When a stepladder is placed as shown, is it possible for the lower ends of the ladder to be 12 feet apart? Explain
Answers
Answer:
No, with the guides in between the two ladders, it is not possible for the lower ends of the ladder to be up to 12 feet apart
Step-by-step explanation:
The given parameters are;
The length of two sides of the step ladder = 12 feet
The maximum value allowable for the included angle between the two 12 feet ladders = 58°
Therefore, the maximum value of the third side facing the included angle is given as follows;
let "a" represent the maximum value of the third side formed by the distance apart of the lower end of the ladder, by cosine rule, we have;
a² = 12² + 12² - 2 × 12 × 12 × cos(58°) = 135.383251901
∴ a = √(12² + 12² - 2 × 12 × 12 × cos(58°)) ≈ 11.64
The maximum value of the third side formed by the distance apart of the lower end of the ladder = a ≈ 11.64 feet < 12 feet
Therefore, it is not possible for the lower ends of the ladder to be up to 12 feet apart.
Related Questions
what is 8029 times 89810
Answers
Answer:
721084490
Step-by-step explanation:
The region R, shown shaded in the diagram, is bounded by four straight lines.
Write down the inequalities that define R.
for some reason i can’t remember how to do this (might be because i’m tired but i’m on my last homework question), can anyone help?
Answers
9514 1404 393
Answer:
1 ≤ y ≤ 30 ≤ x ≤ 2Step-by-step explanation:
The boundaries in the vertical direction are the horizontal lines ...
y = 3 (top boundary)
y = 1 (bottom boundary)
The shaded region is between these lines, so y has values described by ...
1 ≤ y ≤ 3
__
The boundaries in the horizontal direction are the vertical lines ...
x = 0 (left boundary)
x = 2 (right boundary)
The shaded region is between these lines, so x has values ...
0 ≤ x ≤ 2
These are your inequalities.
_____
If you're plotting this on Desmos, you can use the relation ...
max(abs(x-1), abs(y-2)) ≤ 1
assume that the radius of a cylinder is the same as its height. What would happen to the volume of this cylinder if the radius were doubled and its height was half
Answers
9514 1404 393
Answer:
volume is doubled
Step-by-step explanation:
The formula for the volume of a cylinder is ...
V = πr²h
Then the volume of the modified cylinder is ...
V = π(2r)²(h/2) = π(4r²)h/2 = 2πr²h . . . . . double the previous volume
find an equation in standard form of a parabola passing through the points below
(1,-1),(5,31),(6,44).
Answers
Answer:
Basic parabola: y = ax2 + bx + c
We have 3 points we can plug in for (x, y) to create 3 simultaneous equations
(-2, 24): 24 = 4a - 2b + c {equation 1}
(3, -1): -1 = 9a + 3b + c {equation 2}
(-1, 15): 15 = a - b + c {equation 3}
Solve this system to find the values of a, b, c
Let's first eliminate variable c:
4a - 2b + c = 24 {equation 1}
a - b + c = 15 {equation 3}
--------------------- subtract
3a - b = 9
9a + 3b + c = -1 {equation 2}
a - b + c = 15 {equation 3}
-------------------- subtract
8a + 4b = -16
We now have two equations with 2 unknowns we can use to find a, b
3a - b = 9 {equation 4}
8a + 4b = -16 {equation 5}
Multiply equation 4 through by 4 and add equations
12a - 4b = 36
8a + 4b = -6
----------------- add
20a = 30
a = 30/20
a = 3/2
8a + 4b = -6
8(3/2) + 4b = -6
12 + 4b = -6
4b = -6- 12
4b = -18
b = -18/4
b = -9/2
Plug these 2 values into one of the original equations and solve for c
15 = a - b + c {equation 3}
15 = 3/2 + 9/2 + c
15 = 12/2 + c
15 = 6 + c
c = 15-6
c = 9
y = (3/2)x2 - (9/2)x+ 9
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Step-by-step explanation:
Find the inverse if f(x)=6(x+7)
Answers
Answer:
y=1/6 x -7
Step-by-step explanation:
it's easier to just substitute y w/x, and vice versa
x=6y+42
x-42=6y
Jessica measured the amount of precipitation that fell during a week. She determined that 13 centimeters of rain fell. Actually, though, 12 centimeters of rain fell during that week. To the nearest tenth of a percent, what is the percent error of Jessica's measurement?
Answers
Answer:
8.3%
Step-by-step explanation:
The formula for Percentage error is given as:
|Measured value - True value|/True value × 100
The measured value = 13cm
The true value = 12cm
Hence:
Percentage error = |13 cm - 12cm|/12 cm × 100
= 1/12 × 100
= 8.3%
The percent error of Jessica's measurement is 8.3%
Beth adopted a kitten from the animal shelter. The adoption fee was $150. She also bought 4 bags of cat food on the way home. The total amount she spent was $185.84. What was the price for each bag of cat food
Answers
Answer:
$8.96
Step-by-step explanation:
total amount spent minus adoption fee is $35.84
divide this by the number of bags which is 4, your answer is $8.96
90 coins
Use the original price and the markup to find the retail price.
Original price: $50; Markup: 15%
The retail price is $ ?
Answers
Answer:
50 + 50(.15)
50(1+ .15)
50(1.15)
RP= $57.5
Step-by-step explanation:
Jonathan bought a box of stamps to start a collection. He has purchased the same number of stamps each week to add to the collection. The graph
shows the number of stamps Jonathan has at the end of each week. How many stamps were in the box Jonathan bought to start his collection?
Assume that the relationship between the two quantities is linear.
A. 216
B. 120
C. 96
D. 12
Answers
Answer:
120
Step-by-step explanation:
its where the graph starts
Find the domain and range of the function {(1,2) , (2,2) , (3,2) , (4,2)}
Answers
Answer:
Step-by-step explanation:
X-coordinates are domain and y-coordinates are range
Domain= {1,2,3,4}
Range= {2}
Answer:
domain: 1,2,3,4. range:2
Step-by-step explanation:
domain is the input aka the x- values, and the range is the output aka the y-values
calculate the rate of change
Answers
1. f(x) = 4x + 3x3
Is this a monomial,Binomial, or Trinomial
Answers
Answer:
It is a monomial
Step-by-step explanation:
4x+3x3=4x+9.
There is one variable the first power so therefore, it is a monomial.
Please help me with this math problem if you can. You just say yes or no if it’s a square, rectangle, etc. and then give the reason why
Answers
Answer:
Step-by-step explanation:
B) rectangle because the diagonals are congruent
C) Diamond so no it isn't a square or rectangle due to no 90 degree angles
D)Square because the diagonals are perpendicular and congruent
The image of the point (-8, 3) under a translation is (-5,2). Find the coordinates
of the image of the point (9,9) under the same translation.
Answers
Answer:
IMAGE=OBJECT +TRANSLATION
The coordinates are (12, 8).
What is translation?A translation in math moves a shape left or right and/or up or down. The translated shapes look exactly the same size as the original shape, and hence the shapes are congruent to each other. They just have been shifted in one or more directions. Since it is just moving of the shape from one place to other, there is no change in the shape.
Translation is one of the transformations in math. When a shape has been transformed, the original shape is called the preimage and the vertices are usually labeled using uppercase letters (Example: ABCD). The translated shape is called the image and the vertices are labeled using uppercase letters with a “prime” next to each (Example: A′B′C′D′, and is pronounced “A-prime, B-prime, C-prime, D-prime”).
Given:
the point is (-8, 3) whose image point is (-5, 2)
The difference between the coordinates of the image and the coordinates of the original is the same for both points.
X - (9, 9) = (-5, 2) -(-8, 3)
X = (-5, 2) -(-8, 3) +(9, 9) = (-5+8+9, 2-3+9)
X = (12, 8)
Hence, the point is (12, 8)
Learn more about translation here:
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What is the equivalent fractions for 3/10?
Answers
Answer:
6/20, 15/50, 9/30, 30/100, 12/40, 18/60....
Step-by-step explanation:
Its just multiplying the fraction by any whole number.
Make sure to do both the numerator and the denominator!
(hope this helps)
Functions f(x) and g(x) are composed to form h(x) = sqrt(x ^ 3- 2) if f(x) = sqrt(x + 2) and g(x) =x^3+a. What is the value of a
Answers
Answer: a = -4
Step-by-step explanation: Function Composition is when two functions f(x) and g(x) result in another function h(x), such that h(x) = f(g(x)). In other words, put the result of one function into the other one.
In this situation,
h(x) = f(g(x))
which means
h(x) = f(x³+a)
h(x) = [tex]\sqrt{x^{3}+a+2}[/tex]
[tex]\sqrt{x^{3}-2} =\sqrt{x^{3}+a+2}[/tex]
Now, to find a, we separate equal terms:
1) Both are squared, so we can "eliminate" the square;
2) x³ = x³;
3) [tex]-2=a+2[/tex]
[tex]a=-4[/tex]
For function composition h(x) = f(g(x)), the value of a is -4.
Answer:-4 or D
Step-by-step explanation:
a cell phone company charges one $20 for the phone and then $35 a month for phone service another cell phone company charges 55 a month for phone service with a free phone after how many months will the phone services cost the same
Answers
20 + 35x = 0 + 55x
HELP MEEEEEEEEEEEE PLZ
Answers
Answer:
The first 25 prime numbers (all the prime numbers less than 100) are: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97.
-7w²+2w if w=-4 i need the answer please!!!!!!!!!!!!!!
Answers
Answer:
-6,272
Step-by-step explanation:
-7 times -4 equals 28
28 to the power of 2 is 784
2 times -4 equals -8
-8 times 784 equals -6,272
bac
4. Jim has the following cell phone plan.
• Weekday calls cost 10 cents per minute.
• Weekend calls are free.
• Each text message costs 5 cents.
Each month, Jim talks for m minutes on weekdays and f minutes
on weekends, and sends t texts. Which equation represents
Jim's monthly cell phone bill, C?
A.
C = 0.10m - 0.051
B.
C = 0.10m - 0.5t
nents
C.
C = 0.10m - 0.10f-0.10
D
('= 0.10m - f-0.057
Answers
Find the value of X!!!!!!!!
Answers
Help pls 6th grade math i will give brainliest
Answers
Answer:
G because y+y+y is the exact same as 3 y
Jamie bought a handbag for 20$, an umbrella for $5.99, and a scarf for $8.50. If the sales tax rate is 7% how much is the sales tax and the total cost of her purchase
Answers
Answer: $36.9043
Step-by-step explanation:
Given that :
Cost of handbag = $20
Cost of umbrella = $5.99
Cost of scarf = $8.50
Sales tax = 7% = 0.07
Sales tax = 0.07 * (20 + 5.99 + 8.50)
Sales tax = 0.07 * 34.49
Sales tax = $2.4143
Total cost of purchase :
Sales tax + cost of items
$2.4143 + $34.49
= $36.9043
what is the ratio of y to x
Answers
Answer:
5:2
Step-by-step explanation:
3) Angela has 37 coins in dimes and nickels. She has a total of $3.30.
a) Write the system of 2 linear equations.
b) How many dimes does Angela have?
c) How many nickels does Angela have?
Answers
Answer:
hmmmmm b
Step-by-step explanation:
5x + 10y = 330
STEP ONE:
Substitute the variables
x = 37 - y
STEP TWO:
Substitute the values
5(37 - y) + 10y = 330
STEP THREE:
Multiply
185 - 5y + 10y = 330
STEP FOUR:
Subtract 185 from both sides
-5y + 10y = 145
STEP FIVE:
Add
5y = 145
STEP SIX:
Divide
y = 29
STEP SEVEN:
Check
x = 37 - 29
x = 8
Therefore, Angela has 8 nickels and 29 dimes.
Suppose that a school of 452 students is having a debate about gun control, and the students were asked to vote. The results show that 67 percent are in favor of banning guns, and 26 percent are against banning guns. The remaining students chose not to voice their opinions. How many students didn't voice their opinions? Round your answer to the nearest whole number?
Answers
Answer: 32
Step-by-step explanation:
Total number of students = 452
Students in favor of banning guns = 67%
Students against banning guns = 26%
Students who didn't voice their opinions = 100% - (67% + 26%) = 100% - 93% = 7%
The number of students who didn't voice their opinions would be:
= 7% × 452
= 0.07 × 452
= 31.64
= 32 to nearest whole number
Photo is attached I need to solve for x and y please help me
Answers
hope this helped <3
A recipe for apple cider cause for 4 cups of apple juice and 3 cups of water what equation can we use to find extra percent of apple juice in the recipe
Answers
Answer:
% Apple juice = [tex]\frac{4}{7}[/tex] × Y × 100.
Step-by-step explanation:
Given:
Ratio of apple juice to water = 4 : 3 = Y i.e 4+ 3 = 7
To find the exact % of apple juice used in recipe, we use the ratio of juice to water provided, given Y as any amount of apple cider.
∴ equation [tex]\frac{4}{7}[/tex] × Y = amount of apple juice.
for percentage, [tex]\frac{4}{7}[/tex] × Y × 100 = amount of apple juice.
Proof:
In 200ml apple cider, amount of apple juice present
= 4/7 × 200 = 114.2ml of juice
To make upto 00ml cider, add (200-114.2)ml of water.
I hope this was helpful.
What is the slope of the line?
4x -1 = 3y + 5
Choose 1 answer:
Answers
Answer:
The slope is 4/3
Step-by-step explanation:
Answer:
4/3
Step-by-step explanation:
rearrange into slope-intercept form
3y=4x-6
y=4/3x-2
A square picture has a border 5 cm
wide. The picture area is 4/9 of the total
area. Find the area of the picture.
Answers
Answer:
So area of square is: a^2
5^2=25cm^2
4/9 x 25 = 100/9
Area of picture is: 11.11 cm^2
Step-by-step explanation:
The area of the square will be equal to 11.11 square centimetres.
What is an area?
The space covered by the two-dimensional object on a plane is called as an area. The space covered by the square in a two-dimensional plane is called the area of the square.
The square is a quadrilateral having four sides and all the sides of the square are equal to each other.
The the area of the square is calculated as,
a² = 5²=25 cm²
The picture area is 4/9 of the total
area.
4/9 x 25 = 100/9
The area of the picture is: 11.11 cm²
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