A string 60 inches long is to be laid out on a tabletop to make a rectangle of perimeter 60 inches. Write the width of
the rectangle as 15 + x inches. What is an expression for its length? What is an expression for its area? What value
for x gives an area of the largest possible value? Describe the shape of the rectangle for this special value of x.
Answers
Answer:
Okay
Step-by-step explanation:
Hope this helps
Enjoy ur day
a) An expression for its length will be (15 - x) inches.
b) An expression for the area of rectangle will be (225 - x²) inch².
c) At x = 0 the rectangle has maximum area.
d) The shape of a rectangle will be square at x = 0.
What is Perimeter of a rectangle?
The perimeter of a rectangle with length L and width W is defined as;
Perimeter = 2 (L + W)
Given that;
Total length of string = 60 inches
Perimeter of rectangle = 60 inches.
Now,
a) When the width of rectangle is 15 + x inches.
Then, Expression for its length is calculated as;
Perimeter of rectangle = 2 ( length + width)
60 = 2 ( length + (15 + x) )
Divide by 2,
30 = Length + 15 + x
Length = 30 - 15 - x
Length = 15 - x
So, An expression for its length will be (15 - x) inches.
b) Length of rectangle = (15 - x) inches
Width of rectangle = 15 + x inches
Then, Area of rectangle = Length x width
Area of rectangle = (15 - x) × (15 + x)
Area of rectangle = 15² - x²
Area of rectangle = 225 - x²
Thus, An expression for the area of rectangle will be (225 - x²) inch².
c) When all sides of a rectangle is equal to each then, the area of a rectangle is maximum.
So, We can formulate,
Length = width
15 - x = 15 + x
2x = 15 - 15
2x = 0
x = 0
Hence, At x = 0 the rectangle has maximum area.
d) When x = 0,
Then, The sides of a rectangle are equal.
This imply that the shape of a rectangle will be square.
Therefore,
a) An expression for its length will be (15 - x) inches.
b) An expression for the area of rectangle will be (225 - x²) inch².
c) At x = 0 the rectangle has maximum area.
d) The shape of a rectangle will be square at x = 0.
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Related Questions
The graph shows the reciprocal parent function.
Which statement is true?
A. The function has no intercepts.
B. (1,1) is the x- and y-intercept of the function.
C. (0,0) is the x- and y-intercept of the function.
D. (0,1) is the x- and y-intercept of the function.
Answers
Answer:
A
Step-by-step explanation:
What is the volume of a cone with a radius of 6 inches and height of 15 inches .
Answers
Answer:
565.49 inches cubed
Step-by-step explanation:
Answer:
V = approximately 565.49 in3
4(-3)(-2)
How do
I do this?
Answers
Answer:
4(-3)(-2) = 24
Step-by-step explanation:
first solve the numbers in parenthesis.
4(-3)(-2)
= 4(6)
the negative sign cancels out in the product, because both of the numbers you multiplied are negative, which makes the product positive.
now solve for 4(6).
4(6) = 24
Solve: 33 + 27 ÷ 9 + (30 ÷ 5)
Answers
Answer:
42
Step-by-step explanation:
You need to follow P--E--M--D--A--S
A X U I A U
R P L V D B
E O T I D T
N N I T I R
T E P I T A
H N L O I C
E T I N O T
S S C N I
I A O
S T N
I
O
N
1 1/5 - 1/3 =18/15 - ?
Answers
Answer:
25/66
Step-by-step explanation:
please help look at picture
Answers
Answer:
15 cm
Step-by-step explanation:
Answer:
its C 30cm
Step-by-step explanation:
I multiplied 6x5=30
The system of equations y = negative 3 x + one-half and y = one-fifth x minus 1 and four-fifths is shown on the graph below.
What is a reasonable estimate for the solution?
(0.7, –1.7)
(–1.7, 0.7)
(1.4, –3.3)
(–3.3, 1.4)
Answers
Answer:
the -1,17,0.7 but if i get it wrong i can give u free points
Step-by-step explanation:
Answer:
-1,17,0.7
Step-by-step explanation:
Please only 10% of people are smart to answer this
Answers
Answer:
it's the one highlighted in orange
Step-by-step explanation:
I hope this helps with your question :)
1. You notice that you only have 13 pound of cheese and 34 cup of milk. How much
more cheese and milk will you need to get?
2. What if the store only sells the cheese in 1-pound packages and the milk in 4-cup Cartoons? How many of each would u need to buy, and how much would you have left over?
3. Now you decide to mix the dry mustard and salt ahead of time to make a seasoning mix. Add the two ingredients to show how much of the seasoning mix you have.
Answers
Answer:
Yoyo
Step-by-step explanation:
help pls I need help
Answers
Also sorry if it’s wrong
Evaluate each expression if k = -3, 55 - k
Answers
Step-by-step explanation:
=55-k
=55-(-3)
=55+3
=58
hope it helps.
Answer:58
Step-by-step explanation:
=55-(-3)
=55+3
=58
If you found my answer useful than mark me brainliest.
please help meeeeeeright now
Answers
The answer is 4 pairs.
Think of having x number of pairs, and $4.29x for the price of those pairs. 8.58 is standalone, so we focus on writing the equation:
[tex]8.58+4.29x=25.74\\4.29x=25.74-8.58\\4.29x=17.16\\\frac{4.29}{4.29}=\frac{17.16}{4.29} (division)\\x=4[/tex]
Give the ratio for tangent (0) in decimal form to 4 digits.
13
4
7.
Answers
Answer:
0.5714
Step-by-step explanation:
tan theta = perpendicular upon base that is P/B
P= 4
B= 7
P/B = 4/7 = 0.5714
The cost to the store is $45. They will use a 35% markup. What is the selling price?
Answers
And the selling price is Cost + Markup
Therefore $45 + $15.75 = $60.75
An owner buys a used car for $9000. How much is the markup if the percent markup is 7%? Show your work or explain your reasoning to justify your answer.
Answers
Answer:
$9,630
Step-by-step explanation:
7% of $9000 is $630, so you just add $9000 and $630.
help due in 30 min!!!!!!!!!!!!!!!
Answers
Answer:
They have the same slope
Step-by-step explanation:
slope=4
Write value of each digit in 167.7
Answers
The 6 is 60
The first 7 is 7
The second 7 is 0.7
The place value of every digit in 167.7 is:
167.7: 1 hundreds + 60 tens + 7 ones + 7 tenths167.7: 100 + 60 + 7 + 0.7What is place value?Every digit in a number has a place value in mathematics. The value a digit in a number represents based on where it is in the number is known as place value. The place value of 7, for instance, is 700 or 7 hundred. The place value of 7,432 is 7,000, or 7,000, however.So, place the value of each digit of 167.7.
167.7: 1 hundreds + 60 tens + 7 ones + 7 tenths167.7: 100 + 60 + 7 + 0.7So, the place value of each digit is shown.
Therefore, the place value of every digit in 167.7 is:
167.7: 1 hundreds + 60 tens + 7 ones + 7 tenths167.7: 100 + 60 + 7 + 0.7Know more about place value here:
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what does 20 times 90 equal
Answers
Answer:
1800
Step-by-step explanation:
Well the easiest way to do this is just do
9 x 2 = 18 and since in 20 and 90 there are two zeroes, add two zeroes at the end of 18!
Answer:
its equals 1,800
Step-by-step explanation:
1. Line L passes through point (-1, 2) and (-3,-2) on a coordinate plane. Line
M passes through the points (1.1) and (-1, W). For what value of W will make
line L and line M parallel.
Answers
Answer:
Slope of a line passing through ([tex]x_{1}[/tex],[tex]y_{1}[/tex]) and ([tex]x_{2} , y_{2}[/tex]) is given by:
[tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1}}[/tex]
Now,
Slope of line L, (m) = [tex]\frac{-3-(-1)}{-2-2}[/tex] = 0.5
Slope of line M, (n) = [tex]\frac{-1-1}{W-1}[/tex] = [tex]\frac{-2}{W-1}[/tex]
If the lines L and M are parallel to each other,
m = n
or, 0.5 = [tex]\frac{-2}{W-1}[/tex]
or, 0.5 (W - 1) = -2
or, W - 1 = -4
or, W = -3
Therefore the required value of W is -3.
what is the equation of the line passing through the points (-4,-7) and (8,-13)
Answers
Answer:
y=5/3x-79/7
Step-by-step explanation:
(-4, -7)
x1 y1
(8,-13)
x2 y2
y2-y1/x2-x1=
13+7/8+4= 20/12= 10/6= 5/3
y=5/3x+b
-7=5/3(-4)+b
The equation of a line passing through the points (-4,-7) and (8,-13) will be x + 2y + 18 = 0.
What is the linear system?A Linear system is a system in which the degree of the variable in the equation is one. It may contain one, two, or more than two variables.
The given points are (-4,-7) and (8,-13).
Then the equation of a line passing through the points (-4,-7) and (8,-13) will be
[tex]\begin{aligned} y + 13 &= \dfrac{-13+7}{8+4} (x - 8)\\\\y + 13 &= - \dfrac{1}{2} (x - 8)\\\\2y + 26 &= -x + 8\\\\x + 2y + 18 &= 0 \end{aligned}[/tex]
More about the linear system link is given below.
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How many questions are in math map 7th grade
Answers
Answer:
It really depends how well you are doing. It varies from time to time. Mine was about 40-50 questions
The inequality 3x+2>x+8 is equivalent to:
A. x>3
B. x 32
D. x<−32
Answers
Answer:
x>3
Step-by-step explanation:
3x+2>x+8
-2 -2
3x>x+6
-x -x
2x>6
/2 /2
x>3
The solution of the inequality 3x+2>x+8 will be x>3. The correct option is A.
What is inequality?
When two expressions are connected by a sign like "not equal to," "greater than," or "less than," it is said to be inequitable. The inequality shows the greater than and less than relationship between variables and the numbers.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
Given that inequality is 3x+2>x+8. The inequality will be solved as below,
3x+2>x+8
3x>x+6
2x>6
x>3
Hence, the solution is x>3.
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The inverse of F(x) is a function.
Answers
Answer:
Step-by-step explanation:
the word inverse refers to the opposite of another operation.
The inverse of the function f is denoted by f -1.
If you found my answer useful then mark me brainliest.
Are the following triangles similar to each other? If so, why?
Answers
Yes the are simailer because of SSS
what is 2:10 as a percentage
Answers
Answer:
20%
Step-by-step explanation:
2:10 = 2/10. 2/10 = 20/100, which equals 20%.
Can someone give me a 6 digit number stating with 4? I need this number for a project. Also it needs to be a random number.
Answers
Answer:
406789
Step-by-step explanation:
A bacon cheeseburger at a popular fast food restaurant contains 2,070mg of sodium, which is 86% of the recommended daily amount. What is the total recommended daily amount of sodium?
Answers
x(86/100)=2070
and solve for x.
after you solve you will get; 2407 mg
so the recommended daily amount is 2407 my
Answer:
2,407mg of sodium is the recommended daily amount
Step-by-step explanation:
Using the cross multiplication you will get the answer.
1. make the problem as a fraction [tex]\frac{2070}{x} =\frac{86}{100}[/tex]
2. Cross multiply (2070*100=86*x)
3. Simplify the equation left. 207000 = 86x
2407 ≈ x (Divide both sides by 86)
can someone help me please, i’ll give brainly. (10 points)
Answers
Answer:
Gradient of Line A: 0.75
Gradient of Line B: 0.8
Therefore the lines ARE NOT parallel.
Step-by-step explanation:
Find the gradient (slope) of line A and B respectively.
Line A Gradient:
Equation of line A is 3x - 4y = 5
Rewrite this in slope-intercept form as y = mx + b, where m is the gradient (slope).
Thus,
3x - 4y - 3x = -3x + 5
-4y = -3x + 5
Divide both sides by -4
y = ¾x + ⁵/4
The gradient = ¾ = 0.75
Line B Gradient:
Gradient of line passing through (4, 7) and (-1, 3)
[tex] m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{3 - 7}{-1 - 4} = \frac{-4}{-5} = \frac{4}{5} [/tex]
Gradient (m) = ⅘ = 0.8
Since both lines do not have the same gradient, therefore the lines are not parallel.
Is 2/3 less than 2/8
Answers
Answer:
No
Step-by-step explanation:
If there is 2 pizzas and one i cut in tree slices and the other is cut in eight slices the 8 slices are goind to be smaller. Hope this helps
A phone company charges for service according to the formula: C ( n ) = 29 + 0.04 n , where n is the number of minutes talked, and C is the monthly charge, in dollars. The slope in this equation is: ____________
The vertical intercept in this equation is: _____________
Answers
Hello!
Answer:Slope = 0.004
Vertical Intercept = 29.
Explanation:Basically, you can rearrange this equation so that is in the form of y = mx + b.
y = mx + b
C(n) = 0.04n + 29
The slope represents the rate of change of the cost per minute talked, and the 29 (vertical intercept) represents the monthly fee. The monthly fee will stay the same, however, the number of minutes talked is susceptible to change, hence the variable n represents it.