All categories

4 years ago

Kelsey graphed the equation y = 3x + 1 as shown below.

Mathematics

2 answers:

VMariaS [17]4 years ago

7 0

Answer:

the answer is the last option

Step-by-step explanation:

hope this helps

have a good day

did the test on edge

USPshnik [31]4 years ago

4 0

Answer:

D. Kelsey graphed the slope as the y-intercept and the y-intercept as the slope.

Step-by-step explanation:

The equation to graph was : y= 3x + 1 where the slope is 3 and the y-intercept is 1

However, Kelsey graph line passes through points (-3, 0)and (0, 3).From these points the equation of the line is;

m=Δy/Δx where

m=the slope of the graph

Δy= 3-0 =3

Δx= 0--3 =3

m=3/3 = 1

The equation of the line should be;

m=Δy/Δx

1=y-3/x-0

1x= y-3

3+1x= y

y= 1x + 3 ----------where the slope is 1 and y-intercept is 3

So you can see here that in the original equation, the slope m is 3 and y-intercept is 1 as shown in the first attached graph.

While in the Kelsey's graph, the slope is 1 and the y-intercept is 3 as in the second attached graph.

Thus, the correct answer is D : Kelsey graphed the slope,3 as the y-intercept and the y-intercept,1, as the slope.

Answer choice A is incorrect because Kelsey didnot graph the y-intercept, 1 on the x-axis but graphed point (-3,0) on the x-axis.

Answer choice B is incorrect because on Kelsey's equation the y-intercept is 3 and not -3. i.e. y=1x + 3

Answer choice C is incorrect because Kelsey graphed the slope as up 1 right 1 which is okay per the equation , y=1x+3.However, this incorrect because the correct graph has a slope of 3.

You might be interested in

Divide square root 9^2 by square root 18y^2

Klio2033 [76]

I got y^2/2

My Solution:

√9^2/18 · y^2

= 1/2 y^2

Multiply Fractions: a · (b/c) = (a · b)/c

1·y^2/2

=y^2/2

Hope I helped,
Faith xx

6 0

3 years ago

Alyssa says that n = 6 is the solution of the equation 12n = 84. How can you check whether she is correct?

Vikki [24]

Answer:

No. The answer is 72

Step-by-step explanation:

As 12x6=72

4 0

3 years ago

The spread of a virus is modeled by V (t) = −t 3 + t 2 + 12t,

VashaNatasha [74]

Functions can be used to model real life scenarios

The reasonable domain is $\mathbf{[0,\infty)}$ .
The average rate of change from t = 0 to 2 is 20 persons per week
The instantaneous rate of change is $\mathbf{V'(t) = -3t^2 + 2t + 12}$ .
The slope of the tangent line at point (2,V(20) is 10
The rate of infection at the maximum point is 8.79 people per week

The function is given as:

$\mathbf{V(t) = -t^3 + t^2 + 12t}$

(a) Sketch V(t)

See attachment for the graph of $\mathbf{V(t) = -t^3 + t^2 + 12t}$

(b) The reasonable domain

t represents the number of weeks.

This means that: t cannot be negative.

So, the reasonable domain is: $\mathbf{[0,\infty)}$

(c) Average rate of change from t = 0 to 2

This is calculated as:

$\mathbf{m = \frac{V(a) - V(b)}{a - b}}$

So, we have:

$\mathbf{m = \frac{V(2) - V(0)}{2 - 0}}$

$\mathbf{m = \frac{V(2) - V(0)}{2}}$

Calculate V(2) and V(0)

$\mathbf{V(2) = (-2)^3 + (2)^2 + 12 \times 2 = 20}$

$\mathbf{V(0) = (0)^3 + (0)^2 + 12 \times 0 = 0}$

So, we have:

$\mathbf{m = \frac{20 - 0}{2}}$

$\mathbf{m = \frac{20}{2}}$

$\mathbf{m = 10}$

Hence, the average rate of change from t = 0 to 2 is 20

(d) The instantaneous rate of change using limits

$\mathbf{V(t) = -t^3 + t^2 + 12t}$

The instantaneous rate of change is calculated as:

$\mathbf{V'(t) = \lim_{h \to \infty} \frac{V(t + h) - V(t)}{h}}$

So, we have:

$\mathbf{V(t + h) = (-(t + h))^3 + (t + h)^2 + 12(t + h)}$

$\mathbf{V(t + h) = (-t - h)^3 + (t + h)^2 + 12(t + h)}$

Expand

$\mathbf{V(t + h) = (-t)^3 +3(-t)^2(-h) +3(-t)(-h)^2 + (-h)^3 + t^2 + 2th+ h^2 + 12t + 12h}$ $\mathbf{V(t + h) = -t^3 -3t^2h -3th^2 - h^3 + t^2 + 2th+ h^2 + 12t + 12h}$

Subtract V(t) from both sides

$\mathbf{V(t + h) - V(t)= -t^3 -3t^2h -3th^2 - h^3 + t^2 + 2th+ h^2 + 12t + 12h - V(t)}$

Substitute $\mathbf{V(t) = -t^3 + t^2 + 12t}$

$\mathbf{V(t + h) - V(t)= -t^3 -3t^2h -3th^2 - h^3 + t^2 + 2th+ h^2 + 12t + 12h +t^3 - t^2 - 12t}$

Cancel out common terms

$\mathbf{V(t + h) - V(t)= -3t^2h -3th^2 - h^3 + 2th+ h^2 + 12h}$

$\mathbf{V'(t) = \lim_{h \to \infty} \frac{V(t + h) - V(t)}{h}}$ becomes

$\mathbf{V'(t) = \lim_{h \to \infty} \frac{ -3t^2h -3th^2 - h^3 + 2th+ h^2 + 12h}{h}}$

$\mathbf{V'(t) = \lim_{h \to \infty} -3t^2 -3th - h^2 + 2t+ h + 12}$

Limit h to 0

$\mathbf{V'(t) = -3t^2 -3t\times 0 - 0^2 + 2t+ 0 + 12}$

$\mathbf{V'(t) = -3t^2 + 2t + 12}$

(e) V(2) and V'(2)

Substitute 2 for t in V(t) and V'(t)

So, we have:

$\mathbf{V(2) = (-2)^3 + (2)^2 + 12 \times 2 = 20}$

$\mathbf{V'(2) = -3 \times 2^2 + 2 \times 2 + 12 = 4}$

Interpretation

V(2) means that, 20 people were infected after 2 weeks of the virus spread

V'(2) means that, the rate of infection of the virus after 2 weeks is 4 people per week

(f) Sketch the tangent line at (2,V(2))

See attachment for the tangent line

The slope of this line is:

$\mathbf{m = \frac{V(2)}{2}}$

$\mathbf{m = \frac{20}{2}}$

$\mathbf{m = 10}$

The slope of the tangent line is 10

(g) Estimate V(2.1)

The value of 2.1 is

$\mathbf{V(2.1) = (-2.1)^3 + (2.1)^2 + 12 \times 2.1}$

$\mathbf{V(2.1) = 20.35}$

(h) The maximum number of people infected at the same time

Using the graph, the maximum point on the graph is:

$\mathbf{(t,V(t) = (2.361,20.745)}$

This means that:

The maximum number of people infected at the same time is approximately 21.

The rate of infection at this point is:

$\mathbf{m = \frac{V(t)}{t}}$

$\mathbf{m = \frac{20.745}{2.361}}$

$\mathbf{m = 8.79}$

The rate of infection is 8.79 people per week

Read more about graphs and functions at:

brainly.com/question/18806107

6 0

3 years ago

X - 35 > 15 i need answer IMEDIATLEY

SIZIF [17.4K]

I'm assuming you want us to solve this inequality for x, since the question wasn't too clear on that.

$x - 35 > 15$

Add 35 to both sides to remove the "-35" on the left side so we can isolate the x

$x-35+35>15+35$

$x>50$

The solution to this inequality is x>50. Let me know if you need any clarifications, thanks!

~ Padoru

6 0

3 years ago

When x=12, y=8. Find x when y=12

Digiron [165]

x : y is equal to 12 : 8. These can be reduced or cancelled down to 3 : 2 in the same proportions. Therefore, when y is 12, you have to multiply the smallest value y can be by 6, and must do the same to the smallest x value to retain the proportions. x = 18 when y = 12.

6 0

3 years ago