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
Ian has 20 football cards, and Jason has 44 baseball cards. They agree to trade such that jason
gives Ian 2 baseball cards for every card Ian gives to Jason. After how many such trades will Ian
and Jason each have an equal number of cards?
Answers
Answer:
12 trades
Step-by-step explanation:
Let's call 'x' the number of trades they will do.
After each trade, the number of cards Ian has increase by 1 (he gives 1 but receives 2), and the number of cards Jason has decrease by 1 (he receives 1 but gives 2), so after x trades, the number of cards Ian has is 20 + x, and Jason has 44 - x.
To find the number of trades when they will have the same amount of cards, we have that:
20 + x = 44 - x
2x = 24
x = 12 trades
The number of trades will Ian and Jason each have an equal number of cards is 12 trades
The calculation is as follows;
Let's us assume the x' be the number of trades they will do.
20 + x = 44 - x
2x = 24
x = 12 trades
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answer this plz to be rater 5 stars
Answers
Answer:
Step-by-step explanation:
3 min 20 seconds = 3*60 + 20 = 180 +20 = 200 seconds
2 min 44 seconds = 2*60 + 44 = 120 + 44 = 164 seconds
Improvement = 200 - 164 = 36 seconds
Percentage =(36/200) *100
= 18 %
solve the following equation 2x-7/4=x+3/3
Answers
Answer:
x=11/4
Step-by-step explanation:
2x-7/4=x+3/3
2x-7/4=x+1
-x -x
x-7/4=1
+7/4 +7/4
x=11/4
A total of 70 tickets were sold for a concert and earn the organizers $804. If the cost of each ticket is either $10 or $12, how many tickets of each type were sold?
A. $18 tickets cost $10 AND 52 tickets cost $12
B. 52 tickets cost $10 and 18 tickets cost $12
C. 65 tickets cost $12 and 5 tickets cost $10
D. 5 tickets cost $12 and 65 tickets cost $10
WILL GIVE BRAINLIEST WHEN I CAN!!!!!!
Answers
Answer:
52 tickets cost $10 and 18 tickets cost $12
Step-by-step explanation:
10x+12y=804. (1)
x+y=70. (2)
From (2)
x=70-y
Substitute x=70-y into (1)
10x+12y=804
10(70-y)+12y=804
700-10y+12y=804
700+2y=804
2y=804-700
2y=104
y=104/2
y=52
Recall
x+y=70
x+52=70
x=70-52
x=18
52 tickets cost $10 and 18 tickets cost $12
By solving a system of equations we will see that the correct option is A.
How to write and solve a system of equations?
First, let's define the variables:
x = number of $10 tickets sold.y = number of $12 tickets sold.First, we know that 70 tickets were sold, so:
x + y = 70
And we know that they reached $804, then we have:
x*$10 + y*$12 = $804
Then our system is:
x + y = 70
x*$10 + y*$12 = $804
To solve this, we first need to isolate one of the variables in one of the equations, I will isolate x on the first equation:
x = 70 - y
Now we can replace that in the other equation to get:
(70 - y)*$10 + y*$12 = $804
$700 - y*$10 + y*$12 = $804
$700 + y*$2 = $804
y*$2 = $804 - $700 = $104
y = $104/$2 = 52
So, 52 $12 tickets were sold, then the other 18 tickets were $12, so the correct option is A.
If you want to learn more about systems of equations, you can read:
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Find the equation of the circle whose center and radius are given. center ( 5, 6), radius=3
Answers
Answer:
(x-5)^2 + (y-6)^2 = 9
Step-by-step explanation:
The equation of a circle is given by
(x-h)^2 + (y-k)^2 = r^2 where ( h,k) is the center and r is the radius
(x-5)^2 + (y-6)^2 = 3^2
(x-5)^2 + (y-6)^2 = 9
Misha found that the equation –|2x – 10| – 1 = 2 had two possible solutions: x = 3.5 and x = –6.5. Which explains whether or not her solutions are correct? She is correct, because both solutions satisfy the equation. She is not correct, because she made a sign error. She is not correct, because there are no solutions. She is not correct, because there is only one solution: x = 3.5. help plz
Answers
Answer:
She is not correct, because there are no solutions
Step-by-step explanation:
–|2x – 10| – 1 = 2
Add 1 to each side
–|2x – 10| = 3
Divide by -1
|2x – 10| = -3
An absolute value is positive and it would have to equal -3
This cannot happen so there is no solution
Answer:
She is not correct, because there are no solutions
Step-by-step explanation: C
I need help please it’sGeometry
Answers
Answer:
Congruent triangles have the same perimeter so the answer is 13.
Please help ASAP! Which ordered pair is a solution of this
equation?
-5x - 9y = -8
Click on the correct answer
A.
(2,-1)
B.
(-1,2)
C.
(-22)
D.
(2,-2)
Answers
========================================================
Explanation:
For each possible answer choice, you'll plug in the given coordinates to see which results in a true equation or not.
If we try choice A, then we plug in x = 2 and y = -1 to get
-5x-9y = -8
-5(2)-9(-1) = -8
-10+9 = -8
-1 = -8 which is false
So (x,y) = (2,-1) is not a solution. We can cross choice A off the list.
You'll find a similar situation happens with choices B and D. They don't work either.
-------
Choice C works because...
-5x-9y = -8
-5(-2)-9(2) = -8 .... replaced x with -2, replaced y with 2
10-18 = -8
-8 = -8
We get a true equation. So (-2,2) has been confirmed to be a solution.
Jon is playing a game with his friend Mike. Mike rolls two dice three times. Each time Mike rolls the dice, Jon squares both numbers and subtracts the smaller square from the larger square. After all three rolls, Jon adds the three numbers he obtained from the three rolls. If Mike rolls a 4 and a 3 on the first roll, a 6 and a 2 on the second roll, and a 3 and a 1 on the third roll, what is the sum that Jon obtains?
Answers
Answer:47
Step-by-step explanation:
On first roll Mike gets 4 and 3
So number he gets after subtraction of square is
[tex]\Rightarrow 4^2-3^2=7[/tex]
On second roll Mike gets 6 and 2
So number he gets after subtraction of square is
[tex]\Rightarrow 6^2-2^2=32[/tex]
On Third roll Mike gets 3 and 1
So number he gets after subtraction of square is
[tex]\Rightarrow 3^2-1^2=8[/tex]
Sum of numbers[tex]=7+32+8=47[/tex]
John obtains [tex]47[/tex] as sum
What is the greatest decimal place value?
Answers
Answer:
the digit farthest to the left
Answer:
The digit farthest to the left.
Step-by-step explanation:
I hope this helps
Which word describes a triangle with three angles, if each angle measures less than 90°? Please help
Answers
Answer:
acute triangle
Step-by-step explanation:
If an angle measures less than 90 degrees it is an acute angle
A triangle with all acute angles is an acute triangle
Two friends can paddle a canoe at a rate of 6 km/h in still water. It takes them 1 h in total to paddle 2 km up a river and another 2 km back. Find the speed of the current, rounded to the nearest tenth.
Answers
Answer: The speed of the current is 3.5 km/h.
Step-by-step explanation:
When they move in the river, the speed of the canoe is:
Sc is the speed of the canoe and Sr is the speed of the current.
Sc + Sr (when they move in the same direction as the current)
Sc - Sr (when they move in the opposite direction as the current)
So we have that in one hour, they moved 2km and then they returned other 2km.
Now, using the relation:
Velocity*time = distance
we can write 1hour = T1 + T2 such that:
(Sc + Sr)*T1 = 2km
(Sc - Sr)*T2 = 2km
T1 + T2 = 1hour -------> T2 = 1h - T1
Sc = 6km/h.
So we can write this as two equations:
(6km/h + Sr)*T1 = 2km
(6km/h - Sr)*(1h - T1) = 2km.
Now, the first step will be isolate one of the variables in one equation, we can get:
T1 = 2km/(6km/h + Sr)
and replace it in the second equation:
(6km/h - Sr)*(1h -2km/(6km/h + Sr)) = 2km.
Now we solve this for Sr, i will ignore the units, so it is easier to read the math.
(6 - Sr) - 2*(6 - Sr)/(6 + Sr) = 2
(6 - Sr)*(6 + Sr) - 2*(6 - Sr) = 2*(6 + Sr)
6^2 - Sr^2 - 12 + 2*Sr - 12 - 2*Sr = 0
-Sr^2 + 36 -12 -12 = 0
-Sr^2 + 12 = 0
Sr = √12 = 3.5km/h
(where we take the positive value of the square root)
The speed of the current is 3.5 km/h
Speed is the ratio of distance travelled to time taken. It is given by:
Speed = distance / time
Let a represent the speed of the current and t₁ represent the time spent paddling up and t₂ represent the time spent paddling back. Hence:
(6 - a)(t₁) = 2 km
t₁ = 2 / (6 - a) (1)
(6 + a)(t₂) = 2 km
t₂ = 2 / (6 + a) (2)
t₁ + t₂ = 1 hour
[2 / (6 - a)] + [2 / (6 + a)] = 1
12 + 2a + 12 - 2a = 36 - a²
a² - 12 = 0
a = 3.5 km/h
The speed of the current is 3.5 km/h
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What’s 4x^2+28x+24 factored?
Answers
Answer:
[tex](4x + 4)(x + 6) \\ [/tex]
Step-by-step explanation:
[tex]4 {x}^{2} + 28x + 24 \\ 4 {x}^{2} + 24x + 4x + 24 \\ 4x(x + 6) + 4(x + 6) \\ (4x + 4)(x + 6)[/tex]
hope this helps you.
brainliest appreciated
good luck!
have a nice day!
If the point (9, 5) is translated 6 units left and 5 units up, then find the
translated coordinates of the point.
Answers
Answer:
I think it might be (-3,10). I am not a 100% sure.
Step-by-step explanation:
A baseball team won 9 games, which was 60% of the total number of games the team played. How many total games did the team play?
Answers
Answer: The team played 15 games total
Step-by-step explanation: 9 is 60 percent of 15.
What is the value of x in the equation - 3X+9
x+9= 3-37?
Answers
3x+9x=12x+9
3-37=-34
12x+9=-34
Cancel 9 out
12x=-43
Divide by 12
X=-3.5
YEAR 9 MATHS PLEASE QUICKLY HELP THIS WONT TAKE LONG
Here are six shapes made from centimetre squares.
Write down the letter of a shape with rotational symmetry of order 2.
(1 mark)
Answers
Answer:
letter of a shape with rotational symmetry of order 2 is B,D and F
Answer:
Step-by-step explanation:
i strongly believe it is rotational symmetry of order 2 is B,D and F .
hope it helps
-Delilah
Jim, Dan and David share some sweets in the ratio 3:1:5. Jim gets 21 sweets. How many more sweets does David get over Dan?
Answers
Answer:
David gets 28 more than Dan
Step-by-step explanation:
Jim: Dan : David: total
3 : 1 : 5 : 3+1+5 = 9
Jim gets 21
21/3 = 7
Multiply each number by 7
Jim: Dan : David: total
3*7 : 1*7 : 5 *7 : 9*7
21 : 7 : 35 : 63
David has 35 and Dan has 7
35-7 = 28
David gets 28 more than Dan
HELP PLEASE WITH THE IMAGE BELOW it would mean a lot if someone helped me answer this question and maybe even explain how you got it.
Answers
Answer:
65/97 = 0.67
Step-by-step explanation:
using trigonometric ratios
Cosine of angle = [tex]\frac{adj}{hyp}[/tex]
Which arcs are congruent? Check all that apply. Arc B C ≅ Arc M P Arc B C ≅ Arc M O Arc C F ≅ Arc K P Arc E G ≅ Arc K L Arc L O ≅ Arc M P
Answers
Answer:
Step-by-step explanation:
The arcs that are congruent are:
Arc B C ≅ Arc M P. Arc E G ≅ Arc K L. Arc L O ≅ Arc M P.What congruent angles in math?
Two geometric figures can be described as congruent if on can be superpose on the other.
Conclusively, congruent' is said to be a word that connote 'exactly equal' when looking at the shape and size of the angles. The options chosen above are congruent because they have the sides to be equal.
Learn more about congruent from
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What is Three-fourths divided by one-sixth?
Answers
Answer:
9/2 or 4.5
Step-by-step explanation:
3/4 divided by 1/6 changes into multiplication and you switch one of the denominators
it becomes 3/4 times 6/1 which is 18/4 when simplified, it's 9/2
Answer:
9/2
Step-by-step explanation:
Jessica decides to mix grades of gasoline in her truck. She puts in 8 gallons of regular and 8 gallons of premium for a total cost of $41.04. If premium gasoline costs $0.21 more per gallon than regular, what was the price of each grade of gasoline?
Answers
Answer:
The price of the regular gasoline is $2.46, while the premium is $2.67.
Step-by-step explanation:
Let the price of regular gasoline be "x", while the price for the premium be "y", The sum of the amount of each type of gas multiplied by its cost should be equal to the total paid, therefore:
[tex]8*x + 8*y = 41.04[/tex]
We also know that the premium gas costs 0.21 more than the regular one, therefore:
[tex]y = x + 0.21[/tex]
We can apply the second expression on the first, in order to solve for "x".
[tex]8*x + 8*(x + 0.21) = 41.04\\8*x + 8*x + 1.68 = 41.04\\16*x = 41.04 - 1.68\\16*x = 39.36\\x = \frac{39.36}{16} = 2.46[/tex]
[tex]y = 2.46 + 0.21 = 2.67[/tex]
The price of the regular gasoline is $2.46, while the premium is $2.67.
There are 130 people in a sport centre.
76 people use the gym.
60 people use the swimming pool.
32 people use the track.
23 people use the gym and the pool.
8 people use the pool and the track.
20 people use the gym and the track.
6 people use all three facilities.
A person is selected at random.
What is the probability that this person doesn't use any facility?
Answers
Answer:
7/130Step-by-step explanation:
Using set notation to answer the question. let:
n(U) be the total people in a sport centre =130
n(G) be number of people that use the gym. = 76
n(P) be number of people that use the swimming pool. = 60
n(T) be number of people that use the track = 32
n(G∩P) be number of people that uses the gym and the pool = 23
n(P∩T) be number of people that uses the pool and the track = 8
n(G∩T) be number of people that uses the gym and the track = 320
n(G∩P∩T) be number of people that uses all three facilities = 6
Using the relationship below;
n(U)= n(GUPUT)+n(GUPUT)'
where n(GUPUT)' is the number of people that doesn't use any facility.
Before we can get that, we need to know n(GUPUT) using the formula;
n(GUPUT) = n(G) + n(P)+n(T)-n(G∩P)-n(P∩T)-n(G∩T)+n(G∩P∩T)
n(GUPUT) = 76+60+32-23-8-20+6
n(GUPUT) = 123
n(GUPUT)' = n(U)- n(GUPUT)
n(GUPUT)' = 130 - 123
n(GUPUT)' = 7
This means that 7 person doesn't use any facility.
Probability that a person selected at random doesn't use any facility = n(GUPUT)' /n(U) = 7/130
On Monday, 230 students were supposed to go on a trip to the zoo but 22 did not have permission slips. 5 buses were filled and 8 students had to travel in cars. How many students were in each bus
Answers
Answer:
40 kids traveled in each bus
hope this helped
Step-by-step explanation:
230- 22= 208
208-8= 200
200÷5 =40
Answer:
40 students road on each bus
Step-by-step explanation:
230-22=208
208-8=200
200÷5=40
Isosceles and Equilateral triangles question! 60 POINTS!!
How do I figure out what "a" is equal to? Thanks!
Answers
Answer:
a = 43
Step-by-step explanation:
If PQ = PR, then P = R
The sum of the angles of a triangle is 180
P+Q+R = 180
47+2a + 47 = 180
Combine like terms
94 + 2a = 180
Subtract 94 from each side
2a = 180-94
2a = 86
Divide by 2
2a/2 = 86/2
a = 43
Answer:
43
Step-by-step explanation:
PQ = PR, so P = R
P + Q + R = 180
47+2a + 47 = 180
2a = 180 - 47 - 47
2a = 86
= 43
Hope this helps!
What is x value?? :D
Answers
Answer:
x=6
Step-by-step explanation:
You can reach this answer by doing
4+(x-3) = 2x-5
If you do this equation you will get 6 as your answer.
Hope this helps :)
Find the surface area.
Answers
The answer is c
Find the area of the triangle to get 72cm^2. There are two triangles so times 72 by 2 to get 144
Find the area of the first side by doing 12 x 30 = 360cm^2
Find the area of the second side by doing 9 x 30 = 270cm^2
Find the area of the base by doing 18 x 30 = 540cm^2
Add 144+360+270+540 = 1314cm^2
Given the following functions, find each: f(x)=x2+5x−14 g(x)=x−2 (f+g)(x)= (f−g)(x)=
Answers
Answer:
(f+g)(x) = x²+5x-14 + (x-2)
= x²+5x-14+x-2 = x²+6x-16
(f-g)(x) = x²+5x-14 - (x-2)
= x²+5x-14 - x+2
= x²+5x-14-x+2 = x²+4x-12
Which of these is an equation? 8t+4=76 8t+4 8z 8+4
Answers
Answer:
8t+4=76
Step-by-step explanation:
An equation needs an equals sign otherwise it is an expression
What is the decimal multiplier to increase by 39%?
Answers
The decimal multiplier to increase by 39% is 1.39
A decimal multiplier is used when determining the percentage of a particular amount.
From the information given:
the decimal multiplier required to increase by 39% can be determined as follows:
[tex]\mathbf{=\dfrac{100}{100} + \dfrac{39}{100}}[/tex]
[tex]\mathbf{=1 +0.39}[/tex]
= 1.39
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