A scale drawing for a restaurant is shown below.
In the drawing, 5cm represents 6m.
Assuming the dining hall is rectangular, find the area of the real dining hall.
What is the area?
Answers
The area of the real rectangular dining hall (assuming that 5cm on paper is 6m in real) is 72m².
A rectangle is a quadrilateral whose opposite edges are of equal length and the opposite angles are of equal measurements.
Given that
the length of the dining hall, l = 10cm
the width of the dining hall, b = 5cm
As evident from the figure, the dining hall is rectangular, and since it is known that the area of a rectangle is the product of its length and width, therefore,
Area of the hall (on paper) = l × b
= 10 × 5
= 50 square cm.
Also, as it is given in the question that 5cm on paper represents 6m in real, therefore
[tex]Area\ of\ the\ hall\ (in\ real)= (\dfrac{10}{5}\times6)\times(\dfrac{5}{5}\times6)[/tex]
[tex]\\= 2\times6\times6\\= 72\ m^2[/tex]
Hence, the area of the hall in real is 72m².
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Related Questions
What is the equation of a line that passes through point R(−4, −3) and has a slope of 7?
A: y = 7x + 25
B: y = 7x − 25
C: y = 7x + 3
D: y = −7x − 3
Answers
(x,y) = (-4,-3) is the given point
Turn to slope-intercept form and use these values to find b
y = mx+b
-3 = 7(-4)+b ... plug in the given values
-3 = -28+b
-3+28 = -28+b+28
25 = b
b = 25
since we know that m = 7 and b = 25, the equation y = mx+b turns into y = 7x+25
The final answer is choice A
1. Which set of ordered pairs in the form of (x,y) does not represent a function of x? (1 Point)
A. (1, 1.5), (2, -1.5), (3, 1.5), (4, 1.5)
B. (0, 1.5), (3, 2.5), (1, 3.3), (1, 4.5)
C. (1, 1.5), (-1, 1.5), (2, 2.5), (-2, 2.5)
D. (1, 1.5), (-1, -1.5), (2, 2.5), (-2, 2.5)
Answers
Tickets to a concert are available online for $30 plus a one time handling fee of $1.50. The total cost of the function of the number of tickets bought. What is the function rule that models cost of the concert tickets? Evaluate the function of 6 tickets.
Answers
f(x)=30x+1.5
Because no matter what, you'll pay the $1.50 just once.
Now, say 6 tickets are bought:
f(6)=30(6)+1.5
To simplify:
f(6)=180+1.5
f(6)=181.5
So to buy 6 tickets, you would have to form over $181.50
Hope this helps!
find the nonpermissible replacement for the variable x in this expression (x^2)/(2x-4) ? find the nonpermissible replacement for the variable x in this expression (x^2)/(2x-4) ?
Answers
The non-permissible replacements for the variable x in the expression (x^2)/(2x-4) are x = 0 and x = 2.
Explanation:An expression is undefined when its denominator is equal to zero. Therefore, we need to find the values of x that make the denominator, 2x-4, equal to zero.
Solve the equation for x: 2x - 4 = 0 2x = 4 x = 2
Therefore, x = 2 is a non-permissible replacement because it makes the denominator zero.
Additionally, the expression also includes x^2 in the numerator. Since any number multiplied by zero is still zero, dividing any non-zero number by zero results in undefined. Therefore, x = 0 is also a non-permissible replacement.
In conclusion, the non-permissible replacements for the variable x in the expression (x^2)/(2x-4) are x = 0 and x = 2.
Write the equation 16x 11y = −88 in slope-intercept form.
Answers
The equation 16x + 11y = -88 when rearranged in slope-intercept form is y = (-16/11)x - 8, with a slope of -16/11 and a y-intercept of -8.
Explanation:To write the equation 16x + 11y = -88 in slope-intercept form, we need to solve for y in terms of x. The slope-intercept form of a straight line is y = mx + b, where m is the slope and b is the y-intercept. Following the algebra of straight lines, we rearrange the equation as follows:
Subtract 16x from both sides: 11y = -16x - 88.Divide each term by 11 to solve for y: y = (-16/11)x - 8.This gives us the slope-intercept form, where the slope (m) is -16/11 and the y-intercept (b) is -8. The slope means that for every increase of 11 units in the x-direction, y decreases by 16 units. The y-intercept is the point where the line crosses the y-axis, which is at y = -8 when x = 0.
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Use the Distributive Property to complete the following statement:
4(x−1)=4x−
1.
–4.
4.
–1.
Answers
So, lets expand this problem. The distributive property basically states that multiplying two numbers being added together is the same as multiplying the outer number by the two numbers being added individually, then adding those together. Sounds way harder than it is:
[tex]x(y+z) = xy+xz[/tex]
You can apply this to your problem like this: multiply the 4 by each term in your binomial (your two terms in parenthesis), then simplify.
[tex]4(x-1) = 4x-(4)(-1)= 4x-(-4)[/tex]
(One thing to always remember – at least, in terms of algebra and not necessarily life – two negatives always equal a positive. This is not shown above, however, because the symbol on the end of the given problem is a subtraction sign. Your answer, in this case, is (–4), or B. Hope that clears up any confusion).
Hope this helped you out! Feel free to ask me any questions if you need further clarification. :-)
A player moves a knight from location (3, 2) to (5, 1) on a chessboard. If the bottom-left square is labeled (1, 1), which description matches the translation?
2 squares up, 1 square right
1 square down, 2 squares left
1 square down, 2 squares right
2 squares down, 1 square right
Answers
Second number is y axis and it describes if figure is moving up or down.
Now that we said that we can see that x axis increased by 2 while y axis decreased by 1. Description that matches is:
1 square down and 2 squares right.
Answer:
1 square down, 2 squares right
Step-by-step explanation:
In the problem solving process, the final step is to try to ______.
a.
Generate multiple solutions
b.
Review your results
c.
Decide on a solution
d.
Evaluate your choices
Answers
This means that you have to check if the results meet the original requirements or statements.
Ideally, you should try to solve the same problem by a second method, and/or you should substitute the results into the given relationships given in the problem statement to chek coherence of your results.
Then the answer is option b.
Answer:
b. Review your results
Step-by-step explanation:
checking for mistakes should be the last step
2x-3y=13 y=1/2x-7/2 as a substitution problem
Answers
so replace y with 1/2x - 7/2 in ur other equation
2x - 3y = 13
2x - 3(1/2x - 7/2) = 13....distribute through the parenthesis
2x - 3/2x + 21/2 = 13 ...multiply entire equation by 2 to get rid of fractions
4x - 3x + 21 = 26
4x - 3x = 26 - 21...combine like terms
x = 5
2x - 3y = 13
2(5) - 3y = 13
10 - 3y = 13
-3y = 13 - 10
-3y = 3
y = -3/3
y = -1
solution is (5,-1)
add any three numbers of the following and answer should be 60
2 , 6, 10, 14, 18, 22, 26, 30, 34, 38, 42, 46, 50, 54, 58
Answers
x+y+z=60
Fix the value of x to some random number( say 38), now we have 22 more units to be divided between "y" and "z", so by randomly looking at numbers we can say that there are no results possible.
Choose another no. as "x"( say 30) , so we have 30 units between "y" and "z", still not able to reach conclusion.
Choose another no as "x"(say 26), so we have 34 units between "y" and "z", still not able to sum up to 60.
SO after analyzing all probabilities, I came to conclusion that it is indeed a trap question!! and no real solution exists.
But a smart solution, not a mathematical is,
58+2=60, here we have used rather 3 digits(not numbers) to reach our goal.
a number of apples divided into 12 baskets
Answers
So the equation for that word problem would be = a/12.
I hope you find this answer the most helpful! :)
Q: if AB is parallel to CD, which statement is true? Answers: A- AB And CD do not intersect B- AB And CD intersect at 90 angles. C- The perpendicular distance between AB and CD increases as the lines are traversed left to right. D- the perpendicular distance between AB and CD decreases as the lines are traversed right to left.
Answers
Identify each pair of angles as corresponding, alternate interior, alternate exterior, or consecutive interior.
Answers
1.Corresponding,2.alternate exterior, 3.corresponding, 4.consecutive interior, 5.alternate interior, 6.alternate exterior,7.alternate interior,8.alternate exterior
When two or more lines are cut by a transversal, the angles which occupy the same relative position are called corresponding angles .When two lines are cut by a transversal, the pairs of angles on one side of the transversal and inside the two lines are called the consecutive interior angles .When two lines are cut by a transversal, the pairs of angles on either side of the transversal and inside the two lines are called the alternate interior angles .When two lines are cut by a transversal, the pairs of angles on either side of the transversal and outside the two lines are called the alternate exterior angles .So, by the definitions the angles formed are:
Correspondingalternate exteriorcorrespondingconsecutive interior. alternate interioralternate exterioralternate interioralternate exteriorLearn more:https://brainly.com/question/11342335
Corresponding angles, alternate interior angles, alternate exterior angles, and consecutive interior angles are different types of angle pairs formed when a transversal intersects two parallel lines.
Explanation:Corresponding angles:
Corresponding angles are formed when a transversal intersects two parallel lines.They lie on the same side of the transversal but on different lines.They have equal measures.Alternate interior angles:
Alternate interior angles are formed when a transversal intersects two parallel lines.They lie on opposite sides of the transversal and on different lines.They have equal measures.Alternate exterior angles:
Alternate exterior angles are formed when a transversal intersects two parallel lines.They lie on opposite sides of the transversal and on different lines.They have equal measures.Consecutive interior angles:
Consecutive interior angles are formed when a transversal intersects two parallel lines.They lie on the same side of the transversal and on different lines.They have a sum of 180°.Learn more about Angles here:https://brainly.com/question/13954458
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The length of a rectangular jewelry box is 3 inches more than twice the width. the perimeter is 18 inches
Answers
Final answer:
The width of the rectangular jewelry box is 2 inches and the length is 7 inches. These dimensions satisfy the given relationship between the length and width and the specified perimeter of 18 inches.
Explanation:
To solve the problem of finding the dimensions of a rectangular jewelry box where the length is 3 inches more than twice the width, and the perimeter is 18 inches, let's define the width of the box as w inches. Subsequently, the length will be 2w + 3 inches, as stated by the relation given in the problem. The perimeter of a rectangle is calculated by the formula P = 2l + 2w, where l is the length and w is the width of the rectangle. We can set up the equation:
18 = 2(2w + 3) + 2w
Solving the equation for w gives us:
18 = 4w + 6 + 2w
18 = 6w + 6
12 = 6w
w = 2
Now that we have the width, we can find the length:
Length = 2w + 3 = 2(2) + 3 = 7 inches
So, the width of the jewelry box is 2 inches and the length is 7 inches.
Write 9 decimals with two decimal places that when rounded to the nearest tenth round to 8.7
Answers
8.66
8.67
8.68
8.69
8.70
8.71
8.72
8.73
9 decimals with two decimal places that when rounded to the nearest tenth round to 8.7 are 8.65, 8.66, 8.67, 8.68, 8.69, 8.70, 8.71, 8.72 and 8.73.
What is the rounding off numbers?Rounding a number means the process of making a number simpler such that its value remains close to what it was. The result obtained after rounding off a number is less accurate, but easier to use. While rounding a number, we consider the place value of digits in a number.
We need to write 9 decimals with two decimal places that when rounded to the nearest tenth round to 8.7
8.65, 8.66, 8.67, 8.68, 8.69, 8.70, 8.71, 8.72 and 8.73.
Therefore, 9 decimals with two decimal places that when rounded to the nearest tenth round to 8.7 are 8.65, 8.66, 8.67, 8.68, 8.69, 8.70, 8.71, 8.72 and 8.73.
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-7 over -10 simplified
Answers
Between what two integers does the square root of 29 lie?
Answers
Answer: The answer is 5 and 6.
Step-by-step explanation: We are to find the two integers between which the square root of 29 lie.
Let the two integers be 'x' and 'y'.
So,
[tex]x<\sqrt {29}<y\\\\\Rightarrow x<5.38<y.[/tex]
Since 'x' is an integer less than 5.38, so it must be 5. Also, 'y' is an integer that is greater than 5.38, so it will be 6.
Therefore, the two integers are 5 and 6.
Thus, the answer is 5 and 6.
Lisa's age is 4 years older than three times Sammy's age. Lisa is 28 years old. Let s represent Sammy's age.
Which equation can be used to solve for Sammy's age?
s + 4 = 28
3s + 4 = 28
4s + 3 = 28
3s = 28
Answers
Sammy's age can be found by using the formula 3s + 4 = 28.
Lisa's age is 4 years more than Sammy's age multiplied by 3.
Assuming Sammy's age is s, Sammy's age multiplied by 3 is:
= 3s
Lisa's age is 4 more than Sammy's age multiplied by 3 which is:
= 4 + 3s
We know that Lisa is 28 years old and Lisa's age is "4 + 3s." Equating those together will give the expression:
4 + 3x = 28
In conclusion, Sammy's age can be found by the formula 4 + 3x = 28.
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how many times does 28 go into 126????????
Answers
It would be: 126/28 = 4.5
So, your final answer is 4.5
Hope this helps!
Given f(x)=17-x^2, what is the average rate of change in f(x) over the interval [1, 5]?
Answers
Answer:A
Step-by-step explanation:
(f(5) - f(1))/(5 - 1) =
(17 - 5^2 - (17 - 1^2))/4 =
(17 - 25 - 17 + 1)/4 = 6
Write the rule for the nth term of an arithmetic sequence in which a10=46 and d=3
Answers
Final answer:
The rule for the nth term of the arithmetic sequence is given by the formula a_n = 19 + (n - 1)×3, where a1 is the first term of the sequence and d is the common difference.
Explanation:
To write the rule for the nth term of an arithmetic sequence where the 10th term a10 is 46 and the common difference d is 3, we use the formula:
an = a1 + (n - 1)d
We have that:
a10 is the 10th term of the sequence which is 46.
The common difference d is 3.
Firstly, we need to find a1, the first term of the sequence. We can use the given a10 to find a1.
a10 = a1 + (10 - 1)×3
46 = a1 + 9×3
46 = a1 + 27
a1 = 46 - 27
a1 = 19
Now we can write the rule for the nth term:
an = 19 + (n - 1)×3
This formula allows us to calculate any term in the sequence by substituting the desired term number for n.
Which of the following expressions describes the solution set m ≥ -3?
All real numbers that are negative three or greater.
All real numbers that are greater than negative three.
All real numbers that are negative three or less.
All real numbers that are less than negative three.
Answers
m→-3,-2,-1,..
The correct expression of the solution set will be;
''All real numbers that are greater than negative three.''
What is Inequality?
A relation by which we can compare two or more mathematical expression is called an inequality.
Given that;
The solution set is,
m ≥ - 3
Now,
Here, The solution set is,
m ≥ - 3
Clearly, a number 'm' is greater than or equal to - 3.
Thus, We can formulate;
The correct expression of the solution will be;
''All real numbers that are greater than negative three.''
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Mandy told Bill that she has read 16 books this year and reads 2 books each month. Bill wants to catch up to Mandy. He tracks his book reading with a table on his door. Using his table below, what month will Bill have read the same amount of books as Mandy?
Month Books
May 4
June 8
July 12
Answers
Mandy's equation:
16 + 2x
she starts with 16 read books and she reads 2 books each month which is in total 2*x where x is number of months
Bill's equation:
4x
because from table we can see he is reading 4 new books each month.
now we need to make those 2 equations equal to eachother and solve for x because we want to see after how many months both will read the same that is why we set them equal.
16 + 2x = 4x
16 = 2x
x = 8
That means that in december he will catch her (if i counted months correctly :) )
Which of the graphs below represent the function f(x) = x3 - 5x2 + 2x + 8? You may sketch the graph to compare.
Answers
Answer:
The answer in the attached figure
Step-by-step explanation:
we have
[tex]f(x)=x^{3}-5x^{2} +2x+8[/tex]
we know that
The y-intercept is the value of the function when the value of x is equal to zero
The x-intercept is the value of x when the value of the function is equal to zero
Using a graphing tool-------> Find the intercepts of the function
see the attached figure
The y-intercept is [tex]8[/tex]
The x-intercepts are [tex]-1,2,4[/tex]
therefore
the answer in the attached figure
Answer:
II graph is correct
Step-by-step explanation:
Given are 4 graphs and we have to find out the match for
[tex]f(x) = x^3 - 5x^2 + 2x + 8[/tex]
To find y intercept:
Put x=0
y intercept = 8. The second graph has this intercept
To find x intercept
Let f(x) =0 to get y intercepts
The given funciton has factors as
[tex](x+2)(x-1)(x-3)[/tex]
So x intercepts are -2, 1, 3 and this matches with II graph
Increasing:
[tex]f'(x) = 3x^2-10x+2\\[/tex]
f'(x) =0 for x =0.214 and 3.12
OUr II graph has critical points at these values
SO option II is right
What is the simplified form of x + 6/3 - x + 2/3
Answers
The simplified form of the given expression x + 6/3 - x + 2/3 is 8/3 after combining like terms and simplifying the constants.
The question involves simplifying a mathematical expression.
The expression given is:
x + 6/3 - x + 2/3.
To simplify this expression, combine like terms.
Since x is present in both the first and third terms, they cancel each other out.
Next, combine the constant terms 6/3 and 2/3. This results in:
6/3 + 2/3 = (6 + 2) / 3 = 8/3
The simplified form of the expression is therefore 8/3.
This coordinate plane shows the shape of a hang glider. The perimeter of the glider is to be trimmed with a special material. What is the minimum length of material needed?
Answers
now there are lines that are not paralel to x and y so it is not that simple (but not hard either) to calculate lenghts. we can use formula for distance between 2 dots.
we will use dots: (12,7) and (0,2)
from that using pythagoras theorem we can see that distance is:
d = √12^2 + 5^2 = 13
Total lenght is:
2*13 + 24 + 4 = 26 + 28 = 54
X = 24 ft Of Materials
Y = 2 ft Of Distance
X = (12,7)
Y = (0,2)
Using The Pythagoras Theorem
[tex]D=\sqrt{12^{2}+5^{2}}=13[/tex]
Total lenght is:
[tex]\left[\begin{array}{ccc}3*13+24+4=26\\26+28=54\end{array}\right][/tex]
At time t equals or > 0, the acceleration of a particle moving on the x axis is a(t)=t+sint.? ...?
Answers
The integral of acceleration yields velocity, which we are trying to find.
So int(a(t)) = (t^2)/2 - cos(t) + C.
So we can also say that v(t) = (t^2)/2 - cos(t) + C.
*The constant, C, is very important in this case. We need to find when v(t) = 0. We can not do that without first knowing C.
2. Solve for C.
-2 = v(0).
-2 = (t^2)/2 - cos(t) + C.
-2 = -cos(t) + C.
-2 = -1 + C
-1 = C.
Now we have the full velocity equation.
v(t) = (t^2)/2 - cos(t) - 1.
4. Solve for t when velocity is 0.
0 = (t^2)/2 - cos(t) - 1.
t = 1.478 or -1.478
*time cannot be negative, so answer is b.1.48
find the average rate of change of f from pi to 11pi/3. f(x) = cos(x/2) ...?
Answers
The average rate of change of the function f(x) = cos(x/2) from pi to 11pi/3 is (3\sqrt{3}) / (16pi).
Explanation:The average rate of change of a function is the change in the function's value divided by the change in the independent variable. For the function f(x) = cos(x/2), we want to find the average rate of change from pi to 11pi/3. This can be calculated using the following formula:
Average rate of change = (f(b) - f(a)) / (b - a)
Let's calculate f(pi) and f(11pi/3):
f(pi) = cos(pi/2) = 0f(11pi/3) = cos((11pi/3)/2) = cos(11pi/6) = cos(pi/6) since cosine is periodic with period 2picos(pi/6) = \(\sqrt{3}/2\)Now we can substitute these values back into the average rate of change formula:
Average rate of change = (\(\sqrt{3}/2\) - 0) / ((11pi/3) - pi) = \(\sqrt{3}/2\) / (8pi/3) = (3\sqrt{3}) / (16pi)
The average rate of change of [tex]\(f(x) = \cos(\frac{x}{2})\)[/tex] from [tex]\(\pi\)[/tex] to [tex]\(\frac{11\pi}{3}\)[/tex] is [tex]\(-\frac{3\sqrt{3}}{16\pi}\)[/tex]. This represents the slope of the secant line over the given interval.
Let's find the average rate of change of f from π to 11π/3.
[tex]$$f(x)=\cos(\frac{x}{2})$$[/tex]
The average rate of change of a function f over the interval [a, b] is the slope of the secant line that intersects the graph of f at the points (a, f(a)) and (b, f(b)).
In other words, it's the change in f divided by the change in x.
[tex]$$\text{Average rate of change} = \dfrac{f(b) - f(a)}{b - a}$$[/tex]
We are given that [tex]f(x) = \cos(\frac{x}{2}), $a = \pi, and b = \frac{11\pi}{3}.[/tex]
Let's find f(a) and f(b).
[tex]\begin{aligned} f(a) &= f(\pi) \ \ and= \cos(\frac{\pi}{2}) \ \ and= 0 \end{aligned}[/tex]
[tex]$\begin{aligned} f(b) &= f\left(\frac{11\pi}{3}\right) \ \ &= \cos\left(\frac{11\pi}{6}\right) \ \ &= -\frac{\sqrt{3}}{2} \end{aligned}$[/tex]
Now we can plug these values into the formula for the average rate of change.
[tex]$\begin{aligned} \text{Average rate of change} &= \dfrac{f(b) - f(a)}{b - a} \ \ &= \dfrac{-\frac{\sqrt{3}}{2} - 0}{\frac{11\pi}{3} - \pi} \ \ &= \dfrac{-\frac{\sqrt{3}}{2}}{\frac{8\pi}{3}} \ \ &= -\dfrac{3\sqrt{3}}{16\pi} \end{aligned}$[/tex]
Therefore, the average rate of change of f from π to 11π/3 is [tex]-\dfrac{3\sqrt{3}}{16\pi}.[/tex]
Classify the number 0. Check all that apply.
Real
Irrational
Rational
Integer
Whole
Natural
Answers
so think of it as a interger
Name the postulate or theorem you can use to prove the triangles congruent.
Answers
They are two "siamese" right triangles. The side that they share is the hypotenuse of both triangles.
The other sides that are marked as congruent are the heights of each triangle.
Then, you can use the Hypotenuse Leg theorem to prove the congruence of both triangles.
The hypotenuse leg theorem states that any two rigth triangles that have congruent hypotenuse and a corresponding, congruent leg are congruent triangles.