A line has a slope of 3/8 and passes through the point (15.2,-7)

The equation of the line in point-slope form is???
ANSWERS↓↓

The area of the forest after 15 years will be 2189.4

The area is the region bounded by the shape of an object. The space covered by the figure or any two-dimensional geometric shape, in a plane, is the area of the shape.

i = The initial area of the forest = 4200km

r = Per year decrease is = 4.25%

n = Number of years = 15

The required formula is

The area of forest will be

A = i (1-r)^n

A = 4200(1-0.425)^15

A= 2189.4

Hence, the area of the forest will be 2189.4

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The new model {A} for the total number of new green tea and fruit juice sales can be written as {A} = 9t^4 + 3t² + 105 .

What is expression ?

Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation.

Any mathematical statement that includes numbers, variables, and an arithmetic operation between them is known as an expression or algebraic expression. In the phrase 4m + 5, for instance, the terms 4m and 5 are separated from the variable m by the arithmetic sign +.

An algebraic expression is made up of a number of variables, constants, and mathematical operations. We are aware that variables have a wide range of values and no set value. They can be multiplied, divided, added, subtracted, and other mathematical operations since they are numbers. as in 3x Plus 4.

Given is that during a 20-year period, G and I can be modeled by the following equation (where t is the time in years) :

G = 6t^4+ 3t³ – 2t² + 5t + 60

I = 3t^4 - 3t³ + 5t² - 5t + 45

where {G} is the number (in billions) of new green tea sales and {I} be the number in billions of new fruit juice sales.

A new model {A} for the total number of new green tea and fruit juice sales can be written as -

{A} = {G} + {I}

{A} = 6t^4+ 3t³ – 2t² + 5t + 60 + 3t^4 - 3t³ + 5t² - 5t + 45

{A} = 9t^4 + 3t² + 105

Therefore, the new model {A} for the total number of new green tea and fruit juice sales can be written as {A} = 9t^4 + 3t² + 105

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Answer:

  3x -y = 2

Step-by-step explanation:

You want a standard form equation for the line through the points (0, -2) and (2, 4).

The slope of the line is the "rise" divided by the "run". The given point on the right is 3 grid squares above the one on the left. It is one grid square to the right. So, the slope is ...

  m = (squares above)/(squares to the right) = 3/1 = 3

If we consider the actual x- and y-values represented by these grid squares, then the slope is ...

  m = (4 -(-2))/(2 -0) = 6/2 = 3

The point (0, -2) tells you the y-intercept is -2. That is where the line crosses the y-axis.

With this information, we can write the slope-intercept form equation for the line:

  y = mx +b . . . . . . . line with slope m and y-intercept b

  y = 3x -2 . . . . . . . . line with slope 3 and y-intercept -2

The standard form of an equation for a line is ...

  ax +by = c

where a, b, c are generally mutually-prime integers with a ≥ 0. If a=0, then b > 0.

We can rearrange the slope-intercept equation to put it into this form.

  y = 3x -2

  3x -y -2 = 0 . . . . . subtract y

  3x -y = 2 . . . . . . . add 2. This is the standard-form equation of the line.

Answer: She can multiply the numerator and the denominator by the same number. For example, 30/100 × 2/2

So what you're doing multiplying the numerator & the denominator each by 2. 30 ×2 = 60 and 100 x 2 = 200, ending up with 60/200.

when reduced it would simplify back to 30/100.

You can do the same for each similar. Problem asking for an equivalent. Just multiply both the numerator and denominatorby the same number.

Step-by-step explanation:

Answer:

124 degrees

Step-by-step explanation:

Since they are congruent the corresponding angles will be equal. There is only one obtuse in each triangle, Angles Y and N. N is measured to be 124 degrees so Y is also 124 degrees.

The measures of missing angles in trapezoids are listed below:

Case 5: m ∠ J = 75°, Case 7: m ∠ T = 118°

In this question we must determine the measures of missing angles in trapezoids. There are two hints to determine the values of the missing angles:

Now we proceed to determine the missing angles in every trapezoid:

Case 5

m ∠ K + m ∠ J = 180°

21 · x + 15 · x = 180°

36 · x = 180°

x = 5

m ∠ J = 15 · x

m ∠ J = 15 · 5

m ∠ J = 75°

Case 7

m ∠ U = m ∠ T

m ∠ T = m ∠ U

m ∠ T = 118°

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When Malia joined a gym 14 weeks after Jane did, the value of b was 5.

Relationships between two variables where their ratios are equal are known as proportional relationships. The fact that one variable is always a constant value multiplied by the other in a proportionate connection is another way to conceive of them.

A car's fuel capacity and efficiency, as well as how far it can go on a single charge of its electric battery, are important considerations. A nonproportional connection can be used to describe this.

a + b = 14

9 + b = 14

b = 14-9 = 5

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Answer:

Not a function

Step-by-step explanation:

A function is when every input(x) has only one output (y).  The input 1 has two outputs (0 and 1) so it is not a function.

As a result, the answer to the given function question is that the domain and range are both(-∝, ∝) and that the domain is (-∝, ∝).and that the range is(-∝, ∝).

Any input will only result in one or zero outcomes for the function. The expression does not define the function if there are several outputs for a given input. Each value of x must have only one output value of y variable in order for anything to be a function.

Here,

The formula is presented as

k(x) = x² + 9

The aforementioned equation is linear.

 the range is (-∝, ∝) and the domain is(-∝, ∝) 

Formula 2

The formula is presented as

y = (x + 5)² +3

The aforementioned equation is linear.

The range is (-∝, ∝), and the domain is (-∝, ∝).

As a result, the answer to the given function question is that the domain and range are both(-∝, ∝) and that the domain is (-∝, ∝).and that the range is(-∝, ∝).

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Answer:

each box contain 8 x 9 = 72

Answer: Here, let X,Y,ZX,Y,Z indicate the amount in dollars to be invested

Step-by-step explanation: Here, let X,Y,ZX,Y,Z indicate the amount in dollars to be invested

a. The exponential function to represent the spread of Ben's social media post is f(x) = 2(3)^x

b. The exponential function to represent the spread of Carter's social media post is f(x) = 10(2)^x

c. On Day 3, Ben's post will have 2(3)^3 = 227 = 54 shares, Carter's post will have 10(2)^3 = 108 = 80 shares. On Day 10, Ben's post will have 2(3)^10 = 259049 = 118098 shares, Carter's post will have 10(2)^10 = 101024 = 10240 shares.

d. Adding 45 to the function representing Amber's photo shares changes the function to f(x) = 3(4)x + 45. The new function will shift the graph upward by 45 units.

e. Based on the functions, Ben's post travels the fastest because the base of the exponent, 3, is greater than the base of the exponent, 2, for Carter's post.

f. It depends on the goal of the post. If the goal is to reach a larger audience quickly, then having more friends initially but fewer shares like Carter is preferable. But if the goal is to reach a smaller audience but with a more engaged audience, then having fewer friends initially but more shares like Amber is preferable.

An exponential function is one in which the variable is an exponent. Mathematically, it is defined as f of R in R, such that f(x) = ax, where a ϵ R, a > 0 and a ≠ 1. The graph of this function is a curve obtained by finding some ordered pairs that belong to the function and drawing this curve that passes through them.

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Answer:

x = 4

Step-by-step explanation:

i. 8x + 1 = 7x + 5

ii. 8x - 7x = 5 - 1

iii. x = 4

The quadratic equation that describes the function is  

f(x) = x² + 4x + 1

A quadratic equation is a equation that is of the form -

y = f{x} = ax² + bx + c

Given is the table that describes the quadratic function h(x) as follows -

{x}                h{x}

−3               −2

−2               −3

−1                −2

0                  1

1                   6

2                  13

3                  22

The quadratic equation is of the form given -

y = ax² + bx + c

For the point (0, 1), we can write -

1 = c                                                      ..... Eq{1}

For the point (1, 6), we can write -

6 = a + b + 1

a + b = 5                                               ...... Eq{2}

For the point (2, 13), we can write -

13 = 4a + 2b + 1

4a + 2b = 12                                               ...... Eq{3}

From Eq{2}, we can write -

a = 5 - b

So, the equation 3 can be written as -

4(5 - b) + 2b = 12

20 - 4b + 2b = 12

20 - 2b = 12

2b = 8

b = 4                                    ...... Eq{4}

then

a = 1                                ...... Eq{5}

So, we can write the quadratic equation as -

f(x) = x² + 4x + 1

Therefore, the quadratic equation that describes the function is  

f(x) = x² + 4x + 1

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A) The dresses for films set in the 1700s would be 60%.

B) The percentage of dresses that are not for films set in the 1700s is 40%.

C) The percentage of dresses that can be used for films set in the 1700s or during the civil war era is 75%.

D) The percentage of dresses that are not for films set during the civil war era is 85%.

What is a percentage?

The percentage is a way of expressing a number as a fraction of 100. It is often denoted using the symbol "%". It is used to express a proportion of a number out of 100. It is useful in many applications such as finance, statistics, and other fields.

A. Three-fifths of the dresses can be used for movies that take place in the 1700s, which is 3/5 * 100 = 60%.

B. The percent of the dresses that are not for films set in the 1700s is 100% - 60% = 40%. This is found by subtracting the percentage of dresses that are used for 1700s movies from 100%.

C. The percent of the dresses that can be used for films set in the 1700s or during the civil war era is 60% + 15% = 75%. This is found by adding the percentage of dresses that can be used for 1700s movies and the percentage of dresses that can be used for civil war era movies.

D. The percent of the dresses that are not for films set during the civil war era is 100% - 15% = 85%. This is found by subtracting the percentage of dresses that are used for civil war era movies from 100%.

Hence,

A) The dresses for films set in the 1700s would be 60%.

B) The percentage of dresses that are not for films set in the 1700s is 40%.

C) The percentage of dresses that can be used for films set in the 1700s or during the civil war era is 75%.

D) The percentage of dresses that are not for films set during the civil war era is 85%.

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On solving the provided question, we can say that -  f(x) = 3x2 - 6x + 2, and the value of the equation f(x) = +2

An equation is a formula in mathematics that joins two statements with the equal symbol = to represent equality. The definition of an equation in algebra is a mathematical statement proving the equality of two mathematical expressions. In the equation 3x + 5 = 14, for instance, the terms 3x + 5 and 14 are separated by an equal sign. The link between two phrases on either side of a letter is expressed mathematically. There is often only one variable, which is also the symbol. instance: 2x - 4 Equals 2.

f(x) = 3x2 - 6x + 2

x = 1

f(x) = +2

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The graph representing the given pairs is represented by the equation y = (4/5)x + 40.

        {m} - slope                 {c} - intercept along the y - axis.

Given is that Mr. Hart recorded the ratio of the minutes spent driving to the miles driven while on a road trip.

The given table is as follows -

Number of Minutes {m} :      75         60

Number of Miles {M} :          100        80

The slope of this graph will be -

m = (80 - 60)/(100 - 75)

m = 20/25

m = 4/5

The equation of the line can be written as -

y = (4/5)x + c

For the point (75, 100) as follows -

100 = 4/5 x 75 + c

100 = 4 x 15 + c

c = 100 - 60

c = 40

The equation of the graph will be -

y = (4/5)x + 40

Refer to the graph attached.

Therefore, the graph representing the given pairs is represented by the equation y = (4/5)x + 40.

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Using the pythagoras theorem in the given figure, the required length of c is [tex]49\sqrt{6}[/tex].

The relationship between the three sides of a right-angled triangle is explained by the Pythagoras theorem, commonly known as the Pythagorean theorem. The Pythagorean Theorem states that the square of a triangle's hypotenuse is equal to the sum of its other two sides.

The pythagoras theorem is named after the Greek mathematician-philosopher Pythagoras.

To solve for c, first taking the small triangle in the left of the figure,

since one of the angle is 45 degree and another is 90 degree, the unlabelled angle is 45 degree. Which makes this triangle a isosceles triangle, hence the sides a and b are equal in length. i.e a = b

Using pythagoras theorem in this triangle,

[tex](7\sqrt{2} )^{2} = \sqrt{a^{2}+\ a^{2} }[/tex]

Therefore, a = 49[tex]\sqrt{2}[/tex]

Now Taking the small triangle in the right of the given figure,

tan 30 = a/c

or, [tex]\frac{1}{\sqrt{3} }[/tex] *c = 49[tex]\sqrt{2}[/tex]

Therefore , c = 49[tex]\sqrt{6}[/tex]

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Answer: atleast alot

Step-by-step explanation:

Answer:

See below

Step-by-step explanation:

I guess if you look at the zeroes/x-intercepts, we got (3,0) and (-7,0) as zeroes.

Additionally, we can calculate the minimum by expanding the function:

[tex](x-3)(x+7)=x^2+4x-21[/tex]

[tex]\displaystyle x=-\frac{b}{2a}=-\frac{4}{2(1)}=-2\\\\f(-2)=(-2)^2+4(2)-21=4+8-21=12-21=-9[/tex]

So the minimum of the function is (-2,-9)

Also, our y-intercept is (0,-21)

The measure of angle ∠JBC is 56 degrees.

From the question

If m∠ABJ = 28 and ∠ABC ≅ ∠DBJ, then we can set up the following equation:

m∠ABC = m∠DBJ

Since angles ∠ABC and ∠DBJ are congruent, they have the same measure, so the equation above is true.

Since we are trying to find m∠JBC, we can use the fact that the measure of an angle is equal to the sum of the measures of the other two angles in the triangle to set up another equation:

m∠JBC = m∠ABC + m∠ABJ

Substituting the value for m∠ABC from the first equation into the second equation, we get:

m∠JBC = m∠DBJ + m∠ABJ

Substituting the given value of m∠ABJ into this equation, we get:

m∠JBC = m∠DBJ + 28

Since m∠ABJ = m∠DBJ, we can substitute m∠ABJ in for m∠DBJ:

m∠JBC = m∠ABJ + 28

Substituting the given value of m∠ABJ into this equation, we get:

m∠JBC = 28 + 28

Solving this equation, we find that m∠JBC = 56.

Therefore, the measure of angle ∠JBC is 56 degrees.

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Answer:

The researcher compiled a data set consisting of variables such as age, income, and marital status for a sample of 100 retired men

Step-by-step explanation:

A discrete variable is a type of variable that can only take on specific, distinct values that can be counted. Examples of discrete variables include the number of countries visited, shoe size, and number of pets living in a household.

On the other hand, a continuous variable is a type of variable that can take on any value within a certain range through measurement. Examples of continuous variables include pounds of chocolate consumed in the past and height in inches.

The actual length of the modeled truck is 20.4 feet.

The scale factor defines a variable in a ratio of two different measurements.

Sometimes drawings of large models are represented in a scale factor of a smaller unit.

Given, A model diagram of a truck and each gridline represent 1 cm distance.

Now, To find the length of this model we'll count the number of gridlines horizontally from two endpoints of the truck which is 12 gridlines hence 12 cm.

Also given that 1 cm is equal to 1.7 feet.

Therefore, The actual length of the truck is (1.7×12) feet.

= 20.4 feet.

So, the length of the truck is 20.4 feet.

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Answer:

Step-by-step explanation:

The equivalent expression of log₁₂(x⁴√x³) - 2(x+1)⁵ is 11/2log₁₂(x) - 2(x+1)⁵

From the question, we have the following parameters that can be used in our computation:

log 12 x^ 4 sqrt x^ 3 -2 (x+1)^ 5 ?

Express properly

So, we have the following representation

log₁₂(x⁴√x³) - 2(x+1)⁵

Evaluate the exponent

log₁₂(√x¹¹) - 2(x+1)⁵

Apply the power rule of logarithm

This gives

11/2log₁₂(x) - 2(x+1)⁵

Hence, the equivalent expression is 11/2log₁₂(x) - 2(x+1)⁵

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As determined in part, the ball reaches its highest point at time t is 2 seconds

S(t) = 32t - 16t2 is the formula for the displacement s(t) as a function of time t. We presume that the upward motion began at this altitude above the earth.

The ball's starting speed is 64 feet per second.

(A) The velocity is the displacement's first time derivative: v(t) = ds/dt = 32t – 16t. We are just deriving the function s for the first time (t).

(B) v(t = 3) = 32t– 16(3) = –32 feet per second. The ball is currently travelling downhill, according to the negative indication.

(c) The ball briefly pauses as it reaches its highest height before dropping. By setting the velocity to zero to symbolise this halt, we can calculate how long it will take the ball to reach its highest point.

v(t) = 32 - 16t = 0

or 16t = 32

out = 2 seconds.

As determined in part, the ball reaches its highest point at t = 2 seconds (c).

s(t = 2) = 32(2) - 16(2) (2)

2

or 32 feet if s(t = 2).

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By analyzing the inequality and solving, the range of values of x for which the inequality is true is x € (-4/3, 4)

Domain is the input to the function.

Range is the output of the function.

First, we'll consider the case where |2x+1|-x-3<0.

|2x+1|-x-3<0

|2x+1|<x+3

Now we need to take the absolute value of 2x+1, we have two cases to consider:

Case 1:

2x + 1 > 0

2x + 1 < x + 3

2x - x < 3 + 1

x < 4

Case 2:

2x + 1 < 0

-2x - 1 < x + 3

-2x - 1 -x - 3 < 0

-3x - 4 < 0

x > -4/3

Now we must find the intersection between the two cases:

x € (-4/3, 4)

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On one tank of gas Charlie will drive 612 km

At a cost of 149.9, Charlie will fill the tank with the sum of 8994

Annual cost of filling the tank 467688

Information from the problem have it that the efficiency if the Volkswagen golf is 10.2 km/L

Hence, on one liter rides 10.2 km and on a tank which is 60 L Charlie will ride

= 60 * 10.2

= 612 km

Cost of filling the tank

The cost per liter is 149.9 for 60 L we have

= 149.9 * 60

= 8994

Filling the tank once week, the cost for filling in one year is

1 year is 52 weeks

= 8994 * 52

= 467688

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