The question is attached below - Attached below

The notations correctly describe the end behavior of the polynomial graphed is,

x → -∞ ⇒ f(x) → -∞

x → ∞ ⇒ f(x) → -∞

What is end behavior of polynomial?

The polynomial function's leading term can be used to determine the end behavior. The behavior of the leading term will dominate the graph because it has the highest power, which means it will grow significantly faster than the other terms as x gets very large or very small.

From the graph we know that the vertex of this parabola is V(0, 8).

This is a maximum y-value. We also know that the parabola opens downward, so the leading coefficient is negative.

Given that the function is even and the leading coefficient is negative, it follows that the graph falls to the left and right.

In a mathematical language this is:

x → -∞ ⇒ f(x) → -∞

x → ∞ ⇒ f(x) → -∞

Hence, the notations correctly describe the end behavior of the polynomial graphed is,

x → -∞ ⇒ f(x) → -∞

x → ∞ ⇒ f(x) → -∞

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The equation of the normal line of the curve f(x) = x³ - 14x² + 64x - 93 at point (3,0) is y = (-1/7) x +3/7

The slope of a tangent line of a curve at a given point is equal to its derivative at that point.

The normal line is a line which perpendicular to tangent line. Two lines are perpendicular to each other if the product of their slopes is equal to -1.

The equation of the curve is:

   f(x) = x³ - 14x² + 64x - 93

Take the derivative:

f '(x) = 3x² - 28x + 64

Therefore, the slope of the tangent line at point (3,0) is:

f '(3) = 3(3)² - 28(3) + 64 = 7

Hence, the slope of the normal line is:

m = -1/7

The equation of the normal line:

(y - 0) = (-1/7) (x - 3)

y = (-1/7) x +3/7

Your question is incomplete. Most likely, it was:

For each problem, find the equation of the line normal to the function at the given point. If the normal line is a vertical line, indicate so. Otherwise, your answer should be in slope-intercept form.

   f(x) = x³ - 14x² + 64x - 93 at (3,0)

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The least common denominator of the given fractions, can be found to be 72.

The least common denominator of two or more fractions, is the least common multiple of the denominators of the fractions.

With the given fractions of 3 / 8 and 5 / 18 therefore, the least common denominator would be the least common multiple of 8 and 18.

The least common multiple of 8 and 18 is the value of 72 so this must be the least common denominator for the fractions.

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Answer:

Step-by-step explanation:

The value of X is 45 because all the angles of a triangle add up to 180 degrees. The triangle is a right triangle as shown in the picture, the square in the corner of the triangle indicates this, any right angle is 90 degrees and when you minus 90 from 180 you get 90. Now, there are two more angles in the triangle so the value of X is 45, (90/2=45).

Answer: hoped this help. bye.:)

Answer: Part a= The probability of rolling a six on each roll is 1 in 6

So, a 100 in 600 chance but Julie has twice the probability.

So the die is most likely unfair,

Part b= Diagram is not attached to the question so to solve the first branch the probability of drawing show  each of the three colors from the five jellies

On the second draw, there are only four beans left and one of the three suits will be reduced by one. So while the probabilities of the first draw were fractions of 5, the probabilities of the second draw will be fractions of 4. The eight outcomes are the probability space of the two draws, which shows the composition of each event in the space and how likely that event is determined to be. Note that the sum of all eight probabilities is 1. You should be able to use this tree to find the answer to all the questions.

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we are looking for a point to the right of (4,7), the point P is (15/2, x+3) = (15/2, 21/2).

What is polynomial ?

A polynomial is a mathematical expression consisting of variables (also called indeterminates) and coefficients, that involves only the operations of addition, subtraction, multiplication, and non-negative integer exponents of variables.

Let P = (x, y) be a point on L that is four times as far from (2, 5) as it is from (4, 7). Since L contains P, we know that y = x + 3. We also know that the distance from P to (2, 5) is 4 times the distance from P to (4, 7). Using the distance formula, we get:

(x - 2)^2 + (y - 5)^2 = 4[(x - 4)^2 + (y - 7)^2]

Plug in y = x+3 and simplify the equation as ,

(x-2)^2 + (x+3-5)^2 = 4(x-4)^2 + 4(x+3-7)^2

x^2 - 4x + 4 + x^2 - 6x + 9 = 4x^2 - 32x + 48 + 4x^2 - 24x + 36

2x^2 - 30x + 97 = 0

Solving for x, we have x = 15/2 or x = -3/1

Since we are looking for a point to the right of (4,7), the point P is (15/2, x+3) = (15/2, 21/2).

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a) The slope of the line is given as follows: 0.5.

b) The meaning of the slope is that the volume increases by 0.5 gallons per minute.

The slope-intercept definition of a linear function is given as follows:

y = mx + b.

For which the parameters are given as follows:

From the graph, when x increases by 8, y increases by 4, hence the slope m is obtained as follows:

m = 4/8 = 0.5.

As x is the time in minutes and y is the volume in gallons, the meaning of the slope is that the volume increases by 0.5 gallons per minute.

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The method proposed is not fair, it can be adjusted by giving each sibling equal chance of winning.

What is algebra ?

Algebra is a branch of mathematics that deals with mathematical symbols and the rules for manipulating these symbols. It includes the study of operations such as addition, subtraction, multiplication, division, and the extraction of roots, as well as the properties of operations such as commutativity, associativity, and distributivity.

The method proposed by Alan is not fair because it does not take into account the probability of each outcome. The product of the outcomes being even or odd does not guarantee an equal probability of winning for both siblings. To make it fair, each sibling should have an equal chance of winning. A fair method could be to have the arrow spun once, and the sibling whose number is spun gets to choose the new pet. Another fair method could be to have a coin flipped, and the sibling whose side of the coin is facing up gets to choose the new pet.

So , The method proposed is not fair, it can be adjusted by giving each sibling equal chance of winning.

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As per the concept of estimation, Len's estimate and what is the actual sum of the numbers is 342

The rule for decimal in math is known as if the number after the decimal point is greater than or equal to 5 then we have to add one number to the whole number and remove the decimal terms.

Where as if the number after the decimal point is less than 5 then we have to simply remove the decimal term and the whole number is as it is the same.

So, here we have the nearest whole of 16.23 is written as 16 because here the decimal is less than 5, then it is same whole.

And the nearest whole of 215.7 is equal to 216 because here decimal is greater than 5, so we have to add 1 number

Now, the nearest whole of 110.3 is equal to 110 where as the decimal is less than 5 then it is same whole

Then the Estimated sum  is calculated as,

=> 16 + 216 + 110

=> 342

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Leading coefficient: 23

Degree: 8 (The degree of a polynomial is the highest power of the variable in the polynomial. In this case, the highest power of the variable "u" is 8, so the degree of the polynomial is 8.)

Answer:

i) 23

ii) 8

Step-by-step explanation:

i) leading coefficient:

23

ii) Degree

The degree of the polynomial is the highest power in the polynomial.

So,

degree of polynomial=8

If the number y is divided by x, the quotient is p and the remainder is r , then the relation between x,y,p,r is given by the expression [tex]y=xq+r[/tex]  .

What is Euclid's Division Lemma ?

The Euclid's Division Lemma states that for two positive integers , a and b , then there exist unique integers q and r such that : [tex]a=bq+r,\; \; where \; 0\leq r < b[/tex] ;

here , the number y is divided by x , that means , the divisor is "x" , the dividend is "y" ,

the quotient is denoted by "q" ;

and the remainder is denoted by  "r" ;

So , According to Division Lemma :

we can write ; the relation between x,y,p,r as ⇒  [tex]y=xq+r[/tex] , where [tex]where \; 0\leq r < x[/tex] .

Therefore , the relation between  x,y,p,r is [tex]y=xq+r[/tex] .

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The fourth term of the resulting four-term sequence is 206.

Let the four terms of the arithmetic sequence be a a+d, a+2d, and a+3d (where d is common difference)

Let the four terms of the geometric sequence be b, br, br^2, and br^3 (where r is the common ratio)

An arithmetic sequence is a sequence of numbers where the difference between any two consecutive terms is always the same. The difference is called the common difference.

The resulting four-term sequence is a+b, a+d+br, a+2d+br^2, a+3d+br^3

Given that the first three terms of the resulting four-term sequence are 57, 60, and 91, we can set up the following equations:

a + b = 57

a + d + br = 60

a + 2d + br^2 = 91

By substituting the first equation into the second and third equations we get:

d + b(r-1) = 60 - 57 = 3

2d + b(r-1)^2 = 91 - 57 = 34

By substituting the first equation and the second equation into the third one we get:

2(3) + b(r-1)^2 = 34

6+b(r-1)^2 = 34

b(r-1)^2 = 28

Note that either b=28 or b=7. We proceed with casework:

If b=28, then r=2,a=29, and d=25.The arithmetic sequence is 29,4,-21,-46, arriving at a contradiction.

If b=7, then r=3,a=50, and d=-11.The arithmetic sequence is 50,39,28,17, and the geometric sequence is 7,21,63,189. This case is valid.

Therefore, The fourth term of the resulting four-term sequence is [tex]a+3d^{2}+br^{3}= 17 +189 =206[/tex].

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The proofs of both the conditions are given below: we used the distributive property, identity x(x+y) = xy + x^2, identity x + xy = x(1 + y) and identity x + xy = x(1 + y) to prove the given equation.
a) BACD + ABDC + ACBD + ADBC + DCBA = BCD + ACD + ABD + ABC

Using the distributive property:

BACD + ABDC + ACBD + ADBC + DCBA = (B + A)(C + D)(A + B + C + D)

Using the identity x(x+y) = xy + x^2:

BACD + ABDC + ACBD + ADBC + DCBA = BCD + ACD + ABD + ABC

b) YQX + XQYŽ + XZQ7 = (Y(X + 2) + XZ)Q

Using the distributive property:

YQX + XQYŽ + XZQ7 = YQ(X + Z) + XQ(Y + Z)

Using the identity x + xy = x(1 + y):

YQX + XQYŽ + XZQ7 = YQ(X + Z) + XQ(Y + Z) = (YQ + XQ)(X + Y + Z)

Using the identity x + xy = x(1 + y):

YQX + XQYŽ + XZQ7 = (YQ + XQ)(X + Y + Z) = (YQ + XQ)(X + (Y + Z))

Using the distributive property:

YQX + XQYŽ + XZQ7 = (YQ + XQ)(X + (Y + Z)) = (YQX + XQY + YQZ + XQZ) = (Y(X + Q) + XQ)(Y + Z)

Finally, using the identity x + xy = x(1 + y):

YQX + XQYŽ + XZQ7 = (Y(X + Q) + XQ)(Y + Z) = (Y(X + Q) + XZ)Q

In this derivation, we used the distributive property, identity x(x+y) = xy + x^2, identity x + xy = x(1 + y) and identity x + xy = x(1 + y) to prove the given equation.

Therefore, we used the distributive property, identity x(x+y) = xy + x^2, identity x + xy = x(1 + y) and identity x + xy = x(1 + y) to prove the given equation.

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The expression that correctly calculates the perimeter of the shape is given as follows:

P = 2(6s + πr).

In which:

The perimeter of a square of side length s is given as follows:

P = 4s.

Hence, for three squares, the perimeter is given as follows:

P = 3 x 4s

P = 12s.

The perimeter, which is the circumference of a semicircle of radius r, is given by the equation presented as follows:

C = πr.

Hence the perimeter of two semicircles is given as follows:

C = 2πr.

The perimeter of the entire shape is given by the sum of the perimeter of each shape, hence:

P = 12s + 2πr.

P = 2(6s + πr).

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This two options I am going to include in my explanation

a) There is a unique solution.

d) The system is independent and consistent.

The given system of equations can be represented as a matrix equation [A|B] where A is the coefficient matrix and B is the constant matrix.

|1 1 1 | 0 |

|2 -1 3 | 0 |

|3 2 -1 | 0 |

The above system of equation can be written as AX=B, where X=[x,y,z] and A,B are as above.

We can check the rank of A and [A|B], if they are equal then the system is consistent and has a unique solution.

Using Gaussian elimination method, it can be observed that the rank of A and [A|B] both are 3, which means the system is consistent and has a unique solution.

Thus the given system of equations is consistent and has a unique solution.

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The Complete Question  is -

Consider the following system of equations:

x + y + z = 0

2x - y + 3z = 0

3x + 2y - z = 0

Which of the following statements are true about this system of equations?

a) There is a unique solution.

b) The solution is x = 0, y = 0, and z = 0.

c) The system intersects at one point.

d) The system is independent and consistent.

Please check all of the box that apply.

Answer: 22.9

Step-by-step explanation:

1. 40 divided by 1.75 = 22.8571428571

2. Round that up to 22.9

Answer:

You don't need to overthink this one, it's not asking for any exact values or estimates so all you do is 40/1.75 which gives you 22.8571428571. Since it's asking for 1 decimal place then the answer would be 22.9 litres of petrol.

Answer:

The capacity of the pot can be calculated by finding the volume of the clay pot. We can use the formula for the volume of a sphere to find the volume of the inside and outside of the pot and subtract the smaller volume from the larger volume to find the volume of the clay.

Step-by-step explanation:

The formula for the volume of a sphere is:

V = (4/3)πr^3

Where V is the volume and r is the radius.

First, we will calculate the volume of the inside of the pot:

V_inner = (4/3)π(8.2cm)^3 = (4/3)π(530.24cm^3) = 707.68π cm^3

Then, we will calculate the volume of the outside of the pot:

V_outer = (4/3)π(9.1cm)^3 = (4/3)π(710.29cm^3) = 961.12π cm^3

Finally, we will subtract the volume of the inside of the pot from the volume of the outside of the pot to find the volume of the clay:

V_clay = V_outer - V_inner = 961.12π cm^3 - 707.68π cm^3 = 253.44π cm^3

The capacity of the pot is 253.44π cm^3.

Note: The value of pi is 3.14 or approximately 3.14, you can use this value to calculate the capacity of the pot.

Answer:

To solve this problem, we will use the following steps:

Step 1: Nick and Chloe paddled downstream at an average speed of 12 km/h and back upstream at an average rate of 8 km/h. So, we can find the total distance they travelled by finding the distance they travelled downstream plus the distance they travelled upstream.

Step 2: We know that the total trip took 7 hours and they took a 45-minute lunch break. To convert 45 minutes to hours, we can divide 45 by 60, so 45/60 = 0.75 hours.

Step 3: We can then subtract the time they took for lunch break from the total trip time, so 7 - 0.75 = 6.25 hours

Step 4: To find the distance travelled downstream, we can multiply the time spent traveling downstream by the speed of the canoe, so 6.25 x 12 = 75 km

Step 5: To find the distance travelled upstream, we can multiply the time spent traveling upstream by the speed of the canoe, so 6.25 x 8 = 50 km

Step 6: We can then add the distance travelled downstream and the distance travelled upstream to find the total distance travelled, so 75 + 50 = 125 km

Final Answer: Nick and Chloe travelled a total distance of 125 km.

Answer:

[tex]y=\frac{2}{3}x+4[/tex]

Step-by-step explanation:

The line passes through [tex](-3,2)[/tex] and [tex](3,6)[/tex], and so has a slope of [tex]\frac{6-2}{3-(-3)}=\frac{2}{3}[/tex].

Since the line has a [tex]y[/tex]-intercept of [tex]4[/tex], the equaton is [tex]y=\frac{2}{3}x+4[/tex].

Answer:

Its option A I believe (its closest)

Step-by-step explanation:

I used Desmos (the graphing site), and it was the closest answer.

Answer:

You cut the question out so it is impossible to tell but i can guess that

W is the midpoint or something, so WR = 136.8/2 = 68.4

This is just a guess, i can't tell properly as i don't know the question.

1/0 is undefined but not infinity.

In mathematics, expressions like 1/0 are undefined. But the limit of the expression 1/x as x tends to zero is infinity.

                          i.e limx→0 1/x = infinity

Similarly, expressions like 0/0 are undefined. But the limit of some expressions may take such forms when the variable takes a certain value and these are called indeterminate. limit tends to some value of x varies with the expression so as there is limit of some value i.e x but not a particular limit 0f 1/x as x tends to zero is infinity. But 1/0 is not infinity and 0/0 is not indeterminate, since division by zero is not defined.

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The complete question is:

Is 1/0  infinty or undefined?

Answer:

Step-by-step explanation:

35% of 230 can be found by first converting 35% to a decimal. To do this, divide 35 by 100.

35/100 = 0.35

Next, multiply the decimal by the total number you want to find the percentage of, which is 230 in this case.

0.35 * 230 = 80.5

So 35% of 230 is 80.5.

In this situation, the wholesale cost x of every dress is first increased by $20 to obtain the retail price. This is represented by the function f(x) = x + 20.

Then, during a sale, every dress is sold for 75% of the retail price. This is represented by the function g(x) = 0.75x.

To find the composite function gf that describes this situation, we need to substitute f(x) into g(x) and simplify.

gf = g(f(x)) = g(x + 20) = 0.75(x + 20) = 0.75x + 0.75(20) = 0.75x + 15

Therefore, gf = 0.75x + 15 describes the situation where the wholesale cost x of every dress is first increased by $20 to obtain the retail price, and then during a sale, every dress is sold for 75% of the retail price. So, the final cost of the dress is (0.75x + 15)

So, the composite function gf = 0.75x + 15, describes the situation where the shop adds $20 to the wholesale cost, and then sells it for 75% of the retail price.

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To put it simply, any outlier with a high or low value has the same impact on the data set. The standard deviation goes down when the outlier is taken out.

Outliers are data points that deviate from the distribution's typical pattern. a value that is "outside" of the record's typical range (either significantly lower or substantially greater).

The standard deviation increases when the outlier's value is higher than the average of the data, compared to when it doesn't exist. When the outlier is eliminated, the mean decreases if the outlier was lower than the majority of the data, and the standard deviation is once more higher than it would be without the outlier. What makes it different is that, as opposed to a fall in the mean, the removal of the outlier would cause an increase.

To put it simply, any outlier with a high or low value has the same impact on the data set. The standard deviation goes down when the outlier is taken out.

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Given: f(d) = 11(1.01)d, which will display equation of the radius of the algae.

Simple Equation: What Is It? two phrases along either side of a sign are connected by a mathematical equation. Usually, it only includes one variable and an equal sign. Example: 2x – 4 = 2.

Solution:

Part A: 11.79 = 11(1.01)d(1.01)d(1.01)d(1.01)d(1.01)d= 11.79/11 (1.01)d(1.01)d(1.01)d(1.01)d(1.01)d(1.01)d(1.01)d(1.01)d(1.01)d(1.01)d(1.01)d(1.01)d(1.01)d(1.01)d(1.01)d(1.01)d= 1.071818 d = log 1.0718

When domain = 0 d = 0 f(0) = 11, the y-intercept is found (Part B) (1.01)

^{0}11(1.01)0\s= 11 x 1 = 11 f(d) = 11

Part C: Average rate of change, f/d = (f(7) - f(2)) / (7 - 2) = (11(1.01)711(1.01)211(1.01) 2) / 5 = 0.57 / 5 = 0.114

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Given: f(d) = 11(1.01)d, which will display equation of the radius of the algae.

Simple Equation: What Is It? two phrases along either side of a sign are connected by a mathematical equation. Usually, it only includes one variable and an equal sign. Example: 2x – 4 = 2.

Solution:

Given:

f(d) = 11(1.01)d

To Find:

Part A: When the biologist concluded her study, the radius of the algae was approximately 11.79 mm. What is a reasonable domain to plot the growth function?

Part B: What does the y-intercept of the graph of the function f(d) represent?

Part A:

[tex]11.79 = 11(1.01)^{d}11(1.01)d\\(1.01)^{d}(1.01)d\\= 11.79/11(1.01)^{d}(1.01)\\= 1.071818\\d = log 1.071818 / log 1.01\\d = 6.97[/tex]

Part B:

y-intercept is obtained when domain = 0

[tex]d = 0 ⇒ f(0) = 11(1.01)^{0}11(1.01)0\\= 11 x 1 = 11\\f(d) = 11[/tex]

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Answer:

  251.5 square units

Step-by-step explanation:

You want to know the area of the given pentagonal figure.

The figure can be decomposed into a (top) triangle that is 21 units wide and (19-8) = 11 units high, along with a (bottom) trapezoid that is 8 units high and has bases of 21 units and 13 units. The area of the figure is the sum of the areas of these parts.

The area of the triangle is ...

  A = 1/2bh

  A = 1/2(21)(11) = 115.5 . . . . square units

The area of the trapezoid is ...

  A = 1/2(b1 +b2)h

  A = 1/2(21 +13)(8) = 136 . . . . square units

The area of the pentagon shown is the sum of these areas:

  115.5 +136 = 251.5 . . . . square units

Since the graph of a straight line passing through the origin represents two variables in direct variation, with the slope as the coefficient of proportionality,

what was the original temperature, in degrees Fahrenheit, of the cup of hot water?

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The value of d = 26.

A mathematical statement that maintains the equality of two expressions that are joined by the equals sign "=" is known mathematically as an equation.

A mathematical equation can be solved by adding or subtracting the same number on both sides or multiplying or dividing the same number into both sides.

Here we have

1/4(d-2) = 6    

Solve the above equation as follows

=> 1/4(d-2) = 6      

Multiply by the same number on both sides

=> 4[ 1/4 (d - 2) ] = 4 × 6  

=> (d - 2) = 24

Add '2' on both sides

=> (d - 2) + 2 = 24 + 2

=> d = 26

Therefore,

The value of d = 26

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