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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.

Learn more about areas at:

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Answer:

3.2 × 10⁻²

Step-by-step explanation:

→ First multiply the whole numbers

8 × 4 = 32

→ Now add the powers

32 × 10⁻³

→ Convert into standard form

3.2 × 10⁻²

Answer:

4

Step-by-step explanation:

We can find the slope using the slope formula

m = ( y2-y1)/(x2-x1)

    = ( 3 - -1)/( 7-6)

    = ( 3+1)/( 7-6)

    = 4/1

   =4

Answer: 1/4n-12=6

1n/4-12=6

n=72

Step-by-step explanation:

Answer:

72

Step-by-step explanation:

let the number be n , then

[tex]\frac{1}{4}[/tex] n - 12 = 6 ( multiply through by 4 to eliminate the fraction )

n - 48 = 24 ( add 48 to both sides )

n = 72

Answer:

The horizontal shift is 6 units left (so -6).

Step-by-step explanation:

The horizontal shift is located inside the absolute value bars. While F(x) adds 6 to x, so you may think it's 6 units right, horizontal shifts are backwards as opposed to vertical shifts: we go 6 units left.

Answer:

Length=22.5cm, Breadth=11.5cm

Step-by-step explanation:

Let length be l and width be w.

w+22=l

w+w+w+22+w+22=90

4w=90-22-22

    =46

w=46 divided by 4

  =11.5

l=11.5+11

=22.5

Hence,

Length of rectangle=22.5cm

Breadth of rectangle=11.5cm

Hey there! I'm happy to help!

In this case c is equal to 0. There is always a, b, and c, but they might be invisible (for example if a is 1 or b or c are 0).

Then you can choose whichever method you like to factor these (completing the square, quadratic formula, factoring, etc.)

The zeros should be 0 and a number that is about -1.9.

Have a wonderful day and keep on learning! :D

Step-by-step explanation:

Using the power law of indices:

When two numbers with the same base multiply,add the exponents that is

[tex] {a}^{2} \times {a}^{3} = {a}^{2 + 3} = {a}^{5} [/tex]

Again,when two numbers with the same base divide, subtract the exponents,that is

[tex] {a}^{2} \div {a}^{4 } = {a}^{2 - 4} = {a}^{ - 2} [/tex]

There are way too many examples that is why I have elaborated the two laws for your perusal.

So for instance:

1.

[tex] {2}^{2} \times {2}^{5} = {2}^{7} [/tex]

Answer:

2² × 2⁵ = 2⁷

            = 128

4⁴ × 4⁶ = 4¹⁰

           = 1048576

6² × 6⁷ = 6⁹

           = 10077696

9⁸ × 9⁸ = 9¹⁷

           = 1.6677182e+16

Do try the rest out yourself!!! You can do it!!!

Answer:

3π

Step-by-step explanation:

540° = 360° x 1 + 180°

= 2π + π

= 3π

CMIIW

Answer:

6

Step-by-step explanation:

-9+6=-3

Answer:

16

Step-by-step explanation:

5/8= 0.625

10/0.625= 16

Answer:

She didn't change the direction of the sign

Step-by-step explanation:

When dividing both sides by a negative number in an inequality, you must change the sign.

Answer:

3x + 40

Step-by-step explanation:

"More" means addition and "Triple" indicates multiplication.

So, 3x + 40 is the answer.

Answer:

12.08

Step-by-step explanation:

Answer:

the answer is c

Step-by-step explanation:

x - 7, y + 6

- 1 - 7, 4 + 6

- 8, 10

Answer:

1

Step-by-step explanation:

In the equation -7 - (-8), there are two 'minus' signs; we can convert two minus signs into a plus sign according to the 'minus minus equals plus' rule, that would make the equation (-7) + 8 for which the answer is +1.

Answer:

1

Step-by-step explanation:

-7-(-8)

therefore;

  -7-(-8)= -7+8

therefore;

   -7+8= 1

Hope you understand.If you have any problem just ask me I will solve it.

[tex]\\ \sf\longmapsto -2x-4>8[/tex]

[tex]\\ \sf\longmapsto -2(x+4)>8[/tex]

[tex]\\ \sf\longmapsto x+4>\dfrac{8}{-2}[/tex]

[tex]\\ \sf\longmapsto x+4>-4[/tex]

[tex]\\ \sf\longmapsto x>-4-4[/tex]

[tex]\\ \sf\longmapsto x>-8[/tex]

Answer:

x < -6

Step-by-step explanation:

-2x - 4 > 8

Add 4 on both sides

-2x > 12

Divide -2 on both sides

x < -6

Hope this helps!

Answer:

Step-by-step explanation:

remember this:-

if +,- comes: change sign to - (eg. 8+(-4)= 8-4=4)

if -,+ comes: change sign to - (eg. 8-(+4)= 8-4=4)

if -,- comes: change sign to + (eg. 8-(-4)=8+4=12)

if +,+ comes: change sign to + (eg. 8+(+4)=8+4=12)

Answer:

Here,

X=(1,4,7,9)

Y=(2,4,5,9)

Now,

i=(1,2,4,5,7,9)

ii=((4,9)

iii=(1,2,4,5,7,9)

iv=(4,9)

Step-by-step explanation:

Simplifying 4 + -2(x + -3) = 24 Reorder the terms: 4 + -2(-3 + x) = 24 4 + (-3 * -2 + x * -2) = 24 4 + (6 + -2x) = 24 Combine like terms: 4 + 6 = 10 10 + -2x = 24 Solving 10 + -2x = 24 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + -2x = 24 + -10 Combine like terms: 10 + -10 = 0 0 + -2x = 24 + -10 -2x = 24 + -10 Combine like terms: 24 + -10 = 14 -2x = 14 Divide each side by '-2'. x = -7 Simplifying x = -7

Answer:

5th figure is not symmetrical

comment if doubt

Answer:

1. Reason: Given

2. segment PQ is similar to segment PS

3. Reason: Same segment

4. Reason: Side-side-side theorem.

Step-by-step explanation:

Answer:

3 PR=PR

Step-by-step explanation:

show TRI PQR CONGRUENT TRI PSR

QR=SR(GIVEN)

PQ=PS(GIVEN)

PR=PR(COMMON SIDE)

SO BOTH CONGRUENT

Answer: D

Step-by-step explanation:

dim A=(a,b), dim B=(c,d), in order to multiply, c=b

1) dim A=(1,2) , dim B=(1,2) but 2≠1

2) dim A=(2,1) , dim B=(2,2) but 1≠2

3) dim A=(2,2) , dim B=(1,2) but 2≠1

4) dim A=(2,1) , dim B=(1,2) 1=1: result (2,2)

Answer:

√2 and √3

Step-by-step explanation:

Answer:

Step-by-step explanation:

√2 and 5√2 are two irrational numbers

√2 * 5√2 = [tex]5*\sqrt{2*2} = 5 * 2 = 10[/tex]

and here 10 is an integer

Answer:

A. y ≤ 1

Step-by-step explanation:

according to the graph, the coordinates of maximum value is (-3, 1) and besides the graph towards down, so, the range of the function is y ≤ 1

Answer:

3/4 of the ribbon is needed to make a bow

Step-by-step explanation:

12 ÷ 4 = 3

so out of that foot of ribbon you use 3/4 of it for the bow

Answer:

3 times

Step-by-step explanation:

Equation: 810 = 288x

x = 2.8 meaning you need to fill up the tank 3 times