9) A 5 inch by 7 inch picture has a frame surrounding
it on all four sides of width w. The total area of the
picture frame and picture is 80 square inches.
a) Using the diagram and information, write an
expression for the total length, including the
frame, and with an expression for the total
width, including the frame.
Length expression:
Width expression:
b) Using the expressions for total length and width, write an equation for the total
area of the rectangular picture and frame (Hint: Area = l × w).
c) Using your knowledge of factoring, solve the equation from (b) for the width of
the frame surrounding the picture.
Answers
Answer:
w = 3/2
Step-by-step explanation:
Area of a Rectangle
The 5-inch by 7-inch picture has a frame of width w surrounding all four sides.
a)
The total length of the framed picture is 7 + 2w
The total width of the framed picture is 5 + 2w
b)
The total area of the framed picture is:
At = (7 + 2w)(5 + 2w)
c) We know the total area is 80 square inches, thus:
(7 + 2w)(5 + 2w) = 80
Operating:
[tex]35 + 14w + 10w + 4w^2=80[/tex]
Simplifying:
[tex]4w^2 + 24w -45 =0[/tex]
We now write:
[tex]4w^2 + 30w - 6w -45 =0[/tex]
Factor out 2w from the first two terms and -3 from the last two terms:
[tex]2w(2w + 15) - 3(2w + 15) =0[/tex]
Factor out 2w+15
(2w + 15)(2w - 3)=0
The solutions are:
w = -15/2
w = 3/2
The only feasible solution is the positive value, thus
w = 3/2
Related Questions
The profits of mr cash’s company is represented by the equation p(t)=-3t^2+18t-4, where p(t) is the amount of profit in hundreds of thousands of dollars and t is the number of years of operation. he realizes his company is on the down turn and wishes to sell before he ends up in debt. In what year of operation does Mr. Cash’s business show maximum profit? What is the maximum profit? What time will it be too late to sell business? show work
Answers
Answer:
$2300000- max profit5.77 years into operation - zero profit timeStep-by-step explanation:
Given function:
p(t)= -3t^2 + 18t - 4It is a quadratic function with general form of y = ax^2 + bx + c
It opens down if a < 0 and gets maximum value at vertex which is determined at x = -b/2a
For the given function vertex is:
t = -18/-3*2 = 3Maximum value of p is:
p(3) = -3*3^2 + 18*3 - 4 = -27 + 54 - 4 = 23 ($2300000)The time when profit is zero:
-3t^2 + 18t - 4 = 03t^2 - 18t + 4 = 0t = (18 ± √18² - 4*3*4)/2*3 = (18 ± √276)/6 = (18 ± 16.61)/6t = (18 - 16.61)/6 = 0.23 this is the time when company has just started to make profit, it is not applicable as is the past timet = (18 + 16.61)/6 = 5.77 years into operation, after this time there will be no profitNatalia solved the problem 74.4/12=6.2. complete the model with partial products check Natalia's work using multiplication
Answers
Answer:
Natalia's work is wrong.
Step-by-step explanation:
Natalia divided a decimal number by an entire number. Since division is a operation derived from multiplication, the best approach to check if work was good is multiplying the given result by denomination, that is:
1) [tex]x = 6.2\times 12[/tex] Given.
2) [tex]x = \left(6+0.2\right)\times 12[/tex] Definition of addition.
3) [tex]x = 6\times 12 + 0.2\times 12[/tex] Distributive property.
4) [tex]x = 72 + \frac{2}{10}\times 12[/tex] Definitions of multiplication and decimal number.
5) [tex]x = 72 +[2\cdot (10)^{-1}]\cdot 12[/tex] Definition of division/Associative property.
6) [tex]x = 72 + [2\cdot 12]\cdot (10)^{-1}[/tex] Associative property.
7) [tex]x = 72 + 24\cdot 10^{-1}[/tex] Definition of multiplication.
8) [tex]x = 72 + \frac{24}{10}[/tex] Definition of divsion.
9) [tex]x = 72 + 2.4[/tex] Defintion of decimal number.
10) [tex]x = 74.4[/tex] Definition of addition/Result
Natalia's work is wrong.
Explain how you can use a model to find 6 x 17
Answers
here Multiplicand =6
Multiplier=17
First break Multiplier (17) into 1 ten and 7 ones as
17=10+7
Then Multiply 6 to both of the parts of 17 then add it,
6×17
=6(10+7)
=6×10+6×7 [Distributive property]
=60+42=102
Partial Product is a product obtained by multiplying the multiplicand by one digit of the multiplier when the multiplier has more than one digit.
4. 3b - 27
HELP ASAP
Answers
Answer:
3(b-9)
Step-by-step explanation:
The GCF (greatest common factor) is 3. All you have to do is divide both the numbers by 3. You should get 3(b-9). I hope this helps! ;)
At a pizza party, where each person had their own pizza, 12 people ate 100% of their pizza, 7 people ate 75% of their pizza, and 3 people only ate 50% of their pizza. What was the average amount of pizza eaten by all people attending the party?
Answers
Find the missing dimensions in the table. Write the dimensions in simplest form.
Parallelogram
Base
Height
Area
Answers
Answer/Step-by-step explanation:
Parallelogram A:
Area = 5x + 20
Base = x + 4
Height = h = ?
Area of Parallelogram = base * height
Plug in the values
5x + 20 = (x + 4) * h
Divide both sides by x + 4
[tex] \frac{5x + 20}{x + 4} = h [/tex]
[tex] \frac{5(x + 4)}{x + 4} = h [/tex]
[tex] 5 = h [/tex]
Height = 5
Parallelogram B:
Area = 8x - 24
Base = b
Height = 8
Area of Parallelogram = base * height
Plug in the values
8x - 24 = b * 8
Divide both sides by 8
[tex] \frac{8x + 24}{8} = b [/tex]
[tex] \frac{8(x + 3)}{8} = b [/tex]
[tex] x + 3 = b [/tex]
Base = x + 3
Parallelogram C:
Area = 12x + 6y
Base = 6
Height = h = ?
Area of Parallelogram = base * height
Plug in the values
12x + 6y = 6 * h
Divide both sides by 6
[tex] \frac{12x + 6y}{6} = h [/tex]
[tex] \frac{6(2x + y)}{6} = h [/tex]
[tex] 2x + y = h [/tex]
Height = 2x + y
Write an Inequality to represent a graph.
Answers
Answer:
nun of the 3 you gave use so the last one the 4th
Step-by-step explanation:
Helllpp ASAP The sum of -14.3 and a number is positive. Identify a possible value for that
number. Explain your selection.
Answers
Answer: Any number larger than 14.3; one possible value is 20
Note how 20 + (-14.3) = 20-14.3 = 5.7 which is positive.
If we picked something smaller than 14.3, like say 10, then
10+(-14.3) = 10-14.3 = -4.3 which is negative.
----------------
When adding a positive to a negative, you basically subtract the two values. Then whatever the largest value is, that's the sign of your result. For 20+(-14.3), the positive 20 is larger in absolute value so the overall result is positive. On the other hand, the -14.3 is larger in magnitude compared to the 10, which is why 10+(-14.3) has a negative result.
If x=-1, what is n (x)?
n(x)=-3x+7
Answers
Answer:
Step-by-step explanation:
x = -1
n(x = -1) = -3(x) + 7
n(x = -1) = -3(-1) + 7
-3 x -1 = 3
n(x = -1) = 3 + 7
n(x = -1) = 10
I hope this is correct! And I hope this helps :)
Given that P(x)=x^5-8x^3-x^2+2, what is the remainder when it is divided by x-5?
Answers
Answer:
2102
Step-by-step explanation:
The polynomial function P(x)=x^5-8x^3-x^2+2, if it is divided by x-5, first we need to get x from the divisor as shown
since d(x) = x-5
x-5 = 0
x = 5
Substitute x = 5 into the expression to get the remainder
P(x)=x^5-8x^3-x^2+2
P(5)=(5)^5-8(5)^3-(5)^2+2
P(5) = 3125-1000-25+2
p(5) = 2100+2
P(5) = 2102
Hence the remainder is 2102
The following expression models the total money earned by setting up a food stall at a funfair, where x represents the number of cheeseburgers sold.
What does the constant term in the above expression represent?
A.
The constant -10 represents the cost of setting up the food stall even if no cheeseburgers were sold.
B.
The constant -10 represents the total money earned by setting up the food stall.
C.
The constant -10 represents the maximum number of cheeseburgers sold by the food stall at the funfair.
D.
The constant -10 represents the cost of each cheeseburger at the food stall
Answers
Answer:
C
Step-by-step explanation:
I think so im not sure sorry
Please help how to solve
Answers
What is the probability you will roll a number less than 5 on a 6-sided die?
show your work
Answers
Answer:
2/3 chance
Step-by-step explanation:
You want to find numbers less than 5, so there are 4 numbers you can use. 4 out of 6 numbers possible is 4/6, or 2/3.
Which of the following statements best describes the relationship between the point (5,-20) and the system of
inequalities below?
Answers
Answer: The point (5,-20) only satisfies the second inequality statement in the system of inequalities shown.
Step-by-step explanation:
It isn't super clear exactly what you're asking, but the first thing we can do is see if the point (5, -20) satisfies the system of equations.
So, we start by plugging in -20 for y and 5 for x.
y > -2x-3
-20 > (-2)(5) - 3
-20 > -10-3
-20 > -13. - we can see that the coordinates DO NOT satisfy the first inequality, now we can try the second equation.
y ≤ 3x + 2
-20 ≤ 3(5) + 2
-20 ≤ 15 +2
-20 ≤ 17 - this inequality is true because -20 is indeed less than 17.
2 + 5 please help I am really struggling
Answers
Answer:
the answer is 7 the problem is an easy one
Step-by-step explanation:
The graphs of 4 linear functions are shown. Which option COULD correctly give the values for a, b, and c?
A)
a = 3, b = 1, c=4
B)
a = -4, b= -1,C = 3
C)
a = 4, b = -2,c=-4
D
a = -3, b = 2,c = -2
Answers
Answer:
It’s c
Step-by-step explanation:
The graph of the linear functions are solved and a = 4, b = -2 , c = -4
What are Linear Equations?An equation is said to be linear equation in two variables if it is written in the form of ax + by + c=0, where a, b & c are real numbers and the coefficients of x and y, i.e a and b respectively, are not equal to zero.
The linear equations in one variable is an equation which is expressed in the form of ax+b = 0, where a and b are two integers, and x is a variable and has only one solution
On a graph, a linear equation forms a straight line. On a graph, a nonlinear equation produces an S-curve, a bell curve, or another nonlinear shape.
Given data ,
Let the linear function be represented as A
Now , the value of A is
y = f ( x )
Now , the functions on the graph are above and below the y = f ( x )
So , the value of a = positive
And , a = 4
Now , the value of b = negative
And , y = f ( x + b ) is below f ( x )
So , b = -2
And , similarly c = -4
Hence , the linear functions are solved
To learn more about linear equations click :
https://brainly.com/question/10185505
#SPJ2
On a typical day, the snow on Pike Mountain melts at a rate modeled by the function
M(t), given by M(t)=π/6sin(πt/12)
A snow maker adds snow at a rate modeled by the function S, given by
S(t)=0.006t^2−0.12t+0.87
Both M and S have units in inches per hour and t is measured in hours for 0≤t≤6. At time t = 0, the mountain has 40 inches of snow.
a. How much snow will melt during the 6 hour period? Indicate units of measure.
b. Write an expression for I(t), the total number of inches of snow at any time t.
c. Find the rate of change of the total amount of snow at time t = 3.
Answers
Answer:
a. 2in
b. [tex]l(t)=0.002t^{3}-0.06t^{2}+0.87t+2cos(\frac{\pi}{12}t)+38[/tex]
c. l'(3)=0.1938 in/hr
Step-by-step explanation:
a.
In part a, the problem is asking us to find how much snow will melt during the 6 hour period. In order to do so we need to take the M(t) function and integrate it in the given period of time, so we get:
[tex]\int\limits^6_0 {\frac{\pi}{6}sin(\frac{\pi}{12}t)} \, dt[/tex]
So now we solve:
[tex]\frac{\pi}{6}\int\limits^6_0 {sin(\frac{\pi}{12}t)} \, dt[/tex]
this is a known integral, so we get:
[tex]\frac{\pi}{6}[-\frac{12}{\pi}cos(\frac{\pi}{12}t)]^{6}_{0}[/tex]
we can simplify this so we get:
[tex]-2[cos(\frac{\pi}{12}t)]^{6}_{0}[\tex]
[tex]-2[cos(\frac{\pi}{12}(6))-cos(\frac{\pi}{12}(0))][/tex]
[tex]-2[cos(\frac{\pi}{2})-cos(0)][/tex]
[tex]-2[0-1][/tex]
2 in
b)
For part b they want us to write an expression for l(t), the total number of inches of snow at any time t.
in order to do so we need to find an expression for the rate of change of snow. A snowmaker is adding some snow while another amountn of snow is melting, so this rate of change is found by subtracting the two functions, so we get:
l'(t)=S(t)-M(t)
so:
[tex]l(t)=\int {(0.006t^{2}-0.12t+0.87-\frac{\pi}{6}sin(\frac{\pi}{12}t))} \, dt[/tex]
so we integrate this to get:
[tex]l(t)=\frac{0.006}{3}t^{3}-\frac{0.12}{2}t^{2}+0.87t+2cos(\frac{\pi}{12}t)+C[/tex]
and we can simplify this:
[tex]l(t)=0.002t^{3}-0.006t^{2}+0.87t+2cos(\frac{\pi}{12}t)+C[/tex]
so now we need to find what C is equal to, we can use the fact that l(0)=40in so we get:
[tex]40=0.002(0)^{3}-0.006(0)^{2}+0.87(0)+2cos(\frac{\pi}{12}(0))+C[/tex]
which yields:
40=2+C
so
C=40-2
C=38
So the final function is:
[tex]l(t)=0.002t^{3}-0.06t^{2}+0.87t+2cos(\frac{\pi}{12}t)+38[/tex]
c)
for part c we need to find the rate of change of the total amount of snow at time t=3, so in this case we can use the equation we found previously:
l'(t)=S(t)-M(t)
[tex]l'(t)=(0.006t^{2}-0.12t+0.87-\frac{\pi}{6}sin(\frac{\pi}{12}t))[/tex]
and substitute t=3
[tex]l'(3)=(0.006(3)^{2}-0.12(3)+0.87-\frac{\pi}{6}sin(\frac{\pi}{12}(3)))[/tex]
which yields:
l'(t)=0.1938 in/hr
A = {1, 3, 5, 7, 9}
B = {2, 3, 5, 7}
What is A UB?
Answers
Answer:
1234579
Step-by-step explanation:
first apply formula.then solved
A set of pencils sells for $1.75 and costs $0.40 to make. Twenty percent of the profit (the difference between the purchase price and the amount it costs to make) from each set of pencils goes to a school. If 500 sets are sold, what is the amount of money that will go to the school?
Answers
Answer:
$135
Step-by-step explanation:
If each set cost $0.40 to make and sells for $1.75, the profit for each pack is $1.35.
To get 20% of this you do the following: 1.35×0.20
20% of $1.35 is $0.27.
If 500 sets of pencil are sold and the school gets $0.27 from each pack sold, you would multiply $0.27 by 500, which would give you the answer $135.
If u steal point i report
Answers
Answer:
C = y=4x
Step-by-step explanation:
That answer because if you were to multiply on the way it will have the same graph
Answer:
The third option
Step-by-step explanation:
Which is equivalent to the expression below?
Answers
Answer:
A
Step-by-step explanation:
Opening the brackets, you get: 3x^2 - 2x + 5 - 2x^2 + 5x - 1
Simplifying, you get : x^2 + 3x + 4
Answer:
a
Step-by-step explanation:
3x^2 - 2x^2= x^2
-2x + 5x = 3x
5- 1 =5
Amy is applying for a job in two companies. The given table shows the salary in dollars () that Company 1 is offering
if she works x hours. Company 2 is offering $12.50 per hour plus a bonus of $80. If she plans to work 40 hours each
week, in which company will she earn more money in a week and by how much more?
A)
She will earn $20 more in Company 1.
B)
She will earn $40 more in Company 1.
C)
She will earn $20 more in Company 2.
D)
She will earn $40 more in company 2.
Eliminate
Answers
Answer: B is the correct answer
Step-by-step explanation: Lol its B
Glen has 70 toy cars. 30% of the cars are green. How many cars are green?
a.21
b.35
c.18
d.25
Answers
Answer:
21 green cars
Step-by-step explanation:
Answer:
70 x 30/100 = 21
21 cars are green
Step-by-step explanation:
graph the image of this figure after a dilation with a scale factor of 2 centered at the origin use the polygon tool to graph the dilated figure ! Please help 100 pts and brainliest
Answers
Answer:
For this answer, I will label the points. Starting at the top left, then top right, then bottom left and bottom right let the points be A, B, C, D.
The new coordinates will be
A(-4,10)
B(4,10)
C(-4,4)
D(4,4)
Step-by-step explanation:
The question is asking for a dilation which is a transformation that makes an image proportionately smaller or larger by a scale factor. The scale factor is how much smaller or larger the shape will be, if the scale factor is between 0 and 1 then it will shrink, if it is greater than one then the image will stretch (be larger). In this case, the scale factor is 2, therefore the image will stretch. Since the center of dilation is the origin, to find the new coordinates simply multiply each x and y value by the scale factor. So A's original coordinates (-2,5) become (-4,10) and so forth. Therefore the equation for this dilation is (x, y) → (2x,2y).
Answer:
See below
Step-by-step explanation:
Points given on the graph:
(-2, 2), (-2, 5), (2, 5), (2, 2)Dilation by a scale factor of 2 will result in coordinates doubled for each point:
(x, y) → (2x, 2y)And the new points will be:
(-2, 2) → (-4, 4)(-2, 5) → (-4, 10)(2, 2) → (4, 4)(2, 5) → (4, 10)See attached for the graph
1,If 1 − x, x + 3 and 2x + 1 are consecutive terms of an A.P, then find the common
difference.
Answers
Step-by-step explanation:
Since they are consecutive terms in an AP,
(1 - x) + (2x + 1) = 2(x + 3).
=> x + 2 = 2x + 6
=> x = -4.
Therefore the terms are 5, -1 and -7.
=> Common difference = -6.
To take 10% of a number, move the decimal_spaces to the_.
Answers
Answer:
1 space to the right?
Step-by-step explanation:
Answer:
1 space to the left
Step-by-step explanation:
example 5.0 X 10% is the same as 5.0 x .10
5.0 x .10 = .50
11:59 is the deadline please give me the correct answer
Answers
Answer:
[tex]6 - 8x = 5x - 10x + 15 \\10x-8x-5x=15-6\\ - 3x = 9 \\ x = \frac{9}{ - 3} \\ x = - 3[/tex]
-3 is the right answer.Answer:-3
the right answer did ths on paper
1/3 + 4 × 2/3 + (-12) ÷ 4
Answers
Suppose y varies directly with x. When
X is 2, y is 10. What is y when x is 4?
Answers
2/10 = 4/x
Cross multiply
2x X= 10x4
2x = 40
Eliminate
2x/2 = 40/2
x = 20
Kiran's family has completed 40% of a trip. They have traveled 80 miles. How far will the total trip be?
Answers
Answer:200
Step-by-step explanation: