The value of x is 8 cm.
What is the area of a rectangle?The area of a rectangle is the space occupied by the rectangle inside its perimeter. A rectangle's area is calculated by multiplying its length by its width.
Given:
Length of rectangle = 20 cm
Width of rectangle= x cm
Area of rectangle = length × width
= 20x cm²
The dimensions of the smaller rectangle cut out of it are,
Length = 16cm
Width = x-3
Area of the smaller rectangle = length × width
= 16(x - 3) cm²
The area of the shaded portion will be equal to the difference between both areas which is given as 80 square centimeters.
20x - 16(x-3) = 80
Now, we need to solve this equation to obtain the value of x.
20x - 16x + 48 = 80
4x = 80 - 48
4x = 32
x = 32/4
x = 8
Therefore, the value of x is 8 cm.
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The admission fee at an amusement park is $2.50 for children and $5.80 for adults. On a certain day, 380 people entered the park, and the admission fees collected totaled 1544 dollars. How many children and how many adults were admitted?
number of children equals
number of adults equals
Answer:
200 children.
180 adults.
Step-by-step explanation:
let x=Children and y=Adults
create 2 equations.
x+y = 380
2.50x+5.80y = 1544
solve for x in the first equation and plug into the second equation.
x = 380-y
2.50(380-y) +5.80y = 1544
distribute and simplify.
950 + 3.3y = 1544
simplify
3.3y = 594
y = 180
plug y back into first equation and you get that there were 200 children.
n
22
When two musical notes are a "fifth" apart, the frequency of the lower
note is the frequency of the higher note. Using f as the frequency of
the higher note, write an expression for the frequency of the lower
note.
A physics concept called frequency describes how many cycles a wave completes each second. As a result, the following expression is used to get the lower note's frequency [tex]\frac{2}{3}[/tex] f
What is wave ?A wave is a phenomena that moves through a physical medium without leaving any lasting impression on the molecules therein. Energy is transferred from one end of the medium to the other. Sound waves, light waves, electromagnetic waves, etc. are some examples.
Frequency develops during wave propagation. This can be characterized as the number of cycles a wave makes in a second. It's also measured in Hertz.
Let f stand for the upper note's frequency and for the lower note's frequency we have [tex]f_{1}[/tex]. We therefore have;
[tex]f_{1}[/tex] =[tex]f\frac{2}{3}[/tex]
Therefore, the expression for the frequency of the lower notes is [tex]\frac{2}{3}[/tex] f.
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how could you use a graph of a proportional relationship to find any ratio in the the proportional relationship why does this work?
When the graph of a relationship shows a line that passes through the origin, then it is proportional.
How to illustrate the information?If a connection's graph is a line that runs through its origin, it is proportional. If there isn't a line or ray that does this, the ratio isn't proportional. The equation for the proportionality constant is K = y/x.The equation that describes the slope of a straight line in relation to its origin is identical to this one.
When the graph of a proportional connection passes through the origin, any ratio in the proportional relationship can be found.
A relationship is proportional if its graph is a line or ray that passes through the origin. It is not proportional if the line or ray does not go through the origin.
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Twice a number is 34 less than 4 times the number. Find the number.
The number is 17.
Let's assume that the number is x.
So according to the question twice a number is 34 less than 4 times the number.
Then, the equation formed will be as follows
⇒ 2x = 4x - 34
Solving the equation we get the value of x which is the respective number.
Combine the like terms then proceed with calculations.
⇒ 4x - 2x = 34
⇒ 2x = 34
Divide both sides of the equation by 2.
⇒ x = 17
Hence the number whose twice is 34 less than 4 times the number is 17.
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EEKKKK HELP MEEEEEEE I ONLY HAVE 1 MINUTEEEEEE
Estimate and then solve 8,784 ÷ 61 = ___.
3,984 is what % of24.9? how do you solve it?
Answer:
16000
Step-by-step explanation:
3984:24.9*100 =
(3984*100):24.9 =
398400:24.9 = 16000
URRGENT PLEASE HELP!!!! DOC ATTACHED
1. A conditional statement can be written as
If it is sunny then there is daylightThe hypothesis is: It is sunny
The conclusion is: there is daylight
2. The converse of the conditional statement
If there is daylight then it is sunny3. The inverse of the conditional statement
If it is not sunny then there is no daylight4. The contrapositive of the conditional statement
If there is no daylight then it is not sunny5. The biconditional statement and can be written because the statement and the converse are both true
6. The biconditional statement is
it is sunny if and only if there is daylightHow to identify a conditional statementA conditional statement is a term used in logic that refers to the type of statement that has "if-then". It is sometimes called if-then statements. Conditional statement are of two parts the hypothesis required to ensure that the conclusion. Other forms of conditional statements are
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The area of a rectangle is 69.75 square inches. The rectangle has a length of 9.3 inches. What is the width of the rectangle?
Enter the correct answer in the box.
inches
Answer:7.5 inches
Step-by-step explanation:
69.75/9.3=7.5
0.25 meses en días y horas.
Answer:
0.25 Months =7.6099 Days= 7 Days, 14 Hours, 38 Minutes and 19 Seconds
In Spanish
0.25 Meses =7.6099 Días= 7 Días, 14 Horas, 38 Minutos y 19 Segundos
I need this answer in 1 minute I am giving all my points away
Answer:625/27
Step-by-step explanation:
[tex]\huge\text{Hey there!}[/tex]
[tex]\mathsf{\dfrac{5^4}{3^3}}[/tex]
[tex]\mathsf{= \dfrac{5\times5\times5\times5}{3\times3\times3}}[/tex]
[tex]\mathsf{= \dfrac{25\times25}{9\times3}}[/tex]
[tex]\mathsf{= \dfrac{625}{27}}[/tex]
[tex]\huge\text{Therefore, your answer is: \boxed{\mathsf{\dfrac{625}{27}}}}\huge\checkmark[/tex]
[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]
#27 please show work THANK YOU!!
Parametric equation of the give cartesian equation x(y) = 3log(y)+y is
x(t) =3log(t)+t
y(t) = t
The given cartesian equation x(y) = 3log(y)+y
The cartesian equation is an equation of the curve in which variables are the Cartesian coordinates of a point on the curve or surface.
Here we have to convert the cartesian equation into parametric equation.
We can converting the cartesian equation into parametric equation by changing the independent variable in the cartesian equation to t.
The cartesian equation x(y) = 3log(y)+y
Here x is expressed as the function of y.
Define y = t
x(t) = 3log(t)+t
y(t) = t
Hence, the Parametric equation of the give cartesian equation x(y) = 3log(y)+y is
x(t) =3log(t)+t
y(t) = t
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What is infinity? Does it ever end?
Answer:
It is forever, and it does not end.
Step-by-step explanation:
Infinity is the concept of no beginning and no end. It is the concept of all things and everything. So when you think of a deity ( Ex. God ) you think of them being infinite. They have no beginning or end, and have limitless possibilities. They live forever, and they can do anything. That is infinity in a nutshell.
Hope this helps.
A = $16,000, r= 11.0%, t = 5
Answer:
9495.221
Step-by-step explanation:
16000=Pe^(0.11x5)
if point c divides a directed line segment from point A to point B in a 1 : 5 ratio, what are the coordinates of point B?
The location of the point B on the line with the endpoints is 63
How to determine the coordinates of the segment?On the segment, we have the following endpoints
A = -3
C = 8
Rewrite the endpoints of the line segment as
A = (-3,0) and C = (8,0)
The ratio of the line is given as
Ratio, A : B = 1 :5
This means that
Point C = A/A + B
So, we have
C = 1/1 + 5
Evaluate
C = 1/6
The coordinate of point C on the line segment is calculated using
Point C = C * (B - A) + A
So, we have
8 = 1/6 * (B + 3) - 3
This gives
1/6 * (B + 3) = 11
So, we have
B + 3 = 66
Subtract 3
B = 63
Hence, the coordinate of the point B on the line segment is 63
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Possible question
if point c divides a directed line segment from point A to point B in a 1 : 5 ratio, what are the coordinates of point B?
A = -3 and C = 8
i need help, please
Answer:
[tex]\frac{51}{4}[/tex]
Step-by-step explanation:
Since they are similar we can set up direct proportions
FE:CB=DE:AB
y:6=17:8
[tex]\frac{y}{6} =\frac{17}{8}[/tex]
cross multiply
8y=17*6
divide by 8 each side
[tex]\frac{51}{4}[/tex]
word problem for 4x - 3 = 17?????
Answer: My bill was 17 dollars. I gave four tokens of equal monetary value to the cashier who gave me in return 3 one dollar bills. How much was each token worth?
Step-by-step explanation: 4x - 3 = 17.
add 3 to both sides
4x = 20
x = 5. Each token was worth $5.
Pls Help soon as possible
Answer:
The value of the 8 in the front is 800 000 and the value of the second is 80 000. The front value is ten times as big as the second value.
Step-by-step explanation:
For the function f(x)=x2−9, find (a) f(x+h), (b) f(x+h)−f(x), and (c) f(x+h)−f(x) h.
Step-by-step explanation:
a)
[tex]f(x+h) = 2(x+h)-9[/tex]
[tex]f(x+h)=2x+2h-9[/tex]
b)
[tex]f(x+h)-f(x)=2x+2h-9-(2x-9)[/tex]
[tex]f(x+h)-f(x)=2x+2h-9-2x+9[/tex]
[tex]f(x+h)-f(x)=2h[/tex]
c)
[tex]f(x+h)-f(x)h=2x+2h-9-h(2x-9)[/tex]
[tex]f(x+h)-f(x)h=2x+2h-9-2hx+9h[/tex]
[tex]f(x+h)-f(x)h=-2hx+11h+2x-9[/tex]
someone help pleasee
no answer for this question
Find the product. Write your answer as a mixed number in simplest form.
4 × 1 8/9
Answer: 68/9 which simplifies into 7 6/9
A simple random sample of 20 items resulted in a sample mean of 15. The population standard deviation is = 9. Round your answers to two decimal places.
Based on the number of items in the simple random sample, and the sample mean, the standard error of the mean can be found to be 1.12
How to find the standard error?The standard error of a simple random sample can be found by the formula:
= Population standard deviation / √Number of items in simple random sample
Solving for the standard error gives:
= 5 / √20
= 5 / 4.4721359549995793928183473374626
= 1.118
= 1.12
We can therefore conclude that the standard error of this sample is 1.12.
Rest of the question:
What is the standard error of the mean?
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i need help with this
After solving the equation the value of x is 13/5.
What are equations?A mathematical equation is a formula that uses the equals sign to express the equality of two expressions. As in 3x + 5 = 15, for instance. Equations come in a variety of forms, including linear, quadratic, cubic, and others. The point-slope form, standard form, and slope-intercept form are the three main types of linear equations.So, we can see that both triangles are congruent under the SAS condition.
△ABC ≅ △ADEAB ≅ AD (Given)AC ≅ AE (Given)∠A = ∠A (Common angle)Since both triangles are congruent, then we can conclude that side BC will be congruent to side DE under CPCT (Corresponding parts of congruent triangles).
Then, we can form the equation:
5x - 2 = 11Now, solve the equation as follows:
5x - 2 = 115x = 11 + 25x = 13x = 13/5Therefore, after solving the equation the value of x is 13/5.
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In the figure below, X lies between W and Y.
Find the location of X so that the ratio of WX to XY is 1 to 7
Since , X lies between W and Y, the location of X so that the ratio of WX to XY is 1 to 7 is 7.01.
What is the location position about?In regards to math's, position is seen as the looking through a given location and it is one that is pertaining to another kind of thing or the lines.
Note that from the question:
W = -31
Y= -7
So - 7 - (-31) = 38
Now:
WX: XY = 1 :7
XY = 7K
WZ = K
Then 7k + K = 38
K = 38/7
K = 5.43
So XY = 5.43 x 7
= 38.01
So position of X = 38.01 + (-31)
X = 7.01
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What does it mean when the point is on the line on a graph?
Answer:
When data points are marked on the chart, all data points within a single dependent variable are connected with a line, making it very useful tool for analyzing changes over time for one or more variables.
Step-by-step explanation:
I need to find the independent and dependent quantity and a statement that describes the relationship between the independent and dependent quantities
We have two relations between length of the trench and time.
Case: we want to know how many feet we can dig in a certain amount of time.
In this case, and in most of the cases, time is the independent quantity.
Therefore, the dependent quantity is the other variable: length of the trench.
For example, we can write a proportional relationship between time (x) and length (y) as:
[tex]y=k\cdot x[/tex]We know that when x=40 min, y=36 ft, according to the machine advertisement.
Then, we can find k as:
[tex]k=\frac{y}{x}=\frac{36}{40}=0.9\text{ ft/min}[/tex]And we can write the relation as:
[tex]y=0.9\cdot x[/tex]Answer: the independent quantity is time (in minutes).
NOTE:
Which variable is which depends on what we want to calculate.
If we want to know how much it will take to make a certain length of trench, the independent quantity is the length of the trench. The dependent variable is, in this case, time, as we calculate it from the information about the length of the trench.
If we want to calculate the length of the trench we can dig in a certain time, the independent quantity is time and the dependent quantity is the length of the trench.
Factor and SOLVE the following quadratic, 3x^2 + 13x = -4, and select all solutions that apply.-1 4121/3-1/3-4
the equation given
we can rewrite the equation as
[tex]3x^2+13+4=0[/tex]to solve this question, we can use any of the given mehod known to solve quadratic equations which are
1. factorization
2. completing the squares
3. using quadratic equation
for the purpose of this tutoring session, i'll use quadratic equation also know as quadractic formula
the formula is given as
[tex]x=-b\pm\frac{\sqrt[]{b^2-4ac}}{2a}[/tex]next we proceed to identify the variables
[tex]\begin{gathered} 3x^2+13x+4 \\ a=3 \\ b=13 \\ c=4 \end{gathered}[/tex]now we can input the values into the equation (formula) above
[tex]\begin{gathered} x=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a} \\ x=\frac{-13\pm\sqrt[]{13^2-4(3)(4)}}{2(3)} \\ x=\frac{-13\pm\sqrt[]{169-48}}{6} \\ x=\frac{-13\pm\sqrt[]{121}}{6} \\ x=\frac{-13\pm11}{6} \\ x=-\frac{13+11}{6} \\ or \\ x=-\frac{13-11}{6} \\ x=-\frac{2}{6} \\ or \\ x=-\frac{24}{6} \\ x=-\frac{1}{3} \\ or \\ x=-4 \end{gathered}[/tex]from the calculations above, x = -1/3 or x = -4
What is sector length?
Sector length is the distance between two points along a section of a curve.
Answer:
Arc length is calculated using the relation : Arc length = l = (θ/360) × 2πr. Therefore, Perimeter of a Sector = 2 Radius + ((θ/360) × 2πr )
Mike decided to rent an airpod from from applerental.com. The website advertised an Airpod rental of $5 a week with a down payment of $10.
How much is the total cost if Mike rented the Airpod for 6 months? (hint: there are 4 weeks in a month)
If the website advertised an Airpod rental of $5 a week with a down payment of $10, then the total cost he paid if he rented the Airpod for 6 months is $130
The amount he paid for down payment = $10
The rent amount for the airpod for one week = $5
We know,
There are 4 weeks in a month
Number of weeks in 6 month = 6×4
= 24 weeks
The total amount her paid for if he rented the airpod for 6 months = The amount he paid for down payment + (The rent amount for the airpod for one week ×24)
= 10+5×24
= 10+120
= $130
Hence, if the website advertised an Airpod rental of $5 a week with a down payment of $10, then the total cost he paid if he rented the Airpod for 6 months is $130
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One dealer in sports shirts offers a dozen at 5000 list price, less a 15% discount. A second offers the same shirts for 5200 pesos a dozen less a 20% discount. Which is the better offer and by how much?
Call the two offers offer A and B respectively.
For offer A, the list price is 5000 pesos with a 15% discount. So you will pay:
[tex]A=5000(0.85)=4250\text{ pesos}[/tex]For offer B, the list price is 5200 with a 20% discount. So you will pay:
[tex]B=5200(0.8)=4160\text{ pesos}[/tex]So the first deal is costing 4250 pesos and second one costs 4160 pesos.
Hence the second deal is better by 4250-4160= 90 pesos.
The second deal is the better deal by 90 pesos.
-5(x-5)=-5x+27
What’s the answer
Answer:
x = 26/5
Step-by-step explanation:
Distribute
5x - 25 : -5x + 27
Add 25 to both sides
5x = -5x +52
Add 5x to both sides
10x = 52
Divide by 10
x = 52/10
Simplify
x = 26/5