The dimensions of the rectangle is 83 feet x 46 feet
What is the Perimeter of a Rectangle?
The perimeter P of a rectangle is given by the formula, P=2 ( L + W) , where L is the length and W is the width of the rectangle.
Perimeter P = 2 ( Length + Width )
Given data ,
The perimeter P of the rectangle = 258 feet
Let the length of the rectangle be = L
Let the width of the rectangle be = W
And , The width is 37 feet less than the length. ,
So , W = L - 37
Perimeter P = 2 ( Length + Width )
Substituting the values of L and W in the equation , we get
Perimeter P = 2 ( L + L - 37 )
2 ( L + L - 37 ) = 258
( L + L - 37 ) = 129
2L - 37 = 129
Adding 37 on both sides , we get
2L = 166
Divide by 2 on both sides , we get
Length L of the rectangle = 83 feet
Substituting the value of L in equation ,we get
W = L - 37
Width W of the rectangle = 46 feet
Therefore , Length = 83 feet and Width = 46 feet
Hence , the dimensions of the rectangle is 83 feet x 46 feet
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Adaim has a goal to reach 70 miles. If he hikes 8 miles per day, how long will it take him to hike all 70 miles?
The graph of g(x) is the graph of f(x)=x−2reflected across the y-axis. Which equation describes function g?
The required equation of g(x) for reflection of f(x)=x-2 across the y-axis is g(x)=-x-2.
What is reflection?Reflection is basically a mirror image of the shape, in which the image of a given figure changes accordingly to a given line or axis.
Given that,
f(x)=x-2
To find the required equation for g(x) that is reflected across the y-axis, Use reflection property,
According to reflection property,
Reflection Across the y-axis, the x change in -x and the remaining part of the equation remains same.
The equation of f(x) changes in g(x) as g(x)=-x-2,
So, the equation of g(x)=-x-2 .
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For what value of x does the graph of f(x) = e* - 2x have
a horizontal tangent?
The value of x=0.301 at the x the graph of the function have a horizontal tangent.
Given that,
The function is f(x)=eˣ-2x
We have to find the value of x does the graph of the function have a horizontal tangent.
What is the horizontal tangent?Where the derivative of a function is zero, a graph's horizontal tangent line is a mathematical feature. This is so that the derivative, by definition, can provide the slope of the tangent line. The slope of horizontal lines is zero. As a result, when the derivative is zero, the tangent line is horizontal.
For horizontal tangent line,
f'(x)=0
The differentiation of the function is
eˣ-2=0
eˣ=2
Taking logarithm on both sides.
logeˣ=log2
We know that loge=1
So,
x loge=log2
x(1)=log2
x=log2
x=0.301
Therefore, the value of x=0.301 at the x the graph of the function have a horizontal tangent.
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plseas help
There are 7 students in grade 11 and 15 students in grade 12 that are part of the VSS robotics club. A committee consisting of a president, vice president, media rep, and accountant is being chosen.
a. In how many ways could the panel be chosen if the president and vice president must be from different grades?
b. In how many ways could the panel be chosen if it must include at least one grade 11 student and at least one grade 12 student?
The number of ways to form the committees, using the Fundamental Counting Theorem, are given as follows:
a) President and vice from different grades: 79,800.
b) At least one from each: 141,960.
What is the Fundamental Counting Theorem?It is a theorem that states that if there are n independent trials, each with [tex]n_1, n_2, \cdots, n_n[/tex] possible results, the total number of outcomes is calculated by the multiplication of the factorials as presented as follows:
[tex]N = n_1 \times n_2 \times \cdots \times n_n[/tex]
For item a, there are two possible cases for the parameters, as follows:
[tex]n_1 = 7, n_2 = 15, n_3 = 20, n_4 = 19[/tex]: President from grade 11, vice from grade 12, the remaining two roles can be chosen from any student.[tex]n_1 = 15, n_2 = 7, n_3 = 20, n_4 = 19[/tex]: President from grade 12, vice from grade 11, the remaining two roles can be chosen from any student.Hence the number of ways is:
N = 7 x 15 x 20 x 19 + 15 x 7 x 20 x 19 = 79,800.
For item b, the total number of outcomes is obtained as follows:
N = 22 x 21 x 20 x 19 = 175,560.
The number of outcomes with only grade 11 students is:
N = 7 x 6 x 5 x 4 = 840.
The number of outcomes with only grade 12 students is:
N = 15 x 14 x 13 x 12 = 32760.
Hence the number of students with at least one of each is:
N = 175,560 - (840 + 32,760) = 141,960.
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Last year, the student population at Haley Elementary School was 360 students. After rezoning this year, the student population is 10% smaller. HOW MANY STUDENTS ATTEND HALEY ELEMENTARY THIS YEAR?
Answer: 324
Step-by-step explanation: 10% is the same as 1/10
360/10 is 36
360-36= 324
meaning 324 students now attend Haley elementary school <3
hope this helps <33
it costs a paper company 4x+185 dollars to produce x notebooks. how many notebooks can they produce for $285
The paper company can produce 25 notebooks for $285
How to determine the number of notebooks?From the question, the equation of the total cost is given as
Equation = 4x + 185
Rewrite as
Cost = 4x + 185
Express the equation as a cost function
So, we have the following representations
C(x) = 4x + 185
When the total cost is $285, we have
C(x) = 285
This gives
4x + 185 = 285
Subtract 185 from both sides
4x = 100
Divide by 4
x = 25
Hence, the number of notebooks is 25
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PLEASE HELP
19- 4x + x² can be written in the form
(x + a)² + b, where a and b are numbers.
Work out the values of a and b.
Step-by-step explanation:
so, let's do the multiplications and squaring. and then compare the result with the target.
(x + a)² + b = x² + 2ax + a² + b
and the original expression is
x² - 4x + 19
x² = x² done
2ax = -4x
2a = -4
a = -2
a² + b = 19
(-2)² + b = 19
4 + b = 19
b = 15
so, the result is
(x - 2)² + 15
Answer: (x-2)^2+15
Step-by-step explanation:
Given x^2-4x+19
=here b=-4 and c=19
B=b/2=-4/2=-2
C=c-B^2=19-(-2)^2=19-4-15
so
(x-B)^2+C
(x-2)^2+15
Madison needs to order some new supplies for the restaurant where she works. The restaurant needs at least 474 spoons. There are currently 246 spoons. If each set on sale contains 6 spoons, use the drop-down menu below to write an inequality representing s, the number of sets of spoons Madison should buy.
38 sets
474 - 246 = 228
228 ÷ 6 = 38
3. Round 134.76821 to the nearest hundredth.
Answer:
134.77
Step-by-step explanation:
Round 134.76821 to the nearest hundredth
by placing each number in reference to what they represent.
1 - hundreds
3 - Tens
4 - units
.7=Tenth
.76=Hundredth
.768=Thousandth
.7682=Ten Thousandth
.76821= Hundred Thousandth
Nearest hundredth will be
134.[76]821
since 2,1 are both round down numbers they will produce approximately 0
since 8 is a round off number it will produce approximately 10
134.77000
or 134.77
you can award the answer as brainliest
Consider the equation and the following ordered pairs: (−3,y) and (x,2). y=−3x−1 Step 1 of 2 : Compute the missing x and y values so that each ordered pair will satisfy the given equation. Answer Keyboard Shortcuts Complete the table below. x y row 1−3 Answer row 2 Answer 2
Using the equation y = -3x - 1, the missing values are in the ordered pairs, (−3,y) and (x,2), are: x = -1 and y = 8.
How to Compute Missing Values that Satisfies an Equation?An algebraic equation is an expression that has variables. The values of those variables, when plugged into the equation would make the equation true.
Given the equation, y = -3x - 1, substitute x = -3 into the equation to find y:
y = -3(-3) - 1
y = 9 - 1
y = 8
The missing value in the ordered pair is: (-3, 8).
To find the missing value of x in (x, 2), substitute y = 2 into the equation, y = -3x - 1:
2 = -3x - 1
2 + 1 = -3x
3 = -3x
3/-3 = x
x = -1
The missing value is (-1, 2).
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Is this the right answer?
Answer:
Step-by-step explanation:
Yeah you have the correct answer.
In the original line you solve for y where the slope is given -3.
Then it is up to you but I like using the point slope formula so I'll plug in the values and the result is the same as the picture.
y-y=m(x-x)
y-(-6)=-3(x-1)
What must be added to this expression
to make it a perfect square?
9/16 must be added to this expression [tex]x^{2} -3x/2[/tex] to make it a perfect square.
According to the question,
We have the following expression:
[tex]x^{2}[/tex] -3x/2
Now, in the given four options, we only have two perfect squares which 9/16 and 16/9.
Now, 9/16 is the square of 3/4.
So, we will first solve it using 9/16:
[tex]x^{2}[/tex]-3x/2+9/16
Now, this formula is of identity [tex](a-b)^{2}[/tex] where we have a = x and b = 3/4.
The formula of the identity [tex](a-b)^{2} = a^{2} + b^{2} -2ab[/tex].
Now, adding 9/16 make it a perfect whole square.
(More to know: we can add or subtract a number or a term from an expression to make it a perfect square or perfect cube.)
Hence, the correct option is C.
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how do i factor (x + 2)^2 - (y - 2)^2???
The factor of the difference of two squares (x + 2)² - (y - 2)² is (x + y)(x - y + 4).
Difference of two squaresIf for any two squares say a² and b², then their difference a² - b² = (a + b)(a - b).
Given the two squares (x + 2)² and (y - 2)²
then their difference will yeild the factors derived as follows;
(x + 2)² - (y - 2)² = [(x + 2) + (y - 2)][(x + 2) - (y - 2)]
open brackets
(x + 2)² - (y - 2)² = (x + 2 + y - 2)(x + 2 - y + 2)
collect like terms
(x + 2)² - (y - 2)² = (x + y + 2 - 2)(x - y + 2+ 2)
so
(x + 2)² - (y - 2)² = (x + y)(x - y + 4)
Thus, by application of the rule of difference of two squares, we have the factors of (x + 2)² - (y - 2)² to be (x + y 2 - 2) and (x - y + 2+ 2).
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How does knowing the x-intercepts and the vertex of a
function help you graph a quadratic function?
A graph of a quadratic function is a parabola, making an equation of a parabola with help of an x-intercept and vertex can be formed.
The graph is a demonstration of curves that gives the relationship between the x and y-axis.
Here,
With the help of the vertex and the x-intercept, the equation of the parabola can be formed which helps to graph a quadratic function because the equation of the parabola resembles the quadratic function,
Thus, a graph of a quadratic function is a parabola, making an equation of a parabola with help of an x-intercept and vertex can be formed.
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Creating a Function from a Mapping
The mapping shows a relationship between input and
output values.
Input
Activity
-5
SAING
2
40 Intro
Output
T? 7 NO
-3
-2
2
Which ordered pair could be removed to make this
relation a function?
O (-5,0)
-O (-1, -3)
O (4,-2)
O (6,-1)
Done
The ordered pair could be removed to make this relation a function is (4,-2).
What is an ordered pair?
An ordered pair is made up of the ordinate and the abscissa of the x coordinate, with two values given in parenthesis in a certain sequence.
The numeric values in an ordered pair can be integers or fractions.
Here,
A function is when each input has one output. So, for every x there is one y. The x values can not repeat.
But in the given value x is repeating so the ordered pair (4, -2) can be removed.
Hence, the ordered pair could be removed to make this relation a function is (4,-2).
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Define rational number in your own words.
Answer:A rational number is a number thats a quotient or fraction
Step-by-step explanation:
4\6 would be a rational number 8 over 4 as well.
Pls help urgent someone hurry please
Proved that the triangle ABW ≅ triangle DCW
In the given question,
The length of WA = The length of WD
The measure of angle 5 = The measure of angle 7
Here we have to prove that one angle and two sides of the triangle ABW is equal to the one angle and two sides of the triangle DCW
Consider the triangle ADW,
In the triangle ADW the length of the WA is equal to the length of WD.
Therefore the measure of angle A is equal to the measure of angle D.
So in triangle ABW and the triangle DCW, one side and two angles are equal.
Therefore the triangle ABW and triangle DCW are congruent
Hence, proved that the triangle ABW ≅ triangle DCW
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I can't do math so I need someone to help me. what's the answer?
The value of TV for the similar triangles is 25
What are similar triangles?Similar triangles are the triangles that have corresponding sides in proportion to each other and corresponding angles equal to each other. Similar triangles look the same but the sizes can be different.
Similar triangles are not the same as congruent triangles though.
triangle UXW and UTV are similar since line TV cuts lines UX and UW in the same proportion.
Let UV = p, it means also that WV = P. which means WU = 2p
so since the two triangles are similar, the ratio of their corresponding lengths are equal
meaning,
UV/UW = TV/XW
substituting their values, we have
p/2p = TV/50
by cross multiplying,
2p x TV = 50p
2TV = 50
TV = 50/2 = 25
In conclusion, the value of TV is half the value of WX = 25
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Find the probability.
Um A has balls numbered 1 through 8. Urn B has balls numbered 1 through 5. What is the
probability that a 4 is drawn from A followed by a 2 from B?
The probability that a 4 is drawn from from Urn A followed by a 2 from Urn B is 1/40 .
In the question ,
it is given that
the number of balls in Urn A is 8
which are {1,2,3,4,5,6,7,8}
the probability of getting a 4 from Urn A is (P₁) = 1/8
the number of balls in Urn B is 5 .
which are {1,2,3,4,5}
the probability of getting 2 from Urn B is (P₂) = 1/5
So ,the required probability is = P₁ × P₂
On substituting the values of P₁ and P₂ ,
we get
= 1/8 × 1/5
= 1/40
Therefore , the required probability is 1/40 .
The given question is incomplete , the complete question is
Find the probability.
Urn A has balls numbered 1 through 8. Urn B has balls numbered 1 through 5. What is the probability that a 4 is drawn from A followed by a 2 from B?
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Fwam is preheating his oven before using it to bake. Fwam wants to predict the final
temperature after a minutes. He wrote the equation y = 40x+79, where y represents the final temperature in degrees Fahrenheit. What is the meaning of the y- value when x = 1?
The solving linear equation states that the temperature of the oven is 119 after an minute.
What is a linear equation?A linear equation is just an algebraic equation of something like the form y=mx+b that only contains a constant and a first-order (linear) component, where m represents the slope and b is the y-intercept. Sometimes, the aforementioned is referred to as a "linear equation of two variables," where y and x are now the variables.
According to the given data:Given:
y = 40x+79
X = number of minutes using it to bare:
When X = 1
y = 40(1)+79
y = 119
It means that the temperature of the oven is 119 after an minute.
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-353.92 - (-283.56) -131.29
-353.92-(-283.56)-131.29= -20,165
The depth of a local river averages 20 ft, which is represented as |−20|. In January, it measured 6 ft deep, or |−6|, and in July, it was 22 ft, or |−22|. What is the difference between depths in January and July?
Answer: 2 ft.
Step-by-step explanation:
|-20| = 20, |-22| = 22
22 - 20 = 2
PLEASE HURRY I WANT TO FINISH MY TEST AND I NEED THE ANSWER!!
Determine which integer will make the inequality 2(n + 2) < 5(n − 1) true.
The value to make the inequality true is n > 3
InequalityInequality, In mathematics, a statement of an order relationship—greater than, greater than or equal to, less than, or less than or equal to—between two numbers or algebraic expressions.
We need to solve this problem and determine what value will solve this problem.
2(n + 2) < 5(n - 1)
2n + 4 < 5n - 5
Collect like terms
4 + 5 < 5n - 2n
9 < 3n
3n > 9
n > 3
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There are 10 applicants applying for 3 positions Hostess server and busier how many ways
The number of ways to select 3 position out of 10 applicant is 120 ways
What is combination?Combinations implies the selection of things from a given set of things. In this case, we intend to select the objects. Combination formula is illustrated as:
nCr = n! / ((n – r)! r!)
n = the number of items.
r = how many items are taken at a time.
Since there are 10 applicants applying for 3 positions. This will be:
= 10! / (10 - 3)!3!
= 10! / 7!3!
= 10 × 9 × 8 / 3 × 2
= 120
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A motorboat maintained a constant speed of 11 miles per hour relative to the water in going 10 miles upstream and then returning. The total time for the trip was 5.5 hours. Use this information to find the speed of the current.
The speed of the current is 9 miles per hour
How to determine the speed of the current?
Given that: the motorboat maintained a constant speed of 11 miles per hour relative to the water in going 10 miles upstream and then returning.
Total time = 5.5 hours
Let s = speed of the current
speed downstream relative to land = 11 + s
speed upstream relative to the land = 11 - s
speed = distance/time
time = distance/speed
upstream time + downstream time = total time
10/11-s + 10/11+s = 5.5 (find LCM of 11-s and 11+s)
10(11+s) + 10(11-s) /(11-s)(11+s) = 5.5
110+10s+110-10s /(11-s)(11+s) = 5.5
220 = 5.5(11-s)(11+s)
220 = 5.5(121 - 11s + 11s - s²)
220 = 5.5(121 - s²)
220 = 665.5 - 5.5s²
5.5c² = 665.5 - 220
5.5c² = 445.5
s² = 445.5/ 5.5
s² = 81
s = √81 = 9
Therefore, the speed of the current is 9 miles per hour
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7. In one week, Sabrina received 18 letters and
8 bills. What was the ratio of bills to letters?
To determine the size of the county's moose population, naturalists catch 65 moose, tag them and
then set them free. Months later, 48 moose are caught, of which 14 have tags.
The estimated size of the moose population is___?
. (Round to nearest whole moose.)
The size of the moose population, 65 + (48-14)=99.
What is unitary method?The unitary technique involves first determining the value of a single unit, followed by the value of the necessary number of units. What can be values and units.Let's say you go to the store to buy six apples. You are informed by the shopkeeper that he is offering 10 apples for Rs 100. In this instance, the value and the units are the price of the apples.Recognizing the units and values is crucial when using the unitary technique to a problem.Always write the items that need to be computed on the right side and the things that are known on the left side to simplify things. We are aware of the quantity of apples and the amount of money in the aforesaid problem.acc to our question-
naturalists have = 65 moosetheycatch and tag = 48set them free and catch them later,= 14now total moose= 65 + (48-14)99learn more about unitary method click here:
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Rohan bought some tiles for a kitchen floor. 3/5 of the tiles were white, 1/4 of the
remainder were yellow, and the rest were blue. There were 60 more white
tiles than blue tiles. Each tile cost $3. What was the total cost of the tiles?
The cost the tiles are = $182.55
what is unitary method?The unitary technique involves first determining the value of a single unit, followed by the value of the necessary number of units. What can be values and units.Let's say you go to the store to buy six apples. You are informed by the shopkeeper that he is offering 10 apples for Rs 100. In this instance, the value and the units are the price of the apples. Recognizing the units and values is crucial when using the unitary technique to a problem.Always write the items that need to be computed on the right side and the things that are known on the left side to simplify things. We are aware of the quantity of apples and the amount of money in the aforesaid problem.acc to our question-
white tiles =W = 1/4
3/5 = yellow
each tile costs= $3
= 0.25+ 0.6+ 60
= 60.85*3
$182.55
hence,The cost the tiles are = $182.55
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Graph a line with a slope of 1/5 and passes through the point (-2, 2).
The equation of line in slope intercept form
What is equation of line in slope intercept form?
The most general form of equation of line in slope intercept form is given by y = mx + c
Where m is the slope of the line and c is the y intercept of the line.
Slope of a line is the tangent of the angle that the line makes with the positive direction of x axis.
If [tex]\theta[/tex] is the angle that the line makes with the positive direction of x axis, then slope (m) is given by
m = [tex]tan\theta[/tex]
The distance from the origin to the point where the line cuts the x axis is the x intercept of the line.
The distance from the origin to the point where the line cuts the y axis is the y intercept of the line.
Here,
Slope = [tex]\frac{1}{5}[/tex]
Point = (-2, 2)
Required equation of line =
[tex]y - 2 = \frac{1}{5}(x - (-2))\\5y - 10 = x + 2\\5y = x + 2 + 10\\5y = x + 12\\y = \frac{1}{5}x + \frac{12}{5}\\[/tex]
The graph has been attached here.
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what is the answer to
$224.50- $225.00
i already did calculator many different wayss
i will report wrong answers UNLESS you actually tried
Answer:_______________________________________________
-0.5
Answer:
224.50
-225.00
$0.50
- 50 cents
