Given that K is the midpoint of segments RM and JL, and prove Δ RKJ ≅ Δ MKL.


Statements
Reasons
1. K is the midpoint of segments RM and JL
1. Given
2.
2.
3. and
3.
4. RK = MK and JK = LK
4. Definition of Congruent Segments
5. Δ EGF ≅ Δ EGH
5.


What is Reason #3?
a
Given
b
Definition of Midpoint
c
CPCTC
d
SSS Congruence Postulate

To solve this we must be knowing each and every concept related to probability and its calculations. Therefore, the  probability of tossing heads is 0.000976.

Probability is the branch of mathematics concerned with the outcomes of random occurrences. Probability refers to the chance or potential of an outcome. It describes the likelihood of a specific occurrence occurring.

Probability denotes the possibility of something happening. It is a statistical discipline that deals only with probability of such a random event. The number ranges from 0 to 1, with 0 being an improbable event and 1 representing a certain event.

P(getting heads on one toss) = 1/2

P(getting all heads in 10 tosses)=(1/2)¹⁰

                                                     =1/1024

                                                   =0.000976

Therefore, the  probability of tossing heads is 0.000976.

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Answer:

Volume (V) = 2522.0 mm^3

Step-by-step explanation:

The volume of cylinder is :

V = π r 2 h

We know that the height (h) is 19.

We also know the radius (r) is 13/2 = 6.5

So,

V = π 6.5^2*19

V = 2522.0 mm^3

The builder should buy x meters of $20/m fence for the front side and 3x + 2y meters of $10/m fence for the other three sides.

To minimize the cost of the fence, the builder needs to use the least expensive type of fence for the three sides of the land that are not the front. Since the fence along the front of the land costs $20 per meter and the fence for the other three sides costs $10 per meter, the builder should use the $10 per meter fence for the other three sides.

To find out how much of each type of fence the builder needs to buy, we need to determine the total length of the three sides that are not the front. Since the land is a rectangular shape, we can use the formula for the perimeter of a rectangle:

Perimeter = 2(length) + 2(width)

Let's assume the length of the front side is x and the width of the land is y, the perimeter of the land is:

2x + 2y = 60,000

To find out the total length of the three sides that are not the front, we need to subtract the length of the front side from the perimeter of the land:

60,000 - x = 3x + 2y

The total length of the three sides that are not the front is 3x + 2y.

Now we can calculate how much the builder will pay for each type of fence:

Total cost of the fence = $20x + $30x + $20y = $50x + $20y

To minimize the cost, the builder should choose the values of x and y that minimize the total cost of the fence. To do this, the builder should set the derivative of the total cost function with respect to x and y and then set them equal to zero and solve for x and y.

However, in this case, we can simply see that the total cost is minimized by using the $10/m fence for the other three sides and using the $20/m fence only for the front side. Therefore, the builder should buy:

This way, the builder minimizes the cost of the fence and ensures that the security of the land is maintained.

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Answer: A, B, C.

If the stack of cards are shifted so it is not straight, it still has everything the same.

Answer:

It would be triangles A & C

Step-by-step explanation:

This is because all of the angles within triangle add up to 180, with this, you can do the following to find the missing sides:

Tri A:

180-110-30 = 40

Tri B:

180-45-30 = 105

Tri C:

180-110-40 = 30

When you do this, look at the angles of the triangles. You see that Triangle A with the angles 110, 30, and 40 all match with those seen in Triangle C.

Therefore, the two triangles are congruent.

Answer:

1.5

Step-by-step explanation:

a : b = 1 : 12/5

Area of a circle = πr²

Where : = π = pi = 22/7

R = radius  

Let the radius of circle a = 1

Area of circle A = 1π

Radius of circle A = square root of 12/5 = 1.5

The circumference of a circle = 2nr

n = 3.14

circumference of circle A = 2 x n x 1 = 2n

circumference of circle B = 2 x n x 1.5 = 3n

ratio of circumference = 3n / 2n = 1.5

Answer:

Very last choice is the answer.

Step-by-step explanation:

Remark

The thing that is most important is that the horizontal line connect h and the radius is parallel to the cut of the sphere if it was placed right in the middle. That line swings around as though the center was a pivot.

Solution

Answer:

0

Step-by-step explanation:

Given:  3.4% of Americans are vegetarian.

sample size  = 36 people

Therefore, 3.4% of 36 = 1.224.

Hence, out of 36 people only 1.224 people which is approximately 1 is vegetarian.

So, the probability of exactly 4 people being vegetarian out of 36 people would be zero.

As out of 36 only 1 was vegetarian.

Hence, the correct answer would be 0

Answer:

Sum means '+'

is means '='

a number means 'x'

3x + 6 = 8

I hope this helped!

No, triangle ABC is not a right triangle. The equation of a line BC "y=x-11" is a line with slope of 1, which means it has an angle of 45 degrees with respect to the x-axis. The segment AB has a slope of 0, which means it is parallel to the x-axis. A right triangle's legs must be perpendicular, therefore a line with a slope of 1 and a line with a slope of 0 cannot be the legs of a right triangle.

A right triangle is a triangle in which one of the angles is 90 degrees. In order for a triangle to be a right triangle, the two sides (or legs) that form the 90-degree angle must be perpendicular to each other. Perpendicular lines have slopes that are negative reciprocals of each other.

In this case, the equation of the line segment AB is "y = -6", which means it is parallel to the x-axis. The slope of a line parallel to the x-axis is 0. On the other hand, the equation of the line BC is "y = x - 11", which means it has a slope of 1. A slope of 1 means that the line is at a 45 degree angle with respect to the x-axis.

Since the slopes of the two lines are not negative reciprocals of each other (0 and 1), the legs of the triangle cannot be perpendicular. Therefore, triangle ABC cannot be a right triangle.

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Answer:

20x + 10

Step-by-step explanation:

Given that :

Number of $20 bill = x

Number of $10 bill = 1

Total amount of money can be expressed as :

Σ(Value of bill * number of bill)

Hence,

($20 * x) + ($10 * 1)

20x + 10

The expression for the amount of money Donald has is : 20x + 10

For the polynomial p(x) = -3x² - 4x + 10, the degree is 2 and the leading coefficient is -3

Polynomials consist of exponents of variables and numbers forming an equation using operations of addition and subtraction.

Polynomial is an expression composed of variables, constants and exponents combined using mathematical operations such as addition, subtraction, multiplication

Given the polynomial:

p(x) = -3x² + 10 - 4x

Rewriting the polynomial in standard form is done by rearranging based on exponents. Hence:

p(x) = -3x² - 4x + 10

The degree is 2 (x²) and the leading coefficient is -3(-3x²)

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Answer:

h = 4 ft

Step-by-step explanation:

the area (A) of a parallelogram is calculated as

A = bh ( b is the base and h the perpendicular height )

here b = 8 and h = 3 , then

A = 8 × 3 = 24 ft²

Now consider the other base b = 6 with perpendicular height h , then

6h = 24 ( divide both sides by 6 )

h = 4

Answer:

483000

Step-by-step explanation:

To write a linear expression in standard form, rearrange the terms in alphabetical order.

Answer:

48300000

We can write the above number as

4.83 x 10000000

=4.83 x 10 ^7

Answer:

x = 11.2

Step-by-step explanation:

[tex]\frac{6.4}{x}[/tex] = [tex]\frac{4}{7}[/tex]

4x = 44.8

x = 11.2

The temperature at midnight as required to ve determined in the task content is; 14°C.

According to the task content; the temperature was 11.2°C at 2 : 00am.

However, since the temperature dropped 1.4 °c each hour; we have that;

In the two hours between midnight and 2:00am, the total temperature drop is; 2 × 1.4°C = 2.8°C.

On this note, the temperature at midnight can be evaluated as; 11.2°C + 2.8°C = 14°C.

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Answer: C

Step-by-step explanation:

Based on the graph, we know that it is negative if it is under the x-axis. It is also indicated by the negative labels.

A: incorrect

Looking at choice A, it says the interval is from -3<x<-2. This means we have to find x=-3 and x=-2. On the graph, that interval is above the x-axis, so it is positive, not negative.

B: incorrect

Looking at choice B, it says the interval is from 2<x<3. This means we have to find x=2 and x=3. On the graph, that interval is above the x-axis, so it is positive, not negative.

C: correct

Looking at choice C, it says the interval is from 4<x<5. This means we have to find x=4 and x=5. On the graph, that interval is under the x-axis, so it is negative.

Therefore, C is the correct answer.

The equation 3x - 9 = 0 has 3 as a solution out of all the given equations in the options.

Check the solution of equation 3x - 9 = 0

3x - 9 = 0

3x = 9

x = 3

Check the solution of equation 4x - 3 = 0

4x - 3 = 0

4x = 3

x = 3/4

Check the solution of equation 5x - 10 = 0

5x - 10 = 0

5x = 10

x = 10/5

x = 2

Check the solution of equation 7x - 49 = 0

7x - 49 = 0

7x = 49

x = 49/7

x = 7

Thus, only 3x - 9 = 0 satisfy the solution x = 3.

Hence, the correct option is A.

--The given question is incomplete, the complete question is

''Which equation has 3 as a solution set?

A. 3x - 9 = 0

B. 4x - 3 = 0

C. 5x - 10 = 0

D. 7x - 49 = 0''--

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Answer:

12.

Step-by-step explanation:

right!!

Answer:

Integer - 72

Decimal - 72.3

Answer:

.here is the answer ............

Step-by-step explanation:

hope it is helpful to you

The Ball Rolls Downhill, It's Kinetic Energy Increases And It's Potential Energy Maximum.

Hope Helps! :)

[tex] \: \: [/tex]

Answer:

2,302,63

Step-by-step explanation:

................

Answer:

942.50

Step-by-step explanation:

First, multiply 2334.50 by 3 to get 7003.50. Then multiply 1437x3= 4311

7003.50-4311=2692.50 Then take away 1750. 2692.50-1750=942.50

I hope this helps! UWU

Answer:

x = -1

y = -1

Step-by-step explanation:

This is a system of equations- the set up of the problem lends well to using the elimination method. There are always many ways of solving a system of equations, both in methods and different strategies within each method. The problem isn't necessarily complete but I can assume you're being asked to solve for x and y values.

divide the first equation by -2. this means we can use elimination to cancel out the y value, and is also our simplest option (rather than multiplying the second equation by -2.

-2x + 20y = -18 --> x - 10y = 9

x - 10y = 9

8x + 10y = -18

Using the elimination method to essentially add the parts of the equations together, this comes out to 9x = -9 , meaning x = -1 .

We can then return to our original equations, and substitute -1 for x (either equation will work, but the second one is simpler and therefore the better option).

8 (-1) +10y = -18

-8 + 10y = -18

10y = -10

y = -1

CHECKING

Substitute both x and y values back into the original equations to check them. the sides should be equal if our values are correct.

-2 (-1) + 20 (-1) = -18

Our first equation works: 2 - 20 = -18

8 (-1) + 10 (-1) = -18

The second equation works as well: -8-10= -18

Answer:

c = 100 or 10^2

d = 3125 or 5^5

Step-by-step explanation:

c. the answer for C is 10^2 because you just subtract the exponents same goes for d.

Answer:

1. 219.571428571

2. 150.314285714

Answer:

WO = 10

NE = 90

NT = 42

Step-by-step explanation:

scale factor of 6

Answer:

3/22

Step-by-step explanation:

There's a very neat trick for this kind of problem.

First, choose a letter to represent the number.

n = 0.1363636...

Observe that there is a 2-digit block that repeats ("36"), but that block does not repeat immediately to the right of the decimal point.  Do two muliplications, one to put the decimal point in front of the repeating block, the other to put the decimal point after the block.

    10n =    1.363636...

1000n = 136.363636...

Here comes the cool part:  subtract the first equation from the second.

990 n = 135  See? The repeating decimal parts, all lined up as they are, subtract to zeros.

Finally, n = 135/990 = 15/110 = 3/22

To prove that ΔABC is isosceles.

An isosceles triangle is a type of triangle in which the length of its two sides, and measure of its two internal angles are equal. When a bisector of an angle is drawn to one of the internal angles of the triangle, two congruent triangles of corresponding properties are produced.

To prove that ΔABC is isosceles, we have:

<CAD ≅ <BAD                             (definition of an angle bisector)

CD ≅ BD                                      (definition of a midpoint)

AC ≅ AB                                      (congruent sides of an isosceles)

<ACD ≅ <ABD                             (congruent internal angles of an isosceles)

<ADC ≅ <ADB                             (definition of right angle)

Therefore it can be concluded that;

ΔABC is an isosceles triangle    (Angle-Side-Side theorem)

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