Which postulate proves these two triangles are congruent ?

Which Postulate Proves These Two Triangles Are Congruent ?

Answers

Answer 1

Answer:

HL

Step-by-step explanation:

HL is used for right triangles that are congruent. These two triangles are congruent(the same) and they happen to be right triangles, therefore, HL.

Answer 2

The postulate that proves the triangle are congruent is hypotenuse-leg (HL) congruency theorem.

Here, we have,

A triangle is a polygon that has three angles and three sides. The sum of angles in a triangle is 180 degrees.

Types of triangles are isosceles, scalene and equilateral triangles.

Two angles are said to be complementary if their sum is 90 degrees.

Two triangles are said to be congruent if all their corresponding sides and angles are congruent.

This means that the triangles have equal angles and equal sides.

here, we have,

HL is used for right triangles that are congruent.

These two triangles are congruent(the same) and they happen to be right triangles, therefore, HL.

The postulate that proves the triangle are congruent is hypotenuse-leg (HL) congruency theorem.

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Related Questions

8y - 6(3y - 7) what is this simplified?

Answers

Answer:

-10y+42.

Step-by-step explanation:

Distribute.

8y-18y+42

-10y+42

:D I hope this helped you!

Answer:

-10y + 42 would be the answer

What is the answer to the blank?


5% x __ = 3.5

Answers

Answer:

5/100• X = 3.5

X=3.5÷5/100

X=70

The answer is 5% x 70 = 3.5

To solve for the blank in the equation 5% x __ = 3.5, we need to find a number that, when multiplied by 5%, equals 3.5.

First, express 5% as a decimal: 5% = 0.05.

Set up the equation:

0.05 x x = 3.5

Next, solve for x by dividing both sides by 0.05:

x = 3.5 / 0.05

x = 70

Thus, the blank should be filled with 70.

kimi is playing hide-and-seek with Tommy and Manuel. Tommy is hiding 12 feet south of Kimi, and Manuel is hiding due east of Tommy. If Kimi is 20 feet from Manuel, how far apart are Tommy and Manuel?

Answers

Answer:

Tommy and Manuel are 16 ft apart

Step-by-step explanation:

The locations of all three players are shown in the image below

They form a right triangle where the hypotenuse is 20 ft, and one of the legs is 12 ft. We must find the other leg.

We must use Pythagoras's theorem. Being a and b the legs of a right triangle and c its hypotenuse, then

[tex]c^2=a^2+b^2[/tex]

Knowing c and one of the legs, say b:

[tex]a^2=c^2-b^2[/tex]

Using the values c=20, b=12 we find

[tex]a^2=20^2-12^2=400-144=256[/tex]

[tex]a=\sqrt{256}=16[/tex]

So, Tommy and Manuel are 16 ft apart

Using a new app I just downloaded, I want to cut back on my calorie intake so that I can lose weight. I currently weigh 90 kilograms; my plan is to lose 1.2 kilograms a week until I reach my goal. How can I make an equation to model my weight loss for the next several weeks?

Answers

Answer:

[tex]W_{f}  = 90 - 1.2w[/tex]

Step-by-step explanation:

I want to cut back on my calorie intake so that I can lose weight.

I plan to lose 1.2 kg a week from my current weigh 90 kg until I reach my goal.

Therefore, I can model my weight loss for the next several weeks by the equation  

[tex]W_{f}  = 90 - 1.2w[/tex]  

where [tex]W_{f}[/tex] is my final weight after w weeks of treatment. (Answer)

Final answer:

To model your weight loss, you can create a linear equation using your current weight as the starting point, and representing your weekly weight loss as a negative rate of change. The equation W(t) = 90 - 1.2t will allow you to predict your future weight based on this rate of weight loss.

Explanation:

To develop an equation to model your weight loss, you need to translate the information about your weight loss goals into mathematical terms. You mentioned that your current weight is 90 kilograms and you plan to lose 1.2 kilograms per week.

Imagining that each week is a step forward in time, we can say time is represented by the variable 't' in weeks. Likewise, your weight, which will change as time increases, can be represented by 'w' in kilograms.

Giving weight loss a negative sign (since you are losing, not gaining weight), the amount of weight you will lose per week is -1.2 kilograms. When we start, at time t = 0, your weight is 90 kilograms. So we could represent your weight as a function of time with the equation W(t) = 90 - 1.2t.

In this equation, simply substitute 't' for the number of weeks to predict your weight loss. For example, if you want to find out your weight after 3 weeks, you would calculate W(3) = 90 - 1.2 * 3 = 86.4 kilograms. This is a simplified model and actual weight loss may vary due to factors like metabolic rate, type of food ingested and the amount of calories burned per day.

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What is perform multiplication with -3(-3+2)-6

Answers

Answer:

-3

Step-by-step explanation:

We must do the subtraction -3 + 2 BEFORE anything else, because any operations inside parenthesis always take first priority.

We end up with:

-3(-1) - 6.  

We must multiply before addiing or subtracting.  Therefore, multiply (-3)(-1), obtaining 3 and complete result 3 - 6.

Finally do that subtraction; the result is -3.

Mr. Westnoticed grapes were priced at $2.99 per pound, and bananas were priced at $0.99 per pound. How much would 3 pounds of grapes and 2 pounds bananas cost altogether?
A.$3.98
B.$9.96
C.$10.95
D.$2.96

Answers

This is the answer, hope I wasn’t late

A movie theater has a seating capacity of 383. The theater charges $5.00 for children, $7.00 for students, and $12.00 of
adults. There are half as many adults as there are children. If the total ticket sales was $ 2778, How many children,
students, and adults attended?

Answers

194 children, 92 students, and 97 adults attended

Step-by-step explanation:

The given is:

A movie theater has a seating capacity of 383The theater charges $5 for children, $7 for students, and $12 for adultsThere are half as many adults as there are childrenThe total ticket sales was $ 2778

We need to find how many children,

students, and adults attended

Assume that x represents the number of children, y represents the number of students, and z represents the number of adults

∵ There were x children, y students and z adult attended

∵ The movie theater has a seating capacity of 383

x + y + z = 383 ⇒ (1)

∵ The theater charges $5 for children, $7 for students, and

   $12 for adults

∵ The total ticket sales was $2778

5x + 7y + 12z = 2778 ⇒ (2)

∵ There are half as many adults as there are children

- Half means 0.5

z = 0.5x ⇒ (3)

Substitute equation (3) in equations (1) and (2)

∵ x + y + 0.5x = 383

- Add like terms

1.5x + y = 383 ⇒ (4)

∵ 5x + 7y + 12(0.5x) = 2778

∴ 5x + 7y + 6x = 2778

- Add like terms

11x + 7y = 2778 ⇒ (5)

Let us solve equations (4) and (5) to find x and y

Multiply equation (4) by -7 to eliminate y

-10.5x - 7y = -2681 ⇒ (6)

- Add equations (5) and (6)

∴ 0.5x = 97

- Divide both sides by 0.5

x = 194

Substitute the value of x in equations (4) and (3) to find y and z

∵ 1.5(194) + y = 383

∴ 291 + y = 383

- Subtract 291 from both sides

y = 92

∵ z = 0.5 (194)

z = 97

194 children, 92 students, and 97 adults attended

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Which company offers the best deal?

Rent-All, A-1 Rentals, or Car Town

Answers

Answer:

A-1 Rentals

hopefully that helps!!

Answer:

rent all

Step-by-step explanation:

The chance that a positive response is obtained from Chicago fro program 1 is %. The chance that a positive response is obtained from Chicago for program 2 is %.

Answers

Answer:

 The chance that positive response obtained for program 1 is 65.90

And  The chance that positive response obtained for program 2 is 87.50  

Step-by-step explanation:

Given data as :

The positive response for program of different cities in percentage

Now, The positive response is obtained from Chicago for program 1 is 65.90

The total positive response for program 1 in % = 68.80

So, The chance that positive response obtained = 65.90

Again ,

The positive response is obtained from Chicago for program 2 is 87.50

The total positive response for program 1 in % = 81.70

So, The chance that positive response obtained = 87.50

Hence   The chance that positive response obtained for program 1 is 65.90

And  The chance that positive response obtained for program 2 is 87.50  answer

what is the answer/ how do i answer
25 = x + 7

Answers

just subtract 7 from 25. it is 18

Answer:

answer should be x = 18.

Step-by-step explanation:

25 = x + 7

we can also write it as

x + 7 = 25

as we see 7 is positive(+) on LHS( left hand side) so if we move it to RHS( right hand side) the sign will change so the equation will be:

x = 25 - 7

now just simplify it:

x = 18.

The difference between two numbers is 53. Five times the smaller is equal to 3 more than larger. What are the numbers?

Answers

First, let's assign two variables: one for the bigger one, and one for the smaller one. The smaller number will be represented as 's,' and the bigger one will be 'b.'

Since their difference is 53, we can make an equation:
b - s = 53

Since 5 times the smaller is equal to 3 times the bigger, we can make one more equation:
5s = 3b

We can divide both sides by 5 to simplify this equation:
s = 3b/5

Input this value of 's' into our first equation:
b - (3b/5) = 53

In order to get rid of that pesky denominator, multiply everything by 5:
5b - 3b = 265
2b = 265

b = 132.5
Input this into our first equation to find the smaller number:
s = (3*132.5)/5
s = 79.5

The two numbers are 132.5 and 79.5
-T.B.

How much did Elizabeth invest?

Answers

Yeah, I think it is C...

I don't really have an explanation though.

If I'm wrong, correct me. Hope I helped! ☺☼

Answer:

Option D is the nearest answer.

Elizabeth invested = $45,714

Step-by-step explanation:

Given that:

Total amount = $80,000

Ratio given = 3:4

As the total is divided into 7 parts (3+4) so,

Each part equals = 80,000/7

Each part equals = 11,428.57

Now steive invested = 11,428.57 * 3 = $34,286

Elizabeth invested= 11,428.57*4 = $45,714

i hope it will help you

A rectangle is 15 ft longer than it is wide it’s area is 1000ft2 what are it’s dimensions

Answers

The dimension of the rectangle is 25 by 40

Let :

width = x length = x + 15

Area of rectangle = x * (x + 15)

1000 = x² + 15x

x² + 15x - 1000 = 0

solving the quadratic equation

x(x - 25) +40(x - 25)

x = 25 or x = -40

The width cannot be negative.

Hence,

width = 25 Length = 25 + 15 = 40

Therefore, the dimension of the rectangle is 25 by 40

What is the cube root of b27?
ооо

Answers

Answer:

b⁹

Step-by-step explanation:

[tex]\sqrt[3]{b^{27}}=\sqrt[3]{b^{(9)(3)}}\qquad\text{use}\ (a^n)^m=a^{nm}\\\\=\sqrt[3]{(b^9)^3}\qquad\text{use}\ \sqrt[n]{a^n}=a\\\\=b^9[/tex]

Answer:

b^9 :)

Step-by-step explanation:

Solve this system of linear equations. Separate
the x- and y-values with a comma.
7x - 3y = 37
14x + 11y = 23
Enter the correct answer.​

Answers

Answer:

The solution for the given system of equations is ( 4,-3).

Step-by-step explanation:

Here, the given set of equations is:

7 x - 3 y = 37    ....  (1)

14 x + 11 y = 23   .... (2)

Now, we solve this equation by ELIMINATION METHOD,

Multiply the first given equation with ( -2), we get:

(-2) [7 x - 3 y = 37 ] ⇒   -14 x + 6 y = -74  .... (3)

Adding equation (2) and (3), we get:

14 x + 11 y  +   -14 x + 6 y  = 23 -74

or, 17 y = - 51

or, y = -51/17 = 3

y = -3

Now, out the value of y in the given second equation,we get:

14 x + 11 (-3)  = 23

or, 14 x  = 23 + 33 = 56

or, x =  56/14 =  4

x = 4

Hence, the solution for the given system of equations is ( 4,-3).

What is the measure of the apothem

Answers

Answer:

The apothem is also the radius of the incircle of the polygon. For a polygon of n sides, there are n possible apothems, all the same length of course. The word apothem can refer to the line itself, or the length of that line. So you can correctly say 'draw the apothem' and 'the apothem is 4cm'.

Final answer:

To find the apothem in geometry, one must utilize trigonometry, knowing the polygon's side length. In astronomy, calculating distances such as the semi-major axis involves understanding celestial mechanics and requires knowing the aphelion and perihelion distances. The problem content combines concepts from geometry and astronomy to discuss angles and distances.

Explanation:

Calculating the Measure of the Apothem

When attempting to find the measure of the apothem of a geometric figure, you're essentially looking for a segment that connects the center of the figure to the midpoint of one of its sides and is perpendicular to that side. This is especially common in regular polygons. However, this particular problem seems to blend geometry and astronomy, discussing the apparent width of the Moon and comparing it using similar triangles.

To calculate the apothem in a regular polygon, you can use trigonometry if you know the length of one of the sides and the number of sides. On the other hand, if the setting involves celestial bodies like the moon and planets, determining an apothem-like distance would involve understanding the object's orbit, size, and distance from the observer.

To compute the semi-major axis of an elliptical orbit, like that of a planet around a sun, you would use the sum of the aphelion and perihelion, divided by two. For instance, if we know the perihelion (rp) and aphelion (ra), we calculate the semi-major axis (a) as (ra + rp)/2.

Remember, an angle is used in astronomy to measure the apparent separation between celestial objects as seen from Earth. Astronomers use degrees to describe these angles, and knowing the angular size can help in estimating distances in space.

To find the aphelion or semi-major axis of an orbit, certain equations are used that involve these distances. Such calculations are essential for understanding celestial mechanics and the movement of objects in our solar system.

What is the equation of a line in slope intercept form that passes through the points (-4,3) and (-2,4)

Answers

First find slope.

slope=change in y/change in x (y2-y1/x2-x1)

slope=4-3/-2-(-4)=1/2

Now we need to find the x intercept.

y=mx+b

3=1/2(-4)+b

b=5

So the equation is y=1/2x+5.

How do you turn 85 into 9.2

Answers

Answer:

Divide 85 by 9.24

Step-by-step explanation:

Only 6. Please and thanks

Answers

Answer:

Part a) [tex]7.536\ m[/tex]

Part b) [tex]\$34.14[/tex]

Step-by-step explanation:

Part 6)

a) How much edging is needed?

we know that

To find out how much edging is needed determine the circumference of the circular garden

The circumference of the circular garden is equal to

[tex]C=\pi D[/tex]

where

D is the diameter

we have

[tex]D=2.4\ m[/tex]

assume

[tex]\pi =3.14[/tex]

substitute

[tex]C=(3.14)(2.4)[/tex]

[tex]C=7.536\ m[/tex]

Part b) we know that

To find out the cost to edge the garden, multiply the length of edging plastic needed by the cost of $4.53 per meter

so

[tex](7.536\ m)(4.53\ \$/m)=\$34.14[/tex]

I am doing a math problem and i need help. Could you please find the missing fraction?
5/2 - ? = 1/3

Answers

Answer:

?=13/6

Step-by-step explanation:

5/2-?+?=1/3+?

5/2-1/3=?

?=15/6-2/6=13/6

Answer:

13/6???

Step-by-step explanation:

I turned 5/2 into 15/6 and 1/3 into 2/6. I multiplied both their numerators and denomonators by 3. I then subtracted the two numbers and got 13/6.

Use the ALEKS calculator to write 14/15 as a decimal rounded to the nearest tenth.

Answers

Answer:from calculator

0.9333333333

Answer: 3.3

Step-by-step explanation:

49 divided by 15 =3.26

Rounding 3.26 to the nearest tenth gives you 3.3

which fraction is larger 29/71 or 42/100

Answers

Answer:

42/100

The drawings will help

Answer:

42/100

Step-by-step explanation:

Just looking at the fraction, you could guess that one of the fractions is larger. So my guess would be the first one, but I'm guessing which really is only a guess. I like to guess at things like this; it's a little like playing monopoly. Let's find out what the answer really is. So get out your calculator.

29/71: 29 ÷ 71 = 0.4085

42/100: 42/100 = 0.4200

Well if you guessed the second one you are a better guesser than I am

42/100  is larger that 29/71

0.6 + 0.2x = -0.48
.60
What is the answer

Answers

Answer:

x=-5.4

Step-by-step explanation:

0.6+0.2x=-0.48

0.2x=-0.48-0.6

0.2x=-1.08

x=-1.08/0.2

x=-5.4

What is 16.5% of 33?

Answers

Answer:

5.445

Step-by-step explanation:

[tex]\bold{METHOD\ 1:}\\\\p\%=\dfrac{p}{100}\to16.5\%=\dfrac{16.5}{100}=\dfrac{16.5\cdot10}{100\cdot10}=\dfrac{165}{1000}=\dfrac{33}{200}\\\\16.5\%\ of\ 33=\dfrac{33}{200}\cdot33=\dfrac{1089}{200}=5.445[/tex]

[tex]\bold{METHOD\ 2:}\\\\\begin{array}{ccc}100\%&-&33\\\\16.5\%&-&x\end{array}\qquad\text{cross multiply}\\\\\\100x=(16.5)(33)\\\\100x=544.5\qquad\text{divide both sides by 100}\\\\x=\dfrac{544.5}{100}\\\\x=5.445[/tex]

A ladder is resting against a wall. The top of the ladder touches the wall at a height of 12 feet. Find the length of the ladder if the length is 4 feet more than its distance from the wall.

Answers

Answer:

I believe the answer is 48

Step-by-step explanation:

- 4(5a - 3b) simplified is?

Answers

Answer:

-20a+12b

Step-by-step explanation:

Answer:

-20a+12b

Step-by-step explanation:

-4(5a-3b)=-20a+12b

i need answers for 1 and 2

Answers

Answer:

c = 10 , d = 26

Step-by-step explanation:

In the rectangular prism, we know the fact that the three faces are mutually perpendicular to each other. So, it has a rectangular base.

Given, the length and breadth of the rectangle are 8 and 6 units, and the diagonal is c.

Since it is a rectangle, length , breadth and diagonal from a right angled triangle.

So we have, c² = 6² + 8² = 36 + 64 = 100

⇒           c = 10 units

For the side face:

Length = 24 units.

As we can see, the edge of the side face is perpendicular to the base of the prism. Which means, any line on the base of the prism is perpendicular to the 24units side edge.

So we can say that , the diagonal of the rectangular base of the prism (c) is perpendicular to the 24 units side face edge.

Hence, 24 , d and c (which is 10units) form a right angled triangle

From pythagoras theorem:

   d² = 24² + 10² = 576 + 100 = 676

d = 26 units

The cost to take a car across a bay on a ferry is $16.00. The ferry has a capacity of 42cars. The revenue collected is a function of the number of cars, c . R()=16 Use the drop-down menus to complete the statements below about the domain of this function.

Answers

The domain of this function is first restricted to all nonnegative integers because the ferry can carry only a whole number number of cars.

The domain is restricted to number less than or equal to 42  because the ferry cannot carry more cars than capacity .

Final answer:

The domain of this function is the set of non-negative integers.

Explanation:

The domain of a function represents the set of possible input values for that function. In this case, the function represents the revenue collected by the ferry, which depends on the number of cars. The number of cars, denoted as c, must be a non-negative integer because the ferry cannot transport a fraction of a car. Therefore, the domain of this function is the set of non-negative integers, or {0, 1, 2, 3, ...}.



Solve this problem on paper using all four steps.

Ted weighs twice as much as Julie. Mike weighs three times as much as Julie. Together, Ted, Mike, and Julie weigh 210 lbs. What is the weight of each person?

Julie weighs pounds, Ted weighs pounds, and Mike weighs pounds.

Answers

Answer:

Julie weighs 35 lbs, Ted weighs 70 lbs, Mike weighs 105 lbs.

Step-by-step explanation:

Let the weight of Julie be [tex]x[/tex]

Given:

Ted weighs twice as much as Julie

Weight of Ted = [tex]2x[/tex]

Mike weighs three times as much as Julie.

Weight of Mike = [tex]3x[/tex]

Together, Ted, Mike, and Julie weigh 210 lbs.

[tex]x+2x+3x=210[/tex]

Solving above we get;

[tex]6x=210\\x=\frac{210}{6}=35\ lbs[/tex]

Hence Julie weight is 35 lbs.

Weight of Ted = [tex]2x=2\times 35 = 70 \ lbs[/tex]

Hence Ted weight is 70 lbs.

Weight of Mike = [tex]3x=3\times 35 = 105 \ lbs[/tex]

Hence Mike weight is 105 lbs.

Answer:

Julie weighs 35 lbs, Ted weighs 70 lbs, Mike weighs 105 lbs.

I hope this helps you

I am horrible at math plz help

Answers

The answer is B I believe, because the parallelogram b is half parallelogram a and is reflected across the y axis, NOT the x.

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In fact its impact on wages will probably be negligible, since only a very small proportion of all Kirlandic workers are currently receiving less than KD5.50 per hour.Which of the following, if true, most seriously weakens the argument?(A) Most people in Kirlandia who are currently earning the minimum wage have been employed at their current jobs for less than a year(B) Some firms in Kirlandia have paid workers considerably less than KD5.00 per hour, in violation of kirlandic employment regulation(C) Many businesses hire trainees at or near the minimum wage but must reward trained workers by keeping their pay levels above the pay level of trainees.(D) The greatest growth in Kirlandia's economy in recent years has been in those sectors where workers earn wages that tend to be much higher than the minimum wage.(E) The current minimum wage is insufficient for a worker holding only one job to earn enough to support a family, even when working full time at that job. A survey is taken among customers of a fast-food restaurant to determine preference for hamburger or chicken. Of 200 respondents selected, 75 were children and 125 were adults. 120 preferred hamburger and 80 preferred chickens. 55 of the children preferred hamburger and 20 preferred chickens. Set up a 2x2 contingency table using this information and answer the following questions:FoodAge Hamburger Chicken TotalChild 55 20 75Adult 65 60 125Total 120 80 200a) What is the probability that a randomly selected individual is an adult?b) What is the probability that a randomly selected individual is a child and prefers chicken?c) Given the person is a child, what is the probability that this child prefers a hamburger?d) Assume we know that a person has ordered chicken, what is the probability that this individual is an adult? Consolidated Power, a large electric power utility, has just built a modern nuclear power plant. This plant discharges waste water that is allowed to flow into the Atlantic Ocean. The Environmental Protection Agency (EPA) has ordered that the waste water may not be excessively warm so that thermal pollution of the marine environment near the plant can be avoided. Because of this order, the waste water is allowed to cool in specially constructed ponds and is then released into the ocean. This cooling system works properly if the mean temperature of waste water discharged is 60F or cooler. Consolidated Power is required to monitor the temperature of the waste water. A sample of 100 temperature readings will be obtained each day, and if the sample results cast a substantial amount of doubt on the hypothesis that the cooling system is working properly (the mean temperature of waste water discharged is 60F or cooler), then the plant must be shut down and appropriate actions must be taken to correct the problem.(a)Consolidated Power wishes to set up a hypothesis test so that the power plant will be shut down when the null hypothesis is rejected. Set up the null hypothesis H0 and the alternative hypothesis Ha that should be used.H0: (select) 60 versus Ha: (select) 60.(b)Suppose that Consolidated Power decides to use a level of significance of = .05 and suppose a random sample of 100 temperature readings is obtained. If the sample mean of the 100 temperature readings is formula310.mml = 61.498, test H0 versus Ha and determine whether the power plant should be shut down and the cooling system repaired. Perform the hypothesis test by using a critical value and a p-value. Assume = 6. (Round your z to 2 decimal places and p-value to 4 decimal places.)z =p-value =(Select: Reject or Do not reject) H0. So the plant (Select: Should or Should not) shut down and the cooling system repaired. North Company has other operating expenses of $360,000. There has been a decrease in prepaid expenses of $16,000 during the year, and accrued liabilities are $24,000 larger than in the prior period. Using the direct method of reporting cash flows from operating activities, what were North's cash payments for operating expenses?