◆ ARITHMETIC PROGRESSIONS ◆
Heya !
Check the attachment.
Hope it helps you ;)
Answer:
![6x^{13}y^{17}](https://tex.z-dn.net/?f=6x%5E%7B13%7Dy%5E%7B17%7D)
Step-by-step explanation:
We need to multiply
![3x^8y^9.2x^5y^8](https://tex.z-dn.net/?f=3x%5E8y%5E9.2x%5E5y%5E8)
We know the exponent rule of multiplication:
![x^a y^b . x^cy^d = x^{a+c}y^{b+d}](https://tex.z-dn.net/?f=x%5Ea%20y%5Eb%20.%20x%5Ecy%5Ed%20%3D%20x%5E%7Ba%2Bc%7Dy%5E%7Bb%2Bd%7D)
If the bases are same the powers are added.
So,
![=3*2 *x^8*x^5*y^9*y^8\\=^{8+5}y^{9+8}\\=6x^{13}y^{17}](https://tex.z-dn.net/?f=%3D3%2A2%20%2Ax%5E8%2Ax%5E5%2Ay%5E9%2Ay%5E8%5C%5C%3D%5E%7B8%2B5%7Dy%5E%7B9%2B8%7D%5C%5C%3D6x%5E%7B13%7Dy%5E%7B17%7D)
So, the answer is:
![6x^{13}y^{17}](https://tex.z-dn.net/?f=6x%5E%7B13%7Dy%5E%7B17%7D)
Step 1
<u>Find the Greatest Common Factor (GCF)</u>
the prime factorization of each number is equal to
![527=17*31\\ 646=2*17*19\\ 748=2^{2} *11*17](https://tex.z-dn.net/?f=527%3D17%2A31%5C%5C%20646%3D2%2A17%2A19%5C%5C%20748%3D2%5E%7B2%7D%20%2A11%2A17)
The GCF is 17
That means that the maximum number of packets is 17 and the maximum number of the items possible in each packet is
Number of pencils=527/17=31 pencils in each packet
Number of erasers=646/17=38 erasers in each packet
Number of sharpeners=748/17=44 sharpeners in each packet
Area of a triangle is half the area of a rectangle. The area of the triangle whose base length is 10 ft and the height is 30 ft is 1500 ft².
<h3>What is the area of the triangle?</h3>
The area of a triangle is half the area of a rectangle, therefore, it's half the product of the base and height of the triangle.
We know about the formula of the area of a triangle, also, the length of the base(10 ft) and the height(30 ft) of the triangle is given to us, therefore, substitute the values in the formula of the area of the triangle,
![Area\triangle = \dfrac{1}{2} \times base \times height](https://tex.z-dn.net/?f=Area%5Ctriangle%20%3D%20%5Cdfrac%7B1%7D%7B2%7D%20%5Ctimes%20base%20%5Ctimes%20height)
![= \dfrac{1}{2} \times 10\times 30\\\\=1500\rm\ ft^2](https://tex.z-dn.net/?f=%3D%20%5Cdfrac%7B1%7D%7B2%7D%20%5Ctimes%2010%5Ctimes%2030%5C%5C%5C%5C%3D1500%5Crm%5C%20ft%5E2)
Hence, the area of the triangle whose base length is 10 ft and the height is 30 ft is 1500 ft².
Learn more about Triangle:
brainly.com/question/25813512
Answer:
the answer is 221.1
Step-by-step explanation: