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Inga [223]
2 years ago
8

What is the solution to the system of equations? y = 1/3x-10 2x + y = 4

Mathematics
2 answers:
Mazyrski [523]2 years ago
6 0

Answer:

y=-8, x=6

Step-by-step explanation:

Hope this helped!!!

ladessa [460]2 years ago
5 0
Answer: x = 6, y = -8
You might be interested in
<img src="https://tex.z-dn.net/?f=%5Cfrac%7Bd%7D%7Bdx%7D%20%5Cint%20t%5E2%2B1%20%5C%20dt" id="TexFormula1" title="\frac{d}{dx} \
Kisachek [45]

Answer:

\displaystyle{\frac{d}{dx} \int \limits_{2x}^{x^2}  t^2+1 \ \text{dt} \ = \ 2x^5-8x^2+2x-2

Step-by-step explanation:

\displaystyle{\frac{d}{dx} \int \limits_{2x}^{x^2}  t^2+1 \ \text{dt} = \ ?

We can use Part I of the Fundamental Theorem of Calculus:

  • \displaystyle\frac{d}{dx} \int\limits^x_a \text{f(t) dt = f(x)}

Since we have two functions as the limits of integration, we can use one of the properties of integrals; the additivity rule.

The Additivity Rule for Integrals states that:

  • \displaystyle\int\limits^b_a \text{f(t) dt} + \int\limits^c_b \text{f(t) dt} = \int\limits^c_a \text{f(t) dt}

We can use this backward and break the integral into two parts. We can use any number for "b", but I will use 0 since it tends to make calculations simpler.

  • \displaystyle \frac{d}{dx} \int\limits^0_{2x} t^2+1 \text{ dt} \ + \ \frac{d}{dx} \int\limits^{x^2}_0 t^2+1 \text{ dt}

We want the variable to be the top limit of integration, so we can use the Order of Integration Rule to rewrite this.

The Order of Integration Rule states that:

  • \displaystyle\int\limits^b_a \text{f(t) dt}\  = -\int\limits^a_b \text{f(t) dt}

We can use this rule to our advantage by flipping the limits of integration on the first integral and adding a negative sign.

  • \displaystyle \frac{d}{dx} -\int\limits^{2x}_{0} t^2+1 \text{ dt} \ + \ \frac{d}{dx}  \int\limits^{x^2}_0 t^2+1 \text{ dt}  

Now we can take the derivative of the integrals by using the Fundamental Theorem of Calculus.

When taking the derivative of an integral, we can follow this notation:

  • \displaystyle \frac{d}{dx} \int\limits^u_a \text{f(t) dt} = \text{f(u)} \cdot \frac{d}{dx} [u]
  • where u represents any function other than a variable

For the first term, replace \text{t} with 2x, and apply the chain rule to the function. Do the same for the second term; replace

  • \displaystyle-[(2x)^2+1] \cdot (2) \ + \ [(x^2)^2 + 1] \cdot (2x)  

Simplify the expression by distributing 2 and 2x inside their respective parentheses.

  • [-(8x^2 +2)] + (2x^5 + 2x)
  • -8x^2 -2 + 2x^5 + 2x

Rearrange the terms to be in order from the highest degree to the lowest degree.

  • \displaystyle2x^5-8x^2+2x-2

This is the derivative of the given integral, and thus the solution to the problem.

6 0
3 years ago
Researchers investigated whether insomnia is related to education status. Adults living in a certain region were selected to par
Degger [83]

Answer:

A) 8 treatments

  1. Normal​ sleeper, high school dropout
  2. Normal​ sleeper, high school graduate
  3. .Normal​ sleeper, college graduate
  4. Chronic​ insomnia, college graduate
  5. Chronic​ insomnia, high school graduate
  6. Chronic​ insomnia, high school dropout
  7. Normal​ sleeper, some college
  8. Chronic​ insomnia, some college

B) 8 treatments

Step-by-step explanation:

<u>A) determine the number of treatments for this study </u>

The number of treatments for this study can be determined as : 2 * 4 = 8 treatments

and they are :

  1. Normal​ sleeper, high school dropout
  2. Normal​ sleeper, high school graduate
  3. .Normal​ sleeper, college graduate
  4. Chronic​ insomnia, college graduate
  5. Chronic​ insomnia, high school graduate
  6. Chronic​ insomnia, high school dropout
  7. Normal​ sleeper, some college
  8. Chronic​ insomnia, some college

B) eight (8 ) treatments

7 0
3 years ago
What z-score value separates the top 10% of a normal distribution from the bottom 90%?​?
nata0808 [166]
The 90th percentile corresponds to Z ≈ 1.28155.

7 0
3 years ago
Use one or more properties to rewrite each espression as an expression that does not use parenthesis
sineoko [7]
Y+5  can be written to find the value of y by combining  like terms .
4 0
3 years ago
Select the correct answer.
olga55 [171]

Answer:

B

Step-by-step explanation:

An equation of a circle:

(x - a)² + (y - b)² = r²

(a; b) - a coordinates of a center

r - a radius

r = 5; P(6; 1) ⇒ a = 6 and b = 1

therefore

(x - 6)² + (y - 1)² = 5²

check:

A) Q(1; 11)

L = (1 - 6)² + (11 - 1)² = (-5)² + 10² = 25 + 100 = 125

R = 25

L ≠ R

B) R(2; 4)

L = (2 - 6)² + (4 - 1)² = (-4)² + 3² = 16 + 9 = 25

R = 25

L = R - CORRECT

C) S(4; -4)

L = (4 - 6)² + (-4 - 1)² = (-2)² + (-5)² = 4 + 25 = 29

R = 25

L ≠ R

D) T(9; -2)

L = (9 - 6)² + (-2 - 1)² = 3² + (-3)² = 9 + 9 = 18

R = 25

L ≠ R

Answer: B) R(2; 4).

7 0
3 years ago
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