38. A painting without its frame has
a width 2.5 times its height, h,
in inches. Its frame is 3 in. wide
all along its perimeter. What is
an expression for the area of the
framed painting in terms of h?
Simplify your expression, and write
it in standard form.
Answers
Answer:
1.5*w^2 + 15*w + 36
Step-by-step explanation:
We have to make the width of the portrait be 'w'
in addition to that the height of the frameless portrait (h) = 1.5 times its width, i.e. 1.5 * w
Frame width is 3 inches on all sides.
Therefore the area of the framed portrait is the total area of the portrait plus the area of the frame. The figure representing the above scenario is shown below.
I enclose a figure that allows us to see the problem better, the area of the rectangle ABCD is the area of the framed portrait.
From the figure, we have to:
AB = 3 + w + 3 = w + 6
BC = 3 + h + 3 = h + 6 = 1.5 * 2 +6
We know that the area of the rectangle ABCD is given as the product of the length AB and the width BC. Thus,
Area = (w + 6) * (1.5 * w + 6)
Area = 1.5 * w ^ 2 + 6 * w + 9 * w + 36
Area = 1.5*w^2 + 15*w + 36
That is, the expression for the framed portrait area in terms of the width 'w' is:
1.5*w^2 + 15*w + 36
Related Questions
There are 13 students in a kindergarten class, if each kindergartner can have only one tank, in how many ways can the teacher out
the following tasks: line leader, wipe down the tables, pass out papers?
Plsss help takin a test
Answers
Answer:
I believe it’s 2,197 possibilities because there are 13 students and 3 tasks, so you multiply 3 13’s together
13 * 13 * 13 = 2,197
Geometry
Find a:
Fill in the blank
Answers
Answer:
a=15
Step-by-step explanation:
[tex]a^{2} =9*25\\a^{2} =225\\\\\sqrt{a} =\sqrt{222\\a=15[/tex]
Hope it helps
Mrs Baker is preparing her students for their exams. The exams are two weeks away. Mrs Baker advises her students to spend 25% of each day revising.
A) How many hours does Mrs Baker expect her students to revise each day?
B)) How many hours in total will the students have revised if they follow Mrs Bakers advise for the next two weeks?
Answers
Answer:
A. 4 hours
Step-by-step explanation:
100 divided by 25
On a particular day in July, there is a 20% probability of rain in Vancouver, a 65% probability of rain in Calgary, and a 75% probability of rain in Saskatoon. What is the probability that it will rain in all 3 cities on that day?
Answers
Answer:
The probability that it will rain in all 3 cities on that day
P(V∪ C∪S) = 0.93 = 93%
Step-by-step explanation:
Let 'V' be the event of rain in Vancouver
Given that the probability of rain in Vancouver
P( V) = 20% = 0.20
P( V⁻) = 1- P( V) = 1 - 0.20 =0.80
Let 'C' be the event of rain in Calgary
Given that the probability of rain in Calgary
P( C) = 65% = 0.65
P( C⁻) = 1- P( C) = 1 - 0.65 =0.35
Let 'S' be the event of rain in Saskatoon
Given that the probability of rain in Saskatoon
P( S) = 75% = 0.75
P( S⁻) = 1- P( S) = 1 - 0.75 =0.25
First we will prove that the probability that it will not rain in all 3 cities on that day
P( V⁻ ∩ C⁻ ∩ S⁻ ) = P( V⁻) P( C⁻) P(S⁻)
= 0.80 × 0.35 × 0.25
= 0.07
The probability that it will rain in all 3 cities on that day
P(V∪ C∪S) = 1-(P( V⁻ ∩ C⁻ ∩ S⁻ )
= 1 - 0.07
= 0.93
Plssssssss........helppppppp meeeeeee
Answers
Answer:
The coefficient is 12
Step-by-step explanation:
The coefficient is the number next to the variable in the term
12p
The coefficient is 12 and the variable is p
12
Explanation:
The coefficient is the number in front of a variable.
two groups of students order cheeseburgers and chicken nuggets at mcdonald’s. one order of 9 cheeseburgers and 4 chicken nuggets cost $22.37. the other order of 3 cheeseburgers and 4 chicken nuggets cost $15.23. find the cost of a cheeseburger
Answers
Answer:
$1.19
Step-by-step explanation:
Let the cost of a cheeseburger be $b and that of a chicken nugget be $n.
From the given information, we can form 2 equations.
9b +4n= 22.37 -----(1)
3b +4n= 15.23 -----(2)
Notice that the 2 equations have '4n' in them. I'll be using elimination method to solve the equation by getting rid of the 4n.
(1) -(2):
9b +4n -(3b +4n)= 22.37 -15.23
9b +4n -3b -4n= 7.14
6b= 7.14 (simplify)
b= 7.14 ÷6 (÷6 on both sides)
b= 1.19
Thus, a cheeseburger cost $1.19.
Answer:
Step-by-step explanation
1.19
25 points:)
question 2-3
Answers
Answer:
2) r=73
Step-by-step explanation:
all 4 sided shapes add up to 360.
so 90+90=180
180+107=287
360-287=73
so r=73
There are 48 cans of soup on a crate. A supermarket has a delivery of 110 crates for £1980 and sells a can for 41p. How much profit does the supermarket make on the delivery?
Answers
Answer:
I would love to help but i dont know pounds so i will try to help in dollars then convert into pounds
lol :) just wait
Step-by-step explanation:
A box of oranges weighs 4 kg. If one orange weighs 80 g, how many oranges are in the box?
Answers
Answer:
50 oranges
Step-by-step explanation:
Convert the measurements for them to be the same ie 4kg to g
1kg=1000g. 4kgx1000=4000g
4000g is the mass of all oranges
1 orange=80g
? =4000g that is 4000/80
=50 oranges
Answer:
50 oranges
Step-by-step explanation:
Since each orange is measured in grams, we convert the 4 kg to g to start.
4 kg is equal to 4000 g.
Each orange weighs 80 g, so we divide 80g into 4000g.
80 divided by 4000 equals 50.
50 oranges are in the box.
I Hope This Helps!
answer this plz quickly
Answers
Answer: THE ANSWER IS -1/36
Step by step: Find the LCD then combine
The answer is : -1/36
You forgot the 1 for 18 in the last question lol
Hope this helps, pls mark as brainliest :))))
Kelsie sold digital cameras on her website . She bought the cameras for $65 each and includes a 60% markup to get the selling price . To the nearest dollar , what was the selling price for one camera ?
Answers
Answer:
$104
Step-by-step explanation:
First, convert 60% to a decimal.
60% = 0.6
Now, multiply the cost to buy the camera ($65) by the decimal.
$65 × 0.6 = $39
Now, add this amount to the amount it cost to buy the camera.
$65 + $39 = $104
The selling price for the camera will be $104.
Answer:
The answer is $104
The slope of AB is -2/5. Segments CD has endpoints at C(-5,3) and D(10,-3). Are AB and CD parallel, perpendicular or neither? Justify.
Answers
Answer:
AB and CD are parallel
Step-by-step explanation:
AB has the slope of -2/5
lets see what slope the line CD has:
points are (-5, 3) and (10, -3)slope= m= (y2-y1)/(x2-x1)= (-3-3)/(10+5)= -6/15= -2/5as we see AB and CD have same slope, therefore they are parallel
Amanda has at most $40 to spend on flowers. She wants to buy a pair of red rose flowers for $18 dollars and spend the rest on lily flower. Each lily flower costs $11. Write an inequality for the number of lily flowers she can purchase
Answers
Answer:
x ≤ 2
Step-by-step explanation:
2 red rose cost $ 18
x flowers cost $ 11x
"At most " means ≤.
11x + 18 ≤ 40
11x ≤ 40 - 18
11x ≤ 22
x ≤ 2
Using inequality we know that Amanda can purchase 2 lily flowers.
What is inequality?An inequality in mathematics is a relation that compares two numbers or other mathematical expressions in an unequal way. The majority of the time, size comparisons between two numbers on the number line are made.The equation-like form of the formula 5x 4 > 2x + 3 has an arrowhead in place of the equals sign. It is an illustration of inequity.So, the inequality can be:
Monet Amanda can spend is $40.She purchased a pair of roses worth $18.Rest we want to wants to buy lily, which costs $11 each.Now, the inequality will be:
Let, the number of lilies is x and Amanda purchases 2 lilies:
18 + 2x ≤ 4018 + 2(11) ≤ 4018 + 22 ≤ 4040 = 40Therefore, using inequality we know that Amanda can purchase 2 lily flowers.
Know more about inequality here:
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which of the following descriptions represent the transformation shown in the image? Part 3b
Answers
Answer: d) none of the above
Step-by-step explanation:
Start at Black Triangle: B = (0, -4) C = (4, -1) D = (2, -5)
End up at Red Triangle: B = (2, 0) C = (-2, 3) D = (0, -1)
Rotation of 180°: (x, y) → (-x, -y)
Reflection across y-axis: (x, y) → ( -x, y)
Reflection across x-axis: (x, y) → (x, -y)
Reflection across x=1: (x, y) → (2 - x, y)
[tex]a) \\\begin{array}{ccc}\qquad \text{(x, y)}&\text{Rotate 180}^o&\text{reflect across y-axis}\\B:\ (0, -4)&(0, 4)&(0,4)\\C: (4, -1)&(-4,1)&(4,1)\\D: (2, -5)&(-2,5)&(2,5)\end{array}[/tex]
[tex]b) \\\begin{array}{ccc}\qquad \text{(x, y)}&\text{Rotate 180}^o&\text{reflect across x = 1}\\B:\ (0, -4)&(0, 4)&(2,4)\\C: (4, -1)&(-4,1)&(6,1)\\D: (2, -5)&(-2,5)&(4,5)\end{array}[/tex]
[tex]c) \\\begin{array}{ccc}\qquad \text{(x, y)}&\text{Rotate 180}^o&\text{reflect across x-axis}\\B:\ (0, -4)&(0, 4)&(0,-4)\\C: (4, -1)&(-4,1)&(-4,-1)\\D: (2, -5)&(-2,5)&(-2,-5)\end{array}[/tex]
None of the given options transform the black triangle onto the red triangle.
Constructing a Circle through Three Points Not on a Line
Construct a circle through points
X, Y, and z.
Answers
Answer:
the circle has one point even if it is a concentric circle it will have one central point or it needs more collections of the circle at equidistance
Answer:
The circle would look like the image attached
Step-by-step explanation:
What is the probability of getting tails 4 times in a row while flipping a coin?
Answers
Answer:
[tex]P=0.0625[/tex]
Step-by-step explanation:
The probability of getting one tails is a half.
The probability of getting another tails given you had a tails is:
[tex]\frac{1}{2}*\frac{1}{2}=(\frac{1}{2})^2=\frac{1}{4}[/tex]
The probability of getting n tails in general is given by:
[tex](\frac{1}{2})^n = \frac{1}{2^n}[/tex]
So, when we have four tails - our value for n is four.
[tex](\frac{1}{2})^4=\frac{1}{2^4}=\frac{1}{16}=0.0625[/tex]
The temperature increased from (-3) degrees to (+12) degrees on Friday what was the temperature change over the course of the day
Answers
Answer:
+15 degrees
Step-by-step explanation:
-3
-2
-1
0
1
2
3
4
5
6
7
8
9
10
11
12
Can somebody help meeee witthhhh thisss plssss
Answers
Answer:
7.) (m+4)(m-16)
8.) Area= 3x^3-5x^2+7x+3
Step-by-step explanation:
7.) m^2-12m-64
=(m^2+4m)+(-16m-64)
=m(m+4)-16(m+4)
=(m+4)(m-16)
8.) Area = L(W)
x^2-2x+3(3x+1)
=x^2(3x)+x^2(1)+(-2x)(3x)+(-2x)(1)+3(3x)+3(1)
=3x^3+x^2-6x^2-2x+9x+3
=3x^3-5x^2-2x+9x+3
=3x^3-5x^2+7x+3
Write a coordinate proof to prove that the segment that joins the vertex angle of an isosceles triangle to the midpoint of its base is perpendicular to the base .
Answers
Answer:
Given: An Isosceles Triangle ABC with a vertex at B.
Midpoint M of the base AC.
To Prove: BM is perpendicular to AC.
Proof:
Let the coordinates of the points of the isosceles triangle be given as:
A = (-k, 0)
Vertex, B = (0,a)
C = (k, 0)
Midpoint, M = (0,0)
Slope of the base segment, AC:
[tex]=\dfrac{dy}{dx} = \dfrac{0 - 0}{k - (-k)} = \dfrac{0}{2\cdot k}[/tex]
Slope of the base segment, AC= [tex]\dfrac{0}{2\cdot k}=0[/tex]
Slope of the segment that joins the vertex angle of an isosceles triangle to the midpoint of its base, BM.
[tex]\text{Slope of BM =} \dfrac{0 - a}{0 - 0} = \dfrac{-a}{0}\\[/tex]
[tex]\text{Slope of BM = } \dfrac{-a}{0}[/tex] = Undefined
Two lines are perpendicular if the gradient of one is a negative reciprocal of the other.
Since [tex]-\dfrac{a}{0}[/tex] is a negative reciprocal of 0 for arbitrary values of a, BM and AC are perpendicular.
This concludes the proof.
Jacob can run 9 miles in 1 hour and
15 minutes. What is his average running speed per minute?
Answers
Answer:
0.12 miles per minute
Step-by-step explanation:
9/75 is 0.12. 9 miles in 75 minutes
Average speed of Jacob is 0.12 miles per minute.
What is unitary method ?Unitary method is a method of finding value of a single unit.After finding value of a single unit we can determine values of any given unit.
According to the given question Jacob can run 9 miles in 1 hour and
15 minutes.
We know 1 hour is 60 minutes.
∴ 1 hour and 15 minutes is
= (60 + 15) minutes.
= 75 minutes.
So, Jacob can run 9 miles in 75 minutes.
∴ In one minute Jacob can run 9/75 miles shich is
= 0.12 miles per minute.
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Given that f(x) = x^2? + 9x + 18 and g(x) = x + 3, find (f ÷ g) (x) and express the result in standard form.
Answers
Answer:
x + 6
Step-by-step explanation:
(f ÷ g)(x)
= [tex]\frac{x^2+9x+18}{x+3}[/tex] factorise the numerator
= [tex]\frac{(x+3)(x+6)}{x+3}[/tex] ← cancel the factor (x + 3) on numerator/ denominator
= x + 6
Find the equation of the line that is perpendicular to y = -3/4x+1 and contains the point (9,12).
Answers
Answer:
[tex]y = \frac{4}{3} x[/tex]
Step-by-step explanation:
Perpendicular = m1*m2 = -1
[tex]-\frac{3}{4}*\frac{4}{3} = -1[/tex]
[tex]y = \frac{4}{3} x +b[/tex]
[tex]12 = \frac{4}{3}(9)+b\\12 = 12 + b\\b = 0\\y = \frac{4}{3} x+0\\y = \frac{4}{3} x[/tex]
The equation of the line perpendicular to the given line is [tex]y=\frac{4}{3}x[/tex].
Given that, the equation of a line [tex]y=\frac{-3}{4}x+1[/tex] and the coordinate point (9, 12).
What is the slope of perpendicular lines?Slope of a perpendicular line can be computed from the slope of a given line. The product of the slope of a given line and the slope of the perpendicular line is equal to -1. If the slope of a line is m1 and the slope of the perpendicular line is m2, then we have m1.m2 = -1.
From the given equation of a line slope m1=-3/4
The slope perpendicular to equation of line m2 = -1/m1 = 4/3
Now, substitute m=4/3 and (9, 12) in y=mx+c and solve for c.
That is, [tex]12=\frac{4}{3} \times 9 +c[/tex]
⇒ c=0
Put c=0 and m=4/3 in y=mx+c, we get
[tex]y=\frac{4}{3}x[/tex]
Therefore, the equation of the line perpendicular to the given line is [tex]y=\frac{4}{3}x[/tex].
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How much is $100 U.S. dollars in Canadian dollars?
Answers
Answer:
133.98
Step-by-step explanation:
Step by Step Explanation:
Can someone please help me
Answers
Answer:jss needed point srry
Step-by-step explanation:
fully Factorise 7m^2 + 13m
Answers
Answer:
[tex]m(7m + 13)[/tex]
Step-by-step explanation:
[tex]7m {}^{2} + 13m \\ m(7m + 13)[/tex]
May drives a total of 44 miles each day to take her children to and from school. The children go to school 5 days a week. May's vehicle gets 17 miles per gallon of gas. About how many gallons of gas does May need to take her children to and from school each week?
Answers
Answer:
12.94 gallons/week
Step-by-step explanation:
44x5=220
220/17=12.94
Answer:
13 gallons
Step-by-step explanation:
44 miles x 5 days = 220 miles
220 miles / 17mpg = 12.9
12.9 rounded up is 13
Final Answer is 13 gallons
Find (fg)(x) using long division for f(x)=2x3−12x2+7x−27 g(x)=2x2+5 The quotient is The remainder is
Answers
Answer:
f(x)/g(x) = x - 6 + (2x+3)/(2x^2+5)
Quotient = x - 6
Remainder = (2x+3)/(2x^2+5)
Step-by-step explanation:
Getting x-6:
What number multiplies with 2x²+5 to get 2x³+...?
that number is x, so that's your first number. You multiply it with 2x²+5 and subtract it like how you would do divison by hand back in elementary school.
Now what number multiplies with 2x²+5 to get -12x²+ ...?
that number would be 6, so that's your second number. Multiply 2x²+5 with 6 and subtract it from -12x²+ ....
Now you have 2x+3. What number multiplies with 2x²+5 to get 2x+3? That number doesnt exist so 2x+3 is your remainder.
PLEASE HELP
Write an equation to model the data.
x y
−1 2.5
0 5
1 10
2 20
3 40
Answers
Answer:
y = 5(2)ˣ
Step-by-step explanation:
numbers are doubled for y as x is changing by 1
it indicates exponential growth with y intercept 5 and rate 2: y = 5(2)ˣ
Q 1. The area of a certain rectangle is 1 m².What is the area of a triangle that was cut off from that rectangle along a line connecting the midpoints of two adjacent sides?
Answers
Answer:
0.125 m²
Step-by-step explanation:
The area of a rectangle is the product of its length and breadth. Therefore:
area of the rectangle = length (l) × breadth (b) = 1 m².
l × b = 1
A triangle is cut off from that rectangle along a line connecting the midpoints of two adjacent sides, therefore the base of the triangle = length of rectangle/2 and the height of triangle = breadth of rectangle/2.
Area of triangle = 1/2(base × height) = [tex]\frac{1}{2}*\frac{l}{2}*\frac{b}{2}=\frac{1}{8}lb[/tex]
since lb = 1:
Area of triangle = [tex]\frac{1}{8}*1=0.125m^2[/tex]
What’s the answer to this?
Answers
Answer:
125.5 cm²
Step-by-step explanation:
At = A(rectangle) + A(trapeze)
= A = L×W + (b + B)×h/2
= 6.1cm×5cm + (6.1cm + 12.9cm)×10cm/2
= 30.5 cm² + 19cm×5cm
= 30.5 cm² + 95 cm²
= 125.5 cm²
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