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3 years ago

Determine the solution set of each equation

Mathematics

2 answers:

Flauer [41]3 years ago

5 0

Answer:

weak in maths sorry I cannot give answer

maks197457 [2]3 years ago

3 0

A=x1 = -8,x2 =2, B=x1= -5,x2=5, C=y1 = -4, y2 =5, D=y 18 over 5

alternative form

y=3 3over 5, =3.6

And E=x1=0, x2 =2 over 3

Alternative form

x1=0, x2=0.666667.

question A

Solving steps:Solve the quadratic equation

x²+6x-16=0

write 6x as a difference

x2 +8x-2x-16=0

factor out x for the expression

xx(x+8)-2x-16=0

factor out -2 from the expression

xx(x+8)- 2(x+8)=0

factor out x+8 from the expression

(x+8)x(x- 2)=0

when the product of factors equals 0,at least one factor is 0

x+8=0

x - 2=0

solve the equation for x

x= -8

x - 2=0

solve the equation for x

x= -8

x =2

the equation has 2 solution

x1 = -8,X2 =2

answer is

x1 = -8,x2 =2

Solving steps:Number of solution

x²+6x-16=0

Determine the number of solution using the

discriminant D =b²- 4ac

D =6²- 4x1x(-16)

simply the expression

D=100

Since D>0, the quadratic equation has 2 real solution

2 real solution

Answer is

2 real solution

Question B

Solving steps:Solve the quadratic equation

x²-25=0

Move the constant to the right-hand side and change its sign

x²=25

Take the square root of both sides of the equation and remember to use both positive and negative roots

x=+5

Write the solutions,one with a +sign and one with a -sign

x= -5

x=5

The equation has 2 solutions

x1= -5,x2=5

the answer is

x1= -5,x2=5

Solving steps:Number of solution

x²-25=0

Determine the number of solutions using the discriminant D=b²- 4ac

D=0²- 4x1x(-25)

Simply the expression

D=100

Since D>0,the quadratic equation has 2real solutions

Answer is

2real solutions

answer of question C is

y1 = -4, y2 =5

Answer of question D is

y 18 over 5

alternative form

y=3 3over 5, =3.6

Answer of question E is

x1=0, x2 =2 over 3

Alternative form

x1=0, x2=0.666667

Please mark as brainiest

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How is the series 9 + 13+ 17+ ... + 149 represented in summation notation?

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Notice that

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so it's likely that each pair of consecutive terms in the sum differ by 4. This means the last term, 149, is equal to 9 plus some multiple of 4 :

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This tells you there are 35 + 1 = 36 terms in the sum (since the first term is 9 plus 0 times 4, and the last term is 9 plus 35 times 4). Among the given options, only the first choice contains the same amount of terms.

Put another way, we have

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but if we make the sum start at k = 1, we need to replace every instance of k with k - 1, and accordingly adjust the upper limit in the sum.

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The height of the outer grey blocks is 2 blocks more than the Design number, while their rows are 3 blocks more than the Design number

b. The function is $\underline{p(n) = n \cdot (n + 1)}$

c. The function is $\underline{b(n) = (n + 2) \cdot (n + 3) - n \cdot (n + 1)}}$

d. $\underline{t(n) = (n + 2) \cdot (n + 3) = b(n) - p(n) }$

e. The design chosen is Design 9

The number of blocks is 132 blocks

Reasons:

The pattern of the design are;

a. The column height of the grey blocks = 2 blocks more than the column height of the white blocks

Width of the outer grey blocks = 2 blocks more than the width of the inner white blocks

The number of white blocks in a design, n is the product of n and (n + 1)

The number of grey blocks in a design n, is the product of (n + 2) and (n + 3) less the number of white blocks in the design

b. Based on the above, the function that represent the number of picture blocks in Design n, is therefore;

p(n) = n·(n + 1)

c. Based on the above, the function that represent the number of border blocks in Design n, is therefore;

b(n) = (n + 2)·(n + 3) - n·(n + 1)

d. The total number of blocks, t(n) = (n + 2)·(n + 3)

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90 = n × (n + 1)

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t(9) = (9 + 2)·(9 + 3) = 132 blocks

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