At what height does the ladder in Figure 1 rest on the wall?
Approximately how much higher up the wall does the ladder in Figure 2 rest compared to the ladder in Figure 1?
Answers
Answer:
The ladder rests against the wall at 6ft.
The ladder in Figure 2 rests about 3ft higher than the ladder in Figure 1.
Step-by-step explanation:
We can assume both of the figures display the ladder, ground, and wall forming a right triangle because the assignment is titled "apply the Pythagorean theorem", suggesting we should use the Pythagorean theorem and both figures are right triangles.
The Pythagorean theorem states that the sum of each leg squared is equal to the hypotenuse squared, or a^2 + b^2 = c^2, where "a" and "b" are legs and "c" is the hypotenuse.
At what height does the ladder in Figure 1 rest on the wall?
First, identify which sides are the legs and which is the hypotenuse. The hypotenuse is always the longest side and is the side opposite from the right angle. Thus, the hypotenuse in Figure 1 is the ladder length, and the two legs are the distance the ladder is from the wall and the height of the ladder against the wall. In other words, c = 10, a = 8, and b = the missing side length. Now, plug in the values to the Pythagorean theorem:
8^2 + b^2 = 10^2
64 + b^2 = 100
b^2 = 36
b = 6
The height at which the ladder in Figure 1 rests on the wall is 6 ft.
Approximately how much higher up the wall does the ladder in Figure 2 rest compared to the ladder in Figure 1?
We can set up the equation: Figure 2 ladder height - Figure 1 ladder height. We already know how where the ladder height of Figure 1 is, so we only need to solve for the ladder height in Figure 2 to get the result. Applying the same method as in the previous problem, we can input the values of Figure 2 into the Pythagorean theorem:
4^2 + b^2 = 10^2
16 + b^2 = 100
b^2 = 84
b = sqrt84
b ~ 9 ft
Now, we can find the difference between the Figure 2 ladder height and Figure 1 ladder height to get the answer to the question:
9 ft - 6 ft = 3 ft
Related Questions
For the following right triangle, find the side length x, Round your answer to the nearest hundredth.
12
x
6
Answers
Answer:
x=12
Step-by-step explanation:
(1 point) An open-top box is to be constructed from a 8 \ \mbox{in} by 14 \ \mbox{in} rectangular sheet of tin by cutting out squares of equal size at each corner, then folding up the resulting flaps. Let x denote the length of the side of each cut-out square. Assume negligible thickness. (a) Find a formula for the volume, V, of the box as a function of x. \ \ V(x)
Answers
Answer:
Volume=[tex]4x^3-44x^2+112x[/tex]
Step-by-step explanation:
Let x denotes the length of the side of each cut
After Cutting square length will be=8-2x (where 2x for 2 squares as on each side two corners are there thus 2 squares will be cut down)
After cutting square width will be=14-2x (where 2x for 2 squares as on each side two corners are there thus 2 squares will be cut down)
Height = x
Volume=Length*width*Height
Volume=(8-2x)*(14-2x)*x
On solving we will get:
Volume=[tex]4x^3-44x^2+112x[/tex]
Amy sells muffins for 1.35 each the muffins cost 0.39 each to make how much profit will Amy make if she sells 48 muffins?
Answers
Answer:
$46.08
Step-by-step explanation:
Hi,
She gets 48 (1.35) when she sells 48 muffins. That equals 64.8.
But she pays 48 (.39) to make them. That equals 18.72.
64.8 - 18.72 = 46.08
She makes $46.08
I hope this helps :)
A triangle flower bed has a perimeter of 15cm the drawing has a scale of 1:200. What is the perimeter of the actual flower bed
Answers
Answer:
300cm
Step-by-step explanation:
scale 1:200 means 1cm on drawing represent 200cm on ground so 15cm will be 15×200 which is 3000cm
which is a true statement about the two rectangular prism shown below
Answers
A cold water tap can fill a tub in 6 minutes, and a hot water tap can fill the tub in 8 minutes. A drain can empty a full tub in 10 minutes. If both taps are on and the drai is open, how long will it take to fill the tub? It will take
how many minutes?
Answers
Answer:
12 minutes
Step-by-step explanation:
The Hot tap fills 1/30th of the bath in 1 minute. The cold tap fills 1/20th of the bath in one minute. In one minute both taps together will fill (1/30 + 1/20) of the bath, which is 5/60ths or 1/12th of the bath. Since it takes one minute to fill 1/12th of the bath, it’ll take 12 minutes to fill the bath
Riley's grandparents drive from city A to city B every spring. It takes them several days. Each day they use the expression 2+ distance over 54 to figure out how many hours they will be on the road. The first day they were on the road for 7 hours. How far did they travel on the first day?
Answers
9514 1404 393
Answer:
270 miles
Step-by-step explanation:
For h hours of driving the distance d is covered:
h = 2 +d/54
Solving for d, we find the distance covered in h hours is ...
d = 54(h -2)
In 7 hours, the distance they traveled is ...
d = 54(7 -2) = 270 . . . miles
They traveled 270 miles on the first day.
A news report states that the 90% confidence interval for the mean number of daily calories consumed by participants in a medical study is (1920, 2140). Assume the population distribution for daily calories consumed is normally distributed and that the confidence interval was based on a simple random sample of 22 observations. Calculate the sample mean, the margin of error, and the sample standard deviation based on the stated confidence interval and the given sample size. Use the t distribution in any calculations and round non-integer results to 4 decimal places.
1. What is the sample mean?
2. What is the margin of error?
3. What is the sample standard deviation?
Answers
Answer:
ddXvffggf
Step-by-step explanation:
vvzgsgygsv gdhvsysgvs gsvysvvs6sg he's) v gateways tsgsyysgd Yacc subs USB GA t gsd
Help me I need this really bad and I need a good grade I’m behind on school
Answers
Answer:
If you share 7 apples equally with 3 people, then there are 2 1/3 apples per person.
The number 2 represents the number of whole apples each individual gets.
The denominatior, 3, represents how many times an apple will have to be split to divide equally
The numerator, 1, represents how many 3rds each person gets.
100Points! show work
Answers
Using angle sum property
[tex]\\ \sf\longmapsto x+43+73+70=180[/tex]
[tex]\\ \sf\longmapsto x+43+143=180[/tex]
[tex]\\ \sf\longmapsto x+186=180[/tex]
[tex]\\ \sf\longmapsto x=180-186[/tex]
[tex]\\ \sf\longmapsto x=-6[/tex]
Option C is correct
Sum of angles of any triangle is 180°
x+43+73+70=180x+186=180x=180-186x=-6Option C
If x varies inversely as y and x=16 when y=5, find x when y=20.
Answers
9514 1404 393
Answer:
x = 4
Step-by-step explanation:
The inverse variation means that when y goes up by a factor of 20/5 = 4, the value of x goes down by the same factor.
x = 16/4
x = 4
1) Red City is 6 cm away from Blue City on a map but the two cities are actually 240 miles
apart in real. What is the scale on the map?
Answers
Shanna is planning a trip from Dallas, Texas, to San Diego, California. She knows that the distance she will travel is
about 1400 miles. If she looks at a map with a scale of 1 in. = 300 mi, about how far will the trip be on the map?
3
14
in
0 2 in.
in.
WIN
in
Answers
Answer:
4.67 inches
Step-by-step explanation:
Shanna is planning a trip from Dallas, Texas, to San Diego, California.
She will travel about = 1,400 miles
The scale of a map is 300 miles = 1 inches
The trip of 1,400 miles = [tex]\frac{1400}{300}[/tex]
= 4.66666 inches ≈ 4.67 inches
Her trip is 4.67 inches far on the map.
Using the same scenario as above, but now you do not know the population variance. You collect a random sample of n = 21 cereal boxes and find the sample mean is 12.8 and the sample standard deviation to be 0.5. Test the null hypothesis H0: µ = 13 against the alternative hypothesis HA: µ < 13 at level of significance α = 0.01.
Required:
a. Find the test statistic.
b. Using the rejection region, do you reject or not reject the null hypothesis?
c. Find the p-value.
d. Using the p-value, do you reject or not reject the null hypothesis?
e. In context of your problem, what is your conclusion about the ounces contained in cereal boxes?
Answers
Answer:
-1.833 ; we do not reject the Null.
Pvalue = 0.0409 ; We do not reject the Null
There is no significant evidence to conclude that the number of ounces contained in the cereal boxes is less than 13
Step-by-step explanation:
H0 : μ = 13
HA : μ < 13
Test statistic :
(xbar - μ) ÷ s/sqrt(n)
(12.8 - 13) ÷ 0.5/sqrt(21)
-0.2 / 0.1091089
= - 1.833
The critical value at α = 0.01 ; df = 21 - 1 = 20 = 2.528
-1.833 > - 2. 528 (left tailed test) ; Hence we do not reject the Null.
Test statistic :
Pvalue from Test statistic at DF = 20 ; α = 0.01
Pvalue = 0.0409
Pvalue > α
0.0409 > 0.01 ; Hence, we do not reject H0.
There is no significant evidence to conclude that the number of ounces contained in the cereal boxes is less than 13
Determine the missing factor in ■ × 4.2 = 16.8.
Answers
Answer this and I’ll give you a sticker
Answers
F(x)-mx+ b, f(-2)=3 and f(4)=1 , what is the value of m and b
Answers
Answer: [tex]m=\dfrac{-1}{3}, b=\dfrac{7}{3}[/tex]
Step-by-step explanation:
Given
Function is [tex]f(x)=mx+b[/tex]
[tex]f(-2)=3[/tex]
[tex]\therefore 3=m(-2)+b\\\Rightarrow b-2m=3\quad \ldots(i)[/tex]
[tex]f(4)=1\\\therefore 1=4m+b\quad \ldots(ii)[/tex]
from (i) and (ii) we get
[tex]m=\dfrac{-1}{3}, b=\dfrac{7}{3}[/tex]
What would be the new median if 21 was added to the list
Answers
Answer:
52 is the correct answer
5. If the tree's circumference is 141.3ft, what is its diameter?
Answers
Answer:
d ≈ 45 ft
General Formulas and Concepts:
Symbols
π (pi) ≈ 3.14Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightEquality Properties
Multiplication Property of Equality Division Property of Equality Addition Property of Equality Subtraction Property of EqualityGeometry
Circumference of a Circle Formula: C = πdStep-by-step explanation:
Step 1: Define
Circumference C = 141.3 ft
Step 2: Solve for d
Substitute in C [Circumference Formula]: 141.3 ft = πdSubstitute in π (approximation): 141.3 ft ≈ 3.14d[Division Property of Equality] Divide both sides by 3.14: 45 ft ≈ dRewrite: d ≈ 45 fthow do i find the polar form of
1-2i
Answers
Answer:
9
Step-by-step explanation:
can someone help me with this please
Answers
9514 1404 393
Answer:
1. attendance (y), time (x)
2. 1,2: increasing; 3: constant; 4: decreasing
3. attendance increases, remains constant, then decreases
4. increasing; pre-heating the oven
Step-by-step explanation:
It is always difficult to read the mind of the author of questions like these. Usually, specific wording is expected. If your curriculum material has examples you can copy from, you should do that.
__
1. The variables and what they stand for are listed on the axes of the graph. The y-variable stands for attendance. The x-variable stands for time. It isn't clear whether the desired answer is "y and x" or "attendance and time".
__
2. The graph slopes upward in intervals 1 and 2. It can be described as "increasing."
The graph remains level in interval 3. It can be described as "constant."
The graph slopes downward in interval 4. It can be described as "decreasing."
__
3. The attendance is adequately described in question 2. Attendance increases, remains constant, then decreases. It isn't clear how general or specific the answer is supposed to be.
__
4. The graph of the function is "increasing." We don't know if the indicated temperature is the temperature of the bread, the oven, or the room containing the oven. If we assume the indicated temperature is that of the oven, we expect an increase during the oven pre-heat interval.
If the indicated temperature is that of the bread, then the increase would be following insertion of the bread into the oven.
Please help me btw if I see links I’ll report
Answers
Answer:
bro that is easy its 15*1/2
Step-by-step explanation:
Given that f (x )is continuous. f (3 )equals 1, f (1 )equals 6, f (6 )equals negative 2, and f (negative 2 )equals 3. Determine limit as x rightwards arrow 6 to the power of plus of f (x ), and limit as x rightwards arrow negative 2 to the power of minus of f (x ).
Answers
Given:
[tex]f(x)[/tex] is continuous, [tex]f(3)=1,f(1)=6,f(6)=-2,f(-2)=3[/tex].
To find:
The value of [tex]\lim_{x\to 6^+}f(x)[/tex] and [tex]\lim_{x\to -2^-}f(x)[/tex].
Solution:
If a function f(x) is continuous at [tex]x=c[/tex], then
[tex]\lim_{x\to c^-}f(x)=f(c)=\lim_{x\to c^+}f(x)[/tex]
It is given that the function [tex]f(x)[/tex] is continuous. It means it is continuous for each value and the left-hand and right-hand limits are equal to the value of the function.
The function is continuous for 6. So,
[tex]\lim_{x\to 6^-}f(x)=f(6)=\lim_{x\to 6^+}f(x)[/tex]
[tex]\lim_{x\to 6^+}f(x)=f(6)[/tex]
[tex]\lim_{x\to 6^+}f(x)=-2[/tex]
The function is continuous for -2. So,
[tex]\lim_{x\to -2^-}f(x)=f(-2)=\lim_{x\to -2^+}f(x)[/tex]
[tex]\lim_{x\to -2^-}f(x)=f(-2)[/tex]
[tex]\lim_{x\to -2^-}f(x)=3[/tex]
Therefore, [tex]\lim_{x\to 6^+}f(x)=-2[/tex] and [tex]\lim_{x\to -2^-}f(x)=3[/tex].
What is the positive solution to the equation 2x2 + 3x = 2?
Answers
Answer:
x(2x+3)
Step-by-step explanation:
Answer:
X= -2
2. x = 1/2 = 0.500
Step-by-step explanation:
Find the greatest common factor of the following monomials: 20a 46a^2 48a^6
Answers
Pls help 10 ptsssssssssssss
NO LINKS
Answers
Answer:
it is actually a very simple question first you add 4+9=13 then you multiply 5 times 13 which gets you the answer of 65
PLEASE HELP, anything is very appreciated
Answers
Answer:
117.8097 [tex]in^{2}[/tex]
Step-by-step explanation:
Depending on how you're math is going there are two ways to solve this, find the are by the arc or just figure out the whole cookie and divide by 6. Let's try the latter is seems easier to say. I mean easier for me to say.
area of a circle is pi * r^2
the diameter is 30 inches so the radius is half of that or 15 inches
then the whole cookie is
pi*15^2 = 706.858 [tex]in^{2}[/tex]
now divide by 6 or each piece
706.858 [tex]in^{2}[/tex] / 6 = 117.8097 [tex]in^{2}[/tex]
now eat your cookie :p
g(x) = 2x – 4
h(x)=x²-3
Find (g.h)(5)
Answers
Answer:
40
Step-by-step explanation:
This is asking you to plug in the value of h(5) into g(x). First solve for h(5)
x^2-3 = h(x)
5^2-3= 22
h(5) = 22
h(5) is 22. So now, plug that into g(x).
g(h(5)) = 2(22)-4
44-4=40
(g.h)(5) is 40.
someone pls help I'm genuinely confused
I've literally been trying to figure out all three of these for like two hours now but I can't figure it out
Answers
Answer:
the area is 50
Step-by-step explanation:
Answer:
its 0.09637 but round it by urself . please like my answer and brainliest me hshsshhs
pls help me somebody
Answers
Answer:
it is 36 inches
Step-by-step explanation: