Jamie has a ladder that is 15 ft long. She wants to lean the ladder against a vertical wall so that the top of the ladder is 14 ft above the ground.
1A. Use trigonometry to find the angle formed between the ground and the ladder. Round to the nearest whole number
2A. For safety reasons Jamie wants the angle the ladder makes with the ground to be no greater than 75 degrees. Will the ladder be safe the way she has it positioned?
Answers
Answer:
1A. = 68.96 degrees.
2A. = YES
Step-by-step explanation:
Hi, to answer this question we have to apply:
sin (angle ) = opposite side / hypotenuse
Since the triangle formed is a right triangle ( see attachment), the hypotenuse is the length of the ladder (the longest side), and the opposite side to the angle is the distance between the top of ladder and the ground.
Replacing with the value given
sin x = 14/15
Solving for x
x = arcsin 14/15
x = 68.96 degrees. (1A)
Since the angle is lower than 75 degrees, the ladder is safe the way is positioned.
Related Questions
ΔA'B'C' was constructed using ΔABC and line segment EH.
2 triangles are shown. Line E H is the line of reflection. Line segment B B prime has a midpoint at point D. Line segment A A prime has a midpoint at point F. Line segment C C prime has a midpoint at point G.
For to be the line of reflection between and , which statements must be true? Select three options.
BD = DB'
DF = FG
m∠EFA = 90°
The line of reflection, EH, is the perpendicular bisector of BB', AA', and CC'.
ΔABC is not congruent to ΔA'B'C'.
Answers
Answer:1,3,4
Step-by-step explanation:
Polly sold 34 Snow Cones at
her stand. The amount of each
flavor sold is shown in the bar
graph.
Based on the information in
the graph, which flavors of
snow cones were chosen by
50% of the customers?
Answers
Answer:
Melon and Swirl is 50% and Cherry and Grape is 50%
What is the total surface area of the square pyramid? 48square meters 64 square meters 76 square meters 88 square meters
Answers
Answer: 64m is the answer
Answer:
64 Square Meters is the Right answer...
Step-by-step explanation:
I took the test and got it right:D
Robby is considering taking out a cash advance on his credit card to purchase a new television. His credit card offers cash
advances up to $500.00 at an interest rate of 28%. If the television costs $350.00 and Robby plans to pay the balance of in 6
months, how much extra will he pay in interest to purchase the television?
a $29.14
b. $63.18
C. $174.48
d. $379.08
Answers
Answer:
the answer is A.
Step-by-step explanation:
Answer:
A. $29.14
Step-by-step explanation:
How many solutions does this equation have?
4x − 10
2
= 2x − 5
A) no solution
B) exactly one solution
C) exactly two solutions
D) infinitely many solutions
Answers
Answer:
d
Step-by-step explanation:
x=3 then the equation has one soultion like 3=3
The equation is a linear equation with one variable then the solution will be exactly one. Then the correct option is B.
What is the linear system?A Linear system is a system in which the degree of the variable in the equation is one. It may contain one, two, or more than two variables.
The linear equation is given.
4x − 10² = 2x − 5
In the equation above equation, the number of variables is one.
And the equation is a linear equation which means the degree of the x is one then the solution will be unique.
More about the linear system link is given below.
https://brainly.com/question/20379472
what is the slope of the line y= 1/2x + 1?
Answers
I hope this helped! Mark me Brainliest! :) -Raven❤️
Answer:
The slope is 1/2
Hope that helps:)
Tyrone's age is 2 years less than 4 times his younger sister's age. If his younger sister's age is b years, which of the following expressions best shows Tyrone's age?
4b b − 2 2b − 4 4b − 2
Answers
Answer:
Four times his sister's age would be 4b. his age is two years less, so we need to subtract 2.
put together, this is 4b - 2.
Answer:
Your answer will be 4b - 2
Step-by-step explanation:
Hope this helps!!
Write the point-slope form of the equation of the line that passes through the points (6, 6) and (-6, 1). Include your work in your final answer. Type your answer in the box provided to submit your solution.
Answers
The slope of the lines passing through given points is [tex]\frac{5}{12}[/tex].
Step-by-step explanation:
Given,
The given two points are (6,6) and (-6,1).
To find the slope of the line passing through the points.
Formula
The slope of the line passing through ([tex]x_{1} ,y_{1}[/tex]) and ([tex]x_{2} ,y_{2}[/tex]) is [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
Now,
Putting, [tex]x_{1}=6, y_{1}=6, x_{2}=-6, y_{2}= 1[/tex] we get,
Slope = [tex]\frac{1-6}{-6-6}[/tex] = [tex]\frac{-5}{-12}[/tex] = [tex]\frac{5}{12}[/tex]
Hence,
The slope of the lines passing through given points is [tex]\frac{5}{12}[/tex].
Answer:
y=5/12 x+21/6
Step-by-step explanation:
Stephanie works at a store that sells clothing accessories. The supply
function for scarves is P = Q-12, where Pis the price and Q is the quantity of
scarves. If Stephanie sells the scarves for $11 apiece, how many scarves can
the store make?
O
A. 34 scarves
O B. 12 scarves
O c. 23 scarves
O D. 11 marves
Answers
Answer:
23 scarves
Step-by-step explanation:
To solve this you need to plug the price Stephanie sells the scarves for, $11, in for P in the equation and solve for Q.
11 = Q - 12Add 12 to both sides: 23 = QThe quantity she can make is 23 scarves.
mike made a fruit basket of the total fruit 5 were apples 5/8 were bananas and 1/4 were oranges,how many pieces of fruit did mike use?
Answers
Answer: 5 7/8
Step-by-step explanation: 5 + 5/8 + 1/4= 5 7/8
The total number of pieces of fruit Mike used is [tex]40.[/tex]
Based on the information given.
1. Let [tex]\( T \)[/tex] be the total number of pieces of fruit.
2. Mike has [tex]5[/tex] apples.
3. [tex]\(\frac{5}{8}T\)[/tex] are bananas.
4. [tex]\(\frac{1}{4}T\)[/tex] are oranges.
Since these fractions represent parts of the total fruit, the sum of the apples, bananas, and oranges should equal the total number of pieces of fruit:
[tex]\[5 + \frac{5}{8}T + \frac{1}{4}T = T\][/tex]
Rewrite the equation with all terms having the same denominator:
[tex]\[5 + \frac{5}{8}T + \frac{2}{8}T = T\][/tex]
Combine the fractions on the left side:
[tex]\[5 + \frac{7}{8}T = T\][/tex]
Subtract [tex]\(\frac{7}{8}T\)[/tex] from both sides to isolate the constant term:
[tex]\[5 = T - \frac{7}{8}T\][/tex]
[tex]\[5 = \frac{1}{8}T\][/tex]
Multiply both sides by [tex]8[/tex] to solve for [tex]\( T \)[/tex]
[tex]\[5 \times 8 = T\][/tex]
[tex]\[T = 40\][/tex]
The box-and-whisker plot below shows the age distribution of people at a family reunion.
16
24
32
40
48
56
64
Ages
The stem-and-leaf plot below shows the same data.
089
10 1 4 5
3 3 5 6 6
1 6 6 8 9 9 9
0 1 2 4 6
To 236
01
Answers
Answer: CCCCCC
Step-by-step explanation:
James's dad drove a total of 140 miles last week,
He drove the same number of miles each day and he drove every day.
How many miles did he drive each day?
Answers
Answer:
140/24= 5 i think this is the answer
Step-by-step explanation:
if 5^x = 1/125, find the value of x
Answers
The answer is the following:
X = -3
Answer:
Step-by-step explanation:
hello :
5^x = 1/125
5^x = (1/5)^5 but : 1/5 = 5^-1
so : x= -1
Expand.
If necessary, combine like terms.
(3+4.)(3 - 4x) =
Answers
Answer:
-16x^2 +9
Step-by-step explanation:
To start this problem I would rearrange so that the terms with the x's come first. Making it look like this
(4x+3)(-4x+3)
Now you take the 4x and distribute it to the -4x and the 3.
-16x^2+12x This is the first part
Take the 3 and distribute it to the -4x and the 3 as well.
-12x+9
All you do now is combine the twoso you'd have
-16x^2 +12x -12x +9 Notice there are two terms that have a regular x with no exponent. This means you can combine them to simplify further.
-12x+12x=0 So you no longer have to include this term in your answer.
-16x^2+9 Would then be your final answer.
In a arithmetic sequence with a^1=12, d=3 which term is equal to 159?
Answers
Answer:
50th term is 159
Step-by-step explanation:
nth term=159
a + (n -1)*d = 159
12 + (n-1)*3= 159
(n - 1)*3 = 159 - 12
(n - 1)*3 = 147
n -1 = 147/3
n - 1 = 49
n = 49 + 1
n= 50
Answer: n=50th term
Step-by-step explanation:
An= a1+(n-1)d
An= nth term
A1= first term
N= nth position
D= common difference
An =159
A1= 12
D= 3
N= ?
Substitute the values
An=a1+(n-1)d
159=12+(n-1)3
Collect like terms
159-12=(n-1)3
147=3n-3
147+3=3n
150=3n
N=150/3
N= 50
Therefore 50th term will give 156
what does 3 +3 equal?
Answers
Answer:
6
Step-by-step explanation:
3 + 3 = 6
7. What is the area of this figure?
Answers
Answer:
20 m.
Step-by-step explanation:
Formula for rhombus: base x height.
Base: 8
Height: 2.5
2.5 x 8 = 20.
Tip: Usually when finding the area of a rhombus there is another length (in this scenario, 4) to try to fool or trick you. It's the length of the slanted side to the right. A rhombus is a square or rectangle when you take the triangle and piece it into the slanted area, so even though it looks like a complicated parallelogram it really isn't.
Hope this helped ^^
Cindy is shopping for a television. The original price is $612. Store A has the television on clearance for 30% off. Store B has it on clearance for 25% off, and Cindy has a 10% off coupon to use at Store B. At which store will she pay less? How much less?
Answers
Answer:
She will pay less at store B
Step-by-step explanation:
30% off of $612 is $428.4
25% off of $612 is $459
Remember she has a coupon for 10% off
10% off of 459 is $413.1
She would save $198.9
Answer:
Step-by-step explanation: store b
1. 5x + 2 = 27
how to work backwards on this type of problem
Answers
A rectangular parking area measuring 5000 ft squared is to be enclosed on three sides using chain-link fencing that costs $5.50 per foot. The fourth side will be a wooden fence that costs $7 per foot. What dimensions will minimize the total cost to enclose this area, and what is the minimum cost?
Answers
Answer:
Dimensions: 75.3778 ft and 66.3325 ft
Minimum price: $1658.31
Step-by-step explanation:
Let's call the length of the parking area 'x', and the width 'y'.
Then, we can write the following equations:
-> Area of the park:
x * y = 5000
-> Price of the fences:
P = 2*x*5.5 + y*5.5 + y*7
P = 11*x + 12.5*y
From the first equation, we have that y = 5000/x
Using this value in the equation for P, we have:
P = 11*x + 12.5*5000/x = 11*x + 62500/x
To find the minimum of this function, we need to take its derivative and then make it equal to zero:
dP/dx = 11 - 62500/x^2 = 0
x^2 = 65000/11
x = 250/sqrt(11) = 75.3778 ft
This is the x value that gives the minimum cost.
Now, finding y and P, we have:
x*y = 5000
y = 5000/75.3778 = 66.3325
P = 11*x + 62500/x = $1658.31
The dimensions that would minimize the total cost are [tex]66.3 \text{ by } 75.4[/tex]
The minimum cost is [tex]\$1658.3[/tex]
Let the sides of the rectangle be [tex]a[/tex] and [tex]b[/tex],
Let the total cost be given by [tex]T=7a+5.5(2b+a)[/tex]
The area, [tex]5000=a\times b \implies a=\frac{5000}{b}[/tex]
Substitute the formula for [tex]a[/tex] into the formula for [tex]T[/tex] to solve for [tex]b[/tex]
[tex]T=\frac{62500}{b}+11b[/tex]
To find the dimensions that would minimize the total cost,
Differentiate to get where the gradients equal zero[tex]\frac{dT}{db}=11-\frac{62500}{b^2}=0[/tex]
when
[tex]b=\pm \frac{250}{\sqrt{11}}[/tex]
Find the second derivative to find the minima[tex]\frac{d^2T}{db^2}=\frac{125000}{b^3}[/tex]
For minima, [tex]\frac{125000}{b^3}>0[/tex]
This means, [tex]b=+\frac{250}{\sqrt{11}}\approx 75.4 ft[/tex] is a minima
The corresponding value of [tex]a=\frac{5000}{b}=\frac{5000}{250}\times\sqrt{11}=20\sqrt{11}\approx 66.3 ft[/tex]
To find the minimum cost, substitute the above minimum value for [tex]b[/tex] into the formula for the total cost
[tex]T=500\sqrt{11}=\$1658.3[/tex]
Learn more about minima and maxima: https://brainly.com/question/2541083
f(x) = 3x + 2, f(5) = _
Answers
Answer:
17
Step-by-step explanation:
f(x) = 3x + 2
f(5) = 3(5) + 2 = 17
Q4. The dimensions of a rectangular sheet of metal are 9.96m by 5.08 m. Find
a. the perimeter of the metal, correct to 1 significant figure
b. the area of the metal, correct to the nearest 0.1 m2
Answers
Answer:
a) 30m
b) 50.6m²
Step-by-step explanation:
Perimeter = 2(length + width)
= 2(9.96 + 5.08)
= 30.08 m
Area = length × width
9.96 × 5.08
50.5968 m²
There are two questions there. Feel free to just answer one. I’m stuck on these last two.
Answers
Answer:
7. option D
8. option D
Step-by-step explanation:
7. we can assume the height of the radio tower to be x. We're given with its shadow,the height of the person and also their shadow. Since we have 3 known values and an unknown, we can make a proportion comparing the tower's height to the height of the person.
∴ 6/10 = x/ 400
⇒ x= (6 * 400)/10 = 240 feet.
8. The question is similar to the above question where again we have 3 knowns and one unknown. Let us assume the length to be x. We'll again compare the length of the two photographs and make it as a proportion.
∴ 4/6 = x/10
⇒ x = (4 * 10)/6 = 6.7 in
Hope that answers your questions!
Answer:
Someone already answered so you mine will be useless, anyway have a nice day :D
Step-by-step explanation:
What is the solution to the equation 2 (x-3) ^2 =13 help help ASAP !
Answers
Answer:
3+sqrt(13/2)
3-sqrt(13/2)
Step-by-step explanation:
2 (x-3) ^2 =13
Divide each side by 2
2/2 (x-3) ^2 =13/2
(x-3) ^2 =13/2
Take the square root of each side
sqrt((x-3) ^2) =±sqrt(13/2)
x-3 = ±sqrt(13/2)
Add 3 to each side
x-3+3 = 3±sqrt(13/2)
x = 3±sqrt(13/2)
Step-by-step explanation:
x=√3+3,−√1
I tried...
99 POINTS!!! PLEASE HELP ME! I'M FAILING MATH AAAAAAA!!
Answers
Answer:
False
Step-by-step explanation:
Thats the only one i know to amswer sorry but it is false
The measure of arc XZ is 32°.
What is the measure of XYZ?
A. 32°
B. 64°
C. 148°
D. 16°
Answers
Given:
Measure of arc XZ = 32°
To find:
The measure of XYZ
Solution:
The measure of inscribed angle is half of the measure of the intercepted arc.
[tex]$\Rightarrow m\angle XYZ = \frac{1}{2}m(ar XZ)[/tex]
[tex]$\Rightarrow 32^\circ = \frac{1}{2}m(ar XZ)[/tex]
Multiply by 2 on both sides.
[tex]$\Rightarrow 2\times 32^\circ =2\times \frac{1}{2}m(ar XZ)[/tex]
[tex]$\Rightarrow 64^\circ =m(ar XZ)[/tex]
The measure of angle XYZ is 64°.
I need 5 mins!!! pls help!!
60 ÷ 10 × 3 to make it equivalent to 2??
Where should we put the Parentheses?
Answers
Answer:
60÷(10x3)
Step-by-step explanation:
After you do the parenthesis it would be 60÷30=2
Answer:
The answer is you put the parentheses in between 10*3
Step-by-step explanation:
what is the answer to this question jhit .
Answers
all the sides add up to 54
Answer:
the answer is 54
Step-by-step explanation:
hope it helps. can I get brainly please
ALGEBRA 2 PROBLEM! PLEASE HELP ME!
Answers
Answer:
A
Step-by-step explanation:
cos(60) = adjacent/hypotenuse
½ = B/5
B = 5/2
B = 2.5
Refer to the following photo please
10 points easy question
Answers
Answer:
I would like to say both reflections and rotational
Step-by-step explanation: