The area of the rectangular arena can be represented as A = (8y2 - 18y) square feet.
Here, we are given the dimensions of a rectangular arena, which are as follows-
Length = 4y - 9 feet
width = 2y feet
The area of a rectangle is given by the formula-
Area of a rectangle = length x breadth
Thus, in this case, area (A) can be calculated as follows
A = (4y - 9) * 2y
Now, we simplify the equation-
A = (4y)(2y) - 9(2y)
A = 8[tex]y^{2}[/tex] - 18y
Thus, the area of the rectangular arena can be represented by the following equation- A = (8[tex]y^{2}[/tex] - 18y) square feet.
Learn more about area here-
brainly.com/question/25292087
#SPJ9
Find the slope of the line passing through the points (-4, 6) and (3, -8).
11
3 08
X
Undefined
Ś
[tex](\stackrel{x_1}{-4}~,~\stackrel{y_1}{6})\qquad (\stackrel{x_2}{3}~,~\stackrel{y_2}{-8}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{-8}-\stackrel{y1}{6}}}{\underset{run} {\underset{x_2}{3}-\underset{x_1}{(-4)}}} \implies \cfrac{-14}{3 +4}\implies \cfrac{-14}{7}\implies -2[/tex]
Find the length
Of the three line segments that form the triangle pictured below. The units of the grid each represent one centimeter.
4. Show your work or discribe how you found the length of the diagonal segment AB
5. Give the x-coordinate of the midpoint of AC. X=?
6.( same thing as 5 just with BC)
7.(same thing as 6,and 5 just with AB)
Step-by-step explanation:
for the lengths of BC and AC we can count the squares, because the lengths of these lines are the sum of the side lengths of each inducing square.
1.
BC = 7 - -2 = 7 + 2 = 9 cm
2.
AC = 13 - 1 = 12 cm
3.
but for AB we cannot do that, because AB consists of the lengths of all the diagonals of the squares. and a diagonal must always be longer than any side.
just look at the triangle : it is clear that AB must be longer than AC.
no, for a line that goes across the grid squares we need other methods.
in our case, we have a right-angled triangle and can use Pythagoras
c² = a² + b²
c being the Hypotenuse (the side opposite of the 90° angle), a and b being the legs of the triangle (enclosing the 90° angle).
AB is in our case the Hypotenuse, and we get
AB² = 12² + 9² = 144 + 81 = 225
AB = sqrt(225) = 15 cm
4.
as explained, we used Pythagoras.
5.
the coordinates for a midpoint between 2 points (x1, y1) and (x2, y2) are simply
((x1+x2)/2, (y1+y2)/2)
A = (13, -2)
B = (1, 7)
C = (1, -2)
midpoint AC = ((13+1)/2, (-2 + -2)/2) = (14/2, -4/2) =
= (7, -2)
the x coordinate is 7.
6.
midpoint BC = ((1+1)/2, (7+ -2)/2) = (2/2, 5/2) = (1, 2.5)
the y coordinate is 2.5
7.
midpoint AB = ((13+1)/2, (-2+7)/2) = (14/2, 5/2) =
= (7, 2.5)
What is the value of the expression 8^2+3\times78
2
+3×7 ?
The value of the expression 8² + 3 × 78² + 3 × 7 will be 18337.
What is the value of the expression?When the relevant factors and natural laws of a mathematical model are given values, the outcome of the calculation it describes is the expression's outcome.
The expression is given below.
⇒ 8² + 3 × 78² + 3 × 7
Simplify the expression, then we have
⇒ 8² + 3 × 78² + 3 × 7
⇒ 64 + 3 × 6084 + 21
⇒ 85 + 18252
⇒ 18337
The value of the expression 8² + 3 × 78² + 3 × 7 will be 18337.
More about the value of expression link is given below.
https://brainly.com/question/23671908
#SPJ1
HELP HELP HELPP i'll mark brainliest
Solve for x: 3( + 1) − 7( − 1) = 3(2 − 4)
Answer:
10 = -6
Step-by-step explanation:
Answer:
X = - 39
Step-by-step explanation:
x divided by 3x 1 - 7(-1)=3(2-4)X(1/3)+7-3(-2)X times 1/3 +7+-3 x2x/3+7-6x+21/ 3 = -6x+21 + (-3)6X +21 = -3x6x+21 = - 18(x+21) + (-21)= -18 +(-21)X+21-21= - 18-12ANSWER: x+3x7/3 = - 6
Hope this helps u : )
The dot plot shows predictions for the winning time in the 200 meter sprint. the winner finished the race in 22.2 seconds. what is the greatest percent error among the predictions?
The greatest percent error among the predictions time of the race is: 3.15 %
Although part of your question is missing, you might be referring to this dot plot that shows the predictions for the winning time (see image attached)
To solve this exercise, we have to apply the percentage formula:
Error (%) = [(prediction time – real time) / real time] * 100
Information about the problem:
Prediction time= 22.9 secondsreal time =22.2 secondsError (%) =?Applying the percentage formula, we have:
Error (%) = [(prediction time – real time) / real time] * 100
Error (%) = [(22.9 seconds – 22.2 seconds) / 22.2 seconds] * 100
Error (%) = [(0.7 seconds) / 22.2 seconds] * 100
Error (%) = 0.0315 * 100
Error (%) = 3.15 %
What is a percentage?Percentage is defined as the number that represents a ratio of a total that is divided by 100 equal parts. It is represented by the symbol %.
Learn more about percentage at: brainly.com/question/24877689
#SPJ4
what is the sum of all the positive integers from sqrt(14 to sqrt(80
Sum of all the positive integers from √14 to √80=30
Definition of a perfect square-A number system that can be stated as the square of a specific number from the same system is called a perfect square.Assume that N may be expressed as the product of x and x = x²,if x is a perfect square of a number N. Square roots can be used to understand this in another way. We compute the square root of a given number to determine if it is a perfect square or not. The supplied number is a perfect square if the square root is a whole number.However, if the square root value is not a whole number, the given number is not a perfect square.Now according to given question we have to find sum of all the positive inetegers between √14 to √80
√14=3.74165 & √80=8.94427Positive integers between 3.74-8.94 are 4,5,6,7 & 8Sum of 4+5+6+7+8=30∴Sum =30
LEARN MORE ABOUT PERFECT SQUARE HERE:
https://brainly.com/question/385286
#SPJ9
a book weighs 4 3/8 pounds. a store needs to mail 5 copies of the book.
create an equation to find how many pounds the books weigh in all.
Write an equation for the number of miles y it travels in x hours how many miles will it travel in 3
The equation for the given statement is y=3x.
The given equation is the number of miles y it travels in x hours.
What is an equation?In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.
We need to find the number of miles travelled in 3 hours.
Now, using the formula Distance = Time × Speed
y = 3x
Therefore, the equation for the given statement is y=3x.
To learn more about an equation visit:
https://brainly.com/question/14686792.
#SPJ1
Me ayudan urgente por favor y gracias
The result of the linear expression [tex]5-\frac{t}{3}[/tex] is 1.
What is linear expression?
An algebraic expression that uses either a constant or a variable raised to the first power for each term is known as a linear expression. This means that none of the exponents can be greater than 1.
Given [tex]5-\frac{t}{3}[/tex]
Also given that t = 12
Substitute the value of t and we get
[tex]5-\frac{12}{3}\\=5-4\\=1[/tex]
Therefore, the result of the linear expression [tex]5-\frac{t}{3}[/tex] is 1.
To learn more about linear expression from the given link
https://brainly.com/question/2030026
#SPJ9
What value correctly fills in the blank so that the expressions are equivalent?
32 + 72 = blank x (4 + 9)
4
8
12
13
Answer: The answer is 8 because you add 32 + 72 and get 104 x and then 4 +9 = 13 then you divide 104 divided by 13 = 8
Answer:
8, because you add 32 and 72, which will get 104x and then 4+9 which is 13 then you divide 104 divided by 13 = 8
Step-by-step explanation:
hope this helps!
If principal=p,rate of interest=R and time=T,then write the formula to find the compound amount
It is given that P = principal, R = rate of interest and T = time
Formula to find compound interest is:
A = P(1 + R/100)^T
where A = amount received after n years
P = principal amount invested
R = rate of interest
T = time for which the amount is invested
The interest earned on savings that are computed using both the original principal and the interest accrued over time is known as compound interest.
It is thought that Italy in the 17th century is where the concept of "interest on interest" or compound interest first appeared. It will accelerate the growth of a total more quickly than simple interest, which is solely calculated on the principal sum.
Money multiplies more quickly thanks to compounding, and the more compounding periods there are, the higher the compound interest will be.
Learn more about compound interest:
https://brainly.com/question/13155407
#SPJ9
PLS HURRY DUE A HOUR AGO
1. Show an example of two numbers that are additive inverses.
Step-by-step explanation:
Greetings !
Definition:-In mathematics, the additive inverse of a number a is the number that, when added to a, yields zero. This number is also known as the opposite, sign change, and negation.
For example, the additive inverse of 7 is −7, because 7 + (−7) = 0, and the additive inverse of −0.3 is 0.3, because −0.3 + 0.3 = 0. Similarly, the additive inverse of a − b is −(a − b) which can be simplified to b − a. The additive inverse of 2x − 3 is 3 − 2x, because 2x − 3 + 3 − 2x = 0.
Hope it helps!!!
what 30x30x1,000 bydb3yuehwu
the height of a triangle is twice its base the area is 144cm³ find the base
Answer:
12
Step-by-step explanation:
Area of a triangle = 1/2*b*h
[tex]144=(\frac{1}{2})*(2x)*(x)\\12=x[/tex]
Which expression is equivalent to -3[4*-0.50]?
–12x – 1.50
–12x + 1.50
–12x – 2.50
–12x – 3.50
In given expressions no one is equivalent to the expression -3 [4 × -0.50]
Given,
The expression : -3 [4 × -0.50]
We have to find the expression equivalent to the above expression from the given options.
Solve the expression:
-3 [4 × -0.50] = -3 × -2 = 6
Now we can solve the expressions given in the options:
1) -12 × -1.50 = 18
Not equal to the given expression
2) -12 × 1.50 = -18
Not equal to the given expression
3) -12 × -2.50 = 30
Not equal to the given expression
4) -12 × -3.50 = 42
Not equal to the given expression
So, we can conclude that, there is no equivalent expression in the options for the expression -3 [4 × -0.50]
Learn more about expressions here:
https://brainly.com/question/28170201
#SPJ1
Pls help me ASAP. NO ignoring, just give me the answer to my first question.
Unit rate is a rate for one of something. True or false? (NO IGNORING PLEASE)
Answer:
Step-by-step explanation:
True
TRUE AHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHH
5 x 3 x 45 x 67 x 34 x 98 x 19 x 1009
Answer:
2.8888722e+12
Step-by-step explanation:
calculator
10) Your friend has a play tepee. The tepee
has a radius of 4 feet and a height of 6
feet. What is the volume of the tepee?
The volume of the tepee is 100.48 feet³
The formula for the volume of tepee is same as the volume of cone which is given as :
V = 1/3 πr²h (1)
where V = volume
r = radius of the tepee
h = height of the tepee
According to the question we have been given that
radius = 4 feet
height = 6 feet
Putting the required values in equation (1) we get
V = 1/3 π (4)²(6)
= 1/3 (3.14)(96)
= 301.44/3
= 100.48 feet³
Hence the volume of the tepee is 100.48 feet³
Learn more about volume of cone here : https://brainly.com/question/13677400
#SPJ9
Solve each equation. Check your answers.
2 ln 2 x²=1
After solving the equation 2 x² the value of x is equal to 1 [tex]\sqrt{1/2}[/tex]
we are asked to find x in 2x² = 1
⇒ 2x² = 1
⇒ x² = 1/2
⇒ x = [tex]\sqrt{1/2}[/tex]
So, x is equal to [tex]\sqrt{1/2}[/tex]
How to solve an equation?To solve linear equations, utilize the steps that are provided below.
Remove parentheses from each side of the equation and combine similar terms to make it simpler.To separate the variable term on one side of the equation, use addition or subtraction.To find the variable, use division or multiplication.The common denominator can be multiplied by each side of the equation to eliminate fractions.Lets take an example of solve z for 7z – (3z – 4) = 12
Here is no multiplication or division, so this will be easy to solve
⇒ 7z – (3z – 4) = 12
⇒ 7z – 3z + 4 = 12
⇒ 4z = 12 – 4
⇒ 4z = 8
⇒ z = 8/4
⇒ z = 2
See, that was so simple, using the mentioned methods, every linear equation can be solved easily.
Learn more about linear equations
https://brainly.com/question/14323743
#SPJ4
The duck pond game at the capital has a pool whit 75 toy ducks twenti-five of these duck are marked undemeant
Let us organize the information first. The game consists in picking up a numbered duck. Let us denote the number of the duck as xx. The possible prizes are
1≤ x≤ 60 consolation prize
60 ≤ x ≤ 70 stuffed duck
70≤ x ≤ banana
We have 75 possible numbers equally likely to select, and 1111 outcomes where we win the stuffed duck
60, 61, 62, 63, 64, 65, 66, 67, 68, 69 and 70
Therefore, the probability of winning a stuffed duck is
p(60 ≤ x ≤ 70) = 11/75= 0.146
The event of not winning a duck or a banana is that of winning the consolation prize, that is, picking a number 1 ≤x ≤ 60.
Those are 59 equally likely to occur outcomes. Then we have
c= 59/75= 0.786
To check whether this result is right, we can use the complementary events law. That is, the probability of not winning a duck or a banana is 11 minus the sum of the probabilities of winning a duck or a banana. Mathematically this is
p (1 ≤ x ≤ 60) = 1-(p (60≤x≤70)+p(70≤x≤75)
p (1≤ x ≤ 60) = 0.786
which is a desired result.
To know more about probability
visit-:https://brainly.com/question/11234923
SPJ9
The Cohen family desperately needs to catch up on doing laundry. Over the weekend, Mr. and Mrs. Cohen got 3 loads done. Now, during the week, they plan to do 1 load per day.
Write an equation that shows how the total number of loads done, y, depends on how many weekdays have passed, x.
y =
The equation that shows how the total number of loads done, y, depends on how many weekdays have passed, x will be y = 3 + x.
How to calculate the equation?An equation simply has to do with the statement that illustrates the variables given. In this case, it is vital to note that two or more components are considered in order to be able to describe the scenario. It is important to note that an equation is the mathematical statement which can be made up of two expressions which are connected by an equal sign.
In this case, Cohen family desperately needs to catch up on doing laundry. Over the weekend, Mr. and Mrs. Cohen got 3 loads done. Now, during the week, they plan to do 1 load per day.
The equation that shows how the total number of loads done, y, depends on how many weekdays have passed, x will be:
y = 3 + 1(x)
y = 3 + x
Learn more about equations on:
brainly.com/question/2972832
#SPJ1
Create an equation equivalent to x - y = 3 by multiplying each term on both sides by any number you choose.
Step-by-step explanation:
you can plus for obtain a multiply
5×-2y=3
Y=-4x-2 fill in the table using this function rule
How long would it take to double your principal in an account that pavs 6.5 % annual interest compounded continuously?
It will take 4.63 years to double the principal.
The formula for calculating the amount (A) on a principal (P) invested at the rate of r%, compounded continuously after t years is-
A = P[tex]e^{rt}[/tex]
Here r = 6.5%
= 0.065
Let the principal amount be P,
then the amount after t years = 2P
A = P[tex]e^{rt}[/tex]
2P = P[tex]e^{rt}[/tex]
2P/P = [tex]e^{rt}[/tex]
2 = [tex]e^{0.065t}[/tex]
Taking log on both sides-
Log 2 = log [tex]e^{0.065t}[/tex]
Log 2 = 0.065t log e
Log 2 = 0.065t
0.65t = Log 2t
= log 2/ 0.065t
= 0.301/ 0.065 t
= 4.63
Thus, it will take 4.63 years to double the principal.
Learn more about compound interest here- https://brainly.com/question/24274034
#SPJ4
The following data shows the scores Gina obtained on 12 IQ tests:
93, 83, 74, 74, 83, 92, 93, 94, 90, 87, 83, 86
The box plot represents the data:
box plot has minimum value equal to 74, lower quartile equal to 83, median equal to 86.5, upper quartile equal to 92.75 and maximum value equal to 99
Which of the following is shown incorrectly in the box plot?
Median
Lower quartile
Upper quartile
Maximum value
The maximum value of the data is being incorrectly shown by the box plot diagram.
We are given the data:
93, 83, 74, 74, 83, 92, 93, 94, 90, 87, 83, 86
We are also given the box plot diagram of the data which shows that:
Minimum value of the data = 74
Lower quartile = 83
Median quartile = 86.5
Upper quartile = 92.75
Maximum value = 99
We need to tell which is the wrong interpretation among these.
We can see that, the maximum value of the data is only 93 and not 99.
So, that is the wrong representation by the box plot.
Therefore, we get that, the maximum value of the data is being incorrectly shown by the box plot diagram.
Learn more about box plot here:
https://brainly.com/question/14277132
#SPJ9
HELP HELP HELP HELP HELPPPPPPPPPPPPPPPP!!!!!!!!!!
x=3.4
Im writing this bc the app says the answer is too short
HELP PLS WILL GIVE BRAINLIST
Answer:
AB + BC + AC a. segment addition postulate
2x+6x+8 = 32 b. substitution property of equality
8x + 8 = 32 c. Combine like terms
8x = 24 d. subtraction property of equality
x = 3 e. division property of equality
Seven times the sum of 23 and a number
Answer: 161+7n
Explanation: Let the number be n.
7(23+n)
=161+7n
Hope this helps you! Have a great day!!!!! :) :D
Find the greatest integer that is less than the value of the logarithm. Use your calculator to check your answers.
log 5
We need to know about logarithm to solve this problem. The greatest integer that is less than the value of log 5 is 0.
Logarithm is the exponent that is raised to a base to get a certain number. There are a few rules of algorithm, log a+ log b can be written as log ab, log a -log b can be written as log a/b, when a number whose logarithm is being calculated is raised to a certain power then the power can be directly multiplied to the log itself. Logarithm when written as log has a base of 10, the logarithm of a number that is same as it's base is always 1, the log of 1 is always zero, because any nonzero number raised to 0 is 1.We will find the value of log 5 first and then choose the nearest integer that is less than log 5.
log 5=log 10/2 =log 10-log 2=1-0.30=0.7
Therefore the greatest integer that is less than the value of log 5 is 0.
Learn more about logarithm here:
https://brainly.com/question/14393032
#SPJ9
A charge of $8.99 is automatically deducted from Ari's bank account each
month for a live TV streaming service. What is the change in Ari's bank
account after 6 months for this service?
Ari loss 53.94% of his account balance for this live tv streaming service.
Given,
The charge for a live tv streaming service that is automatically deducted from Ari's bank account each month = $8.99
This deduction continues for 6 months.
We have to find the change in Ari's bank account after 6 months for this service.
Charge for 1 month = 8.99
Charge for 6 months = 6 × 8.99 = 53.94
That is if Ari had $100 in his account, now after 6 months 53.94% deducted for the tv streaming service charge.
Now, he has an account balance:
100 - 53.94 = 46.06
In terms of amount, he has an account balance of $46.06.
In terms of percentage,
Ari lost 53.94% from his account balance and now he has 46.06% account balance.
Learn more about deduction here:
https://brainly.com/question/14073495
#SPJ1