The dimensions x and x+50 are 150 ft by 200 ft. When two polygonal or polyhedral vertices are not on the same edge, a diagonal is a line segment connecting them.
How to calculate the dimensions of the parking if it measures 250 ft diagonally?When two polygonal or polyhedral vertices are not on the same edge, a diagonal is a line segment connecting them. Any sloping line is known as a diagonal informally.
If you draw a diagonal, you have 2 right triangles, each with leg lengths of x and x + 50.
The diagonal is the hypotenuse, h = 250
Using Pythagorean theorem:
X² + (x+50)² = 250²
x² + x²+ 100x + 2500 = 62500
2x²+ 100x - 60000 = 0
All are even, so factor out a 2:
x² + 50x - 30000 = 0
From quadratic equation: x = [-50±√(50²-4(1)(-30000))]/(2(1))
x = (-50 ± 350)/2
We can disregard the negative so
x = (-50 + 350)/2 = 300/2 = 150 ft
The dimensions x and x+50 are 150 ft by 200 ft
The complete question is: A rectangular parking lot is 50ft longer than it is wide. Determine the dimensions of the parking lot if the diagonal distance from corner to corner of the lot is 250ft.
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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 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.
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 me out! I don't get it.
Answer:
The perpendicular slope is the negative reciprocal of the original slope:
For example: the perpendicular slope for y/x is -x/y
In this case, we want the slope from x +4y = 28
x +4y = 28
4y = 28 - x
y = 7 -x/4
so the answer is: 4/x
Find the area of a circle with diameter 14 in.
Use the value 3.14 for , and do not round your answer.
Be sure to include the correct unit in your answer.
The area of the circle is 153.86 inches square.
What is a circle?
Every point in a plane that is at a specific distance from the centre, or the circle's centre, forms a shape. To put it another way, it is the curve that a moving point in a plane draws to keep a constant distance from another point.
Main Body:
given:
diameter = 14 in
[tex]\pi[/tex] = 3.14
radius = diameter/ 2
= 14/2
r = 7 in
Area of circle is given by = [tex]\pi r^{2}[/tex]
Inserting the value of [tex]\pi[/tex] and r ,
area of circle = 3.14* [tex]7^{2}[/tex]
HENCE, Area of circle = 153.86 inches square
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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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2(x + 4) (x - 2) = 0
Answer:
x=-4 or x=2
Step-by-step explanation:
2(x+4)(x-2)=0
Subtract 4 from both sides:
(x+4)=0
Simplify:
x=-4
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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A certain data set has a line-of-best-fit that travels through these two points: (6, 275) and (8, 450) write the equation for that line-of-best-fit.
The equation of the line is - 175 x + 2 y = - 500
From the question, we have
Point 1 :
x-coordinate, x1 = 6
y-coordinate, y1 = 275
Point 2 :
x-coordinate, x2 = 8
y-coordinate, y2 = 450
We know that,
y-275 = (275-450)/(6-8)*(x-6)
y-275 = 175/2*(x-6)
- 175 x + 2 y = - 500
Slope of a Line :
A line's slope in mathematics is defined as the ratio of the change in the y coordinate to the change in the x coordinate.
Both the net change in the y-coordinate and the net change in the x-coordinate are denoted by y and x, respectively.
As a result, m = change in y/change in x = y/x is the formula for the change in y-coordinate with respect to the change in x-coordinate.
where "m" represents a line's slope.
The line with m as the slope, m and c as the y-intercept is the graph of the linear equation y = mx + c. The values of m and c are real integers in the slope-intercept form of the linear equation.
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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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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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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°
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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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
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
each of cats has fleas. if two cats (and their fleas) are removed, and three fleas are removed from each remaining cat, the total number of fleas remaining would be half the original total number of fleas. what is the value of ?
1 is the value of cat in linear equation.
What is an explanation of a linear equation?
A linear equation is a first-order (linear) term plus a constant in the algebraic form y=mx+b, where m is the slope and b is the y-intercept. Sometimes, the aforementioned is referred to as a "linear equation of two variables," where x and y are the variables.number of cats = n
number of fleas per cat = 2n
total number of fleas = (number of fleas per cat) * (number of cats) = 2n * n = 2n2
If we take the total number of fleas, subtract the fleas of two cats, then subtract 3 for every remaining cat, we get half the total number of fleas.
(total number of fleas) - 2(number of fleas per cat) - 3(n - 2) = (total number of fleas)/2
2n2 - 2(2n) - 3(n - 2) = (2n2)/2
2n2 - 4n - 3n + 6 = n2
Subtract n2 from both sides and combine like terms.
n2 - 7n + 6 = 0
Factor the left side
(n - 6)(n - 1) = 0
n = 6 or n = 1
n must be 6 because we can't remove 2 cats if there is only 1 cat to begin with.
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The complete question is -
Each of n cats has 2n fleas. If two cats (and their fleas) are removed, and three fleas are removed from each remaining cat, the total number of fleas remaining would be half the original total number of fleas. What is the value of n?
What is 5.37 divided by 3 equals explain your answer solve the question by using the paper.
The value of 5.37 divided by 3 will be 1.79.
How to do the division?The necessary steps include:
Take the first digit of the dividend from the left. Then divide it by the divisor and write the answer on top as the quotient.Subtract the result from the digit and write the difference below.It should be noted that it's important to bring down the next digit of the dividend. For long division problems, always follow the divide, multiply, subtract, and drop down process until each digit in the dividend has been divided.
Therefore, 5.37 ÷ 3 = 1.79.
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Write a recursive definition for sequence starting with 12, 6?
The recursive formula for sequence starting with 12, 6 is, [tex]a_1=a_0-\frac{a_0}{2}[/tex].
What is recursive formula?
Any term of a series can be defined by its preceding term in a recursive formula (s).
For instance: An arithmetic series has the recursive formula [tex]a=a_n_-_1+d[/tex] . [tex]a_n=a_n_-_1r[/tex] is the recursive formula for a geometric sequence.
Given two terms are, 12, 6.
The first term is 12, so [tex]a_0=12[/tex].
The second term is 6, which is half of the first term.
So, [tex]a_1=a_0-\frac{a_0}{2}[/tex]
Therefore, the recursive formula for the sequence starting with 12, 6 is
[tex]a_1=a_0-\frac{a_0}{2}[/tex].
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tonnie divides a 2 liter bottle of iced tea among 8 people. how many millimeters does each person get?
please help asap tysm <3
Determine the unknown angle measures?
Answer:
Step-by-step explanation:
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
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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47°
131° 107°
X
X =
[?]°
Enter the number that goes in the green box.
-5|3+4k|=-115
Need the answer!!!!!
Answer:
k = {- 6.5; 5}=====================================
Solution in steps:
-5 |3 + 4k| = -115 Given|3 + 4k| = - 115/ - 5 Divide both sides by - 5|3 + 4k| = 23 Open absolute value 3 + 4k = 23 and 3 + 4k = - 23 Two scenarios, subtract 3 from both sides4k = 20 and 4k = - 26 Simplifyk = 20/4 and k = -26/4 Divide by 4k = 5 and k = - 6.5 AnswerAnswer:
k = 5 (or) k = -6.5
Step-by-step explanation:
Given equation,
→ -5|3 + 4k| = -115
Then the value of k will be,
→ -5|3 + 4k| = -115
→ |3 + 4k| = -115/-5
→ 3 + 4k = 23 || → 3 + 4k = -23
→ 4k = 23 - 3 || → 4k = -23 - 3
→ k = 20/4 || → k = -26/4
→ [ k = 5 ] || → [ k = -6.5 ]
Hence, values are 5 and -6.5.
Buying a car simple interest activity. Can you guys help me?
Answer:
BANK A
I=5700.825
T.P=25190.83
BANK B
I=3274.32
P=22764.32
Two cell phone plans offer differing text packages. The two plans are outlined below:
Plan A: $5.00 per month charge along with a charge of $0.03 per text.
Plan B: No per month charge,but a charge of 0.10 per text. Is there a certain number of texts,when the two plans cost the same amount? Determine your answer by setting up a system of equations that model the two plans.
The system of equation for the given condition is: 5+0.03x = 0.10x, where x is the number of texts.
There is no certain number of texts for which two plans are equal.
Let the number of texts for which two plans amount to same number be = x
Plan A: $5.00 per month charge along with a charge of $0.03 per text.
So, Plan A: 5+0.03x
Plan B: No per month charge but a charge of 0.10 per text.
Plan B: 0.10x
Since the plans amounted to same for x texts. So, the suitable system of equation is,
5+0.03x = 0.10x
Solving the equation we get,
0.10x - 0.03x = 5
0.07x = 5
x = 5/0.07 = 71.42 (approximately)
Since the number of texts cannot be decimal number so there is no such number of texts for which plans are equal.
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Help!
im very confused.
Answer:
458.7 cm
Step-by-step explanation:
to find circumference we multiply diameter by pi
146(pi)
458.673
And we round to 1 d.p.
458.7
Hopes this helps please mark brainliest
June was given 5/7 of the fruit basket .what fraction of the fruit basket is left?
Answer:
[tex]\frac{2}{7}[/tex]
Step-by-step explanation:
Another name for 1 is [tex]\frac{7}{7}[/tex]
[tex]\frac{7}{7}[/tex] - [tex]\frac{5}{7}[/tex] = [tex]\frac{2}{7}[/tex]
I NEED HELP Asap thank uu
Answer: 422.39
Step-by-step explanation:
To find the shaded region (I'm assuming it's the area inside the circle but outside the rectangle), subtract the area of the rectangle from the area of the circle.
The formula for circle area: πr^2
r is the radius, and it is given that r = 12, so the area of the circle is:
π * 12^2 ---> 144π is the area of the circle
Next, find the area of the rectangle: 3 * 10 = 30
Finally, find subtract the area of the rectangle from the area of the circle to find the shaded region:
144π - 30 ≈ 422.39
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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