from your scale drawing, find the actual distance between the opposite corners of the school ball
Answers
The actual distance between the opposite corners of the school hall is; 10√34 m
How to use a Scale Drawing?The scale drawing showing the corners of the hall has been drawn and attached.
Now, from the attached scale drawing it was drawn with the scale;
1 cm to represent 5 m.
Now, the distance between the opposite corners of the hall measuring 50 m and 30 m is indicated as D on the scale drawing. Thus, to find the distance between the opposite corners, we will use Pythagoras theorem to get;
D² = 30² + 50²
D² = 900 + 3500
D² = 4400
D = √4400
D = 10√34 m
Thus, the actual distance between the opposite corners of the school hall is; 10√34 m
Complete question is;
Make a scale drawing of a rectangular school hall which is 50 m long and 30 m wide using a scale of 1 cm to 5 m. From your scale drawing, find the actual distance between the opposite corners of the hall.
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Related Questions
13. In A ABC, if m
BF is an angle bisector, find
m
Answers
If in the triangle ABC , BF is an angle bisector and ∠ABF=41° then angle m∠BCE=8°.
Given that m∠ABF=41° and BF is an angle bisector.
We are required to find the angle m∠BCE if BF is an angle bisector.
Angle bisector basically divides an angle into two parts.
If BF is an angle bisector then ∠ABF=∠FBC by assuming that the angle is divided into two parts.
In this way ∠ABC=2*∠ABF
∠ABC=2*41
=82°
In ΔECB we got that ∠CEB=90° and ∠ABC=82° and we have to find ∠BCE.
∠BCE+∠CEB+EBC=180 (Sum of all the angles in a triangle is 180°)
∠BCE+90+82=180
∠BCE=180-172
∠BCE=8°
Hence if BF is an angle bisector then angle m∠BCE=8°.
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find the perimeter of parallelogram PORS when side PQ=12cm and QR =7cm (with solution)
Answers
The answer is 38cm.
The formula used is perimeter of rectangle so in this case it will be 2(PQ+QR).
So,
=2×(12+7)
=2×19
=38cm
Which construction requires both endpoints of the diameter and the points where the arcs intersect the circle to be connected, in order, by line segments? an equilateral triangle inscribed in a circle a square inscribed in a circle a similar circle inscribed in a circle a regular hexagon inscribed in a circle
Answers
A regular hexagon inscribed in a circle is the construction that requires both endpoints of the diameter and the points where the arcs intersect the circle to be connected, in order, by line segments. Option D. This is further explained below.
What is a segment?Generally, any of the pieces into which something may be separated or which naturally separates over time. a section that is removed from a figure (such as a circle) using a line or plane as the cutting tool. a segment of a straight line that includes the territory between two points.
In conclusion, For the construction of a regular hexagon that is inscribed inside a circle, it is necessary for the ends of the diameter as well as the locations at which the arcs meet the circle to be linked, in the correct sequence, by line segments.
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Complete Question
Which construction requires both endpoints of the diameter and the points where the arcs intersect the circle to be connected, in order, by line segments?
an equilateral triangle inscribed in a circle a square inscribed in a circle a similar circle inscribed in a circle a regular hexagon inscribed in a circleWhat is the solution to the inequality 3x - 12| ≥ 6?
0-6
02
Ox<-6 or x> 18
Ox≤2 or x ≥6
Answers
========================================
Work Shown:
|3x-12| ≥ 6
3x-12 ≥ 6 or 3x-12 ≤ -6 ..... see note below
3x ≥ 6+12 or 3x ≤ -6+12
3x ≥ 18 or 3x ≤ -6+12
3x ≥ 18 or 3x ≤ 6
x ≥ 18/3 or x ≤ 6/3
x ≥ 6 or x ≤ 2
x ≤ 2 or x ≥ 6
----
Note: if |A| ≥ B, then A ≥ B or A ≤ -B where B is some positive number.
Example: |x| ≥ 5 means either x ≥ 5 or x ≤ - 5
When Kenny's electricity went out one night, his clock stopped at 8:39 p.m. when Kenny woke up the next morning his power was back on and his clock read 5:34 a.m. When he called the time services, the time was actually 7:11 a.m. How long was his electricity off?
Answers
Answer:
Step-by-step explanation:
Let's look at this in this perspective. There are 60 minutes in 1 hour. What I would do first is get rid of the 39 minutes at the end of 8:39. Now you have 8:00. Count until you get to 7 AM. 9, 10, 11, 12, 1, 2, 3, 4, 5, 6, 7. That's 11 hours from 8 PM to 7 AM. 60 x 11 = 660. Now, there are 11 minutes more on that 7-o clock and the 39 minutes we got rid of in the beginning. 11 + 39 = 40. 660 + 40 = 700.
Answer: Kenny's energy was off for 700 minutes, or 11 hours and 40 minutes.
What is the equation of a line in point-slope form passing through (-4,6) and (2, 3)?
Answers
The answer is y - 3 = -1/2 (x - 2).
First, let's find the slope.
m = y₂ - y₁ / x₂ - x₁m = 3 - 6 / 2 + 4m = -3/6m = -1/2Then, the point slope form will be :
y - 3 = -1/2 (x - 2)Answer: y=-0,5x+4.
Step-by-step explanation:
[tex]A(-4;6)\ \ \ \ B(2;3)\\Straight \ line\ equation\ is:\\\displaystyle\\\boxed {\frac{x-x_1}{x_2-x_1} =\frac{y-y_1}{y_2-y_1}} \\\frac{x-(-4)}{2-(-4)}=\frac{y-6}{3-6} \\ \frac{x+4}{2+4}=\frac{y-6}{-3} \\\frac{x+4}{6}=\frac{y-6}{-3} \\ Multiply\ the\ left\ and\ right\ sides\ of\ the\ equation \ by\ -3:\\\frac{-(x+4)}{2} =y-6\\-0,5x-2=y-6\\y=-0,5x+4.[/tex]
The variable used to predict another variable in a regression analysis (usually x) is called the?
Answers
The variable used to predict another variable in a regression analysis (usually x) is called the independent variable.
The regression analysis is used to determine the effect on the dependent variable with every one unit change in the independent variable.
The dependent variable is also known as response.
and the independent variable is also known as predictor.
In case of simple linear regression there is only one independent variable and in cases of multiple linear regression there are more than one independent variables.
The general form of simple linear regression is:
[tex]y=mx+c[/tex]
The general form of multiple linear regression is:
[tex]y=c+m_1x_1+m_2x_2+...+m_nx_n[/tex]
The dependent variable are usually denoted by the letter "y" and the independent variables are usually denoted by the letter "x".
Therefore, the variable used to predict another variable in a regression analysis (usually x) is called the independent variable.
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Based on the scatterplot, which equation BEST represents the relationship between velocity and time?
Answers
The line of best-fit that represents the relationship between velocity and time is:
v = 2.19t + 6.7.
How to find the equation of linear regression using a calculator?To find the equation, we need to insert the points (x,y) in the calculator.
For this problem, the points (t,v) are given as follows:
(0, 6.1), (2.1, 12.2), (5.3, 17.4), (8.2, 26.4), (10, 28.1), (12.1, 32.8).
Hence, inserting these points into a calculator, the equation is given by:
v = 2.19t + 6.7.
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In the graph above, which vertical line (V) and horizontal line (H) can be used to graph point D?
Question 5 options:
A)
V: x = –4; H: y = 4
B)
V: y = –4; H: x = –4
C)
V: y = 4; H: x = –4
D)
V: x = 4; H: y = 4
Answers
Answer: A. V: x = –4; H: y = 4
Step-by-step explanation:
Which of the following scatter plots does not have a zero correlation?
Answers
Plot the axis of symmetry and the point where the maximum value occurs for this function: h(x) = -(x 2)2 8.
Answers
See attachment for the axis of symmetry and maximum point.
What is a function?A function from a set X to a set Y allocates exactly one element of Y to each element of X. The set X is known as the function's domain, while the set Y is known as the function's codomain. Originally, functions were the idealization of how a variable quantity depends on another quantity.To plot the axis of symmetry:
The given function is: [tex]h(x) = -(x+2)^{2} +8[/tex]This function is in the form: [tex]g(x) = a(x-h)^{2} +k[/tex]Where the axis of symmetry is given by, x = h.y comparison, we have -h=2.This implies h=-2Therefore the axis of symmetry is x = -2.
Therefore, the maximum value occurs at the vertex, given by (h,k)=(-2,8).
So, see attachment for the axis of symmetry and maximum point.
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PLS HELP LOTs OF POINTS!!!!What is the difference of….
Answers
[tex]\frac{-2x^{2} +25 }{(x-2) (x-5)} ,x\neq 2,x\neq 5[/tex] is the difference.
What is an expression?
⇒ An expression is a combination of numbers, variables, and functions (such as addition, subtraction, multiplication or division, etc.)
Calculation :
⇒ [tex]\frac{3x^{2} }{(x^{2} -7x+10)}- \frac{5x} {x-2}[/tex]
⇒ [tex]\frac{3x^{2} }{(x-2)(x-5)}- \frac{5x} {x-2}[/tex]
⇒1/(x-2) [(3x²-5x{x-5})/(x-5)]
⇒1/(x-2) [(3x²-5x²+25x)/(x-5)]
⇒1/(x-2) [ (-2x²+25x)/(x-5)]
⇒[tex]\frac{-2x^{2} +25x }{(x-2)(x-5)}[/tex]
at x=2 and x=5 the denominator becomes zero If the denominator of a fraction is zero, the expression is not a legal fraction because its overall value is undefined.
⇒ [tex]\frac{-2x^{2} +25 }{(x-2) (x-5)} ,x\neq 2,x\neq 5[/tex] is the difference
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A boat takes 10 hours to sail a distance of 100 nautical miles with the current.
Against the current, it takes the boat 25 hours to sail the same distance. Find
the rate of the current.
Answers
The rate of the current is 6 mile/hour.
What does a rate mean ?In this context, the rate is tantamount to speed o velocity in a linear motion. The S.I unit will be mile per hour.
Given that a boat takes 10 hours to sail a distance of 100 nautical miles with the current. The rate at which the boat move will be
The rate R1 = 100/10
R1 = 10 mile/hour
And when it moves against the current, it takes the boat 25 hours to sail the same distance. The rate at which the boat move will be
The rate R2 = 100/25
R2 = 4 mile/hour
The rate of the current R will be the difference between the two calculated rate. That is,
R = R1 - R2
R = 10 - 4
R = 6 mile/hour
Therefore, the rate of the current is 6 mile/hour.
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Quick algebra 1 question for 10 points!
Only answer if you know the answer, quick shout-out to tariqareesha2 and MrBrainly, tysm for the help!
Answers
[tex]y = 2x {}^{2} - 4x - 16 \\ \delta = b {}^{2} - 4ac \\ \delta = ( - 4) {}^{2} - 4(2)( - 16) \\ \delta = 16 + 128 \\ \delta = 144 > 0 [/tex]
[tex]x = \frac{ - b + \sqrt{ \delta} }{2a} = \frac{4 + 12}{2 \times 2} = \frac{16}{4} = 4[/tex]
[tex]x = \frac{ - b - \sqrt{ \delta} }{2a} = \frac{4 - 12}{2 \times 2} \frac{ - 8}{4} = - 2[/tex]
[tex]x = 4 \: \: \: \: \: or \: \: \: \: x = - 2 \\ (x - 4) = 0 \: \: \: \: \: or \: \: \: \: \: (x + 2) = 0[/tex]
[tex]f(x) = \alpha (x - 4)(x + 2) \\ f(x) = \alpha x { }^{2} + 2 \alpha x - 4 \alpha x - 8 \alpha \\ f(x) = \alpha x {}^{2} - 2 \alpha x - 8 \alpha \\ by \: comparison \\ \alpha = 2[/tex]Factors are:1) 22) x - 43) x + 2P= ().()
Q=(),()
Please help thanks so much
Answers
The coordinates for P and Q are as follows,
P = (a, a)
Q = (0, a)
Finding the Missing Coordinates:
Triangle OPQ is an isosceles triangle, hence two of its legs are equal.
Since the coordinates of the end point of the leg OQ lies on the y-axis, and OP is parallel to x-axis, OQ ⊥ QP ............ (1)
Also, it indicates that the x- coordinate of point Q is 0.
⇒ The coordinates of point Q are (0, a)
From (1), we can infer that,
OP = OQ [∵ OP is the hypotenuse]
⇒ The distance of point P from x-axis = a
The distance of point P from y-axis =a
Hence, the coordinates of point P are given as (a, a).
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Finding the area of a regular polygon
Answers
360° ÷ 10 ÷ 2 = 18°
So the length of the decagon side is:
10 × tan18° × 2 = 20 × tan18°
The area is: ½ × 20 × tan18° × 10 × 10 = 1000 × tan18°
≈ 324.9
.: 324.9 is the final answer.
I hope this helps.
Select the correct answer. emily wants to find the number that appears in the middle of a set of 25 numbers arranged in ascending order, in a spreadsheet. which statistical function will help her do so? a. mode b. rank c. median d. average
Answers
The correct answer is option (C) median.
The median will help Emily to find the number that appears in the middle of the 25 numbers that are arranged in ascending order.
What is the mean, median and mode?The mean, median, and mode are the three most commonly used measures of central tendency for populations that do not have much data, that is, they do not need to be grouped.
The mean, also known as average, is the value obtained by dividing the sum of a cluster of numbers by the number of them.
When arranging the numbers from least to largest, the median sits exactly in the middle of the values that are above. The median is a set that is a value that is in the middle of the other values.
The number that appears most frequently in a set of numbers is called the mode.
So, The median will help Emily to find the number that appears in the middle of the 25 numbers that are arranged in ascending order.
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Ask your teacher find the limit. use l'hospital's rule where appropriate. if there is a more elementary method, consider using it. lim x→1 [ln(x5 − 1) − ln(x3 − 1)]
Answers
Answer:
ln(5/3)
Step-by-step explanation:
The desired limit represents the logarithm of an indeterminate form, so L'Hopital's rule could be applied. However, the logarithm can be simplified to a form that is not indeterminate.
LimitWe can cancel factors of (x-1), which are what make the expression indeterminate at x=1. Then the limit can be evaluated directly by substituting x=1.
[tex]\diplaystyle \lim\limits_{x\to1}{(\ln(x^5-1)-\ln(x^3-1))}=\lim\limits_{x\to1}\ln{\left(\dfrac{x^5-1}{x^3-1}\right)}\\\\=\lim\limits_{x\to1}\ln\left(\dfrac{x^4+x^3+x^2+x+1}{x^2+x+1}\right)=\ln{\dfrac{5}{3}}[/tex]
The following are the distances (in miles) to the nearest airport for 11 families. 9, 11, 11, 16, 16, 24, 28, 30, 34, 42, 45 Notice that the numbers are ordered from least to greatest. Give the five-number summary and the interquartile range for the data set.
Answers
Here is the five-number summary, range and interquartile range:
Minimum: 9
Lower quartile: 11
Median: 24
Upper quartile: 34
Maximum: 45
Interquartile range: 23
What is the five-number summary?The minimum number is the smallest number in the data. The minimum number is 9. The maximum number is the biggest number in the dataset. The maximum number is 45.
The first quartile, third quartile and the interquartile range are used to measure dispersion.
The first quartile : 1/4(n + 1)
1/4 x (12) = 3rd term = 11
The third quartile : 3/4 x (n + 1)
3/4 x (12) = 9th term = 34
Interquartile range = third quartile - first quartile
34 - 11 = 23
Median can be described as the number that is at the center of the dataset when the number is arranged in either ascending or descending order.
Median = 25
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The following two points are on a line: (2,3), (-2,5). What is the slope of the line?
Answers
Answer:
D
Step-by-step explanation:
slope = rise / run
slope = (5 - 3) / (-2 - 2)
slope = 2 / -4
slope = -2 / 4
slope = -1/2
triangle ABC is reflected across the y-axis and then dilated by a factor of 1/2 centered at the origin. which statement correctly describes the resulting image
Answers
Answer:
Step-by-step explanation:
The reflection preserves the side lengths and angles of triangle ABC. The dilation preserves angles but not side lengths.
what is the measure of an angle if it is 660 less than 6 times its own supplement
Answers
Answer:
60
Step-by-step explanation:
Since this angle is unknown, let's just represent it with the variable "x". So the supplement angle of "x" is essentially, the value of the angle that we need to add to "x" to get 180. In other words let's just say that the supplement angle is "y". This means that: [tex]x+y=180[/tex]. If we subtract x from both sides we can represent "y" or the supplement angle as: [tex](180-x)[/tex].
Since it's 660 less than 6 times it's own supplement let's first multiply the supplement by 6
[tex]6(180-x) = 1,080-6x[/tex]
Now let's subtract 660 from it, since it's 660 less
[tex](1,080 - 6x) - (660) = 420 - 6x[/tex]
This value should be equal to the angle, which is represented as "x". So let's set it equal to x
[tex]420-6x=x[/tex]
Add 6x to both sides
[tex]420=7x[/tex]
Divide both sides by 7
[tex]60 = x[/tex]
for f(x)=7x and g(x)=x+1, find the following functions. a.(fog)(x); b.(gof)(x); c.(fog)(4); d.(gof)(4)
Answers
Answer:
[tex]a.(fog)(x) = 7x + 7 \\ b.(gof)(x) = 7x + 1 \\ c.(fog)(4) = 35 \\ d.(gof)(4) = 29[/tex]
Step-by-step explanation:
Greetings !
a. (fog)(x)= f[g(x)] = 7(x+1)
(fog)(x)= 7x+7b. (gof)(x) = g[f(x)] =7x+1
c. (fog)(4)=7(4)+7=28+7=35
d. (gof)(4)= 7(4)+1=28+1=29
(fog)(x)
f(g(x))f(x+1)7x+7(gof)(x)
g(f(x))g(7x)7x+1(fog)(4)
7(4)+735(gof)(4)
7(4)+129Which function has a domain of x>5 and a range of y≤3?
Oy=√x-5+3
Oy=√x+5-3
O y=-√x-5+3
O y = -√x+5-3
Answers
The correct option is the third one.
y = -√(x - 5) + 3
Which function has a domain of x>5 and a range of y≤3?Remember that a square root can only be evaluated in values equal or larger than zero.
So, if we want the domain to be x > 5, then we must have:
√(x - 5)
Now we also want the range to be equal or smaller than 3, then we should have a constant term equal to 3, and a negative coefficient before the square root, then we get:
y = -√(x - 5) + 3
So the correct option is the third one.
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Can you help me solve this, please?
Answers
Answer:
Step-by-step explanation:
Using Euler's formula, how many
edges does a polyhedron with 9
faces and 14 vertices have?
[?] edges
Euler's Formula: F+ V=E+2
Answers
Answer:
Euler's Formula = F+V=E+2
F=9
V=14
So, 9+14=E+2
23=E+2
23-2=E
21=E
Hence, E (edges) = 21
Step-by-step explanation:
Solve:
4(2 + a) = 24
A =
Answers
Answer:
a=4Step-by-step explanation:
Simplify both sides of the equation:
4 (2 + a) = 24
( 4 )( 2 ) + ( 4 )( a ) = 24 (Distribute)
8 + 4a = 24
4a + 8 = 24
subtract 8 from both sides:
4a + 8 − 8 = 24 − 8
4a = 16
Divide both sides by 4:
4 a/4 = 16/4
a = 4
Multiple bracket out first:
4 x 2 =8
4 x a = 4a
8 +4a = 24
-8
4a. = 16
÷4
a = 4
Hope this helps!
The figure below is made of 222 rectangular prisms.
What is the volume of this figure?
A shape made up of two rectangular prisms. The first rectangular prism has a base that measures 9 inches length by 6 inches width, and has a height of 3 inches. The second rectangular prism sits behind the first rectangular prism. It has a base that measures 10 inches length by 7 inches width and has a height of 3 inches.
please help its a khan question and i have a timer :'D
Answers
Answer:
372 in^3.
Step-by-step explanation:
The volume of the first prism = 9*6*3
= 162 in^3.
Volume of second prism
= 10*7*3
= 210 in^3.
Total vol = 162 + 210
= 372 in^3.
The required volume of the composite prism is 372 cubic inches,
Volume is defined as the mass of the object per unit density while for geometry it is calculated as profile area multiplied by the length at which that profile is extruded.
here,
To determine the volume of the composite prism,
As we can see there is two rectangular prisms,
Calculate the volume of two individual prisms and add their volume to the composite volume of the figure.
The volume of the first prism
= lenght × width × height
= 9 × 6 ×3 = 162 in³
The volume of the second prism
= lenght × width × height
= 10 × 7 ×3 = 210 in³
The total volume of the composite figure = 162 + 210 = 372 in³.
Thus, the required volume of the composite prism is 372 cubic inches,
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grade 9 math
useing frist diff is this a linear relation yes or no show your work
Answers
Answer:
not linear since all first differences are not equal
Step-by-step explanation:
To find the first differences, subtract each y value from the next y value.
Use only y values.
here are the 4 first differences you need to calculate.
1 - 0 = 1
4 - 1 = 3
9 - 4 = 5
16 - 9 = 7
Now you place them in the appropriate column in the table.
x y first difference
0 0 1
1 1 3
2 4 5
3 9 7
4 16
If the first differences were all equal, the function would be a linear function.
In this case, the first differences are all different, 1, 3, 5, 7, so the function is not linear.
Cross-multiplication is helpful in: a. quadratic equations c. linear equations b. solving proportions d. word problems please select the best answer from the choices provided a b c d
Answers
Correct option is B)
Cross-multiplication is helpful in Solving proportions.
What is Solving Proportions?Solving proportions is simply a matter of stating the ratios as fractions, setting the two fractions equal to each other, cross-multiplying and solving the resulting equation.
What are the 2 methods for solving proportions?Method I: Draw a double-sided number line, label the parts, set up a proportion and solve.
Method II: Using any method, calculate unit rate and then calculate how many pounds you can get for $30. Method III: Graph a point to represent the original ratio.
What is the rule for solving proportions?The product of the means is equal to the product of the extremes.
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I understand the the question you are looking for is :
Cross-multiplication is helpful in:
a. quadratic equations
b. solving proportions
c. linear equations
d. word problems
please select the best answer from the choices provided a b c d
