PLEASE HELP ME
An article claimed the state's typical price of a gallon of gasoline is $2.69. The prices from 5 gas stations surveyed were $2.79, $2.99, $2.69, $2.89, and $2.69.

According to this data, what is wrong with the article's statement?

Answer:

The domain is all real numbers.

The initial value is 3.

The simplified base is 3√2.

The statements accurately describe the function f(x) = 3(√18)x are:

The domain is all real numbers.

The initial value is 3.

The simplified base is 3√2.

A function is an expression that illustrates the connection between two or more variables and numbers. A function defined by several subfunctions, each of which is applicable to a distinct interval in the domain, is said to be piecewise.

We have function,

f(x) = 3√18 x

now, simplifying the function we get

f(x) = 3 (3√2)x

f(x) = 9x√2

So, we can conclude that.

The domain is all real numbers.

The initial value is 3.

The simplified base is 3√2.

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The inequality that correctly compares the numbers is 0.47 < 125% < three and two fifths

The numbers are given as:

125%, 0.47, and three and two fifths

Rewrite properly as:

125%, 0.47, and 3.4

Express the percentage as decimal

1.25, 0.47, and 3.4

Reorder the numbers in ascending order

0.47, 1.25 and 3.4

Rewrite as

0.47, 125% and three and two fifths

Include the less than inequality symbol

0.47 < 125% < three and two fifths

Hence, the inequality that correctly compares the numbers is 0.47 < 125% < three and two fifths

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Answer:

a) 0.02

b) 0.7

c) 7

Step-by-step explanation:

0.2 × 0.1

1 - (0.2 + 0.1)

10 - (2+1)

Answer:

x + y = -3.

Step-by-step explanation:

x + y = 2y = -x + 2   - the slope of this line is -1 . The line parallel to it will also have a slope of -1.It also passes through (-7,4) so we havey - 4 = -1(x - -7)y - 4 = -1(x + 7)y - 4 = -x - 7x + y = -3 is the required equation.

Answer: division property of equality

Step-by-step explanation:

Answer:

Step-by-step explanation:

y=2x1-

So this is a very simple question.

First, analyze the problem

It says y=2x-1

The answer is +1 or 1 I believe

Someone pls correct me If I'm wrong.

Answer:

  52 ounces

Step-by-step explanation:

You want the number of ounces of pure acid to be added to 300 ounces of 12% acid solution to produce a solution that is 25%.

Let x represent the number of ounces of acid added. Then the amount of acid in the desired solution is ...

  12%(300) +100%(x) = 25%(300 +x)

Subtracting (25%(x) +12%(300)) from both sides, we get ...

  75%(x) = 13%(300)

Dividing by the coefficient of x, we find ...

  x = (13)(300)/75 = 52

52 ounces of pure acid should be added to make a 25% acid solution.

__

Additional comment

In the original solution, there are 12%(300) = 36 ounces of acid. In the 352 ounces of final solution, there will be 36+52 = 88 ounces of acid, a proportion of 88/352 = 1/4 = 25%.

The solution to the expression (2.8 × 10⁻⁹) − (6.9 × 10⁻⁸) gives -6.62 * 10⁻⁸

An equation is an expression that shows the relationship between two or more numbers and variables.

Given the equation:

(2.8 × 10⁻⁹) − (6.9 × 10⁻⁸)

Making the exponents to be similar gives:

(2.8 × 10⁻⁹) − (69 × 10⁻⁹)

Simplifying gives:

-6.62 * 10⁻⁸

The solution to the expression (2.8 × 10⁻⁹) − (6.9 × 10⁻⁸) gives -6.62 * 10⁻⁸

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The length of BC to the nearest while meters is 143m

Given the following parameters

AC = 108 m

<A = 53°

Using the SOH CAH TOA identity

tan 53 = opp/hyp

tan53 = BC/108

Determine the measure of BC

BC = 108tan53

BC = 143.32m

Hence the length of BC to the nearest while meters is 143m

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First of all we know about the Estimation.

What is the Estimation?

To estimate the result of multiplication (product), round the numbers to some close numbers that can easily multiply . One method of estimation is to round all factors to the biggest digit (place value) they have.

General rule for rounding:

1 ) If the number you are rounding is followed by 5, 6, 7, 8, or 9, round the number up.

2 ) If the number you are rounding is followed by 0, 1, 2, 3, or 4, round the number down.

So the last digit of number is 44 which is less then 50 so the number is down to its 10's.

thats the reason why when we estimate the product of 416x9 =3,744 is 3,600.

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Step-by-step explanation:

Answer:

The distance between the two given points is equal to √85.

Step-by-step explanation:

Let's recall what the distance formula is:

\displaystyle \huge\math\boxed{d = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2} }\math

d= (x 1 −x2 ) 2 +(y 1 −y 2) 2

We are defined our two points as:

(x₁, y₁) → (1, -7)

(x₂, y₂) → (7, 0)

We can rewrite this into our different "variables":

x₁ = 1

y₁ = -7

x₂ = 7

y₂ = 0

Now given our distance formula and our variables, we can find the distance between the two points:

\begin{gathered}\displaystyle\huge\begin{aligned}d & = \sqrt{(1 - 7)^2 + (7 - 0)^2} \\& = \sqrt{(-6)^2 + (7)^2} \\& = \sqrt{36 + 49} \\& = \math\boxed{\sqrt{85}} \\\end{aligned}\end{gathered}

d= (1−7) 2+(7−0) 2= (−6) 2+(7) 2 = 36+49=\math 85

∴ since the radical is already in its simplest form, our distance between the two points is equal to √85.

Hope this helps!

We use parenthesis if an interval is infinite on both boundries in order to exclude end-points .

Square brackets mean the set of all points from a to b .

If we use square brackets , it would mean we are including - infinity and + infinity , which is practically impossible .

When we , use parenthesis only the nos . lying between the two points are taken into consideration , the two points are not included .

So , we use parenthesis to exclude - infinity and + infinity .

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While solving the quadratic equation, in the step 2, Priya did not correctly complete the square.

A quadratic equation is of the form of ax²+bx+c=0.

The given quadratic equation is of the form:

x²-6x-11=0

Now solving it by completing the square we get:

or, x²-6x=11  (take all the variable to one side)

or, x²-6x+9=11+9  (complete the square when b=3)

or, (x-3)²=20     (factor and square the polynomial)

or, x = 3 ± √20    (use inverse operations so that the variable is isolated)

Hence Priya made a mistake while completing the square of the equation.

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I hope this pictures help

In linear equation , the negative solution is x = -4 .

What is a formula for linear equations?

Let's assume that the number is x

Now according to the question,

When 36 is subtracted from the square of a number, the result is 5 times the number.

 x² -36 = 5x

x² -5x -36 = 0

x²- 9x + 4x -36 = 0

x ( x - 9) +4( x - 9 ) = 0

(x-9) ( x + 4 ) = 0

 x  = 9 , -4

So the negative solution is x = -4

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Answer:

A. tenths

because there's only two digits after a comma

The height of the tree is 21 feet if manny stands 512 feet tall, and his shadow is 414 feet long. The tree's shadow extends 17 feet in length.

A ratio is defined as a relationship between two quantities, it is expressed as one divided by the other

The length of Manny's shadow, which is 414 feet long, is 512 feet.

The tree's shadow extends 17 feet.

Here, we'll assume that the height is x.

According to the data given, the calculation is as follows:

414 : 512 = 17 : x

⇒ 414 / 512 = 17 / x

⇒ (414)x = (512)(17)

⇒ x = (512)(17)/(414)

⇒ x =21.02

⇒ x = 21 feet

Therefore, the height of the tree is 21 feet if manny stands 512 feet tall, and his shadow is 414 feet long. The tree's shadow extends 17 feet in length.

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Your question is incomplete, probably the complete question is:

One triangle shown is formed by the tree, its shadow, and a line of sight from the ground to the top of the tree. The other is formed by Manny, his shadow, and a line of sight from the ground to the top of his head. Manny is 512 feet tall, and his shadow is 414 feet long. The shadow of the tree is 17 feet long. How can you determine the height of the tree?

[tex]{ \orange{ \tt{k = 1}}}[/tex]

Step-by-step explanation:

-2 = k+7/3

cross multiply 3 with -2 then,

-6 = k+7 (OR) k+7 = -6.

k = -6+7

k = 1.

Answer:

Step-by-step explanation:

After solving the inequality we get the value of x as x ∈ (₋5,3)

Given the inequality is 2 |x + 1|  < 8

Divide both sides of the inequality by the coefficient of variable.

|x + 1| < 8/2

Reduce the fraction

|x + 1| < 4

Now convert the absolute inequality to standard inequality.

₋4 < x₊1 < 4

separate compound inequalities into system of inequalities.

x ₊ 1 > ₋4  (1)

x ₊ 1 < 4 (2)

for (1) x ₊ 1 > ₋4

rearrange variables to the left side of the equation.

x > ₋4 ₋1

calculate the sum.

x > ₋5

for (2) x ₊ 1 < 4  (2)

rearrange the terms.

x < 4 ₋ 1

x < 3

therefore ₋5 < x < 3

Hence we get the value ranging from (₋5 , 3)

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Answer:

Step-by-step explanation:

Whats 21 - 20 x 2?

21 - 20 x 2 =

21 - 40 =

-19

Answer:

6.4675

Step-by-step explanation:

Answer:

Solved using 2 different methods, used the definition of derivative aswell.

Answer:

4

Step-by-step explanation:

the sequence is like [tex]1^{2}[/tex],[tex]2^{2} ,4^{2},8^{2} ,16^{2} ,32^{2}[/tex]

The value of x is 1 and -8.

To solve this problem we need to understand the concept of quadratic equation.

To solve Quadratic equation we need to understand the concept of equation which says the factor of the product of coefficient of [tex]x^{2}[/tex] and constant must on adding or substracting give the coefficient of x.

Here the equation is [tex]x^{2} +7x-8=0[/tex]

The product of coefficient  is 8. The factors of 8 is 8 and 1 which gives 7 on substracting.

Now,

[tex]x^{2} +8x-x-8=0[/tex]

⇒[tex]x(x+8)-1(x+8)=0\\[/tex]

⇒[tex](x-1)(x+8)=0[/tex]

∴ x=1,-8.

So, the required values of x is 1 and -8.

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The expression for the perimeter is P = 12x - 16

The given parameters are

Length = 3x + 1

Width = 3x - 9

The perimeter is calculated as

P = 2 * (Width + Length)

So, we have

P = 2 * (3x + 1 + 3x - 9)

Evaluate

P = 2* (6x - 8)

Expand

P = 12x - 16

Hence, the expression for the perimeter is P = 12x - 16

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The required value of a is 2 if ​the coefficient of x² is 1104 of the expansion (1 + ax)²⁴.

According to the binomial theorem, it is possible to expand any non-negative power of binomial (x + y) into a sum of the form,

(x+y)ⁿ = ⁿC₀xⁿy₀ + nC₁ xⁿ⁻¹y₁ + nC₂ xⁿ⁻² y2 + ... + nC x¹yⁿ⁻¹ + nCn x°yⁿ

where n ≥ 0 is an integer and each ⁿCₓ is a positive integer known as a binomial coefficient.

We have been given that the expansion as

(1 + ax)²⁴

As per the binomial theorem expansion of the term 3,

T₃ = ⁿC₂ a² x²

Since the coefficient of x² = 1104

⇒ n!/2!(n-2)a² x² = 1104

Here n = 24

⇒ 24!/2!(24-2)a² = 1104

⇒ 276a² = 1104

⇒ a² = 1104/276

⇒ a² = 4

⇒ a = 2

Therefore, the required value of a is 2 if ​the coefficient of x² is 1104 of the expansion (1 + ax)²⁴.

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Answer:

The point in the middle/center of the line joining two points (also known as endpoints) is called a midpoint. Given one endpoint and a midpoint, the other midpoint can be calculated using the midpoint formula.

Step-by-step explanation:

The point in the middle/center of the line joining two points (also known as endpoints) is called a midpoint. Given one endpoint and a midpoint, the other midpoint can be calculated using the midpoint formula.