The sum of two numbers is 31.5. The difference is 5.25. Find the numbers

Write an equation for this model and solve for x. х = 3 x = -3 x = 4 x = -4

Ahat [919]

Answer:

c

Step-by-step explanation:

4 0

2 years ago

(x,-4) and (2,8); m=_3

DerKrebs [107]

$\bf (\stackrel{x_1}{x}~,~\stackrel{y_1}{-4})\qquad (\stackrel{x_2}{2}~,~\stackrel{y_2}{8}) \\\\\\ slope = m\implies \cfrac{\stackrel{rise}{ y_2- y_1}}{\stackrel{run}{ x_2- x_1}}\implies \cfrac{8-(-4)}{2-x}=\stackrel{\stackrel{m}{\downarrow }}{-3}\implies \cfrac{8+4}{2-x}=-3 \\\\\\ \cfrac{12}{2-x}=-3\implies 12=(2-x)(-3)\implies 12=-6+3x \\\\\\ 18=3x\implies \cfrac{18}{3}=x\implies 6=x$

5 0

3 years ago

In 1992, the moose population in a park was measured to be 4260. By 1996, the population was measured again to be 3660. If the p

masha68 [24]

In 1992, the moose population in a park was measured to be 4260. By 1996, the population was measured again to be 3660. If the population continues to change linearly: A.) Find a formula for the moose population, P , in terms of t , the years since 1990. P ( t ) = B.) What does your model predict the moose population to be in 2008?

Answer:

Model predict the moose population to be in 2008 is 1860

Solution:

Let us consider this problem on graph, taking the x axis to be years since 1990 and y on the graph be the number of moose

We have two points on the graph: (2, 4260) and (6, 3660)

Using the slope formula we can find the slope :

$\mathrm{m}=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}$

$m=\frac{(3660-4260)}{(6-2)}$

m = -150

Now that we have the slope of the line, we can use the point-slope formula to find the equation for the line as follows:-

$\begin{array}{l}{y-y_{1}=m\left(x-x_{1}\right)} \\\\ {y-4260=-150(x-2)} \\\\ {y-4260=-150 x+300} \\\\ {y=-150 x+4560}\end{array}$

Since the formula that is being sought is supposed to be interms of P and t, we will replace y with P and x with t

P(t) = -150t + 4560

Number of years from 1990 to 2008 is

2008 - 1990 = 18

So, population in 2008 will be

P(18) = -150 (18) + 4560

P(18) = -2700 + 4560

P(18) = 1860

Thus the model to predict the moose population in 2008 is found

4 0

2 years ago

The rate at which a quantity M of a certain radioactive substance decays is proportional to the amount of the substance present

anzhelika [568]

Answer:

2. dM/dt = -0.11M

Step-by-step explanation:

Differential equations for proportional amouts:

A differential equation for proportional amounts is given by:

$\frac{dx}{dt} = ax$

In which a is the constant rate. If the amount increases, a is positive. If it decays, b is positive.

In this question:

Decays, so a < 0.

Proportional to the amount of the substance present at a given time, which means that a multiplies the amount M.

This means that the correct answer is given by option 2.

3 0

2 years ago

Pls help solve for x |3x-8|+7=2

goldenfox [79]

Answer:

No solution

Step-by-step explanation:

To solve first you need to isolate the absolute value sign. Do this by subtracting 7 from each side.

|3x-8| = -5

Now an expression inside absolute value bars is set to a negative. Since absolute value makes terms and expressions positive, there is no x-value that could make this true. Therefore, there are no solutions.

6 0

2 years ago