What is the equation of this trend line?
Enter your answers by filling in the boxes.
K= J+

Answer:

81 Degrees

Step-by-step explanation:

The triangles are congruent and a triangle is 180 degrees total. So, 57+42=99. 180-99=81

So the answer is 81 degrees.

Answer:

A) It will get to a temperature of 125°F at 9:19 PM

B) It will get to a temperature of 150°F at 9:16 PM

C) as time passes temperature approaches the initial temperature of 450°F

Step-by-step explanation:

We are given;

Initial temperature; T_i = 450°F

Room temperature; T_r = 70°F

From Newton's law of cooling, temperature after time (t) is given as;

T(t) = T_r + (T_i - T_r)e^(-kt)

Where k is cooling rate and t is time after the initial temperature.

Now, we are told that After 5​ minutes, the temperature is 300°F.

Thus;

300 = 70 + (450 - 70)e^(-5k)

300 - 70 = 380e^(-5k)

230/380 = e^(-5k)

e^(-5k) = 0.6053

-5k = In 0.6053

-5k = -0.502

k = 0.502/5

k = 0.1004 /min

A) Thus, at temperature of 125°F, we can find the time from;

125 = 70 + (450 - 70)e^(-0.1004t)

125 - 70 = 380e^(-0.1004t)

55/380 = e^(-0.1004t)

In (55/380) = -0.1004t

-0.1004t = -1.9328

t = 1.9328/0.1018

t ≈ 19 minutes

Thus, it will get to a temperature of 125°F at 9:19 PM

B) Thus, at temperature of 150°F, we can find the time from;

150 = 70 + (450 - 70)e^(-0.1004t)

150 - 70 = 380e^(-0.1004t)

80/380 = e^(-0.1004t)

In (80/380) = -0.1004t

-0.1004t = -1.5581

t = 1.5581/0.1004

t ≈ 16 minutes.

Thus, it will get to a temperature of 150°F at 9:16 PM

C) As time passes which means as it approaches to infinity, it means that e^(-kt) gets to 1.

Thus,we have;

T(t) = T_r + (T_i - T_r)

T_r will cancel out to give;

T(t) = T_i

Thus, as time passes temperature approaches the initial temperature of 450°F

Answer:

The rate increases at 398mi/h

Step-by-step explanation:

Given

[tex]\frac{dx}{dt} = 460mi/h[/tex] --- rate when [tex]y = 2[/tex] --- distance

The given parameters is represented with the attached figure

Using Pythagoras theorem [take the attached image as a point of reference]

[tex]y^2 = x^2 + 1^2[/tex]

[tex]y^2 = x^2 + 1[/tex]

Differentiate with respect to time (t):

[tex]2y \frac{dy}{dt} = 2x \frac{dx}{dt}[/tex]

Divide both sides by 2

[tex]y \frac{dy}{dt} = x \frac{dx}{dt}[/tex] --- (1)

When y = 2:

[tex]y^2 = x^2 + 1^2[/tex] --- Pythagoras Theorem

[tex]2^2 = x^2 + 1[/tex]

[tex]4 = x^2 + 1[/tex]

Collect like terms

[tex]x^2 = 4 -1[/tex]

[tex]x^2 = 3[/tex]

Solve for x

[tex]x = \sqrt 3[/tex]

So:

[tex]y \frac{dy}{dt} = x \frac{dx}{dt}[/tex]

Substitute: [tex]x = \sqrt 3[/tex], [tex]\frac{dx}{dt} = 460mi/h[/tex] and [tex]y = 2[/tex]

[tex]2 * \frac{dy}{dt} = \sqrt 3 * 460[/tex]

[tex]2 * \frac{dy}{dt} = 460\sqrt 3[/tex]

Divide by 2

[tex]\frac{dy}{dt} = 230\sqrt 3[/tex]

[tex]\frac{dy}{dt} = 230*1.7321[/tex]

[tex]\frac{dy}{dt} = 398.383[/tex]

[tex]\frac{dy}{dt} \approx 398[/tex]

Answer:

x = 6 ± 5[tex]\sqrt{3}[/tex]

Step-by-step explanation:

Given

x² - 12x = 39

Using the method of completing the square

add ( half the coefficient of the x- term)² to both sides

x² + 2(- 6)x + 36 = 39 + 36

(x - 6)² = 75 ( take the square root of both sides )

x - 6 = ± [tex]\sqrt{75}[/tex] = ± 5[tex]\sqrt{3}[/tex] ( add 6 to both sides )

x = 6 ± 5[tex]\sqrt{3}[/tex] ← solutions in exact form

Answer:

x = 6 ± 5* OR 6 - 5*

Step-by-step explanation:

In decimal form it would be either 14.66025403... or -2.66025403

Hope this helps!

Answer:

can you send me a pic of how it looks because it's confusing to understand

Answer:

18.84

Step-by-step explanation:

Answer:

Step-by-step explanation:

If the 2 is an exponent, it needs to be written as ^2.

(5+√3)²  = 5² + 10√3 + 3 = 28 + 10√3

Answer:

i think its

[tex]P(x) = i ^{3}[/tex]

Step-by-step explanation:

Answer is in the file below

tinyurl.com/wpazsebu

Answer:

Step-by-step explanation:

1.   perpendicular slope will be the negative of the reciprocal

2.  so this will be -3 ( since the reciprocal of 1/3 is 3 and its negative is -3

3.  So use the values given for x and y (3,-4)

4.   substitute in the given equation using the -3 for the slope instead of 1/3

5.  To find a new b we substitute  for x and y

5.  y = 1/3x + 10

6.  -4 =  -3 (3) + b

7.   -4= -9+ b

8. b = 5

Equation of the line will be y = -3x + 5

Answer:

aSDFGHJLLMNNBBBBVCDDG

Step-by-step explanation:

Answer:

Step-by-step explanation:

Answer:

5x - ((2x-1)÷2) = 5-----(1)

(1) multiply by 2;

2 *(5x - ((2x-1)÷2) = 5)

10x - (2x-1) = 10

10x - 2x + 1  = 10

8x + 1 =10

8x = 10-1

x=9 /8

Step-by-step explanation:

Answer:

x = 9/8

Step-by-step explanation:

5x - ((2x - 1) ÷ 2) = 5​

2 × (5x - ((2x - 1) ÷ 2) = 5

10x - (2x-1) = 10

10x - 2x + 1  = 10

8x + 1 = 10

8x + 1 - 1 = 10 - 1

8x = 10 - 1

8x = 9

8x ÷ 8 = 9 ÷ 8

x = 9 ÷ 8

x = 9/8 or 1 and 1/8

Answer: A plane has two dimensions because it is a flat surface that has length and width but no depth.

Answer:

Surface answer

Step-by-step explanation:

Because the surface has a length and width and does not have a depth

Answer:

37.7 inches

Step-by-step explanation:

Formula of circumference:

[tex]2\pi r[/tex]

r = radius

In the current case,

radius is 6 inches

Hence,

circumference=

[tex]2*\pi *6\\= 12\pi\\= 37.6991118431[/tex]

≅ 37.7 inches

Feel free to mark it as brainliest

Answer:

Expression that represents the sale price of the wedding dress is  

Solution:

Given that, the dress is on sale for 35 % off the regular price

Let the regular price of dress be "w"

To find: Expression that represents the sale price of the wedding dress

Let "s" be the sale price of wedding dress

Sale price = Regular price - discount price

Discount price is given as:

Discount price = 35 % of regular price

Discount price = 35 % of w  

Thus discount price = 0.35w

Expression for the sale price of the wedding dress:

Sale price = Regular price - discount price

s = w - 0.35

s = 0.65

s= 0.65

Thus expression that represents the sale price of the wedding dress is

s=0.56

Answer:

Step-by-step explanation:

Answer: C. Daphne's test score is 2.50 standard deviations above the average test score of students in the course.

Step-by-step explanation: That's what Z-score is

Answer:4x1/3=4/3

Step-by-step explanation:

In the pictures there’s 4 one thirds and if u add them together is 4/3

Answer:

x=6 x=-1

a=1.5 a=-2

n=-1.5 n=4

Step-by-step explanation:

(a) (b) (c)

10a2+5a-30

x=-b+-√b2-4ac/2a

a=-5+-√(5)2-4(10)(-30)/2(10)

a=-5+-√25+1200/20

a=-5+-√1225/20

a=-5+√1225/20

a=1.5

a=-5-√1225/20

a=-2

Answer:

is this a multiple-choice question?

Step-by-step explanation:

**i'll go back and change my answer, i promise**

Answer:

Step-by-step explanation:

1.values of x at y=0 are 1

2.5

3.

(3,-4)

4.

it is a minimum.

5.

axis of symmetry is x=3

Answer: 803mm

Step-by-step explanation:

Answer:

7.065 sq. units

Step-by-step explanation:

The circumference is given, thus you can use the equation 2πr = circumference to find out the radius first, r = 1.5.

Area = πr²

∴The required area is 7.065 sq. units

Answer:

Not to conclude that the drug is safe, when, in fact, it is safe.

Step-by-step explanation:

A type ii error is an error that occurs in a hypothesis testing when a person goes ahead to accept a null hypothesis when it is actually false and should be rejected.

To continue, here are the hypothesis:

H0: the drug is unsafe

H1: drug is safe.

A type ii error was committed here because H0, which is the null was accepted and it was concluded that the drug was unsafe, When in fact it should have been rejected. The conclusion should have been that the drug was safe.