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3 years ago

Place the indicated product in the proper location on the grid (x+y+3)(x+y-4)

Mathematics

1 answer:

pashok25 [27]3 years ago

6 0

Solution:

we have been asked to find the product of (x+y+3)(x+y-4).

we will multiply term by term as below

$(x+y+3)(x+y-4)=x(x+y+3)+y(x+y+3)-4(x+y+3)\\\\\ (x+y+3)(x+y-4)=x^2+xy+3x+xy+y^2+3y-4x-4y-12\\\\\text{Now take the like terms together and simplify we get}\\\\(x+y+3)(x+y-4)=x^2+y^2+2xy-x-y-12\\$

Hence the the product of (x+y+3)(x+y-4) is $x^2+y^2+2xy-x-y-12$

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stich3 [128]

Answer:

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Step-by-step explanation:

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3 years ago

A. [4 marks]

storchak [24]

The value of d is -2

Step-by-step explanation:

The nth term of the arithmetic sequence is $u_{n}=u_{1}+(n-1)d$ , where

$u_{1}$ is the first term
d is the common difference between each 2 consecutive terms

The nth term of the geometric sequence is $u_{n}=u_{1}r^{n-1}$ , where

$u_{1}$ is the first term
r is the common ratio between each two consecutive terms $r=\frac{u_{2}}{u_{1}}=\frac{u_{3}}{u_{2}}$

∵ $u_{1}$ of an arithmetic sequence is 1

∵ The common difference is d, where d ≠ 0

∵ $u_{2}$ , $u_{3}$ , $u_{6}$ are the first 3 terms of a geometric sequence

∵ $u_{2}$ = 1 + (2 - 1)d

∴ $u_{2}$ = 1 + d

∵ $u_{3}$ = 1 + (3 - 1)d

∴ $u_{2}$ = 1 + 2d

∵ $u_{6}$ = 1 + (6 - 1)d

∴ $u_{2}$ = 1 + 5d

∴ The first 3 terms of the geometric sequence are (1 + d) , (1 + 2d) ,

(1 + 5d)

∵ The common ratio in the geometric sequence is $r=\frac{u_{2}}{u_{1}}=\frac{u_{3}}{u_{2}}$

∴ $r=\frac{1+2d}{1+d}=\frac{1+5d}{1+2d}$

- Use cross multiplication with the equal fractions

∵ $\frac{1+2d}{1+d}=\frac{1+5d}{1+2d}$

∴ (1 + 2d)(1 + 2d) = (1 + d)(1 + 5d)

∴ 1 + 2d + 2d + 4d² = 1 + 5d + d + 5d²

- Add like terms in each side

∴ 1 + 4d + 4d² = 1 + 6d + 5d²

- Subtract 1 from both sides

∴ 4d + 4d² = 6d + 5d²

- Subtract 4d from both sides

∴ 4d² = 2d + 5d²

- Subtract 4d² from each side

∴ 0 = 2d + d²

- Take d as a common factor

∴ 0 = d(2 + d)

- Equate each factor by 0

∴ d = 0 but we will reject it because d ≠ 0

∴ 2 + d = 0

- Subtract 2 from both sides

∴ d = -2

The value of d is -2

Learn more:

You can learn more about the sequence in brainly.com/question/1522572

#LearnwithBrainly

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3 years ago

In order to test for the significance of a regression model involving 5 independent variables and 123 observations, the numerato

allochka39001 [22]

Answer: The numerator and denominator degrees of freedom (respectively) for the critical value of F are 4 and 118 .

Step-by-step explanation:

We know that , for critical value of F, degrees of freedom for numerator = k-1

and for denominator = n-k, where n= Total observations and k = number of independent variables.

Here, Numbers of independent variables(k) = 5

Total observations (n)= 123

So, Degrees of freedom for numerator = 5-1=4

Degrees of freedom for denominator =123-5= 118

Hence, the numerator and denominator degrees of freedom (respectively) for the critical value of F are 4 and 118 .

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3 years ago

Monique runs 1/4 mile five times a week. How many miles does she run each week?

Hoochie [10]

Answer:

1 and 1/4 of a mile each week

Step-by-step explanation:

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3 years ago

15 less than twice a number is less than or equal to -23. Into an equation

Dafna1 [17]

I hope it’s correct!

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3 years ago