Answers
Answer:
25
Step-by-step explanation:
By Geometric mean theorem:
[tex] {12}^{2} = y \times 16 \\ \\ 144 = y \times 16 \\ \\ y = \frac{144}{16} \\ \\ y = 9 \\ \\ x = y + 16 \\ \\ x = 9 + 16 \\ \huge \red{ \boxed{ x = 25}}[/tex]
The missing length AC is approximately 25.61 units.
In the right-angled triangle ABC, the hypotenuse is AC, and the other two sides are AB and BC. We are given that BD = 12, DC = 16, and triangle ABC is right-angled at B.
To find the missing length AC, we can use the Pythagorean theorem:
[tex]AC^2 = AB^2 + BC^2[/tex]
Since triangle ABC is right-angled at B, we can use the given lengths to find AC.
We know that BD is perpendicular to AC, so it divides triangle ABC into two smaller right-angled triangles: ABD and BDC.
In triangle ABD:
[tex]AB^2 = BD^2 + AD^2\\\\AB^2 = 12^2 + AD^2\\\\AB^2 = 144 + AD^2[/tex]
In triangle BDC:
[tex]BC^2 = BD^2 + DC^2\\\\BC^2 = 12^2 + 16^2\\\\BC^2 = 144 + 256[/tex]
We also know that AB = BC (since they are opposite sides in an isosceles right-angled triangle), so we can equate the two expressions:
[tex]144 + AD^2 = 144 + 256[/tex]
Simplifying, we get:
[tex]AD^2 = 256[/tex]
Taking the square root of both sides:
AD = 16
Now we can substitute the value of AD back into the expression for [tex]AB^2[/tex]:
[tex]AB^2 = 144 + AD^2\\\\AB^2 = 144 + 16^2\\\\AB^2 = 144 + 256\\\\AB^2 = 400[/tex]
Again, since AB = BC (in an isosceles right-angled triangle), we can say:
[tex]400 = 144 + BC^2\\\\BC^2 = 400 - 144\\\\BC^2 = 256[/tex]
Taking the square root of both sides:
BC = 16
Finally, we can substitute the values of AB and BC into the Pythagorean theorem equation to find AC:
[tex]AC^2 = AB^2 + BC^2\\\\AC^2 = 400 + 256\\\\AC^2 = 656[/tex]
Taking the square root of both sides:
AC = √656
AC ≈ 25.61
Therefore, the missing length AC is approximately 25.61.
To know more about length, refer here:
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Related Questions
Find all the missing angle measures. Remember you cannot assume right angles of diameters. Also think about how many degrees are in a triangle. Given: PA and BD are tangents, mCR=18*, mAC=70*, mBE=130*, and mBR=80*. What are angles 1-15
Answers
.
this is answer ok? ok :) leleelellelelelelelelel
Please answer this question now in two minutes
Answers
Answer: mKLJ = 60ᴼ
Step-by-step explanation:
MLO and KLJ are vertical angles, which means their measures are congruent.
simplify -5(3m2 + 7n2) + 8n2
Answers
Answer:
-15m² - 27n²Step-by-step explanation:
-5(3m² + 7n²) + 8n²
Expand brackets.
-15m² + -35n² + 8n²
Combine like terms.
-15m² + -27n²
Answer:
[tex]\boxed{\red{= - 3(5 {m}^{2} + 9 {n}^{2} )}}[/tex]
Step-by-step explanation:
[tex] - 5(3 {m}^{2} + 7 {n}^{2} ) + 8 {n}^{2} \\ - 15 {m}^{2} - 35 {n}^{2} + 8 {n}^{2} \\ = - 15 {m}^{2} - 27 {n}^{2} \\ = - 3(5 {m}^{2} + 9 {n}^{2} )[/tex]
Find the fourth term in the sequence defined by the following recursive formula.
t1 = 5
tn = 3tn-1 - 12
1) -75
O 2 3
3) -3
4) -21
Answers
Answer
Part 1
Step-by-step explanation:
T2=3(5)-12=3
T3=-3
T4=-21
T5=-75
please help i will give out brainliest
Answers
Answer: Pls brainliest this took forever, but was really fun :)
Step-by-step explanation:
Imagine you are looking at the structure from the front or the side. What would you see? If you want a detailed explanation on orthogonal drawings, just ask :)
Will give brainliest.
Answers
Answer:
x=8
Step-by-step explanation:
Those angles are supplementary so:
140+5x=180
5x=40
x=8
Which is equal to a rotation of 90°ccw?
A. 180°cw rotation about the origin
В. 270°cw rotation about the origin
C. 180ºccw rotation about the origin
D. 270ºccw rotation about the origin
Answers
Answer:
В. 270°cw rotation about the origin
Step-by-step explanation:
We can rotate a total of 360 degrees in a circular pattern.
If we rotate x degrees in one direction, this rotation is equivalent to rotating (360 - x) in the other direction, because we would arrive in the same place.
So if we rotate 90 degrees in the counter clockwise direction, this is equivalent to rotating (360 - 90) = 270 degrees in the opposite direction, that is, in the clockwise direction.
So the correct option is B. -> 270°cw rotation about the origin.
find x. A. 6√2 B. 2√2 C. 4 D. 2–√
Answers
Answer:
Option B is the correct answer
Step-by-step Explanation:
[tex] \sin 45 \degree = \frac{x}{2} \\ \\ \frac{1}{ \sqrt{2} } = \frac{x}{2} ..( \because \: \sin 45 \degree =\frac{1}{\sqrt 2}) \\ \\ \huge \purple{ \boxed{ x = \frac{ \sqrt{2} }{2}}} \\ \\ [/tex]
Using the trigonometric ratio sine, we find that x = [tex]\sqrt{2}[/tex], making option D to be correct.
The six trigonometric ratios are sine (sin), cosine (cos), tangent (tan), cotangent (cot), cosecant (cosec), and secant (sec). These trigonometric ratios deduce a relationship between angles of right angle triangle ( other than the right angle ) and the sides of the triangle : base, perpendicular, hypotenuse.
We have used trigonometric ratio sine here.
sin[tex]\theta[/tex] = [tex]\frac{perpendicular}{hypotenuse}[/tex]
In the given question,
from the point of view of angle 45° which is marked in the figure,
base = y
perpendicular = x
hypotenuse = 2
Using, sin[tex]\theta[/tex] = [tex]\frac{perpendicular}{hypotenuse}[/tex]
sin 45 = [tex]\frac{2}{x}[/tex]
[tex]\frac{1}{\sqrt{2} } = \frac{x}{2} \\\\x = \frac{2}{\sqrt{2} } = \sqrt{2}[/tex]
Learn more about trigonometric ratios here
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What is the distance from the point (3,8) to the point (7,-6)?
Answers
Answer: Distance is 14.6
Step-by-step explanation:
[tex]d = √((x2-x1)2 + (y2-y1)2)[/tex]
[tex](x2-x1) = (7 - 3) = 4[/tex]
[tex](y2-y1) = (-6 - 8) = -14[/tex]
add it all together
[tex](4)2 + (-14)2 = 16 + 196 = 212[/tex]
Square 212
[tex]\sqrt{212} =14.5602[/tex]
round to the nearest tenth
=14.6
PLEASE MARK BRAINLIEST
Answer: d=14.6
Step-by-step explanation:
√212=14.5602
round=14.6
The number of squares that are required to fill a rectangle of 512 cm by 108 cm, if each square of length 8 cm is _____________. a. 838 b. 864 c. 752 d. 440
Answers
Answer:
864
Step-by-step explanation:
512÷8=64
108÷8=13.5
64×13.5=864
Answer:
b) 864 squares
Step-by-step explanation:
A(rectangle) = 512cm x 108cm = 55296 cm²
A(square) = 8cm x 8cm = 64 cm²
Ar/As = 55296cm²/64cm² = 864 squares
The sum of exterior angles of a regular polygon are equal TRUE\FALSE
Answers
Answer:
The sum of exterior angles of a regular polygon are equal true that is equals to 360°
Step-by-step explanation:
i hope this will help you :)
Answer:
true
Step-by-step explanation:
The sum of exterior angles of a regular polygon are 360°
During a sale, a shop allows 20% discount off the marked price of clothing. What will a customer pay for a dress with a marked price of $30? * 1 point
Answers
Answer:
$24
Step-by-step explanation:
Let the full price of $30 be 100%.
If the discount allowed is 20%, then the percentage of the original price that a customer will pay is:
[tex]P=100\%-20\%\\P=80\%[/tex]
80% of a marked price of $30 is:
[tex]80\%*\$30\\\$24[/tex]
A customer will pay $24.
Can any one help me in this please if you can I really need help please help me thank you
Answers
this my first time to ues this app the answer is right, hope you got it
A movie theater has a seating capacity of 275. The theater charges $5.00 for children, $7.00 for students, and $12.00 of adults. There are half as many adults as there are children. If the total ticket sales was $ 1986, How many children, students, and adults attended? CHILDREN ATTENDED= ? STUDENTS ATTENDED= ? ADULTS ATTENDED=?
Answers
Answer:
Adults = 61
Students = 92
Children = 122
Step-by-step explanation:
a adults
x students
c children
a + c + x = 275
c / a = 2
5c + 7x + 12a = 1986
Simplify and solve the system.
a + 2a + x = 275
3a +x = 275
x = 275 - 3a. and c= 2a
The revenue equation can be written in terms of just one variable, a.
5(2a) + 7(275-3a) + 12a = 1986
Solve for a
a = 61
use it to find x and c.
c = 2a = 2 x 61 = 122
x = 275-a-c
x = 275 - 61-122
x = 92
Geraldo is driving 504 miles to his grandparents’ house for the holidays. So far he has driven 21 miles in 20.3 minutes. If he continues to drive at this average rate of speed, estimate how long the entire trip will take.
Answers
Answer: about 5 hours and 3 min
Step-by-step explanation:
Answer:
about 8 hours and 7 minutes
Step-by-step explanation:
have 60 minutes divided by 20.3 minutes to find the correct ratio to find themph if the speed remained constant. It is about 2.95567 and using this number multiply to 21 to get the miles per hour. the speed is about 62.069 mph. then divide the 504 miles by the mph of the car to find how long it will take to get there. It is about 8 hours 7 minutes and 20 seconds give or take, or 8.12 hours.
What is the slope of the line? x+3y=10
Answers
Answer:
m = -1/3
Step-by-step explanation:
First, write the equation in slope-intercept form:
3y = 10 - x
y = 10/3 - x/3
y = 10/3 - 1/3x
Since our slope is the coefficient of the x term, our slope is -1/3.
Increase £16470.45 by 3.5% Give your answer rounded to 2 DP pls help
Answers
Answer:
$17046.90
Step-by-step explanation:
Write out the equation for increase:
16470.45(1 + 0.035)
16470.45(1.035)
17046.90
what are the soultions of 3(x-4) (2x-3)= 0 check all
Answers
Answer:
{3/2, 4}
Step-by-step explanation:
Set x - 4 = 0 and solve for x: x = 4 is a solution.
Seet 2x - 3 = 0 and solve for x: 3/2 is another solution.
At a frozen yogurt shop, 7/25 of sales are chocolate, 0.09 of sales are mocha, 2/5 of sales are vanilla, and the rest are strawberry. What percent of sales is strawberry?
Answers
Answer:
22%.
Step-by-step explanation:
7/25 = 28%
0.09 = 9%
2/5 = 40%
29% + 9% + 40% = 78%
100% - 78% = 22%
And you have your answer. Hope this helped.
Solve the equation below algebraically for the exact value of x. 6 − 23(x + 5) = 4x
Answers
Answer:
See below.
Step-by-step explanation:
6 - 23(x+5) = 4x
First, distribute.
6 - 23x - 115 = 4x
Reorder the terms.
6 - 115 - 23x = 4x
Subtract.
-109 -23x = 4x
Add 23x to both sides.
-109 = 27x
Divide by 27.
x = -109/27 (This cannot be simplified)
6-23x-115=4x
-109=27x
x=4.03
what is the volume of a box that will hold exactly 567of these cubes with 1.3 inch side
Answers
Answer:
21 inch cube
Step-by-step explanation:
(1/3)(1/3)(1/3)=1/27 is the volume of the cube
the volume of the box : 567*(1/27)=567/27=21
help me :( ill give u brainly! :)
Answers
Answer:
6.61387 stones
Step-by-step explanation:
Answer:
6.6 stones
Step-by-step explanation:
1 kg= 2.2 pounds
1 stone =14 pounds ⇒ 1 pound= 1/14 stone
42 kg= 42*2.2 pounds= 92.4 pounds
92.4 pounds = 92.4 * 1/14 stone= 6.6 stones
To best estimate the quotient in scientific notation, what number should replace m?
StartFraction 6.33 times 10 Superscript 9 Baseline Over 1.79 times 10 Superscript 5 Baseline EndFraction almost-equals 3 times 10 Superscript m
Answers
Answer:
m=4
Step-by-step explanation:
6.33 × 10^9 / 1.79 × 10^5=3.54 × 10^m
Find m
6.33 × 10^9 / 1.79 × 10^5 =3.54 × 10^m
Divide the multipliers
6.33/1.79
=3.54
Divide the other multipliers
10^9/10^5
Division in scientific notation with superscript with the SAME base requires subtraction of the superscript using one of the bases
10^9/10^5
= 10^9-5
=10^4
Therefore,
6.33 × 10^9 / 1.79 × 10^5 = 3.54 × 10^4
m = 4
Answer:
4 :)
Step-by-step explanation:
Use the diagram to find the indicated angle measures. m∠1 = degrees m∠2 = degrees m∠3 = degrees
Answers
Answer:
m∠1 = 131°
m∠2 = 49°
m∠3 = 112°
Step-by-step explanation:
We find the m∠2 using Vertical Angles Theorem
We find the m∠1 using Definition of a Line
We find the m∠3 also using Vertical Angles Theorem
HELP IMA GIVE BRAINLY AND A LIKE
Answers
Answer: 18 animals
Step-by-step explanation:
3 out of 20 pet owners get their pet from a breeder.
To find how many animals have been bought from a breeder, you need to find 3/20 of the 122 animals.
3/20 = 0.15
122 * 0.15 = 18.3
18.3 rounds down to 18
There are 18 animals who have been bought from a breeder.
simplify
[tex] \frac{3x - 12x {y}^{2} }{6 - 3y - 18 {y}^{2} } [/tex]
Answers
Answer:
[tex]\dfrac{2xy+x}{3y+2}[/tex]
Step-by-step explanation:
Factor numerator and denominator and cancel common factors.
[tex]\dfrac{3x-12xy^2}{6-3y-18y^2}=\dfrac{-3x(4y^2-1)}{-3(6y^2+y-2)}=\dfrac{x(2y-1)(2y+1)}{(2y-1)(3y+2)}\\\\=\boxed{\dfrac{2xy+x}{3y+2}}[/tex]
4(13) + (18 4 27)
4(10) + 4(3) + (18 + 27)
40 - 12 + (+ 27)
Answers
Answer: Associative Property: (40+(12+18)+27. Evaluate: 97
Which trigonometric ratio is correct for triangle DEF? (Hint: Use Pythagorean Theorem first) A.) Sin(D)= 24/7 B.) Tan(D)= 24/25 C.) Cos(E)= 24/25 D.) Sin(E)= 7/24
Answers
Answer:
Cos E= 24/25
Step-by-step explanation:
Length of hypotenuse: 7^2+24^2=625. 625 square root=25
Thus, DE is 25.
Sin D= 24/25, so that is false.
Tan D= 24/7, so that is false.
Cos E= 24/25, so that is true
Sin E= 7/25, so that is false.
Please sb help and write it down on paper then send a pic❤️
Answers
Answer:
Step-by-step explanation:
1) We would determine the cube root of 27 and find its square.
Cube root of 27 = 3
3² = 9
Solution = 9
2) 36³ = 46656
√36³ = √46656 = 216
3) we would find the 5th roof of - 243 and find its cube
5th root of - 243 = - 3
- 3³ = - 27
Solution = - 27
4) Looking at the expression, 40⅔, we can see that
a = 2
b = 3
c = 40
Answer: 1) We would determine the cube root of 27 and find its square.Cube root of 27 = 33² = 9Solution = 92) 36³ = 46656√36³ = √46656 = 2163) we would find the 5th roof of - 243 and find its cube5th root of - 243 = - 3- 3³ = - 27Solution = - 274) Looking at the expression, 40⅔, we can see that a = 2b = 3c = 40
Step-by-step explanation:
Please answer this question in two minutes
Answers
Answer:
FGH and BCD
it's obvious.
no common lines between them