could you help with
Answers
This can be solve using the pythagorean theorem. In this case the hypotenuse will be the length of the ladder and the distance from the house is one leg.
The other leg will be the height.
Using the theorem we have:
\(\begin{gathered} h^2+4^2=20^2 \\ h^2=400-16 \\ h^2=384 \\ h=\sqrt[]{384} \\ h=19.5959 \end{gathered}\)Therefore the height will be approximately 19.596 ft and the answer is the second option.
Related Questions
simplify (1+tan^2x)/(tan^2x)
[?]^2x
Answers
Answer:
1+tan2x=sec2x.
Explanation: Change to sines and cosines then simplify.
Which points are on the graph of f(x) = 26.5)^x? (-1,-1) (2,2.25) (-2,-8) (0,2) (1,1)
Answers
f(x) = 2•(0.5)^ x
Then calculate
2•(0.5)^ (-1)= 4. NOT VALUE
2•(0.5)^(2) = 2•0.25 = 1. NOT VALUE
2•(0.5)^(-2)= 8. IS NOT
2•(0.5)^(0) = 2. RIGHT VALUE
2•(0.5)^(1)= 1. Right VALUE
Find the equation for the circle with center (3,−5) and diameter of length 8.
Answers
Answer:
(x-3)² + (y+5)² = 16
Step-by-step explanation:
Radius will be half of diameter means that radius = r = 8/2 = 4.
With Center (h,k) the equation of circle is
(x-h)² + (y-k)² = r²
so by putting values answer will be
(x-3)² + (y+5)² = 4²
(x-3)² + (y+5)² = 16
Copy the problem, mark the givens in the diagram and write a statement/reason proof
Answers
Answer:
Step-by-step explanation:
<E = <T Given
M is the midpoint of TE Given
TM = ME Definition of a midpoint
<TMI = <RME Property of Vertically Opposite Angles
ΔTMI = ΔRME ASA = ASA
MI = ME Corresponding parts of Congruent triangles are Congruent
answer: reasoning:
<E = <T given
M is the midpoint of TE given
TM = ME definition of a midpoint
<TMI = <RME property of Vertically Opposite Angles
ΔTMI = ΔRME ASA = ASA
MI = ME corresponding parts of congruent triangles are Congruent
hope this helps!
You invested $4000 between two accounts paying 3% and 4% annual interest. If the total interest earned for the year was $130, how much was invested at each rate?
Answers
You invested $3000 at 3% annual interest rate, and the remaining amount of $4000 - $3000 = $1000 was invested at 4% annual interest rate.
Let's assume you invested an amount, x, at 3% annual interest rate. This means the amount invested at 4% annual interest rate would be $4000 - x.
To calculate the interest earned from the investment at 3%, we multiply x by 3% (0.03). Similarly, the interest earned from the investment at 4% is calculated by multiplying ($4000 - x) by 4% (0.04).
According to the given information, the total interest earned from both investments is $130. So we can set up the equation:
0.03x + 0.04($4000 - x) = $130
Simplifying the equation:
0.03x + 0.04($4000 - x) = $130
0.03x + $160 - 0.04x = $130
-0.01x = $130 - $160
-0.01x = -$30
x = -$30 / -0.01
x = $3000
Therefore, you invested $3000 at 3% annual interest rate, and the remaining amount of $4000 - $3000 = $1000 was invested at 4% annual interest rate.
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5. a tourist wants to visit six out of thirteen american cities; seven of them are on the east coast, three on the west coast and three in the middle of the country. in how many ways can she do that if i) the order of the visits does not play a role; ii) the order of the cities is important; iii) the order is not important, but she wants to visit at least three cities on the east coast and at least two on the west coast.
Answers
There are 105 ways for a visitor to visit six American cities while adhering to the guidelines and without taking the sequence of the stops into account.
i) To find the number of ways to choose 6 cities out of 13 when the order of the visits does not matter, we can use the combination formula:
\(${{13}\choose{6}} = \frac{13!}{6!(13-6)!} = 1,716$\)
Therefore, there are 1,716 ways for the tourist to visit six American cities without considering the order of visits.
ii) To find the number of ways to choose 6 cities out of 13 when the order of the visits does matter, we can use the permutation formula:
\($P_{13,6} = \frac{13!}{(13-6)!} = 1,235,520$\)
Therefore, there are 1,235,520 ways for the tourist to visit six American cities while considering the order of visits.
iii) To find the number of ways to choose 6 cities out of 13 when the order of the visits does not matter and the tourist wants to visit at least three cities on the east coast and at least two on the west coast, we can use the inclusion-exclusion principle.
First, we calculate the total number of ways to choose 6 cities out of 13:
\(${{13}\choose{6}} = 1,716$\)
Then, we calculate the number of ways to choose 6 cities without any restrictions on the coast:
\(${{7}\choose{3}}{{3}\choose{2}}{{3}\choose{1}} = 210$\)
Here, we have used the multiplication principle to find the number of ways to choose 3 cities out of 7 on the east coast, 2 cities out of 3 on the west coast, and 1 city out of 3 in the middle of the country.
However, this count includes the cases where the tourist visits only one or none of the west coast cities, which does not meet the requirement of visiting at least two west coast cities. So we need to subtract these cases from the count.
The number of ways to choose 6 cities while visiting only one or none of the west coast cities is:
\(${{7}\choose{3}}{{3}\choose{1}}{{3}\choose{2}} + {{7}\choose{3}}{{3}\choose{0}}{{3}\choose{3}} = 105$\)
Here, we have used the multiplication principle to find the number of ways to choose 3 cities out of 7 on the east coast, 1 city out of 3 on the west coast, and 2 cities out of 3 in the middle of the country, or to choose 3 cities out of 7 on the east coast and all 3 cities in the middle of the country.
Therefore, the number of ways to choose 6 cities while visiting at least three cities on the east coast and at least two cities on the west coast is:
\($210 - 105 = 105$\)
So, there are 105 ways for the tourist to visit six American cities while meeting the given requirements and without considering the order of visits.
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what is a cube number?
Answers
Answer:
A cube number is a number that is obtained by multiplying a number by itself three times. In other words, a cube number is the result of raising a number to the power of 3.
Step-by-step explanation:
For example, 2 × 2 × 2 = 8, so 8 is a cube number. Similarly, 3 × 3 × 3 = 27, so 27 is also a cube number. Cube numbers are also known as perfect cubes.
Solve the equation below. Pls include work
28.10 = 15.5 + 5x
Answers
Answer:
2.52
Step-by-step explanation:
5x + 15.5 = 28.1
subtract 15.5 from both sides
5x = 12.6
divide both sides by 5
x = 2.52
Answer:
x=2.52
Step-by-step explanation:
28.1 = 15.5 + 5x
(take 15.5 from both sides)
28.1-15.5=15.5-15.5+5x
12.6=5x
(Divide both sides by 5)
12.6/5=5x/5
2.52=x
11.
D
Name the postulate, if possible, that makes the triangles
congruent.
E
A
B
a) SSS
b) SAS
c) ASA
d) Not Possible
Answers
Answer:
Step-by-step explanation:
The two angles at E that are enclosed by DE and CE (<DEC) and AE and BE (AEB) are vertically opposite. Therefore you have 2 sides and an included angle.
The Postulate is SAS
Write each as a decimal and round to the thousandth place.
65%
O.3%
445%
Answers
0.3% = .003
445% = 4.45
Answer:
0.650
.003
4.450
Step-by-step explanation:
Each side of a square is increasing at a rate of 4 cm/s. At what rate (in cm2/s) is the area of the square increasing when the area of the square is 25 cm2
Answers
Answer:
The area of the square is increasing at a rate of 40 square centimeters per second.
Step-by-step explanation:
The area of the square (\(A\)), in square centimeters, is represented by the following function:
\(A = l^{2}\) (1)
Where \(l\) is the side length, in centimeters.
Then, we derive (1) in time to calculate the rate of change of the area of the square (\(\frac{dA}{dt}\)), in square centimeters per second:
\(\frac{dA}{dt} = 2\cdot l \cdot \frac{dl}{dt}\)
\(\frac{dA}{dt} = 2\cdot \sqrt{A}\cdot \frac{dl}{dt}\) (2)
Where \(\frac{dl}{dt}\) is the rate of change of the side length, in centimeters per second.
If we know that \(A = 25\,cm^{2}\) and \(\frac{dl}{dt} = 4\,\frac{cm}{s}\), then the rate of change of the area of the square is:
\(\frac{dA}{dt} = 2\cdot \sqrt{25\,cm^{2}}\cdot \left(4\,\frac{cm}{s} \right)\)
\(\frac{dA}{dt} = 40\,\frac{cm^{2}}{s}\)
The area of the square is increasing at a rate of 40 square centimeters per second.
What is the value of
3
0 1000
27
0 1000
9
10
27
0 10
3
10
?
Answers
Answer:
27/1000 is your answer
Step-by-step explanation:
Help !! Pls :3:’dnmdnsnms
Answers
The congruent reason for the triangles is (b) HL theorem
How to determine the congruent statement?From the question, we have the following parameters that can be used in our computation:
Triangles = FGH and JHK
The SSS similarity theorem implies that the corresponding sides of the two triangles in question are not just similar, but they are also congruent
From the question, we can see that the following corresponding sides on the triangles:
Sides GH and HK
Sides FH and JK
These parameters are given in reasons (2) and (3) and it implies that these sides are congruent sides
For the triangle to be congruent by SSS, the following sides must also be congruent
GH must be congruent to HK
The above statement is true because point H is the midpoint of line GK
This is indicated in reason (2)
Hence, the congruent statement is SSS.
However, we can also make use of the HL theorem in (B)
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(3,4) m=0
Formula
Y-y=m(x-x1)
Answers
Answer:
\(y1 = 4 \\ x1 = 3\)
\(y - y1 = m(x - x1)\)
\(y - 4 = 0(x - 3)\)
\(y - 4 = 0\)
\(y = 4\)
Max scored 2,347 points in a video game. That was 1,356 points more than Danteʼs score in the same game. How many points did Dante score?
Answers
Answer: Dante scored 991 points
Step-by-step explanation:
2,347 - 1,356=991
PLEASE ANSWER UNDER 5 MIN!!!! ily!!!!
what is the period of the sinusoidal function? enter your answer in the box.
Answers
Answer:
Step-by-step explanation:
10
Ws
Identify the decimals labeled with the letters A, B, and C on the scale below. Letter A represents the decimal Letter B represents the decimal Letter C represents the decimal
Answers
\(10\) divisions between $389$ and $390$ so each division is $\frac{390-389}{10}=0.1$
A is 8 division from $389$, so, A is $389+8\times 0.1=389.8$
similarly, C is one division behind $389$ so it is $389-1\times 0.1=388.9$
and B is $390.3$
A system of two linear equations is graphed on a coordinate plane. If the system of equations has infinitely many
solutions, which statement must be true?
A) On the graph, there are no points (z, y) that satisfy both equations.
B) On the graph, there is exactly one point (z,y) that satisfies both the equations.
C) On the graph, any point (z,y) that satisfies one of the equations cannot satisfy the other equation.
D) On the graph, any point (z,y) that satisfies one of the equations must also satisfy the other equation.
Answers
Monica med 3 ounces of blue paint with 2 ounces of yellow paint. She decided to create 20 ounces of the same mixture. How many ounces of
yellow paint does Monica need for the new mixture?
Answers
Answer:
Step-by-step explanation:
So she will need 8 ounces of yellow paint to get 20 ounces of the desired mixture.S
Answer:
I'm pretty sure she would need 8 ounces of yellow paint.
Step-by-step explanation:
Blue: Yellow
3: 2 = 5
6: 4 = 10
9: 6 = 15
12: 8 = 20
To pour the concrete sidewalk shown in the figure, approximately how many cubic feet of topsoil will you need to remove for the 4"-thick sidewalk if the owner wants the finish surface of the sidewalk to be level with the adjacent topsoil? ROUND YOUR ANSWER TO THE NEAREST CUBIC FOOT. _____ cu ft
Answers
Answer: 109 cu ft
Step-by-step explanation: had it on a test
Solve the system of equations.
5y−4x=−7
2y+4x=14
Answers
Two kinds of crated cargo, A and B, are to be shipped by truck. Each crate of cargo A is 50 cubic feet in volume and weighs 200 pounds, whereas each crate of cargoB is 10 cubic feet in volume and weighs 360 pounds. The shipping company charges $75 per crate for cargo A and $100 per crate for cargo B. The truck has a maximum load limit of 7200 pounds and 1000 cubic feet. Write a system of inequalities that represent the constraints in this problem.
a. 50a+10b> 7200; 200a+360b> 1000; a> 0; b>0
b. 50a+10b<1000; 200a+360b < 7200; a> 0; b>0
c. 50a+10b7200; 200a +360b < 1000; a s 0; b< 0
d. 50a+ 10b> 1000; 200a+360b> 7200; a s 0; b<0
Answers
Answer:
The correct answer is option b)
50a+10b<1000; 200a+360b < 7200; a> 0; b>0
Step-by-step explanation:
We are given that Two kind of crated cargo namely A and B to be shipped by truck.
Cargo A:
Volume of each crate of cargo A = 50 cubic ft
Weight of each crate of cargo A = 200 pounds
Let number of crates of cargo A to be shipped = a
Total volume of 'a' crates of cargo A = 50a cubic ft
Total weight of 'a' crates of cargo A = 200a pounds
Cargo B:
Volume of each crate of cargo B = 10 cubic ft
Weight of each crate of cargo B = 360 pounds
Let number of crates of cargo B to be shipped = b
Total volume of 'b' crates of cargo B = 10b cubic ft
Total weight of 'b' crates of cargo B = 360b
Total volume allowed in the truck is 1000 cubic ft
Total volume of 'a' crates of Cargo A and Total volume of 'b' crates of Cargo B = 50a+10b cubic ft (This sum should be less than volume of truck so that it can fit in the truck)
So, the inequality becomes
\(50a+10b<1000\) ....... (1)
Total weight allowed (load limit) in the truck is 7200 pounds
Total weight of 'a' crates of Cargo A and Total weight of 'b' crates of Cargo B = 200a+360b cubic ft (This sum should be less than volume of truck so that it can fit in the truck)
So, the inequality becomes
\(200a+360b<7200 ...... (2)\) ....... (1)
And number of crates of cargo A and B are always a positive number.
So, a > 0 and b > 0.
So, the correct answer is option b.
b. 50a+10b<1000; 200a+360b < 7200; a> 0; b>0
Compare the investment below to an investment of the same principal at the same rate compounded annually.
principal: $5,000, annual interest: 9%, interest periods: 4, number of years: 18
After 18 years, the investment compounded periodically will be worth $? more than the investment compounded annually.
(Round to two decimal places as needed.)
Answers
After 18 years, the investment compounded periodically (quarterly) will be worth $1,230.23 more than the investment compounded annually.
What is compounded interest?Compounded interest refers to the interest system that charges interest on both principal and accumulated interest.
The period of compounding in a year determines the worth of the future value.
The future value can be ascertained using an online finance calculator as follows:
Interest periods: = 4 times yearly (Quarterly)
Principal = $5,000
Annual interest rate = 9%
Number of years: 18
N (# of periods) = 72 quarters (18 years x 4)
I/Y (Interest per year) = 9%
PV (Present Value) = $5,000
PMT (Periodic Payment) = $0
Results:
Future Value (FV) = $24,815.83
Total Interest = $19,815.83
Interest periods: = Annually
N (# of periods) = 18 years
I/Y (Interest per year) = 9%
PV (Present Value) = $5,000
PMT (Periodic Payment) = $0
Results:
Future Value (FV) = $23,585.60
Total Interest = $18,585.60
Difference in Future Values $1,230.23 ($24,815.83 - $23,585.60)
Thus, an investment compounded periodically earns more than an investment compounded annually.
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How many fifths are there in 3⅗
Answers
Answer:
18/5
Step-by-step explanation:
5 1/5 = 1 thus 3 are 15 + 3 = 18/5
Answer:
The answer is 18 fifths.
Step-by-step explanation:
3 = 15/3 + 3/5 = 18/3 fifths.
Use the quadratic formula to find the exact solutions of 3x2 − 6x + 2 = 0.
a. negative 1 plus or minus the square root of 3 divided by 3
b. 1 plus or minus the square root of 3 divided by 3
c. negative 1 plus or minus the square root of 15 divided by 3
d. 1 plus or minus the square root of 15 divided by 3
Answers
The exact solutions of the qudratic equation 3x^2 - 6x + 2 = 0 are:
a. negative 1 plus or minus the square root of 3 divided by
3 (x = (-1 ± √3) / 3) .So, option a is the correct answer.
To find the solutions of the quadratic equation 3x^2 - 6x + 2 = 0, we can use the quadratic formula, which states that for an equation of the form ax^2 + bx + c = 0, the solutions are given by:
x = (-b ± √(b^2 - 4ac)) / (2a)
In this case, a = 3, b = -6, and c = 2. Substituting these values into the formula, we have:
x = (-(-6) ± √((-6)^2 - 4(3)(2))) / (2(3))
x = (6 ± √(36 - 24)) / 6
x = (6 ± √12) / 6
x = (6 ± 2√3) / 6
x = (3 ± √3) / 3
Therefore, the exact solutions of the equation 3x^2 - 6x + 2 = 0 are:
a. negative 1 plus or minus the square root of 3 divided by 3 (x = (-1 ± √3) / 3)
So, option a is the correct answer.
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What is the value of (3 minus 5) Superscript 4 Baseline (2) minus 16 divided by 2?
Answers
Answer:
it is 24.
Step-by-step explanation:
The value of (3 minus 5) Superscript 4 Baseline (2) minus 16 divided by 2 is 24. This answer is correct and helpful.
Answer:
24
Step-by-step explanation:
The last line of a proof represents
the
given
information.
the argument.
the conclusion.
O the assumptions.
Answers
HELPP QUICKKK its timedd
Answers
Answer:
10
Step-by-step explanation:
Help help help ASAP IXL
Answers
hope it helps you
907.46 is the answer.
dina called her friend to tell her that she saved 30% on her new skirt at a discount store. Her friend told her that she could have gotten a better deal at a different store that was advertising 1/3 off of all clothing. If the original price of Dima's skirt was $54, how much more could she have saved at the store her friend suggested
Answers
Answer:
She could have saved 1.8 more dollars.
Step-by-step explanation:
30% is the same as 0.3. 0.3 times 54$ is 16.2$. 1/3 times 54$ is 18$. 18$ - 16.2$ is 1.8$.