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3 years ago

Y + x = 4 and y = 2x - 8 Solve the system of equations.

Mathematics

2 answers:

MakcuM [25]3 years ago

8 0

Answer:

x = 4, y = 0.

As an ordered pair it is (4, 0).

Step-by-step explanation:

Rewriting the second equation as the same format as the first:

y + x = 4

y - 2x = - 8 Subtract (1) - (2):

0 + 3x = 12

x = 4.

Plug x = 4 into the first equation:

y + 4 = 4

y = 0.

Check in the second equation:

y = 0 = 2(4) - 8 = 8 -8 = 0. OK.

bonufazy [111]3 years ago

3 0

Is this substitution? if it is the answer is (4,0)

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Joanna is making a recipe that uses 1 1/2 teaspoon of salt for every 2 cups of sugar. If Joanna increases the recipe to use 5 of

GrogVix [38]

Answer: B. 3 3/4

Step-by-step explanation:

From the question, we are told that Joanna is making a recipe that uses 1 1/2 teaspoon of salt for every 2 cups of sugar. Since, uses 1 1/2 teaspoon of salt for every 2 cups of sugar, 1 cup of sugar will use 1/2 of 1 1/2 teaspoon of salt. This will be:

= 1/2 × 1 1/2

= 1/2 × 3/2

= 3/4 teaspoon of salt.

We then multiply the value used for a cup of sugar by 5 since Joanna increases the recipe to use 5 cups of sugar. This will be:

= 3/4 × 5

= 15/4

= 3 3/4

8 0

3 years ago

Xiao Ming is now 15 years

insens350 [35]

Answer:

Step-by-step explanation:

father's age=46

half of father's age=46/2=23

Xiao's age=15

so when Xiao is half of her father age =23-15=8

then add 8 to his sister's age

so 8+8=16

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4 0

4 years ago

Read 2 more answers

Someone please help me with these too://

algol [13]

Answer:

The slope is 2

The y-intercept is -10

equation: y = 2x - 10

Slope: 2.5

y-intercept: 1

Equation: y = 2.4x + 1

Step-by-step explanation:

x y

2 12

4 16

8 24

10 28

from 12 to 16 you add 4

from 2 to 4 you add 2

y/x = 4/2 = 2

The slope is 2

The y-intercept is -10

equation: y = 2x - 10

I got the y-intercept because I went from 12 to 0 which is -12, and then 2 - 12 and it's -10

__________________________________________________________

x y

5 4

20 10

30 14

35 16

from 4 to 10, u add 6

from 5 to 20 you add 15

y/x = 15/6 = 2.5

Slope: 2.5

y-intercept: 1

Equation: y = 2.4x + 1

I got the y-intercept because I went from 4 to 0 which is -4, and 5 - 4 is 1.

Hope this helped

7 0

3 years ago

Please help me I’m terrible at math

olga55 [171]

Answer:

168.6 in

Step-by-step explanation:

Use the formula for circumfrence

$2\pi \: r$

Plug in 26.85 as the radius and solve. Remember to use 3.14 instead of the pi key.

4 0

4 years ago

Calculus 2 Master needed, show steps with partial fraction decomposition <img src="https://tex.z-dn.net/?f=%5Cint%283x%5E2-26x%2

Vladimir79 [104]

Answer:

-ln|x−5| + 2 ln(x²+4) + 3 tan⁻¹(x/2) + C

Step-by-step explanation:

The fraction will be split into a sum of two other fractions.

The first fraction will have a denominator of x − 5. The numerator will the a polynomial of one less order, in this case, a constant A.

The second fraction will have a denominator of x² + 4. The numerator will be Bx + C.

$\frac{3x^{2}-26x+26}{(x-5)(x^{2}+4)}=\frac{A}{x-5} +\frac{Bx+C}{x^{2}+4}$

Combine the two fractions back into one using the common denominator.

$\frac{A}{x-5} +\frac{Bx+C}{x^{2}+4}=\frac{A(x^{2}+4)+(Bx+C)(x-5)}{(x-5)(x^{2}+4)}$

This numerator will equal the original numerator.

$A(x^{2}+4)+(Bx+C)(x-5)=3x^{2}-26x+26\\Ax^{2}+4A+Bx^{2}-5Bx+Cx-5C=3x^{2}-26x+26\\(A+B)x^{2}+(C-5B)x+(4A-5C)=3x^{2}-26x+26$

Match the coefficients.

$A+B=3\\C-5B=-26\\4A-5C=26$

Solve the system of equations.

$A=-1\\B=4\\C=-6$

So we can rewrite the integral as:

$\int {(\frac{-1}{x-5}+\frac{4x-6}{x^{2}+4}) } \, dx$

Solving:

$\int {\frac{-1}{x-5}\, dx + \int {\frac{4x}{x^{2}+4}} \, dx - \int {\frac{6}{x^{2}+4} } \, dx$

$-\int {\frac{1}{x-5}\, dx + 2\int {\frac{2x}{x^{2}+4}} \, dx - 6\int {\frac{1}{x^{2}+4} } \, dx$

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$-ln|x-5| + 2ln(x^{2}+4) - 3 tan^{-1}(\frac{x}{2} ) + C$

5 0

3 years ago