The dimensions of new rectangular playing field are 183 yards and 44 yards, by the concept of perimeter of rectangle.
What is perimeter of rectangle?The whole distance that the sides or limits of a rectangle cover is known as its perimeter. Since a rectangle has four sides, its perimeter will be equal to the sum of those four sides. Given that the perimeter is a linear measurement, the rectangle's perimeter will be expressed in meters, centimeters, inches, feet, etc.
Formula, perimeter of rectangle =2× (length +width)
Given, perimeter of rectangular playing field = 454 yards (equation 1)
Let us assume, width =x
According to question length = 4x+7 (quadruple=4times)
By the above equations,
Perimeter=2×(4x+7+x)
2×(5x+7) =454 (by equation 1)
Dividing the above equation by 2 both the sides
(5x+7) =227
Subtracting the above equation by 7 both the sides
5x=220
Dividing the above equation by 5 both the sides
x=44
Therefore, the required width of new rectangular playing field is 44 yards and length of new rectangular playing field is 183 yards
To know more about perimeter of rectangle, visit:
https://brainly.com/question/15287805
#SPJ13
what is the value of 6 3/4 (-11.5)
We are given the following expression
[tex]6\frac{3}{4}(-11.5)[/tex]As you can see, a mixed number is being multiplied with a negative decimal number.
First, convert the mixed number to a simple fraction then multiply with the decimal number
[tex]6\frac{3}{4}=\frac{6\cdot4+3}{4}=\frac{24+3}{4}=\frac{27}{4}[/tex]Now multiply it with the negative decimal number
[tex]\frac{27}{4}(-11.5)=-\frac{310.5}{4}=-77.625[/tex]So the resultant decimal number may be written back into the mixed form as
[tex]-77.625=-77\frac{5}{8}[/tex]Therefore, the result of the given expression is -77 5/8
consider the line y=2/5x. What is the slope of a line perpendicular to this line?
What is the slope of a line parallel to this line?
Answer:
- 5/2
Step-by-step explanation:
If the slope of a line is m then the slope of the perpendicular line is -1/m
The slope of y = 2/5 x is 2/5
Slope of perpendicular line = - 5/2
Triangle MNO has its vertices at the following coordinates:M(2, 2) N(-1,3) O(1,5)Give the coordinates of the image triangle M'N'O' after a 90° counterclockwise rotation about the origin.
The counter clockwise rotation of any point X(x,y) about origin results in change of coordinates as,
[tex]X(x,y)\rightarrow X^{\prime}(-y,x)[/tex]Determine the coordinates of the vertices of the triangle M'N'O'.
[tex]M(2,2)\rightarrow M^{\prime}(-2,2)[/tex][tex]N(-1,3)\rightarrow(-3,-1)[/tex][tex]O(1,5)\rightarrow(-5,1)[/tex]So coordinates of triangle M'N'O' are;
M'(-2,2)
N'(-3,-1)
O'(-5,1)
I would like some help on how to solve this problem!(please and thank you)
Answer
GH is congruent to JH and FH is congruent to HI. ∠GHF should be congruent to ∠JHI by Vertical Angles Theorem. Since GH is congruent to JH, ∠GHF is congruent ∠JHI, and FH is congruent is congruent to HI, ΔGHF is congruent ΔJHI, by SAS. Then one can assume that FG is congruent to IJ by CPCTC.
Triangle A has a 18.3cm side and a 3cm base. Find the hypotenuse.
Given:
The length of the sides is a=18.3 cm,
The base of the triangle is b =3 cm.
Required:
We need to find the hypotenuse.
Explanation:
Use the Pythagorean theorem.
[tex]c^2=a^2+b^2[/tex]Substitute a =18.3 and b=3 in the equation.
[tex]c^2=18.3^2+3^2[/tex][tex]c^2=343.89[/tex]Take square root on both sides.
[tex]\sqrt{c^2}=\sqrt{343.89}[/tex][tex]c=\pm18.5442[/tex]Length is always positive.
[tex]c=18.54[/tex]Final answer:
The hypotenuse is 18.54cm.
X + 2y = 3x = 5Enter your answer as a point using parenthesis and a comma. Do not use any spaces in youranswer.If there are no solutions, type "no solutions." If there are infinitely many solutions, type"infinitely many."Answer:
thats the explanation
answer is : (5, -1)
Solve equation for x. 5x^2 - 4x =6
Answer:
Step-by-step explanation:
use the quadratic formula
5x^2-4x-6
4+-[tex]\sqrt{16+120}[/tex] all over 10
4+-[tex]2\sqrt{34}[/tex]/10
2+-[tex]\sqrt{34}[/tex]/5
D
X -5x+4 =015.x+6=0A rectangular painting is 3 feet shorter in length than it is tall (height).12. Write a polynomial to represent the area of the painting.13. Write a polynomial to represent the perimeter of the painting.14. The painting has the unique quality of having an area that has a value that is equal to the value of theperimeter. Find the height of the painting.15. What is the extraneous solution to the polynomial created when the area is set equal to the perimeter?
The rectangular painting is 3 feet shorter in length than in height.
Let "x" represent the painting height, then its length can be expressed as "x-3"
12.
The area of the rectangular painting can be calculated by multiplying its length by its height.
[tex]A=l\cdot h[/tex]For the painting
h=x
l=x-3
-Replace the formula with the expressions for both measurements:
[tex]A=(x-3)x[/tex]-Distribute the multiplication on the parentheses term:
[tex]\begin{gathered} A=x\cdot x-3\cdot x \\ A=x^2-3x \end{gathered}[/tex]The polynomial that represents the area of the painting is:
[tex]A=x^2-3x[/tex]13.
The perimeter of a rectangle is calculated by adding all of its sides, or two times its length and two times its height. You can calculate the perimeter of the painting as follows:
[tex]P=2l+2h[/tex]We know that
h=x
l=x-3
Then the perimeter can be expressed as follows:
[tex]P=2(x-3)+2(x)[/tex]-Distribute the multiplication on the parentheses term:
[tex]\begin{gathered} P=2\cdot x-2\cdot3+2x \\ P=2x-6+2x \end{gathered}[/tex]-Order the like terms together and simplify them to reach the polynomial:
[tex]\begin{gathered} P=2x+2x-6 \\ P=4x-6 \end{gathered}[/tex]14.
The painting has the unique quality of having an area that is equal to the value of the perimeter, then we can say that:
[tex]A=P[/tex]-Replace this expression with the polynomials that represent both measures:
[tex]x^2-3x=4x-6[/tex]To solve the expression for x, first, you have to zero the equation, which means that you have to pass all therm to the left side of the equation. Do so by applying the opposite operation to both sides of the equal sign.
[tex]\begin{gathered} x^2-3x-4x=4x-4x-6 \\ x^2-7x=-6 \\ x^2-7x+6=-6+6 \\ x^2-7x+6=0 \end{gathered}[/tex]We have determined the following quadratic equation:
[tex]x^2-7x+6=0[/tex]Using the quadratic formula we can calculate the possible values for x. The formula is:
[tex]x=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a}[/tex]Where
a is the coefficient that multiplies the quadratic term
b is the coefficient that multiplies the x term
c is the constant of the quadratic equation
For our equation the coefficients have the following values:
a=1
b=-7
c=6
Replace these values in the formula and simplify:
[tex]\begin{gathered} x=\frac{-(-7)\pm\sqrt[]{(-7)^2-4\cdot1\cdot6}}{2\cdot1} \\ x=\frac{7\pm\sqrt[]{49-24}}{2} \\ x=\frac{7\pm\sqrt[]{25}}{2} \\ x=\frac{7\pm5}{2} \end{gathered}[/tex]Next is to calculate the addition and subtraction separately:
-Addition
[tex]\begin{gathered} x=\frac{7+5}{2} \\ x=\frac{12}{2} \\ x=6 \end{gathered}[/tex]-Subtraction
[tex]\begin{gathered} x=\frac{7-5}{2} \\ x=\frac{2}{2} \\ x=1 \end{gathered}[/tex]The possible values of x, i.e., the possible heights of the painting are:
x= 6ft
x=1 ft
15.
To determine the extraneous solution created when the area was set equal to the perimeter you have to calculate the corresponding length for both possible values of the height:
For the height x= 1ft, the corresponding length of the painting would be -2ft. This value, although mathematically correct, is not a possible measurement for the painting's length since these types of measures cannot be negative.
What is the smallest fraction?5/1210/15 1/32/4
Answer:
1/3
Explanation:
In order to get the smallest fraction, we will need to express each of the fractions as a percentage as shown below:
For 5/12;
[tex]\begin{gathered} =\frac{5}{12}\times100 \\ =\frac{500}{12} \\ =41.7\% \end{gathered}[/tex]For 10/15;
[tex]\begin{gathered} =\frac{10}{15}\times100 \\ =\frac{1000}{15} \\ =66.7\% \end{gathered}[/tex]For the fraction 1/3
[tex]\begin{gathered} =\frac{1}{3}\times100 \\ =\frac{100}{3} \\ =33.3\% \end{gathered}[/tex]For the fraction:
[tex]\begin{gathered} =\frac{2}{4}\times100 \\ =\frac{200}{4} \\ =50\% \end{gathered}[/tex]From the resulting percentage, we can see that the smallest among the fraction is 1/3.
A boat heading out to sea starts out at Point A, at a horizontal distance of 1357 feet
from a lighthouse/the shore. From that point, the boat's crew measures the angle of
elevation to the lighthouse's beacon-light from that point to be 9°. At some later time
the crew measures the angle of elevation from point B to be 3°. Find the distance
from point A to point B. Round your answer to the nearest tenth of a foot if
necessary.
The distance from point A to point B is 2744.1 feet.
Define Trigonometric ratio
The ratios of the sides of a right triangle are called trigonometric ratios. Three common trigonometric ratios are the sine (sin), cosine (cos), and tangent (tan).
Given, horizontal distance = 1357 feet
Let h = height of the lighthouse
tan(A) = perpendicular / base
where, perpendicular = h
base = 1357 feet
Angle is 9°
so now, put these value in trigonometric ratio
tan(9) = h / 1357
where, tan(9) = 0.1584
h = 1357 * 0.1584
h = 214.9 feet
Let d = distance from point B to the Lighthouse base
Angle is 3°
h = 214.9 feet
so, tan(3) = 214.9 / d
where, tan(3) = 0.0524
0.0524 = 214.9 / d
d = 214.9 / 0.0524
d = 4101.1 feet
Distance between point A to B = 4101.1 - 1357
= 2744.1 feet
Therefore, the distance from point A to point B is 2744.1 feet
To read more about the Trigonometric ratio.
https://brainly.com/question/25870256
#SPJ13
What is the reference angle for 289°? A. 71° B. 19° C. 11° D. 89°
Given:
Angle θ=289°.
For angles from 270° to 360°, the reference angle can be calculated by subtracting the given angle from 360° .
The reference angle of θ can be calculated as:
[tex]\begin{gathered} 360\degree-\theta=360\degree-289\degree \\ =71\degree \end{gathered}[/tex]Therefore, reference angle of 289° is 71°.
hardest question on brainly stumbles college students!
Applying the vertical angles theorem and other properties, the value of x is 20. The reason for each statement has been explained below.
What are Vertical Angles?A pair of vertical angles are formed when two straight lines intersect each other at a common point. The angles that face each other directly are vertical angles and they are congruent or equal to each other.
Given the diagram below, to find the value of x, the following are the each reason that justifies each of the statements in each step:
Statement Reasons
1. m∠DOB = m∠DOE + m∠BOE 1. Angle Addition Postulate
2. m∠DOB = 90 + x 2. Substitution
3. m∠AOC = m∠DOB 3. Vertical Angels Theorem
4. 110 = 90 + x 4. Substitution
5. x = 20 5. Algebra
To solve using algebra, step 4 is solved as explained below:
110 - 90 = 90 + x - 90
20 = x
x = 20.
Therefore, applying the above steps and reasons that includes the use of vertical angles theorem, the value of x is determined to be: x = 20.
Learn more about vertical angles on:
https://brainly.com/question/14362353
#SPJ1
PRYZ is a rhombus. If RK=5, RY = 13, and YRZ = 67, find each measure.
The Solution:
The correct answer is 67 degrees.
Given the rhombus below:
We are required to find the measure of angle PRZ.
Considering trianglePRZ, we can apply the law of cosine to the angle of interest, which is, angle PRZ.
[tex]R=\cos ^{-1}(\frac{p^2+z^2-r^2}{2pz})[/tex]In this case,
[tex]\begin{gathered} p=(5+5)=10 \\ z=13 \\ r=13 \\ R=\text{?} \end{gathered}[/tex]Substituting these values in the formula, we get
[tex]R=\cos ^{-1}(\frac{10^2+13^2-13^2}{2(10)(13)})[/tex][tex]R=\cos ^{-1}(\frac{100^{}+169^{}-169^{}}{2(10)(13)})=\cos ^{-1}(\frac{100^{}}{260})=67.380\approx67^o[/tex][tex]m\angle\text{PRZ}\approx67^o[/tex]Therefore, the correct answer is 67 degrees.
find 2x:3y if x:y = 2:5
4 : 15
Explanation:[tex]\begin{gathered} \text{x : y = 2: 5} \\ \frac{x}{y}\text{ = }\frac{2}{5} \\ \\ 2x\text{ : 3y = ?} \end{gathered}[/tex][tex]\begin{gathered} 2x\colon\text{ 3y = }\frac{2x}{3y} \\ 2x\colon3y\text{ = }\frac{2}{3}\times\frac{x}{y} \end{gathered}[/tex][tex]\begin{gathered} \text{substitute for x/y in 2x:3y} \\ \frac{2}{3}\times\frac{x}{y}\text{ =}\frac{2}{3}\times\frac{2}{5} \\ =\text{ }\frac{4}{15} \\ \\ \text{Hence, 2x:3y = }\frac{4}{15} \\ or \\ 4\colon15 \end{gathered}[/tex]Which of the following sets does the number - 12.12532 ... belong to?Select all correct answers.Select all that apply:Whole NumbersIntegersURational NumbersIrrational NumbersReal NumbersUNone of the Above
Answer:
Explanation:
Let's define each of the given types of numbers;
*Whole numbers are a set of all positive integers including 0. E.g 0, 1, 2,
*Integers
Use a proportion to solve the problem. 34% of 83x/100=34/83;40.96x/100=34/83;2.822x/83=34/100;28.22x/83=34/100;56.44
34% in decimal is equal to 0.34, which in fraction is equivalent to 34/100.
Therefore we can solve this as
x/83 = 34/100; 28.22.
need help assap look at file attached
Answer:
length is 27, width is 9
Step-by-step explanation:
72/4= 18
2x27+ 2x9 = 54 + 18 = 72
le Figure Score: 7/100 1/13 answered Question 2 < > A pennant is in the shape of an isosceles triangle. inches, the height is 15 inches, and the length of th the area of the pennant? inches squared
The area of a triangle is given by:
[tex]A=\frac{1}{2}bh[/tex]in this case b=9.5 and h=15. Plugging the values in the formula we have:
[tex]\begin{gathered} A=\frac{1}{2}\cdot9.5\cdot15 \\ =71.25 \end{gathered}[/tex]Therefore the area is 71.25 square
1. A table is 2 feet wide. It is 6 times as long as it is wide. Table= A-Label the diagram with the dimensions of the table.B-find the perimeter of the table
Width(w) = 2 feet
Length (L)= 6w = 6(2) = 12 feet
a. Table = 2 x 12
b: Perimeter of a rectangle:
P = 2w+ 2L = 2(2)+2(12) = 4+24 = 28 feet
7/11% of a quantity is equal to what fraction of a quantity
7/11% can be written as:
[tex]\begin{gathered} \frac{\frac{7}{11}}{100}=\frac{7}{11}\times\frac{1}{100} \\ \frac{\frac{7}{11}}{100}=\frac{7}{1100} \end{gathered}[/tex]So 7/11% of a quantity is equal to 7/1100 fraction of a quantity
Answer:41/10,000
7/17% = 0.41% = 0.0041
41/10,000
Step-by-step explanation:
Angel Corporation produces calculators selling for $25.99. Its unit cost is $18.95. Assuming a fixed cost of $80,960, what is the breakeven point in units?
The breakeven point is 11,500, meaning that if the sell that number of units, the profit will be zero.
How to get the breakeven point?
Here we know that the unit price is $25.99, so if they sell x units, the revenue is
R(x) = $25.99*x
And the cost per unit is $18.95, plus a fixed cost of $80,960
Then the cost of x units is:
C(x) = $80,960 + $18.95*x
The breakeven point is the value of x such that the cost is equal to the revenue, so we need to solve:
$25.99*x = $80,960 + $18.95*x
$25.99*x - $18.95*x = $80,960
$7.04*x = $80,960
x = $80,960/%7.04 = 11,500
Learn more about cost and revenue:
https://brainly.com/question/16232387
#SPJ1
What are the values of n in the following equation? Select all that apply. 4n + 2 = 34
The given equation is
[tex]4x+2=34[/tex]First, we subtract 2 from each side
[tex]\begin{gathered} 4x+2-2=34-2 \\ 4x=32 \end{gathered}[/tex]Then, we divide the equation by 4
[tex]\begin{gathered} \frac{4x}{4}=\frac{32}{4} \\ x=8 \end{gathered}[/tex]Hence, the answer is x = 8.polygon wxyz has vertices W( 1, 5 ), X( 6, 5), Y( 6, 10), and Z(1, 10)
If w' x' y' z' is a dilation of wxyz with scale factor 5, give the coordinates of w' x' y' z'
The coordinates of W'X'Y'Z' are W'(5, 25), X'(30, 25), Y'(30, 60) and Z'(5, 10) respectively.
Given that, polygon WXYZ has vertices W( 1, 5 ), X( 6, 5), Y( 6, 10), and Z(1, 10).
What is a dilation?Dilation is the process of resizing or transforming an object. It is a transformation that makes the objects smaller or larger with the help of the given scale factor. The new figure obtained after dilation is called the image and the original image is called the pre-image.
We know that, scale factor = Dimension of the new shape ÷ Dimension of the original shape
Dimension of the original shape W'= 5(1, 5) = (5, 25)
X' =5(6, 5) = (30, 25)
Y' =5(6, 10) = (30, 60)
Z' =5(1, 10) = (5, 10)
Therefore, the coordinates of W'X'Y'Z' are W'(5, 25), X'(30, 25), Y'(30, 60) and Z'(5, 10) respectively.
To learn more about the dilation visit:
https://brainly.com/question/13176891.
#SPJ1
PLEASE HELP: Which of the following are identities? Check all that apply. A. (sin x + cos x)^2 = 1 + sin 2x B. sin 3x - sinx/ cos3x + cosx = tan xC. sin 6x = 2 sin3x cos3x D. sin 3x/sin x cos x = 4 cos x - sec x
All the options are correct
Explanations:A quick and smart way is to substitute a value for x in each of the options and verify if the right hand side equals the left hand side
Let x = 30
A) (sin x + cos x)² = 1 + sin 2x
(sin 30 + cos 30)² = 1.866
1 + sin 2(30) = 1.866
Therefore (sin x + cos x)² = 1 + sin 2x
B)
[tex]\begin{gathered} \frac{\sin3x-\sin x}{\cos3x+\cos x}=\tan x \\ \frac{\sin3(30)-\sin30}{\cos3(30)+\cos30}=0.577 \\ \tan \text{ 30 = 0.577} \end{gathered}[/tex]Therefore:
[tex]\frac{\sin3x-\sin x}{\cos3x+\cos x}=\tan x[/tex]C) sin 6x = 2 sin3x cos3x
sin 6(30) = 0
2 sin3(30) cos3(30) = 0
Therefore sin 6x = 2 sin3x cos3x
This can also be justified by sin2A = 2sinAcosA
D.
[tex]\frac{\sin3x}{\sin x\cos x}=\text{ 4}\cos x-\sec x[/tex][tex]\begin{gathered} \frac{\sin 3(30)}{\sin 30\cos 30}=\text{ 2.31} \\ 4\cos 30-\sec 30=\text{ }2.31 \end{gathered}[/tex]Options A to D are correct
Labron James made 255/310 baskets. What percent of the baskets did he make?
82.26%
Explanations:The ratio of baskets made by Lebron James = 255/310
To find the percentage equivalent of the ratio, multiply it by 100%
Percentage of the baskets made by Lebron James = 255/310 x 100%
Percentage of the baskets made by Lebron James = 82.26%
the table below shows an inspectors measurement of the lengths of four bridges
Given
Table which ahows an inspectors measurement of the lengths of four bridges
Find
Order from shortest to longest lengths of bridges.
Explanation
First we convert the lengths of Bridges in improper form , then in decimal form.
[tex]\begin{gathered} M=1\frac{49}{60}=\frac{109}{60}=1.817 \\ \\ N=1\frac{79}{100}=\frac{179}{100}=1.79 \\ \\ O=1\frac{52}{75}=\frac{127}{75}=1.693 \\ \\ P=1\frac{97}{120}=\frac{217}{120}=1.80 \end{gathered}[/tex]so , O has shortest length and M has longest length.
Final Answer
Therefore ,
the order from shortest to longest is
Bridge O , Bridge N , Bridge P and Bridge M , so the correct option is 1
need help with this problem, find the length of the darkened arc. C is the center of the circle
Notice that the central angle measures 138 degrees, We have a property of the circle that says that the measure of a central angle is equal to the arc between its sides.
Therefore, the arc measures 138 degrees
the quotient of 7 and p
To get the quotient we divide.
[tex] = 7 \div p \\ = \frac{7}{p} [/tex]
Household Income
Under $50,000
$50,000 under $75,000
$75,000 under $150,000
$150,000 or above
Percentage
27.2
27.3
37.2
8.3
Event
ABCD
Suppose that a household with home Internet access only is selected at random. Apply the
special addition rule to find the probability that the household obtained has an income
a. under $75,000.
b. $50,000 or above.
c. between $50,000 and (under) $150,000
d. Interpret each of your answers in parts (a) - (c) in terms of percentages
e. Use the complement rule to answer part (b) in this exercise.
The probability for household with income under $75,000 is 54.5/100. the probability for household with income $50,000 or above is 72.8 /100, and the probability for household with income between $50,000 and (under) $150,000 is 64.5/100.
What is probability?
Probability describes potential. This area of mathematics examines how random events happen. The value might be between 0 and 1. Mathematicians have used probability to forecast the likelihood of certain events. In general, probability relates to how likely something is to happen. You can better understand the potential results of a random experiment by using this fundamental theory of probability, which also holds true for the probability distribution. To calculate the likelihood that an event will occur, we first need to know how many possible possibilities there are.
As given in the question,
Household with Income $50,000 are 27.2%
$50,000 - $75,000 are 27.3%
$75,000 - $150,000 are 37.2%
$150,000 or above are 8.3%
a) we have to find the probability for household with income under $75,000
So, Households having income under $75,000 are equal to:
(27.3 + 27.2)% = 54.5%
Therefore, probability = 54.5/100
b) we have to find the probability for household with income $50,000 or above,
So, household with income $50,000 or above are equal to:
(27.3 + 37.2 + 8.3)% = 72.8%
Therefore, probability = 72.8 /100
c) we have to find probability for household with income between $50,000 and (under) $150,000.
so, household with income between $50,000 and (under) $150,000 are equal to:
(27.3 + 37.2)% = 64.5%
Therefore, probability = 64.5/100
d) answer a can be interpret in percentage as 54.5%
answer b can be interpret in percentage as 72.8%
answer c can be interpret in percentage as 64.5%
To know more about probability, go to link
https://brainly.com/question/13604758
#SPJ13
Curt and melanie are mixing blue and yellow paint to make seafoam green paint. Use the percent equation to find how much yellowp they should use.
To solve the exercise you can use the rule of three, like this
[tex]\begin{gathered} 1.5\text{ quarts}\rightarrow100\text{ \% }\Rightarrow\text{ Green paint} \\ x\text{ quarts}\rightarrow30\text{ \%}\Rightarrow\text{ Yellow paint} \end{gathered}[/tex][tex]\begin{gathered} x=\frac{30\text{ \% }\ast\text{ 1.5 quarts}}{100\text{ \%}} \\ x=0.45\text{ quarts} \end{gathered}[/tex]Therefore, Curt and Melanie should use 0.45 quarts of yellow paint to make seafoam green paint.