Suppose a triangle has sides a, b, and c, and that a2 + b2 > c2. Let 0/ be the
measure of the angle opposite the side of length c. Which of the following
must be true? Check all that apply.
A. 0/ is an acute angle.

B. cos 0/ > 0

C. The triangle is a right triangle.

D. The triangle is not a right triangle.

Suppose A Triangle Has Sides A, B, And C, And That A2 + B2 > C2. Let 0/ Be Themeasure Of The Angle

Answers

Answer 1

Hello,

Answer A

Indeed:

[tex]c^2=c^2+b^2-2ab*cos(\theta) < a^2+b^2\\\\-cos(\theta)<0\\\\cos(\theta)>0\ \Longrightarrow \theta < 90^o[/tex]

Answer 2

True statements are:

A.  [tex]\theta[/tex] is an acute angle.

C. The triangle is a right triangle.

D. The triangle is not a right triangle.

What is angle?

An angle is a combination of two rays (half-lines) with a common endpoint.

Given:

a² + b² > c²

as, the triangle with sides a, b and c.

If this is a right triangle, then the condition a² + b² > c² apply.

Using cosine law.

angle> 90 degrees which is an obtuse angle.

Also, cos [tex]\theta[/tex] is negative.

Hence, the conditions that are true are A, C and D.

Learn more about this concept here:

https://brainly.com/question/1619127

#SPJ2


Related Questions

7x-3=5x+9 solve for x​

Answers

Given :-

7x - 3 = 5x + 9

To Find :-

The value of x.

Solution :-

Taking the given equation ,

=> 7x -3 = 5x + 9

=> 7x - 5x = 9 + 3

=> 2x = 12

=> x = 12 ÷ 2

=> x = 6

Hence the required answer is 2 .

8.a. Simplify: 10a+46-(3a+2b)​

Answers

The answer is 7a+46-2b

10a+46-(3a+2b)

= 10a + 46 - 3a - 2b

= 7a - 2b + 46

A car with a passenger of mass 56 kg can travel a distance of 120 km using 10 l of petrol. If the number of passengers increases to 4 people with a total mass of 224 kg, the distance travelled decreases by 10%.
What is the total distance that the car carrying 4 passengers can travel using 10 l of petrol?​

Answers

Answer:

120 * 0.90 = 108 km

Step-by-step explanation:

Answer:

108km

Step-by-step explanation:

Please help due incredibly soon!!!!

Answers

Answer:

The surface area is 116.

Step-by-step explanation:

In triangle XYZ. the measurements of angle X and angle Y are 45° Which is the longest side of the triangle

Answers

Answer:

the side XY

Step-by-step explanation:

we know 2 angles in a triangle. but are 45 degrees.

that means the third angle Z is 180-45-45 = 90 degrees.

the side opposite of the largest angle is the longest side.

opposite of Z is the side XY.

Write a pair of integers whose sum gives: a) a negative integer
b) zero
c) an integer smaller than the both integers

Answers

Answer:

a) 4-5 = -1

b) -6+6 = 0

c) 6+(-4) = 2

A standard deck of cards contains 52 cards. Of these cards there are 13 of each type of suit (hearts, spades, clubs, diamonds) and 4 of each type of rank (A – K). Two cards are drawn from the deck and replaced each time back into the deck. What is the probability of drawing the King of Clubs and a heart from the deck of cards?

Answers

Answer: 13%

Step-by-step explanation:

What would this be helpppp

Answers

Answer:

The last answer choice, or [-15 14  4a]

                                             [-4 5b -23]

                                             [  ?   ?   ?  ]

Step-by-step explanation:

In order to subtract matrices, they have to have the same dimensions, which this problem provides(both 3x3) Then, just subtract the numbers on the right from the corresponding numbers on the left. Example: -3-12=-15, which is the top left answer. Repeat with all positions.

If 260 people donated $10.00 to an organization how much money would said organization have received in total?

Answers

Answer:

$ 2,600

Step-by-step explanation:

It's given that 260 People donated $10 is to an organisation . We need to find the total money received by the organisation .

Here we just need to the number of people with the amount each person gave , that is ;

[tex]\implies \rm Total \ amount = \$ 10 \times 260 \\\\\rm\implies Total \ amount = \$ 2,600 [/tex]

Hence the total money received by the organisation is $ 2600 .

Find the inverse of the function y = x2 – 12

Answers

Answer: [tex]y=\sqrt{x+12}[/tex]

Step-by-step explanation:

I hope you mean y = x² - 12 and not y = 2x - 12.

You switch the y and x variables:

x = y² - 12

And solve for y:

x + 12 = y²

[tex]y=\sqrt{x+12}[/tex]

A unit of gas costs 4.2 pence on averge ria uses 50.1 units of gas a week she pays for the gas she uses in 13 weeks work out an estimsate for the amount ria pays

Answers

Answer:

Step-by-step explanation:

Cost per unit of gas = 4.2 pence

Average units of gas used per week = 50.1 units

Total cost of gas per week = Cost per unit of gas × Average units of gas used per week

= 4.2 pence × 50.1

= 210.42 pence

= £ 2.1042

Amount ria pays for gas for 13 weeks = cost of gas per week × number of weeks

= 210.42 pence × 13

= 2,735.46 pence

2,735.46 pence = £ 27.3546

Find the measure of the indicated angle

Answers

Answer:

[tex]AB=AC\:(given)[/tex]

∠B=∠C

[tex]x=70^{o}[/tex]

-------------------------------

HOPE IT HELPS

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find the measure of the complementary angles that satisfy each case. the measure of the first angle is 30 greater than the measure of the second angle

Answers

Answer:

First angle: 60°

Second angle: 30°

Step-by-step explanation:

Let the two angles be signified by the variables x & y.

Let the first angle = x, and the second angle = y.

It is given that:

"The measure[ments] of the complementary angles...": x + y = 90°

"The measure of the first angle is 30 greater than the measure of the second angle": x = y + 30°

Use the system of equations. Plug in y + 30 for x in the first equation:

(y + 30) + y = 90

Combine like terms:

(y + y) + 30 = 90

2y + 30 = 90

Isolate the variable, y. Note the equal sign, what you do to one side, you do to the other. Do the opposite of PEMDAS. First, subtract 30 from both sides of the equation:

2y + 30 (-30) = 90 (-30)

2y = 90 - 30

2y = 60

Next, divide 2 from both sides of the equation:

(2y)/2 = (60)/2

y = 60/2

y = 30°

Plug in 30 for y in one of the equations:

x = y + 30

x = (30) + 30

x = 60°

Your answers:

First angle: 60°

Second angle: 30°

Can someone help me with this math homework please!

Answers

Answer:

The first one is X=4

the second one is 5n - 300= 1,500

Step-by-step explanation:

Find the mean and the MAD. [Note: Type your answers as decimal numbers, rounded to the nearest tenth.] 135, 160, 145, 155, 170, 150, 142

Answers

Answer:

Mean = 151

MAD = 9.14

Step-by-step explanation:

Given the data:

135, 160, 145, 155, 170, 150, 142

Mean = Σx / n

Mean = 1057 / 7

Mean = 151

Mean absolute DEVIATION (MAD) : Σ(x - μ) / n

[(135-151) + (160-151) + (145-151) + (155-151) + (170-151) + (150-151) + (142-151)] / 7

Mean absolute deviation = 9.14

A line passes through the points (-1, -1)
and (5,8). Which points lie on the same
line? Select all that apply.
(-3, -4)
(9, 14)
(1, 2)
(4, 7)
(3,5)
(-2,-2)

Answers

Given:

A line passes through the points (-1, -1) and (5,8).

To find:

Which points lie on the same line?

Solution:

If a line passes through two points, then the equation of the line is:

[tex]y-y_1=\dfrac{y_2-y_1}{x_2-x_1}(x-x_1)[/tex]

A line passes through the points (-1, -1) and (5,8). So, the equation of the line is:

[tex]y-(-1)=\dfrac{8-(-1)}{5-(-1)}(x-(-1))[/tex]

[tex]y+1=\dfrac{8+1}{5+1}(x+1)[/tex]

[tex]y+1=\dfrac{9}{6}(x+1)[/tex]

[tex]y+1=\dfrac{3}{2}(x+1)[/tex]

Multiply both sides by 2.

[tex]2(y+1)=3(x+1)[/tex]

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

[tex]2y=3x+3-2[/tex]

[tex]y=\dfrac{3}{2}x+\dfrac{1}{2}[/tex]

So, the equation of the line is [tex]y=\dfrac{3}{2}x+\dfrac{1}{2}[/tex].

Now, check each point for this equation.

Putting [tex]x=-3[/tex], we get

[tex]y=\dfrac{3}{2}(-3)+\dfrac{1}{2}[/tex]

[tex]y=\dfrac{-9+1}{2}[/tex]

[tex]y=\dfrac{-8}{2}[/tex]

[tex]y=-4[/tex]

Similarly,

For [tex]x=9,y=15[/tex].

For [tex]x=1,y=2[/tex].

For [tex]x=4,y=6.5[/tex].

For [tex]x=3,y=5[/tex].

For [tex]x=-2,y=-2.5[/tex].

Therefore, the points (-3,-4), (9,14), (1,2) and (3,5) lie on the same line but the points (4,7) and (-2,-2) are not on that line.

One number is 9 times another. Their product is 27 times their sum. Find the numbers.


the answer is not 3 btw

Answers

Answer:

270 & 30

Step-by-step explanation:

let the number is n,

the equation :

n× 1/9 n= 27(n +1/9 n)

1/9 n² = 27n + 3n

1/9 n² = 30n

1/9n²- 30n = 0

n(1/9n -30)= 0

n = 0 or

1/9n = 30 => n = 30×9 = 270

270 is a number,

the other : 270/9 = 30

Identify the ethical issue(s) in each experiment. Beginning in the 1940s, the Department of Medicine at the University of Chicago tested anti-malaria medications on inmates at the Stateville Penitentiary. Inmates readily volunteered, as their parole would be reviewed upon completion of their sentence. Inmates who participated in the study reported that they were informed of the risks involved in participating in the study, including the possibility of death.
In the 1960s, Stanley Milgram studied the willingness of subjects to obey an authority figure, even at the risk of being harmed. The subjects believed they were taking part in a study on learning. They were assigned to the role of teacher and were ordered to administer electrical shocks with increasing voltage to the learner whenever the learner made an error. The learner was an actor who remained unharmed. The subjects were not initially told that it was a study of obedience, as this might affect the outcome, and they were not prepared for possible psychological distress.
In the 1950s and 60s, Saul Krugman infected mentally disabled children enrolled at the Willowbrook State School in New York with hepatitis in order to better understand how the disease spread and how it could be combatted. Parents agreed to enroll their children in the study in exchange for admission to the school.

Answers

Full question attached

Answer:

1. Subjects were not aware of the purpose of the experiment.

2. Subjects were not aware of all potential risks.

Subjects were not aware of the purpose of the experiment.

3. Subjects were coerced into participating

Explanation:

Ethics are the moral principles and codes that guide our daily decisions and actions. Ethical issues in conducting experiments or research aim at protecting the dignity of subjects or participants in the research. Major ethical issues in conducting research include: Respect for anonymity and confidentiality, beneficence(should not harm participants), and informed consent(independently volunteers after clear comprehensive information on research).

1. Experiment violates informed consent as participants were not aware of the purpose of research.

2. Experiment violates informed consent and beneficence as participants weren't fully informed and faced the risk of being harmed.

3. Experiment violates beneficence and informed consent as participants faced the risk of being harmed and did not independently volunteer for the research.

Evaluate the expression. 24.32

Answers

2^4×3^2 = 144

___________

Answer:

144 would be the answer.

Step-by-step explanation:

Question:- [tex]2^{4}[/tex] · [tex]3^{2}[/tex]

[tex]2^{4}[/tex] = 2 x 2 x 2 x 2

   = 4 x 2 x 2

   = 8 x 2

   = 16

[tex]3^{2}[/tex] = 3 x 3

   = 9

So, [tex]2^{4}[/tex] · [tex]3^{2}[/tex] = 16 x 19

              = 144

Self Practice 5.3
1. Find the sum of the following arithmetic progression.

(a) -20, -15, -10, ..., 100

Answers

Answer:

5

Step-by-step explanation:

Have a phd in mathematics! Congrats on your first question!!!! Send me a brainlist :)

5 times the complement of an angle is 15 more than two times the supplement of the angle. Find the angle,
the complement, and the supplement.

Answers

Answer:

The angle measures 25°; the complement measures 65°; the supplement measures 155°.

Step-by-step explanation:

The sum of the measures of two complementary angles is 90.

If the angles measure x and y, then x + y = 90.

Given angle x, then y = 90 - x.

The sum of the measures of two supplementary angles is 180.

If the angles measure x and y, then x + y = 180.

Given angle x, then y = 180 - x.

Let the angle be x.

Its complement is 90 - x.

Its supplement is 180 - x.

5(90 - x) = 2(180 - x) + 15

450 - 5x = 360 - 2x + 15

-3x = -75

Angle: x = 25

Complement: 90 - x = 90 - 25 = 65

Supplement: 180 - x = 180 - 25 = 155

Answer: The angle measures 25°.;, the complement measures 65°; the supplement measures 155°.

1. The diagram shows a semicircle OABC. If the arc AB has length 3.2 cm, calculate (a) the length of the radius, (b) the length of the arc BC. r 0.8 rad С o r A​

Answers

Step-by-step explanation:

— If the arc AB has length 3.2 cm, calculate (a) the length of the radius, (b) ... the length of the radius, (b) the length of the arc BC. r 0.8 rad С o r A .

The following system of equations represents the total distance a flight from point A to point B flies based on its initial, I, and return, R, journey speeds, as well as the total time in the air for the round trip. Determine the amount of time each leg of the journey takes.
120I+200R=2000
I+R=15

10 hours, 5 hours
12 hours, 20 hours
12.5 hours, 2.5 hours
No Solution

Answers

Answer:

ewan ask mo kay ma'am para alam mo po

Simplify:

-4a + 2(a + 9)

A. -2a + 9
B. -2a + 18
C. 2a + 9
D. 2a + 18

Answers

Answer:

B. - 2a + 18

Step-by-step explanation:

- 4a + 2( a + 9 )

= - 4a + 2a + 18

= - 2a + 18

Answer:

B

Step-by-step explanation:

got it right on edge :))

look at the image for the question and answers​

Answers

Answer:

C

Step-by-step explanation:

Answer:

2 units

Step-by-step explanation:

Using the given formula

P = 2(l + w)

  = 2([tex]\frac{2}{3}[/tex] + [tex]\frac{1}{3}[/tex] )

   = 2(1)

   = 2 units

Someone help me please!!!

Answers

yes the answer to this is 1/5

CAN SOMEONE PLEASE HELP ME!!

Answers

Answer:

29.8

Step-by-step explanation:

a^2+b^2=c^2

a^2+7^2=11^2

a = h = 8.5

A= 1/2*b*h

A= 1/2*8.5*7

A=29.8

Division method of 298116 using short Division method​

Answers

Answer:

I think you are being asked to evaluate the square root of 298116 by division method. Here is how its done:

546

51298116

125

104 81 10416

10861 0 0 6516 1006516

Please feel free to ask if something is not clear.

Here are the steps you will need to follow:

Step 1:

We find the largest square smaller than 29, that's 25. Subtract the 25 from the 29, which leaves 4, and enter a 5 as the first digit of your quotient.

Step 2:

104

What are equivalent expressions please explain

Answers

Answer:

Equivalent expressions are expressions that are the same, even though they may look a little different. If you plug in the same variable value into equivalent expressions, they will each give you the same value when you simplify.

Step-by-step explanation:

I you borrow 500 for 4 years at an annual interest rate of 6% HOW MUCH WILL YOU PAY altogether ​

Answers

Answer:

620

amount= p+i , to find interest .I=500*4*6/100 =120 amount=500+120=620

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