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2 years ago

Find the solution of this system of equations. Separate the x- and y-values with a comma. x= 2 + y 3x – 7y= 10

1 answer:

4 0

Hello :
x= 2 + y ....(1)
3x – 7y= 10 ....(2)
subsct in (2) :
3(2+y) -7y = 10
6+3y -7y = 10
-4y = 4
y=-1
x = 2-1 = 1
the solution of this system of equations is (1 , -1)

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M∠1=(3x+21)° and m∠3=(4x+9)° what is the value of x

Scorpion4ik [409]

Step-by-step explanation:

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2 years ago

Need to evaluate integral pls help me

olga nikolaevna [1]

Answer:

$\displaystyle \int\limits^2_0 {f(x)} \, dx = \frac{159}{10}$

General Formulas and Concepts:

Calculus

Integration

Integrals
Integral Notation

Integration Rule [Reverse Power Rule]: $\displaystyle \int {x^n} \, dx = \frac{x^{n + 1}}{n + 1} + C$

Integration Rule [Fundamental Theorem of Calculus 1]: $\displaystyle \int\limits^b_a {f(x)} \, dx = F(b) - F(a)$

Integration Property [Multiplied Constant]: $\displaystyle \int {cf(x)} \, dx = c \int {f(x)} \, dx$

Integration Property [Addition/Subtraction]: $\displaystyle \int {[f(x) \pm g(x)]} \, dx = \int {f(x)} \, dx \pm \int {g(x)} \, dx$

Integration Property [Splitting Integral]: $\displaystyle \int\limits^c_a {f(x)} \, dx = \int\limits^b_a {f(x)} \, dx + \int\limits^c_b {f(x)} \, dx$

Step-by-step explanation:

Step 1: Define

Identify.

$\displaystyle f(x) = \left \{ {{9x^9 ,\ 0 \leq x \leq 1} \atop {4x^3 ,\ 1 \leq x \leq 2}} \right.$

$\displaystyle \int\limits^2_0 {f(x)} \, dx = \ ?$

Step 2: Integrate

[Integral] Rewrite [Integration Property - Splitting Integral]: $\displaystyle \int\limits^2_0 {f(x)} \, dx = \int\limits^1_0 {f(x)} \, dx + \int\limits^2_1 {f(x)} \, dx$
[Integrand] Substitute in function: $\displaystyle \int\limits^2_0 {f(x)} \, dx = \int\limits^1_0 {9x^9} \, dx + \int\limits^2_1 {4x^3} \, dx$
[Integrals] Rewrite [Integration Property - Multiplied Constant]: $\displaystyle \int\limits^2_0 {f(x)} \, dx = 9 \int\limits^1_0 {x^9} \, dx + 4 \int\limits^2_1 {x^3} \, dx$
[Integrals] Integration Rule [Reverse Power Rule]: $\displaystyle \int\limits^2_0 {f(x)} \, dx = 9 \bigg( \frac{x^{10}}{10} \bigg) \bigg| \limits^1_0 + 4 \bigg( \frac{x^4}{4} \bigg) \bigg| \limits^2_1$
Integration Rule [Fundamental Theorem of Calculus 1]: $\displaystyle \int\limits^2_0 {f(x)} \, dx = 9 \bigg( \frac{1}{10} \bigg) + 4 \bigg( \frac{15}{4} \bigg)$
Simplify: $\displaystyle \int\limits^2_0 {f(x)} \, dx = \frac{159}{10}$

Topic: AP Calculus AB/BC (Calculus I/I + II)

Unit: Integration

4 0

2 years ago

Read 2 more answers

Find the equation of the line that passes through (1,6) and (3,10).

anastassius [24]

Answer:

m = (y2 - y1) / (x2 - x1) = (10 - 6) / (3 - 1) = 2 slope of line

y = m x + b standard form of straight line

y = 2 x + b where b is the intercept at x = 0

b = y - 2 x

b = 6 - 2 = 4 from our first equation

Also, b = 10 - 6 = 4 check from second equation

y = 2 x + 4 is our equation

Check if y = 6 and x = 1 then

y = 2 * 1 + 4 = 6 verifying the first point given

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2 years ago

What are the multiples of 88

NARA [144]

88 * 2 = 176 ;
88 * 3 = 264 ;
88 * 4 = 362 ;
...................

8 0

2 years ago

Suppose you are at a train station in Connecticut. Trains headed to New York city arrive at the station at 15 minute intervals s

guajiro [1.7K]

Answer:

The answer is below

Step-by-step explanation:

a) For the person to get to New York city, the person must arrive at a time after the train to Boston has left and before the train to New York leaves. Between 7 and 8 am, there is a total of 60 minutes. For the person end up in New York city he has to arrive at the train station between the following intervals:

7:05 to 7:15 or 7:20 to 7:30 or 7:35 to 7:45 or 7:50 to 8:00

Let X represent the minutes the passenger arrives between 7 am to 8 am, hence:

P(goes to New York) = P(5 < X < 15) + P(20 < X < 30) + P(35 < X < 45) + P(50 < X < 60) = 10/60 + 10/60 + 10/60 + 10/60 = 40/60 = 2/3

b) As explained in part A, Let X represent the minutes the passenger arrives between 7 am to 8:10 am. But since time uniformly distributed between 7:10 and 8:10 am, this means 10 < X < 70:

For the person end up in New York city he has to arrive at the train station between the following intervals:

7:10 to 7:15 or 7:20 to 7:30 or 7:35 to 7:45 or 7:50 to 8:00 or 8:05 to 8:10

P(goes to New York) = P(10 < X < 15) + P(20 < X < 30) + P(35 < X < 45) + P(50 < X < 60) + P(65< X <70)= 5/60 + 10/60 + 10/60 + 10/60 + 10/60 + 5/60= 40/60 = 2/3

3 0

2 years ago