM = 2 × ∠ACK + ∠CAK

However, ∠CBM + ∠CAK + 90° = 180° (Sum of angles in right triangle ΔABC)

∴∠CBM + ∠CAK = 180° - 90° = 90°

Adding equations (1) and (2), we have;

2 × ∠BCM + ∠CBM + 2 × ∠ACK + ∠CAK = 180° + 180° = 360°

Which gives;

2 × ∠BCM + 2 × ∠ACK + ∠CBM + ∠CAK = 360°

Where;

∠CBM + ∠CAK = 90°, we have;

2 × ∠BCM + 2 × ∠ACK + 90° = 360°

∴ 2 × ∠BCM + 2 × ∠ACK = 360° - 90° = 270°

∠BCM + ∠ACK = 270°/2 = 135°

∠BCM = ∠CMB

∴ ∠CMB + ∠ACK = 135°

Also, ∠CMB = ∠CMK and ∠ACK = ∠MCK

Hence, ∠CMK + ∠MCK  = 135°

However, ∠CMK + ∠MCK + ∠MCK = 180° (Sum of interior angles in a triangle)

Which gives;

∠CMK + ∠MCK + ∠MCK = 135° + ∠MCK = 180°

∴ m∠MCK = 180° - 135° = 45°.

The measure of ∠MCK, m∠MCK = 45°.


Related Questions

Melinda works at a cafe. Each day that she works, she records x, the total dollar amount of her customers’ bills and then y, her total daily wages. The table shows her data for 2 weeks. A 2-column table with 11 rows. The first column is labeled x with entries 50, 100, 75, 80, 90, 140, 150, 95, 125, 160, 165. The second column is labeled y with entries 36, 43, 38, 40, 42, 50, 60, 43, 46, 50, 55. A graph shows the horizontal axis numbered 40 to 160 and the vertical axis numbered 10 to 60. A line increases from 0 to 160. According to the line of best fit, what is the minimum amount, to the nearest dollar, Melinda will earn for each day of work, even if she serves no customers? $18 $26 $36 $40

Answers

Answer:

$26

Step-by-step explanation:

In the picture attached, the table, the plot and the line of best fit are shown. There we can see the next equation:

y = 0.177x + 25.936

where x is the total dollar amount of her customers’ bills and then y is her total daily wages.

This means that even if she serves no customers (x = 0) she will earn $26  ($25.936 rounded to the nearest dollar)  for each day of work.

Answer:

$26

Step-by-step explanation:

Looking at the graph when x is 0 y is about a little more that 25 but less than 30. Meaning 26 fits the questions answer.

Which of the following is the simplified form of 7sqrtx 7sqrtx 7sqrtx

Answers

Answer:

First option is the correct answer

[tex] {x}^{ \frac{3}{7} } [/tex]

Step-by-step explanation:

[tex] \sqrt[7]{x} \times \sqrt[7]{x} \times \sqrt[7]{x} \\ \\ = \sqrt[7]{x\times x\times x } \\ \\ = \sqrt[7]{ {x}^{3} } \\ \\ = {x}^{ \frac{3}{7} } [/tex]

Given a segment with endpoint coordinates (0,4) and (-4,-3) find the
coordinates of the midpoint.
Enter the x-coordinate value here
Enter the y-coordinate value here​

Answers

Answer:

(-2 , 1/2)

Step-by-step explanation:

x = -2

y = 1/2 or 0.5

Help please!
Which expressions are equivalent to -5/19

Answers

Answer:

Options 3, 4, and 5 are all equivalent

The expressions equivalent to -5/19 are options 3, 4, and 5 are all equivalent.

We have given that

-5/19

What is the expression?

An expression is a sentence with a minimum of two numbers and at least one math operation.

1) 5/19

Option 1 is not correct.

2)-5/-19

Implies that 5/19.

Option 2 is also not correct.

3) -5/19

Option 3 is correct.

4) 5/-19=-5/19

This is the correct option.

5)-(5/19)=-5/19

This is also the correct option.

Therefore, the expressions equivalent to -5/19 are options 3, 4, and 5 are all equivalent.

To learn more about the expression visit:

https://brainly.com/question/723406

How are the following three expressions different from each other, if needed they are? Do not just state the value of each but explain what may be same or different.

That what my teacher said I’m confused plz help
Thank u so much to the people who helped me answer it.

Answers

Answer:

2 and 3 are same since in both the cases we need to square 2 only not the negative 1 in it

1 is not same to 2 and 3 since in 1 we need to square 2 and negative 1 in it also.

Step-by-step explanation:

We are given the three expressions different from each other

We are supposed to find  what may be same or different.

1) [tex](-2)^2[/tex]

[tex]\Rightarrow (-1)^2 \times (2)^2\\\Rightarrow -1 \times -1 \times 2 \times 2 \\\Rightarrow 4[/tex]

2)[tex]-2^2[/tex]

[tex]\Rightarrow -1 \times 2^2\\\Rightarrow -1 \times 2 \times 2 \\\Rightarrow -4[/tex]

3)[tex]-(2)^2[/tex]

[tex]\Rightarrow -1 \times (2)^2\\\Rightarrow -1 \times 2 \times 2 \\\Rightarrow -4[/tex]

Now 2 and 3 are same since in both the cases we need to square 2 only not the negative 1 in it

1 is not same to 2 and 3 since in 1 we need to square 2 and negative 1 in it also.

Please help! For the function f(x) = 2x^6 + 3x^4 - 4x^3 + (1/x) - sin(2x) find the first four derivatives.

Answers

Answer:

Step-by-step explanation:

First derivative

[tex]12x^5+12x^3 -x^{-2}-2cos (2x)[/tex]

Second derivative

[tex]60x^4+36x^2+2x^{-3}+4sin(2x)[/tex]

Third derivative

[tex]240x^3+72x-6x^{-4}+8cos(2x)[/tex]

Fourth derivative

[tex]720x^2+72+24x^{-5}-16sin(2x)[/tex]

681/4 i dont know this

Answers

Answer:

170.25

Step-by-step explanation:

It's a bit tricky to do not on plain paper, but here:

Just assume the long division symbol looks right

  _1_7_0_.25

4 ) 681

    -4

     2 8

     -2 8

          0  1

The remainder is "1", so you'll just have to write that as either a fraction or decimal, whatever is assigned.

Fraction: 170 1/4

Decimal: 170.25

The answer is 170.25

please see the attached picture for full solution

hope it helps

Good luck on your assignment

Consider the function f(x)= 10^x and the function g(x), which is shown below.

How will the graph of g(x) differ from the graph of f(x)?

g(x)= f(x - 6) = 10^(x-6)

A. The graph of g(x) is the graph of f(x) shifted 6 units elown.
B. The graph of g(x) is the graph of f(x) shifted to the left 6 units.
C. The graph of g(x) is the graph of f(x) shifted 6 units up.
D. The graph of g(x) is the graph of f(x) shifted to the right 6 units.

Answers

Answer:

B. The graph of g(x) is the graph of f(x) shifted to the left '6' units

Step-by-step explanation:

Type of transformation                                   change to co-ordinate point

Vertical translation up 'd' units                          (x ,y) changes to (x , y+d)

Vertical translation down 'd' units                    (x ,y) changes to (x , y-d)

Horizontal translation left 'c' units                    (x ,y) changes to (x-c , y)

Horizontal translation Right 'c' units                  (x ,y) changes to (x+c , y)

Given f(x) translation left 'c' units                       f(x) changes to f(x-c)

Given f(x) translation right 'c' units                     f(x) changes to f(x+c)

Given  Function f(x) = 10 ˣ

The given graph  f(x) translation left '6' units

g(x) = f(x -6) = [tex]10^{x-6}[/tex]

Final answer:-

The graph of g(x) is the graph of f(x) shifted to the left '6' units

g(x) = f(x -6) = [tex]10^{x-6}[/tex]

Answer:

D. The graph of g(x) is the graph of f(x) shifted to the right 6 units.

Step-by-step explanation:

Use GeoGebra to graph those two function

f(x) = 10^x

g(x) = 10^(x-6)

The side lengths of a triangle are 6, 8 and 12. Is this a right triangle?

A. Yes, because 6 to the 2nd power + 8 to the 2nd power < 12 to the 2nd power.
B. No, because 6 + 8 ≠ 12.
C. Yes, because 6 to the 2nd power + 8 to the 2nd power = 12 to the 2nd power.
D. No, because 6 to the 2nd power + 8 to the 2nd power ≠ 12 to the 2nd power.

Answers

Answer:

No it's not. 6 to the 2nd power + 8 to the 2nd power ≠ 12 to the 2nd power

Step-by-step explanation:

If you square the shorter lengths and add them together, they add up to one hundred

6^2 + 8^2 --> 38 + 64 = 100

Once you square 12 it equals 144

144 does not equal 100. There for it can't be a right triangle. To be a right triangle, it has to have a ratio pf 3: 4: 5.

Ex: 6: 8: 10,  12: 16: 20, etc.

Hope this helps!

Which ordered pair is a viable solution if x represents the number of books he orders and y represents the total weight of the books, in ounces?

Answers

Answer:

The answer is "(0,0)"

Step-by-step explanation:

In the given some information is missing that is point so, the correct answer to this question can be described as follows:

book Number = x  

overall Book weight = y  

Neither x nor y can be negative. We have to be positive values, then.  

Since x indicates the number of books, that must be a positive integer. It can not be a decimal number or fractional number.  

So the only viable solution from the given options is (0, 0).

Answer:

6 ounces. Which ordered pair is a viable solution if x represents the number of books he orders

Step-by-s6 ounces.

Simplify the following expression.
11 - X 7

Answers

Answer:

11-7x  its already simplified

by-step explanation:

multiply

To compute a product; to perform a multiplication.

This is already simplified as can be

Write the set using roster notation: The set of even natural numbers less than 10.

Answers

Answer:

A={2,4,6,8}

Let the set be A

Even numbers are those numbers which can be divided by 2.

hope it helps

Good luck on your assignment

Answer:

A={2,4,6,8}

Step-by-step explanation:

Let the set be A

even numbers means the numbers can be divide by 2

but they said that it has to be less than 10

Now, let's create the set

[tex]a = {2 \: \: 4 \: \: 6 \: \: 8 \: \: } [/tex]

hope this helps

brainliest appreciated

good luck! have a nice day!

what is the correct expanded form and value of (One-fifth) Superscript 4?
A. 1/5+1/5+1/5+1/5=4/5
B. 1/5 x 1/5 x 1/5 x 1/5= 1/625
C.1+1+1+1/5 x 4 = 4/20
D.1/5x4=4/5

Answers

Answer:

B, 1/5*1/5*1/5*1/5=1/625

Answer:

B.

Step-by-step explanation:

because furries are alwasy right

The figure is made of rectangular prisms. What is the volume?
6 cm
15 cm
10 cm
3 cm
6 cm
3 cm
3 cm
3 cm
318 cm
225 cm
13
159 cm

Answers

What are the sides of the rectangular prisms ?

D= 90* AC=17 cm AD=10 cm CD=?cm

please in need help in this

Answers

Answer:

Step-by-step explanation:Idon't say u must have ro mark my ans as brainliest but if u think it has really helped u plz don't forget to thank me....

Answer:

CD=

[tex] \sqrt{189} [/tex]

Step-by-step explanation:

using phaythagorous theorem

CD^2+10^2=17^2

CD^2= 17^2-10^2

CD^2=289-100

CD^2=189

CD=

[tex] \sqrt{189} [/tex]

What is the median of the data displayed in the box and whisker plot?

Answers

Answer:

The median is the middle number in a you box/whisker plot. The median is sometimes used as opposed to the mean when there are outliers in the sequence that might skew the average of the values

Step-by-step explanation:

The median is "the middle number" in short...

ex: 1,5,8,9,8648

the middle number would be 8

Brainliest plz

Answer:

median is where the middle line in the box is

Step-by-step explanation:

someone please help asap !

Answers

Answer:

Step-by-step explanation:

2w-4=10

2w=14

w=7

(2y-5)+67+48=180

2y-5+115=180

2y+110=180

2y=70

y=35

2x+17=(2y-5)

2x+17=(2*35-5)

2x+17=(70-5)

2x+17=65

2x=48

x=24

z=48, since angle BIG is congruent to angle RAC

Which figure has a greater volume and by how much?
3 cm
3 cm
5 cm
5 cm
8 cm
6 cm
15 cm
15 cm
Figure 1
Figure 2
The volume of figure 1 is 45 cm greater than the volume of figure 2.
The volume of figure 2 is 45 cm greater than the volume of figure 1.
The volume of fioure 1 is 10mg areater than the volume of figure 2

Answers

Answer:

Step-by-step explanation:

The volume of figure 1 is 45 cm greater than the volume of figure 2.

The volume of figure 2 is 45 cm greater than the volume of figure 1.

The volume of fioure 1 is 10mg areater than the volume of figure 2

Find last​ year's salary​ if, after a 4 % pay​ raise, this​ year's salary is $ 33,280.

Answers

Answer:

32000

Step-by-step explanation:

1.04x=33280

32000

I need help asap pls help me

Answers

Answer:

36 ft

Step-by-step explanation:

The first step is to find the length of the hypotenuse of the newly formed right triangle. Using the Pythagorean theorem:

[tex]x=\sqrt{10^2+24^2}=\sqrt{100+576}=\sqrt{676}=26[/tex]

Adding this to the 10 foot tall part of the tree that remains standing, you get an initial height of 26+10=36 feet. Hope this helps!

Another question worth brainliest and 30 points!
But give me correct answers and i’ll give it to u

Write 18 in lowest terms
30

A. 3/10
B. 3/5
C. 4/5
D. 6/10

Answers

Answer:

B. 3/5

Step-by-step explanation:

I actually dont know how to explain srry

Answer: B; 3/5

Step-by-step explanation: There are multiple different ways for solving this. We could guess and check, convert into a decimal, and/or percentage. Just to keep things simple, I will be converting these to decimals.

First, 18/30=.6

Now we have to convert the following multiple choice into decimals to find out which is equivalent.

3/10=.3 --> This is not .6 so this is incorrect

3/5=---->.6, so this is one choice we could pick

4/5--->.8, so this is incorrect

6/10---> which is also .6, so this option qualifies.

But then, in the question it states the lowest terms. So your answer would be 3/5.

hope this helps

-Carrie

P.S. be sure to mark BRAINLIEST

Solve d = rt if r = 46 and t = 5

Answers

Hey!!

r=46

t=5

now,

D=RT

= 46*5

=230

the value of d is 230

hope it helps..

Answer:

230 is the answer

Step-by-step explanation:

Since r and t are given in the question as

r=46 and t=5

Substitute the value of r and t which is given in the polynomial

So it'll be,

d=rt

d = 46 x 5

= 230

Therefore d is 230 units

Hope this helps!

P
L
Z

H
E
L
P

M
E
!
!
!

Answers

Answer:

slope = - 4

Step-by-step explanation:

Calculate the slope m using the slope formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = - 1, 22) and (x₂, y₂ ) = (1, 14) ← 2 ordered pairs from the table

m = [tex]\frac{14-22}{1-(-1)}[/tex] = [tex]\frac{-8}{2}[/tex] = - 4

How should the decimal point in 6.8 be moved to determine the product of 6.8
and 100?
()) two places to the left
1)) three places to the right
<)) three places to the left
()) two places to the right

Answers

The answer is two places to the right. For every 0 you move the decimal one place. And since the 100 is positive you move the decimal to the right.

The correct answer is two places to the right

The following information should be considered:

For each and every 0 you have to move the decimal one place. And since the 100 is positive you move the decimal to the right.

Learn more: https://brainly.com/question/17429689?referrer=searchResults

According to the water surface area rule, a fish tank can be
stocked with one inch of fish for each twelve square inches of
surface area. The fish that you are interested in putting in your
fish tank are each 2 inches. Your fish tank has a surface area of
576 square inches. According to the water surface area rule,
what is the maximum number of fish you can put in your tank?

Answers

Answer:

24 fishes

Step-by-step explanation:

If for 1 inch of fish corresponds 12 square inches of  surface area, then for 2 inches correspond 24 square inches. Given that each fish is 2 inches, then for 1 fish 24 square inches of  surface area is needed. To know how many fish you can put in your tank, we need to solve the following proportion:

1 fish / x fish = 24 square inches / 576 square inches

x = 576/24

x = 24 fishes

PLEASE HELP! WILL MARK THE FIRST CORRECT ANSWER BRAINLIEST!
There are n gallons of gas in a tank. After x gallons have been used, in terms of n and x, what percent of the gas has not been used?

Answers

Answer:

((n-x)/n)*100

Step-by-step explanation:

The Answer is:

((n-x)/n)100

the diameter of a circle is 5 ft. Find the circumference TO THE NEAREST TENTH

Answers

Answer:

15.7

Step-by-step explanation:

3.14(5)

is a diameter of circle O. If m∠ACB = 30°, what is m∠DBA? A. 30° B. 50° C. 60° D. 70° E. 90°

Answers

Every triangle equals 180 degrees, and we're trying to find the angle of DBA. So, we can identify DAB as a 90 degree angle to start. Then we can identify that ACB = ADB, meaning ADB is 30 degrees. With that information, we have this equation:

DBA = 180 - 90 - 30

DBA = 60

The measure of the angle ∠DBA will be 60°. Then the correct option is C.

What is a circle?

It is the close curve of an equidistant point drawn from the center. The radius of a circle is the distance between the center and the circumference.

The diagram is given below.

BD is the diameter of circle O. If m∠ACB = 30°.

We know that the central angle is double the angle at the periphery that was subtended by the same chords.

∠AOB = 2∠ACB

∠AOB = 2 x 30

∠AOB = 60°

We know that the triangle AOB is an equilateral triangle, in which each angle will be 60°.

Thus, the measure of the angle ∠DBA will be 60°.

Then the correct option is C.

More about the circle link is given below.

https://brainly.com/question/11833983

#SPJ2

In a far-off land three fish can be traded for two loaves of bread and a loaf of bread can be traded for four bags of rice. How many bags of rice is one fish worth?

Answers

2.5 bags of rice are worth one fish

Answer:

One fish can be traded for 2 2/3 bags of rice.

Step-by-step explanation:

Key:

F = One fish

L = Loaf of bread

R = Bag of rice

So, with that set we see that:

3F = 2L & L = 4R

2L for 2 x 4 = 8R

So,

3F = 8R OR 3:8 OR 8/3

8/3 = 2 2/3, which is the answer.

a right triangle has a leg of 3 feet and hypotenuse of 4 feet. what is the length of the other leg? enter your answer, as a decimal rounded to the nearest tenth, in the box?

Answers

Answer: 2.6

Step-by-step explanation:

a^2 + b^2 = c^2

3^2 + b^2 = 4^2

9 + b^2 = 16

b^2 = 7

b = 2.6

Answer:

√7 = 2.6

Step-by-step explanation:

a²+b²=c²

9+b²=16

b²=7

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