Which function has the greatest y-intercept?

f(x)
h(x)
g(x)

[tex](\stackrel{x_1}{-4}~,~\stackrel{y_1}{-8})\hspace{10em} \stackrel{slope}{m} ~=~ 4 \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{(-8)}=\stackrel{m}{ 4}(x-\stackrel{x_1}{(-4)}) \implies y +8= 4 (x +4) \\\\\\ y+8=4x+16\implies {\Large \begin{array}{llll} y=4x+8 \end{array}}[/tex]

Answer:

17.1

Step-by-step explanation:

Exponential Functions:

y=ab^x

a=starting value = 310

r=rate = 6.4%=0.064

Exponential Decay:

b=1−r=1−0.064=0.936

Write Exponential Function:

y=310(0.936)^x

Put it all together

Plug in y-value:

100=310(0.936)^x

100/310 = 310(0.936)^x/310

​

Divide both sides by 310

0.322581=0.936^x

\log 0.322581=\log 0.936^x

Take the log of both sides

log0.322581=xlog0.936

Use power rule to bring x to the front

log0.322581/log0.936 = xlog0.936/log0.936

​

Divide both sides by log(0.936)

17.106221=x

x≈17.1

17.12 will it take until there are 100 grams of the element remaining

Two or more expressions with an Equal sign is called as Equation.

Given that  element with a mass of 310 grams decays by 6.4% per minute.

we need to find the time will it be until there are 100 grams of the element remaining

y=abˣ

a=starting value = 310

r=rate = 6.4%=0.064

Exponential Decay:

b=1−r

=1−0.064

=0.936

Plug in these values in the formula

y=310(0.936)ˣ

100=310(0.936)ˣ

Divide both sides by 310

100/310 = (0.936)ˣ

0.322581=0.936ˣ

Apply log on both sides

log 0.322581=xlog0.936

Divide both sides by log0.936

log0.322581/log0.936 = xlog0.936/log0.936

17.106221=x

Hence, 17.12 will it take until there are 100 grams of the element remaining

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Solution

Step 1

Write out the expression for the probability of an event occurring

For this question,

The number of required events = The number of students that are male and Junior= 2

The total number of events = The total number of male students= 4+6+2+2 = 14

Step 2

Find the required probability after substitution

Hence the probability the student is a junior given its a male = 1/7

In percentage, the probability will be

Where x is the required percentage, to the nearest whole percent, the final answer is 14%

Answer:

[tex]46, 10[/tex]

Step-by-step explanation:

A median is the segment drawn from the vertex of a triangle that bisects the opposite side.

Simplify the expression

Removing all the parentheses, taking special care to change the signs of the last three terms:

Now collect like terms:

In linear equation, 10 feet and 8 inches will require 4.6 pints.

What are instances of linear equations?

For 10 feet and 8 inches,          

12 inches = 1 foot,

therefore 8 inches = 8/12 foot = 0.6 foot

10 feet 8 inches = 10 + 0.6 = 10.6 feet

6 feet 8 inches required 3 pints

1 foot would have required (3/6.8) pints

10.6 feet will then require   (3/6.8)*10.6 = 4.6 pints.

Therefore 10 feet and 8 inches will require 4.6 pints.

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Answer:

7.5/3

Step-by-step explanation:

7x-7.5 = 4x

-7.5 = -3x

x= 7.5/3

The height of the actual building, given the height of the model, can be found to be 1, 455 feet

The model is such that every inch of the building on the model is 75 feet of the actual building.

This means that if the height of the building in the model is 19 ² / ₅ inches, then the height of the actual building would be:

= Height of building in model x Scale factor per inch

= 19 ² / ₅  x 75

= 97 / 5 x 75

= 1, 455 feet

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Answer:

Equation of line is given as y = mx + c, where m is the gradient and c is the y-intercept.

First, rearrange x + 7y = 21 into y = mx + c form.

x + 7y = 21

7y = - x + 21

y = -1/7x + 3

Parallel lines have the same gradient so gradient of line is -1/7.

Equation of line is now y = -1/7x + c.

Substitute (-14,4) into the equation to find c.

4 = -1/7(-14) + c

4 = 2 + c

c = 2

Hence, equation of line is y = -1/7x + 2.

The price charge is $235 and the maximum revenue is $165675.

It is a plane curve that is mirror-symmetrical. It is approximately U-shaped. It is a plane curve generated by a point moving so that its distance from a fixed point is equal to its distance from a fixed-line. It is the locus of a fixed point that moves on a plane. It has many important applications. In Mathematics, the parabola plays a crucial role.

Number of members in club = 360

Monthly membership is of $350

For $ 1 price decrease and 3 people joinining

Membership charge will be = 350-x

Members will be 360+3x

Revenue equation will be

R (x) (350-1x)(360+3x)=0

126,000-360x+1050x-3x² =0

126,000+690x- 3x²-=0

This is a parabolic equation. Maximize the function to get

Differentiate to get the parabola vertex

R'(x) = 690-6x

So, 690-6x =0

x =115

Therefore, the price charge is

350-115 = $235

The number of members is

3360+115 = 705

The maximum revenue is given as

$235 × 705=$165675

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Answer:

y=3x-11

Step-by-step explanation:

In this question, we will use the point slope form:

Which has the equation:

[tex]y-y_1=m(x-x_1)\\subsitute:\\y+5 = 3(x-2) , (y--5=+5)\\y+5=3x-6\\y=3x-11[/tex]

Hope this helps!

The graph of the inequality is a straight line on the x-axis

from -2 to 5 also, -2 & 5 are not included in the graph.

Given, an inequality

-2 < x < 5

we have to draw a graph for the given inequality,

as the value of 'x' is from -2 to 5.

So, the graph of the inequality is a straight line on the x-axis

from -2 to 5 also, -2 & 5 are not included in the graph.

Hence, the graph of the inequality is a straight line on the x-axis

from -2 to 5 also, -2 & 5 are not included in the graph.

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The slope of the given situation of selling breakfast platters is 0.90.

Given, the platter of 12 bagels costs $10.80.

The extra cost of $6.50 for a gallon of coffee.

To find the slope of the situation, we convert the situation into the equation of the line.

y=mx+c

here c is the extra cost that is 6.50.

12m=10.80

For 12 bagels , the cost is 10.80, then the slope will be the cost of each bagel.

m=10.80/12

m=0.90

m=$0.90

Therefore, option c 0.90 is the slope of the given situation of the bakery selling the breakfast platter of 12 bagels and a gallon of coffee.

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EXPLANATION

The unit rate is given by the following relationship:

Unit rate= $200/15ft = $13.3333.../ft

Then, rounding to the nearest hundreth:

Unit rate = $13.33/ft

Answer: D.

Hope it helps

From the graph given, we are asked to find the equation of line, with our answer in point slope form.

from the graph:

y = 9, x = 10

y1 = 5, x1 = 6

recall, the equation of a line is:

y = mx + b

slope m = y - y1/x - x1

m = 9 - 5/10 - 6

m = 4/4

m = 1

y = 1x + b

y = x + b

using the point slope form:

y - y1 = m(x - x1)

Where:

y = y coordinate of second point

y1 = y coordinate of point one

m = slope

x = x coordinate of second point

x2 = x coordinate of point one.

Therefore, the point slope equation is:

y - 5 = 1(x - 6)

y - 5 = x - 6

The equation of line are given as y = 5x - 10 and y = 2x + 8 respectively

The point slope form is used to find the equation of the straight line which is inclined at a given angle to the x-axis and passes through a given point. The equation of a line is an equation that is satisfied by each and every point on the line. This means that a linear equation in two variables represents a line. The equation of a line can be found through various methods depending on the available information.

In this case, we have can proceed to write the equation of a straight line which is given as y = mx + c

Let's find the y - intercept and write the equation.

y = mx + c

5 = 5(3) + c; c = 5 - 15 = -10

y = 5x - 10

2) We have the slope as 2 and the points are (-1, 6)

The equation of the line can be written in form of y = mx + c

6 = 2(-1) + c

6 = -2 + c; c = 8

The equation is given as y = 2x + 8

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The equation used to determine y, the number of water bottles remaining at the music festival x hours after 5:00 P.M will be;

⇒ y = - 500x + 5500

What is Equation of line?

The equation of line in point-slope form passing through the points

(x₁ , y₁) and (x₂, y₂) with slope m is defined as;

⇒ y - y₁ = m (x - x₁)

Where, m = (y₂ - y₁) / (x₂ - x₁)

Given that;

The table shows the linear relationship between the number of water bottles remaining and the number of hours since 5:00 P.M.

Now,

Find the linear equation for the given table as;

Take number of hours = x

And, Number of remaining bottles = y

So, Two points for the linear equation as;

⇒ (x, y) = (1, 5000) , (2, 4500)

Thus, The linear equation for the table is,

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

⇒ y - 5000 = (4500 - 5000) / (2 - 1) (x - 1)

⇒ y - 5000 = - 500 (x - 1)

⇒ y - 5000 = - 500x + 500

⇒ y = - 500x + 500 + 5000

⇒ y = - 500x + 5500

Thus, The equation used to determine y, the number of water bottles remaining at the music festival x hours after 5:00 P.M will be;

⇒ y = - 500x + 5500

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Let,

The expression to calculate the distance between two points is,

Thus, the length of the line RS is 8.5 units, and the correct option is option C.

Recall the definition of the sine of an angle on a right triangle:

On the other hand, according to this diagram, the values for tan(A) and cos(A) are given by:

Since 180≤A≤270, the right triangle that corresponds to the angle A on the coordinate plane looks as follows:

Where a and b are negative distances.

Since sin(A)=-4/7, we can assume that a=-4 and c=7. Use the Pythagorean Theorem to find the exact value of b:

We know that b should be negative. Then:

Substitute b=-sqrt(33) and c=7 to find the exact values for cos(A) and tan(A):

Therefore, the exact values for cos(A) and tan(A) are:

Answer:

multiply 1 is the correct answer

12×1 - 15 = -3

ANSWER

N = 11

EXPLANATION

Given:

3N + 5 = 38

Desired Outcome:

Value of N

Solve for N

Hence, the value of N is 11.

The parent quadratic function is 2 unit right and 3 units up.

Given function is

f(x) = (x-2)² +3

= x² - 2² - 2×x×2 + 3

= x2 - 4 - 4X + 3

= X² - 4X -1

Parent function g(x) = x²

The parent function is shifted to 2 units in right and 3 units up.

Parent function transformations are shown in blue. This is a 1 unit shift down. Mirroring of the x-axis is done functionally by multiplying the superordinate function by the negative function.

A parent function is the simplest function that satisfies the definition of a particular function type. For example, consider linear functions that form a family of functions.

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Disclaimer:- your question is incomplete, Please see below for the complete question.

Which phrase best describes the transformation(s) of the following graph from the parent quadratic function? f(x)=(x-2)^2+3

The translation rule is (x, y) ---> (x+8)(x-4).

What is translation rule?

A translation is a type of transformation that moves each point in a figure the same distance in the same direction. The second notation is a mapping rule of the form (x,y) → (x−7,y+5).

A translation in math moves a shape left or right and/or up or down. The translated shapes look exactly the same size as the original shape, and hence the shapes are congruent to each other.

Given,

let A =(x, y) ----> (x+9,y-2) and B =(x, y) ----> (x-1,y-2)

which means A is translated 9 units right and 2 units down

and B is translated 1 unit left and 2 units down.

Therefore, rule for composition is A+B

= (x, y) ------> (x+9-1, y-2-2)

(x,y) -----> (x+8,y-4)

which means translation is 8 units right and 4 units down.

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year's

this year´s profit is $ 472857

Explanation

we can easily solve this by using a rule of three

so

Step 1

a)let x represents this year's profit

so

if it is decreases by 2.1 %

so, this year's profit is 97.9% of the last year profit

hence

we can make a proportion

finally, solve for x,

therefore

this year´s profit is $ 472857

I hope this helps you

The simplified form is 7x - 2y.

Distributive property: What Is It?

This property states that multiplying the total of two or more addends by a number will produce the same outcome as multiplying each addend by the number separately and then adding the results together.

According to question,

5x-4y+2(y+x)

5x-4y+2y+2x

7x-2y

Hence, simplified form is 7x - 2y.

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The GPA of a student who studies for 15 hours a week is 2.935.

What is a GPA?

Grade point average, or GPA, is a conventional method of evaluating academic performance in the United States on a scale of 0 to 4.

How to calculate GPA?

To calculate your GPA, divide the total number of grade points earned by the total number of letter-graded units undertaken.

Here,

We have an equation y = 0.164x + 0.475

put x= 15

we get,

y = 0.164* 15 + 0.475

y = 2.935

Hence, The GPA of a student who studies for 15 hours a week is 2.935

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To get (f-g)(x), we're essentially just factoring out x from f(x) and g(x).

-> f(x) - g(x) = x(f-g), and by the properties , x(f-g) is the same as (f-g)(x).

Therefore, (f-g)(x) = 5x - 7 - (-4x + 2) = 5x - 7 + 4x - 2 = 9x - 9.

Answer:

[tex](f-g)(x)=9x - 9[/tex]

Step-by-step explanation:

Given functions:

[tex]\begin{cases}f(x) = 5x-7 \\ g(x) = -4x + 2\end{cases}[/tex]

To find (f - g)(x), subtract function g(x) from function f(x):

[tex]\begin{aligned}(f-g)(x)&=f(x)-g(x)\\&=(5x-7)-(-4x+2)\\&=5x-7+4x-2\\&=5x+4x-7-2\\&=9x-9\end{aligned}[/tex]

Therefore, the solution to the given composite function is: