the temperature at sunrise is 48°F . each hour the temperature rises 6°F write an equation that models the temperature y in degrees Fahrenheit after x hours. what is the graph of the equation.

Answer:

the answer is 26

Step-by-step explanation:

j+2h

(2) + 2(12)

2 + 24

26

Step 1

Given;

Required; To find the measure of angle F

Step 2

Answer;

We know the domain is the set of all x when is represented by ordered pairs: (x, y)

In this case {(-8,-12),(4,-8), (2, -10),(-10.-16) } we can observe that there are four x (the first number of each pair):

Domain = { -8, 4, 2, -10}

If angle ∠4 = 29 degrees, then

The m∠4 = 29 degrees

Part 1

The angles on a straight line add up to 180 degrees.

∠4 + ∠1 = 180

29 + ∠1 = 1180

∠1 = 180-29

= 151 degrees

Part 2

The angles on a straight line add up to 180 degrees.

∠1 + ∠2 = 180

151 + ∠2 = 180

∠2 = 180-151

= 29 degrees

Part 3

The angles on a straight line add up to 180 degrees.

∠2 + ∠3 = 180

29 +  ∠3 = 180

∠3 = 180-29

= 151 degrees

Hence, If  angle ∠4 = 29 degrees, then

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Answer:

Step-by-step explanation:

study

The exponential model A=64.5e^0.02t describes the population, A of a country in millions, t years after 2003. The population of the country will be 108 million in

we have the expression

A=64.5e^0.02t

For A=108

substitute

108=64.5e^0.02t

108/64.5=e^0.02t

Apply ln both sides

ln(108/64.5)=ln(e^0.02t)

ln(108/64.5)=0.02t(ln(e))

ln(108/64.5)=0.02t

solve for t

t=ln(108/64.5)/0.02

t=26 years

therefore

2003+26=2029

answer is

ANSWER :

The answer is B. y = (x + 4)^2 + 9

EXPLANATION :

From the problem, we have :

Group the terms in which the constant term and the terms with variables are separated.

add and subtract a variable m to the parenthesis to maintain equivalency.

Calculate the value of m using b^2/4a^2 with a = 1 and b = 8

Then :

The first parenthesis will be a perfect square trinomial.

Factor and simplify :

The equation of the car can be given as and the price of the car after 8 years is $4445.

What is an exponential function?

A function of the form [tex]a^{x}[/tex] is known as exponential function. In short the function which has an exponent is known as exponential function.

We are given that the value of a new car after 2 years was $11,200. When the car is 6 years old, the value has dropped to $6100.

Let the original price of the car be [tex]P_{0}[/tex]

After two years the price of the car is $11200

Mathematically it can be given as

[tex]11200= P_{0}e^{2x}[/tex]

After 6 years the price of the car is $6100

Mathematically it can be given as

[tex]6100=P_{0}e^{6x}[/tex]

Dividing both equations we get,

[tex]1.83=e^{-4x}[/tex]

Which can also be written as

[tex]e^{4x}=0.54[/tex]

on solving we get,

x=-0.154

Hence the rate at which price of the car is dropping is

[tex]P=P_{0}e^{-0.154t}[/tex]

No we have to find the original price of the car

To do so we substitute t=2 in the equation

we get

11200=[tex]P_0e^{-0.308}[/tex]

On solving we get,

15240=[tex]P_0[/tex]

Now we find the price of the car after 8 years

P=15240·[tex]e^{-1.232}[/tex]

On simplifying we get

P=$4445

Hence the price of the car after 8 years will be $4445

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If we draw a vertical line and it crosses the figure more than once, then it is not a function.

So, the only graph that a vertical line will intersect the line once is graph A:

B, C and D are intersected more than 1 time, so they are not functions.

Answer: A

Answer:

x=12

Step-by-step explanation:

(x-6)=6

x=12

Answer:

??

Step-by-step explanation:

The inequality is 2(3x - 5) ≤ (4x + 6) and the solution of the inequality is (-0, 8]

Let the number be x,

Twice the difference of three times a number and five = 2(3x - 5)

The sum of four times a number and six is  (4x + 6)

2(3x - 5) ≤ (4x + 6)

6x - 10 ≤ 4x + 6

6x - 4x ≤ 6 + 10

2x ≤ 16

x ≤ 8

x can be any positive number less than or equal to 8.

Therefore, the inequality is 2(3x - 5) ≤ (4x + 6) and the solution of the inequality is (-0, 8]

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If they meet in 2 hr the rate of the slower car is 86.

What is rate?

rate is the ratio between two of  related quantities in the  different units. If the denominator of the ratio is expressed as of a single unit of one of those quantities.

Sol- as per the given question

{d =380

{t=2

Substitute {d=380 formula

                 {t=2

d=v×t

380=2v

=2(18+2x)=380

Apply the distributive property

36+4x=380

Rearrange variables to the left side of the equation

4x=380-36

4x=344

Divided both side of the equation by the coefficient of variable

X=344/4

By cross out the common factor we get

X=86

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Answer:

$195

Step-by-step explanation:

40% represents £130

40% : $130

100% : total

To find total:

($130 / 40) x 100 = $325 is the total

If $130 spent:

$325 - $130 = $195 is the amount left

Hello there!

If a bag has 12 balls labelled 1 through 12, that means that the balls inside the bag includes:

1  2  3  4  5  6  7  8  9  10  11  12

When creating a fraction for a probability, the numerator usually consists of a specific probability you are trying to find; the denominator usually consists of the total amount of samples in the bag.

In this example: What is the probability of picking an even number?

Ask yourself: What are we trying to find?

We are trying to find the probability of even numbers.

Then ask yourself: What is the amount of possibilities that we can get an even number from the bag?

The bag consists of: 1  2  3  4  5  6  7 8  9  10  11  12

Even numbers are divisible by 2 and has a remainder of 0 ; which means in this bag, the bolded numbers are even.

Then we can conclude that in this bag, counting all of the bolded numbers, we have 6 possibilities of choosing an even number.

Finally, think about: What is the total amount of samples in this bag?

We know that there are 12 balls, so 12 would be the total amount.

To conclude, we can find 6 even numbers in a bag of 12 balls;

Therefore, the chances you can pick an even number is [tex]\frac{6}{12} ,[/tex] or [tex]\frac{1}{2}[/tex].

The solution to the equation given as 4(3m + 1) − 2m = −16 is m = -2

The equation is given as

4(3m + 1) − 2m = −16

Open the brackets in the above equation

So, we have

12m + 4 − 2m = −16

Collect the like terms in the above equation

So, we have the following equation

12m − 2m = −16 -4

Evaluate the like terms in the above equation

So, we have the following equation

10m = −20

Divide both sides by 10

m = -2

Hence, the soluton is m = -2

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The increase in the national debt from 2005 to 2015 using scientific notation is 1.3176 × 10^13.

Scientific notation simply means a way of expressing numbers that are either too large or too small.

The U.S. national debt was 1.815 x 10^13 dollars on September 30, 2015 and in September 29,

2005, the national debt was 4.974 x 10^12 dollars.

The increase will be the difference between the two notations. This will be:

= 1.815 x 10^13 - 4.974 x 10^12

= 1.3176 × 10^13

The increase is 1.3176 × 10^13.

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The required respective increase in the national debt of America for the period 2005 to 2015 is 1.3176 × 10¹³.

As of the given condition,
According to the United States Treasury Department, the U.S. national debt was 1.815 x 10^13 dollars on September 30, 2015. On September 29, 2005, the national debt was 4.974 x 10^12 dollars.

Here,
The required increase in the debt is evaluated as the arithmetic difference of the debt in the years 2015 and 2005.

So.
Increase in debt = 1.815 × 10¹³ - 0.4974 × 10¹³ = 1.3176 × 10¹³

Thus, the required respective increase in the national debt of America for the period 2005 to 2015 is 1.3176 × 10¹³.

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Answer:

The equation of the line is;

Explanation:

Given that the line has a slope of;

And passes through the point;

Applying the point-slope equation of straight line;

substituting the given values and solving;

Therefore, the equation of the line is;

The concentration of A 0.29M and Concentration B  0.755M  that the initial concentration of a is 1.0 moll−1 and that no b is present at the beginning of the reaction.

a A (g)⇔ b B (g)          k =2.4

when a= 1  and b= 1

                         A⇔B

initial                  1      0

concentration

change             -x       +x

equilibrium       1-x        x

concentration  

so, k = [tex]\frac{B}{A}[/tex] = [tex]\frac{x}{1-x}[/tex]= 2.4

x = 2.4 (1-x)

x = [tex]\frac{2.4}{3.4}[/tex] = =0.755

The equilibrium concentration are

concentration of A  = 1-x = 1- 0.755 = 0.29M

Concentration B =  x = 0.755M

The first measured the concentration of the compound in the substance.

The best way to determine the rate constant k for a first-order half-life  is to determine the half-life using experimental data. This is because the first-order half-life is independent of the initial concentration of its initial value. So based on the above relationship, the half-life of a first-order reaction does not depend on the initial  concentration.

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a. The average mass of one apple in kilograms is 150g.

b. The cost of 500 grams of apples is R6.5

A. When the mass of eight apples is 1 200g, the average mass of one apple in kilograms will be:

= Total mass / Number of Apple

= 1200g / 8

= 150g

B. A 5 kg bag of apples costs R65. The cost per kg will be:

= Amount / Number of g

= R65 / 5000

= R0.013

The cost for 500 grams will be:

= 500 × R0.013

= R6.50

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Using the Hypothesis testing and statistic Z- test we , find that the bag sample is not underfilled at a significance level of 0.025 i.e., 25% .

In the given question, we shall check the bag is underfilled at given level or not .

We can use the hypothesis testing, The Null and Alternative hypothesis are given as below :

H₀ : u = 411 : the bags are not underfilled

Hₜ : u < 411 : the bags are underfilled

Check it now using statistic Z-test and the test Statistic formula is given by

= ( M – u ) / S.D / √n , where M = mean of sample and S.D = standard deviations n is the number of bags used .

From given data we get, n= 19 ; M = 437 ; S.D = √ variance = √ 441 = 21

Including all of the above variables in formula

Z = (437-411)/21/√19

= 26/21/√19

= 5.395

This is right -tail test in statistic Z -test

P- value = 1 – 0.9999 = 0.111 ( by using Z-table or P-value for Z in Excel )

The sufficient evidence level is 0.025 i.e., alpha (α) = 0.025

P- value >α , this implies that Null hypothesis is not Rejected .

There is sufficient evidence to suggest that bag is not underfilled.

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Answer:

(x + 3)² + (y - 6)² = 9

Step-by-step explanation:

the equation of a circle in standard form is

(x - h)² + (y - k)² = r²

where (h, k ) are the coordinates of the centre and r is the radius

here (h, k ) = (- 3, 6 ) and r = 3 , then

(x - (- 3 )² + (y - 6)² = 3² , that is

(x + 3)² + (y - 6)² = 9

The area of the rectangle would be 4.90 units which is shown in the given graph.

The area of a rectangle is defined as the product of the length and width.

The rectangle is given which has:

verticals at  A(-4,0), B(-3,1) C(0,-2) and D(-1,-3)

The length of segment AB = √ (-3 - (-4))² + (1 - 0)² = √ (1 + 1) = √2

The length of segment BC = √ (-3 - 0)² + (1 - (-2))² = √ (9 + 3) = √12

The area of the rectangle = length of segment AB x length of segment BC

The area of the rectangle = √2 x √12

The area of the rectangle = √24

The area of the rectangle = 4.90 units

Thus, the area of the rectangle would be 4.90 units

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Based on the vertices of the triangle, the area of the triangle can be found to be 8 cm²

First, find the lengths of JK, KL, and JL. When given vertices, you can find the length of a line by the formula:

= √ ( (x₂ - x₁)² + (y₂ - y₁)²)

The length of JK is therefore 2.83 units

The length of KL is therefore 5.66 units

The length of JL is therefore 6.32 units.

Given these units, the area of the triangle can be found by the formula:

= √ s(s - a) ( s - b) ( s - c)

Where:

s = semi perimeter

a, b, and c are the sides of the triangle which are JK, KL, and JL.

The semi-perimeter can be found by the formula:

= ( a + c + c) / 2

= 15.47 / 2

= 7.74

The area of the triangle is therefore:

= √ s(s - a) ( s - b) ( s - c)

= √ 7.74 (7.74  - 2.83) ( 7.74 - 5.66) ( 7.74 - 6.32)

= 8 cm²

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To solve this expression we have to add 2 to both sides of the equation:

So, the correct option is: B: 5.5

The equations of the line according to the given points will be:

We know that,

The equation of a line passing through two points is:

( y -y 1) / ( x - x1 ) = ( y2 - y1 ) / ( x2 - x1 )  

(y - 2) / (x - 5) = (-4 - 2) / (3 - 5)

=> (y - 2) / (x - 5) = -6 / -2

=> y - 2 = 3 (x - 5)

=> 3x - 15 - y + 2 = 0

=> 3x - y - 13 = 0

Some more equations of the same line can be calculated just by multiplying the coefficients of x and y so that they remain proportional to the previous equation.

For Example,

Here we can see that the coefficients of x and y and also the constant term are proportional to every equation compared with each other.

These lines are also called coincident lines.

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The values of variable x are x₁ = 16, x₂ = - 4.

The measure of angle R is 60°.

The lengths of side RS are RS₁ = 256 and RS₂ = 16.

The lengths of side RT are RT₁ = 256 and RT₂ = 16.

In this problem we need to find the values of four variables related to a triangle, which is seen in the picture, indicating an equilateral triangle. The solution of this question must be done by using definitions and theorems from Euclidean geometry:

Value of variable x

According to Euclidean geometry, the measures of the three sides in an equilateral triangle are the same. Then, the variable x can be found by solving the following equation:

RT = RS

x² = 12 · x + 64

x² - 12 · x - 64 = 0

(x - 16) · (x + 4) = 0

There are two possible solutions:

x₁ = 16, x₂ = - 4

Measure of the angle R

Equilateral triangles have three internal angles of 60°. Therefore, m ∠ R = 60°.

Length of side RS

There are two options:

RS₁ = 16²

RS₁ = 256

RS₂ = (- 4)²

RS₂ = 16

Length of side RT

There are two options:

RT₁ = 12 · 16 + 64

RT₁ = 256

RT₂ = 12 · (- 4) + 64

RT₂ = 16

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The inequality of the two triangle are 32° < x < 68° and the range of the value x is defined as  x ≥ 4.

Inequality:

Inequality means the relationship between two values that are not equal is defined by inequalities which means they are not equal.

Given,

Here we have the two triangles with some angle values.

Now, we need to find the inequality of these triangle.

To find the inequality of the triangle first we have to write down the values provided, they are,

77, 11x - 33, 68°, 32°

Through this we have identified that, the value of x is lies in between 68° and 32°.

So, it ca be written as,

32° < x < 68°

The next this is to use the triangle inequality theorem, that is,

"The sum of any two sides of a triangle is greater than or equal to the third side; in symbols, a + b ≥ c."

Therefore, based on the given equation we have written it as,

11x - 33 ≥  77

Subtract 33 on both sides then we get,

11x ≥ 44

Therefore, x ≥ 4.

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