The bottom of the ladder is now 96 feet closer to the house compared to its initial position.
To solve this problem, we can use the concept of similar triangles. Let's denote the distance between the bottom of the ladder and the base of the wall as x (in feet). We are given the following information:
Initial ladder position:
Top of the ladder is 16 feet above the ground.
Bottom of the ladder is 12 feet away from the base of the wall.
New ladder position:
Top of the ladder is 18 feet above the ground.
Since the triangles formed by the ladder, the ground, and the wall are similar, we can set up a proportion to find the new distance between the bottom of the ladder and the base of the wall.
Using the initial position of the ladder:
(16 ft) / (x + 12 ft) = (18 ft) / (x)
Cross-multiplying:
16 ft * x = 18 ft * (x + 12 ft)
Expanding:
16x = 18x + 216 ft
Moving the terms involving x to one side:
16x - 18x = 216 ft
Simplifying:
-2x = 216 ft
Dividing by -2:
x = -108 ft
Since distance cannot be negative, we discard the negative solution. The distance between the bottom of the ladder and the base of the wall is 108 ft.
Now, to find how much closer to the house the bottom of the ladder is, we can subtract the initial distance (12 ft) from the new distance (108 ft):
108 ft - 12 ft = 96 ft
for such more question on triangles
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Your house had a value of $480,000 and increased in value by 3.5%. How much is your house worth now?
Answer:
$496,800
Step-by-step explanation:
Present cost = $480,000
%increase = 3.5%
Present price of the house = 480,000 + 3.5% of 480,000
= 480,000 + 0.035 * 480,000
= 480,000 + 16,800
= $496,800
Present price of the house = $496,800
What is 6 1/12 - 3 6/12? Move numbers to the boxes to show the answer. If there is no whole number put a 0 in the first box
6/12
- 1/12
= 5/12
6 - 3 = 3
= 3 5/12
Points A, B, C, and D are the vertices of a square. Points E and F are the center of two congruent semicircles that are tangent to each other at point G. Which value is closest to the area of the shaded regions?
Answer:
8 sq units
Step-by-step explanation:
to find the area of shaded region:
area of square minus sum of areas of each semi-circle
A(square) = 6² = 36
A (semi-circle) = πr²/2
= π3²/2
= 4.5π
Since there are two semi-circles, that makes one complete circle with an area of 9π
A(circle) ≈ 28 sq units
36-28 = 8 sq units
Pls I need help ASAP❤️
Answer: third option 60t + 24t
Step-by-step explanation:
Answer: 60[tex]x^{3}[/tex]-24[tex]x^{2}[/tex]
Step-by-step explanation:
It takes 70 pounds of seed to completely plant a 9 -acre field.
How many pounds of seed are needed per acre?
Answer:
7.8 to 1 decimal place
Step-by-step explanation:
70 pounds for 9 acre
for one acre it'll be 70/9
7.7 recurring or 7.8 to 1dp or 8 to the nearest whole number
Answer:
7/9 pounds
Step-by-step explanation:
I did 70/9 to get 7/9 pounds
Which expression is represented by this model
Answer:
A
Step-by-step explanation:
The distance between 0 and 4/6 is 4/6. This distance is repeted two times
so we have 4/6 + 4/6 or 2 x 4/6
HELP WILL COUNT BRAINLIEST
Hoy vamos de excursión con la escuela y nos ha tocado hacer los bocadillos para toda la clase. Si para hacer los bocadillos para mis 4 hermanos gastamos 2 barras de pan, ¿cuántas barras de pan necesitaremos para hacer los bocadillos de los 24 alumnos que hay en clase?Regla de tres
Answer:
12barras
Step-by-step explanation:
Hoy vamos a hacer una excursión con la escuela y tuvimos que hacer sándwiches para toda la clase. Si gastamos 2 hogazas de pan para hacer sándwiches para mis 4 hermanos, ¿cuántas hogazas de pan necesitaremos para hacer sándwiches para los 24 estudiantes de la clase?
De la pregunta anterior:
4 personas = 2 barras de pan
24 personas = x
Multiplicar cruzada
4 × x = 24 × 2 barras de pan
x = 24 × 2 barras de pan / 4
x = 12 barras de pan
A furniture designer builds a trapezoidal desk with a semicircular cutout. What is the area of the desk?
Answer:
[tex]Area = 26478cm^2[/tex]
Step-by-step explanation:
Given
See attachment for desk
Required
The area
First, calculate the area of the semicircular cutout
[tex]Area = \frac{\pi r^2}{2}[/tex]
Where
[tex]r = 60cm[/tex]
So:
[tex]A_1 = \frac{3.14 * 60^2}{2}[/tex]
[tex]A_1 = \frac{11304}{2}[/tex]
[tex]A_1 = 5652cm^2[/tex]
Next, the area of the complete trapezium
[tex]Area= \frac{1}{2}(a + b) * h[/tex]
Where
[tex]a = 300[/tex]
[tex]b = 2 * r = 2 * 60 = 120[/tex]
[tex]h = 153[/tex]
So:
[tex]A_2 = \frac{1}{2} * (300 + 120) * 153[/tex]
[tex]A_2 = \frac{1}{2} * 420 * 153[/tex]
[tex]A_2 = 32130cm^2[/tex]
The area of the desk is:
[tex]Area = A_2 - A_1[/tex]
[tex]Area = 32130cm^2 - 5652cm^2[/tex]
[tex]Area = 26478cm^2[/tex]
If a=2i+4j, b=2i-5j.What is the vector equation of line AB?.
Answer:
9j
Step-by-step explanation:
vector AB means going to B from A.
= pos. final - pos. initial
= pos.B - pos.A
= (2i + 4j) - (2i - 5j)
= 2i + 4j - 2i + 5j
= 9j
please provide a solution
26. What is the approximate length of RS 7
18 in
S
21 in
R
A. 9.5 in
B. 10.8 In
C 12.1 In
D. 12.8 In
I NEED AN ANSWER ASAP PLEASE!!!
Answer:
40% properties are Semi-detached
Step-by-step explanation:
Given,
Percentage of Bungalow = 10%
Percentage of Detached properties = 30%
Percentage of Apartments = 20%
∴Total percentage of properties deducting the semi-detached properties
= (10 + 30 + 20) %
= 60%
∴ Percentage of semi detached properties = (100 - 60) %
= 40%
So, 40% properties are Semi-detached.
These are 230 calories in 4 ounce of a type of ice cream how many calories are in 6 ounces of that ice cream
Answer:
345
Step-by-step explanation:
230/4 = 57.5
57.5 times 6 = 345 calories
Can somebody help with this
Answer:
B
Step-by-step explanation:
Domain is the x value and it is asking your for the coordinates with the same x value.
The figure below shows a triangular piece of cloth: What is the length of the portion BC of the cloth?
6 cos 32°, 6 sin 32°, cos32°/6, sin32°/6
Answer:
the answer is simple
Step-by-step explanation:
hope you got mu explanation
Answer:
6 sin 32°
Step-by-step explanation:
Hope this helps :)
PLEASE HELP GONNA FAIL WILL GIVE BRAINLESS
Answer: P = 166 units
Step-by-step explanation: Each point on the triangle has lines that are tangent to the circle in the triangle, meaning that those lines form a 90° angle to the middle point in the circle. There is also a rule that states if there are tangent lines coming from the points and if the points have at least one given side length, the other side will have the same side length. So if one side on point D is 41, then the other side connected to the point is 41. I added up all of the side lengths; 41 + 41 + 30 + 30 + 12 +12 = 166 units.
I hope this helps!
Given that f(x) = 3x - 2, g(x) = x2 + 3x and h(x) = 4.2^x
Find x in each image below. Simplify any radicals.
To Find :
The value of x.
Solution :
We know, when two chords intersect outside the circle.
[tex]21\times ( 21 + 45 ) = x \times ( x+5x)\\\\1386 = 6x^2\\\\x^2 = 231\\\\x = \sqrt{231}[/tex]
Hence, this is the required solution.
What are the solutions to the equation x² + 16x + 14 = 0?
Answer:
-8+5√2 and -8-5√2
Step-by-step explanation:
Given the expression x² + 16x + 14 = 0
USing the general formulas
x = -16±√16²-4(14)/2
x = -16±√256-56/2
x = -16±√200/2
x = -16±10√2/2
x = -8±5√2
Hence the required solutions are -8+5√2 and -8-5√2
How many distinct triangles can be drawn by using three of the seven dots below? (Two
triangles are considered different if they don’t share the same three vertices.)
Answer:
With 3 dots, you can only draw 1 triangle.
Step-by-step explanation:
All Triangles must have 3 sides, and 3 angles.
Note:
Pls, brainliest.
Thank you!
1,100,300 in written in words please!
Answer:
one million one hundred thousand three hundred
PLS HELP I WILL GIVE BRIANLY!
Francine bought 3 skirts that cost $2500 each before the discount. What was her total after
the discount?
Find the circumference of the given circle given a diameter of 40 cm.
Use 3.14 as an approximation of Pi.
Answer:
c. 125.6
Step-by-step explanation:
Pi= 3.14
r= d/2 = 40/2 = 20
[tex]2\pi \: r[/tex]
= 2 × 3.14 × 20
=125.6
find and interpret the slope
Answer:
y interpret is 60
slope 60/4=20x
hope this helps
have a good day :)
Step-by-step explanation:
Could you help ? It says “ a nursery plants a new tree and attaches a guy wire to help support the tree while it’s roots take hold. An eight foot wire is attached to the tree and to a stake in the ground the angle of elevation of the connection with the tree is 42 degrees . Find the nearest tenth of a foot, the height of the connection point on the tree” .
Answer:
5.4'
Step-by-step explanation:
See diagram attached.
The 8' wire is the hypotenuse of the triangle, with a base angle of 42°.
Hence the height is the length of the hypotenuse multiplied by sin(42°)
H = 8sin(42°) = 8 *0.6691 = 5.353'
(see similar or identical question 23903470)
Help !Which of the following functions are linear?
Function A
Function b
Function a and b
Or none of the above
Answer:
function A
Step-by-step explanation:
_______________
Please help with this ASAP
Answer:
7w^3/5v
Step-by-step explanation:
42v^3w^4/30v^4w
42 = 6 * 7
30 = 6*5 , factor
6*7v^3w^4/6*5v^4w
6 is common, cancel
7v^3w^4/5v^4w
simplify w^4/w = w^3
v^3/v^4 = 1/v
therefore, 7w^3/5v is the answer
Pam had some toy cars. She got 4 more cars. Then her friend gave her 2 more cars. Now Pam has 18 toy cars in all. Which equation shows this word problem? O A. A. 0 +4+2 = 18 О B. D +4- 2 = 18 O + C. 4+ 2 + 18 = 0 O D. 4+2 – 18 = 1
Find the values of x and y. State which theorems you used
Answer:
Step-by-step explanation:
5/6.
use that alternate exterior angles are congruent
3x= 5x -64; 64 = 5x-3x; 64= 2x ; 32 =x
use that lines form 180°
y+ 5x-64= 180
y= 180 +64 -5*32; y= 84
7/8.
use that alternating exterior angles are congruent
x=86
use that same side exterior angles are supplementary
x+y = 180; y= 180 -86; y= 94
9/10.
use that vertical angles are congruent
2y=59; y= 59/2; y= 29.5
use that alternate exterior angles are congruent
3x-4= 2y; 3x = 2y+4; x= (59+4)/3; x=21