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3 years ago

Which of the following is the equation of a line that has a slope of -2 and passes through the

Mathematics

2 answers:

Eddi Din [679]3 years ago

4 0

Answer: B. (y=-2x+8)

explanation: use slope point intercept
y-y1=m(x-x1)
y-6=-2(x-1)
y-6=-2x+2
y=-2x+8

KATRIN_1 [288]3 years ago

3 0

Answer:

B. y = -2x + 8

Step-by-step explanation:

So the slope is the number that comes before the x, and if the slope is -2, that means the number before is -2, and it is.

And to know if it goes through (1, 6), put those numbers into the equation and see if they match up (x is the y-intercept)

6 = -2(1) + x

6 = -2 + x

x = 8

The one with both of these is B, which means B is the answer

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Identify the type of function represented by... please help

Vladimir [108]

Answer:

Exponential decay.

Step-by-step explanation:

You can use a graphing utility to check this pretty quickly, but you can also look at the equation and get the answer. Since the function has a variable in the exponent, it definitely won't be a linear equation. Quadratic equations are ones of the form ax^2 + bx + c, and your function doesn't look like that, so already you've ruled out two answers.

From the start, since we have a variable in the exponent, we can recognize that it's exponential. Figuring out growth or decay is a little more complicated. Having a negative sign out front can flip the graph; having a negative sign in the exponent flips the graph, too. In your case, you have no negatives; just 2(1/2)^x. What you need to note here, and you could use a few test points to check, is that as x gets bigger, (1/2) will get smaller and smaller. Think about it. When x = 0, 2(1/2)^0 simplifies to just 2. When x = 1, 2(1/2)^1 simplifies to 1. Already, we can tell that this graph is declining, but if you want to make sure, try a really big value for x, like 100. 2(1/2)^100 is a value very very very veeery close to 0. Therefore, you can tell that as the exponent gets larger, the value of the function goes down and gets closer and closer to zero. This means that it can't be exponential growth. In the case of exponential growth, as the exponent gets bigger, your output should increase, too.

3 0

3 years ago

In this exercise, T: R2 → R2 is a function. For each of the following parts, state why T is not linear. (a) T(a1, a2)= (1, a2) (

DENIUS [597]

Answer:

a) T is not homogeneous
b) T is not additive
c) T is not homogeneous
d) T is not additive
e) T is not additive

Step-by-step explanation:

In each case there is an example where one property of linear functions fails.

a) $T(2(1,0))=T((2,0))=(1,0); 2T((1,0))=2(1,0)=(2,0)$ . These vectors are not equal, then T doesn't satisfy the condition of scalar multiplication (homogeneity).

b) $T((1,2)+(2,3))=T(3,5)=(3,9); T((1,2))+T((2,3))=(1,1)+(2,4)=(3,5)$ . Because these vectors are not equal, T doesn't satisfy the property of vector addition (additivity).

c) $T(\frac{1}{2}(\pi,0))=T((\frac{\pi}{2},0))=(\sin(\frac{\pi}{2}),0)=(1,0); \frac{1}{2}T((\pi,0))=\frac{1}{2}(0,0)=(0,0)$ so T is not homogeneous.

d) $T((-1,0)+(1,0))=T(0,0)=(0,0); T((-1,0))+T((1,0))=(1,0)+(1,0)=(2,0)$ then T is not additive.

e) $T((0,0)+(1,0))=T(1,0)=(2,0); T((0,0))+T((1,0))=(1,0)+(2,0)=(3,0)$ then T is not additive.

8 0

3 years ago

Find the approximate value of the circumference of a circle with the given radius. Use pi = 3.14. Round your results to one more

svetlana [45]

C = 2πr
C = 2 * 3.14 * 5.1
C = 32.028

You can round that to A. 32.03, because if the decimal after 2 is greater than it, then you round it to the number which is higher than it, which is 3.

4 0

3 years ago

Read 2 more answers

What force would have been applied to the bus from t=16 s to t=21 s? Assume the mass of the bus was 50 kg.

Svetllana [295]

Applying Newton's Second Law, it is found that the force, in Newtons, is given by:

$F = 10[v(21) - v(16)]$

Newton's Second Law states that Force, in Newtons, is mass times acceleration, that is:

$F = ma$

In this problem, mass of 50 kg, thus $m = 50$

Acceleration is change in velocity divided by change in time, that is:

$a = \frac{\Delta_v}{\Delta_t}$

In this problem, we don't know the velocities, but know that time is from 16s to 21s, thus:

$\Delta_t = 21 - 16 = 5$

$\Delta_v = v(21) - v(16)$

Thus, the force is given by:

$F = ma$

$F = m\frac{\Delta_v}{\Delta_t}$

$F = 50\frac{[v(21) - v(16)]}{5}$

$F = 10[v(21) - v(16)]$

A similar problem is given at brainly.com/question/18801986

7 0

3 years ago

BEST ANSWER GETS BRAINLIEST

Alexandra [31]

Answer:

1. The speed of the truck, S = D/T.

2. The formula that connects D and T is: S = D/T.

3. The coefficient of variation, k, is the ratio of the standard deviation to the mean speed.

Step-by-step explanation:

a) The speed of a truck at a fixed speed is given as the distance covered by the truck divided by the time it takes the truck to cover the said distance. This implies that speed is a function of distance and time. However, this formula represents the mean speed. There are variations in speed.

b) If the truck covers a distance of 60 kilometers, for example, under 3 hours, we can conclude that the speed is 20 kilometers per hour (60/3) or 20 km/hr.

4 0

3 years ago