Answer/Step-by-step explanation:
Perimeter of the remaining sector = length of arc + 2×radius
= θ/360 × 2πr + 2r
θ = 360° - 120° = 240°
r = 21 cm
Plug in the values
Perimeter of the remaining sector = 240/360 × 2×π×21 + 2(21)
= 129.964594 ≈ 130 cm
Therefore, the perimeter of the remaining portion is 130 cm
Answer:
x=3
Step-by-step explanation:
Because the shape is a rhombus that means that WZ and XY are parallel
This means we can use the co-interior angles rule to conclude that ∠WZY and ∠XYZ add up to 180°
This means that ∠WZY is 44°
Because the shape in a rhombus ZX and WY are perpendicular
This means that ∠ZRY is a right angle (90°)
Because ZX and WY are perpendicular that means that ∠ZYX is split in half which makes ∠ZYW 68°
Because the angles in a triangle add up to 180°
(10x-8)+68+90=180
(10x-8)+158-158=180-158
10x-8+=22+8
10x/10=30/10
x=3
Given:
There are given the quadratic equation:

Explanation:
To find the value of x by using completing the square, first, we need to subtract 59 on both sides of the given equation:
So,
From the given equation:

Now,
Take half of the x term and square it:
So,
From the x term,

Then,
Add 64 on both sides of the above equation.
So,

Hence, an option first is correct:

Now,
From the above square:
![\begin{gathered} (x+8)^2=5 \\ x+8=\pm\sqrt[]{5} \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%20%28x%2B8%29%5E2%3D5%20%5C%5C%20x%2B8%3D%5Cpm%5Csqrt%5B%5D%7B5%7D%20%5Cend%7Bgathered%7D)
Then,
Subtract 8 from both sides of the equation;;
So,
![\begin{gathered} x+8=\pm\sqrt[]{5} \\ x+8-8=\pm\sqrt[]{5}-8 \\ x=\pm\sqrt[]{5}-8 \\ x=\sqrt[]{5}-8,\pm\sqrt[]{5}-8 \\ x=-5.7639,-10.236067 \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%20x%2B8%3D%5Cpm%5Csqrt%5B%5D%7B5%7D%20%5C%5C%20x%2B8-8%3D%5Cpm%5Csqrt%5B%5D%7B5%7D-8%20%5C%5C%20x%3D%5Cpm%5Csqrt%5B%5D%7B5%7D-8%20%5C%5C%20x%3D%5Csqrt%5B%5D%7B5%7D-8%2C%5Cpm%5Csqrt%5B%5D%7B5%7D-8%20%5C%5C%20x%3D-5.7639%2C-10.236067%20%5Cend%7Bgathered%7D)
Final answer:
Hence, the value of x is shown below:
The answer is c because you have to say 27 minus the number minus 3
Hi there!
Thanks for asking for help!
I believe Part A of your answer is the expression: n+2n.
Because that is the answer for Part A, Part B is the answer: "The expression for the bookcases is n+2n because the problem says 'the larger bookcase holds twice as much as the smaller one,' and 'let n represent the amount of books the smaller bookcase holds'.
Since you need to find an expression for the amount both bookcases needs to hold you would add n (capacity of the smaller bookcase) and 2n (capacity of the larger bookcase) together to have an expression that represents the amount both hold.
Part C: 90=3n
I know this is the correct equation based on the expression written above since n+2n=3n, and the problem says "the amount both bookcases hold together is 90 books"
btw, bookcase 1 holds 30 books and the large bookcase holds 60.
Hope this helps you out! :)