The area of a figure is the amount of space the figure can occupy. [tex]18a^4 + 10[/tex] of the door will be made from the wood.
Given
[tex]Length = 6a^2 + 2[/tex]
[tex]Width = 3a^2 + 5[/tex]
First, calculate the area of the rectangular door
[tex]Area = Length \times Width[/tex]
[tex]Area =(6a^2 + 2) \times ( 3a^2 + 5)[/tex]
[tex]Area = 18a^4 + 6a^2 + 30a^2 + 10[/tex]
[tex]Area = 18a^4 + 36a^2 + 10[/tex]
Next, calculate the area of the glass panel
The dimension of the glass panel is not given, and the diagram is not attached. So, I will assume the dimension of the square glass panel is [tex]6a[/tex].
So, the area of the glass panel is:
[tex]Area = 6a \times 6a[/tex]
[tex]Area = 36a^2[/tex]
To calculate how much wood that will be needed for the rectangular door, we simply subtract the area of the glass panel from the area of the door
[tex]Wood = 18a^4 + 36a^2 + 10 - 36a^2[/tex]
Collect like terms
[tex]Wood = 18a^4 + 10 + 36a^2 - 36a^2[/tex]
[tex]Wood = 18a^4 + 10[/tex]
Considering the assumed value, [tex]18a^4 + 10[/tex] of the door will be made from the wood.
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1. 3x + y = -3
What is the x intercept
Answer:
Step-by-step explanation:
When calculating x-intercept, always think: y=0.
Putting this into the formula creates:
3x+0 = -3
3x = -3
x = -1
HELP FAST A vertical slice through a three-dimensional solid produces a two-dimensional shape. (shape is a triangle)
Answer:
the surface of "C" would be a triangle if sliced vertically
Step-by-step explanation:
If vertical slice through a three-dimensional solid produces a two-dimensional shape is triangular prism, option C is correct.
What is Three dimensional shape?a three dimensional shape can be defined as a solid figure or an object or shape that has three dimensions—length, width, and height.
If a vertical slice through a three-dimensional solid produces a two-dimensional shape which is a triangle, it means that the solid has a triangular cross-section.
In other words, the cross-section of the solid that is perpendicular to its base is in the shape of a triangle.
A triangular prism is a solid shape that has a triangular cross-section. If you were to take a vertical slice through the prism, the resulting two-dimensional shape would be a triangle.
Hence, if vertical slice through a three-dimensional solid produces a two-dimensional shape is triangular prism
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find the value of x if 8=3-5x
step by step
Answer:
8=3-5x
5x=3-8
5x=-5
x=-5/5
x=-1
is the required answer
The manager of a theater wants to know whether majority of his patrons are adults or children. One day, 5400 tickets were sold and the receipts totaled $41,616. The adults admission is $9.50, and the children's admission is $6.50. How many adults patrons were there?
Answer:
2,172 adults
Step-by-step explanation:
Let adults = x
children = y
x + y = 5400
9.5x + 6.5y = 41,616
Let's use the elimination method to solve this.
Multiply the top equation by -6.5
(x + y = 5400)-6.5
-6.5x - 6.5y = -35100
This will allow us to eliminate the y and add up the other terms
9.5x + 6.5y = 41,616
-6.5x - 6.5y = -35100
3x = 6516
Divide both sides by the coefficient, 3, to isolate the variable, x
3x/3 = 6516/3
x = 2172
Find the height of a clock tower if the angle of elevation from a horizontal point 430 m from its base is 40°.
[tex]\\ \sf\longmapsto tan40=\dfrac{P}{430}[/tex]
[tex]\\ \sf\longmapsto 0.83=\dfrac{P}{430}[/tex]
[tex]\\ \sf\longmapsto P=430(0.83)[/tex]
[tex]\\ \sf\longmapsto P\approx361m[/tex]
P=Height of towerfactor of -2800 and -2
Step-by-step explanation:
factors of -2 = -1 and -2
factors of -2800 = -1 -2 -4 -5 -7 -8 -10 -14 -16 -20 -25 -28 -35 -40 -56 -70 -80 -100 -112 -140 -175 -200 -280 -350 -400 -560 -700 -1400 -2800
MARK AS BRAINLIST IF IT IS USEFUL
express 2/3 of a straight angle into radian?
[tex]\\ \sf\longmapsto \dfrac{2}{3}\:of\:180[/tex]
[tex]\\ \sf\longmapsto \dfrac{2}{3}\times 180[/tex]
[tex]\\ \sf\longmapsto 2(60)[/tex]
[tex]\\ \sf\longmapsto 120[/tex]
Convert to radians
[tex]\\ \sf\longmapsto 120\times \dfrac{\pi}{180}[/tex]
[tex]\\ \sf\longmapsto \dfrac{2\pi}{3}rad[/tex]
A car traveling at 22.4 m/s skids to a stop in 2.55 s. Determine the skidding distance of
the car (assume uniform acceleration).
Answer:
57.12 m
Step-by-step explanation:
velocity= distance/time
distance= velocity×time
=22.4×2.55
=57.12 m
Answer:
d = 28.6 m
Step-by-step explanation:
Given:
vi = 22.4 m/s
vf = 0 m/s
t = 2.55 s
Find:
d = ??
d = (vi + vf)/2 *t
d = (22.4 m/s + 0 m/s)/2 *2.55 s
d = (11.2 m/s)*2.55 s
d = 28.6 m
three times the difference of a number cubed and 10 in algebraic expression
Answer:
3 × x³ - 10
Step-by-step explanation:
three times = 3×
difference = -
number cubed (unknown so we use x) = x³
10 = 10
Hope this helps!
I'm sorry if wrong :(
4 - 2(x-4)/ 3= 3(2x+5)/2
linear equation in one variable
no spamms❌❌❌❌
Step-by-step explanation:
4-2x+8/3 = 6x+15/2
12-2x+8/3= 6x+15/2 ( taken LCM. of 1,3,3 in LHS)
20-2x/3=6x+15/2
Do cross multiplication
2(20-2x) = 3(6x+15)
40-4x=18x+45
-4x-18x=45+40
-22x= 85
-x= 85/22
x= - 3.86..
hope it helps
DF is the altitude to the hypotenuse EC. What is the length of DE?
Select the best answer from the choices provided.
A. 3
B. 6
C.12
D. 24
Answer:
D
Step-by-step explanation:
Using the Altitude- on- hypotenuse theorem
DF² = CD × DE , substitute values
12² = 6 DE
144 = 6 DE ( divide both sides by 6 )
24 = DE → D
Solve: XXVI - IV. Show your answer in standard form. Standard Number 1 5 10 50 100 500 1,000 Roman Numeral 1 V x L lulolz A) 22 B) 20 C) 19
Answer:
22
Step-by-step explanation:
these i can do keep sendin em in
Answer:
22
b/c XXVI - IV
(26 - 4 )
=22
The graph of f (x) is shown which is the axis of symmetry of the graph f (x)
Answer:
B) x = 3
Step-by-step explanation:
This is the axis of symmetry because the graph is symmetric in this line
How do I write 5,248,663,711 in expanded form
Answer:
5,000,000,000+200,000,000+40,000,000+8,000,000+600,000+60,000+3,000+700+10+1
Step-by-step explanation:
5,000,000,000 + 200,000,000+ 40,000,000+ 8,000,000+ 600,000+ 60,000+ 3,000
+ 700 + 10 + 1
g(r) = -1 - 77
g(6)=
Answer:
g(6) = -1 -77
because the expression doesn't have r
Step-by-step explanation:
I need helppppp plus!!!!
if f(X+4) =3x+2 ,then find the value of f(4) please explain our answer in a clear way
[tex]\\ \sf\longmapsto f(x+4)=3x+2[/tex]
Taking y=x+4 so x=y-4[tex]\\ \sf\longmapsto f(y)=3(y-4)+2[/tex]
[tex]\\ \sf\longmapsto f(y)=3y-12+2[/tex]
[tex]\\ \sf\longmapsto f(y)=3y-10[/tex]
Hence
[tex]\\ \sf\longmapsto f(x)=3x-10[/tex]
So
[tex]\\ \sf\longmapsto f(4)=3(4)-10[/tex]
[tex]\\ \sf\longmapsto f(4)=12-10[/tex]
[tex]\\ \sf\longmapsto f(4)=2[/tex]
Answer: 2
hi,
Step-by-step explanation:
[tex]f(x+4)=3x+2\\\\Let\ say\ y=x+4\ or\ x=y-4\\\\f(y)=3*(y-4)+2=3y-12+2=3y-10\\\\so\ f(x)=3x-10\\\\and\ f(4)=3*4-10=12-10=2\\[/tex]
-2/3y - 3/4 = 5? with work please!
Answer:
-69/8
Step-by-step explanation:
-2/3y - 3/4 = 5
-2/3y = 23/4
y = -69/8
n÷102=0.123
What is the value of n
Answer:
n = 12.546
Step-by-step explanation:
to find the value of n we need to transpose
n ÷ 102 = 0.123
n = 0.123 × 102
n = 12.546
Help with the length of the third side?
Answer:
C. c = 10
Step-by-step explanation:
You have to use the Pythagorean theorem:
c² = 6² + 8²
c² = 36 + 64
c² = 100
c = √100
c = 10
Answer:
c = 10
Step-by-step explanation:
Since this is a right triangle, we can use the Pythagorean theorem
a^2 + b^2 = c^2 where a and b are the legs and c is the hypotenuse
6^2 + 8^2 = c^2
36+64= c^2
100 = c^2
Take the square root of each side
sqrt(100) = sqrt(c^2)
10 -c
a goat is six times as heavy as its kid if their total mass is 70 kg find each of their masses in kg
plzz help i need it fast
Answer:
10kg and 60 kg.
Step-by-step explanation:
Let the kid's mass be x kg, then the goat's mass is 6x.
x + 6x = 70
7x = 70
x = 10.
Which number comes first when the numbers are listed from least tò greatest?
Answer:
the least
Step-by-step explanation:
Answer:
-∞
Step-by-step explanation:
Negative numbers are the smallest on the number line. Since the number range is not specified -∞ would be a preferred answer.
The insects, birds, snakes, and plants that live in a local wetland make up a
A. molecule
B. organism
C. population
D. community
can somebody please explain how to do this:)
[tex]\\ \sf\longmapsto \dfrac{sin40.sin120}{sin110-sin340}[/tex]
[tex]\\ \sf\longmapsto \dfrac{sin(90-50).sin(90+30)}{sin(90+20).sin(360-20)}[/tex]
[tex]\\ \sf\longmapsto \dfrac{cos50.cos30}{cos20.(-sin20}[/tex]
[tex]\\ \sf\longmapsto \dfrac{cos50cos30}{-sin20cos20}[/tex]
[tex]\\ \sf\longmapsto -\dfrac{cos30cos50}{sin20cos20}[/tex]
The freshman class is planning a picnic. The cost of a permit to use the park is
$250. To pay for the permit, there is a fee of $.75 for each freshman and $1.25 for
each guest who is not a freshman. Two hundred freshman plan to attend. How many
guests must attend in order to at least pay for the permit? Let g represent the number
of guest attending.
Answer:
80
Step-by-step explanation:
If hexagon ABCDEF is similar to hexagon KLMNOP, which of the following must be true?
Step-by-step explanation: Similar figures have the same shape, but not necessarily the size. If two figures are similar, then their corresponding angles are congruent so <E ≅ <O because these are the corresponding angles in the similarity statement.
Answer: <E ≅ <O
Step-by-step explanation:
V = (pi r^2 h/3)...solve for h
Answer:
h = (3×V)/ (pi×r²)
Step-by-step explanation:
[tex]v = \frac{\pi {r}^{2} h}{3} [/tex]
[tex]3 \times v = \pi {r}^{2} h[/tex]
[tex]h = \frac{3v}{\pi {r}^{2} } [/tex]
In a series of three numbers, the second number is 3 less than the first, and the third is three times the second. If the first number is
x,
how much greater than the second number is the third number
third number?
Please help explanation if possible
Answer:
r/2 = w
Step-by-step explanation:
r = 2w
Divide each side by 2
r/2 = 2w/2
r/2 = w
If x≠0, which expression is equivalent to this expression?
Step-by-step explanation:
Here radical rule is that [tex]\sqrt[n]{x^{m} } = x^{m/n}[/tex] ; [tex]x\neq 0[/tex] so
[tex]\sqrt[4]{x^3} = x^{3/4}[/tex]
>>[tex](x^{3/4})/x^{1/12}[/tex]
>>[tex]x^{2/3}[/tex]