Use the bar diagram to write an equation. Then solve. Drag numbers to complete the equations.

The equation of the graph is f(x) = |x - 3| + 5

The graph represents the given parameter

From the graph, we have the following highlights:

This means that

Vertex = (3, 5)

Rewrite the vertex as

(h, k)

An absolute value function is represented as

f(x) = a|x - h| + k

Substitute the known values in the above equation

So, we have the following equation

f(x) = a|x - 3| + 5

On the graph, we have

(x, f(x)) = (2, 6)

So, we have

6 = a|2 - 3| + 5

This gives

a = 1

So, we have

f(x) = 1 * |x - 3| + 5

Evaluate

f(x) = |x - 3| + 5

Hence, the graph has an equation of f(x) = |x - 3| + 5

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The derivative of f(x) is option A.

What is derivative?

The instantaneous pace at which one quantity changes in relation to another is referred to as a derivative in mathematics.

Main Body:

Since the derivative of [tex]e^{x}[/tex] is just [tex]e^{x}[/tex] , application of the chain rule to a composite function with [tex]e^{x}[/tex] as the outside function means that:

         [tex]\frac{dy}{dx} (e^{f(x)} )= e^{f(x) }.f'(x)[/tex]

Now the derivative of 1/x = [tex]\frac{-1}{x^{2} }[/tex]

Hence derivative of f(x) = [tex]-e^{\frac{1}{x} } /x^{2}[/tex].

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Dominic is on the 8.75 mile of the bike path

From the question, the given parameters are:

The above parameters implies that

Dominic's position = 70% of the total distance

Represent the total distance with x

So, we have the following representation

Dominic's position = 70% * x

Where

x = 12.5

So, we have

Dominic's position = 70% * 12.5

Evaluate the products

Dominic's position = 8,75

Hence, Dominic's position is 8,75 miles

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The coordinates of each image are G'(-2,9), and H'(1,-3).

What are the coordinates?

A pair of numbers that use the horizontal and vertical separations from the two reference axes to define a point's location on a coordinate plane. typically expressed by the x-value and y-value pair (x,y).

Here, we have

R₍₁₈₀°,₀ (GH)

H(-1,3)

G(2,-9)

Now we need to the rotation of 180°  about the origin.

By following the rule, we get,

(x , y) ⇒ (-x , -y)

After solving,

G(2,-9) ⇒ G'(-2,9)

H(-1,3)  ⇒ H'(1,-3)

Hence, the coordinates of each image are G'(-2,9), and H'(1,-3).

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The new yield strength of the 1040 steel will be the intercept on the curve for 30.56 %of cold work which is between700 to 800 MPA

Given original diameter do = 12 mm

Ao = [tex]\pi[/tex]/4 x 12² = 113.097 mm²

Deformed diameter d =10mm

Ad = [tex]\pi[/tex]/4 x 10² = 78.54 mm²

Degree of cold work %CW = (Ao - Ad/Ao)X 100

                                             =(113. 097 - 78. 54/113.097) x 100

                                             = 30.56%

% CW is 30.56 %

Therefore, the intercept on the curve for 30.56% of cold work, which is between 700 and 800 MPA, will represent the new yield strength of the 1040 steel.

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The value of x and y in the triangle given are 15 and 4 respectively

An Equilateral triangle is a triangle in which all three sides are equal and angles are also equal. The value of each angle of an equilateral triangle is 60 degrees therefore, it is also known as an equiangular triangle. The equilateral triangle is considered as a regular polygon or a regular triangle as angles are equal and sides are also equal.

In the triangle given, we can equate equal sides and find the missing sides on the triangle.

12/18 = y + 12 / 18 + 6

12/18 = y + 12 / 24

2/3 = y + 12 / 24

solve for y

y = 4

Taking another side and solve for x

12 / x = 12 + y / x + 5

but y = 4

12 /x = 12 + 4 / x + 5

12/x = 16 / x + 5

x = 15

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The cross-sectional area is (h × w ) + ((1 ÷ 2) × 0.9 × w²) and the dimensions of the window which minimize the perimeter is (A - [tex]c_{0}[/tex][tex]w_{0}^{2}[/tex]) ÷ [tex]w_{0}[/tex] = 2√A[tex]c_{1}[/tex]([tex]c_{2}[/tex] - [tex]c_{0}c_1[/tex]) = 0.60592√A.

height of rectangle = h

height of the triangle = t

T = 0.9

width of the rectangle = w

The formula of Cross-sectional area is,

A = h × w + (1 ÷ 2)T × w

A = (h × w ) + ((1 ÷ 2) × 0.9 × w²)

Perimeter,

P = w + (2 × h) + 2√(T² + (w ÷ 2)²)

P = w + (2 × h) + 2√((0.9)² + (1 ÷ 2)²)

P = 2h + 2√((0.9)² + (1 ÷ 2)² + 1) × w

Therefore, [tex]C_{0}[/tex] = 0.9 ÷ 2, [tex]C_{1}[/tex] = 2, [tex]C_{2}[/tex] = 2√((0.9)² + (1 ÷ 2)² + 1)

minP=[tex]c_1[/tex]h+[tex]c_2[/tex]w

A = (h × w) + [tex]c_{0}[/tex]w²

substituting h = (A - [tex]c_{0}[/tex]w²) ÷ hw in P,

P = [tex]c_1[/tex]w + ([tex]c_1[/tex](A - [tex]c_{0}[/tex]w²) ÷ w)

Differentiating both sides,

(dP ÷ dw) = -2[tex]c_{0}[/tex][tex]c_{1}[/tex] + [tex]c_{2}[/tex] - ([tex]c_{2}[/tex](A - [tex]c_{0}[/tex]w²) ÷ w²) = 0

[tex]w_{0}[/tex] = (√[tex]c_{1}[/tex]A ÷ (√[tex]c_{2}[/tex] - [tex]c_{0}c_1[/tex])) = 0.962445√A

and consequently,

[tex]h_{0}[/tex] = (A - [tex]c_{0}[/tex][tex]w_{0}^{2}[/tex]) ÷ [tex]w_{0}[/tex] = 2√A[tex]c_{1}[/tex]([tex]c_{2}[/tex] - [tex]c_{0}c_1[/tex]) = 0.60592√A

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The value of x in 3² × [tex]3^{x}[/tex] = 3² is 0.

According to the question,

We have the following information:

3² × [tex]3^{x}[/tex] = 3²

We know that when two numbers with the same base are in multiplication then the powers of the numbers are added. So, in this case, 2 will be added to x. And this expression of addition will be equal to the powers of the number on the right hand side.

Now, we have the following expression:

2+x = 2

x = 2-2

x = 0

Hence, the value of x in 3² × [tex]3^{x}[/tex] = 3² is 0.

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Bisector-When anything is divided into two equal or congruent portions, usually by a line, it is said to have been bisected in geometry. The line is then referred to as the bisector.

What are the steps to create a bisector?

By following these steps to create a bisector in the provided curve:-

1) Join the extreme points and make a line.

2) By using compass, take width as length of a line joined in step 1.

3) Draw a curve taking extreme points.

4) Draw a line from the intersection of the curve to the line.

The above following steps should be performed  error free and you will get bisector.

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The numeric value of the expression sec²(54º) - 1, using a trigonometric identity, is given as follows:

tan²(54º) = 1.8944.

Before applying the trigonometric identity, we have to define the secant and the tangent of an angle, as follows:

The identity that exists between the squares of these measures is given as follows:

tan²(x) + 1 = sec²(x).

Hence, isolating the tangent:

tan²(x) = sec²(x) - 1.

In this problem, the expression is given as follows:

sec²(54º) - 1

Applying the identity, the expression is given as follows:

sec²(54º) - 1 = tan²(54º).

Using a calculator, the numeric value of the expression is given as follows:

tan²(54º) = 1.8944.

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The number of ride tickets that were sold are 8 and the number of food tickets that were sold  are 24  .

In the question ,

it is given that

total number of tickets bought by the family at carnival = 32 tickets

total amount spent by the family of tickets = $90

let the number of ride tickets be [tex]=[/tex] x

let the number of food tickets be [tex]=[/tex] y

So , x + y = 32

x = 32 - y

cost of 1 ride ticket = $1.50

cost of 1 food ticket = $3.25

So the total cost is 1.25x + 3.25y = 90

Substituting x = 32 - y in the equation 1.5x + 3.25y = 90 ,

we get ,

1.5(32 - y) + 3.25y = 90

48 - 1.50y + 3.25y = 90

1.75y = 90 - 48

1.75y = 42

y = 24

So , x = 32 - 24 = 8

Therefore , The number of ride tickets that were sold are 8 and the number of food tickets that were sold  are 24  .

The given question is incomplete , the complete question is

A family buys a total of 32 tickets at a carnival. Ride tickets cost $1.50 each and food tickets cost $3.25 each. The family pays a total of $90 for the tickets store. How many of each type of ticket were sold ?

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The probability that we will see at least two meteors in the first minute is 1251.5.

So, the probability that we will see at least 2 meteors in the first minute:

Then, in 1 minute:

Now, at least 2 meteors in 1 minute:

Solve as follows:

Therefore, there is a 1251.5 percent probability that we will observe two meteors or more in the first minute.

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Explanation:

The slope of the line

y = x + 17 is ___. 1

2. The slope of the line

y = x - 7/9 is ___. 1

Answer:

The answer is C, I had this same quiz today and I got 100%

The overall profit of the corporation as during time period is $ 2.5 x 10⁷

As the question expressed-

Earned profit - $2. 5 x 10 to the 4th power

In scientific notation - $2. 5 x 10⁴

Number of days - 1 x 10 to the 3rd power

In scientific notation - 1.0 x 10³

Total profit = Earned profit x Number of days

Total profit = $2. 5 x 10⁴ x 1.0 x 10³

Total profit = $ 2.5 x 10⁷

Thus, the overall profit of the corporation as during time period is $ 2.5 x 10⁷.

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Answer:

4√3

Step-by-step explanation:

This is a special right triangle with angle measures 30°-60°-90° and side lengths represented with a-a√3-2a respectively to angle measures.

Here, hypotenuse is given as 8 which is represented with 2a, so a = 4

Then x will be 4√3 as it's represented with a√3.

The value of x is [tex]4\sqrt{3}[/tex] .

What is a trignometric function?

The trigonometric functions are real functions which relate an angle of a right-angled triangle to ratios of two side lengths.

Mention all trignometric function ?

sinФ ,cosФ ,tanФ ,cosecФ ,secФ ,cotФ

What is the trick to remember trignometric formulas ?

Some People Have Curly Brown Hair Turned Permanently Brown

sinФ=[tex]\frac{p}{h}[/tex]

cosФ=[tex]\frac{b}{h}[/tex]

tanФ=[tex]\frac{p}{b}[/tex]

cosecФ=[tex]\frac{h}{p}[/tex]

secФ=[tex]\frac{h}{b}[/tex]

tanФ=[tex]\frac{b}{p}[/tex]

Given:

A right angled triangle with

base, b

perpendicular, p

hypotenuse, h=8

angle ,Ф = 60°

So by trignometric formulas ,we get

sinФ = sin60° =[tex]\frac{p}{h}[/tex]

⇒[tex]\frac{\sqrt{3} }{2} = \frac{x}{8}[/tex]

⇒[tex]x = 4\sqrt{3}[/tex]

Hence ,the value of x is obtained .

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Check the picture below.

The missing side lengths are (m = 4[tex]\sqrt{6}[/tex] , n =  6[tex]\sqrt{2}[/tex]).

According to given triangle, Using triangular formula;

tan 30 = [tex]\frac{2\sqrt{6} }{n}[/tex]

⇒[tex]\frac{1}{\sqrt{3} }[/tex]  = [tex]\frac{2\sqrt{6} }{n}[/tex]

⇒ n = [tex]6\sqrt{2}[/tex]

  n = [tex]6\sqrt{2}[/tex]

Similarly,

sin 30 = [tex]\frac{2\sqrt{6} }{m}[/tex]

⇒ [tex]\frac{1}{2}[/tex] = [tex]\frac{2\sqrt{6} }{m}[/tex]

⇒ m = [tex]4\sqrt{6}[/tex]

   m = [tex]4\sqrt{6}[/tex]

so,

    m = [tex]4\sqrt{6}[/tex] and n = [tex]6\sqrt{2}[/tex]

So, the correct option is D.

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Answer:

Value of x is 1440

Step-by-step explanation:

According to the question,

720 ÷ 50 gives same answer as x ÷ 100

[tex] \therefore[/tex]

[tex] \rm \implies \dfrac{720}{50} = \dfrac{x}{100} \\ \\ \rm \implies x = \frac{720}{50} \times 100 \\ \\ \rm \implies x = 720 \times 2 \\ \\ \rm \implies x = 1440[/tex]

The maximum number of deaths could be 5840000.

acc to our question-

hence,The maximum number of deaths could be 5840000.

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By solving  a system of two simultaneous linear equations, it can be calculated that

Alicia will need 3 twigs and 6 flowers

What is simultaneous linear equation?

At first it is important to know about linear equation

Equation shows the equality between two algebraic expressions by connecting the two algebraic expressions by an equal to sign.

A one degree equation is known as linear equation.

Two or more linear equations, which can be solved together to obtain common solution are known as simultaneous linear equation.

Here, a system of two simultaneous linear equation needs to be solved

Let the number of twigs Alicia needed be x and the number of flowers Alicia needed be y

Alicia has to create an arrangement of twigs and flowers that has a total of 9 objects.

x + y = 9 ..... (1)

Alicia wants the arrangement to have twice as many flowers as twigs

2x = y .... (2)

Putting the value of x in (1)

x + 2x = 9

3x = 9

[tex]x = \frac{9}{3}[/tex]

x = 3

Putiing the value of x in (2),

y = 2 [tex]\times[/tex] 3

y = 6

Alicia will need 3 twigs and 6 flowers

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The point (-2, 7) is not on the graph of y = -2x + 1

From the question, we have the following equation

y = -2x + 1

This equation represents the equation of the graph

Also, we have the following points

(-2, 7)

This point implies that

(x, y) = (-2, 7)

Substitute (x, y) = (-2, 7) in the equation y = -2x + 1

So, we have

7 = -2 x -2 + 1

Evaluate

7 = 5

This is false

Hence, the point is not on the graph

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Answer:

B) n>6

Step-by-step explanation:

-2n<-12

divide both sides by -2

n>6

A and C can not be the answer because it is not equal to therefore the dot should not be filled in

Answer:

9ty(3t - 2y)

Step-by-step explanation:

27t²y - 18ty² ← factor out 9ty from each term

= 9ty(3t - 2y)

Answer:

Step-by-step explanation:

Noah- 4 1/6 miles/hour

Emily- 8 1/10 miles/hour

Anna- 3 1/2 miles/ hour

Emily ran the quickest.

Answer:

Anna was the fastest.

Step-by-step explanation:

Following are the steps we take to determine each one's speed:

speed=distance/time

Noah went 4 1/6 miles an hour, Emily went 4 1/2 miles an hour, and Anna went 5 5/9 miles an hour. Therefore, Anna was the fastest.

The amount of wire that can be bought from 21 cents is 7 inches.

It is given in the question that 12 inches of wire costs 36 cents.

We have to find the amount of wire that can be bought from 21 cents.

We will use the unitary method to solve this question.

Amount of wire that can be bought from 1 cent = 12/36 = 1/3 inches

Hence, according to the data given in the question, we can write,

The amount of wire that can be bought from 21 cents = (1/3)*21 = 7 inches.

Unitary method

The unitary method is a mathematical problem-solving technique where the value of a single unit is found out from the value of multiple units prior to finding the necessary result.

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