Which is the length of the hypotenuse for a right triangle with leg a = 8 and leg b = 15 cm?
Answers
Answer:
[tex] \huge{ \boxed{ \tt{17 \: cm}}}[/tex]
Option D is the correct choice.
☪ First , Let's know about right triangle , legs and hypotenuse :
A right triangle is a triangle with an angle of 90°.The two sides that form the right angle are called legs.The opposite side of right angle is the hypotenuse.☥ Let's explore about The Pythagorean Theorem :
Pythagoras was one of the first mathematician to recognize the relationship between the sides of a right triangle. This special relationship forms ' The Pythagorean Theorem '.The Pythagorean theorem states that the sum of the squares of the legs of a right triangle equals the square of the length of a hypotenuse. In algebraic terms , The Pythagorean Theorem is stated as : [tex] \boxed{ \sf{ {a}^{2} + {b}^{2} = {c}^{2} }}[/tex]------------------------------------------------------------
☯ Now , let's start to solve :
✑ [tex] \underline{ \underline{ \text{Given}}} : [/tex]
a = 8 cm , b = 15 cm✑ [tex] \underline{ \underline{ \text{To\: Find}}} : [/tex]
Length of a hypotenuse ( c )✐ [tex] \underline{ \bold{ \underline{Using \: Pythagorean \: Theorem}}} \: : [/tex]
☞ [tex] \boxed{ \bold{ \sf{ {a}^{2} + {b}^{2} = {c}^{2} }}}[/tex]
Substitute the known values :
↦ [tex] \sf{ {8}^{2} + {15}^{2} = {c}^{2}}[/tex]
↦ [tex] \sf{64 + 225 = {c}^{2} }[/tex]
↦ [tex] \sf{289 = {c}^{2} }[/tex]
↦ [tex] \sf{ {c}^{2} = 289 }[/tex]
Take the square roots of both sides :
↦ [tex] \sf{ \sqrt{ {c}^{2} } = \sqrt{289}} [/tex]
↦ [tex] \boxed{ \sf{c = 17 \: cm}}[/tex]
The length of the hypotenuse is [tex] \boxed{ \bold{ \text{17 \: cm}}}[/tex].
And we're done!!
Hope I helped!
Have a wonderful day ! ツ
~TheAnimeGirl ♡
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Answer:
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Step-by-step explanation:
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Answer:
Step-by-step explanation:
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one side of a parallelogram has endpoints (3, 3) and (1, 7). what are the endpoints for the side opposite? (8, 1) and (6, 5) (6, 1) and (8, 5) (8, 1) and (6, 7) (6, 1) and (2, 3)
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The endpoints of the opposite side of the parallelogram are (8, 1) and (6, 5).
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Using the given exponential function, determine the growth/decay factor as well as the rate of increase/decrease. Type your answers in as numbers. Example: Growth Factor: 3.5, Rate of Increase: 2.5. (Do not input your rate of increase as a percent. If there are fractions, you can input your answer as a fraction. i.e. - 4/5, or 1/10)
f(x)=200(4/5)^x
Answers
Answer:
Growth rate is -1/5
Growth factor is 4/5
Step-by-step explanation:
Here, we want to get the growth rate and the growth factor
Generally for an exponential function given as;
y = a(1 + r)^n
r is the growth rate
1 + r is the growth factor
We can express the given exponential function as follows;
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using these two points, (3, 6) and (4, 9); what is the slope?
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EXPLANATION:
y2-y1
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Help me out pls? Namjesus will bless.
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Answer:
y = 44
Step-by-step explanation:
Slopes of parallel lines are equal.
P(15, 7)
Q(20, 14)
[tex]m_{PQ}[/tex] = [tex]\frac{14-7}{20-15}[/tex] = [tex]\frac{7}{5}[/tex]
G(3, 2)
F(33, y)
[tex]m_{PQ}[/tex] = [tex]m_{GF}[/tex] = [tex]\frac{y-2}{33-3}[/tex] = [tex]\frac{7}{5}[/tex]
5(y - 2) = 7(30)
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Someone please help me with 16-18 please it’s due in 30 mins
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9514 1404 393
Answer:
16. 134°
17. 20°
18. 94°
Step-by-step explanation:
An inscribed angle is half the measure of the arc it intercepts.
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16. Arc QT is twice the measure of inscribed angle QST, given as 67°.
Arc QT = 2×67°
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17. Angle STR is half the measure of arc SR, so is ...
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m∠STR = 20°
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arc ST = 180° -40° = 140°
Angle RST subtends a semicircle, so is 180°/2 = 90°. We know angle QST is 67°, so the remaining portion, angle QSR must be the complement of that:
m∠QSR = 90° -67° = 23°
Arc RQ will be twice this measure, or 46°.
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Use index notation when giving your answer.
Answers
Answer:
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Step-by-step explanation:
Here are the first several prime numbers: 2, 3, 5, 7, 11, 13, 17, 19, 23
To find the prime factorization of a number, start by dividing the number by the smallest prime number it is divisible by. Keep dividing by that prime number until you can't anymore. You only divide by prime numbers that divide evenly. Then move on to the next prime number that divides evenly, and do the same. You eventually will get to 1. Then you put together all the prime factors.
This is much easier to do than it sounds like in this explanation.
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Step-by-step explanation:
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Step-by-step explanation:
Answer:
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Step-by-step explanation:
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Answer:
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Step-by-step explanation:
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Answer:
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Step-by-step explanation:
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Answer:
x = 3 is the solution
Step-by-step explanation:
3x + 4 = 5x - 2
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Answer:
3x +4= 5x-2
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9+4= 15-2 (do the multiplication on both sides)
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Step-by-step explanation:
good right solve it and rate my answer
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If sea level = 0, write an integer that represents 25 feet below sea level.
Answers
Answer: -25
Step-by-step explanation:
The required integer that shows that 25 feet below the sea level is -25.
Given that,
To determine the in integer that represents 25 feet below sea level.
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The sea level is set to equal to 0,
Now height above the seal level comprises of positive sign, and the height below the sea level comprises of negative sign.
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PLEASE HELP!!!
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Answers
Answer:
14. y= 3/5x-2
15. y= -1x-2
17. -1/2
Step-by-step explanation:
Since you have a point and a slope put it in point-slope form first.
Point-slope form: y-y1=m(x-x1)
Then solve for y.
Then you'll get the slope-intercept form.
For number 17 use the slope-intercept form y=mx+b
rise/run= m= y2-y1/x2-x1
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O 3 cm
O 4 cm
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Answers
Answer:
The length from the external point to the center of the circle is 5 cm
Step-by-step explanation:
Here, we want to calculate the distance from the center of the circle to the external point
Please check attachment for diagram
Now, from what we know, the tangent and the radius meets at right angle
So we have a right-angled triangle with the length from the external point to the center of the circle as hypotenuse;
While the radius and the length of the tangent to the circle as the other sides
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Answers
Answer:
$13.50
Step-by-step explanation:
(8*2) - (1.25*2) =
16 - 2.50 =
13.50
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Answers
Answer:
B)203
Step-by-step explanation:
FE is 23 plus H which is a straight line which means that is 180. Add 23 and 180 that get's you 203
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Answer:
(6,4) I believe
Step-by-step explanation:
Answer:
(6,4)
Step-by-step explanation:
The vertex is either the highest or lowest point on a parabola, in this case, the highest.
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Can someone explain to me how to combine like terms?(7th grade)
Like can you give me an example problem then tell how to solve it.
Answers
HOPE THIS HELPS!!!! IF YOU STILL DONT UNDERSTAND PLS LET ME KNOW
Answer:
When two numbers in an equation have the same variable and or charge, then you use the commutative property to put them next to each other.
Step-by-step explanation:
Example:
4x + 2 + 3x - 1 <--- Here is the original equation.
4x + 3x + 2 - 1 <---Use the commutative property to add the like terms
together. 3x and 4x end in the same variable. 2 and 1 both
have no variable. Therefore both of the groups are like
terms.
7x + 1 <--- Add/subtract the live terms together.
8x <--- Here is your answer.
Hope this helps! :D