The dimensions of the paint, obtained by factoring the polynomial function for the area of the tray, 42·x + 135·x + 108 are as follows;
(a) The width of the tray = 6·x + 9
(b) Area of the square paint compartment is 9 in²
(c) The width of the edges is 12 inches
What are the factors of a polynomial?The factors of a polynomial are other polynomials of lesser degree, that when multiplied together, produces the polynomial which is factored.
The area of the paint tray = 42·x² + 135·x + 108 in²
The dimensions of the square paint compartment are the same
Space along the edge of the tray = 2 × space between the squares
(a) The length of the tray obtained from the diagram in the question = 7·x + 12 inches
Using an online tool, we get;
42·x² + 135·x + 108 = 3·(2·x + 3)·(7·x + 12)
The area of a rectangle = Length × Width
Therefore, the width of the tray = The area ÷ The length
Width = (42·x² + 135·x + 108)/(7·x + 12) = 3·(2·x + 3)
The width of the tray = 3·(2·x + 3) = 6·x + 9(b) Let s represent the side length of each square paint compartment, we get;
Width of four compartments + 3 spaces between compartments = (7·x + 12) - 2 × 2·x
Width of four compartments + 3 spaces between compartments = 4·s + 3·x
4·s + 3·x = (7·x + 12) - 2 × 2·x = 3·x + 12
4·s = 3·x + 12 - 3·x = 12
s = 12/4 = 3
s = 3
The side length of each square = 3 inches
The area of each square paint compartment = s²
s² = 3² = 9
The area of each square paint compartment = 9 square inches(c) Where the width = 45 inches, we get;
3·(2·x + 3) = 45
2·x + 3 = 45/3 = 15
2·x + 3 = 15
2·x = 15 - 3 = 12
x = 12/2 = 6
x = 6
The width of the edges of the tray = 2·x
2·x = 2 × 6 = 12
The width of the edges of the tray = 12 inches
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Tell whether the ordered pair is a solution of the system of equations. Y=3x-3 Y=-x+5 (3,6)
9514 1404 393
Answer:
not a solution
Step-by-step explanation:
The given pair does not satisfy the second equation.
y = -x + 5
6 = -3 + 5 . . . . . . . . false for (x, y) = (3, 6)
The ordered pair is not a solution to the system of equations.
If x and y vary directly and x=25 when y=100 find x when y=24.
PLEASE HELP FASTTTTTTT
Answer:
x = 6
Step-by-step explanation:
Given that x and y vary directly then the equation relating them is
y = kx ← k is the constant of variation
To find k use the condition x = 25 when y = 100 , then
100 = 25k ( divide both sides by 25 )
4 = k
y = 4x ← equation of variation
When y = 24 , then
24 = 4x ( divide both sides by 4 )
6 = x
Which postulate or theorem proves that triangle JHG and
triangle EFG are congruent?
•HL Congruence Theorem
• ASA Congruence Postulate
•SAS Congruence Postulate
• AAS Congruence Theorem
Answer:
The answer is AS A Congruence Postulate.
Step-by-step explanation:
Mike earned $150 by selling 75 boxes of cookies to his neighbors using the same rate for the cost of one box of cookies how many more boxes of cookies would mike need to sell to earn, show your work!
Answer:
to earn what
Step-by-step explanation:
Answer:
2 boxes of cookies
Step-by-step explanation:
It would be $150/75 which equals 2.
can someone help please lol
Answer:
1. (an closed circle) on the negative 2 mark, then shade everything on the right. (Meaning anything greater than -2, such as -1, 0, 1, 2)
2. (an open circle) on the positive 3 mark, then shade everything right. (Meaning anything greater than 3, such as 4, 5, 6)
in
After seling 15 lemonades. Jessicamade $5. After seling 42 lemonades, she
made $18.50. Write and solve an equation to find how much Jessica spent
on supples.
Answer:Let x be the number of full cup sold Let y be the number of half cup sold Whether the cup was full or not, they used 37 cups. Therefore, x + y = 37 How much money did they make selling half cup lemonade? They made y × 0.25 How much money did they make selling full cup lemonade? They made x × 0.50 Money made selling full cup + money made selling half cup = 15 x × 0.50 + y × 0.25 = 17 You end up with a system of linear equation to solved x + y = 37 x × 0.50 + y × 0.25 = 17 x + y = 37 equation 1 0.50x + 0.25y = 17 equation 2 Solve for y in equation 1 x + y = 37 x - x + y = 37 - x y = 37 - x Replace y in equation 2 0.50x + 0.25 (37 - x) = 17 0.50x + 0.25 × 37 - 0.25x = 17 0.50x + 9.25 - 0.25x = 17 0.25x + 9.25 = 17 0.25x + 9.25 - 9.25 = 17 - 9.25 0.25x = 17 - 9.25 0.25x = 7.75 Divide both sides by 0.25 0.25x/0.25 = 7.75/0.25 x = 31 y = 37 - x = 37 - 31 = 6 Sasha and Francisco sold 31 full cup and 6 half cup of lemonade It seems like people love their lemonade
Step-by-step explanation:
hoped this helpedddd
105 students in 3 Classes
Answer:
35
Step-by-step explanation:
just divide em
How many solutions does -7+5x=5x+9
Answer:
There are no solutions. This question is impossible.
Step-by-step explanation:
Yoko's fish tank has 18 liters of water in it. She plans to add 5 liters per minute until the tank has more than 48 liters. What are the possible numbers of minutes Yoko could add water?
Answer:
7 minutes, 8 minutes, 9 minutes, or more
Really any minute more than 6 should do.
Step-by-step explanation:
48 - 18 = 30
30 ÷ 5 = 6
It says the tank should have more than 48 liters, so the answer should be more than 6 minutes.
how do you simplify 1/5 x 22
Answer:
The person above is correct
Step-by-step explanation:
Answer: 4 2/5
Step-by-step explanation:
Smart people answer please
Answer:
what the other guy said
Step-by-step explanation:
lol
I need help with this problem Try not to answer this try to give me steps
Answer:
Step-by-step explanation:
80 inches = 6 feet and 8 inches
Q5) 60% of a number is 54. What is 50 % of the same?
Answer:
45
Step-by-step explanation:
we multiply 50 by 54 and divide 60 my the number you get after multiplying
so 50*54/60 that is 45
a straight line has equation 4y-5x=2 work out the gradient of this line
Answer:
gradient = [tex]\frac{5}{4}[/tex]
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope (gradient) and c the y- intercept )
Given
4y - 5x = 2 ( add 5x to both sides )
4y = 5x + 2 ( divide the terms by 4 )
y = [tex]\frac{5}{4}[/tex] x + [tex]\frac{1}{2}[/tex] ← in slope- intercept form
with gradient m = [tex]\frac{5}{4}[/tex]
Encierra todo los números que sean menores para 25,000 003
Which value of x would make FG || BC?
с
В
х+ 3
ОООО
х+6
6
G
F
X-1
х+1
A
Answer:
9Step-by-step explanation:
Find the diagram attached
Using the similarity theorem
A F/F B = AG/GC
x+1/x+6 = x-1/x+3
Cross multiply
(x-1)(x+6) = (x+1)(x+3)
Expand
x²+6x-x-6 = x²+x+3x+3
5x - 6 = 4x+3
5x-4x = 3+6
x = 9
Hence the value of x is 9
You have 8 names of people on a list. If you randomly chose pairs of two's, how many potential pairs are there?
Answer:
56
Step-by-step explanation:
Because there are 8 names and when you choose a name there are 7 people that can be a pair so 7*8=56
Factor the expression: 12x + 16
Answer:
12x+16
~Grouping~
12+16
4(3+4)
~Solution~
4(3+4)
Step-by-step explanation:
Hope that helps!!! :)
Answer:
Step-by-step explanation:
All you can do with this is take out a common factor of 4
12x / 4 = 3x
16 / 4 = 4
So the answer is
4 (3x + 4)
Which equation below can you use to solve for the width, w, of this rectangle?
A=2w + 2(w-2.3) =53
B=2(2w) + 2.3w = 53
C=2w + 2 (w+2.3) = 53
D=2w + 2w + 2.3
Answer:
w=2Step-by-step explanation:
3x + 80 = 12x - 1
what’s the value of x ?
Answer:
9
Step-by-step explanation:
3x+80=12x-1
80=12x-3x-1
80=9x-1
9x=80+1
9x=81
x=81/9
x=9
Ifj. 1. what is the value of i
Answer:
i
Step-by-step explanation:
The square root of a negative number is identified as an imaginary number (i )
An imaginary number (i) with exponent 3 or any other exponent remains an imaginary number.
The answer is:
i
A game and a controller are on sale for 45% off. The regular price of the game is $80. The regular price of the controller is $120. What is the sale price for the game
What is the answer to this ? I totally forgot how to this kind of math 5/7 x 1/2
Answer:
5/14
Step-by-step explanation:
Answer:
5/14 or 0.357
Step-by-step explanation:
just multiply across (5x1 and 7x2 --> 5/14)
2-2 and its reciprocal
Answer:
2^-2= 4^-1 =1\4
1\4=4
so I hope you get to it
please help and show work
To prove that the triangle is scalene, calculate all the lengths of the sides.
The formula for a line like this is basically pythagorean theorem, which is
[tex]p = \sqrt{ {(y2 - y1)}^{2} + {( x2 - x1})^{2} } [/tex]
(x1, y1) and (x2, y2) are the respective vertexes.
5 Which equation is equivalent to
3(2 x – 5) = 4( x + 3)?
A 2x= -27
B 2 x= 27
C 10 x=-27
D 10 x=-3
Answer:
I think its B
Step-by-step explanation:
Let's solve your equation step-by-step.
3(2x−5)=4(x+3)
Step 1: Simplify both sides of the equation.
3(2x−5)=4(x+3)
(3)(2x)+(3)(−5)=(4)(x)+(4)(3)(Distribute)
6x+−15=4x+12
6x−15=4x+12
Step 2: Subtract 4x from both sides.
6x−15−4x=4x+12−4x
2x−15=12
Step 3: Add 15 to both sides.
2x−15+15=12+15
2x=27
Step 4: Divide both sides by 2.
The equation is equivalent to given equation is 2x=27. Therefore, option B is the correct answer.
What is an equivalent equation?Algebraic equations with equivalent solutions or roots are called equivalent equations. An analogous equation is one that is created by adding or removing the identical quantity or expression from both sides of a given equation. An equation is equivalent if both sides are multiplied or divided by the same non-zero value.
The given equation is 3(2x-5)=4(x+3).
Now, 6x-15=4x+12
6x-4x=12+15
2x=27
The equation is equivalent to given equation is 2x=27. Therefore, option B is the correct answer.
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Mr. Hepworth bought a new refrigerator for $975 after a 25% discount, how much did the refrigerator cost originally?
Answer:
954
Step-by-step explanation:
Answer:
1218.75
Step-by-step explanation:
25% of $975 = 243.75
Discounted price + Discount = Original Price
$975 + 243.75 = 1218.75
Your friend's house is 6 miles south and 14.4 miles east of the bank. How far is your friend's house from the bank?
Answer: 15.6 miles
Step-by-step explanation:
If you draw it out it makes a triangle which you can then use the pythagorean theorem to find the actual distance between the house and the bank. Your equation should be sqroot of 6^2+14.4^2 which equals 15.6 miles. Hope this helps. :)
John drew a scale drawing of a house and its lot. The house's driveway is 4 inches wide in the
drawing. The actual driveway is 20 feet wide. What scale did John use?
Answer:
John used the metric scale.
Step-by-step explanation:
Answer:
Step-by-step explanation:
20ft=(20)12=240in
4/240=1/60
Angle A and angle B are supplementary angles. If the measure of angle A = (3x - 12) and the measure of angle B = (4x - 25), find the measure of angle B.
Answer:
what is x so I can help you.