Evaluate p(x)=−3+4x when x=−2,0, and 5 .

Answer:

P=7.75t+13

t = 19 weeks

Step-by-step explanation:

Linear Modeling

Some situations can be modeled as linear functions. If we are in a situation where a linear model is suitable, then we need two sample points to make the model and predict future behaviors.

The linear function can be expressed in the slope-intercept format:

y = mx + b

Another equation of the line can be used when two points are given.

The equation of a line passing through points (x1,y1) and (x2,y2) can be written as follows:

[tex]\displaystyle y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)[/tex]

The population of beetles is a situation where we must apply linear modeling. Two points are given. For time t=0, the population is P=13. The point is (0,13). For time t=8, P=75. The point is (8,75).

Find the equation of the line:

[tex]\displaystyle P-P_1=\frac{P_2-P_1}{t_2-t_1}(t-t_1)[/tex]

[tex]\displaystyle P-13=\frac{75-13}{8-0}(t-0)[/tex]

[tex]\displaystyle P-13=\frac{62}{8}t[/tex]

[tex]\displaystyle P-13=7.75t[/tex]

The explicit formula is:

P = 7.75t + 13

Now we find when the beetle population is 161:

161 = 7.75t + 13

161 - 13 = 7.75t

7.75t = 148

t = 148/7.75

t = 19 weeks

Answer:

so m=2 so y=2x+-3

Step-by-step explanation:

The equation of the line will be written as y = 2x - 3.

An equation of the line is defined as a linear equation having a degree of one. The equation of the line contains two variables x and y. And the third parameter is the slope of the line which represents the elevation of the line.

The general form of the equation of the line:-

y = mx + c

m = slope

c = y-intercept

Slope = ( y₂ - y₁ ) / ( x₂ - x₁ )

Given that a line passes through points (2, 1) and (6, 9). The equation of the line will be written by calculating the slope and y-intercept.

Slope = ( y₂ - y₁ ) / ( x₂ - x₁ )

Slope = ( 9 - 1 ) / ( 6 - 2 )

Slope = 8 / 4

Slope = 2

The y-intercept will be calculated as,

y = mx + c

1 = ( 2 x 2 ) +C

C = 1 - 4 = -3

The equation will be written as,

y = 2x - 3

To know more about an equation of the line follow

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Answer:

x+(x+4)=52

Step-by-step explanation:

let the small number be x

The greater number is 4 more than the small number=x+4

sum of numbers= x+ (x+4)

Answer:

a = 37/6

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Equality Properties

Step-by-step explanation:

Step 1: Define equation

-12(a - 2) = -50

Step 2: Solve for a

Step 3: Check

Plug in a into the original equation to verify it's a solution.

Here we see that -50 does indeed equal -50.

∴ a = 37/6 is a solution of the equation.

Answer:

a = [tex]\frac{37}{6}[/tex]

Step-by-step explanation:

-12(a - 2) = -50

-12a + 24 = -50

-12a = -74

a = [tex]\frac{74}{12}[/tex] = [tex]\frac{37}{6}[/tex]

Answer:

x - 31  [tex]\geq[/tex] 69

Tonisha has to make at least $100 in revenue

Step-by-step explanation:

Set up the inequality:

x - 31 represents her profit

Since she wants to make at least $69 a day, use [tex]\geq[/tex] 69

So, the inequality is x - 31  [tex]\geq[/tex] 69

Then, solve for x to find how much she has to sell:

x - 31  [tex]\geq[/tex] 69

x [tex]\geq[/tex] 100

So, Tonisha has to make at least $100 in revenue

Answer:

lines b and c are perpendicular

Step-by-step explanation:

Use slope

slope for parallel is the same

slope for perpendicular is negative reciprocal

line a slope- 1-3/-2-0 is -2/-2 or 1

line b slope- 1-4/4-6 is -3/-2 or 3/2

line c slope- 3-1/1-4 is 2/-3 or - 2/3

none are the same so none are parallel

- 2/3 is the negative reciprocal of 3/2 so lines b and c are perpendicular

Answer:

$20,000

Step-by-step explanation:

Let the new car price before tax be p.  If the sales tax was $1400, then the following is true:  0.07p = $1400, and p = $20,000

$1400 is 7% of the before-tax new car price, which is $20,000

I think you were talking about the formula:

y = mx+b

y= 3(1)

or y=3

Answer:

We can use quadratic formula

a=3, b= -1, c=4

Step-by-step explanation:

Answer: B

Hope this helps :)

Answer:

The equation for relationship between the thickness and the number of weeks is f(x)=3.8 -0.2*x

Step-by-step explanation:

Ice thickness decreases at a rate of 0.2 meters per week. This can then be represented by the expression

f(x) = k - 0.2*x

where k is the thickness of the ice before the melting starts and x is the number of weeks.

After 7 weeks, the ice is only 2.4 meters thick. This means that x has a value of 7, while f (7) = 2.4. Replacing in the previous expression:

2.4=k -0.2*7

and solving you get:

2.4=k- 1.4

2.4 + 1.4= k

3.8= k

Then, the equation for relationship between the thickness and the number of weeks is f(x)=3.8 -0.2*x

Answer:

See explanation

Step-by-step explanation:

From the attachment, the question has been answered. However, the explanation is as follows;

Given that

[tex](x,y) = (7,4)[/tex]

This means that

[tex]x = 7[/tex]

[tex]y = 4[/tex]

See attachment (1)

Step 1: Locate point 7 on the x axis

Step 2: Locate point 4 on the y axis

Trace these two points until they intersect.

The point at which they intersect, is the required point (7,4) --See attachment (2)

Arc length is equal to its corresponding central angle.

That means that the arc measures 120° too.

Answer:

≈ 4.2 cm

Step-by-step explanation:

The arc length is calculated as

arc = circumference of circle × fraction of circle

     = 2πr × [tex]\frac{120}{360}[/tex] ( r is the radius )

    = 2π × 2 × [tex]\frac{1}{3}[/tex]

   = 4π ÷ 3

   ≈ 4.2 cm ( to 1 dec. place )

Answer:

A only

Step-by-step explanation:

you can't get x^2 from any other choices

what do you need help with (no pic or no question)

Answer:

what is the question>?>

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

decreasing is a key word meaning negitive

Answer:

B

Step-by-step explanation:

Decrease shows negative and also if temperature decreases , it mostly is negative

Answer:

The equation is;

x^2 + 4x + 4 = 0

Step-by-step explanation:

Here, we want to give a quadratic equation with a real solution that has a multiplicity of two

Generally, there are only two solutions to a quadratic equation since it is a polynomial of degree two

Since we have a multiplicity of 2, it means that the real roots are repeated

Let us have a solution of x = -2

With the multiplicity;

we have x + 2

So let us expand this

(x+2)(x+2)

= x^2 + 4x + 4

The equation is;

x^2 + 4x + 4 = 0

Answer:

∠A = 120° (180°-60°)

∠W = 60° (b/c ∠W=∠X)

∠Y = 100° (b/c 180°-80°)

∠X = 60° (180°-120°)

∠Z = 120° (180-60°)

Step-by-step explanation:

im unsure about A and W

Answer:

Answer:

-4.6 Repeating

Step-by-step explanation:

This will be a repeating Decimal. :)

Answer:

0.6666

Step-by-step explanation:

you divide 2 by three and then you get your answer

Answer:

106.95

Step-by-step explanation:

there are 31 days in july so if multiply 3.45 and 31 you get your answer

Answer:

8 and -8

Step-by-step explanation:

0-8= -8

0+8= 8

Both 8 jumps from 0

Answer: (6, 9) I believe. If you graph the two points, you can see that the slope is 5x (Up 5, right 1). If you make another point on that line, you would raise it from (5, 4). So B = (6, 9). Comment if you need more explaining

Answer:

AAS

Step-by-step explanation:

AAS stands for Angle-Angle-Side. Here, you are given two angles and one side that is not included in the angles that are corresponding to the angles and side of another triangle, so they are congruent by the AAS rule.

You may be asking why the ASA (angle-side-angle) is not applicable. This is because the side in the ASA rule should be between the two angles, in this case, the 10-unit-side is not in between the two angles but rather nearer to the angle 70°, so ASA is not the right answer.

Answer:

9/10

Step-by-step explanation:

no

Answer:  J = −0.45

explanation: Isolate the variable by dividing each side by factors that don't contain the variable.

Answer:

pretty sure its communitive property