1.39 to 1 decimal point

The equation of the quadratic function is f(x) = x²+ 2/3x - 1/9

From the question, the given parameters are:

Roots = (-1 - √2)/3 and (-1 + √2)/3

The quadratic equation is then calculated as

f(x) = The products of (x - roots)

Substitute the known values in the above equation

So, we have the following equation

[tex]f(x) = (x - \frac{-1-\sqrt{2}}{3})(x - \frac{-1+\sqrt{2}}{3})[/tex]

This gives

[tex]f(x) = (x + \frac{1+\sqrt{2}}{3})(x + \frac{1-\sqrt{2}}{3})[/tex]

Evaluate the products

[tex]f(x) = (x^2 + \frac{1+\sqrt{2}}{3}x + \frac{1-\sqrt{2}}{3}x + (\frac{1-\sqrt{2}}{3})(\frac{1+\sqrt{2}}{3})[/tex]

Evaluate the like terms

[tex]f(x) = x^2 + \frac{2}{3}x - \frac{1}{9}[/tex]

So, we have

f(x) = x²+ 2/3x - 1/9

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Step-by-step explanation:

x + 3y = 1

x = 1 - 3y-(i)

7x + 8y = 11

x= 11-8y/7-(ii)

substituting eqn (i) in eqn (ii)

11-8y/7= 1-3y

11-8y=7-21y

13y=-4

y=-4/13

putting the value of y in eqn (i)

x=1-(-12/13)

x=25/13

Answer:

1. 4:3

2. 5:7

3. 9:4

4. 3:5

5. 7:12

Step-by-step explanation:

I'm sure you don't care how to get the answers, you just want them :)

The net amount due on the order after partial payment done is $8700

Given,

A retailer purchases some merchandise;

The invoice price for the merchandise = $19,500

Terms of sale for the merchandise = 5/15, n/45

On 15th day partial payment done = $10,800

We have to find the net amount due on the order after partial payment is done.

Here,

Net amount due = Invoice price - Partial payment

Net amount due = 19,500 - 10,800

Net amount due = 8700

That is,

The net amount due on the order after partial payment done is $8700

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Answer:

Step-by-step explanation:

Factorize the polynomial using the given details.

Since one of the factors known, try to factor it out and futher:

Find its zero's:

Answer:

[tex]x=1, \quad x=\dfrac{3}{2}, \quad x=2[/tex]

Step-by-step explanation:

Factor Theorem

If f(x) is a polynomial, and f(a) = 0, then (x – a) is a factor of f(x).

If the coefficients in a polynomial add up to 0, then (x - 1) is a factor.

Given polynomial function:

[tex]f(x)=2x^3-9x^2+13x-6[/tex]

Sum the coefficients:

[tex]\implies 2-9+13-6=0[/tex]

As the sum of the coefficients is zero, (x - 1) is a factor.

Therefore:

[tex]\implies f(x)=(x-1)(ax^2+bx+c)[/tex]

Expand the brackets:

[tex]\implies f(x)=ax^3+bx^2+cx-ax^2-bx-c[/tex]

[tex]\implies f(x)=ax^3+(b-a)x^2+(c-b)x-c[/tex]

Compare the coefficients with the given polynomial.

As the coefficient of the leading term of the polynomial is 2:

[tex]\implies a=2[/tex]

As the coefficient of the term in x² is -9:

[tex]\implies b-a=-9[/tex]

[tex]\implies b-2=-9[/tex]

[tex]\implies b=-7[/tex]

As the constant of the given polynomial is -6:

[tex]\implies c=6[/tex]

Substitute the found values of a, b and c into the factored form of the polynomial:

[tex]\implies f(x)=(x-1)(2x^2-7x+6)[/tex]

Factor the quadratic:

[tex]\implies 2x^2-7x+6[/tex]

[tex]\implies 2x^2-4x-3x+6[/tex]

[tex]\implies 2x(x-2)-3(x-2)[/tex]

[tex]\implies (2x-3)(x-2)[/tex]

Therefore, the fully factored polynomial is:

[tex]\implies f(x)=(x-1)(2x-3)(x-2)[/tex]

To find the zeros, set the function to zero:

[tex]\implies f(x)=0[/tex]

[tex]\implies (x-1)(2x-3)(x-2)=0[/tex]

Apply the zero-product property:

[tex]\implies x-1=0 \implies x=1[/tex]

[tex]\implies 2x-3=0 \implies x=\dfrac{3}{2}[/tex]

[tex]\implies x-2=0 \implies x=2[/tex]

Therefore, the real zeros of the given polynomial are 1, ³/₂ and 2.

In linear equation,  R = 4c is an equation to represent the amount R Natalia and her friends raised after selling c cakes.

What are a definition and an example of a linear equation?

The equation that will represent the amount raised after selling the cakes to be written in slope-intercept form is given as .

Where,

y = R (amount of cake sold in dollars)

x = c (cakes sold)

m = slope

b = y-intercept.

The equation would look like

R = mc + b

We need to find the value of m and b, to get an equation to represent the situation.

The first point we have from the information given is (15, 60) => 15 cakes sold for $60.

The second point is (22, 88) => 22 cakes sold for $88.

Slope(m) = 88 - 60/22 - 15 = 28/7 = 4

To find b, substitute c = 15, R = 60 and m = 4, into R = mc + b

  60 = 4(15) + b

  60 = 60 + b

   b = 0

Since b = 0, this means there is a proportional relationship between R and c.

Substitute m = 4 and b = 0 into   R = mc + b to derive an equation to represent the amount R Natalia and her friends raised after selling c cakes.

    R = 4c + 0

    R = 4c

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Using concepts of statistics, we got 7% people are from age 18-24,and 15% for criminal arrests,65 and older are in 13% population and cover less than 1% crime rate.

The topic of crime in the United States is very large, technically covering any action that is punishable under a state or federal law. Any analysis of the topic  requires division into further sub-categories. One common way to do this is  by limiting analysis to crimes involving jail time (i.e. misdemeanors and felonies, which generally differ via the length of jail time involved), then differentiate between violent crimes or property crimes. Violent crimes are described as offenses which involve force or the threat of force, while property crime majorly includes offences involving the taking of money or property, but where there is not any  force or threat of force against the victims. Property crimes are outnumbering violent crimes in the U.S. in 2020, numbering 6.45 million and 1.31 million respectively. Larceny was the actually most common property crime with 4.6 million incidents, while the aggravated assaults accounted for around two thirds of violent crimes.

Hence, percentage of people whose age is in between 18-24 is 7%,

people from age 18-24 engaged in illegal work=15%,

percentage of people whose age is 65 or more than =13%,

people involved in crime having age more than or equal to 65=1%

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The angle measures in this problem are given as follows:

1. Angle SVT: 79º.

2. Angle BEC: 65º.

Angles SVT and SVR are vertical, meaning that they have the same measure, hence we can find the value of y as follows:

8y - 33 = 5y + 9

3y = 42

y = 42/3

y = 14.

Hence the measure of the angle SVT is of:

m<SVT = 5y + 9 = 5(14) + 9 = 79º.

The two angles given in this problem are also vertical, meaning that we can solve for x as follows:

5x - 10 = 3x + 40

2x = 50

x = 50/2

x = 25º.

Then the bottom angle is:

3 x 25 + 40 = 115º.

The bottom angle is supplementary with angle BEC, hence we can find the measure of angle BEC as follows:

115 + m<BEC = 180

m<BEC = 180 - 115

m<BEC = 65º.

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The given scatterplot has no correlation. This is because there is no pattern among the dots on the scatterplot.

Correlation is a measure that is used in statistics to measure the linear relationship that exists between two variables. Correlation can either be positive, negative or zero. The closer the correlation coefficient is to one, the higher the correlation.

Positive correlation is when two variables move in the same direction. When drawn on a scatterplot, the line of best fit is upward sloping. The coeffect of correlation for positive correlation is always positive.

Negative correlation is when two variables move in different directions.  When drawn on a scatterplot, the line of best fit is downward sloping. The coeffect of correlation for negative  correlation is always negative.

Zero correlation or no correlation is when there is no relationship between the variables. When drawn on a scatterplot, there is no discernible patterns among the variables.

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Answer:

B. Opposite angles in a parallelogram are congruent.

Explanation:

The figure shows a parallelogram. In this parallelogram, ∠R and ∠T are opposite angles and ∠Q and ∠S are opposite angles.

Since the information says that ∠R is congruent to ∠T and ∠Q is congruent to ∠S, the theorem is opposite angles in a parallelogram are congruent.

So, the answer is B. Opposite angles in a parallelogram are congruent.

The given elevation of New Orleans of 2 feet below sea level gives the possible elevation of Salton City by using a number line, as 3 feet below sea level.

A number line pictorially presents the set of real numbers, showing their position in order of their magnitude, such that the numbers increases positively as we move from left to right with negative numbers increasing from the zero mark as we move further left.

The given elevation of New Orleans with reference to the sea level = 2 feet below (lower than) sea level

The elevation of Salton City = Lower than the elevation of New Orleans

Required; The possible elevation of Salton City

The elevation of Salton City can be found by presenting the given information on a number line as follows;

Let SL represent the sea level, let N represent New Orleans and let S represent Salton City, we have;

<___|-3______|-2____|0______>

' S. N. SL

A level higher than the elevation of New Orleans is given by a point to the right of the -2 mark on the above number line, while an elevation lower than that of New Orleans is given by a point to the left of -2 on the number line. The location of Salton City should therefore be to the left of -2, which is a point, x < -2 feet

The elevation of Salton City is less than 2 feet below sea level, which is given by the set x < -2 feet

-3 feet is less than -2 feet, therefore, a possible elevation in feet of Salton City is x = 3 feet below sea level, which is less than (<) 2 feet below sea level

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72.1232 rounded to the nearest thousandth is 72.123.

The term "rounding to the nearest thousandth" refers to the practice of rounding any decimal number to the next thousandth value. Thousandth in the decimal system signifies (1/1000) or 0.001. 3.125, for example, is the number 3.1249 rounded to the closest thousandth.

To round it to the closest thousandth, we must focus on the number following this spot - tens of thousandths. This figure will determine whether we round up or round down. "Five and above go up like a bird," as the phrase goes. Therefore, this will give a value of 72.123.

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In a case whereby I baked a cake for my siblings ad  My brother ate large fraction 1/8 of the cake and my sister ate \large frac 3/4 ,  the amount of cake is left for me is 1/8.

In this question , we are dealing with fraction, which implies that the number of the cake that i am having is 1.

And we are told that 1/8 of the cake is been eaten by my brother, where 3/4 of the cake is been eaten by my sister, then to know the amount of cake that was left for me, we will need to perform some simplification as:

1-(1/8) - (3/4) =1/8.

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If a cake is baked, In which her brother ate 1/8 and sister ate 3/4. Then 1/8 of cake is left me.

A fraction represents a part of a whole

Given that a cake was baked for her  siblings.

Her big brother ate large part of the cake that is 1/8.

Her sister ate 3/4 of the cake.

We need to find the left out cake for her.

To do that we have to remove 1/8 and 3/4 from 1.

1-(1/8)-(3/4)

(8-1-6)/8

1/8

Hence she has 1/8 of cake which is left.

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The points that he average on the last two tests will be 93 points.

A mean is the average of the set of numbers that are given.

On the first five tests that he took, he averaged 86 points. The total points will be:

= 86 × 5

= 430 points

He averaged 88 points on all seven tests. The total will be:

= (88 × 7)

= 616 points

The point average on the last two tests will be:

= (616 - 430)/2

= 186/2

= 93 points

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The value of (f- g)(x) is  2x - 26.

This is a question of subtraction of functions.

Subtraction of functions

The subtraction of function involves the creation of a new function through the addition of two other functions.

Subtraction of one real-valued function from another.

Let h: X → and p: X → be any two real functions, where X ⊆ Real numbers. Then, we can define h - p: X → by h - p x = h(x) – p(x), for all x ∈ X.

Given that:-

f(x) = 2x + 1

g(x) = 27

We have to find the value of (f- g)(x)

We know that,

(f- g)(x) = f(x) - g(x)

Hence, we can write,

(f- g)(x) = 2x + 1 - 27 = 2x - 26

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Answer:

[tex] 7^2[/tex]

Step-by-step explanation:

Answer:

7²

Step-by-step explanation:

the product of a number and its multiplicative inverse is equal to 1 , that is

a ×[tex]\frac{1}{a}[/tex] = 1

given

[tex]7^{-2}[/tex] , then multiplicative inverse is [tex]\frac{1}{7^{-2} }[/tex] = 7² and

[tex]7^{-2}[/tex] × 7² = [tex]7^{0}[/tex] = 1

Rule for a dilation with center (0,0)

k is the scale factor.

For point P (0,3):

Plotted Answers:

12.) See attached for my work

13.) See attached for my work

14.) See attached for my work

Simplified Answers:

12.) y > –24

13.) x ≥ –12

14.) x > –7

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The equivalent expression of  4(8g + 5) + 6 is 4(5 + 8g) + 6

Equivalent expressions are expressions that work the same even though they look different.

In other words, two expressions are said to be equivalent if they have the same value irrespective of the value of the variable(s) in them.

Therefore, let's find the equivalent expression of 4(8g + 5) + 6.

Hence,

4(8g + 5) + 6

32g + 20 + 6

32g + 26

Hence, the equivalent expression is 32g + 26 or 4(5 + 8g) + 6

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Answer:

6.25 weeks

Step-by-step explanation:

Take 18.75 ÷ 3. The construction crew finishes 3 km per week. You should receive 6.25 by solving the equation. So, this is the answer.

The given polynomials are as ,

We have to subtracrt these given polynomials,

Option D is correct.

⇒Given that the general rule to find the nth term is

[tex]T_{n} =-2+6(n-1)[/tex]

⇒To find the 11th term this means that they need a term which is in the position 11

⇒To get the number we plug in the 11 which is the position in the place of n and simplify.

[tex]T_{11} =-2+6(11-1)\\T_{11} =-2+6(10)\\T_{11} =-2+60\\T_{11} =58[/tex]

The 11th term is 58

Goodluck!!!

The measure of ∠ A is 44 degrees.

Given that:-

∠ A and ∠ B are complementary angles.

∠ A = (6x +2) degrees

∠ B = (4x + 18) degrees

We have to find the measure of ∠ A.

We know that the sum of two complementary angles is 90 degrees.

Hence, we can write,

(6x + 2) + (4x + 18) = 90

(6x + 4x) + (2 + 18) = 90

10x + 20 = 90

10x = 90 - 20

10x = 70

x = 70/10

x = 7 degrees

Hence,

∠ A = 6*7 + 2 = 42 +2 = 44 degrees.

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Here, 144=12×12=12². Therefore, 144 is a perfect square.

The given numbers are 29, 78, 144 and -6.

A perfect square is a positive integer that is obtained by multiplying an integer by itself. In simple words, we can say that perfect squares are numbers that are the products of integers by themselves.

By perfect square definition

29=29×1

78=2×2×17

144=2×2×2×2×3×3=12×12

-6=-2×3

So, from the above factors it is clear that, 144 is a perfect square.

Here, 144=12×12=12². Therefore, 144 is a perfect square.

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Given the following function:

f(x) = 3x - 3

Let's determine the value at f(-3),

This means that we will be replacing all x variables of f(x) by -3.

We get,

f(x) = 3x - 3

f(-3) = 3(-3) - 3

= -9 - 3

f(-3) = -12

Therefore, f(-3) = -12

Given the following function:

f(x) = 3x - 3

Let's determine the value at f(-3),

This means that we will be replacing all x variables of f(x) by -3.

We get,

f(x) = 3x - 3

f(-3) = 3(-3) - 3

= -9 - 3

f(-3) = -12

Therefore, f(-3) = -12

When the remainder is zero, the statement that isn't true is that C. The solution of the divisor is a zero.

A dividend simply means the value that is divided by another value in order to far the result. It is the base of the division problem.

For example, 12 divided by 6 is 2. In this case, 6 is the dividend. 6 is a factor of 12.

Therefore, the correct option is C

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Answer:

3500

Step-by-step explanation:

split 7000 in half for stocks and treasury= 3500 each.

7 percent on 3500 is 3724, 7 percent of 3500 is 245 dollors. 535 x 7 is 3745 = 3500 invested in treasury.

The average cost of each book that Nancy got is $32

Cost refer to the amount or value of a product. cost is usually valued in money hence one has to pay some money to h]]get the commodity of choice

In the question, the commodity is mundane books

given that

Nancy had 209 dollars to spend

number of books = 6

amount remaining after buying = $17

The question can be represented mathematically as

6x + 17 = 209

where x is the cost of the each book

6x + 17 = 209

6x = 209 - 17

6x = 192

dividing through by 6

6x / 6 = 192 / 6

x = 32

hence each book costs $32

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Answer:

n>-1/40

Step-by-step explanation:

Hope this helps!! (I promise...it's the right one)

Answer:

b) n > (-1/40)

Step-by-step explanation:

Given equation,

→ n - (3/8) > (-2/5)

Now the value of n will be,

→ n - (3/8) > (-2/5)

→ n > (-2/5) + (3/8)

→ n > (-16/40) + (15/40)

→ n > (-16 + 15)/40

→ [ n > (-1/40) ]

Hence, value of n is -1/40.