If you are examining a triangle with given measurements for one leg and the hypotenuse, how will you determine the measure of the unknown leg? Explain.
Answers
By using Pythagoras theorem, length of one leg of triangle can be determined.
Given:
A triangle with length of one leg and the hypotenuse
According to question,
Let the length of one leg of triangle which can be base [tex](b)[/tex] or perpendicular [tex](p)[/tex] and hypotenuse represented by [tex](h)[/tex].
Now, using Pythagoras theorem which states that if a triangle is right-angled ([tex]90[/tex] degrees), then the square of the hypotenuse is equal to the sum of the squares of the other two sides.
From the figure,
In [tex]\Delta AOB, \;\angle O=90^\circ[/tex]
[tex]\rm{H^2=P^2+B^2}\\\rm{AB^2=AO^2+OB^2[/tex]
[tex]h^2=p^2+b^2[/tex]
[tex]b=\sqrt{h^2-p^2}\\[/tex]
or
[tex]p=\sqrt{h^2-b^2}\\[/tex]
Therefore, length of one leg of the triangle is determined by using Pythagoras theorem.
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Related Questions
In ΔABC, ∡A is a right angle, and m∡B = 45°. What is the length of BC? If the answer is not an integer, leave it in simplest radical form. The diagram is not drawn to scale.
Answers
BC² = 121 + 121
BC² = 242
BC = √242
BC = 11√2
Answer: 11√2
Answer:
The length of BC is 11√2 ft.
Step-by-step explanation:
Given,
A right angled triangle ABC,
In which,
AC = 11 ft ( By diagram ),
∠A = 90°,
∠B = 45°,
By the law of sine,
[tex]\frac{sin B}{AC}=\frac{sin A}{BC}[/tex]
[tex]\implies BC\times sin B = AC\times sin A[/tex] ( By cross multiplication )
[tex]\implies BC = \frac{AC\times sin A}{sin B}[/tex]
By substituting the values,
[tex]BC=\frac{11\times sin 90^{\circ}}{sin 45^{\circ}}[/tex]
[tex]=\frac{11}{\frac{1}{\sqrt{2}}}[/tex]
[tex]=11\sqrt{2}[/tex]
Hence, the length of BC is 11√2 ft.
The outer edge of the dime is about 55mm. What is the approximate length of the radius?
Answers
C = 2 x pi x r
55 = 2 x 3.14 x r
55 = 6.28 x r
6.28 6.28
r = 9.2 mm
The approximate radius is 9.2 mm.
I NEED ANSWER ASAP!!! TEST DUE IN 30 MINUTES!!
What is the volume of the composite figure?
1,024 cm^3
896 cm^3
832 cm^3
64 cm^3
Answers
Answer:
896 cm^3
Step-by-step explanation:
formula for the triangle prism is
V= 1/3 Bh
V = 1/3 (8 x 3) (8) The base is 8 seen the base of the rectangel prism is 8 to its consider as base to.
V= 1/3 (24 x 8)
V= 1/3 (192)
V = 64
Now we need to find the volume so the rectangle formula is
V= lwh
V= (13x 8) (8)
V= 832cm
Add your two answers and u get
832 + 64 = 896 cm^3
The solution is : 896 cm^3 is the volume of the composite figure.
What is volume?In mathematics, volume is the space taken by an object. Volume is a measure of three-dimensional space. It is often quantified numerically using SI derived units or by various imperial or US customary units. The definition of length is interrelated with volume.
Here, we have,
Volume formula for the triangle prism is
V= 1/3 Bh
V = 1/3 (8 x 3) (8)
The base is 8 seen the base of the rectangle prism is 8 to its consider as base to.
V= 1/3 (24 x 8)
V= 1/3 (192)
V = 64
Now we need to find the volume so the rectangle formula is
V= lwh
V= (13x 8) (8)
V= 832cm
Add your two answers and u get
832 + 64 = 896 cm^3
Hence, The solution is : 896 cm^3 is the volume of the composite figure.
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what is the product? -9x(5-2x) 18x2 -45x -18x2-45x -18x-45 18-45x
Answers
Answer: A.
Step-by-step explanation:
The product of equation is 18x² - 45x.
What is linear equation?Each term in a linear equation has an exponent of 1, and when this algebraic equation is graphed, it always produces a straight line. It is called a "linear equation" for this reason.
Both linear equations with one variable and those with two variables exist.
Given equation -9x(5 - 2x)
product = -9x(5) - (-9x)(2x)
= -45x + 18x²
= 18x² - 45x
Hence the product is 18x² - 45x.
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A football is selling for $35 off the original price. The original price was $60. What is the sale price of the football?
Answers
HELP ME PLEASE I DONT UNDERSTAND THIS PROBLEM!!!!! Worth 20PT
a ball is thrown with a slingshot at a velocity of 100 ft/sec at an angle 21 above the ground from a height of 5ft approximately how long does it take for the ball to hit the ground? acceleration due to gravity is 32 ft/s^2
Answers
We use the equation h(t)=-1/2gt²+v₀t+h₀ to set this up. g is the acceleration due to gravity, v₀ is the initial velocity and h₀ is the initial height:
h(t) = -1/2(32)t² + 100t + 5
h(t) = -16t² + 100t + 5
We will use the quadratic formula to solve this:
[tex]t=\frac{-b\pm\sqrt{b^2-4ac}}{2a} \\ \\=\frac{-100\pm\sqrt{100^2-4(-16)(5)}}{2(-16)} \\ \\=\frac{-100\pm\sqrt{10000--320}}{-32} \\ \\=\frac{-100\pm\sqrt{10320}}{-32} \\ \\=\frac{-100\pm101.59}{-32} \\ \\=\frac{-100+101.59}{-32}\text{ or }\frac{-100-101.59}{-32} \\ \\=\frac{1.59}{-32}\text{ or }\frac{-201.59}{-32} \\ \\=-0.05\text{ or }6.3[/tex]
Since a negative amount of time makes no sense, the answer is 6.3.
Answer:
D) 2.37 seconds
Step-by-step explanation:
Took the test and got it wrong.
Anna and Ryelin together have 895 songs downloaded. Ryelin has 177 more songs downloaded than Anna. How many songs do each of them have?
Answers
x = number of songs downloaded by Anna
y = number of songs downloaded by Ryelin
Then,
x + y = 895 ----- (1)
But, it is also indicated that,
y = x+177
Substituting for y in (1);
x+(x+177) = 895
2x + 177 = 895
2x = 895-177 = 718
x = 718/2 = 359 songs
y = x+177 = 359+177 = 536 songs
∴ Songs downloaded by Anna = 359 songs
Songs downloaded by Ryelin = 536 songs
Cindy and Giovanni plan to make spaghetti sauce. Cindy needs 4 3/4 pounds of tomatoes for her recipe. Giovanni needs 5 /34 pounds of tomatoes for his recipe. If they make both recipes, how many pounds of tomatoes do they need?
Answers
Answer:
[tex]10\frac{1}{2}\text{ pounds}[/tex]
Step-by-step explanation:
Given,
For a recipe,
Cindy needs tomatoes = [tex]4\frac{3}{4}[/tex] pounds,
While, Giovanni needs tomatoes = [tex]5\frac{3}{4}[/tex] pounds,
If they make both recipes,
Then, total tomatoes they need = [tex]4\frac{3}{4}+5\frac{3}{4}[/tex]
[tex]=\frac{19}{4}+\frac{23}{4}[/tex]
[tex]=\frac{42}{4}[/tex]
[tex]=10\frac{2}{4}[/tex]
[tex]=10\frac{1}{2}\text{ pounds}[/tex]
98 POINTS AND BRAINLIEST!!!!!!!!!!!
Answers
p(x) = r(x) - c(x)
p(x) = [ r(x) ] - [ c(x) ]
p(x) = [18x] - [5x+20]
p(x) = 18x - 5x - 20
p(x) = 13x - 20
Answer is choice A
Hello!
I believe the answer is A) p(x) = 13x -20.
I hope it helps!
Seven of the 10 children at art camp make an average of 8 paintings. The remaining children make an average of 12 paintings. What is the average number of paintings made by children at the art camp? Enter your answer in the box.
Answers
Geometry question, will give brainiest
Answers
Corresponding parts of congruent figures are the same
THEN ANGLE R IS EQUAL TO ANGLE X
SINCE ANGLE R = 135 THEN ANGKE X ALSO EQUALS 135
Complete the area model to identify the factored form of the quadratic expression it represents. A) (x + 2)(x + 5) B) (x − 2)(x + 5) C) (x + 2)(x − 5) D) (x − 2)(x − 5)
Answers
The correct answer is D (x - 5)(x - 2)
You can tell this because in the picture, we are looking for all of the cross sections to multiply to their appropriate boxes. In the bottom right corner, we see the number 10. This means that the bottom number and the right number must multiply to 10. This only happens in A and D, whereas in B and C those equal -10.
To determine between A and D, you must find the ones that have negatives, since the two x values are both negatives. D is the only one with negative numbers out of the ones we are left working with. Therefore, D is the correct answer.
Answer:
its C i just did that question
Step-by-step explanation:
What is the solution to the equation 1/square root of 8 = 4^(m + 2)?
m = −15/4
m = −11/4
m = 5/4
m = 9/4
Answers
[tex]\log_{4}(\frac{1}{\sqrt{8}}) = m + 2[/tex]
[tex]\frac{-1}{2} \log_{4}(4^{\frac{3}{2}})-2 = m[/tex]
[tex]-2 \frac{3}{4}= m[/tex]
The appropriate choice is ...
m = -11/4
The population of a major U.S. city is 8,550,405. The land area of the city is 1213.4 square kilometers. What is the best approximate population density of the city? 7047 peoplekm2 7124 peoplekm2 7167 peoplekm2 7500 peoplekm2
Answers
people
7047 ---------
km^2
The population of a major U.S. city = 8,550,405
Area of the city = 1213.4 sq.km
Density = [tex] \frac{Population}{area} [/tex]
Density = [tex] \frac{8,550,405}{1213.4} [/tex]
Density = 7046.6499 [tex] \frac{People}{km^{2}} [/tex]
As the density here will not be in decimal so after rounding the density in whole number,
Density = 7047 [tex] \frac{People}{km^{2}} [/tex]
Option A is the answer
A 3 inch wide border is wrapped around a rectangular prism. the length of the rectangular prism is 8 inches longer than its width. the surface area covered by the border is 383 square inches. what is the width of the rectangular prism? answer in units of inches.
Answers
The lateral area of a cone is 555 \pi cm^2 and the radius is 15.1 what is the slant height?
Answers
[LA]=pi*r*l
where
LA is the lateral area of the cone
r is the radius
l is the slant height
l=LA/(pi*r)
r=15.1 cm
LA=555*pi cm²
l=(555*pi)/(pi*15.1)----> l=36.75 cm
the answer is
the slant height is 36.75 cm
solve the equation
3x-3= -18
Answers
3x-3=-18
+3 +3 Remember: What you do to one side, you have to do to the other.
3x = -15
Now divide by the coefficient (the number in front of x).
(3x)/3 = (-15)/3
x = -5
The solution of the equation 3x-3= -18 is -5.
The algebraic expressions which are separated by an equal symbol in between them and with the same value is called is an equation
Example = 5x + 5 = 12
here, x is a variable and 5 and 12 are constants.
Given equation;
3x-3= -18
To find the value of x add 3 to both side, we get
3x = -18 +3
we get
3x = -15
divide both side by 3 we get
[tex]x = \dfrac{-15}{3}[/tex]
Convert in into the lowest form we get,
x = -5
The solution of the equation 3x-3= -18 is -5
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The figure below shows a shaded circular region inside a larger circle:
Will insert pic below
What is the probability that a point chosen inside the larger circle is not in the shaded region?
24%
36%
50%
64%
Answers
Probability=(area of unshaded part)/(area of the large circle)
Area of unshaded part will be:
A=(area of large circle)-(area of small circle)
area of large circle=πR²=π×5²=25π in²
area of small circle=πr²=π×3²=9π
Area of un-shaded part=25π-9π=16π in²
thus the probability that part chosen is not shaded will be:
16π/25π
=0.64
=64%
Answer: 64%
Answer:
the answer is 64%
Step-by-step explanation:
A metal washer is made by cutting out a circle 13.2 mm in diameter from a larger circle. To the nearest tenth, what is the area of the washer?
547.1 mm2
972.6 mm2
60.8 mm2
243.3 mm2
Answers
Answer: [tex]243.3\ mm^2[/tex]
Step-by-step explanation:
Given: The diameter of smaller circle = 13.2 mm
Then the radius of smaller circle r =[tex]\frac{13.2}{2}=6.6\ mm[/tex]
Also, the radius of larger circle R= [tex]6.6+4.4=11.0\ mm[/tex]
Now, the area of the washer is given by :-
[tex]\text{Area of washer=Area of larger circle-Area of smaller circle}\\\\\Rightarrow\\text{Area of washer}=\pi R^2-\p r^2\\\\\Rightarrow\\text{Area of washer}=\pi(R^2-r^2)\\\\\Rightarrow\\text{Area of washer}=(3.14159265359)((11.0)^2-(6.6)^2)\\\\\Rightarrow\\text{Area of washer}=243.284935094\approx243.3\ mm^2[/tex]
The area of the washer is 0 mm2.
Explanation:To find the area of the washer, we first need to find the area of the larger circle and the area of the smaller circle. The formula for the area of a circle is A = πr^2.
The larger circle has a diameter of 13.2 mm, so the radius is half of that, which is 6.6 mm. Plugging this value into the formula, the area of the larger circle is approximately 136.78 mm2.
The smaller circle has a diameter of 13.2 mm, so the radius is again 6.6 mm. Using the same formula, the area of the smaller circle is also approximately 136.78 mm2.
To find the area of the washer, we subtract the area of the smaller circle from the area of the larger circle: 136.78 mm2 - 136.78 mm2 = 0 mm2. Rounded to the nearest tenth, the area of the washer is 0 mm2.
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Solve the equation using square roots. 3x2 – 27 = 0
Answers
The answers are x = 3 and x = -3.
[tex]3 {x}^{2} - 27 = 0[/tex]
Add 27.
[tex]3 {x}^{2} = 27[/tex]
Divide by 3.
[tex] {x}^{2} = 9[/tex]
Take the root and the negative root.
[tex]x = \sqrt{9} = 3 \: \: or \: \: x = - \sqrt{9} = - 3[/tex]
Therefore, the answers are x = 3 and x = -3.
~ Hope this helps you!
The value of X are x = 3 and x = -3. using square root.
What is square root?A square root can be regarded as a factor of a number in the sense that when that number is multiplied by itself, it gives the original number.
3x²– 27 = 0
⇒3x²= 27
⇒x²= 27/3
⇒x² = 9
⇒x = sqrt(9)
⇒ x =±3
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please help me figure out this probability problem!!!
Answers
The probability that the first ball is red: [tex]P(R)=\dfrac{10}{16}=\dfrac{5}{8}[/tex]
The probability that the second ball is black: [tex]P(B)=\dfrac{1}{15}[/tex]
Together:[tex]P(R)\cdot P(B)=\dfrac{5}{8}\cdot\dfrac{1}{15}=\dfrac{1}{24}[/tex]
So your answers are....
First ball being red: 5/8
Second ball being black: 1/16
Hoped this helped. Have a nice day!
HELPP ILL GIVE MAD POINTS!!
Which series has a sum of 5?
Answers
Answer:
C
Step-by-step explanation:
The formula is S=a1/1-r
The series third has a sum of 5 option (C) is correct because the sequence represents the sum of the infinite terms.
What is a sequence?It is defined as the systematic way of representing the data that follows a certain rule of arithmetic.
We have a series shown in the picture.
The geometric sequence is shown in the options.
As we know, in the geometric sequence there is a first term and common difference
In the first sequence:
First term a = 2
Common difference = 2(0.1)/2
Common difference d = 0.1
The sum of the infinite series is:
S = a/(1 - r)
S = 2/(1 - 0.1)
S = 2.22
In the second sequence:
First term a = 15
Common difference = 15(0.3)/15
Common difference d = 0.3
The sum of the infinite series is:
S = a/(1 - r)
S = 15/(1 - 0.3)
S = 21.42
In the third sequence:
First term a = 4
Common difference = 4(0.2)/4
Common difference d = 0.2
The sum of the infinite series is:
S = a/(1 - r)
S = 4/(1 - 0.2)
S = 5
Thus, the series third has a sum of 5 option (C) is correct because the sequence represents the sum of the infinite terms.
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Help me please & thank ya
Answers
Hope this helps.
Which pair of points forms a vertical line segment that is 4 units long?
Answers
So, this pair of points are in the general forms as follow:
[tex]P_{1}( x_{1}, y_{1})[/tex]
[tex]P_{2}( x_{2}, y_{2})[/tex]
Given that the straight line is vertical, then:
[tex]x_{1}=x_{2}[/tex]
Then the point 2 is modified as:
[tex]P_{2}( x_{1}, y_{2})[/tex]
We need to find a point which is 4 units long, so:
[tex]d = y_{2} - y_{1} = 4[/tex]
∴ [tex]y_{2} = 4+ y_{1}[/tex]
So, we can find infinite points given a value of [tex]y_{1}[/tex], therefore if:
[tex]y_{1} = 2[/tex] then:
∴ [tex]y_{2} = 6[/tex]
Thus, if [tex] x_{1} = 1 [/tex] then a pair of points are:
[tex]P_{1}(1,2)[/tex]
[tex]P_{2}(1,6)[/tex]
It takes 60 pounds of seed to completely plant a 10-acre field. How many acres can be planted per pound of seed
Answers
You divide the amount of space planted by the weight of seeds it took
10 / 60 = 0.6
It takes 0.6 pounds of seeds to plant 1 acre of land
Hope this helps!
If sinA/sinB=p,cosA/cosB=q,find tanA and tanB
Answers
cosA/cosB=q
tanA/tanB=p+q
Find the diameter of a circle whose equation is x2+(y−2)2=100x2+(y−2)2=100.
400
20
10
100
Answers
Take the square root of 100
sqrt(r^2) = sqrt(100)
r = 10
But you want the diameter.
d = 2 * r
d = 20
B answer.
Which expression is equivalent to x3 – 7x – 6?
Answers
The function is f(x) = (x + 2)(x + 1)(x - 3)
Answer is D.
How do you complete the square of x^2-14x+33=0?
Answers
Subtract 33 from both sides
x² - 14x = - 33
Divide the b term by 2 and then square the result. Then add that to both sides.
- 14 / 2 is - 7. (- 7)² = 49. Add that to both sides
x² - 14x + 49 = - 33 + 49
Combine the constants and factor the trinomial
(x - 7)² = 16
Square root both sides
x - 7 = +/- 4
or
x - 7 = - 4 and x - 7 = 4
You have to place a plus-minus statement because (- 4)² and 4² both equal 16.
Now we solve for x in each equation. Add 7 to both sides to isolate our variable.
x = 3 and x = 11
Final answer:
To complete the square for the equation x^2-14x+33=0, the constant 33 is moved to the other side, and the number needed to make the left side a perfect square trinomial, 49, is added to both sides, resulting in factoring and solving (x - 7)^2 = 16 to find x = 11 and x = 3.
Explanation:
To complete the square for the equation x^2-14x+33=0, you need to form a perfect square trinomial on the left side of the equation. First, you'll move the constant term to the right side:
x^2 - 14x = -33
Next, find the value that completes the square for the x-terms. This value is obtained by taking half of the coefficient of x (which is -14 in this case) and squaring it, giving us (-7)^2 = 49.
Add 49 to both sides of the equation:
x^2 - 14x + 49 = -33 + 49
x^2 - 14x + 49 = 16
Now, the left side of the equation is a perfect square trinomial, and can be factored into:
(x - 7)^2 = 16
To solve for x, take the square root of both sides:
x - 7 = [tex]\sqrt{16}[/tex]
x - 7 = +- 4
Finally, solve for x by adding 7 to both sides:
x = 7 +- 4
x = 11 or x = 3
How to find the area of a triangle with a base of 32ft