A ladder is leaning against a wall. The top of the ladder is 9 feet above the ground. If the bottom of the ladder is moved 3 feet farther from the wall, the ladder will be lying flat on the ground, still touching the wall. How long, in feet, is the ladder?
Answers
A² +b²=c²
the a² and B² Being the height and length and label the third side c²
so..
9²+3²=c²
9×9+3×3=c²
81+9=c²
40=c²
√40=√c²
6.32=c
therefore the ladder is 6.32
well i think that is how you answer
[tex]\bf \textit{using the pythagorean theorem}\\\\ r^2=x^2+y^2\implies r=\sqrt{x^2+y^2} \\\\\\ r=\sqrt{x^2+9^2}\implies r=\sqrt{x^2+81}\impliedby \textit{leaning ladder} \\\\\\ r=\sqrt{(x+3)^2+0^2}\implies r=\sqrt{(x+3)^2}\impliedby \textit{flat ladder}\\\\ -------------------------------\\\\[/tex]
[tex]\bf \sqrt{x^2+81}=\sqrt{(x+3)^2}\implies x^2+81=(x+3)^2 \\\\\\ x^2+81=x^2+6x+9\implies 81-9=6x\implies 72=6x\implies \cfrac{72}{6}=x \\\\\\ \boxed{12=x}\\\\ -------------------------------\\\\ \textit{now, the ladder "r" is }\sqrt{(x+3)^2}\implies \sqrt{(12+3)^2}\implies 15[/tex]
Related Questions
The Pyramid of Giza is one of the largest pyramid structures still standing in Egypt. It is a right pyramid with a square base, a base length of 230 m, and height of 150 m. The area of the base is __________ The volume is ________
Answers
Answer:- The area of base is 52900 square meters. The volume is 2654000 cubic meters.
Explanation:-
Base length of right pyramid (square) a =230m
Height of right pyramid = 150m
Area of base of right pyramid[tex]=a^2=(230)^2=52900\ m^2[/tex]
Volume of right pyramid with square base[tex]=\frac{1}{3}a^2h\\=\frac{1}{3}\times52900\times150=2645000\ m^3[/tex]
Thus, the area of base is 52900 square meters and the volume is 2654000 cubic meters.
The area of the base of the pyramid is 52900 m²
The volume of the square base pyramid of Giza is 2645000 m³
The pyramid is a square base pyramid. Therefore,
volume of a square base pyramid;v = 1 / 3 Bhwhere
B = base area
h = height
h = 150 m
Therefore,
area of the base = l²
where
l = length of side
area of the base = 230² = 52900 m²
Volume = 1 / 3 × 52900 × 150
volume = 7935000 / 3
volume = 2645000 m³
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Which point satisfies both f(x)=2^x and g(x)=3^x (0,1) (0,-1) (1,0) (-1,0)
Answers
Both [tex]2^0[/tex] and [tex]3^0[/tex] are equal to 1, so the answer is [tex](0,1)[/tex].
so the point must be (0,1)
can someone help me please
Answers
Perform the operation(s) and write the answer in simplest form.
( 1/2 + 1/3) / 15/4
A.) 3 1/8
B.) 53/90
C.) 2/9
D.) 8/75
Answers
Hope the explanation helped!
On monday eliza read her book. on tuesday she read three times as long as she read on monday. on wednesday she read 20 minutes less than tuesday. on thursday she read for 20 minutes which was half as long as she read on wednesday. how many minutes did eliza read over the 4-day period
Answers
tuesday : 3x
wednesday : 3x - 20 = 40
thursday: 20
3x - 20 = 40
3x = 40 + 20
3x = 60
x = 60/3
x = 20
monday : 20 minutes
tuesday : 3x....3(20) = 60 minutes
wednesday : 40 minutes
thursday: 20
for a total of : 140 minutes <===
A cold front moved in last weekend. In 8 hours overnight, the temperature outside dropped from 14 degrees to -10. What was the average temperature change for each hour?
I need the answer as quick as I can and I put it at max points!
Answers
Answer:
Step-by-step explanation:
The difference between 14 and 0 is 14, and the difference between 0 and -10 is 10. 14+10=24 for total change. For the average over 8 hours, we have 24/8=3 degrees
How many sixteenth notes would be needed to have the same duration as 3 quarter notes? Represent this as a fraction
Answers
1 eight note=2 sixteenth notes
so
1 quarter note=4 sixteenth note
so
times 3 both sides
3 quarter notes=12 sixteenth notes
In triangle ABC, angle B = 30°, a = 210, and b = 164. The measure of angle A to the nearest degree is a0
Answers
a/SinA = b/SinB of which we have all but one of those values. Our particular equation looks like this then: 210/SinA = 164/Sin30. Cross multiply to get
210Sin30 = 164SinA. Divide both sides by 164 to get 210Sin30/164 = SinA. Do the math on the left and get ,6402 = SinA. Now use the inverse Sin on your calculator (2nd button then Sin button and then enter .6402) and get an angle of 39.8 degrees.
The length of the third side of the triangle would be 106.5 units approx.
What is a triangle?A triangle is a two - dimensional figure with three sides and three angles.
The sum of the angles of the triangle is equal to 180 degrees.
∠A + ∠B + ∠C = 180°
Given is that in triangle ABC, angle B = 30°, a = 210, and b = 164.
The cosine formula is given as follows -
c² = a² + b² + 2abcos(α)
c = √(a² + b² + 2abcos(α))
c = √(210)² + (164)² + 2(210)(164)cos(30°)
c = 106.5 units approx.
Therefore, the length of the third side of the triangle would be 106.5 units approx.
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Five students visiting the student health center for a free dental examination during national dental hygiene month were asked how many months had passed since their last visit to a dentist. their responses were as follows. 5 18 12 24 28 assuming that these five students can be considered a random sample of all students participating in the free checkup program, construct a 95% confidence interval for the mean number of months elapsed since the last visit to a dentist for the population of students participating in the program. (give the answer to two decimal places.)
Answers
To find for the value of the confidence interval, let us first calculate for the values of x and s, the mean and standard deviation respectively.
x = (5 + 18 + 12 + 24 + 28) / 5
x = 17.4 months
s = sqrt{[(5 – 17.4)^2 + (18 – 17.4)^2 + (12 – 17.4)^2 + (24 – 17.4)^2 + (28 – 17.4)^2]/(5-1)}
s = 9.21
The formula for the confidence interval is given as:
Confidence Interval = x ± t s / sqrt(n)
Where t can be taken from standard distribution tables at 95% level at degrees of freedom = n – 1 = 4, t = 2.132. Therefore:
Confidence Interval = 17.4 ± 2.132 * 9.21 / sqrt(5)
Confidence Interval = 17.4 ± 8.78
Confidence Interval = 8.62 months, 26.18 months
Final answer:
To construct a 95% confidence interval for the mean number of months elapsed since the last visit to a dentist, use the sample mean and sample standard deviation. Calculate the confidence interval using the formula and given data.
Explanation:
In order to construct a confidence interval for the mean number of months elapsed since the last visit to a dentist for the population of students participating in the program, we can use the sample mean and sample standard deviation. The formula for constructing a confidence interval for the mean is:
Confidence Interval = sample mean ± (critical value) × (sample standard deviation / √sample size)
Using the given data, the sample mean is 17.4 months and the sample standard deviation is 9.18 months. With a confidence level of 95%, the critical value is 2.776. Plugging these values into the formula, we get:
Confidence Interval = 17.4 ± (2.776) × (9.18 / √5)
Calculating this, we find that the 95% confidence interval for the mean number of months elapsed since the last visit to a dentist is approximately 4.81 to 29.99 months.
Explain how you would use a number line to find the absolute value of –12.
Answers
Absolute Value
∞ # of spaces away from zero
∞ how far away a number is from zero
1). Draw a number line.
2). Label it from -12 to 0.
3). Count on the number line from -12 to 0 and see how many units to the right you have to go to reach zero. The answer is 12, so that is the absolute value.
|-12| = 12
A rectangle has a base of 3 inches and a height of 9 inches. If the dimensions are doubled, what will happen to the area of the rectangle?
Answers
how many times is 27 into 108?
Answer:
Area will increase by 4 times
Step-by-step explanation:
Given: A rectangle has a base of 3 inches and a height of 9 inches.
To find: If the dimensions are doubled, what will happen to the area of the rectangle?
Solution:
It is given that a rectangle has a base of 3 inches and a height of 9 inches.
Now, to find if the dimensions are doubled what will happen to the area, first we need to find the original area.
Original area of rectangle, when base is 3 inches and height 9 inches is
[tex]9\times3=27[/tex] square inches
Now, when dimensions are doubled , the base becomes 6 inches and height becomes 18 inches
So, new area becomes [tex]6\times18=108[/tex] square inches.
Now,
[tex]\frac{\text{new area}}{\text{original area} }=\frac{108}{27}[/tex]
[tex]\implies\frac{\text{new area}}{\text{original area} }=\frac{4}{1}[/tex]
Hence, the area will increase by 4 times.
Find the y-intercept and x-intercept of the line.
5x - 4y = 15
y-intercept: __
x-intercept: __
Answers
x-intercept: y = 0
5x = 15
x = 3
so x-intercept: (3, 0)
y-intercept: x = 0
-4y = 15
y = -15/4
so y-intercept: (0, -15/4)
answer
x-intercept: (3, 0)
y-intercept: (0, -15/4)
Julio just bought a $267,900 house. He had a 20 year mortgage with a fixed rate of 5.875%. Julio's monthly payments are $1558.09. What percent of the purchase price was Julio's down payment?
Answers
The formula is
Pv=pmt [(1-(1+r/k)^(-kn))÷(r/k)]
Pv present value?
PMT monthly payment 1558.09
R interest rate 0.05875
K compounded monthly 12 because the payment is monthly
N time 20 years
Pv=1,558.09×((1−(1+0.05875
÷12)^(−12×20))÷(0.05875÷12))
=219,684.92
Subtract the amount of the present value from the purchase price of the house to get the amount of the down payment
267,900−219,684.92=48,215.08
So the percent of the purchase price was Julio's down payment is
48,215.08÷267,900
=0.17997×100=17.997% round your answer to get 18%
Answer: c
Step-by-step explanation:
Mr. calloway is an algebra teacher. every class period he draws a piece of paper out of a hat without looking to determine the number of homework problems he will assign. each different color of paper represents a different number of homework problems. the hat contains 2 blue, 6 red, 10 yellow, and 7 purple pieces of paper.what is the probability that mr. calloway draws a purple piece of paper during the first class period and a blue piece of paper during the second class period if he replaces all pieces of paper before each drawing?
Answers
Since all pieces of paper are returned, the probability of drawing a blue piece during the second class is 2/25 since there are 2 blue pieces out of a total of 25 pieces of paper
The wording is meant to trick you here. If the purple paper from the morning was not replaced before drawing the probability of drawing a blue piece in the second class would increase.
Always remember to reduce fractions where you can
The probability that Mr. Calloway will draw a purple piece of paper during the first class period and a blue piece during the second class period with replacement is [tex]\frac{14}{25}[/tex].
The question involves calculating the probability of drawing a purple piece of paper during the first class period and a blue piece of paper during the second class period with replacement. To find this probability, we first calculate the probability of each event separately since the events are independent. Mr. Calloway's hat contains a total of 25 pieces of paper (2 blue, 6 red, 10 yellow, and 7 purple).
The probability of drawing a purple piece of paper in the first class period is the number of purple papers divided by the total number of papers:
P(purple) = Number of purple pieces / Total pieces = [tex]\frac{7}{25}[/tex]
Since the pieces are replaced, the probabilities in the second class period are the same as in the first. Thus, the probability of drawing a blue piece of paper in the second class is:
P(blue) = Number of blue pieces / Total pieces = [tex]\frac{2}{25}[/tex]
Because these events are independent, we multiply the probabilities of each event happening:
Total probability = P(purple) times P(blue) = ([tex]\frac{7}{25}[/tex]) times ([tex]\frac{2}{25}[/tex]) = [tex]\frac{14}{25}[/tex].
Therefore, the probability that Mr. Calloway draws a purple piece of paper during the first class period and a blue piece of paper during the second class period with replacement is [tex]\frac{14}{25}[/tex].
Which of the following equations have graphs that are parallel to the graph of the equation y=-3/2x+8?
I. 3x + 2y = 10
II. 2x − 3y = 9
III. 6x + 4y = 28
IV. 3x − 2y = 8
I and III only
II and III only
IV only
III only
Answers
y = -3/2x + 8....slope = -3/2....y int = 8
(I) 3x + 2y = 10
2y = -3x + 10
y = -3/2x + 5....slope = -3/2, y int = 5....this IS parallel
(II) 2x - 3y = 9
-3y = -2x + 9
y = 2/3x - 3...slope = 2/3, y int = -3....is not parallel
(III) 6x + 4y = 28
4y = -6x + 28
y = -3/2x + 7...slope = -3/2, y int = 7....this IS parallel
(IV) 3x - 2y = 8
-2y = -3x + 8
y = 3/2x - 4...slope = 3/2...y int = -4...this is not parallel
solution is : I and III
which statement is true about angles 1 and 2
Answers
Answer:
Option a) They are adjacent angles
Step-by-step explanation:
Given is a picture of a graph with angles 1 to 6 around it.
Out of these angle 2 and 5 are right angles.
1 and 2 are adjacent to each other.
They are not complementary because 1+2 not equals 90
They are neither supplementary since sum does not equal 180
They cannot be vertical because they are not formed by intersection of two lines.
Hence only option a is right
Option a) They are adjacent angles
Math help needed. Thank you
Answers
Which Graph correctly represents x+2y≤4?
Answers
Answer with Step-by-step explanation:
We are given an inequality:
x+2y≤4
We have to determine its correct graph
In graph A and graph C (0,4) lies in shaded region but (0,4) does not satisfy the inequality(since, 0+2×4=8 which is not less than or equal to 4)
Hence, A and C are not the graph of this inequality
In graph D (0,2) does not lie in shaded area but it satisfies the inequalityHence, D is also not the graph of this inequality
Hence, correct graph of x+2y≤4 is:
Graph B
The following is a geometric sequence 5,3,1,-1
Answers
3/5 !=1/3
So it is not a geometric sequence.
It IS an arithmetic sequence though, as all arithmetic sequences have a common difference that is a constant found when you find the difference between any term and the term preceding it.
3-5=1-3=-1-1=d=2
So there is a common difference of 2 so this is an arithmetic sequence. And all arithmetic sequences can be expressed as:
a(n)=a+d(n-1), a(n)=nth term, a=initial term, d=common difference, n=term number, in this case a=5 and d=-2 so
a(n)=5-2(n-1) which of course can be simplified...
a(n)=5-2n+2
a(n)=7-2n
Kara has 90 lollipops, 36 chocolate bars, and 72 gumballs to put in goody bags for her party. What is the largest number of goody bags that Kara can make so that each goody bag has the same number of lollipops, the same number of chocolate bars, and the same number of gumballs?
Answers
90/18 = 5 lollipops
36/18 = 2 chocolate bars
72/18 = 4 gumballs
answer : Kara can make 18 goody bags, each containing 5 lollipops, 2 chocolate bars, and 4 gumballs
The largest number of goody bags that Kara can make are [tex]18[/tex] .
What is Highest Common Factor ?Highest or greatest Common Factor is the largest common factor that all the numbers have in common.
We have,
Number of Lollipops [tex]=90[/tex]
Number of chocolate bars [tex]=36[/tex]
Number of gumballs [tex]=72[/tex]
So,
To find the number of bags;
First find out the Highest Common Factor of [tex]90,36,72[/tex];
[tex]90=2*3*3*5[/tex]
[tex]36=2*2*3*3[/tex]
[tex]72=2*2*2*3*3[/tex]
So, from the factors of all numbers we have,
Highest Common Factor [tex]=18[/tex]
Now,
Lollipops [tex]=\frac{90}{18} =5[/tex]
Chocolate bars [tex]=\frac{36}{18} =2[/tex]
Gumballs [tex]=\frac{72}{18} =4[/tex]
So, the largest number of goody bags that Kara can make are [tex]18[/tex] so that each goody bag has [tex]5[/tex] number of lollipops, [tex]2[/tex] number of chocolate bars, and [tex]4[/tex] number of gumballs.
Hence, we can say that the largest number of goody bags that Kara can make are [tex]18[/tex] .
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(6.3 × 1011) ÷ (7 × 105)
Answers
(6.3 * 1011)/(7 * 105)
6369.3/735
8.666 or 8.67
how much would $500 invested at 6% interest compounded annually be worth after 4 years
Answers
A = 500(1 + .06)^4
A = $631.24
Find all values of $x$ such that $6= \dfrac{35}{x} -\dfrac{49}{x^2}$. If you find more than one value, then list your solutions in increasing order, separated by commas.
Answers
if you want the step-by-step then you just try to isolate x and it is pretty self-explanatory from there on. Hope this helped!
:P
Answer:
[tex]x=\frac{7}{3} , \frac{7}{2}[/tex]
Step-by-step explanation:
[tex]6= \frac{35}{x} - \frac{49}{x^2}[/tex]
Now we need to solve for x
To get 'x' alone we make the denominators same
LCD = x^2
WE multiply the whole equation by x^2
[tex]6x^2 = 35x - 49[/tex]
Now we the equation =0, move all the terms to left hand side
[tex]6x^2-35x + 49=0[/tex]
Now we apply quadratic formula to solve for x
a= 6, b= -35 , c= 49
[tex]x= \frac{-b+-\sqrt{b^2-4ac}}{2a}[/tex]
[tex]x= \frac{-(-35)+-\sqrt{(-35)^2-4(6)(49)}}{2*6}[/tex]
[tex]x= \frac{35+-\sqrt{49}}{12}[/tex]
[tex]x= \frac{35+-7}{12}[/tex]
Now frame two equations , one with + and another with -
[tex]x= \frac{35+7}{12}[/tex] [tex]x= \frac{35-7}{12}[/tex]
[tex]x= \frac{42}{12}[/tex] [tex]x= \frac{28}{12}[/tex]
[tex]x= \frac{7}{2}[/tex] [tex]x= \frac{7}{3}[/tex]
So value of x= {7/3, 7/2}
16x^2=100
How many solutions will there be to the following equation?
Answers
x^2 = 100/16
x^2 = 6.25
x = (+-) sqrt 6.25
x = (+-) 2.5
x = 2.5 and x = - 2.5........2 solutions
Answer:
There are two solutions [tex]x=\frac{5}{2},-\frac{5}{2}[/tex]
Step-by-step explanation:
Given : Equation [tex]16x^2=100[/tex]
To find : How many solutions will there be to the following equation?
Solution :
Equation [tex]16x^2=100[/tex]
Solve the equation,
Divide by 16 both side,
[tex]\frac{16x^2}{16}=\frac{100}{16}[/tex]
[tex]x^2=\frac{100}{16}[/tex]
Taking root both side,
[tex]x=\sqrt{\frac{100}{16}}[/tex]
[tex]x=\sqrt{\frac{10^2}{4^2}}[/tex]
[tex]x=\pm\frac{10}{4}}[/tex]
[tex]x=\pm\frac{5}{2}}[/tex]
Therefore, There are two solutions [tex]x=\frac{5}{2},-\frac{5}{2}[/tex]
∠EFG and ∠GFH are a linear pair, m∠EFG=3n+19, and m∠GFH=55+33 What are m∠EFG and m∠GFH?
Answers
3n + 19 + 55 + 33 = 180
3n + 107 = 180
3n = 180 - 107
3n = 73
n = 73/3
so < EFG = 3n + 19 = 3(73/3) + 19 = 73 + 19 = 92
and < GFH = 55 + 33 = 88
What is the correct name for this circle?
Answers
hope this helped!
Find the product of (x − 2i)^2.
Answers
*** First of all remember that i = √-1
(x - 2i)²
(x - 2i)(x - 2i)
(x² - 2xi - 2xi + 4i²) -----> i² = (√-1)² = -1
(x² - 4xi - 4)
That is your final answer!
Hope this helps you :D
The product of (x-2i)²=x²-4+i4x
What is the process of multiplication of complex numbers?The product or multiplication of two complex numbers is also a complex number. The formula for multiplying complex numbers is: (a + ib) (c + id) = (ac - bd) + i(ad + bc).
Given here (x-2i)² =(x-2i) (x-2i)
=x²-4+i4x
Hence, the product is x²-4+i4x
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Use ABC to find the value of sin A. See picture below. Thanks!
Answers
Given: The coordinates of iscosceles trapezoid JKLM are J(-b, c), K(b,c), L(a,0), and M(-a,0).
Prove: The diagonals of an isosceles trapezoid are congruent.
As part of the proof, find the length of KM
A) a2+b2+c2
B) (-a+b)2+c2
C) (a+b)2+c2
Answers
Answer with explanation:
It is given that, coordinates of Isosceles trapezoid J K L M are J(-b, c), K(b,c), L(a,0), and M(-a,0).
To Prove: The diagonals of an isosceles trapezoid are congruent.
Proof:
Distance formula , that is distance between two points in x y plane is given by
[tex]=\sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2}[/tex]
Where, [tex](x_{1},y_{1}),(x_{2},y_{2})}[/tex] are coordinates of two points in the plane.
Length of Diagonal J L
[tex]=\sqrt{(a+b)^2+(0-c)^2}\\\\=\sqrt{(a+b)^2+c^2}[/tex]
Length of Diagonal K M
[tex]=\sqrt{(a+b)^2+(0-c)^2}\\\\=\sqrt{(a+b)^2+c^2}[/tex]
So, we can see that,
J L = KM [tex]=\sqrt{(a+b)^2+(c)^2}[/tex]
Hence,The diagonals of an isosceles trapezoid are congruent.
So ,
[tex]KM=\sqrt{(a+b)^2+c^2}[/tex]
Option C
type the slope-intercept equation of the line that passes through the points (0,2) and (2,0) y={?]x+{ }
Answers
b = 2
equation
y = -x + 2
hope it helps