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3 years ago

Solve the following: a) 4x – 3 = 2x + 7 b) 2x + 6 = 7x - 14

Mathematics

2 answers:

pickupchik [31]3 years ago

8 0

Answer:

a) x = 5

b) x = 4

Step-by-step explanation:

a) 4x - 3 = 2x + 7 collect like terms

4x - 2x = 7 + 3

2x = 10 divide both sides by the coefficient of x

x = 5

b) 2x + 6 = 7x - 14 collect like terms

2x - 7x = -14 - 6

-5x = -20 divide both sidess by the coefficient of x

x = 4

Yuliya22 [10]3 years ago

6 0

Answer:

gxtuj

Step-by-step explanation:

gvgxhg

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Subtract the function f(x) = 6x -- 5 from the function g(x) = -2% +9.

densk [106]

We want h(x) = g(x) - f(x).

h(x) = -2x + 9 -(6x - 5)

h(x) = -2x + 9 -6x + 5

h(x) = -8x + 14

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2 years ago

How many millimeters are there in 5 centimeters?

sergejj [24]

Answer:

50 millimeters

Step-by-step explanation:

5=50

3 0

2 years ago

Let X be the waiting time for a car to pass by on a country road, where X has an average value of 35 minutes. If the random vari

Gelneren [198K]

Answer:

Probability that the wait time is greater than 37 minutes is 0.3474.

Step-by-step explanation:

We are given that the random variable X is known to be exponentially distributed and X be the waiting time for a car to pass by on a country road, where X has an average value of 35 minutes.

Let X = waiting time for a car to pass by on a country road

The probability distribution function of exponential distribution is given by;

$f(x) = \lambda e^{-\lambda x} , x >0$ where, $\lambda$ = parameter of distribution.

Now, the mean of exponential distribution is = $\frac{1}{\lambda}$ which is given to us as 35 minutes that means $\lambda = \frac{1}{35}$ .

So, X ~ Exp( $\lambda = \frac{1}{35}$ )

Also, we know that Cumulative distribution function (CDF) of Exponential distribution is given as;

$F(x) = P(X \leq x) = 1 - e^{-\lambda x}$ , x > 0

Now, Probability that the wait time is greater than 37 minutes is given by = P(X > 37 min) = 1 - P(X $\leq$ 37 min)

P(X $\leq$ 37 min) = $1 - e^{-\frac{1}{35} \times 37}$ {Using CDF}

= 1 - 0.3474 = 0.6525

So, P(X > 37 min) = 1 - 0.6525 = 0.3474

Therefore, probability that the wait time is greater than 37 minutes is 0.3474.

4 0

3 years ago

Can someone please help me I don’t understand this. I keep getting it wrong

kicyunya [14]

Answer:

K- (-8, -2)

L- (2, -2)

J- (-8, -5)

M- (2, -5)

Step-by-step explanation:

Vertices refer to the points where the lines connect, or corners. In this problem they're represented by K, L, J, and M.

The current coordinates are-

K- (-8, -4)

L- (2, -4)

J- (-8, -7)

M- (2, -7)

Since the Y coordinate refers to vertical distance and the X coordinate refers to horizontal distance, translating them two units up would involve adding positive two to each y coordinate.

Therefore the new coordinates would be

K- (-8, -2)

L- (2, -2)

J- (-8, -5)

M- (2, -5)

Hope this was helpful! Sorry if I messed up askdjasjk

7 0

3 years ago

which choice is the explicit formula for the following geometric sequence 0.5,-0.1, 0.02, -0.004, 0.0008

defon

Hello,

Answer is C

$a_1=0.5=\dfrac{1}{2} \\\\a_2=-0.1=-\dfrac{1}{10} =a_1*(-\dfrac{2}{10} )=a_1*(-\dfrac{1}{5} )\\\\a_3=0.02=\dfrac{2}{10^2} =a_2*(-\dfrac{2}{10} )=a_2*(-\dfrac{1}{5} )=a_1*(-\dfrac{1}{5} )^2\\...\\a_n=a_1*(-\dfrac{1}{5} )^{n-1}\\\\\boxed{a_n=0.5*(-0.2)^{n-1}}\\$

8 0

3 years ago