The distance between two opposite corners of the floor is 15.
What is the Diagonal of a Rectangle?
A line segment that connects any two of a rectangle's non-adjacent corners is said to be it's diagonal.
The formula for calculating a rectangle's diagonal length (d) is
[tex]d = \sqrt{l^{2} + w^{2} }[/tex]
where,l = length of the rectangle
w = width of the rectangle
Given, the length of floor (l) = 9 meters
width of the floor (w) = 12 meters
Then, diagonal, [tex]d = \sqrt{l^{2} + w^{2} }[/tex]
or, [tex]d = \sqrt{9^{2} + 12^{2} }[/tex]
or, [tex]d = \sqrt{81 + 144 } = \sqrt{225} = 15[/tex]
Hence, the distance between two opposite corners is 15.
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Which pair of triangles is congruent by SAS?.
The two triangles called congruent if two sides the associated angle in one triangle is congruent with two sides and the contained angle in the other triangle.
Explain the Side-Angle-Side (SAS) congruency?According to the Side-Angle-Side theorem of congruency, two sides and the angle they produce are congruent if they are equivalent to two sides as well as the angle of another triangle.
The Side-Angle-Side rule is used to demonstrate the congruency of a particular collection of triangles. According to the SAS rule, triangles are congruent if their two sides and that included angles are equivalent to those of another triangle's two sides and included angle.Thus, two triangles are termed to be comparable if their two sides are in the same ratio as the two sides of some other triangle and their two sides' angles inscribed in both triangles are equal.
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5 Mr. Roberts has 12
papayas,
23 star fruits and 15
mangos. What is the ratio of
mangos to the total number of
pieces of fruit ?
Answer:
3:10 ratio of mangos to rest of the fruits or 15:50 unsimplified
Step-by-step explanation:
There are 50 fruits in total with 15 of them being mangos. Simplify this (divide by both numbers by 5) to get 3:10
The old film-style cameras created photos that were best printed at 3.5 inches by 5 inches. Today's new digital cameras create photos that are best printed at 4 inches by 6 inches. Neither size picture will scale perfectly to fit in an 11-inch by 14-inch frame. Which type of camera will you minimize the loss of the edges of your picture?
The new digital camera that creates photos that are best printed at 4 inches by 6 inches will minimize.
What is Ratio?The ratio is defined as a relationship between two quantities, it is expressed as one divided by the other.
Since the aspect ratio of 4:6 is closer to that of an 11-inch by 14-inch frame (which is approximately 1:1.5) than the aspect ratio of 3.5:5 (which is approximately 7:10).
By minimizing the difference in aspect ratio between the photo and the frame, you will minimize the loss of the edges of the picture when trying to fit it into the frame.
The new digital camera that creates photos that are best printed at 4 inches by 6 inches will minimize the loss of the edges of the picture when trying to fit it into an 11-inch by 14-inch frame.
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a model of a car is 1 feet wide and 3 feet long. if the actual car is 15 feet long, what is the width of the actual car?
Answer:
Step-by-step explanation:
width:length =1:3
width:15=1:3
width =5
The width of the actual car is 45 feet.
Given that,
A automobile model is 3 feet long and 1 foot wide. Considering that the automobile is 15 feet long
To find : The width of the actual car
Model Car's Width (W) = 1 foot
Model Car's Length (L) = 3 feet
Actual Car's Length (l) = 15 feet
Actual Car's Width (w) = x feet
To solve,
We know that,
Product of Means = Product of Extremes which means ,
1 : 3 :: 15 : x
1 * x = 15 *3
x = 45.
Therefore, the Actual Car's Width (w) is 45 feet.
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Find the cost of 25 kilogram of sugar, if it was sold at the rate of $150 for 100 grams.
Thx so much ^^
Answer:
$37,500
Step-by-step explanation:
There are 10 lots of 100g in 1kg
so $150 * 10 = $1,500 per kg
$1,500 * 25 = $37,500
You catch 3 fish that weigh a total of 12.05 pounds. About how much does each fish weigh?
3 pounds
2 pounds
6 pounds
4 pounds
Answer:
4 pounds
Step-by-step explanation:
12/3=4 remember it says about!
Identify the solution set of
6 In e=e^ln 2x
O {2}
O {3}
O {6}
The solution set of 6 ㏑ e = e ^ ㏑ 2x is 3
What is relation between Exponents and logarithms ?
Exponents and logarithms are inverse functions, you can use exponents to "undo" logarithms and use logarithms to "undo" logarithms. Exponents specify the number of times you must multiply a value, while logarithms specify which exponent to apply to obtain a certain value.
The given expression is,
6 ㏑ e = e ^ ㏑ 2x
we know, ㏑ (e) = 1 and e ^ ㏑(x) = x
Put these values,
6 * 1 = 2x
Now, find x
6 = 2x
x = 3
Hence, the solution set of 6 ㏑ (e) = e ^ ㏑ (2x) is 3
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What does 100% increase mean???
Answer:
double whatever you got
100 percent increase of 2 is 4
Step-by-step explanation:
hopes this helps please mark brainliest
Answer:
It means that whatever you have just doubled.
Step-by-step explanation:
If I have a total of 100 widgets, that is 100%. If I have a 100% increase of that value, that means I now have 200 widgets.
7) Seventy-four students have signed up to go on a field trip. There is room for no more than
120 students. How many more students can go on the field trip?
Answer:
46 more people can go on the field trip
Six customers are buying gasoline at Miguel's Gasoline Station. The number of gallons bought and the total cost of their purchases are plotted on the graph below.
What is the price per gallon at Miguel's Gasoline Station?
Responses
$2.50
Based on the line on the graph, the price per gallon at Miguel's Gasoline Station is equal to: B. $2.50
How to calculate the price per gallon?In order to calculate the price per gallon at Miguel's Gasoline Station, we would have to determine the slope of the line representing the number of gallons bought and the total cost of their purchases are plotted on the graph below (see attachment).
Mathematically, the slope of any straight line can be calculated by using this formula;
Slope, m = (Change in y-axis, Δy)/(Change in x-axis, Δx)
Slope, m = (y₂ - y₁)/(x₂ - x₁)
By critically observing the graph (see attachment), we can logically deduce that the line passes through the following points:
Points (x, y) = (4, 10)Points (x, y) = (8, 20)Substituting the given parameters into the formula, we have;
Slope, m = (20 - 10)/(8 - 4)
Slope, m = 10/4
Slope, m = 2.5
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Please help, I'm having trouble understanding.
Answer:
y = x-5
Step-by-step explanation:
-x + y = - 5
y = - 5 + x
y = x - 5
M. Carey wrote the equation 3x-7-2/3 (9x-6)=15 on the board. What i the olution to the equation? how your work
The solution of equation written by M. Carey is -6.
We will use PEMDAS rule to solve the equation. So, firstly solving the bracket by multiplying it with 2/3.
3x - 7 - 6x + 12/3 = 15
Simplifying this equation
3x - 7 - 6x + 4 = 15
Rewriting the equation with identical variables on each side
3x - 6x = 15 + 7 - 4
Solving the part of equation on Right Hand Side
3x - 6x = 18
Performing subtraction on Left Hand Side of the equation
-3x = 18
Shifting 3 to Right Hand Side of the equation
x = 18/-3
Performing division on Right Hand Side of the equation
x = -6
Thus, the solution of equation is -6.
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Hello! Can anybody help me with the steps to this problem? I was doing a correction form, but don't know how to get to the answer...
-0.3n ≤ 5.4 n ≥ -18
The solution set for both inequalities overlap and are same.
What is the general equation of a Straight line inequality?The general equation of a straight line inequality is -
[y] < [m]x + [c]
[y] > [m]x + [c]
[y] [m]x + [c]
[y] < [m]x + [c]
where -
[m] → is slope of line which tells the unit rate of change of [y] with respect to [x].
[c] → is the y - intercept i.e. the point where the graph cuts the [y] axis.
We have the following inequalities -
-0.3n ≤ 5.4
n ≥ -18
Plot the graph of both inequalities. The common region would be the solution set. Refer to the graph below. The solution region of both inequalities overlap with each other. Hence, the solution set for both inequalities is same.
Therefore, the solution set for both inequalities overlap and are same.
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Write the point-slope form of the line that passes through (1, -5) and is parallel to a line with a slope of 1. Include all of your work in your final answer. Type your answer in the box provided to submit your solution.
To write the point-slope form of the line that passes through (1, -5) and is parallel to a line with a slope of 1.
A perpendicular line will have a negative reciprocal slope. All that means is " flip " the slope and change the sign. So if we have a slope of 1 or 1/1. our perpendicular line needs a slope of -1.
y - y1 = m(x - x1)
slope(m) = -1
(1,-5)...x1 = 1 and y1 = -5
now we sub...pay close attention to your signs
y - (-5) = -1(x - 1)....not done yet
y + 5 = -1(x - 1)...or it can also be written as : y + 5 = - (x - 1)
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The line y = mx + 6 passes through the point ( 1, 3). find m.
Answer:
m = - 3
Step-by-step explanation:
since the line passes through (1, 3 ) then the coordinates of the point make the equation true.
substitute x = 1, y = 3 into the equation and solve for m
3 = m + 6 ( subtract 6 from both sides )
- 3 = m
The sampling distribution of the sample mean will always have the same _________ as the original distribution.
The sampling distribution of the sample mean will always have the same Mean as the original distribution.
Sampling distribution:
Sampling distribution means a probability distribution of a statistic that is obtained through repeated sampling of a specific population.
Given,
Here we have the statement "The sampling distribution of the sample mean will always have the same _________ as the original distribution."
Now, we have to find the missing word in the statement.
We know that, the mean of the sampling distribution of the sample mean will always be the same as the mean of the original non-normal distribution. Simply said that the sample mean is equal to the population mean.
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In this figure, AB¯¯¯¯¯¯¯¯∥CD¯¯¯¯¯¯¯¯ and m∠2 = 61°.
What is m∠6?
Answer:
m∠6 = 61°
Step-by-step explanation:
Given a transversal crossing parallel lines AB and CD, you want the measure of angle 6 given that angle 2 is 61°.
Angles at a transversalWhere a transversal crosses parallel lines, corresponding angles and vertical angles are congruent. This has the effect of making all acute angles congruent, and all obtuse angles congruent.
Acute angle 6 is congruent to acute angle 2, which measures 61°. (They are "corresponding" angles.)
m∠6 = 61°
The velocity-time graph for a cycle is shown.
Velocity (m/s)
10
8
6
4
2
0
0
2
4
6
8
10
12
14
16
18
20
Time (seconds)
a) Work out the distance travelled on the cycle in the first 14 seconds.
b) Work out the acceleration in the first 4 seconds.
a) The distance travelled on the cycle in the first 14 seconds is; 96 m
b) The acceleration in the first 4 seconds is; 2 m/s²
How to Interpret the Velocity Time Graph?
The velocity time graph for a cycle is as attached.
The distance covered will be the area under the curve.
Formula for area of trapezium is;
A = (1/2)(sum of parallel sides) * height
Area for 0 to 14 sec is a trapezium formed with parallel sides as 14 and 10 while distance between them is 8 is solved as;
Area = (1/2)(14 + 10) * 8
Area = 24 * 4 = 96
Thus;
Distance covered = 96 m
Distance travelled on the cycle in the first 14 seconds is 96 m.
Therefore, the acceleration in first 4 seconds = (8 - 0)/(4 - 0)
= 8/4 = 2 m/s²
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we have a dataset of ages of 100 kids born in some neighborhood. we calculate its mean and standard deviation, we denote them by m1 and s1, respectively. 3 years later, all of those kids are still alive and included in the dataset. using the new values for their age, we calculate the mean and standard deviation of the ages, denoted by m1 and s2. which is true?
The option B is true which is m2=m1+3, s2=s1
From the given information,
The required correct answers are,
m2= m1 + 3
s2= s1
Hence,
Option b. is correct.
A standard deviation (or σ) is a proportion of how distributed the information is comparable to the mean. A low standard deviation implies information is grouped around the mean, and an elevated requirement deviation demonstrates information is more fanned out.
The standard deviation of a population or sample and the standard error of measurement (e.g., of the example mean) is very unique however related. The example implies the standard error is the standard deviation of the arrangement of implies that would be found by drawing an endless number of samples from the population and registering a mean for each sample. The mean standard error ends up equaling the population standard deviation partitioned by the square base of the example size and is assessed by utilizing the example standard deviation separated by the square foundation of the sample size.
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What are the domain and range of the function the quantity of x squared minus 4 x minus 12, all over x plus 2?.
The Domain is R i.e all real numbers and the range is [-16,∞).
What is the domain and range of function?
A function's domain and range are its components. A function's range is its potential output; its domain is the set of all conceivable input values. Domain, Function, and Range. If a function f: A B exists that maps every element in A to an element in B, then A is the domain and B is the co-domain. The image of an element 'a' under a relation R is provided by 'b,' where (a,b) R. The set of photographs makes up the function's range.
f(x)=x²-4x-12
For Domain it can take all the real numbers as there is no term in the denominator. so Domain is "R"
Range will be f(x) is minimum at x = 2 i.e. f(x=2) = -16
f(x) maximum value is +infinity.
So Range [-16,∞)
Hence the Domain is R and Range is [-16,∞).
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HELPPP MATH 30 pointsss
Answer:
-11
Step-by-step explanation:
3(-2)-5
-6-5
-11
h=-11
In this figure, AB || CDand m/2 = 60°.
What is m/6?
Enter your answer in the box.
Answer:
∴ m∠6 = 60°
Step-by-step explanation:
Since AB is parallel to CD,
m∠2 = m∠6 = 60°
A gallon of water contain 128 fluid ounce. A rain barrel can hold 6,400 ounce of rainwater. Etimate how many gallon of water can the barrel hold?
If a gallon of water contain 128 fluid ounce and a rain barrel can hold 6,400 ounce of rainwater, then the number of gallons of water that can the barrel hold is 50 gallons
A gallon of water in ounce = 128 ounce
Number of ounce of water that rain barrel can hold = 6400 ounce
To find the number of gallon of water we have to apply division
number of gallons of water that can the barrel hold = Number of ounce of water that rain barrel can hold / A gallon of water in ounce
= 6400 / 128
= 50 gallons
Hence, if a gallon of water contain 128 fluid ounce and a rain barrel can hold 6,400 ounce of rainwater, then the number of gallons of water that can the barrel hold is 50 gallons
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Which of these equations have no solution? Check all that apply.
2(x+2)+2 =2(x+3)+1
2x + 3(x+5) = 5(x-3)
4(x + 3) = x + 12
4-(2x+5)= 1/2 (-4x-2)
5(x+4) - x = 4(x+5)-1
someone please help!
The answer to the question is 5.
The calculation can be calculated as follows :
3√125
= 3√(5 x 5 x 5)
= 5
We can write 125 as 5 x 5 x 5.
Or 5 power 3.
The value of the cube root of 125 is 5.
It is the real solution of the equation x3 = 125.
The number 125 is called a perfect cube number since its cube root value is a whole number.
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Use the properties of operations to multiply the expressions. 2x(5 - 0.4x)
The multiplied form of the Algebraic expression is 10x -0.8[tex]x^{2}[/tex]
What is an Algebraic expression?An algebraic expression is a mathematical statement that contains a combination of numbers, symbols, variables and mathematical operators.
These expressions may be linear, quadratic or polynomials and the numbers in front of each term is called coefficient while the symbols or letters are called variable
2x( 5 - 0.4x)
we multiply each term in the bracket by 2x
2x x 5 - 2x x 0.4x = 10x - 0.8[tex]x^{2}[/tex]
In conclusion, 2x(5 - 0.4x) reduces to 10x - 0.8[tex]x^{2}[/tex]
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I need some help here
They are congruent by SAS as follows if I understand you correctly:
Since x is shared by both NR and AG, it must be at their intersection.
Because it lies in the middle of both, NX = XR and AX = XG.
We join point A to point N and point R to point G to complete the triangles (any 2 points define a line).
Due to the fact that there are two triangles on either side of the point X, angle AXN is perpendicular to angle RXG. Angle AXN is equal to angle RXG because the vertical (opposite) angles formed by two intersecting lines are equal.
The following is how the SAS evidence of congruency is established:
Angle RXG in triangle RXG and angle AXN in triangle AXN are congruent (vertical angles)
Triangles AX in AXN and XG in RXG are congruent (midpoint X of line AG created these).
Triangle RXG and triangle AXN's NX and XR are congruent.
By SAS, triangles are congruent. this means they have two corresponding sides that are congruent and the angle between those 2 corresponding sides is congruent also.
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Which of the following strategies is helpful when solving the following word problem?
There were 52 lbs. of vegetables from four farmers in the area that were to be delivered to the local food bank. If Mr. Greenjeans provided 7 pounds of vegetables, Mr. Cowpatrick provided 12 pounds of vegetables, and Mrs. Chickenroost provided 10 pounds of vegetables, how many pounds of vegetables did Mrs. Turkeyroast provide?
According to the information, it can be inferred that the strategy that will help us solve the problem will be "solve algebraically" (option B).
What is an algebraic operation?An algebraic operation is a term that refers to any type of arithmetic operations such as:
AdditionSubtractionMultiplicationDivisionRaising to a power of a whole numberRoot extractionBased on the above, we can infer that the best strategy to solve the problem about the vegetables that will go to the food bank is an algebraic operation because we can add the amount contributed by Mr. Greenjeans, Mr. Cowpatrick, and Mrs. Chickenroost and then subtract the total number of pounds, to find the amount that Mrs. Turkeyroast contributed as shown below:
29lbs - 52lbs = 23lbs
Note: This question is incomplete because there is some information missing. Here is the complete information:
Question:
Which of the following strategies will help you solve word problems?
a. Draw an illustration
b. Solve algebraically
C. Make a table
d. all of the above
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a total of $689 tickets were so far School play they were either adult tickets or student tickets there were 61 fewer students tickets so then adult tickets how many adult tickets were sold
Answer:
375 adult tickets314 student ticketsStep-by-step explanation:
You want to know the number of adult ticket sold if there were 61 fewer student tickets sold and the total number sold was 689.
SetupLet a = the number of adult tickets sold. Then a-61 is the number of student tickets sold, and the total is ...
a + (a -61) = 689
SolutionSimplifying, we get
2a -61 = 689
2a = 750 . . . . . . add 61
a = 375 . . . . . . . divide by 2
The number of adult tickets sold was 375.
__
Additional comment
The number of student tickets is 375-61 = 314.
What is the value of f(x1) when f(x) = 2x + 2?
Enter your answer in the box:
F(-1) = [____]
The value of f(-1) when f(x) is defined as given in the question is 0.
What is the substitution method?
One method for solving simultaneously linear equations using algebra is the substitution method. It involves changing the value of any one of the variables in one equation & applying it to another one.
Given, f(x) = 2x + 2 ......... (i)
Now, we need to find the value of f(-1), by substituting the value of x = -1 in above equation (i), then
f(-1) = 2*(-1) + 2 = -2+2 = 0
Hence, the required answer of f(-1) is 0.
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