A ladder is leaning against a house at an angle of 35° at the roof line. The base of the ladder is 8 feet from the house. How long is the ladder to the nearest whole foot? Use a calculator if needed.
A. 27 feet
B.43 feet
C. 8 feet
D. 14 feet
E. 35 feet
Answers
Answer:
D
Step-by-step explanation:
Remark
What you are trying to solve for is the hypotenuse of a right triangle. You will use the sine to do it.
Givens
Base = 8 feet
angle = 35 degrees
hypotenuse = ?
Formula
Sin(35) = base / hypotenuse
Solution
Sin (35) = 8 / hypotenuse Multiply both sides by the hypotenuse
hypotenuse * sin(35) = hypotenuse * 8/hypotenuse
hypotenuse * sin(35) = 8 Divide by sin(35)
hypotenuse = 8/sin(35) Substitute value of sin(35)
hypotenuse = 8 / 0.5736
hypotenuse = 13.94
Answer
The ladder is about 14 feet long or D
Related Questions
Select the correct answer.
Graph the following system of inequalities.
y < 2x + 1
y <-x– 1
Answers
See the attachment for the graphed inequalities.
144x^2-100 factor completely
Answers
[tex]144x^2-100[/tex]
looking at the original equation, you'll notice that it is a difference of squares therefore the factored form will look like something like this:
[tex](ax-b)(ax+b)[/tex] where a and b are the two numbers and the x represents the variable.
This would be the factored form:
[tex](12x-10)(12x+10)[/tex]
It can then be simplified to this:
[tex]2(6x-5)2(6x+5)[/tex]
and this would be its fully factored form:
[tex]4(6x-5)(6x+5)[/tex]
The distance around a triangle is 36 cm. If two sides are equal and the length of the third side is 14 cm what is the length of each of the other two sides?
Answers
Answer: 11 cm
Step-by-step explanation:
Let x be the length of one of the other sides. If two are equal, then they both will be 2x.
Then one side is equal to 14 cm.
All the sides added together, the perimeter, is equal to 36 cm.
We will take the numbers we pulled from the problem, create an equation, and solve for x.
36 cm = 14 cm + 2x
22 cm = 2x
11 cm = x
The length of each of the two other sides is 11 cm.
The equation whose roots are multiplied by 3 of those of 2x^2 + 3x – 1=0 is
Answers
Answer:
Here is rest of explanation
Yo! Can someone help me with this?
Answers
Answer:
w=39 degrees and r=51 degrees
Step-by-step explanation:
The sum of the angles in a triangle should equal 180 degrees. Knowing this we take (38+103) - 180 = 39. Since opposite angles are always congruent, we can conclude that w is also 39 degrees. Thus we take (39+90)-180 = 51 degrees. (We know that one side is 90 degrees because it has a right angle)
Hope that helps! :)
If a number is divisible by 2 and 3, why is it also divisible by 6?
Answers
Answer:
They have 6 when multiplying it
Step-by-step explanation:
HELP ME PLEASE!!!!!!
Answers
Answer:
94 square inches.
Step-by-step explanation:
Surface area is the area around a surface. Thus, in order to calculate the surface area of a rectangular prism, we just need to add up the different faces of it.
There are 2 5x4 faces, 2 3x5 faces, and 2 4x3 faces.
Thus, we get 2*20 + 2*15 + 2*12 = 40 + 30 + 24 = 94 square inches.
First you have to find area of all the sides of the shape.
You so this by multiplying 4*5=20, 3*4=12, and 3*5=15
Then double all the products because there are two of each one of the sides on the shape because it is a rectangular prism.
You get 40, 24, and 30.
Finally add all of those numbers together to get the surface area. 40+24+30=94.
94 is the surface area
An ellipse has foci F1(−5, 5) aF2(0, 7) and the point (0, 5) is on the ellipse. Identify the constant sum for the ellipse.
Answers
The constant sum for the ellipse with the foci (-5,5) and (0,7) and the point (0,5) is 7
How to determine the constant sum?The foci of the ellipse are given as:
F1(−5, 5) aF2(0, 7)
The point is then given as:
Point (0, 5)
Calculate the distance between each focus and the point using:
[tex]d = \sqrt{(x_2 -x_1)^2 + (y_2 -y_1)^2}[/tex]
So, we have:
[tex]F_1 = \sqrt{(-5-0)^2 + (5-5)^2}[/tex]
Evaluate
[tex]F_1 = 5[/tex]
Also, we have:
[tex]F_2 = \sqrt{(0-0)^2 + (7-5)^2}[/tex]
Evaluate
[tex]F_2 = 2\\[/tex]
The constant sum is then calculated using:
Constant sum = F1 + F2
So, we have:
Constant sum = 5 + 2
Evaluate
Constant sum = 7
Hence, the constant sum is 7
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find the slope of the line thatpasses through these two points: (-3, 4): (2,-1)
Answers
Answer:
y=-x+1
Step-by-step explanation:
find the arc JML of the circle
Answers
Answer:
JML = 176°
Step-by-step explanation:
JML = 2 angle JKL
= 2 × 88°
= 176°
HOPE THIS HELPS AND HAVE A NICE DAY <3
2) Compare these sets of data. Choose the TWO sets of data with the MOST symmetrical distributions.
Answers
Answer:
when you are comparing two sets of data, and one set is strongly skewed and the other is symmetric, which measures of the center and variation should you choose for the comparison?
PLEASE HELP WILL MARK BRSINLIEST!!!!!
Answers
Explanation:
The corresponding sides are congruent, so we simply need to state that fact and invoke the SSS congruence postulate.
__
Statement . . . . Reason
AB≅DC, CA≅BD . . . . given
BC≅CB . . . . reflexive property
ΔABC ≅ ΔDCB . . . . SSS congruence postulate
What is the value of this expression when d = 4 7/8 and f = 3 1/2
6 (d - f) + f
Answers
7+(10−4)2:4⋅231=7+62:4⋅81=7+36:4⋅81=7+9⋅81=7+89=7+181=881
In which step does a mistake first occur?
8 + 2 + (3 X 3 -2)
Step 1: 8 +2 + (3 x 1)
Step 2: 8 +2 + 3
Step 3: 4 + 3
Step 4: 7
Answers
Step 1: 8 + 2 + (3 × 1)
Step 2: 8 + 2 + 3
Step 3: 10 + 3 [ corrected]
Step 4: 13
Hope it helpsSolve for m/a renter answer in the box round to your final answer to the nearest degree.
Answers
Answer:
50 degrees
Step-by-step explanation:
For a RIGHT triangle tan A = opposite side / adjacent side
tan A = 12/10
arctan ( tan A) = A = arctan (12/10) = 50.19 degrees
If a and ß are the roots of he equation 3 x² + 6x - 2 = 0, Calculate the value a^3 - B^3
Answers
Answer:
[tex]\alpha^3-\beta^3 = \frac{28}{3}\sqrt{\frac{5}{3}}[/tex]
Step-by-step explanation:
Given quadratic equation is: [tex]3x^2 +6x-2=0[/tex]Comparing it with [tex]ax^2+bx+c=0[/tex], we find:[tex]a = 3,\: b= 6,\: c = -2[/tex]It is given that: [tex] \alpha\: and \: \beta[/tex] are roots of the given quadratic equation. So, we find the sum and the products of the roots.[tex] \implies \alpha + \beta =-\frac{b}{a}=-\frac{6}{3}=-2[/tex][tex] \& \:\alpha.\beta =\frac{c}{a}=-\frac{2}{3}[/tex]Since, one of the factors of [tex] \alpha^3-\beta^3[/tex] is [tex](\alpha - \beta)[/tex] . Therefore, now we will find the value of [tex](\alpha - \beta),[/tex] which can be obtained by the following formula.[tex]\alpha-\beta=\sqrt{(\alpha+\beta)^2-4\alpha\beta}[/tex][tex]\implies \alpha-\beta=\sqrt{(-2)^2-4\bigg(-\frac{2}{3}\bigg)}[/tex][tex]\implies \alpha-\beta=\sqrt{4+\frac{8}{3}}[/tex][tex]\implies \alpha-\beta=\sqrt{\frac{12+8}{3}}[/tex][tex]\implies \alpha-\beta=\sqrt{\frac{20}{3}}[/tex][tex]\implies \alpha-\beta=2\sqrt{\frac{5}{3}}[/tex][tex]\alpha^3-\beta^3 =(\alpha-\beta)^3+3\alpha\beta(\alpha-\beta)[/tex][tex] \implies \alpha^3-\beta^3 =\bigg(2\sqrt{\frac{5}{3}}\bigg)^3+3\bigg(-\frac{2}{3}\bigg)\bigg(2\sqrt{\frac{5}{3}}\bigg)[/tex][tex] \implies \alpha^3-\beta^3 =8\bigg(\sqrt{\frac{5}{3}}\bigg)^3-\bigg(\frac{6}{3}\bigg)\bigg(2\sqrt{\frac{5}{3}}\bigg)[/tex][tex] \implies \alpha^3-\beta^3 =8\times \frac{5}{3}\bigg(\sqrt{\frac{5}{3}}\bigg)-4\bigg(\sqrt{\frac{5}{3}}\bigg)[/tex][tex] \implies \alpha^3-\beta^3 = \frac{40}{3}\bigg(\sqrt{\frac{5}{3}}\bigg)-4\bigg(\sqrt{\frac{5}{3}}\bigg)[/tex][tex] \implies \alpha^3-\beta^3 = \bigg(\frac{40}{3}-4\bigg)\bigg(\sqrt{\frac{5}{3}}\bigg)[/tex][tex] \implies \alpha^3-\beta^3 = \bigg(\frac{40-12}{3}\bigg)\bigg(\sqrt{\frac{5}{3}}\bigg)[/tex][tex] \implies \alpha^3-\beta^3 = \frac{28}{3}\sqrt{\frac{5}{3}}[/tex]The value of a³-B³ from the given quadratic equation is 12.05.
What are roots of a quadratic equation?The roots to the quadratic equation are the values of the unknown variable x, which satisfy the equation. These solutions are called roots or zeros of quadratic equations. The roots of any polynomial are the solutions for the given equation.
Given that, a and B are the roots of the equation 3x²+6x-2=0
By comparing 3x²+6x-2=0 with ax²+bx+c=0, we get a=3, b=6 and c=-2
The roots of a quadratic equation ax² + bx + c = 0 are given by x = [-b ± √(b² - 4ac)]/2a.
Now, substitute a=3, b=6 and c=-2 in quadratic formula
That is, x = [-6 ±√(6² - 4×3×(-2))]/2×3
= [-6 ±√60]/6
= (-6±2√15)/6
= (-3±√15)/3
So, a=(-3+√15)/3 and B=(-3-√15)/3
Now, a³-B³ = [(-3+√15)/3]³- [(-3-√15)/3]³
= 12.05
Therefore, the value of a³-B³ from the given quadratic equation is 12.05.
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What is the slope intercept equation for this line?
Answers
Answer:
y=-3x+4.
Step-by-step explanation:
1) the slope can be calculated according the formula:
slope=(y_end-y_init)/(x_end-x_init);
2) according to the formula above:
slope=(3-1)/(0-1)=-3.
3) according to the given graph the interception is 4, then
4) finally, the required equation is y=-3x+4.
PLS HELP I NEED TO TURN THIS IN
Answers
There are 16 parents.
12 of the parents match the criteria.
12/16×100
=75%
Shelley read 40 business proposals between 6 am and 11 am. On average how many proposals did she read per hour
Answers
Answer: 8 proposals per hour
Step-by-step explanation: 40/5 = 8
Cole has 5 times as many pencils as
Connor. Together they have 18
pencils. How many pencils does Cole
have?
Answers
Answer:
Cole has 15 pencils.
Step-by-step explanation:
First, we have the equation c + o =18, c representing cole, and o representing connor.
From there, we get 5o=c
Using substitiution, we get o=3
5(3)=15
15+3=18
In the figure below,ABC is an isosceles triangle with |AB|=|AC|.|BC| is extended to D such that |AC|=|CD|.If
Answers
The perimeter of the triangle ABC is [tex]10+\sqrt{10}[/tex] [tex]units[/tex].
The given parameters:
Triangle ABC = Isosceles triangleThe length of AC = 3-(-2) = 5 unit
The length of AC = length of BC = 5 unit
The length of BC is calculated by applying Pythagoras theorem as follows;
[tex]BC^2=(4-1)^2+(3-2)^2[/tex]
[tex]BC^2=3^2+1^2[/tex]
[tex]BC^2=10[/tex]
[tex]BC=\sqrt{10}[/tex]
The perimeter of the triangle ABC is calculated as follows;
[tex]P=AB+AC+BC[/tex]
[tex]P=5+5+\sqrt{10}[/tex]
[tex]P=10+\sqrt{10[/tex] [tex]units[/tex]
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I need help solving this problem
Answers
Answer:
First option, incorrect....
Step-by-step explanation:
This is because the interval is either below or above 26.8 by 0.6
-+ means
26.8 + 0.6 = 27.4
26.8 - 0.6 = 26.2
The confidence interval % can change
- The second option states 28 but that is not in the interval
- The third option is somewhat right but the parameter should be emphasized how confident you are
- The last option is wrong since it has the word "every young" when the initial sentence was the mean
I NEED HELP PLSS. The athletic director of a large school district with about 1,500 seventh-grade students in five different middle schools wants to know which sport is most popular among seventh graders. Which survey method is the best to use?
A
Survey 50 randomly selected seventh-grade students at each of the district’s middle schools.
B
Survey 50 randomly selected seventh-grade students at one of the middle schools.
C
Survey 50 randomly selected seventh-grade students who are participating in school sports this year.
D
Survey 50 randomly selected eighth-grade students who participated in school sports last year.
Answers
Survey 50 randomly selected seventh-grade students at each of the district’s middle schools. Then the correct option is A.
What is a sample?A sample is a group of clearly specified components. The number of items in a finite sample is denoted by a curly bracket.
The athletic director of a large school district with about 1,500 seventh-grade students in five different middle schools wants to know which sport is most popular among seventh graders.
The survey method is the best to use will be
Random sampling is the method of selecting the subset from the set to make a statical inference.
Survey 50 randomly selected seventh-grade students at each of the district’s middle schools.
Thus, the correct option is A.
More about the sample link is given below.
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help please 100 brainlest
Answers
Answer:
friday
Step-by-step explanation:
8th day will be monday
then 32 nd will be monday.
so 36th is friday
Which graph represents the solution of the inequality 24x – 17x ≥ 13x + 15?
Answers
Answer:
See below ~
Step-by-step explanation:
Solving the inequality :
24x - 17x ≥ 13x + 157x ≥ 13x + 15-6x ≥ 15x ≤ -2/5Plotted graph :
Kindly note the line drawn should be a solid line for the inequality to be trueWhen you draw on a graph, kindly remember this and don't directly copy from the attached graphfind the least common multiple for x^2-100, x-100
Answers
Answer:
(x+10)(x-10)
Step-by-step explanation:
The factor for x+10 is x+10 itself.
(x+10) = x+10
(x+10) occurs 1 time.
The factor for x-10 is x-10 itself.
(x-10) = x-10
(x+10) occurs 1 time.
The LCM of x+10, x-10 is the result of multiplying all factors the greatest number of times they occur in either term.
(x+10)(x-10)
Admission to the county fair costs $9 per person. The ride tickets cost $2.50 each.
Which equation represents the total cost, C, of visiting the fair where r represents the number of ride tickets bought?
Answers
Answer:$11.5
Step-by-step explanation:
Admission = $9 charged once
each ride = $2.5x (x=number of rides)
Total cost for x rides
=2.5x+9
17. You roll a number cube. How likely is it that you will roll a number less than 7?
Explain
Answers
Answer:
1 or 100%.
Step-by-step explanation:
The probability of rolling less than 7 is equal to the probability of rolling 1 or 2 or 3 or 4 or 5 or 6. That is 1/6 + 1/6 + 1/6 + 1/6 + 1/6 + 1/6 = 6/6. So any number from the dice can come up when you roll it because a perfect dice has 6 sides.
HELP PLS If there were 180 minions with you in the lab and only three-fifths made it through the door, how many minions are still with us?
Answers
Answer:
they all passed away so they went back to GRU and he burried them and at their f l e s h, The rest all ran away.
WHAT IS THE CO-EFFICIENT OF b in the expression b^2 - b5 + 18?
Answers
Answer:
-5 is the coefficient of b
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[tex]\blue{\textsf{\textbf{\underline{\underline{Question:-}}}}[/tex]
What is the coefficient of b² in the expression b²-b⁵+18?
[tex]\blue{\textsf{\textbf{\underline{\underline{Answer:-}}}}[/tex]
1
[tex]\blue{\textsf{\textbf{\underline{\underline{How to Solve:-}}}}[/tex]
The coefficient is defined as a number before a variable.
If there's no number, then the coefficient is 1.
Since b² has no number next to it, its coefficient is 1.
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