The structure's length is 93 feet long and its width is 62 feet.
What is rectangle?We also refer to a rectangle as an equiangular quadrilateral since all of its angles are equal. A closed 4-sided shape is called a quadrilateral.A rectangle can also be referred to as a right-angled parallelogram because its sides are parallel. A quadrilateral with equal and parallel opposite sides is referred to as a parallelogram. Paralleograms are a specific instance of rectangles.acc to our question -
Let W stand for the rectangle's flower garden's width and L for its length.
A rectangle flower garden with a width that is precisely two thirds of its length is created by an architect.
The following can be written:
W=2/3L
Given that the fence is 310 feet long, the rectangle's perimeter must also be 310 feet.
Perimeter = 2 (L + W)
The perimeter surrounding it)
2w + 2h = 310
2((2/3) * h) + 2h = 310
4h/3 + 2h = 310
10h/3 = 310
10h = 930
h = 93 feet
w = (2/3) * 93
w = 62 feet
Hence, The structure's length is 93 feet long and its width is 62 feet.
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QUEST
Find the median of the numbers in the following list.
Select the correct answer below:
O22
O 21
26
O24
O 14
26, 13, 39, 22, 42, 39, 18, 21, 32, 14
Step-by-step explanation:
first order them from least to greatest
13,14,18,21,22,26,32,39,39,42
then just look for the term in the middle
sunset there are 2 numbers in the middle you will add them both and subtract them by 2
42+39 then / 2 =40.5
A transversal intersects two lines. Which condition would always make the two lines parallel?
If a transversal intersects two lines such that a pair of alternate interior angles is equal , then the two lines are parallel.
What do you mean by traversal line?
A transversal is a line that, at two different locations in the geometry, cuts through two lines in the same plane. Various sorts of angles in pairs, including successive internal angles, corresponding angles, and alternate angles, are produced by a transversal intersection with two lines.
What do you mean by angle?
An angle is defined as the figure, in which two rays meet at a common point called the vertex. The angle is denoted using the symbol “∠”.
From the figure,
x + 1 = 180°
y + 2 = 180°
Adding above equations,
x + y + 1 + 2 = 360°
Given ,
x + y = 1 +2
x + y + x + y = 360°
2(x + y) = 360°
x + y = 180°
Angles made on same side of transversal is supplementary . So the lines are parallel.
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Given the coordinate, perform the following transformation and give the new coordinates.
12. Reflect (2, 3) over the x axis: (
13. Reflect (7, -2) over the y axis: (
14. Rotate (4, 5) 90° about the origin: (
15. Rotate (-3, -2) 270° about the origin:
16. Reflect (17, -23) over the line y=x.
The reflection of the point (2,3) over the x-axis is (2,-3). The reflection of the point (7,-2) over the y-axis is (-7,-2).
What is a reflection?A reflection is referred to as a flip in geometry. A reflection is the shape's mirror image. A line, called the line of reflection, will allow an image to reflect through it. Every point in a figure is said to reflect the other figure when they are all equally spaced apart from one another.
The reflection of the point (2,3) over the x-axis is calculated as,
(2,3) ⇒ (2,-3)
The reflection of the point (7,-2) over the y-axis is calculated as,
(7,-2) ⇒ (-7,-2)
Therefore, the reflection of the point (2,3) over the x-axis is (2,-3). The reflection of the point (7,-2) over the y-axis is (-7,-2).
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Find all x ∈ R that are solutions to this equation:
0 = ( 1- X- X^2-...) (2- X- X^2-...)
The solution of the geometric equation is x = 1/2 or x = 1
What is an equation?An equation is a mathematical expression that shows the relationship between variables.
What is a geometic series?A geometric series is the sum of a geometric sequence.
How to find the solution to the equation?Since the equation 0 = ( 1 - X - X²-...) (2 - X - X²-...). To solve this, let the series x + x² + ... = p
So, 0 = ( 1 - X - X²-...) (2 - X - X²-...).
0 = (1 - [X + X²+...) (2 - [X + X²+...).
Substitute x + x² + ... = p. So,
0 = (1 - [X + X²+...) (2 - [X + X²+...).
0 = (1 - p)(2 - p).
So, (1 - p) = 0 or (2 - p) = 0
p = 1 or p = 2
Since x + x² + ... = p, the left side of the equation is the sum to infinity of a geometric series.
What is the sum to infinity of a geometric series?The sum to infinity of the geometric series is given by
S = a/(1 - r) where
a = first term and r = common ratioFor the given series,
a = x and r = xSo, S = a/(1 - r)
= x/(1 - x)
Since S = p, we have that
x/(1 - x) = 1 or x/(1 - x) = 2
So, x = 1 - x or x = 2 - x
x + x = 1 or x + x = 2
2x = 1 or 2x = 2
x = 1/2 or x = 2/2
x = 1/2 or x = 1
So, the solution is x = 1/2 or x = 1
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Find the measure of EACH numbered angle. 18° m
The measure of the angle 1, angle 2, angle 3 is 68°, 94°, 25° respectively.
What is angle?
An angle is created where two straight lines or rays meet at a single point. The point from where two lines converge is known as an angle's vertex. The name "angle" comes from the Latin word "angulus," which meaning "corner."
Let's firstly find angle 1,
We know that, the sum of the all three angles of a triangle is 180°.
So,
18° + 94° + angle 1 = 180°
112° + angle 1 = 180°
angle 1 = 180° - 112°
angle 1 = 68°
Now, we know that, opposite angle are always equal
Therefore,
angle 2 = 94°
Now, again applying the property of triangle that sum of all three angles are equal:
Therefore,
angle 3 + angle 2 + 61° = 180°
angle 3 + 94° + 61° = 180°
angle 3 = 25°
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(31x²y)/x^5y
can be written as a x x^b times y^c where:
a=
b=
c =
The value of a, and c is 1, -3, and 0;, using the factorization of factors.
What is factorization of expressions?
To factorize an algebraic statement, we first identify the terms' greatest common factors and then arrange the terms into groups in accordance with those groups. In plain English, factorization is the process through which an algebraic statement gets expanded in the opposite direction.
Not every term may share a factor in some algebraic formulas. For instance, have a look at the algebraic formula 12a + n -na - 12. There is no specific factor that unites the terms in this statement, yet the first and last terms share a factor of 12. The common factor between the second and third terms is n. Consequently, the terms can be rearranged as follows:
12a + n - na - 12= 12a - 12 + n - an
12a - 12 - a plus n = 12(a - 1) -n (a -1)
Following regrouping, each term's common component may be shown to be (a-1): 12a + n -na - 12=(a-1) (12 – n)
In the given question,
The expression is:
[tex]\frac{31x^{2}y}{x^{5}y}[/tex]
and after simplifying the expression, we get:
[tex]\frac{31}{x^{3}}[/tex]
So, Now comparing the equation, with a[tex]x^{b}[/tex]×[tex]y^{c}[/tex], we get;
b = -3;
c = 0;
a = 1;
Hence, The value of a, and c is 1, -3, and 0;
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Three of the 30 computers are out of service. What percent of the computers are not working?
The percentage of computers not working is 10%.
What is the percentage?The percentage is defined as representing any number with respect to 100. It is denoted by the sign %. The percentage stands for "out of 100." Imagine any measurement or object being divided into 100 equal bits.
Given that there are three of the 30 computers are out of service.
The percentage of the computers which are out of service will be calculated as,
P = 3 / 30
P = 0.1
P = 0.1x 100
P = 10%
Therefore, the percentage of computers not working is 10%.
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Determine whether the polygons to the right are similar.
Answer:
A the scale factor is 2 from LMN to CDF (or 1/2 from CDF to LMN).
Step-by-step explanation:
shadows are similar, when they have the same angles, abd if there is one scale factor for all sides and other lengths from one shape to the other.
8×2 = 17
15×2 = 30
17×2 = 34
help me please so i can pass my semester
plot 5/3 and its opposite on the number line
The numbers are plotted in the attached graph.
What is a number line?A number line is a representation of real numbers in the form of a graded straight line.
Note that 5/3 is approximately equal to 1.7.
Similarly, -5/3 is approximately equal to -1.7.
Now, use the number line to mark the points -1.7 and 1.7, the numbers lie near -2 and 2 respectively.
The numbers are plotted in the attached graph.
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A picosecond is one trillionth of a second. If one trillionth = 1 × 10 − 12, how many picoseconds are there in 6 minutes?
The picoseconds that are there in 6 minutes is 3.6 × 10^14.
What is an exponent?An exponent is the number of times that a number is multiplied by itself. It should be noted that the power is an expression which shows the multiplication for the same number.
In this case, picosecond is one trillionth of a second. If one trillionth = 1 × 10^12
The seconds in 6 minutes will be:
= 60 × 6
= 360 seconds
= 3.6 × 10^2
The picoseconds in 6 minutes will be:
= 1 × 10^12 × 3.6 × 10^2
= 3.6 × 10^14
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The radius of a circle is 8 ft. Find its area in terms of pi
Answer:
Step-by-step explanation:
201.06ft²
Answer:
Step-by-step explanation:
A solution contains 7% salt. How much water should be added to 30 ounces of this solution to make a 5% solution?
12 ounces of water.
Step-by-step explanation:1. Set the initial values.Total mass of the solution: 30 ounces.
Total mass of salt (solute): (30*0.07)= 2.1 ounces.
Total mass of water (solvent): (30*0.93) 27.9 ounces.
2. Find an equation that relates amount of water and percentage of salt.
Since we know that the amount of salt is 2.1 ounces, and it has to remain constant, we have to create a function such that the variable is the amount of water and it gives us the percentage of solution we are looking for. The function should look like this:
[tex]\frac{2.1}{x} =0.05[/tex]; where x is the mass of the water in the solution.
Side note: The number "0.05" is 5% converted into a decimal.
3. Solve the equation for x.[tex]\frac{2.1}{x} =0.05\\ \\\frac{x}{2.1} =\frac{1}{0.05} \\ \\x=\frac{2.1}{0.05} \\ \\x=42[/tex]
42 would be the total amount of ounces the solution should have in order to be a 5% solution. Therefore, 12 ounces (42-30) have to be added.
4. Conclude.12 ounces of water have to be added to this solution in order to make it a 5% solution, where 2.1 ounces is salt and 39.9 is water.
5. At PrintAll copying, a new copying machine can produce five more than twice the number of copies per hour of the old copy machine. If the new machine produces 205 copies per hour, how many copies can the old machine produce? Show the equation you used to determine the answers.
6. A recipe calls for 2 cups of milk for every 6 1/4 cups of flour. If you increase the flour to 43 3/4 cups, how many cups of milk will you use?
Step-by-step explanation:
5.
xnew = 205 = 2×xold + 5
200 = 2×xold
xold = 100
the old city machine can produce 100 copies per hour.
6.
2 cups of milk relate to 6 1/4 cups of flour.
such recipes represent a direct dependency of one variable on the other. one variable is always the other variable multiplied by a constant factor.
m = cups of milk
f = cups of flour
m = n×f
2 = n×(6 1/4) = n×(6×4 + 1)/4 = n×25/4
8 = 25n
n = 8/25
now, f = 43 3/4 = (43×4 + 3)/4 = 175/4
so,
m = 8/25 × 175/4 = (8×175)/(25×4) = 2×7 = 14
you will need 14 cups of milk.
Subtract and simplify.
With the help of subtraction we can say that the answer is =21/15
What is subtraction?The process of subtracting one number from another is called subtraction. The way to calculate the difference between two numbers is by using the basic arithmetic operation of subtraction, which is represented by the symbol (-).The operation of subtraction is used to calculate the difference between two numbers. If you remove a few items from a collection of things, the group will get smaller.Acc to the question-
32/15 - 11/15as the denominator is same21/15more simplifying we get = 1.4Hence,The answer is = 21/15
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Answer:
21/15
Step-by-step explanation:
Given problem,
→ (32/15) - (11/15)
Let's solve the given problem,
→ (32/15) - (11/15)
→ (32 - 11)/15
→ 21/15
Hence, the answer is 21/15.
Mrs. Reed is buying seeds to start a vegetable garden. She purchases 12 packets of bean seeds, 15
packets of carrot seeds, and 2 packets of corn seeds. Choose Yes or No to tell if each statement about
the purchase is correct.
Step-by-step explanation:
Mrs. Reed is buying seeds to start a vegetable garden. She purchases 12 packets of bean seeds, 15
packets of carrot seeds, and 2 packets of corn seeds. Choose Yes or No to tell if each statement about
the purchase is correct.
6.) One clothing Store has a dress for $6.20
and a belt for $3.50. Customers
buy 3 dresses for $15.20. How much
would be saved by buying 3 dresses
Than by buying per piece?
5y=15x+10 but in standard form?
Answer:
y=3x+2
Step-by-step explanation:
Divide by 5 on all sides.
3x-y=-2
Step-by-step explanation:
Given that capital is fixed, what do you figure is the marginal cost or additional cost of producing another:
haircut
sandwich
Ferris Wheel ride
The marginal cost is the labor utilized in order to provide an additional cost of a haircut.
What is the marginal cost?The marginal cost is the extra cost of generating one additional unit of output.
The example of a haircut, the marginal cost is the labor utilized in order to provide an additional haircut; employees offer their time, which is valued in pay, resulting in the marginal cost of labor.
Thus, in all circumstances, such as the sandwich and Ferris Wheel, there will be an additional labor cost because labor is necessary to make each of the items.
Change in cost / Change in quantity Equals Marginal cost.
The firm will incur an increased labor expense because of one more haircut, and the laborer will be paid more because of the rise in one more quantity of haircut delivered. This pay rise is the marginal cost.
Thus, the marginal cost is the labor utilized in order to provide an additional cost of a haircut.
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4). $1,200, 3.9%, 8 months
The simple interest on $1,200, 3.9%, 8 months is $31.356.
How to calculate the interest?From the informationm, we want to calculate the simple interest of the amount that is given.
The simple interest is calculated thus:
Simple interest = PRT / 100
where
P = Principal = $1200
R = Rate = 3.9%
T = Time = 8 months = 8/12 = 0.67 years
The interest will be:
Simple interest = PRT / 100
Simple interest = (1200 × 3.9 × 0.67) / 100
Simple interest = 31.356
The interest is $31.356.
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Complete question
Calculate the simple interest on $1,200, 3.9%, 8 months
Write the word sentence as an equation. Then solve. The sum of a number y and −3 is −8. Equation: Solution: y=
Considering the definition of an equation and the way to solve it, the equation is y +(-3)=-8 and the solution is -5.
Definition of equationAn equation is an algebraic equality in which letters appear with unknown value.
In an equation appears:
The members, which are each of the expressions that appear on both sides of the equal sign The terms, which are the addends that form the members of an equation.The solution of a equation means determining the value that satisfies it. In this way, by changing the unknown to the solution, the equality must be true. To solve an equation, keep in mind:
When a value that is adding, when passing to the other member of the equation, it will subtract.If a value you are subtracting goes to the other side of the equation by adding.When a value you are dividing goes to another side of the equation, it will multiply whatever is on the other side.If a value is multiplying it passes to the other side of the equation, it will pass by dividing everything on the other side.Equation and solution in this caseBeing "y" a number, and knowing that sum of a number and -3 is -8, the equation in this case is:
y + (-3)= -8
Solving:
y -3= -8
y= -8 +3
y= -5
Finally, the number "y" is -5.
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How do I solve this question
Answer:
the answer is down there
I dont understand, please help
The slope is 5 and the y-intercept is -2000.
(b) The slope tells us about the rate of change in weekly profit and the y-intercept tells us about the minimum profit.
(c) The situation can be modeled as y = 5x -200. Here, y= profit per week and x= number of customers per week.
(d) If the state world roller rink reached a maximum capacity of 2,500 customers per week then the weekly profit will be $10,500.
What is meant by slope intercept form?In order to make the y-intercept (where the line crosses the vertical y-axis) and slope (steepness) immediately apparent, a line's equation must be written in the slope-intercept form. This version is frequently known as y = mx + b. the equation of a straight line in the form of y = mx + b, where m is the line's slope and b is its y-intercept. The slope intercept formula y = mx + b is used when you know the line's slope and the provided point is also the line's y-intercept (0, b). y = mx + b, where m represents the line's slope, is the slope-intercept form of a line.
(a) Consider two points
(x₁, y₁) = (400, 0)
(x₂, y₂) = (500, 500)
The slope is given as
m = (y₂ - y₁)/ (x₂ - x₁)
= (500-0)/(500-400)
= 500/100
= 5
To find y- intercept put (x, y) = (400,0) in y= mx+b (slope-intercept form of a line)
0 = 5(400)+b
0 = 2000 + b
b= - 2000
(b) The slope tells us about the rate of change in weekly profit and the y-intercept tells us about the minimum profit.
(c) Let the number of customers per week = x
And the profit per week = y
Then, the situation can be modeled using slope-intercept form as
y = 5x -200
(d) Put x= 2500 in y = 5x -200
y = 5(2500)-2000
= 12,500-2000
= 10,500
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19.)x+ tan (xy) = 0
The value of y is, [tex]y = \frac{tan^-^1(-x) + \pi n}{x}[/tex].
What is tangent function?
One of the primary six trigonometric functions, the tangent function is typically expressed as tan x. When considering the angle in a right-angled triangle, it is the ratio of the opposite side to the adjacent side.
Consider, the given function
x + tan(xy) = 0
Subtract x from both sides,
x + tan(xy) - x = -x
tan(xy) = -x
Apply tan inverse on both sides,
[tex]xy = tan^-^1(-x) + n\pi[/tex] (Tangent function is a periodic function)
Divide both sides by x,
[tex]y = \frac{tan^-^1(-x)}{x} + \frac{n\pi }{x}[/tex], x ≠ 0
Hence, the value of y is, y = [tex]y = \frac{tan^-^1(-x)}{x} + \frac{n\pi }{x}[/tex].
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Mia was out at a restaurant for dinner when the bill came. Her dinner came to $28. After adding in a tip, before tax, she paid $37.24. Find the percent tip.
The percentage of the tip will be equal to 24.81%.
What is the percentage?The percentage is defined as representing any number with respect to 100. It is denoted by the sign %. The percentage stands for "out of 100." Imagine any measurement or object being divided into 100 equal bits.
Given that Mia was out at a restaurant for dinner when the bill came. Her dinner came to $28. After adding in a tip, before tax, she paid $37.24.
The percentage tip will be calculated as,
P = ( (37.24 - 28 ) / 37.24
P = 9.24 / 37.24
P = 0.2481 x 100
P = 24.81%
Therefore, the percentage of the tip will be equal to 24.81%.
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Solve for j ??????????????????????????
Answer:
j=24
Step-by-step explanation:
j/8 - 2 = 1
j/8 - 2 + 2 = 1 + 2
j/8 = 3
8 * j/8 = 8 * 3
j=24
Karen is waiting for a pot of soup to cook off before serving it. After 4 3/4 min the soup has cooled from 100°C to 78° C. What was the average change in temperature each minute.
Answer:
Karen is waiting for a pot of soup to cool off before serving it. After 4 min the soup has cooled from 100°C to 78°C. What was the average change in temperature each minute?
✓ Answer:It went down 5.5°C a minute.Step-by-step explanation:You have to look for the difference of 100 and 78, which is …
PLEASE HELP!!!
Dianelys accepted a new job at a company with a contract guaranteeing annual raises. In the first year, Dianelys' salary will be $40000, and she will get a raise of $2500 every year. Make a table of values and then write an equation for S,S, in terms of n,n, representing Dianelys' salary after working nn years for the company.
Number of Years at the Company Dianelys' Salary (Dollars)
00 40000\hspace{3px}\color{green}{\checkmark}40000
11 42500\hspace{3px}\color{green}{\checkmark}42500✓42500
22 45000\hspace{3px}\color{green}{\checkmark}45000✓45000
33 47500\hspace{3px}\color{green}{\checkmark}47500✓
1. The table of values for Dianely's salary can be represented for 4 years as follows:
Year Salary
1 $40,000
2 $42,500
3 $45,000
4 $47,500
2. The equation that models Dianely's salary after n years is S = 40,000 + 2,500n.
What is an equation?An equation is a mathematical statement stating that two mathematical expressions are equivalent or equal.
For instance, given the number of years, one can claim that Dianely's salary will be a given amount based on the above equation.
Equations involve variables, numbers, and the use of the equation sign (=) with some mathematical operands.
Initial salary = $40,000
Salary raise per year = $2,500
Disney's salary after n years in equation form, S = 40,000 + 2,500n.
Table of Values for Dianely's Salary:
Year Salary
1 $40,000
2 $42,500 (40,000 + 2,500)
3 $45,000 (42,500 + 2,500)
4 $47,500 (45,000 + 2,500)
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A resort has 380 rooms with space for 6 people. Estimate the greatest number of people who could be in these rooms at the same time. Explain your thinking to a friend or family member.
Using the multiplication operation, the greatest number of people who could be in the 380 rooms with space for 6 persons at the same time is 2,280.
What is multiplication operation?Multiplication operation is one of the basic mathematical operations, including subtraction, addition, and division.
A multiplication operation involves applying the multiplier to the multiplicand to result in a product.
The total number of rooms in the resort = 380
The number of people per room = 6
380 x 6 = 2,280
Thus, by multiplication, if 6 persons occupy each of the 380 rooms, the resort will have 2,280 persons at a time.
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The regression equation for 2 variables is y = -2.6 x + 10 If the value of R2 is 0.810, what is the value of R?
If the value of R² in the regression equation is 0.810, the value of R is 0.9
How to determine the value of r?From the question, we have the following parameters that can be used in our computation:
Regression equation: y = -2.6x + 10
Value of R2 = 0.810
Rewrite the above parameters properly
So, we have the following representation
y = -2.6x + 10
R² = 0.810
The variable r² represents the coefficient of determination
Recall that
R² = 0.810
This gives
r² = 0.810
Take the square roots of both sides
r = 0.9
Hence, the value of r is 0.9
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