E is the midpoint of DF¯¯¯¯¯, DE=6x+1 and EF=7x−4. Find DE, EF, and DF.

31, 31, 56
37, 37, 74
31, 31, 62
22, 22, 44

Parallel lines have the same slope, so the slope is 5.

The equation in point-slope form is y-10=5(x-3). Substituting x=0, we get y - 10 = -15, and thus the y intercept is (0, -5).

The function f (x) = (x - 13)² is shifted 13 units to the left, the function f (x) = | x + 6 | is shifted 6 units to the right and the function f (x) = | x - 4| is shifted 4 units to the left from the parent function.

We are given the following functions:

f (x) = (x - 13)²  …(1)

f (x) = | x + 6 |  …(2)

f (x) = | x - 4|    …(3)

We need to find the transformations for the given functions.

For function (1), we get that:

It is shifted 13 units to the left.

For function (2), we get that:

It is shifted 6 units to the right.

For function (3), we get that:

It is shifted 4 units to the left.

Therefore, we get that, the function f (x) = (x - 13)² is shifted 13 units to the left, the function f (x) = | x + 6 | is shifted 6 units to the right and the function f (x) = | x - 4| is shifted 4 units to the left from the parent function.

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Answer:

I think the answer is 11 in my opinion

Answer:

C. -5/6x+(8)

Step-by-step explanation:

mmmm math, love me some math, love me math, mmmm

[tex]x^{3} / y^{6}[/tex] is the simplest form

The expression is

[tex](x^{1/3 }/ y^{2/3} ) ^{9}[/tex]

We have to multiply the root of 9 with the root of the numerator and denominator.

So we will get

[tex](x^{1/3} )^{9} /( y^{2/3})^{9}[/tex]

[tex]x^{1/3*9} / y^{2/3 *9}[/tex]

We will get

[tex]x^{9/3} /y^{18/3}[/tex]

=[tex]x^{3} / y^{6}[/tex]

So now we get the equation in the simplest form in the form of x and y

i.e [tex]x^{3} / y^{6}[/tex]

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The unit price of strawberries at the grocery mart is $1.5, the unit price of strawberries at the Baldwin hills is $1.30

In order to get the unit price of an item, you would have to divide the cost of the item by the total quantity bought.

With this definition, at the grocery mart

price = 2.99 dollars

quantity bought = 2

unit price = 2.99 / 2

= 1.5 dollars

At the Baldwin hills

price = 3.99 dollars

quantity bought = 3

unit price = 3.99 / 3

= $1.30

Hence the unit prices at the two markets are $1.5 and $1.30

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At Grocery Mart,strawberries cost $2.99 for 2lb., and at Baldwin Hills Market strawberries are $3.99 for 3 lb.What is the unit price of strawberries at each grocery store? If necessary , round to the nearest penny.

According to the question, the polynomial equation that is [tex]x^{4}+3x^{3}+16x^{2} -19x+8[/tex] is divided by the binomial [tex]x-1[/tex]. And in this, the coefficient of [tex]x^{2}[/tex] in the quotient is [tex]2[/tex].

The given expression can be written as:

Expression = [tex]\frac{x^{4}+3x^{3}+16x^{2} -19x+8}{x-1}[/tex]

Now, find the factors of the numerator term:

f(x) = [tex]x^{4}+3x^{3}+16x^{2} -19x+8 = (x-1)(x^{3}+4x^{2} -11x-30 )[/tex]

From the above equation, the coefficient of [tex]x^{2}[/tex] is [tex]4[/tex].

The solution for the given expression is [tex]4[/tex].

What is polynomial function?

Polynomial functions are those function whose variables contains varying degrees as well as non-zero coefficients and positive integers. It has different forms like quadratic equation or cubic equation etc.

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Answer:

[tex]270.33\%[/tex]

Step-by-step explanation:

so generally when we want to calculate how much "percent" a number is of another number we do, [tex]100(\frac{part}{whole})[/tex]

In this question, it's asking what percent of 182 is 492, and this wording might be a bit tricky at first. It might help a bit to reword it into, "492 is what percent of 182"

So in this question, the 492 is the part (despite it being bigger), and 182 is the whole

So now we use the equation: [tex]100(\frac{part}{whole})=100(\frac{492}{182})\approx270.33\%[/tex]

The values of a and b are - 2 and 5, respectively.

In this problem we must expand the quadratic polynomial and find the values of two coefficients by direct comparison, the complete procedure is now introduced:

x² - 4 · x + 9 = (x + a)² + b

x² - 4 · x + 9 = x² + 2 · a · x + a² + b

Then, by direct comparison, we find the following system of equations:

2 · a = - 4            (1)

a² + b = 9            (2)

By (1):

a = - 2

(1) in (2):

b = 9 - a²

b = 9 - (- 2)²

b = 5

The values of a and b are - 2 and 5, respectively.

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Answer:

x > -6.

Step-by-step explanation:

-3x < 18

Divide both sides by -3.

x > -6.

(Note that the sign is flipped as we are dividing by a negative quantity).

Answer:

1/8th

10 litres

Step-by-step explanation:

There are two values of b such that the minimum value of the function is - 1, then the solutions are b₁ = - 2 and b₂ = 2, respectively.

In this problem we know a quadratic equation of the form g(x) = x² + b · x, of which we must determine the value of b such that the y-value of the minimum is - 1. Graphically speaking, quadratic equations are represented by parabolae, which have either a minimum or a maximum know as vertex.

First, we must determine the vertex form of the equation of the parabola:

y = x² + b · x

y = x² + 2 · (b / 2) · x

y + b² / 4 = x² + 2 · (b / 2) · x + b² / 4

y + b² / 4 = (x + b / 2)²

The coordinates of the vertex are (h, k) = (- b / 2, - b² / 4). Then, the y-coordinate of the vertex is:

- b² / 4 = - 1

b² / 4 = 1

b² = 4

b = ± 2

There are two values of b such that the minimum value of the function is - 1, then the solutions are b₁ = - 2 and b₂ = 2, respectively.

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The value of x is 1.14 or x = -1.47

We find the value of x in the quadratic equation 3x^2 +x-5=0

Using the formula: (-b ± √ (b²- 4 a c)) / (2a)

Where the value of a = 3, b = 1 and c = -5

Substituting the above values (a = 3, b = 1 and c = -5)

in the formula:

(-1 ± √ (1²- 4 3 (-5))) / (2*3)

= (-1 ± √ (1+60)) / (6)

= (-1 ± √ (61)) / (6)

= (-1 ± 7.81) / (6)

= (-1 + 7.81) / (6) or (-1 -7.81) / (6)

= (6.81) / (6) or (-8.81) / (6)

=1.135 or -1.468

Hence the value of x= 1.14 or -1.47

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According to the question, to write the solution for the logarithmic function, the concept of indices is also needed.

Therefore, the given expression is [tex]ex^{-2}=12[/tex]

The values get multiplied in addition. Therefore, the above expression can be written as by taking log on both the sides:

[tex]ln(ex^{-2} )=ln(12)\\-2(ln(e)+ln(x)) = ln(4)+ln(3)= 2ln(2)+ln(3)[/tex]

Using logarithmic definition, we can write:

The solution for the given expression is [tex]-2(1+ln(x)) = 2+ln(3)[/tex]

What is logarithmic function?

In terms of mathematics, the logarithmic function can be defined as the inverse of exponential function. It is always on the positive side of the ordinate axis.

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The true statements about the integer are:

The statement is given as

The sum of -5 and another integers is a positive integer

Let the other integer be x

So, we have

The sum of -5 and x is a positive integer

A positive integer is greater than 0

So, we have

-5 + x > 0

Add 5 to both sides of the inequality

So, we have

x > 5

The above means that x is greater than 5

Hence, the sign of the integer is positive

The statement is given as

The sum of -5 and another integers is a positive integer

Let the other integer be x

So, we have

The sum of -5 and x is a positive integer

A positive integer is greater than 0

So, we have

-5 + x > 0

Add 5 to both sides of the inequality

So, we have

x > 5

The above means that x is greater than 5

Hence, the value of the integer is greater than 5

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The equation which gives relation between entry fee collected and number of visitors in theme park: f = 6v.

The given condition is;

The total collect cost for entry in theme park =  $900.

The total number of visitors = 150.

Let 'f' be the collected fee.

Let 'v' be the number of visitors.

Then, the amount collected varies directly with the number of visitors on a particular day.

f ∝ v

Removing proportional will bring the constant k;

f = kv  .......eq1

v = 150 and  f = 900

Put the values;

900 = 150 k

k = 6  ; put in eq 1.

f = 6v

Thus, the relation between fee and number of visitors is given by equation; f = 6v.

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The radius of each cylinder is approximately 3.49 cm and the length of the plastic strip is approximately 65.84 cm.

Cylinder is a basic 3 dimensional solid with a curved surface. A cylinder can be identified as a prism with circular base.

The cross-section of a cylinder gives a circle whose area can be represented by πr² where r is the radius of the base of the cylinder.

Here the plastic wire encloses the area of cross-section of three cylinders.

Therefore area of cross-section of one cylinder=115÷3=(115/3) cm ²

Since area of cross-section of a cylinder=πr²

Therefore πr²=(115/3)

or, r=3.4931...

or, r≈3.49 cm

Hence the radius of each cylinder is approximately 3.49 cm

Now the plastic strip covers 3 cylinders .

Circumference of each cross-section of cylinder is given by =2πr

Total length of 3  cylinders = 2πr×3 = 6πr cm

Therefore total length= 64.843...cm ≈ 65.84 cm

Therefore the length of the plastic strip is approximately 65.84 cm

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The required total amount paid for magazine and pencil is 108p.

Simplification generally means finding an answer for the complex calculation that may involve numbers on division, multiplication, square roots, cube  roots, plus and minus.

Now it is given that,

Costing of a magazine = 83p

Costing of pencil = 45p

Thus, Total costing = Costing of a magazine + Costing of pencil

Putting the values we get,

Total costing = 83p + 45p = 128p

Now voucher gives 20p off

So, Final Costing = Total costing - Voucher off

⇒ Final Costing = 28p - 20p

⇒ Final Costing = 108p

this is the equired total amount paid for magazine and pencil.

Thus, the required total amount paid for magazine and pencil is 108p.

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For the given word problem on the recommended weight of a soccer ball, we have:

An absolute value equation can be defined as a type of equation that consist of an algebraic equation, which is placed within absolute value symbols.

In order to write and solve this absolute value equation, we would assign a variable (x) to the actual weight and then evaluate the resulting algebraic equation as follows:

Let x represent the actual weight.

Next, we would write an absolute value equation as follows:

|x - 430| ≤ ±20

-20 ≤ x - 430 ≤ 20

By applying the addition property of inequalities, we have:

x ≤ 430 - 20

Minimum acceptable soccer weights, x = 430 - 20 = 410 grams.

x ≤ 430 + 20

Maximum acceptable soccer weights, x = 430 + 20 = 450 grams.

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Answer:

A

Step-by-step explanation:

3x-8y+2x^2+3y-8x

2x^2-5x-5y

Answer:

4, 8, 12, 16, 20, 24, 28,32, 36, 40, 44, 48, 52

Transformation of y= b*x into y = 2.3 *x will take place by vertical dilation by a scale factor of  2.3.

A parent function is the simplest form of a particular family of functions. A family of operations is a group of tasks with the same highest degree and therefore the same graph shape.

Function transformations "move" "resize" or "mirror" the graph of the parent function.

Mathematically speaking, the transformation of the function y = f(x) is usually y = a f(b(x + c)) + d. where a, b, c, and d are arbitrary real numbers representing transformations. Note that all outer numbers (outside the brackets) represent vertical translations, and all inner numbers represent horizontal translations. Addition and subtraction are translations, and multiplication and division are dilations. Every time a minus sign is multiplied it means  it is a reflection here,  'a' stands for vertical stretch, 'b' stands for horizontal stretch, 'c' stands for horizontal movement, 'd' stands for vertical movement

We have given two functions y=b x  and y = 2.3x which means that first, y  changes into 2.3 x  i.e., vertical dilation by a scale factor of 2.3.

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Answer:

720

Step-by-step explanation:

A foot is 12 inches, so 60ft = 60(12) inches
60 x 12 = 720

The smallest amount that Caleb could have converted will be £ 59.

We are given that:

At shop A, Gavin converted £ 30 into € 36.60

At shop B, Amna converted £ 73 into € 86.14

Also, Caleb converted some pounds and got € 71.98.

Rate of conversion at shop A is:

£ 30 = € 36.60

£ 1 = € 36.60 / 30

£ 1 = € 1.22

rate of conversion at shop B is:

£ 73 = € 86.14

£ 1 = € 86.14 / 73

£ 1 = € 1.18

Now, we can see that the rate of conversion is more at shop A.

So, the smallest amount that Caleb might have converted will be:

Pounds = € 71.98 / € 1.22

Pounds = £ 59

Therefore, the smallest amount that Caleb could have converted will be £ 59.

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If mean is 276 yards, percentile is 80, sample mean is 290 yards then the standard deviation is equal to 16.63.

Given that mean is 276 yards, percentile is 80, sample mean is 290 yards.

We are required to find the value of standard deviation.

A Z-score is basically a numerical measurement that describes a value's relationship to the mean of a group of values.

Z=(X-μ)/σ--------1

Z score for 80th percentile is 0.842.

X is given as 290 and μ as 276.

We have to just put the values of mean and Z score in formula 1 to find the standard deviation.

0.842=(290-276)/σ

σ=14/0.842

σ=16.63

Hence if mean is 276 yards, percentile is 80, sample mean is 290 yards then the standard deviation is equal to 16.63.

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The possible values of x < 21.6.

When two mathematical statements or two numbers are compared in an unequal way, it is known as inequality in mathematics. Inequalities can generally be classified as either algebraic or numerical or as a combination of the two. When a polynomial of degree 1 is compared to another algebraic expression of a degree less than or equal to 1, this is an example of a linear inequality, which is an inequality involving at least one linear algebraic expression. Different types of linear inequalities can be represented in a number of different ways. As with multi-step linear equations, start by separating the variable from the constants when resolving multi-step linear inequalities with one variable. According to the laws of inequality, it is crucial that we remember to flip the inequality sign when multiplying or dividing with negative values while resolving multi-step linear inequalities.

so, from the question, the equation becomes,

x+15.5+14.2<51.3

x= 51.3-29.7

x= 21.6 Inches

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