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2 years ago

Y = -2x + 8 y = x^2 - 9x + 18 solve the system of nonlinear equation

Mathematics

1 answer:

ryzh [129]2 years ago

3 0

Substitution

-2x+8=x^2-9x+18

x^2-7x+10=0

Factoring, we get

(x-5)(x-2)=0

x=5, x=2

If x equals 5,

y=-2(5)+8=

-10+8=

-2

Therefore, we derive our first solution:

Now we solve for our second x

If x=2,

y=-4+8=

Therefore, we derive our second solution:

-Hunter

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A bag of peanuts weighs 1/4 pound. How much do 1 1/2 weigh?

Nataly [62]

Answer:

I think it would weigh 1 1/8, love

Step-by-step explanation:

I'm not good at explaining but I'll try.

One bag weighs 1/4 pound meaning that half a bag would weigh 1/8 pound

Hope I helped sweetheart

7 0

2 years ago

F almonds sell for $1.20 per pound, and walnuts sell for $.75 per pound, how many pounds of each must be used to make 45 pounds

lukranit [14]

Answer:

Option A.) 20 pounds of walnuts and 25 pounds of almonds is correct.

Step-by-step explanation:

i) let x be the the number of pounds of almonds

ii) let y be the number of pounds of walnuts

iii) therefore x + y = 45 pounds of the mixture

iv) 1.2x + 0.75y = 1.00 $\times$ 45 = 45

v) Multipling equation in iv) by 4 we get

4.8x + 3y = 180

vi) multiplying equation in iii) by 3 we get

3x + 3y = 135

vii) subtracting equation vi) from equation v) we get 1.8x = 45

ix) therefore we get x = 45/1.8 = 25 pounds of almonds

x) therefore 25 + y = 45 .... substituting value of x from ix) in iii) we get

therefore y = 20 pounds of walnuts

Therefore option A.) 20 pounds of walnuts and 25 pounds of almonds is correct.

7 0

2 years ago

Factor the expression below

Mazyrski [523]

Answer:

(2x² + 5x + 2) = (2x + 1)(x +2)

Step-by-step explanation:

Given expression is (2x² + 5x + 2).

We have to factorize the given expression.

(2x²+ 5x + 2) = 2x² + 4x + x + 2

= 2x(x + 2) + 1(x + 2)

= (2x + 1)(x + 2)

So the factored form of the given expression will be (2x + 1)(x + 2).

6 0

2 years ago

Jensen is building a snow fort. Each block in the fort weighs about 1 kilogram. Jensen hopes to make about 40 blocks for the for

babymother [125]

Answer: 13,333 snowflakes

Step-by-step explanation:

For this exercise let be "x" represents the number of snowflakes that will be in the fort.

According to the information given in the exercise, the weight of one block is 1 kilogram. Knowing that the fort must have 40 blocks, the total weight is:

$total\ weight=(1\ g)(40)\\\\total\ weight=40\ g$

Since each snowflake weighs $3* 10^{-3}$ grams, need to divide the total weight calculated above by the weight of a snowfake.

Therefore, through this procedure you get the following result:

$x=\frac{40\ grams}{3 * 10 ^{-3}\ grams}\\\\x\approx13,333$

Therefore, the there will be 13,333 snowflakes in the fort.

5 0

3 years ago

VEEL

Andre45 [30]

Answer:

$a_n=-3(3)^{n-1}$ ; {-3,-9, -27,- 81, -243, ...}

$a_n=-3(-3)^{n-1}$ ; {-3, 9,-27, 81, -243, ...}

$a_n=3(\frac{1}{2})^{n-1}$ ; {3, 1.5, 0.75, 0.375, 0.1875, ...}

$a_n=243(\frac{1}{3})^{n-1}$ ; {243, 81, 27, 9, 3, ...}

Step-by-step explanation:

The first explicit equation is

$a_n=-3(3)^{n-1}$

At n=1,

$a_1=-3(3)^{1-1}=-3$

At n=2,

$a_2=-3(3)^{2-1}=-9$

At n=3,

$a_3=-3(3)^{3-1}=-27$

Therefore, the geometric sequence is {-3,-9, -27,- 81, -243, ...}.

The second explicit equation is

$a_n=-3(-3)^{n-1}$

At n=1,

$a_1=-3(-3)^{1-1}=-3$

At n=2,

$a_2=-3(-3)^{2-1}=9$

At n=3,

$a_3=-3(-3)^{3-1}=-27$

Therefore, the geometric sequence is {-3, 9,-27, 81, -243, ...}.

The third explicit equation is

$a_n=3(\frac{1}{2})^{n-1}$

At n=1,

$a_1=3(\frac{1}{2})^{1-1}=3$

At n=2,

$a_2=3(\frac{1}{2})^{2-1}=1.5$

At n=3,

$a_3=3(\frac{1}{2})^{3-1}=0.75$

Therefore, the geometric sequence is {3, 1.5, 0.75, 0.375, 0.1875, ...}.

The fourth explicit equation is

$a_n=243(\frac{1}{3})^{n-1}$

At n=1,

$a_1=243(\frac{1}{3})^{1-1}=243$

At n=2,

$a_2=243(\frac{1}{3})^{2-1}=81$

At n=3,

$a_3=243(\frac{1}{3})^{3-1}=27$

Therefore, the geometric sequence is {243, 81, 27, 9, 3, ...}.

6 0

3 years ago