For the following right triangle, find the side length x . Round your answer to the nearest hundredth.
Answers
[tex]\huge\bold{Given:}[/tex]
Length of the base = 9
Length of the hypotenuse = 16 [tex]\huge\bold{To\:find:}[/tex]
✎ The length of the perpendicular ''[tex]x[/tex]".
[tex]\large\mathfrak{{\pmb{\underline{\orange{Solution}}{\orange{:}}}}}[/tex]
The length of the perpendicular [tex]x[/tex] is[tex]\boxed{±13.229}[/tex].
[tex]\large\mathfrak{{\pmb{\underline{\red{Step-by-step\:explanation}}{\orange{:}}}}}[/tex]
Using Pythagoras theorem, we have
[tex]({perpendicular})^{2} + ({base})^{2} = ({hypotenuse})^{2} \\ ⇢ {x}^{2} + {(9})^{2} = ({16})^{2} \\ ⇢ {x}^{2} + 81 = 256 \\ ⇢ {x}^{2} = 256 - 81 \\ ⇢x = \sqrt{175} \\ ⇢x = ±13.229[/tex]
[tex]\sf\blue{Therefore,\:the\:length\:of\:the\:perpendicular \:"x"\:is\:±13.229.}[/tex]
[tex]\huge\bold{To\:verify :}[/tex]
[tex]( {13.229})^{2} + ({9})^{2} = ({16})^{2} \\ ⇢ 175 + 81 = 256 \\ ⇢ 256 = 256 \\⇢ L.H.S.=R. H. S[/tex]
Hence verified. ✔
[tex]\circ \: \: { \underline{ \boxed{ \sf{ \color{green}{Happy\:learning.}}}}}∘[/tex]
Related Questions
Sarah can do 68 push ups in 4 minutes . At this rate how many push ups can she do each minute?
Answers
Answer:
Sarah can do 17 push-ups each minute.
Step-by-step explanation:
4 minutes = 68 push ups
68 divided by 4 = 17 push ups
1 minute = 17 push ups
The area of A PQR is 15 m², and p = 5 m, q = 10 m.
Find the possible measure of angle R (in degrees)
Answers
if x=-4 then what is x^2? in an equation for my homework, they have the solution as positive instead of negative and I don’t understand why.
Answers
X^2 = -4^2
16.
Answer:
see explanation
Step-by-step explanation:
Given
x² , then when x = - 4
x² = - 4 × - 4 = + 16
[ the product of a negative and a negative results in a positive ]
Find Z for the following sequence:
210, 209, 213, 186, 202, Z
Answers
Answer:
77
Step-by-step explanation:
as far as I can tell the steps between the given numbers are
-1
+4
-27
+16
1 can be expressed as 1³
4 can be expressed as 2²
27 can be expressed as 3³
16 can be expressed as 4²
my best guess is that next one is minus 5³ = -125
edit: technically the given steps can be expressed as
(-1)³
(-2)²
(-3)³
(-4)²
somewhat nicer pattern there
11x+x^2= 2y
Y + x = 19
Answers
Answer:
x = -15,46 thì y ≈ 34,46
x = 2,46 thì y ≈ 16,54
Step-by-step explanation:
x + y = 19 => x = 19 - y (1)
thay x = 19 -y vào phương trình 11x + x^2 = 2y ta có:
11 * (19 - y) + (19 - y)^2 =2y
=> 209 - 11y + 361 - 38y + y^2 = 2y
=> y^2 - 51y + 570 = 0
=> y ≈ 34,46 và y≈16,54
thay y ≈ 34,46 vào phương trình (1) có:
x = 19 - 34,46 = -15,46
thay y ≈ 16,54 vào phương trình (1) có:
x = 19 - 16,54 = 2,46
Answer:
Step-by-step explanation:
11x+x^2= 2y
Y + x = 19
Multiply and re-arrange second equation:
2y = 38 - 2x
Substitute into first equation:
11x + x^2 = 38 - 2x
Re-arrange:
x^2 + 13x - 38 = 0
Solve using quadratic formula:
x = (-13+(13^2-4*(-38))^(1/2))/2 or (-13-(13^2-4*(-38))^(1/2))/2
x = 2.46 or -15.46
Substitute back to solve for y:
y = 19 - 2.46 or 19 + 15..46
y= 16.54 or 34.46
Joan can mow a 7- acre field in 5 hours. How long would it take her to mow a 5.6- acre field?
Answers
Answer:4 hours
Step-by-step explanation:
7 divided by 5= 1.4
1.4x4=5.6
Which choice is equivalent to the fraction below when x is an appropriate
value? Hint: Rationalize the denominator and simplify.
4
4 - 6x
A. 8+226x
16 - 6x
B. 8+ 2162
846
C.
2 + V6
4- 6x
D. 8. 216
8 - 3x
UN
Answers
1. 8^3 * 8^2, 8^5, and (2^3)^5
2. 6^9, and 6^5 x 6^4
Answer:
8+2√6x / 8-3x
Step-by-step explanation:
yes
What is the value of ?
Answers
Answer:
x=3
Step-by-step explanation:
Log base 5 of 125=x
that is equal to 5x5x5 which is 125
5 is multiplied 3 times so x is 3
help please i need it
Answers
9514 1404 393
Answer:
the shape is a trapezoiduse the area formula48783 mm²Step-by-step explanation:
The top and bottom edges are parallel, and the shape has 4 sides. That means it is a trapezoid. The area can be found using the formula for the area of a trapezoid:
A = 1/2(b1 +b2)h
A = 1/2(85 mm + 218 mm)(322 mm) = 1/2(303)(322) mm² = 48783 mm²
Student spend 5 minutes of every 60 minutes at school moving from class to class. Which fraction is equivalent to the number of minutes student spend moving from class to class?
Answers
Answer:
10/120
Step-by-step explanation:
Which of the following are the domain and range that represent the inverse of the function f(x), given the mapping diagram of f(x) below? 1 AWN O 2. 4 6 8
Answers
Answer:b
Step-by-step explanation:
PLEASE HELP i dont know the answer for: Chose an equivalent ratio 15 cats to 20 dogs. choices: A. 4 to 5. B. 3 to 4. C. 3 to 5. D. 10 to 15.
Answers
Answer:
D 10 to 15 is the answer correct
Which is an asymptotic of the graph of the function y=cot [x- 2pi/3]
Answers
Answer:
B
Step-by-step explanation:
The asymptote of the function [tex]y = cot(x - \frac{2\pi}{3})[/tex] is at x = - π/3.
What are periodic functions?A periodic function has a range that is determined for a fixed interval and a domain that includes all real number values.
Any function that has a positive real integer p such that f (x + p) = f (x), with all x being real values, is said to be periodic.
We know, tan = sin/cos.
Hence 1/tan = cos/sin = cot.
So, The denominator sin can not be zero, And sin is zero on π and - π.
Given, A function [tex]y = cot(x - \frac{2\pi}{3})[/tex].
At, x = - π/3.
Therefore, [tex]y = cot(\frac{\pi}{3} - \frac{2\pi}{3})[/tex].
[tex]y = cot(-\pi)[/tex], Which is undefined.
learn more about asymptotes here :
https://brainly.com/question/17767511
#SPJ7
PLS HELP ILL GIVE BRAINLIEST
Answers
Answer:
-40% change
Step-by-step explanation:
This change is a decrease, so first you need to find the difference between the two numbers--> 125 - 75 = 50Next, you divide by the original number, so 50 ÷ 125 = 0.4Finally, you multiply your answer by 100, so 0.4 x 100 = 40%. Because this is a decreasing change, you add a negative sign.At the supermarket, a certain brand of plain yogurt comes in thre
different sizes. The 6-ounce container of yogurt costs $0.72. The
16-ounce container of yogurt costs $1.76. The 32-ounce
container of yogurt costs $4.48. Which size is the best deal?
6 oz container
B 32 oz container
C 16 oz container
D All three sizes have the same unit cost.
Answers
Answer:
C. 16oz container
Step-by-step explanation:
I can explain my answer in the comments if needed, but C is the correct answer :)
An airplane flying at an altitude of 37,000 feet is still A horizontal distance of 100 miles (100 miles = 5280 ft) from the airport. What angle of depression does the airplane need to use to reach the runway?
Answers
Given :
An airplane flying at an altitude of 37,000 feet is still A horizontal distance of 100 miles (100 miles = 5280 ft) from the airport.
To Find :
What angle of depression does the airplane need to use to reach the runway?
Solution :
Let, angle of depression is [tex]\theta[/tex] .
So,
[tex]tan\ \theta = \dfrac{ Altitude \ in \ which \ plane \ is \ flying}{Horizontal \ Distance}\\\\tan \ \theta = \dfrac{37000}{5280}\\\\tan \ \theta = 7.00\\\\\theta = tan^{-1} 7\\\\\theta = 81.87^o[/tex]
Hence, this is the required solution.
HIGHSCHOOL GEOMETRY
LAWS OF COS/SIN
please help
it also says that it is acute, and I dont know how to factor that into my answer
Answers
Answer:
B = 75°
Step-by-step explanation:
Using the Sine rule:
a / sin A = b / sin B = c / Sin C
a / sin A = b / sin B
20 / sin 48 = 26 / sin B
Cross multiply :
Sin B * 20 = sin 48 * 26
Sin B = (sin 48 * 26) / 20
Sin B = 0.9660882
B = sin^-1(0.9660882)
B = 75.036
B = 75°
Can someone help me? Question attached, 20 points.
Answers
Answer:
6
Step-by-step explanation:
[tex]V = A * b = 5A[/tex]
[tex]5A = 141.3[/tex]
[tex]A = 28.26[/tex]
[tex]\pi r^2 = 28.26[/tex]
[tex]3.14 r^2 = 28.26[/tex]
[tex]r^2 = 9[/tex]
[tex]r = 3[/tex]
[tex]D = 2r = 2 * 3 = 6[/tex]
A.3 1/4
B.1 3/4
C.2 1/4
D.3/3
Answers
Answer:
A. 3 [tex]\frac{1}{4}[/tex]
Step-by-step explanation:
I need help with this with work asap thank you
Answers
Answer:
multiply all sides (5.5 x 6 x 8.5) which results to 261.5 ft squared
solve
(3431)−2/3÷(491)3/2
a. 16807
b.343
c.49
d.2401
Answers
Which of the following is geometric sequence
A. 1,1/2,1/4,1/8
B.2,4,6,8
C.1,1,2,3,5
D.7,4,1,-2
Answers
Answer:
A
Step-by-step explanation:
...................
Answer:
here's the whole unit test
Step-by-step explanation:
ur welcomeeeee ;)
Help me...!
!!
!!
!!
!!
Answers
The answer to this question is:
2 ¾ inches.
- 12. What is the greatest common factor of 120 and 84?
e.
a. 3
b. 6
12
18
d.
Answers
Answer:
12 (the third one is the greatest common factor of 120 and 84)
Answer:
12
Step-by-step explanation:
factors of 120. 1,2,3,4,5,6,8,10,12,15,20,24,30,40,60,80,120
factors of 84: 1,2,3, 4,6,7,12,14,28,42,84
greatest common factor=12
The area of a sector created by a 120° angle is 4 pi in squaredWhat is the area of a sector created by an angle of 30°
in the same circle
Answers
Answer:
π in²
Step-by-step explanation:
We'll begin by calculating the radius of the circle. This can be obtained:
Area of sector (A) = 4π in²
Angle (θ) = 120 °
Radius (r) =?
The radius of the circle can be obtained by using the formula for calculating the area of a sector. This is illustrated below:
A = θ/360 × πr²
4π = 120/360 × πr²
4π = ⅓ × πr²
Cross multiply
3 × 4π = πr²
12π = πr²
Divide both side by π
r² = 12π / π
r² = 12
Take the square root of both side
r = √12 in
Thus, the radius is √12 in.
Finally, we shall determine the area of the sector created by 30 °. This can be obtained as follow:
Radius (r) = √12 in
Angle (θ) = 30 °
Area of sector (A) = ?
A = θ/360 × πr²
A = 30/360 × π(√12)²
A = 1/12 × 12π
A = π in²
Therefore, the area of the sector created by 30 ° us π in².
Solve for x round to nearest tenth
Answers
Answer:
15.9 units
Step-by-step explanation:
use the pathagorean theorem to find x.
a^2 + b^2 = c^2
6^2 + b^2 = 17^2
36 + b^2 = 289
-36 -36
[tex]\sqrt{b^{2} }[/tex]= [tex]\sqrt{253}[/tex]
b = 15.90597372
b = 15.9
{3/4 x (3/3/4 ÷ 5/16)} -3/1/3
Answers
Someone tell me what the answer
Answers
Answer:
can you please put a better picture?
Solve for x. Round to the nearest tenth, if necessary. C С B x 25 34° А
Help with this problem please.
Answers
Answer:
59 or I’m wrong
Step-by-step explanation:
Answer:
x=20.7
Step-by-step explanation:
using cosine...
cos 34=adjacent/hypotenuse
cos 34=x/25
Cross multiply
x=cos 34 ×25
x=20.72593931
x≈20.7(to the nearest tenth)
The sum of two numbers is 49.one number is 15 more than the other one.find the numbers
Answers
Answer:
17 and 32
Step-by-step explanation:
x + (x + 15) = 49
2x + 15 = 49
2x = 34
x = 17
x + 15 = 32
15+x=49
49-15=34
X=34