An architect designs a house that is 10 m wide. The rafters holding up the roof are equal length and meet at an angle of 65°. The rafters extend 0.4 m beyond the supporting wall. How long are the rafters?
Answers
The length of the rafter when the architect design a house is 12.778m.
How to calculate the length?The information illustrates that the architect designs a house that is 10 m wide and that the rafters holding up the roof are equal length and meet at an angle of 65°.
The rafters extend 0.4 m beyond the supporting wall. Then, the length will be:
cos65° = BC / AC
cos 65° = (5 + 0.4)/x
cos 65° = 5.4/x
x = 5.4 / 0.4226
x = 12.778m
The length is 12.778m
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Related Questions
Write a recursive formula for the following arithmetic sequence.1, 12, -25, -38, ...a 1=an= for n ≧2
Answers
First, let's see the progression of the sequence of numbers
As you can see from the second term the sequence continues with a constant change of -13 which means d=-13.
The answers will be the expressions inside the red square box in each case.
Please help:State the implied domain and range: f(x)= 1/x−4 +3
Answers
ANSWER
[tex]Domain:(-\infty,\text{ 4\rparen U\lparen4, }\infty),\text{ \textbraceleft x \mid x}4\rbrace[/tex][tex]Range:\text{ \lparen-}\infty,\text{ 3\rparen U\lparen3, }\infty),\text{ \textbraceleft y \mid y}3\rbrace[/tex]EXPLANATION
Given:
[tex]f(x)\text{ = }\frac{1}{x\text{ - 4}}+\text{ 3}[/tex]Desired Outcome:
1. Domain
2. Range
Determine the domain of the function
Note: We want to include only input values that do not require the denominator to be 0 when there is a denominator. As a result, we'll set the numerator to 0 and solve for x.
[tex]\begin{gathered} 0\text{ = x - 4} \\ x\text{ = 4} \end{gathered}[/tex]We'll now remove 4 from the domain. All of the answers are real numbers x > 4 or x < 4. We will also use Union notation to combine the two sets.
That is:
[tex]Domain:(-\infty,\text{ 4\rparen U\lparen4, }\infty),\text{ \textbraceleft x \mid x}4\rbrace[/tex]
Determine the range of the function
Set x to 4 to find y
[tex]\begin{gathered} y\text{ = }\frac{1}{4-4}\text{ + 3} \\ y\text{ = 3} \end{gathered}[/tex]We'll also remove 3 from the range. All of the answers are real numbers y > 3 or y < 3. We will also use Union notation to combine the two sets.
That is:
[tex]Range:\text{ \lparen-}\infty,\text{ 3\rparen U\lparen3, }\infty),\text{ \textbraceleft y \mid y}3\rbrace[/tex]
Which of the following criterion will accurately complete the proof in step 4
Answers
2.
[tex]\begin{gathered} \angle RAG\text{ and }\angle RET\text{ are vertical angles} \\ \Rightarrow\angle RAG\cong\angle RET \end{gathered}[/tex]The reason for 2 is 'the angles are vertical'.
3. In the diagram below, we can identify the alternate interior angles more easily
Therefore, Therefore, the statements of the third step are
[tex]\begin{gathered} \angle AGR\cong\angle ETR \\ \text{and} \\ \angle GAR\cong\angle\text{TER} \end{gathered}[/tex]Finally, the corresponding angles of triangles GRA and TRE are all congruent; thus, the two triangles are congruent because of the AA similarity criterion. The answer is AA similarity criterion. The length of the sides is not involved in the demonstration.
At the fast food restaurant, four cheeseburgers and five small fries have a total of 2,310 calories. Three cheeseburgers and two small fries have a total ofapplication
Answers
Problem
At the fast food restaurant, four cheeseburgers and five small fries have a total of 2,310 calories. Three cheeseburgers and two small fries have a total of 1,330 calories. How many calories does each item contain?
Solution
For this case we can set up the following notation
x= number of cheeseburgers
y= small fries
4x +5y= 2310
3x + 2y= 1330
From the first equation we can solve for x and we got:
x= 577.5 - 5/4 y
And now we can replace this into the second equation and we got:
3(577.5 -5/4 y) +2y= 1330
And we can solve for y:
1732.5 - 15/4 y + 2y = 1330
-7/4 y = -402.5
y= 230 cal
And solving now for x we have:
x= 577.5 - 5/4 (230) = 577.5 - 287.5 = 290 cal
What is the product 6x1,167
Answers
Answer:
7,002
Step-by-step explanation:
The product is the answer of a multiplication problem. You just have to multiply the numbers by using the techniques to solve it. Hope this helps!
Factor: x(3y-5)+3(3y-15)
Answers
3xy-5x+9y-45
Step-by-step explanation:
Step by Step Solution
STEP1:STEP2:Pulling out like terms
2.1 Pull out like factors :
3y - 15 = 3 • (y - 5)
Equation at the end of step2: (x • (3y - 5)) + 9 • (y - 5) STEP3:Equation at the end of step 3 x • (3y - 5) + 9 • (y - 5) STEP4:Trying to factor a multi variable polynomial
4.1 Split 3xy-5x+9y-45
4.1 Split 3xy-5x+9y-45
into two 2-term polynomials
-5x+3xy and +9y-45
This partition did not result in a factorization. We'll try another one:
3xy-5x and +9y-45
This partition did not result in a factorization. We'll try another one:
3xy+9y and -5x-45
This partition did not result in a factorization. We'll try another one:
3xy-45 and +9y-5x
This partition did not result in a factorization. We'll try another one:
-45+3xy and +9y-5x
This partition did not result in a factorization. We'll try
hello I'm a 7th grader can u please help me with my math summer package and explain it in a way that a 7th grader can understand it..writing and. evacuating expressions
Answers
The price will increase if number of students increase
By multiplying the number of students with cost
Number of students varies in this example
The expression shown for trip amount is c = 10+13x.
The cost for 10 students is 140
The cost for 17 students is 231
What is the definition of evaluate an expression?Finding the value of an algebraic expression when a specified integer is used to replace a variable is known as evaluating the expression. We use the given number to replace the expression's variable before applying the order of operations to simplify the expression.
1). The price will increase if number of students increase.
2). By multiplying the number of students with cost.
3). Number of students varies in this example.
4). Let the number of students
Then total amount(c) of the trip is given by
c = 10+13x ------ equation (1)
5). Put x = 10 in equation (1)
c = 10+13(10)
c = 140
6). Put x = 17 in equation (1)
c = 10+13(17)
c = 231
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5. Stabiliţi dacă numerele următoare sunt prime: 37, 93, 123, 377, 602, 769, 1 243, 1999.
Answers
Answer:
Numere prime:37,377,769,1243,1999
Sunt numere prime deoare au ca divizori doar 1 si ei insusi
t hits the square dartboard shown below at a random point. Find the probability that the dart lands in the shaded circular region. Each side of the dartbozn, and the radius of the shaded region Is 2 in.the value 3.14 for T. Round your answer to the nearest hundredth.
Answers
Given:
Required:
To find the probability that the dart land will be in the shaded region.
Explanation:
Area of the circle is given by the formula:
[tex]A=\pi r^2[/tex]Where r = radius
Thus the area of the circular region
[tex]\begin{gathered} =(3.14)\times(2)^2 \\ =3.14\times4 \\ =12.56\text{ square in.} \end{gathered}[/tex]The area of the square is given by the formula:
[tex]=(side)^2[/tex]Thus the area of the given square
[tex]\begin{gathered} =(6)^2 \\ =36\text{ square in.} \end{gathered}[/tex]The probability of an event is given by the formula:
[tex]P=\frac{number\text{ of possible outcomes}}{Total\text{ number of outcomes}}[/tex]The probability that the dart land will be in the shaded region
[tex]=\frac{Area\text{ of the shaded region}}{Area\text{ of the square}}[/tex]Thus probability
[tex]\begin{gathered} P=\frac{12.56}{36} \\ P=0.3488 \\ P=0.349 \end{gathered}[/tex]Final answer:
Thus the probability that the dart land will be in the shaded region is 0.349.
Suppose you have $2750 in your savings account at the end of a certain period of time. You invested $2000 at a 4.36% simple annual interest rate. How long, in years, was your money invested ? (State your results to the nearest hundredth of a year.)
Answers
The money was invested for 8.60 years
Explanation:Given:
Amount in the savings account = $2750
Amount invested = $2000
rate = 4.36% = 0.0436
To find:
the time it took to invest the money to obtain the amount in the account
The investment was done using simple interest. So to get the time, we will apply simple interest formula
[tex]\begin{gathered} I\text{ = PRT} \\ I\text{ = interest} \\ R\text{ = rate} \\ T\text{ = time} \end{gathered}[/tex][tex]\begin{gathered} Interest\text{ = amount in the account - amount } \\ \\ Interest\text{ = 2750 - 2000} \\ \\ Interest\text{ = \$750} \end{gathered}[/tex][tex]\begin{gathered} The\text{ simple interest formula becomes:} \\ 750\text{ = 2000}\times0.0436\text{ }\times\text{ T} \\ \\ 750\text{ = 87.2T} \end{gathered}[/tex][tex]\begin{gathered} divide\text{ both sides by 87.2:} \\ T\text{ = }\frac{750}{87.2} \\ \\ T\text{ = 8.60 year} \end{gathered}[/tex]Write the equation x2 + y2 + 6x + 8y + 24 = 0 in vertex form.
Answers
ANSWER
[tex](x+3)^2+(y+4)^2=1[/tex]EXPLANATION
We want to write the equation of the circle in vertex form:
[tex]x^2+y^2+6x+8y+24=0[/tex]The first step is to group the x terms and y terms together and take the constant to the right-hand side of the equality sign:
[tex]x^2+6x+y^2+8y=-24[/tex]Now, complete the square for the x terms:
[tex]\begin{gathered} x^2+6x+(\frac{6}{2})^2+y^2+8y=-24+(\frac{6}{2})^2 \\ x^2+6x+9+y^2+8y=-24+9 \\ (x+3)^2+y^2+8y=-15 \end{gathered}[/tex]Repeat the process for the y terms:
[tex]\begin{gathered} (x+3)^2+y^2+8y+(\frac{8}{2})^2=-15+(\frac{8}{2})^2 \\ (x+3)^2+y^2+8y+16=-15+16 \\ (x+3)^2+(y+4)^2=1 \end{gathered}[/tex]That is the equation of the circle in vertex form.
Write each rational number as a decimal. If there’s no phone number, make sure to include a zero in the beginning. So if your answer is 0.7 make sure to put the zero in the beginning.
Answers
Calculate the given division, as shown below
Therefore, 33/40 is equal to 0.825. The answer is 0.825A jet flies at an average speed of 230
miles per hour. How long will it take to
fly from New York to Amsterdam, a
distance of 3,647 miles? (distance =
rate time)
.
Answers
Answer:
15.9 hours.
Step-by-step explanation:
speed = distance / time.
230 = 3647 / time.
time = 3647 / 230.
time = 15.9 hours.
Find the LCM of 18, 54, and 63.
Answers
Answer:
378
Step-by-step explanation:
Start with prime factoriazation
18 = 2 * 3 * 3
54 = 2 * 3 * 3* 3
63 = 3 * 3 * 7
2 * 3 * 3 * 3 * 7 = 378
Ann is a software salesperson. Her base salary is $1900 and she makes $90 more for every copy of History is Fun she sells. Her total pay, P (in dollars), after
selling e copies is given by the following.
P=1900+90c
Answer the following questions.
(a) What is Ann's total pay if she sells 24 copies?
(b) If Ann's total pay is $4780, how many copies did she sell?
copies
Answers
Answer:
A - $4060
B - 32 copies
Step-by-step explanation:
A -
P = 1900 + 90c
P = 1900 + 90(24)
P = 1900 + 2160
P = 4060
Total if Ann sold 24 copies: $4060
B -
1900 + 90c = 4780
90c = 4780 - 1900
90c = 2880
c = 32
Total copies: 32
Which expression is equivalent to -0.26v + v - 0.07?(answer choices are below)
Answers
To simplify the expression
-0.26v + v - 0.07
we will only add the ones with variable v
0.74v -0.07
The correct option is
0.74v - 0.07
What is the solution to the system?
2x+3y=1
-2x-y=9
A (-7,5)
B (5,-3)
C (5,-7)
D (-3,5)
Answers
Answer:
A
Step-by-step explanation:
Adding the equations,
[tex]2y=10 \implies y=5 \\ \\ \therefore 2x+3(5)=1 \implies x=-7[/tex]
HELP ASAP I NEED ANSWER NOWW IT'S MISSING PLEASE HELP 50 POINTS
Answers
Answer:
She worked for 4 hours and made 16 shirts (work below)
Step-by-step explanation:
let h = number of hours worked
and s = number of shirts made :]
28h+2s = 144
4h = s
28h+8h=144
h=4, s=16
:]
You want to buy new kitchen appliances 3 years from now, and you plan to save $3,000 semiannually, beginning immediately. You will deposit your savings in an account that pays 7.2% interest. How much will you have 3 years from now?
Answers
The final amount after 3 years compounded semi-annually is $3709.20
Compound Interest
To solve this problem, we simply need to use compound interest formula which is given as
[tex]A = p(1 + \frac{r}{n})^n^t[/tex]
where
A = final amountP = initial amount or principalr = rate n = number of times compoundedt = timeLets substitute the values into the formula and solve
[tex]A = p(1 + \frac{r}{n})^n^t\\A = 3000(1 + \frac{0.072}{2})^2^*^3\\ A = 3709.20[/tex]
The amount accrued 3 years from now is $3709.20
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It costs $35 per hour to rent a boat at the lake.
You also need to a pay a $25 fee for safety equipment.
You have $200.
How long can you rent the boat?
Answers
Answer:
7 hours
Step-by-step explanation:
25x + 25 = 200.
25x = 175
175/25 = 7.
Answer:
25 + 35h = 200
and
h = 5
(5 hours)
Step-by-step explanation:
you have 200.
costs:
35 per hour
and
25 fee
h will represent the total hours spent renting a boat
25 + 35h = 200
now we will do inverse operations
subtract 25 from both sides
35h = 175
now divide both sides by 35
h = 5
Put the following equation of a line into slope-intercept form, simplifying all fractions.
12y-2x=12
Answers
Answer:
y = 1/6x + 1
Step-by-step explanation:
Add 2x to both sides of the equation.
12y = 12 + 2x
Divide each term in 12y = 12 + 2x by 12 and simplify.
y = 1 + x/6
Write in y=mx+b form.
y = 1/6x + 1
Which of the following equations is not exponential?
Y=1^x
Y=(1/2)^x
Y=-2^x
Answers
The first equation given in the question as, y = 1^x is not exponential.
What do you mean by exponential?
A mathematical function with the form f (x) = a^x is an exponential function. "x" is a variable, while "a" is a constant that serves as the function's base and must be bigger than 0. The transcendental no., or roughly 2.71828, is the most often used exponential function on regular basis.
The equation, y = 1^x is not an exponential because for any integer value of x, y always equals to zero. Which makes it simple equation and not an exponential equation.
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What number should go in the gap to factorise this expression?
6x+14= (3x+7)
Answers
The number that should go in the gap to factorise the given expression is 2
Factorizing an expressionFrom the question, we are to determine the number that should go in the gap in order to factorise the given expression.
The given expression is
6x + 14
To determine the number that should go in the gap,
First we will factorize the given expression
6x + 14
The greatest common factor (GCF) of 6 and 14 is 2
Thus,
We can factor out 2 as follows
2(3x + 7)
The factored form of the expression is 2(3x + 7)
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Calculate the standard score of the given X value, X=83, where μ=88.1 and σ=87. Round your answer to two decimal places.
Answers
The standard score for the given X value is -0.06
Standard Score
Standard score or Z - Score is inversely varies with the standard deviation and directly varies with the difference of the raw score and the mean score.
The formula to calculate standard score is
z - score = (X - μ)/σ
Where
Z = standard score
x = observed value
μ = mean of the sample
σ = standard deviation of the sample
Given,
Here we have the value of X = 83, μ=88.1 and σ=87.
Now, we need to find the standard score for this values and we have also round off the result to two decimal places.
Apply the given values on the z-score formula, then we get,
z-score = (83 - 88.1)/87
When we simplify the numerator, then we get,
z - score = -5.1/87
After the division of these numbers we get the value of z-score as,
z - score = -0.0586
When we round off the result into two decimal place then we get the value of standard score as -0.06.
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Question
Gloria deposited $500 into a bank account that earned 7.5% simple interest each year. She earned $225 in interest before closing the account. No money was deposited into or withdrawn from the account.
How many years was the money in the account?
Round your answer to the nearest whole year.
Enter your answer in the box.
Answers
If Gloria deposited $500 into a bank account that earned 7.5% simple interest each year and she earned $225 in interest before closing the account, then the number of years that the money in the account is 6 years
The deposited amount = $500
The simple interest = 7.5%
The interest she earned = $225
Then the final amount = The deposited amount + The interest she earned
= 500+225
= $725
The equation of simple interest
A = P(1+rt)
Where A is the final amount
P is the initial amount
r is the interest rate
t is the time period
725 = 500(1+(7.5/100)×t)
(1+0.075t) = 1.45
0.075t = 0.45
t = 0.45/0.075
t = 6 years
Hence, if Gloria deposited $500 into a bank account that earned 7.5% simple interest each year and she earned $225 in interest before closing the account, then the number of years that the money in the account is 6 years
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Consider the sample space of the following experiment:We roll two dice and each time we record numbers on both of them.How many elements are in the sample space?
Answers
Answer: 36
One die has a total outcome of 6 elements (1, 2, 3, 4, 5, 6). Now, if we roll two dice, each time you roll a number on the first die, there are another 6 possible outcomes for the second die.
Therefore, the number of elements in the sample space would be:
[tex]6\times6=36[/tex]There would be 36 elements in the sample space.
Solve for x. Represent your answer on a number line.½x − 3 < − 4
Answers
The equation is
[tex]\frac{1}{2}x-3<-4\Rightarrow\frac{x}{2}<-4+3\Rightarrow\frac{x}{2}<-1\Rightarrow x<-2[/tex]Therefore x<-2. The number line representation is
FIND SLOPE AND Y INTERCEPT EASY QUESTION WILL GIVE BRAINLIEST ANSWERRRR HELPPP URGENT DUE IN A FEW MINUTESS
Answers
Simplify the equation 4x+9y = -9 in slope-intercept form of equation.
[tex]\begin{gathered} 4x+9y=-9 \\ 9y=-4x-9 \\ y=-\frac{4}{9}x-\frac{9}{9} \\ =-\frac{4}{9}x-1 \end{gathered}[/tex]So slope of line is -4/9 and int
A quiz consists of seven multiple choicequestions. Each question has four choices.A student who forgot to study guessesrandomly on every question. What is theprobability that the student answersexactly five questions correctly?
Answers
Solution
- The probability of him getting 1 queston correctly given tahat there is only one correct option out of 4 optins,
[tex]\begin{gathered} P(correct)=\frac{1}{4} \\ \\ P(incorrect)=1-P(correct) \\ P(incorrect)=1-\frac{1}{4}=\frac{3}{4} \end{gathered}[/tex]- Since here are questions, it implies that there are multiplye trials the student has.
A hospital parking lot charges 3.50$ for the first hour and 1.75$ for each additional hour. what is the minimum and the maximum number of hours Jose can park his car at the carage if he can spend between 12.25$ and 19.25
Answers
Jose can park his car for the maximum time of 9 hours and the minimum time of 5 hours.
What is Equation Modelling?Equation modelling is the process of writing a mathematical verbal expression in the form of a mathematical expression for correct analysis, observations and results of the given problem.
Given is a hospital parking lot charges 3.50$ for the first hour and 1.75$ for each additional hour.
The modelled equation representing the above scenerio is -
y = 3.5 + 1.75x
where (x) represents the number of hours for which the car is parked.
Maximum amount with Jose = $19.25
Therefore -
3.5 + 1.75x ≤ 19.25
1.75x ≤ 15.75
x ≤ 9 hours [Maximum time]
Minimum amount with Jose = $12.25
3.5 + 1.75x ≥ 12.25
1.75x ≥ 8.75
x ≥ 5 hours [Minimum time]
Therefore, Jose can park his car for the maximum time of 9 hours and the minimum time of 5 hours.
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