The width of the flag is 640 ft and the length is 1040 ft
To calculate this we can take the width of the flag can be represented as "w" and the length as "l".
From the information given, we know:
l = w + 400 (because the length is 400 ft greater than the width)
2 * (w + l) = 2080 (because the perimeter is 2,080 ft)
We can substitute the first equation into the second equation to get:
2 * (w + w + 400) = 2080
2w + 800 = 2080
2w = 1280
w = 640
Therefore, the width of the flag is 640 ft and the length is 1040 ft (since l = w + 400)
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ABC has vertices A(0, 0), B(0, 4), and C(3, 0). Write the equation for the line containing the
altitude AR in standard form.
y= -4/3 x
4y-3x = 0
3y-4x=0
3x-4y=0
The equation for the altitude AR of triangle ABC will be 4y-3x=0 i.e. B.
What is a triangle?
Triangles are polygons in geometry that have three sides and three vertices. This figure is two-dimensional and has three straight sides. A triangle is a three-sided polygon. A triangle's three angles added together equals 180°. A single plane contains the triangle. The triangle is classified into six forms based on its sides and angles.
A triangle is categorized into three categories based on its sides, namely:
Scalene Triangle - Each side has a distinct length.
Isosceles Triangle - A triangle with two sides of equal length and one side of a different length.
Equilateral Triangle - A triangle has three sides that are of the same length.
A triangle is categorized into three categories based on its angles, namely:
Acute Angle Triangle - A triangle with all of its angles smaller than 90°.
Obtuse Angle Triangle - A triangle with one of its angles larger than 90°.
Triangle with a Right Angle - A triangle with one of its angles equal to 90°.
Now,
The general form of the linear line is:
y = mx + c where m is the slope and c is the y-intercept
Step 1: getting the slope:
Since AR is the altitude of ABC, therefore, AR is perpendicular on BC which means that slope of AR = -1/slope of BC
Therefore, we will need to get slope of BC:
We have point B = (0,4) and point C = (3,0)
slope of BC = (y2-y1) / (x2-x1) = (0-4) / (3-0) = -4/3
This means that:
slope of AR = m = 3/4
Step 2: getting the y-intercept:
Since point A belongs to the altitude, therefore, point A satisfies the equation of the line. So, to get the y-intercept, we will use point A to substitute in the equation of the line and solve for c as follows:
y = mx + c
y = (3/4) x + c
0 = (3/4)(0) + c
c = 0
Hence,
y = (3/4) x
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AWARDING THE MOST POINTS FOR BEST ANSWER! HELP ME ANSWER THIS FAST!!!!!!!!!!!!
The Johnson family buys furniture and appliances for a new house for $10,000. 00 with a credit card that has a 15% APR.
The Johnsons make a $325. 00 monthly payment. How many months will it take to pay off the balance? Enter your answer as a whole number, such as: 20
Total thirty-nine months will be take by Johnson family to pay off the balance, $10,000.00.
The monthly payment is the amount paid per month to pay off the principle in the time period of the loan. If your rate is r%, divide r/100 by 12 to calculate your monthly interest rate. Formula for monthly payment is, M = Pr(1+r)ⁿ/{(1+r)ⁿ - 1 }
where, P --> principle
r--> rate of interest in months
n --> number of periods (in months )
In this problem, Johnson family bought the furniture and appliances for a new house that is principle, P = $10,000
Rate of interest, R = 15%
In terms of months, R = 0.15/12
= 0.0125 per month
Monthly payment, M = $325.00
Plugging all known values in above formula we get, $325.00 = {$10,000 × 0.0125(1 + 0.0125)ⁿ}/{(1+ 0.0124)ⁿ - 1 }
=> 325 = 125(1.0125)ⁿ/{(1.0125)ⁿ - 1}
=> 325 {(1.0125)ⁿ - 1} = 125(1.0125)ⁿ
=> 325(1.0125)ⁿ - 325 = 125(1.0125)ⁿ
=> 325(1.0125)ⁿ - 125(1.0125)ⁿ = 325
=> 200 (1.0125)ⁿ = 325
=> (1.0125)ⁿ = 325/200 = 13/8 = 1.6250
Taking natural logarithm both sides
=> ln(1.0125)ⁿ = ln (1.6250)
=> n ln(1.0125) = ln (1.6250) = 0.4855
=> n×0.0124 = 0.4855
=> n = 0.4855/0.0124 = 39.153 ~ 39
Hence, required months are 39.
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What is longitude and latitude explain with diagram?.
Longitude and latitude are geographic coordinates that indicate a location on the Earth's surface. They are used to locate a specific point on a map or globe.
Longitude is the measure of a location's east-west position on the Earth's surface. It is measured in degrees east or west of the Prime Meridian, which is an imaginary line that runs from the North Pole to the South Pole through the Royal Observatory in Greenwich, England. Longitude values range from -180 degrees (West) to 180 degrees (East).
Latitude, on the other hand, is the measure of a location's north-south position on the Earth's surface. It is measured in degrees north or south of the Equator, which is an imaginary line that runs around the Earth's middle, dividing it into the Northern and Southern Hemispheres. Latitude values range from -90 degrees (South) to 90 degrees (North).
The diagram below illustrates how longitude and latitude work together to pinpoint a location on the Earth's surface. The intersection of the red line (longitude) and the blue line (latitude) represents the specific location.
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When the degree of a polynomial is 2 it is called *?.
A polynomial of degree 2 is called a quadratic equation. It is a type of equation that can be solved by using the quadratic formula, which looks like this:
where x is the unknown variable and y is the solution to the equation. The quadratic equation can be written in several different ways, but all of them involve solving for y using equations similar to the one above.
Polynomials of degree 2 are common in everyday life, and are used to solve problems such as solving for the slope or height of a line, determining the points at which two lines intersect, or finding the distance between two points.
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heelllpppp pleaseeeeeeesssss
in the figure PQ is parallel to RS the length of PQ is 2 cm; the length of RS is 6 cm; the length of QT is 4 cm what is the length of TS
The length of TS in ΔTRS using Similarity of triange is 12 cm .
What is Similarity of Triangles ?If two items have the same shape or have the same shape as their mirror images, they are said to be Similar. One can be produced from the other more accurately by evenly scaling it, perhaps with the addition of further translation, rotation, and reflection.
If the sides are in the same ratio or proportion and the angles are equal (corresponding angles), two triangles will be comparable (corresponding sides). Similar triangles may have varying individual side lengths, but they must have equal angles and the same scale factor or matching ratio of the side lengths. If two triangles resemble one another, then
Triangles with similar angle pairings have all the same angles.Triangles have proportionate sides on all matching sides.In ΔTPQ and ΔTPS
∠T is common in both triangle
PQ ║ RS
∴∠TPQ = ∠TRS (Corresponding Angles)
similarly ,
∠TQP = ∠TSR
∴ Δ TPQ ~ ΔTRS
So,
PQ/ RS = TQ/ TS
⇒ 2/ 6 = 4 / TS
⇒TS = (4*6)/2 = 12
The length of TS in ΔTRS using Similarity of triange is 12 cm .
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What is limit in maths class 11?.
The limit is normally defined as
[tex]lim _{x- > c} f(x) = L[/tex]
It is read as “the limit of f of x, as x approaches c equals L”.
In mathematics, limits are the points at which a function approaches the output for the specified input values. Calculus and mathematical analysis depend heavily on limits, which are required to determine integrals, derivatives, and continuity. It is applied during the analysis process and always focuses on the function's behaviour at a certain time. The idea of the limit of a topological net broadens the definition of the limit of a sequence and relates it to the limit and direct limit in the theory category. In general, there are two sorts of integrals: definite integrals and indefinite integrals. The upper limit and lower limit for definite integrals are correctly defined.
Limits in maths are unique real numbers. Let us consider a real-valued function “f” and the real number “c”, the limit is normally defined as
[tex]lim _{x- > c} f(x) = L[/tex]
It is read as “the limit of f of x, as x approaches c equals L”. The “lim” shows the limit, and fact that function f(x) approaches the limit L as x approaches c is described by the right arrow.
A function may get close to two distinct limits. There are two scenarios: one in which the variable approaches its limit by values larger than the limit, and the other by values smaller than the limit. The right and left-hand limits still exist even though the limit is not specified in this situation.
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please help simplify:2^2010×5^2011/10^1000
Answer:
2^1010 x 5^1011
Step-by-step explanation:
This expression can be simplified by combining the exponents of the similar bases.
2^2010 x 5^2011 / 10^1000 = (2^2010 x 5^2011) / (2^1000 x 5^1000)
= (2^1010 x 5^1011) / 10^1000
The final answer is 2^1010 x 5^1011.
Challenge A family wants to rent a car to go on vacation. Company A charges $70.50 and 17¢ per mile. Company B
charges $30.50 and 8¢ per mile. How much more does Company A charge for x miles than Company B?
CITS
For x miles, Company A charges
dollars more than Company B.
(Simplify your answer. Use integers or decimals for any numbers in the expression.)
Challenge To travel on vacation, a family wants to rent a car. Company A bills $70.50 plus 17 cents each mile. Charges from Company B are $30.50 plus 8 per mile. For every x miles that Company A charges, Company B is (39.24x)
What is mathematical equation?An equation is a mathematical statement that proves two mathematical expressions are equal in algebra, and this is how it is most commonly used. In the equation 3x + 5 = 14, for instance, the two expressions 3x + 5 and 14 are separated by the symbol "equal." The link between two expressions on either side of the sign is represented by a mathematical equation. One variable and an equal sign are typically present. For instance, 2x – 4 = 2.Before figuring out their difference for x miles, we must first determine their difference for one mile.
Difference per mile = ($70.50 + $0.14) - ($30.50 + $0.90)
= $70.64 - $31.40
= $39.24
Difference for x miles = $39.24 × x miles
= $(39.24x)
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The sum of the measures of angle P and angle Q is 90°.
. The measure of angle P is (3x + 5)°.
. The measure of angle Q is 49°.
What is the value of x in degrees?
Enter your answer to the space provided below. Enter only number answer with no unit
x=
Answer:
12
Step-by-step explanation:
3x+5+49=90
3x+54=90
3x=90-54
3x=36
3x/36/3
x=12
What is the easiest way to find equivalent expressions?.
The easiest way to determine equivalent expressions for algebraic expression is by using the factoring.
Equivalent expression : In Algebra, equivalent expressions are algebraic expressions that, although they look different, turn out to really be the same. And since they are the same, they will produce the same results when same value substitute for their variables. For example, 3(x + 2) and 3x + 6 are equivalent expressions because the value of both expressions remains the same for any value of x. When writing equivalent expressions, we must be sure that each side of the equal number corresponds to the same number. Using the factoring :
Identify the common factors in the parts of the equation.It may be necessary to divide the equation to find an equivalent expression.If the expression is, 2xy + 4x, In this case, both numbers are divisible by 2.Take out the first common number :2(xy + 2x). As y see that there is
another common factor, x. So, we
get the result as 2x(y + 2).
Thus, the required equivalent expression is determined.
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Re-write the quadratic function below in Standard Form y= -8(x-5)(x+1)
Answer:
y = -8[tex]x^{2}[/tex] + 32x + 40
Step-by-step explanation:
y= -8(x-5)(x+1)
y = (-8x + 40) (x + 1)
y = -8[tex]x^{2}[/tex] -8x + 40x + 40
y = -8[tex]x^{2}[/tex] + 32x + 40
What is derivative of log 2x?.
The derivative of log 2x is 1/x. This is obtained by applying the formula of derivative of log x.
Let y is the given function = log 2x.
Differentiating with respect to x on both sides, we have,
d/dx(y) = d/dx(log 2x)
dy/dx = 1/2x × d/dx(2x)
dy/dx = 1/2x × 2
dy/dx = 1/x
Chain rule is applied in the above solution.
Its formula is given as, d/dx [f(g(x)] = d/dx [f(g(x)] × d/dx[g(x)]
where, f(x) and g(x) are a function of function.
In the above solution, f(x) is log x and g(x) is 2x.
Thus, the derivative of log 2x is 1/x.
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What is the answer to this problem I need help please and thank you .9-z+3-2z=
Answer:
12 - 3z or 3 .9 - 3z
Step-by-step explanation:
1 - if it is just a "9" and not a "0 .9" the answer is "12-3z". You will have to isolate the expressions with the "z" (the 2z and the z). They have a "-" before them, so they are negative expressions (-2z and -z). When the letter is alone, we supose that is a whole, not a decimal, expression, so it is like "1z". After all, you will have two negative expressions, the "-1z" and the "-2z", then you will just add "-1z" and "-2x" (-1z + (-2z) = -1z -2z = -3z
Now, you will need to add "9" and "+3" (9 + (+3) = 9 + 3 = 12).
Now, you have a "-3z" and the "12", and you will add they (-3z + 12 = 12 + (-3z) = 12 - 3z).
2 - But, if it is a "0 .9" ( "0 .9" is the same of " .9" and not a "9" the answer is "3 .9 - 3z". Now it is the same as the number 1 (just do the same from the "You will have" to the "-1z -2z = -3z".
Now, you need to add "0 .9" and "+3" ( .9 + (+3) = .9 + 3 = 3 .9).
So, you have the "-3z" and the "3 .9", and you need to add them ( 3 .9 + (-3z) = 3 .9 - 3z ).
I recommend you to study more of rule of signs, like (-) + (-) = (+) and things like this.
Hope that I could help you
What are the zeros of the polynomial function f x x3 − 2x2 − 24x?.
The zeros of polynomial function f(x) = x³ - 2x² - 24x are x = 0, x = -4 and x = 6
Consider given function f(x) = x³ - 2x² - 24x
We know that the zeros of a function are nothing but the values of the variable of the function that makes the function value equal to 0.
To find the zeros of function f(x), we need to equate f(x) to zero then solve it for x.
⇒ f(x) = 0
⇒ x³ - 2x² - 24x = 0
⇒ x (x² - 2x - 24) = 0
⇒ x = 0 OR x² - 2x - 24 = 0
Now we solve quadratic equation x² - 2x - 24 = 0
x² - 2x - 24 = 0
x² - 6x + 4x - 24 = 0
(x - 6)(x + 4) = 0
x = 6 OR x = -4
Thus x = 0, x = -4 and x = 6 are zeros of given polynomial function.
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The complete question is:
What are the zeros of the polynomial function f(x) = x³ - 2x² - 24x?.
The movie marathon starts at 1:15 p.m. and ends at 8:05 p.m. How long is the movie marathon?
To create an entry code, you mut firt chooe 3 letter and then, 3 ingle-digit number. How many different entry code can you create?
The total entry code can create by the dataset given is 17576000.
How to determine the total entry code?Assume the entry character that is n. As per requirement given are the first three entry are 3 letter then then n1 = 26 , n2 = 26, n3 = 26. Then, the three after that is a single digit number, so n4 = 10, n5 = 10, n6 = 10. Since we have find the value of each entry character then we can determine total entry code as follow:
Total entry code = n1 x n2 x n3 x n4 x n5 x n6
Total entry code = 26 x 26 x 26 x 10 x 10 x 10 = 26³ x 10³
Total entry code = 17576 x 1000
Total entry code = 17576000
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a pie is made up of 8 slices. if 37.5% of the pie slices remain after dinner, how many slices of pie remain after dinner?
Answer:
3 slices
Step-by-step explanation:
37.5% = 0.375
We take
8 times 0.375 = 3 slices
So, 3 slices of pie remain after dinner.
R m O Q Figure 1 1. Figure 1 shows the right angled triangle PQR, whose vertices are located at P(-6, -2) and Q(6,6). It is further given that PQR = 90°. (a) Find an equation for the straight line 1, which passes through Q and R. [3]
Right angled triangle PQR, whose vertices are located at P(-6, -2) and Q(6,6). It is further given that PQR = 90° . y = 0.666666666667 x + 2 is the equation of the straight line .
What is called straight line?y = 0.6666666667x + 2 Points ( -6 , -2 ) , ( 6 , 6 ) ( 6 , 6 ) Formula (y = mx + b) y = 0.666666666667 x + 2 Slope in metres : 0.66666666667 , 2. Y-intercept 0. 6666666666 x Plus any number of parallel lines 1.5 x + any number for parallel lines.
Any line without curves is said to be straight. Consequently, a straight line is one that is uncurved and stretches beyond infinity on both sides. a diagram of a graph in which each edge is a section of a straight line. Additional terms to consider are grid drawing, orthogonal drawing, planar straight-line graph, and Bresenham's algorithm. A straight line has the equation y=mx+c, where c is the height at which the line crosses the y-axis, also known as the y-intercept, and m is the gradient.
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HELP
18 kg of apples cost $106.20. How much would 31 kg cost?
(second post cause why not)
Answer:
$182.90
Step-by-step explanation:
Find the cost per kg. To do so, divide the total cost, with the amount of kg that is bought:
(Total Cost/Total weight) = (cost/unit):
[tex]\frac{106.20}{18} = 5.9\\\\[/tex]
$5.9 per kg of apple.
~
Next, solve for the amount that 31 kg of apples would cost. Multiply the unit cost with the amount of kg of apples purchased:
(Total weight of apples x Cost per kg for apples) = Total cost:
[tex]31 * $5.9 = Total Cost\\Total Cost = 182.9[/tex]
$182.90 is your answer.
~
Rotate 180 about the origin
The vertices of the rotation of 180⁰ are P'(2, 2), Q'(-1, 2), R'(-2, 4) and S'(3, 4)
What is the rotation about an angle?The angle of rotation is a measurement of the amount, of namely angle, that a figure is rotated about a fixed point, often the center of a circle
When we rotate a figure of 180 degrees about the origin either in the clockwise or counterclockwise direction, each point of the given figure has to be changed from (x, y) to (-x, -y) and graph the rotated figure.
Before Rotation After Rotation
(x, y) (-x, -y)
Let P(-2, -2), Q(1, -2), R(2, -4) and S(-3, -4) be the vertices of a four sided closed figure. If this figure is rotated 180° about the origin, find the vertices of the rotated figure and graph.
Here, the given is rotated 180° about the origin. So, the rule that we have to apply here is
(x, y) ----> (-x, -y)
Based on the rule, we have to find the vertices of the rotated figure.
Also, (x, y) ----> (-x, -y)
P(-2, -2) ----> P'(2, 2)
Q(1, -2) ----> Q'(-1, 2)
R(2, -4) ----> R'(-2, 4)
S(-3, -4) ----> S'(3, 4)
There, the vertices of the rotated figure are
P'(2, 2), Q'(-1, 2), R'(-2, 4) and S'(3, 4)
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Complete question:
Let P(-2, -2), Q(1, -2), R(2, -4) and S(-3, -4) be the vertices of a four sided closed figure. If this figure is rotated 180° about the origin, find the vertices of the rotated figure and graph.
I WILL GIVE YOU 100 POINTS. PLEASE HELP ME
To conserve water, many communities have developed water restrictions. The water utility charges a fee of $29, plus an additional $1.41 per hundred cubic feet (HCF) of water. The recommended monthly bill for a household is between $54 and $82 dollars per month. If x represents the water usage in HCF in a household, write a compound inequality to represent the scenario and then determine the recommended range of water consumption. (Round your answer to one decimal place.)
A 54 ≤ 1.41x + 29 ≤ 82; To stay within the range, the usage should be between 17.7 and 37.6 HCF.
B 54 ≤ 1.41x + 29 ≤ 82; To stay within the range, the usage should be between 17.7 and 58.2 HCF.
C 54 ≤ 1.41x − 29 ≤ 82; To stay within the range, the usage should be between 38.2 and 78.7 HCF.
D 54 ≤ 1.41x − 29 ≤ 82; To stay within the range, the usage should be between 58.9 and 78.7 HCF.
Ms.Rivers has art for specials every 2nd day, and Ms.Meyer has art 9th day. When will both classes have are on the same day?
Answer:
18th day
Step-by-step explanation:
so you basically have to find the Least common multiple
add the difference of 7 and m to 4
The expression would be "4 + (7 - m)" .
This expression takes the value of m, subtracts it from 7, and then adds the result to 4.
Algebraic expression : A number increased by three times the number
The algebraic expression for the a number that has been multiplied by three is: x + 3*x. In this statement, x stands for the number, while 3*x, or 3x, stands for the number times three.
What is the Algebraic expression?An algebraic expression is a combination of numbers, variables, and mathematical operations, such as addition, subtraction, multiplication, and division. Algebraic expressions can be evaluated for specific values of the variables in order to find a numerical result.
What sort of algebraic expression would that be?A mathematical statement with variables, constants, coefficients, or algebraic operations is known as an algebraic expression. A good example of an algebraic expression is 5x2+6xyc. Algebraic expression do not utilize equal signs, in contrast to algebraic equations.
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How large does the strength of an earthquake differ for a 1. 0 increment in the Richter magnitude scale?.
The strength of an earthquake differ for a 1. 0 increment in the Richter magnitude scale by 31 units.
American seismologists Charles F. Richter and Beno Gutenberg developed the Richter scale (ML), a numerical indicator of an earthquake's size, in 1935. The height of the greatest seismic wave, as measured by the logarithm of its amplitude (height), is used to calculate the earthquake's magnitude.
Although the original Richter scale has been supplanted by other, more precise scales in modern science, the Richter scale is still frequently used incorrectly in news reporting of earthquake severity as a catch-all name for the logarithmic scale that earthquakes are measured on.
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What is x divided 12;x= 2/3
Answer:
X is 18
Step-by-step explanation:
2/3 = 0.6666666666666667
12 divided by 18 = 0.6666666666666667
How do you solve a 3 variable system of equations?.
When solving systems of equation with three variables we use the elimination method or the substitution method to make a system of two equations in two variables.
There are several methods to solve a system of equations with three variables, including substitution, elimination, and graphing. One common method is to use elimination, also known as the addition/subtraction method. This involves adding or subtracting equations in order to eliminate one of the variables and creating an equation with only two variables. Once you have a system of two equations with two variables, you can solve for one of the variables, substitute that value back into one of the original equations, and then solve for the remaining variable. After that you can use the value of the variables to find the values of the other variables.
Hence, When solving systems of equation with three variables we use the elimination method or the substitution method to make a system of two equations in two variables.
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The triangle with coordinates (2,-3),(2,1),(-4,2) is reflected
across the y-axis and then translated by vector
(3,-2).
Part A
Find the new coordinates
Part B
What is the composition of functions for the
given sequence of transformations?
(x, y) → (
Answer:
PART A : points to graph (7,0)(1,-1)(2,-5)
PART B: (x, y) => (-x+3, y-2)
Explanation step by step :
Reflected across y axis means y-coordinate of every point remains same and x-cordinate become opposite
(x, y) become (-x, y)
Here,
(-4, 2) become (4, 2)
(2, 1) become (-2, 1)
(1,-3) become (-1,-3)
Similarly a point P(x, y) translated by vector <3, -2> means the point P become P'(x+3, y-2)
(4, 2) become (7,0)
(-2, 1) become (1, -1)
(-1,-3) become (2,-5)
So the composition of function for the given sequance of transfermation is (x, y) = (-x+3, y-2)
Note : graph not accurate, just for explanation.
9x+3=57
hjdddddddddddd
Answer:
the value of x is 55/9 ok hope it helps
