The **formula **for Rn for the given function is[tex]\int\limits^5_{-1} {9x^2} \, dx =\sum_{i=1}^{n}\frac{54}{n}\left(1-\frac{12i}{n}+\frac{36i^2}{n^2}\right)[/tex]. And the** area **is 378 units².

The approximate area under the graph of a function f(x) throughout the range [a, b] can be calculated using a **Riemann sum**. Then, the formula to determine the length of each subinterval is given by [tex]\Delta x=\frac{b-a}{n}[/tex].

Substituting the given interval in the above formula, we get,

[tex]\begin{aligned}\Delta x &=\frac{5+1}{n}\\&=\frac{6}{n}\end{aligned}[/tex]

Now, the sample point [tex]x_i[/tex] is given as

[tex]\begin{aligned}x_i&=a+i\Delta x\\&=-1+i\left(\frac{6}{n}\right)\\&=\frac{6i}{n}-1\end{aligned}[/tex]

The formula for Rₙ is calculated as follows,

[tex]\begin{aligned}R_n&=\sum_{i=1}^{n}f(x_i)\Delta x\\&=\sum_{i=1}^{n}9\left(-1+\frac{6i}{n}\right)^2\frac{6}{n}\\&=\sum_{i=1}^{n}\frac{54}{n}\left(1-\frac{12i}{n}+\frac{36i^2}{n^2}\right)\end{aligned}[/tex]

Then, the **area** under the curve is computed as follows,

[tex]\begin{aligned}\int\limits^{5}_{-1} {9x^2} \, dx&= \lim_{n \to \infty} \sum_{i=1}^{n}\frac{54}{n}\left(1-\frac{12i}{n}+\frac{36i^2}{n^2}\right)\\&=\lim_{n \to \infty}\left( \sum_{i=1}^{n}\frac{54}{n}-\sum_{i=1}^{n}\frac{648i}{n^2}+\sum_{i=1}^{n}\frac{1944i^2}{n^3}\right)\\&=\lim_{n \to \infty}\left(\frac{54}{n}\sum_{i=1}^{n}(1)-\frac{648}{n^2}\sum_{i=1}^{n}(i)+\frac{1944}{n^3}\sum_{i=1}^{n}(i^2)\right)\end{aligned}[/tex]

Solving this we get,

[tex]\begin{aligned}\int\limits^5_{-1} {9x^2} \, dx &=\lim_{n \to \infty}\left(\frac{54}{n}(n)-\frac{648}{n^2}\left(\frac{n(n+1)}{2}\right)+\frac{1944}{n^3}\left(\frac{n(n+1)(2n+1)}{6}\right)\right)\\&=\lim_{n \to \infty}\left(54-\frac{324(n+1)}{n}+\frac{324(n+1)(2n+1)}{n^2}\right)\\&=\lim_{n \to \infty}\left(54-324\left(1+\frac{1}{n}\right)+324\left(2+\frac{1}{n}+\frac{2}{n}+\frac{1}{n^2}\right)\right)\end{aligned}[/tex]

As the value of n tends to ∞, then 1/n is zero. Substituting these n values, we get,

[tex]\begin{aligned}\int\limits^5_{-1} {9x^2} \, dx&=54 -324+324(2+0)\\&=\mathrm{378\;units^2} \end{aligned}[/tex]

The required **answers** are [tex]\int\limits^5_{-1} {9x^2} \, dx =\sum_{i=1}^{n}\frac{54}{n}\left(1-\frac{12i}{n}+\frac{36i^2}{n^2}\right)[/tex] and 378 units².

The complete question is -

Find a formula for Rₙ for the function f (x) = (3x)² on [− 1, 5] in terms of n. Compute the area under the graph as a limit.

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This table reflects the result of a survey conducted in a town to find out the number of cars of a particular color.

Which of the following ranges would be appropriate to use in order to represent the numerical data on the vertical axis of a Bar Graph?

A. 10 to 20

B. 20 to 100

C. 0 to 50

D. 0 to 30

the range that would be the** most appropriat**e to represent the **numerical data **on th**e vertical axis** is **B. 20 to 100.**

the table is not included but the range of **20 to 100** is most **appropriate **for the number of cars in town with a particular color.

this is because **towns **would normally have between **hundreds **and thousands of cars which means that cars of a particular **color **would be between 20 and 100 at least.

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The range that would be the most approx to represent the numerical data on the vertical axis is B. 20 to 100.

Bar graph :

Bar graphs are the pictorial representation of data (generally grouped), in the form of vertical or horizontal rectangular bars, where the length of bars is proportional to the measure of data

The range that would be the most approximately to represent the numerical data on the vertical axis is B. 20 to 100.

because

it is not possible to have zero number of cars that have a particular color,

in That way, we can eliminate options C and D .

in option A the range is too small which is not possible.

the table is not included but the range of 20 to 100 is most appropriate for the number of cars in town with a particular color.

this is because towns would normally have between hundreds and thousands of cars which means that cars of a particular color would be between 20 and 100 at least.

The following data show the height, in inches, of 11 different plants in a garden:

9

4

10

9

5

2

22

10

3

3

5

After removing the outlier, what does the mean absolute deviation of this data set represent?

On average, the height of a plant varies 2.8 inches from the mean of 6 inches.

On average, the height of a plant varies 3.2 inches from the mean of 5 inches.

On average, the height of a plant varies 2.8 inches from the mean of 5 inches.

On average, the height of a plant varies 3.2 inches from the mean of 6 inches.

On average, the height of a plant varies** 3.2 inches **from the **mean of 6 **inches.

An** outlier** is a number that is way smaller or way larger than that of other numbers in a data set. The **outlier** is 22.

**Mean absolute deviation** = (1/n) x ∑ l x - m(x) l

**Mean **without the** outlier **: (9 + 4 + 10 + 9 + 5+ 2 + 10 + 3 + 3+ 5) / 10 = 6

(1/10) x ∑ l (9 - 6) + (4 - 6) + (10 - 6) + (9 - 6) + (5 - 6) + (2 - 6) + (10 - 6) + (3 - 6) + (3 - 6) + ( 5 - 6) = **3.2**

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Which of the following characteristics describe the graph of an exponential function?

**Answer:**

A GENERAL NOTE: CHARACTERISTICS OF THE GRAPH OF THE PARENT FUNCTION

f

(

x

)

=

b

x

An exponential function with the form

f

(

x

)

=

b

x

,

b

>

0

,

b

≠

1

, has these characteristics:

one-to-one function

horizontal asymptote:

y

=

0

domain:

(

−

∞

,

∞

)

range:

(

0

,

∞

)

x-intercept: none

y-intercept:

(

0

,

1

)

increasing if

b

>

1

decreasing if

b

<

1

**Step-by-step explanation:**

hope it helps you

how can i got 24.8 show your work

I hope this helpssssss:)

Linear functions f(x) and g(x) have been combined by addition and multiplication. The table shows values for the sum, s(x), and product, p(x).

Which statements correctly compare the sum and product? Check all that apply.

Both functions have a constant rate of change.

The sum is linear and the product is quadratic.

The x-intercepts are the same.

The sum has one y-intercept and the product has two x-intercepts.

Both functions decrease for x ≥ 2.

The statements that correctly compare the sum and product of the **function** are:

A linear **function** simply means a function that represents a straight line on the **coordinate** plane.

In this case, the sum is linear and the product is quadratic while the sum has one **y-intercept** and the product has two x-intercepts.

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9. For Investment Plan A to C, solve for the future value at the end of the term based on the

information provided.

Investment Plan Principal

A

$7,500

B

$53,000

C

$19,000

Interest Rate

8% compounded quarterly

6% compounded monthly

5.75% compounded semi-annually

Term

3 years

4

years and 3 months

6 years and 6 months

The **future value **of **Investment A** is 9511.81

The **future value **of **Investment B is **68,351.02

The **future value **of **Investment C is**29.067.07.

When an amount earns a **compound interest, **it means that both the amount invested and the interest rate already accrued increases in value at the next compounding date. For example, if **interest **is **compounded quarterly, **both the amount invested and the interest accrued increases every quarter.

The formula for calculating **future value:**

FV = P (1 + r)^nm

FV = Future value P = Present value R = interest rate m = number of compoundingN = number of years**Investment A** = 7500 x [(1 + (0.08/4)]^(4 x 3) = 9511.81

**Investment B** = 53,000 x [(1 + (0.06/12)]^[(4 x 12) + 3) = 68,351.02

**Investment C** = 19,000 x [(1 + (0.0575/2)]^{6 x 2) + 6/2) = 29.067.07

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A state uses a combination of three letters (A-Z) followed by three digits (0-9) for their license plates. How many different license plates are possible? (Exact steps shown for credit)

A state uses a combination of three letters (A-Z) followed by three digits (0-9) for their **license plates**. So, there are 17576000 **license plates** can be made.

Given** **that, license plates consists of 3 letters followed by 3 digits.

Let the numbers on license plates be **N**

Let the letters on license plates be **L**

So, the license plate consisting of 3 letters and 3 digits will be **LLLNNN.**

Letters can be anything from A to Z.

There are 26 letter **combinations** for the first letter. That is applicable for the following 2 letters.

So, the **combination** for letters = 26×26×26 = 17576

Numbers can be anything from 0 to 9.

There are 10 combinations for each place.

So, the **combination **for numbers = 10×10×10 = 1000

Now, the combination for letters and numbers= 17576×1000

= 17576000

Therefore, 17576000 license plates can be made.

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Which of the following functions best describes this graph?

**Answer:**

C

**Step-by-step explanation:**

We can use process of elimination

D is incorrect because the roots are 3 and -4 and there are no negative roots visible

B is wrong because the roots -3 and -6 are both negative

You can factor A into (x-2)(x-3) and the roots are 2 and 3 but the roots on the graph look closer to 3 and 6

For C it can be factored as (x-6)(x-3) so the roots are 3 and 6 which look accurate

In the year 2000, The U.S. Budgeted $25,003 million for Natural Resources and Environment. In 2014, they budgeted $40,156 million. What was the absolute and relative change in environmental spending from 2000 to 2014?

Using it's concepts, we have that:

TheThe absolute change between two values is given by the absolute value of the **difference **between two values.

In this problem, the values are of **$40,156 million,** which is the final value, and **$25,003 million**, which is the initial value, hence the **absolute change** is:

A = 40,156 - 25,003 = $15,153 million.

What is the relative change?The relative change is the absolute change multiplied by 100% and divided by the initial value, hence:

(15,153/25,003) x 100% = 60.60%.

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What is the y-intercept of the liner function? (y=3x-2)

The **y-intercept **of the linear **function** y = 3x - 2 is -2

The **function** is given as

y = 3x - 2

The above function is a **linear function**, and the **y-intercept **is the point on the **graph**, where x = 0 i.e. the point (0, y)

As a general rule, **linear functions** are those functions that have constant rates or **slopes**

Next, we set x to 0, and calculate y to determine the value of the ** y-intercept**

y = 3(0) - 2

Remove the bracket in the above **equation**

y = 3 * 0 - 2

Evaluate the product of 3 and 0 i.e. **multiply **3 and 0

y = 0 - 2

Evaluate the difference of 0 and -2 i.e. **subtract **0 from 2

y = -2

The above means that the **value **of y when x is 0 is -2

Hence, the **y-intercept **of the **linear function **y = 3x - 2 is -2

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Find the area of the figure.

i hope this helpssss :))

Express the confidence interval (0.065,0.143) in the form of p - E

The **confidence interval** expressed in the form p - E is:

(0.104 - 0.039, 0.104 + 0.039).

What are the mean and the margin of error of a confidence interval?The **mean **is the mean of the bounds, hence:

p = (0.065 + 0.143)/2 = 0.104.

The **margin of error** is the difference between the bounds and the mean, hence:

E = 0.104 - 0.065 = 0.143 - 0.104 = 0.039.

Hence the interval in the **desired format** is:

(0.104 - 0.039, 0.104 + 0.039).

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Find the equation of the line through point (−2,−1) and perpendicular to 5x+6y=−6

**Answer:**

**Step-by-step explanation:**

eq. of any line perpendicular to 5x+6y=-6 is

5y-6x=c

where c is a constant.

it passes through (-2,-1) so

5(-1)-6(-2)=c

c=-5+12=7

so reqd. eq. is 5y-6x=7

or 6x-5y=-7

or

slope of given line =-5/6

slope of reqd. line=6/5

eq. of line through (-2,-1) with slope 6/5 is

y+1=6/5(x+2)

5y+5=6x+12

5y=6x+12-5

or 5y=6x+7

or

6x-5y=-7

What is the domain of the function given below

**Answer:**

c. [-1, infinity)

**Step-by-step explanation:**

the domain the interval or set of valid x values (while the range is the same for the valid y values).

what is the smallest value of x we see for the graph ?

for x values we need to look left and right.

and the more left the value, the smaller it is.

so, in other words, what is the left-most x value e can find ?

x = -1

that is the "starting point" of the function. there is no functional value for any smaller x.

and then clearly, the function goes on and on to the right without any boundary in sight. so, it keeps going to the right in all eternity, that means it goes to infinity.

therefore the answer.

keep in mind that "infinity" is not a number, only a concept. so, when writing "infinity" at an interval end, it is not included (and we use a round bracket).

What are the fourth roots of -3+3√3i?

Enter your answer by filling in the boxes. Enter the roots in order of increasing angle measure in simplest form.

By **De Moivre's formula**, we have the following four **roots**: [tex]z_{1} = 1.565 \cdot \left(\cos \frac{\pi}{6} + i\,\sin \frac{\pi}{6} \right)[/tex], [tex]z_{2} = 1.565\cdot \left(\cos \frac{2\pi}{3} + i\,\sin \frac{2\pi}{3} \right)[/tex], [tex]z_{3} = 1.565\cdot \left(\cos \frac{7\pi}{6}+i\,\sin \frac{7\pi}{6} \right)[/tex] and [tex]z_{4} = 1.565\cdot \left(\cos \frac{5\pi}{3} + i\,\sin \frac{5\pi}{3} \right)[/tex].

According to **complex analysis**, the *fourth* **roots** of a *complex* **number** can be found by **De Moivre's formula**:

[tex]\sqrt[n]{z} = \sqrt[n]{r}\cdot \left[\cos \left(\frac{\theta + 2\pi\cdot i}{n} \right)+ i\,\sin \left(\frac{\theta + 2\pi\cdot i}{n} \right)\right][/tex], for [tex]i = \{0, 1, ..., n - 1\}[/tex] **(1)**

Where:

r - Magnitude of the complex number.θ - Direction of the complex number, in radians.First, we find the **magnitude** and **direction** of the *complex* **number**:

[tex]r = \sqrt{(-3)^{2}+(3\sqrt{3})^{2}}[/tex]

r = 6

[tex]\theta = \tan^{-1} \left(\frac{3\sqrt{3}}{-3} \right)[/tex]

[tex]\theta = \frac{2\pi}{3} \,rad[/tex]

Now we find the four *quartic* **roots** of the *complex* **number**:

[tex]z_{1} = 1.565 \cdot \left(\cos \frac{\pi}{6} + i\,\sin \frac{\pi}{6} \right)[/tex]

[tex]z_{2} = 1.565\cdot \left(\cos \frac{2\pi}{3} + i\,\sin \frac{2\pi}{3} \right)[/tex]

[tex]z_{3} = 1.565\cdot \left(\cos \frac{7\pi}{6}+i\,\sin \frac{7\pi}{6} \right)[/tex]

[tex]z_{4} = 1.565\cdot \left(\cos \frac{5\pi}{3} + i\,\sin \frac{5\pi}{3} \right)[/tex]

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Determine the output voltage of the op-amp circuit shown below:

The output **voltage** of the op-amp circuit shown is -5v.

It should be noted that **voltage** is the electric potential difference between two points l.

In this case, the **output voltage** will be:

= -5 × i

where I = 1.

**Voltage** = -5 × 1

= -5v

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Find the axis of symmetry:

Picture is below.

**Answer:**

x = -3

**Step-by-step explanation:**

Axis of symmetry is the vertical line that divides the parabola into two equal halves and it passes through the vertex of the parabola.

From the graph, Vertex (-3, 4)

Axis of symmetry: x = -3

A mail carrier can deliver mail to 36 houses in 30 minutes. Mark wants to determine how many houses the carrier can deliver mail to in 7.5 minutes at this rate. He thinks that to find the answer, he should do the following.

1. First divide 36 houses by 30 minutes to find a unit rate of 1.2 houses per minute.

2. Then multiply 1.2 houses per minute by 7.5 minutes to get 9 houses.

Mark's method is** correct, **because even though it is impossible to deliver **mail** to 1.2 houses in minute, it represents the** unit rate of houses per minute .**

The first step is to determine the **unit rate of houses per minute. **This can be done by **dividing **36 houses by 30 minutes.

36/30 = 1.2 houses per minute

The second step is to **multiply **1.2 by 7.5: 1.2 x 7.5 = **9 houses**

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How many fewer people live in Elmira than White Plains

*Population density* implies the **number** of an object, items, or people that can be found in a *unit area* at a particular time. Therefore, the **number** of fewer people that live in Elmira *than *in White Plains is 27,653.

*Population density* implies the total number of objects, items, or people that exist in a unit area or a place at a *particular time*. So that the number of people that *exist* in a place, area, city, or country can be referred to as population, in a particular period.

Thus in the given question, it can be deduced that;

The population of people living in White Plains =56,853

The population of people living in Elmira = 29,200

So, the difference in the population between the two cities can be determined as;

= 56,853 - 29,200

= 27,653

Thus, the number of fewer people living in Elmira than in White Plains is 27,653

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Solve the logarithmic equation by writing in exponential form or by

graphing.

log (5-2x) = 0

**Answer:**

Hello,

**Step-by-step explanation:**

[tex]log(5-2x)=0\\\\\ \Longleftrightarrow\ 10^{log(5-2x)}=10^0\\\\\\\Longleftrightarrow\ 5-2x=1\\\\\Longleftrightarrow\ 2x=5-1\\\\\\\Longleftrightarrow\ x=\dfrac{4}{2}\\\\\\\Longleftrightarrow\ \boxed{x=2}\\[/tex]

Evaluate functions from their graph Problem g(3) =

See attached for the correct answer!

The notation g (3), left parenthesis, 3 refers to the output of the function when the input is x=. If the point (3, b) is on the graph, then g (3) =b.

We should look for the point on the graph whose x- coordinate is 3 is the point )3, 4).

The point on the graph whose x-coordinate is 3 is the point (3,4).

Therefore, g (3) = 4

The **value** of g(3) is g(3) = 4

The **function **value is given as:

g(x)

The **notation **g(3) implies that:

We determine the value of g(x) when x = 3

From the **graph**, the **function **has a point at (3,4)

This means that:

When x = 3, g(x) = 4

i.e. g(3) = 4

Hence, the **value** of g(3) is g(3) = 4

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Which equations can be used to find the lengths of the legs of the triangle? Select three options. 0.5(x)(x + 2) = 24 x(x + 2) = 24 x2 + 2x – 24 = 0 x2 + 2x – 48 = 0 x2 + (x + 2)2 = 100

The** equations** that can be used to find the lengths of the legs of the triangle are as follows:

The **equation** that can be used to find the length of the leg of the right triangle uses Pythagoras theorem,

Therefore,

**c² = a² + b²**

where

c = hypotenuse sidea and b are the other legsTherefore,

10² = (x + 2)² + x²

**100 = (x + 2)² + x²**

Therefore, using the area of a triangle,

area of a triangle = 1 / 2 bh

where

b = baseh = heightTherefore,

area of the triangle = 1 / 2 × (x + 2)(x)

**24 = 0.5 × (x + 2)(x)**

24 = x² + 2x / 2

cross multiply

48 = x² + 2x

**x² + 2x - 48 = 0**

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SKETCHPAD

Question 5

Given AABC shown on the coordinate plane below.

AA"B"C" = Ro (T(-4,3)(ABC))

90°

Draw AA'B'C'' if

You may use different colors for the separate transformations. Indicate your final

answer. Feel free to use the Dynamic Geometry Tool to complete the

transformations.

The attached figure represents the image of A"B"C" after the **transformation**

The **transformation rule **is given as:

A"B"C" = Ro90° (T(-4,3)(ABC))

This means that we **rotate **the **triangle 90 degrees clockwise**, and then translate the **triangle**

From the figure, the **coordinates **of ABC are

A = (-1, 2)

B = (1, 4)

C = (3, -1)

The rule of **90 degrees clockwise rotation **is

(x,y) ⇒ (y,-x)

So, we have

A' = (2, 1)

B' = (4, -1)

C' = (-1, -3)

The **translation **of the **triangle** by T(-4,3) is

(x,y) ⇒ (x - 4, y + 3)

So, we have

A'' = (-2, 4)

B'' = (0, 2)

C'' = (-5, 0)

See attachment for the image of the **transformation**

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If cot theta = 3/2, what is the value of csc theta?

The **value **of **csc theta **is [tex]\frac{3. 61}{2}[/tex]

It is important to note that the ratio for cot is given as;

Cot theta = adjacent/opposite

cosec theta = hypotenuse/opposite

If cot theta = 3/2, then

Adjacent = 3

Opposite = 2

Using Pythagoras theorem, we have

Hypotenuse square = opposite + adjacent square

[tex]H = \sqrt{2^2 + 3^2}[/tex]

[tex]H = \sqrt{4 + 9}[/tex]

[tex]H = 3. 61[/tex]

Cosec theta = [tex]\frac{3. 61}{2}[/tex]

Thus, the **value **of **csc theta **is [tex]\frac{3. 61}{2}[/tex]

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**Answer:**

3.16/2

**Step-by-step explanation:**

Have a great day

If f(x) = x and g(x) = 2, what is (fog)(x)?

**Step-by-step explanation:**

=fog(x)

−2x=0

x(x−2)=0

x=0,2

Explain how to determine if Carlos’s allowance is directly proportional to the number of chores he completes.

A 2-column table with 3 rows. Column 1 is labeled number of chores with entries 10, 13, 15. Column 2 is labeled Allowance with entries 75 dollars, 97 dollars and 50 cents, 112 dollars and 50 cents.

Using a** proportional relationship**, it is found that Carlos earns an **allowance of $7.5 for each chore** that he completes.

A proportional relationship is a **function **in which the output variable is given by the input variable multiplied by a constant of proportionality, that is:

y = kx

In which **k **is the constant of proportionality.

In this problem, the **constant **is:

k = 75/10 = 97.5/13 = 112.5/15 = 7.5.

Hence Carlos earns an **allowance of $7.5 for each chore** that he completes.

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f(x) = √2x

g(x) = √8x

Find (f g)(x). Assume x ≥ 0.

OA. (f g)(x) = 4x

OB. (f g)(x) = 8x

O C. (f g)(x) = 4√√x

OD. (f.g)(x) = √/10x

**Answer:**

**Step-by-step explanation:**

hello :

f(x) = √(2x)

g(x) = √(8x)

(f g)(x) = f(x)×g(x) =√(2x)×√(8x) = √(16x²) =4/x/

x ≥ 0: /x/ = x ** (f g)(x) = 4x....**..(answer : A)

A jar contains 100ml of a mixture of oil and water in the ratio 1:4. Enough oil is added to make the ratio of oil to water 1:2. How much water must be added to make the ratio oil to water 1:3?

**Answer:**

**Step-by-step explanation:**

Initial volume of mixture is **100 ml **with oil to water **ratio of 1 : 4**.

First, let's **find the volume of each component**.

If the **oil is x** then **water is 4x** according to ratio and their sum is 100 ml:

So, we have **20 ml of oil** and **80 ml of water**.

Now, let's added volume of oil be **y**. Then we have **the ratio**:

So, we have **40 ml of oil** and **80 ml of water.**

Lastly, let's **added water be z**. Then we have the **ratio**:

We must add **40 ml of water**.

10 - 13x + 2 in words

The simplification of the equation above in words is = **Twelve minus thirteen X.**

In mathematics, **coefficients** are those numbers that multiplies a variable. For example in 13x, the coefficient is **13** which multiplies a variable known as **X**.

The equation given is,

**10 - 13x + 2**

Arrange the **digits** without a coefficient together.

That is ,

10+2 -13x

12 - 13x

Therefore the simplification of the given equation in words is **Twelve minus thirteen X.**

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Select all of the following that are quadratic equations.

5x-1=3x+8

5 x- 3 = 0

x²-2x = 4x+1

2x²+12 x = 0

x³-6x² + 8 = 0

9x²+6x-3=0

The **quadratic equations** among all the options given are [tex]x^{2} -2x=4x+1[/tex],[tex]2x^{2} +12x=0[/tex] and [tex]9x^{2} +6x-3=0[/tex].

Given six **equations** as under:

We are required to find the **quadratic** equations among the above equations.

Quadratic equations are those **equations** in which the highest power of the **variable** present in the equation is 2.

It is in form of [tex]ax^{2} +bx+c=0[/tex].

In our options quadratic equations are [tex]x^{2} -2x=4x+1[/tex],[tex]2x^{2} +12x=0[/tex] and [tex]9x^{2} +6x-3=0[/tex].

5x-1=3x+8: It is not a quadratic equation as the highest **power** is 1.

5 x- 3 = 0:It is also a linear equation not quadratic equation.

x³-6x² + 8 = 0:It is a cubic equation not a quadratic equation.

Hence the **quadratic equations** among all the options given are [tex]x^{2} -2x=4x+1[/tex],[tex]2x^{2} +12x=0[/tex] and [tex]9x^{2} +6x-3=0[/tex].

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