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natka813 [3]
2 years ago
9

A system of equations is shown:

Mathematics
1 answer:
Harrizon [31]2 years ago
6 0

Answer:

<h2>(1, 4)</h2>

Step-by-step explanation:

\left\{\begin{array}{ccc}2x=-y+6&(1)\\-4x+3y=8&(2)\end{array}\right\\\\(1)\\-y+6=2x\qquad\text{subtract 6 from both sides}\\-y=2x-6\qquad\text{change the signs}\\y=6-2x\\\\\text{substitute it to (2):}\\\\(2)\\-4x+3(6-2x)=8\qquad\text{use the distributive property}\\-4x+(3)(6)+(3)(-2x)=8\\-4x+18-6x=8\qquad\text{subtract 18 from both sides}\\-10x=-10\qquad\text{divide both sides by (-10)}\\x=1\\\\\text{put the value of x to (1):}\\\\y=6-2(1)\\y=6-2\\y=4

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6. Let A and B be nxn matrices . Compute (A + B) (A + B). Explain all steps.
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Answer:

(A+B)(A+B)=A.A+B.A+A.B+B.B

Step-by-step explanation:

Given that matrices A and B are nxn matrices

We need to find (A+B)(A+B)

For understanding the multiplication of matrices let'take A is mxn and B is pxq matrices,we can multiple only when n=p,so our Ab matrices will be mxq.

We know that that in matrices AB is not equal to BA.

Now find  

(A+B)(A+B)=A.A+B.A+A.B+B.B

So from we can say that (A+B)(A+B) is not equal to A.A+2B.A+B.B because AB is not equal to BA in matrices.

So (A+B)(A+B)=A.A+B.A+A.B+B.B

4 0
2 years ago
How to multiply numbers with exponets and different bases
o-na [289]
When the bases are diffenrent and the exponents of a and b are the same, we can multiply a and b first:
a n ⋅ b n = (a ⋅ b) n
Example:
32 ⋅ 42 = (3⋅4)2 = 122 = 12⋅12 = 144

When the bases and the exponents are different we have to calculate each exponent and then multiply:
a n ⋅ b m
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5 0
3 years ago
Which equation can be used to determine the value of x?​
SSSSS [86.1K]

Answer:

choice 1) 2x + 40 = 180

Step-by-step explanation:

(x + 10) + (x + 30) = 180

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8 0
2 years ago
Read 2 more answers
5
Dimas [21]

Answer:

0.150 < (Proportion of Sandy's pie) < 0.167

15% < (Percentage of Sandy's pie) < 16.7%

Step-by-step explanation:

Total percentage of pie = 100% or 1

George, Sandy, Carlos, and Michelle all ate a piece of the pie.

George ate a fraction of 0.150

Michelle ate a fraction of (1/6) = 0.167

Carlos ate a fraction of (1/7) = 0.143

The amount of pie left = 1 - 0.15 - (1/6) - (1/7) = 0.5405

And Sandy is known to eat more than two of her friends, but less than one of them.

Of the amount of pie eaten by the first 3 friends, (1/6) is the highest proportion.

Hence, it is evident that Sandy ate more than 0.143 and 0.150 (Carlos and George) but less than Michelle (0.167).

So, mathematically, the possible proportion of cake that Sandy ate is

0.150 < (Proportion of Sandy's pie) < 0.167

Hope this Helps!!!

7 0
2 years ago
A cylinder has a height h, and a radius (3h-2)
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Answer:

V= 4\pi (9h^2 -12h + 4)

Step-by-step explanation:

Given

Shape: Cylinder

Radius = 3h - 2

Height = h

Base\ Area = \pi (3h - 2)^2

Required

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The volume is calculated as:

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Substitute values for Base Area and Height

V= \pi(3h-2)^2*h

Expand the bracket

V= \pi(3h-2)(3h-2)*h

Open brackets

V= \pi (9h^2 -6h - 6h + 4) *h

V= \pi (9h^2 -12h + 4) *h

V= 4\pi (9h^2 -12h + 4)

6 0
2 years ago
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