haley pays a monthly fee of $20 for her cell phone and then pays 5 cents per minute used. the total cost of haley’s monthly cell phone bill can be expressed by the function c(m)

the formula for a function of the form y= a е⁻ˣ +b x with global minimum at (1,10)  is  y= 5е¹ ⁻ ˣ +5 x

We can use first and second derivative tests to determine all coefficients of the function described in statement so that the point given is an absolute minimum. The expressions for such tests are introduced below:

First Derivative Test

-a .е⁻ˣ +b = 0   (1)

b=a .е⁻ˣ

Second Derivative Test

y''= a . .е⁻ˣ  (2)

Where y'' >0

If we know that ( x,y) = 9 1,10) , then we have the following system:

10 = a е⁻¹ +b (3)

b= a е⁻¹  (4)

y'' = a е⁻¹  (5)

By (4) in (3):

10= 2aе⁻¹

a=10/2е⁻¹

a= 5е

By (5) we prove that y''>0, and we get the value of  by (4):

b=5

Thus, the formula for a function of the form y= a е⁻ˣ +b x with global minimum at (1,10)  is . y= 5е¹ ⁻ ˣ +5 x

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Answer:

Step-by-step explanation:

a)

[tex]x^2+10x+16=\\x^2+2x+8x+16=\\x(x+2)+8(x+2)=\\(x+2)(x+8)[/tex]

b)

[tex]x^2+7x+12=\\x^2+3x+4x+12=\\x(x+3)+4(x+3)=\\(x+3)(x+4)\\[/tex]

c)

[tex]x^2+13x+12=\\x^2+x+12x+12=\\x(x+1)+12(x+1)=\\(x+1)(x+12)[/tex]

Answer:

[tex]\textsf{(a)} \quad (x+8)(x+2)[/tex]

[tex]\textsf{(b)} \quad (x+4)(x+3)[/tex]

[tex]\textsf{(c)} \quad (x+12)(x+1)[/tex]

Step-by-step explanation:

Factoring quadratics

[tex]\textsf{Given}: \quad x^2+10x+16[/tex]

Two numbers that multiply to 16 and sum to 10 are: 2 and 8.

[tex]\implies x^2+2x+8x+16[/tex]

Factor the first two terms and the last two terms separately:

[tex]\implies x(x+2)+8(x+2)[/tex]

Factor out the common term (x + 2):

[tex]\implies (x+8)(x+2)[/tex]

[tex]\textsf{Given}: \quad x^2+7x+12[/tex]

Two numbers that multiply to 12 and sum to 7 are: 3 and 4.

[tex]\implies x^2+3x+4x+12[/tex]

Factor the first two terms and the last two terms separately:

[tex]\implies x(x+3)+4(x+3)[/tex]

Factor out the common term (x + 3):

[tex]\implies (x+4)(x+3)[/tex]

[tex]\textsf{Given}: \quad x^2+13x+12[/tex]

Two numbers that multiply to 12 and sum to 13 are: 1 and 12.

[tex]\implies x^2+x+12x+12[/tex]

Factor the first two terms and the last two terms separately:

[tex]\implies x(x+1)+12(x+1)[/tex]

Factor out the common term (x + 1):

[tex]\implies (x+12)(x+1)[/tex]

Answer:

34.98is the answer ............ .............

Answer: 34.98

Step-by-step explanation:

'Percent (%)' means 'out of one hundred':

6% = 6 'out of one hundred',

p% is read p 'percent',

6% = 6/100 = 6 ÷ 100

What does it mean to calculate the percentage of a number?

6% of 583 = ?

... is equivalent to multiplying them:

6% × 583 = ?
6% of 583 =

6% × 583 =

6/100 × 583 =

(6 ÷ 100) × 583 =

6 × 583 ÷ 100 =

3,498 ÷ 100 =

34.98

Answer:

j = 2

Step-by-step explanation:

Slope of a line is given by:
[tex]\medium \text{$\dfrac{y_{2}-y_{1}}{x_{2}-x_{1}}$}[/tex]

where (x₁, y₁) and (x₂, y₂) are two points on the line

This is commonly referred to as rise/run

Given the two points (6, 1) corresponding to (x₁, y₁) and (9, j) corresponding to (x₂, y₂)

[tex]\text{Slope = }\dfrac{\ensuremath{j}-1}{9-6}=\dfrac{j-1}{3}[/tex]

But we are given the slope as 1/3

So we get
[tex]\dfrac{j-1}{3} = \dfrac{1}{3}[/tex]

Multiplying by 2 on both sides gives us:

j - 1 = 1

Adding 1 to both sides gives us

j - 1 + 1 = 1 + 1

j = 2

[tex]\quad \huge \quad \quad \boxed{ \tt \:Answer }[/tex]

[tex]\qquad \tt \rightarrow \:The \:\: angles \:\: are \:\: 60° \:\: and \:\:30° [/tex]

____________________________________

[tex] \large \tt Solution \: : [/tex]

Sum of two complementary angles is 90°

Let's assume one of them to be x, the other one will be x/2 as one of the angles is complementary to other one.

[tex]\qquad \tt \rightarrow \: x + \dfrac{x}{2} = 90[/tex]

[tex]\qquad \tt \rightarrow \: \dfrac{2x + x}{2} = 90[/tex]

[tex]\qquad \tt \rightarrow \: 3x = 90 \times 2[/tex]

[tex]\qquad \tt \rightarrow \: x = 180 \div 3[/tex]

[tex]\qquad \tt \rightarrow \: x = 60 \degree[/tex]

and

[tex]\qquad \tt \rightarrow \: \dfrac{x}{2} = 60 \div 2 = 30 \degree[/tex]

Answered by : ❝ AǫᴜᴀWɪᴢ ❞

Answer:

Yes, 7 x [tex]10^{-3}[/tex] in standard form is 0.007mm

8 x [tex]10^{-5}[/tex] in standard form is 0.00008 mm.  The mask will catch particles that are much smaller than 0.007 in diameter.

Step-by-step explanation:

For f(x) = 2x + 3 and g(x) = -x^2 + 1, The composite function defined by (f o g)(x) is equal to (f o g)(x) = - 2 x^2 + 5

As per the question statement, We are given f(x) = 2x + 3 and g(x)=x^2+1

and we are supposed to find the composite function defined by (f o g)(x)

(f o g)(x) = f(g(x))

(f o g)(x) = 2 (g(x)) + 3

(f o g)(x) = 2( -x^2 + 1 ) + 3

(f o g)(x) = - 2 x^2 + 5

Hence, For f(x) = 2x + 3 and g(x) = -x^2 + 1, The composite function defined by (f o g)(x) is equal to (f o g)(x) = - 2 x^2 + 5

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The number line that correctly compares √24 and 4.256 is number line C.

A number line can be defined as a type of graph with a graduated straight line which contains both positive and negative numbers (numerical values) that are placed at equal intervals along its length.

This ultimately implies that, a number line can be used for the comparison of two or more numbers such as √24 and 4.256. Also, a number line typically decreases in numerical value towards the left and increases in numerical value towards the right.

Taking the square root of √24, we have:

√24 = 4.899

In this context, we can reasonably and logically deduce that 4.899 is greater than 4.256 (4.899 > 4.256) and would be placed at the right hand side of the number line and further from 4.899 as shown in number line C in the image attached below.

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the provided graph is not a function .

s

Answer:

15 pounds

Step-by-step explanation:

Kevin is making potato casserole for a dinner party. He needs 2½ pounds of potatoes per guest. How many pounds of potatoes will he need for 6 guests?

15 pounds

6.5 pounds  

25 pounds

12.5 pounds

2.5lb × 6 guest = 15 pounds

Answer: 15 pounds of potatoes.

Step-by-step explanation:

Kevin will perform basic multiplication to find how many potatoes he needs for all of the guests. Since each person requires 2 1/2 pound of potatoes and there are a total of 6 guests, multiplying these two values will find the pounds of potatoes that are needed for all of the guests.

2 1/2 * 6 = 15 pounds of potatoes

Therefore, Kevin needs 15 pounds of potatoes to make potato casserole for everyone at the dinner party.

The equation of the line parallel to the given line that contains C is obtained as y = x + 6.

For the given question;

The equation of the line is given as;

y = x + 4

The standard form of the equation of line in slope intercept form is;

y = m x + c

where, m is the slope and c is the y intercept.

On comparing;

m₁ = 1

Now, the other lien is parallel to the given line.

Thus, slopes of both lines will be equal.

m₁ = m₂ = 1

The passing points of the line are;

(x₁, y₁) = C(1, 7)

Now, the equation of lien will be;

y - y₁ = m₂(x - x₁)

Put the values;

y - 7 = 1(x - 1)

Simplifying.

y = x + 6

Thus, the equation of the line parallel to the given line that contains C is obtained as y = x + 6.

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Answer:

80 degrees

Step-by-step explanation:

The area of the triangle in the image is 10 square units, thus, option C is the correct one.

For a triangle of height H and a base B, the area is given by:

A = H*B/2.

In the image we can see that the base of the triangle goes from (0, 0) to (5, 0), then the length of the base is 5 units.

While the height goes from (0, 0) to (0, 4), so the height is 4 units.

Then the area will be:

A = (4 units)*(5 units)/2 = (20 square units)/2 = 10 square units.

The area is 10 square units.

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Answer:

Kareem takes longer to drive the 25 miles. Kadeen takes 10 minutes longer than Quinn.

Step-by-step explanation:

The formula for time is distance over speed (distance/speed)

Kadeem

distance/speed = 25/50 = 1/2 hour = 30 minutes

Quinn

distance/speed = 25/75 = 1/3 hour = 20 minutes

In the coordinate plane shown we can say that the y-coordinate of point A is 3.

Let us now take the statement one by one and try to find out if they are true or false.

A. True. The y-coordinate for A is 3

B. False. Point D has x-coordinate of 5 and E has 6

C. True The x-coordinate for F is 7

D. True The ordered pair for point G is (8,6)

E. False. Point H names the ordered pair (9,10).

F. false point B is √34 units away from origin

G. True.

The coordinate plane is a two-dimensional surface created by combining two number lines. A single horizontal number line makes up the x-axis. The name of the vertical number line, which is the other number line, is the y-axis. The intersection of the two axes is the origin. The graphing of points, lines, and other objects can be done using the coordinate plane.

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Sunday-56 fluid ounces of water require to reach your goal.

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The roots of the function f(x) = [tex]x^2+2x-1[/tex] are

x = [tex]-1+\sqrt{2}[/tex]

x = [tex]-1-\sqrt{2}[/tex]

The function is given f(x)=  [tex]x^2+2x-1[/tex]

The roots of given function will be at f(x) = 0

Substitute the value in the equation

[tex]x^2+2x-1[/tex] =0

Here to find the roots of the function, we have to use the quadratic formula in the given function

Roots of the function = [tex]\frac{-b+/-\sqrt{b^2-4ac} }{2a}[/tex]

From the given function the values of

a = 1

b = 2

c = -1

Substitute the values in the quadratic formula and find the roots of the function

= [tex]\frac{-2+/-\sqrt{2^2-4(1)(-1)} }{2(1)}[/tex]

= [tex]\frac{-2+/-\sqrt{4+4} }{2}[/tex]

= [tex]\frac{-2+/-2\sqrt{2} }{2}[/tex]

The roots of the given functions are

x = [tex]-1+\sqrt{2}[/tex]

x = [tex]-1-\sqrt{2}[/tex]
Hence, the roots of the function f(x) = [tex]x^2+2x-1[/tex] are

x = [tex]-1+\sqrt{2}[/tex]

x = [tex]-1-\sqrt{2}[/tex]

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one may note that y = 4 is a horizontal line, and a line perpendicular to a horizontal line will be a vertical one, Check the picture below.

The depth of the bottom of the hole after the second day is 36 feet using addition operation.

In math, addition is the process of adding two or more integers together. Addends are the numbers that are added, while the sum refers to the outcome of the operation.

Given the depth on the first day is 26 ½ feet.

Depth on the second day = 9½ feet more than on the first day i.e. 9½ feet + depth on the first day

This implies, depth on the second day = 9½ + 26 ½

= 36 feet

Therefore, the depth of the bottom of the hole after the second day is 36 feet.

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Answer:

x=4

Step-by-step explanation:

15-9=6

10-6=4

Answer:

x = 6 cm

Step-by-step explanation:

The two shapes are similar. That means one figure is exactly a multiple of the other figure

We can see that the ration of the length of the bigger rectangle  to the length of the smaller rectangle is 15/9 = 5/3  

Therefore the ratio of the width of the bigger rectangle  to the width of the smaller rectangle must also be 5/3

Given width of big rectangle = 10 and that of small rectangle is x

We get

10/x = 5/3

Multiply by x both sides:
x ×   10/x   =   x × 5/3

10 = 5x/3

Multiply by 3 both sides

30 = 5x

5x = 30

Dividing by 5 both sides
5x/x = 30/5
x = 6 cm

The percent increase in her salary resulted from her promotion is 6.67%.

The annual salary of Marisol as an engineer = $75000.

After, the promotion salary of Marisol as an engineer = $80000.

We have to find the increment in her salary after promotion in percentage.

Before finding the increment in percentage we find the total increment in dollar in her salary after promotion.

Total increment in dollar = Salary after Promotion − Salary before Promotion

Total increment in dollar = $80,000 − $75,000

Total increment in dollar = $5000

As we know that we can find the percentage by multiplying the required number by 100 because percentage is the ratio with 100.

So, the increment in salary after promotion in percentage.

% increment = (Total increment/Salary before) * 100

% increment [tex]= (\frac{5000}{75000})*100[/tex]

% increment = 0.0667 * 100

% increment = 6.67%

Now we see that percent increase in her salary resulted from her promotion is 6.67%.

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a. The complete table for the ordered pairs that are solutions to y = x³ - 4 is

x             y

-1            -5

0            -4

1             -3

2            4

b. The graph of the equation is shown below

From the question, we are to complete the given table of ordered pairs that are solutions to the given equation.

The given equation is

y = x³ - 4

Now, we will determine the values of y for the given values of x

When x = -1

y = x³ - 4

y = (-1)³ - 4

y = -1 - 4

y = -5

(-1, -5)

When x = 0

y = x³ - 4

y = (0)³ - 4

y = 0 - 4

y = -4

(0, -4)

When x = 1

y = x³ - 4

y = (1)³ - 4

y = 1 - 4

y = -3

(1, -3)

When x = 2

y = x³ - 4

y = (2)³ - 4

y = 8 - 4

y = 4

(2, 4)

Thus,

The table is

x             y

-1            -5

0            -4

1             -3

2            4

The graph is shown below

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Answer:

0.31

Step-by-step explanation:

√13.7/3.05^2 + 2.6

= 3.7/ 9.3 + 2.6

= 3.7/ 11.9

= 0.31

==========================================================

Explanation:

The given translation rule is (x, y) → (x+8, y - 3) which says "shift 8 units right and 3 units down".

The inverse transformation will undo each to get "8 units left and 3 units up"

So the inverse is (x, y) → (x-8, y + 3)

Use this inverse to determine the preimage of point T'(2,-6)

[tex](\text{x},\text{y})\to(\text{x}-8,\text{y}+3)\\\\(2,-6)\to(2-8,-6+3)\\\\(2,-6)\to(-6,-3)\\\\[/tex]

Therefore, preimage point T is located at (-6,-3) which points us to answer choice B

If we were to apply the rule of "shift 8 units right and 3 units down" to T(-6,-3), you should arrive at T'(2,-6)

The inches of ribbon that Anais use to trim the curtains is 12 inches.

From the information, Anais bought 2 1/2 yards of ribbon and then he had 1 feet 6 inches of ribbon left after trimming some curtains.

It should be noted that 12 inches = 1 feet

Therefore, the inches that will be left will be:

= 2 1/2 - 1 6/12

= 2 1/2 - 1 1/2

= 1 feet

It should be noted that 1 feet = 12 inches.

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Answer: No, this is not a function.

Functions exist when there are a unique set of x-values and each can match with a y-value. There cannot be a repeating x-value because this creates a discontinuity in the graph. You can have as many repeating y-values as you’d like as long as they each have a unique x-value and are not duplicate plot points.

Since x = 7 repeats in the domain of x-values, this cannot be a function.

Answer: -3 and -4

Step-by-step explanation:

The sum of -3 + -4 = -7

The product of -3 x -4 = 12 (a negative times a negative equals a positive)

The total area of the sandbox is given by 6x^2-11x+5

Width of the sandbox = (x-1)

Length of the sandbox = (6x-5)

Rectangle area in geometry refers to the area that a rectangle occupies on a two-dimensional plane. A quadrilateral, a form of a two-dimensional object with four sides and four vertices, is what a rectangle is. The rectangle's four angles are all right angles or exactly 90 degrees. The rectangle's opposing sides are equal and parallel to one another.

The formula for the area of a rectangle:

Area of rectangle = Length*Width

Substituting the value in the formula we get:

Area of rectangle = (x-1)*(6x-5)

= 6x^2-5x-6x+5

= 6x^2-11x+5

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