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.
Answers
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]
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.
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Related Questions
Which of the statements proves that the lines a and b are parallel?
Answers
Answer:
C
Step-by-step explanation:
1,2 are both supplementary
Please help timed question (question included in photo). I'll mark as brainiest!
Answers
Answer:
Step-by-step explanation:
This is a right triangle trig problem. Picture a right triangle. The height of the triangle is the height of the lighthouse, your distance from the base of the lighthouse is what we are solving for, and the reference angle is 2 degrees, which is the angle of inclination from where you stand to the top of this lighthouse. We have the reference angle, the side opposite the reference angle, and we are looking for the side adjacent to the reference angle. This is the tangent ratio: the side opposite the reference angle over the side adjacent to the reference angle. We know the measure of the reference angle and we know the value of the side opposite the reference angle. Filling in:
[tex]tan(2)=\frac{200}{x}[/tex] and
[tex]x=\frac{200}{tan(2)}[/tex] so
x = 5727.25 feet, the third choice down
Answer:
[tex]tan2=200/x[/tex] [tex]x=200/tan2[/tex]
[tex]x=5,727.25[/tex]
------------------------
hope it helps..
have a great day!!
What is the median of the data set given below?
19, 22, 46, 24, 37, 16, 19,33
A. 24
B. 23
C, 19
D. 27
Answers
Answer:
B. 23
Step-by-step explanation:
16, 19, 19, 22, 24, 33, 37, 46
Median = n/2
= 8/2
= 4//
(22 + 24)÷2 = 46 ÷ 2
= 23
How do I write
(28/4) - (x+7) in written form?
Answers
Answer: The quotient of 28 and 4 minus the sum of a number and 7
Step-by-step explanation:
Prove that the value of the expression: (3^5 - 3^4)(3^3 + 3^2) is divisible by 24. Answer format: The value of the expression is 24 • __
Answers
Step-by-step explanation:
(3^5 - 3^4) (3^3 + 3^2)
= (243 - 81) (27 + 9)
= (162) (36)
= 5832
24 = 8*3
since 832 is divisible by 8 and 5+8+3+2 = 18 is divisible by 3
5832 is therefore divisible by 24
check:
5832/24 = 243
If x + 10 = 70, what is x?
Answers
Answer:
x=60
Step-by-step explanation:
First, you subtract 10 from both sides. Your final answer is 60.
What is
the vertex of this
absolute value
function?
Answers
Answer:
C
Step-by-step explanation:
The vertex is the point where the 2 lines meet on the V shape
The vertex is at (3, 2 ) → C
Answer:
Option c is the answer I think so if the answer is correct plz mark me as brainliest
PLEASE ANSWER CORRECTLY FOR BRAINLIEST:
25.
26.
27.
29.
Answers
Answer:
x = 6
Step-by-step explanation:
5 (x - 3) + 2 = 5 (2x - 8) - 3
remove the parenteses
5x - 15 + 2 = 10x - 40 - 3
calculate5x - 13 = 10x - 43
move the terms5x - 10x = -43 + 13
collect like terms calculate-5x = -30
divide both sidesSolution
x = 6
check all that apply. if cos0 = 13/5, then: ?
Answers
Answer:
D
Step-by-step explanation:
if cosec is 13/5 then sin is 5/13
A cubical water tank can contain 1000/125 cubic meters of water. Find the length of a side of the water tank.
Answers
Given:
Volume of cubical tank = [tex]\dfrac{1000}{125}[/tex] cubic meters.
To find:
The length of a side of the water tank.
Solution:
The volume of a cubical tank is:
[tex]V=a^3[/tex]
Where, a is the side length.
It is given that the volume of cubical tank is [tex]\dfrac{1000}{125}[/tex] cubic meters. So,
[tex]a^3=\dfrac{1000}{125}[/tex]
[tex]a^3=\dfrac{(10)^3}{5^3}[/tex]
Taking cube root on both sides, we get
[tex]a=\dfrac{10}{5}[/tex]
[tex]a=2[/tex]
Therefore, the length of a side of the water tank is 2 meters.
the diameter of circle Q is 14 cm. Find the arc length of PR.
Answers
Answer:
4.15, or 1.32pi
Step-by-step explanation:
arclength is circumference(34/360)
so pi x d (34/360)
3.14 x 14 x (34/360) = 4.15, or 1.32pi
The arc length PR is 4.151 cm.
What is a circle?A circle is a closed, two-dimensional object where every point in the plane is equally spaced from a central point. The line of reflection symmetry is formed by all lines that traverse the circle. Moreover, every angle has rotational symmetry around the centre.A section of a line that runs from a circle's centre to any point on the circle itself. "R" or "r" stand for the circle's radius.
As per the given data:
The diameter of circle Q = 14 cm
From the given diagram:
∠PQR = 34°
For finding out the arc length PR:
arc length = angle in radian × radius
radius = diameter / 2 = 14 / 2 = 7 cm
angle in radian = 34° × (π / 180°) = 0.593 radians
arc length PR = 0.593 × 7 = 4.151 cm
Hence, the arc length PR is 4.151 cm.
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work out 1 2/3 x 1 1/5
pls give the full answer with working out
{NOTE:the 2/3 and the 1/5 are fractions and the 1's are the whole numbers}
Answers
Answer:
5/3*1/5= 1/3
Step-by-step explanation:
change the mixed fraction into improper fraction which is 1*3+2=5
then multiply
A can of cashews mixed with almonds costs $24.60. Cashews cost $4.25//lb and almonds cost $3.80/lb. There are twice as many cashews as almonds in the can. How many pounds of each type are in the can?
Answers
Answer: 2 and 4 lb
Step-by-step explanation:
Given
There are twice as many cashews as almonds in the can
Cashews costs [tex]\$4.25\ lb[/tex]
Almonds costs [tex]\$3.80\ lb[/tex]
Can costs $24.60
Suppose there are x lb almonds, so there is 2x lb cashews
[tex]\Rightarrow (2x)4.25+x\cdot 3.80=24.60\\\Rightarrow 8.5x+3.8x=24.60\\\Rightarrow 12.3x=24.60\\\Rightarrow x=2\ lb[/tex]
Amount of cashews =4 lb
Amount of almonds =2 lb
Express your answer as a decimal (to the nearest hundredth).
What part of an hour is 20 minutes?
0.25
0 0.375
0.50
0.33
Answers
Answer:
0.33
Step-by-step explanation:
An hour is 60 minutes. 20 goes into 60 three times, so it is 1/3 of an hour or 0.333333333333, etc. As a percent, 20 minutes is 33.33%. Converted to a decimal, it is 0.33 or 1/3 of an hour
Daisy is trying to find the equation
of a linear function. Based on the
graph, she can tell the line goes
through (2, 20) and (3, 28). What is
the y-intercept?
Answers
Answer:
Your answer is (0,4)
Step-by-step explanation:
write the expression that represents the phrase: the quotient of 10 and x
Answers
Answer:
Step-by-step explanation:
[tex]Quotient \ of \ 10 \ and \ x = 10 \div x[/tex]
(-6)^-1 multiply by x = 27^-1. find x
Answers
to get rid of a negative exponent, you use the reciprocal of the number.
so (-6)^-1 would be 1/-6
27^-1 would be 1/27
rewrite is as
(1/-6)x = 1/27
multiply both sides by reciprocal or 1/-6 to cancel it and make x by itself
it’s would be x = 1/27(-6)
multiply
x = -6/27
simplify
the final answer is x=-2/9
In a deck of 52 playing cards, what is the probability, as a fraction, of drawing a picture card (A, K, Q, and J) that is also a diamond then a card numbered 2-9?
Answers
Answer:
4.8%
if we assume that the first card is REPLACED (otherwise the formula gets complex)
[tex](\frac{4}{52} )(\frac{32}{52} ) = \frac{8}{169} = .048[/tex]
Step-by-step explanation:
13/52 is the probability, as a fraction, of drawing a picture card (A, K, Q, and J) that is also a diamond then a card numbered 2-9
What is Probability?It is a branch of mathematics that deals with the occurrence of a random event.
Given,
In a deck of 52 playing cards
We need to find the probability, as a fraction, of drawing a picture card (A, K, Q, and J) that is also a diamond then a card numbered 2-9
n(S) =52
And the probability, as a fraction, of drawing a picture card (A, K, Q, and J) that is also a diamond then a card numbered 2-9 is,
n(E) =13 a set of a diamond suit, because a diamond suit has {A, K ,Q ,J ,2,..,9}
Thus, the probability, as a fraction, of drawing a picture card (A, K, Q, and J) that is also a diamond then a card numbered 2-9 is 13/52 or 1/4 .
Hence, 13/52 is the probability, as a fraction, of drawing a picture card (A, K, Q, and J) that is also a diamond then a card numbered 2-9
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I NEED THE ANSWER ASAP PLZ ;C
Answers
The top right quadrant is quadrant 1.
The top left quadrant is quadrant 2.
The bottom left quadrant is quadrant 3.
The bottom right quadrant is quadrant 4.
Therefore, point D is in the fourth quadrant.
I need help ASAP !!!!
Answers
Answer:
{-4,2,6,9}
Step-by-step explanation:
Mathematically, the domain refers to the possible x-values
what this mean in the relation view are the values listed in the left ellipse
So we have the domain as;
{-4,2,6,9}
Can someone help me please?!!!!
Answers
Answer: meh
Meh
Step-by-step explanation:
What should you substitute for y in the bottom equation to solve the system by the substitution method?
A. y=3x+15
B. y =-x-5
C. y=x+5
D. y=-3-15
Answers
Step 1: Determine which equation to change
Since we will be using the substitution method, we will need to substitute y from the bottom equation with information from the top equation. This will be the equation we change.
Step 2: Change the equation
Let’s rewrite the equation we will be working with.
3x+3y= -15
Our goal will be to get y alone on the left side. To start, let’s subtract 3x from both sides, leaving only 3y on the left side.
3x+3y= -15
3y= -3x-15
Now we need to get y completely alone by eliminating the coefficient of 3. Let’s do this by dividing each term by 3.
3y= -3x-15
y= -x-5
This is your answer. Hope this helps! Comment below for more questions.
Find the values of x and y.
Answers
Answer:
x=14
y=24
Step-by-step explanation:
4y+42=8y-54
4y-8y=54-42
-4y/4=96/-4
y=24
solving for x
5x-28=7x-56
5x-7x=-56+28
-2x/-2=-28/-2
x=14
Simplify this expression:
-(x+2)+4
i have no idea im not good with math ;(
Answers
ANSWER :
- ( x+ 2 ) + 4
-x - 2 + 4
-x + 2
Answer:
−x+2
Step-by-step explanation:
-(x+2)+4 Distribute the negative sign (-) outside of the parenthesis with x and 2 and that will turn into -x-2+4.
Add -2 and 4 and that will turn into -x+2.
Tegan is checking her tax bill for the last year.
The tax rates were as follows:
• No tax on the first £11 000 of earnings
• Earnings in excess of £11 000 and up to £43 000 taxed at a rate of 20%
• Earnings in excess of £43000 and up to £150 000 taxed at a rate of 40%
• Earnings over £150 000 taxed at a rate of 45%
Last year, Tegan earned £48 300 before tax.
How much tax did she pay in total?
Answers
Answer:
£8520
43000-11000=32000
20/100×32000
£6400
48300-43000=5300
40/100×5300=2120
£8520
Rewrite the sentences below to make them more concise. During that time period, many car buyers preferred cars that were pink in color and shiny in appearance.
Answers
Answer:
Pink, shiny cars were preferred by buyers at that time
Step-by-step explanation:
Rewriting the sentence, removing unnecessary words
Write down five numbers so that:the mean is 6,the median is 5 and the mode is 4
Answers
Answer:
4 , 4 , 5 , 6 , 11
Step-by-step explanation:
Mode = 4
So at least two times 4 should be there in the data.
And median is 5. So the middle term ( 3rd term} should 5.
Let x and y be the 4th term and 5th term
Data set:
4 , 4 , 5 , x , y
Mean =6
[tex]\frac{4+4+5+x+y}{5}=6\\[/tex]
4+4+5 +x + y = 6*5
13 + x + y = 30
x + y = 30 - 13
x + y = 17
x ,y can be any numbers that sum up to 17.
x , y can be 10 , 7 or 6, 11
Data set: 4 , 4 , 5 , 6, 11
Fifth grade students from Garden City Elementary School left for a field trip at the time shown on the clock.(6:54am) They returned from the field trip at 10:24 p.M. How long were the students on this field trip?
Answers
Answer:
15 hour(s) and 30 minute(s).
Step-by-step explanation:
Answer:
krkrkrl4k3?8999kekek
Step-by-step explanation:
the UK. I have been a while. I have been a while. I have been a while. I have been a while 6e5 the UK. I have been a while. I have been a while. I have
. How do we have a look at the moment. The comments for the first time in the UK. I
A metal smith is mixing two molten metals
Answers
Answer:
I think the answer is going to be A (15)(0.75) and 0.7(15 – x) + 0.9x, I hope this helps!! :)
Step-by-step explanation:
1
What is the value of x in the equation x - y = 30, when y = 152
200
Answers
[tex]\displaystyle\bf 1) \ if\ y=152 \Longrightarrow x=30+152=182 \\\\2) \ if \ y =200 \Longrightarrow x=200+30=230\\\\3) \ if \ y=80 \Longrightarrow x=30+80=110\\\\4) \ if \ y=4 \Longrightarrow x=4+30=34 \\\\5)\ if \ y=8 \Longrightarrow x=30+8=38[/tex]