The degree of the polynomial function f(x) is 3.
The roots of the equation f(x) = 0 are -1, 0, and 4.
Which graph could be the graph of f(x)?l

A) ∠1 and ∠8 are alternate exterior angles

B) ∠4 and ∠6 are same side interior angles

E) ∠3 and ∠6 are alternate interior angles

Let's check the each options.

A) ∠1 and ∠8 are alternate exterior angles

The exterior angles are ∠1, ∠2, ∠7 and ∠8.

This is correct.

B) ∠4 and ∠6 are same side interior angles.

∠4 and ∠6 are inside the line m and n, they are in the same side, you can see it on the figure.

This is correct

C) ∠5 and ∠7 are vertical angles

∠5 and ∠7 are supplementary angles.

This is not correct.

D) ∠2 and ∠8 are  corresponding angles

These are same side of exterior angles.

This is not correct.

E) ∠3 and ∠6 are alternate interior angles

These are interior angles and alternative to each other.

This is correct.

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Answer and Explanation:

Let x be the total weight of the silver alloy costing $3.50 per ounce and y be the the total weight of the other that costs $7.00 per ounce.

The total weight of the resulting alloy is 30 ounces.

x+y=30x+y=30

Each ounce of the mixture must cost $6.30. The total cost of the resulting silver alloy is:

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8 ounces of silver alloy that costs $5.50 per ounce should be mixed with 12 ounces of silver alloy that costs $8.00 per ounce to make a new 20-ounce alloy that costs $7.00 per ounce.

Linear equations are equation involving one or more expressions including variables and constants and the variables are having no exponents or the exponent of the variable is 1.

Let x be the number of ounces of silver alloy which costs $5.50 per ounce and y be the number of ounces of silver alloy that costs $8.00 per ounce.

We have,

x + y = 20

5.50x + 8.00y = 7 × 20

From the first equation, x = 20 - y

Substituting this in the second equation,

5.5 (20 - y) + 8y = 140

(5.5 × 20) - 5.5y + 8y = 140

110 + 2.5y = 140

2.5y = 30

y = 12

x = 20 - y = 20 - 12 = 8

Hence the number of $5.50 cost per ounce silver alloy used is 8 ounces and the other alloy used is 12 ounces.

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Answer:

1st- x=140°

2nd-x=90°

Step-by-step explanation:

The interior angle of a 9 -sided polygon is 140x9=1260

divide by 9

The interior angles of a triangle always add up to 180

90°each

Answer: 73015

Step-by-step explanation:

multiply both of them together

The required time at which the ball reaches a height of 10 ft is 0.5 sec.

Given that,
A ball is thrown into the air with an upward velocity o 12ft/s. The equation for the ball’s height (h) at any time (t) is h (t) =-4t^2+12t+5 find the time(s) at which the ball reaches a height of 10ft.

Here,
Given equation,
h(t) =-4t²+12t+5
For height 10 ft time,
10 = -4t² + 12t + 5
4t² - 12t + 5 = 0
4t² -10t - 2t + 5 = 0
2t(2t - 5) - 1(2t - 5) = 0
(2t-1)(2t -5) = 0
t = 1/2, 5/2  (5/2 can be negelected)

Thus, the required time at which the ball reaches a height of 10 ft is 0.5 sec.

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x-intercept, 7/2

y-intercept, -7/3

The points where a line crosses an axis are known as the x-intercept and the y-intercept, respectively. the location on the y axis where a graph crosses it. • x = 0 at the same location. An intercept in mathematics is a location on the y-axis through which the line's slope passes. It is a place on the y-axis where a straight line or a curve crosses. This is reflected in the equation for a line, which is written as y = mx+c, where m denotes slope and c denotes the y-intercept.

Given that,

The graph of the equation 2x-3y=7 is a line.

2x-3y=7

Divide 7 on both sides

2x/7- 3y/7=1

[tex]\frac{x}{7/2}- \frac{y}{7/3} =1[/tex]

x-intercept, 7/2

y-intercept, -7/3

Therefore, x-intercept, 7/2, y-intercept, -7/3.

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The diagram attached below shows the rectangles with the following:

a. Perimeter = 30 cm; b. Perimeter = 30 cm

c. Length = 8 cm; Width = 4 cm

Length = 10 cm; Width = 2 cm

Length = 7 cm; Width = 5 cm

A rectangle is a four sided shape that has two opposite sides that are parallel and equal to each other.

The perimeter of a rectangle is the sum total of all the four sides of the rectangle and can be calculated using the formula:

Perimeter of a rectangle =2(length + width).

3. a. The diagram of the rectangle that has the following parameters is shown as rectangle 1 in the image attached below, where:

Length of rectangle = 10 cm

Width of rectangle = 5 cm

Perimeter of rectangle 1 = 2(10 + 5) = 30 cm

b. Rectangle 2 in the diagram shows the parameters given:

Length of rectangle = 20 cm

Width of rectangle = 10 cm

Perimeter of rectangle 2 = 2(20 + 10) = 60 cm

c. Rectangles 3, 4 and 5 shows the different measures a rectangle with a perimeter of 24 cm can be:

Rectangle 3: Length = 8 cm; Width = 4 cm

Rectangle 4: Length = 10 cm; Width = 2 cm

Rectangle 4: Length = 7 cm; Width = 5 cm

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The coordinates of Hector's friend's house are (18,3).

Given:

Coordinates of Hector's house = (-7,11)

Coordinates of zoo = (-7,3)

He walked a total distance of 25 blocks from the zoo towards the east.

This means that he walked horizontally on the y-axis to reach his friend's house. So, the y-coordinate remains 3 and only the x-coordinate varies.

To find the coordinates of Hector's friend's house,

As given each unit on the map represents one block.

25 units = 25 blocks

Adding 25 units to the x- coordinate of the zoo keeping the y-coordinate same to obtain the required coordinates.

- 7 + 25 = 18

Therefore, the coordinates of Hector's friend's house are (18,3).

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Step-by-step explanation:

students who like both festivals

140+150=290

290-260=30

=30

students who like one festival

260-150=110

=110

∠FED and ∠DEW are complementary because it is a sum of 90 degrees.

By the law of addition of complementary angles,m∠FED + m∠DEW = 90°

m∠FED + m∠DEW = m∠FEW by the Angle addition postulate.

By the substitution property of equality, m∠FEW = 90°.

The ∠FEW is a right angle by the definition of right angles.

Complementary Angles defined as angles that sum up to 90 degrees.

Now, we are given that;

∠FED and ∠DEW are complementary.

We want to prove that ∠FEW is a right angle. Thus;

∠FED and ∠DEW are complementary because it is a sum of 90 degrees.

By the law of addition of complementary angles, we can say that;

m∠FED + m∠DEW = 90°

Also,

m∠FED + m∠DEW = m∠FEW by the Angle addition postulate.

By the substitution property of equality, m∠FEW = 90°.

The ∠FEW is a right angle by the definition of right angles.

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Using  Unitary Method  16 Oz for $2,24 ounces for $3 is a true statement.

As given in the question,

16 Oz for $2,24 ounces for $3 is solved by Unitary Method as follows:

16 Oz for $2

24 ounces for $3

Above statement is true.

If $2 fetches 16 Oz

then $1 will fetch 8 Oz

hence $3 will fetch 24 Oz (by Unitary Method)

Thus the given statement is true.

Alternately, the statement can be verified to be true or false as follows:

16 Oz for $2

1 Oz for $(2/16)

24 Oz for $ (24x2/16) = $3

Therefore, the given statement is valid and true. The Unitary Method has been applied either way to check the validity of the given statement and found to be valid (true). It is worthwhile to mention that Oz stands for ounces (abbreviation)

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If you just want to conduct a flyby and aren't planning to stay, it will take you approximately 600 days, and if you want to enter orbit, it will take you about 2,000 days.

Astronomical distances are expressed in terms of a light-year, which is also spelt light year. Its length is approximately 9.46 trillion kilometers, or 5.88 trillion miles.

NASA's Pioneer 10 was the first spacecraft to ever travel across the distance between the Earth and Jupiter. On March 3, 1972, it was launched, and on December 3, 1973, it arrived. There were 640 days of flight time altogether.

However, Pioneer 10 was passing by while en route to study the outer solar system. Before NASA lost communication with it, the spacecraft traveled another 11 years into deep space after approaching the planet at a distance of 130,000 kilometers, where it snapped the first-ever close-up images of Jupiter.

Pioneer 11 launched and touched down one year later. It traveled there in 606 days, flying by Jupiter at a considerably closer distance (21,000 kilometers), and also stopped by Saturn.

The Voyager spacecraft arrived next. Voyager 1 arrived on March 5, 1979, in only 546 days, and Voyager 2 took 688 days.

Consequently, it will take between 550 and 650 days to complete a flyby.

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Answer: 310

Step-by-step explanation:

(190/38) x 100 = 500 total students

500-190 = 310 students

According to the solving the following equation:

The standard form: x³ + 3x² - 6x - 8

degree: 3

constant term: 8

A polynomial is a mathematical equation made up of variables, constants, and exponents that are mixed using addition, subtraction, multiplication, and division operations.

No part of an algebraic expression should be - Variables' square roots. variable powers that are fractional. variable powers that are negative. variables in any fraction's denominator.

Given polynomial, (x + 4) (x - 2) (x + 1)

Keeping the third bracket constant while simplifying the first two results in,

= (x² - 2x + 4x - 8)(x +1 )

= (x² + 2x - 8)(x+1)

On further simplifying we get,

= x³ + 2x² +x² -8x +2x -8

= x³ + 3x² - 6x - 8

So, the standard form is x³ + 3x² - 6x - 8  , degree is 3, leading co-efficient is 1 and the constant term is -8

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The coordinate of Point A is ([tex]\frac{1}{2} ,\frac{\sqrt{3} }{2}[/tex])

Given in the question;

From the figure,

To see the graph:

To find the coordinates of point A.

Now, According to the question and picture :

Point A is on the unit circle and

The angle between point A and the origin and

The X - axis is [tex]\frac{\pi }{3}[/tex] = 60°.

The radius of the unit circle is 1.

So, the x - coordinate of point A is :

X cos 60° = 1/2

The Y coordinate of point A is :

X sin 60° = [tex]\frac{\sqrt{3} }{2}[/tex]

Hence, The coordinate of Point A is ([tex]\frac{1}{2} ,\frac{\sqrt{3} }{2}[/tex]).

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Answer:

Where's a photo or sum??

Answer:

i think n = 7 idrk

Step-by-step explanation:

gl

The number of adult tickets sold is 920 , and the number of child tickets sold is 500 .

In the question ,

it is given that

ticket cost for adult = $40

ticket cost for children = $10

and the number of total tickets sold is 1420

let the number of adult tickets sold = x

and the number of children ticket sold = y

According to the question

total tickets sold = number of adult tickets sold+ number of children ticket sold

Substituting the values, we get

x+y = 1420

y = 1420 - x   ...(i)

the total receipts for adult tickets= $40x

the total receipts for children tickets= $10y

given that total amount of tickets sold = $41800

According to the question

40x + 10y = 41800

Substituting the value of y from equation(i) , we get

40x + 10(1420-x) = 41800

40x + 14200 - 10x = 41800

30x + 14200 = 41800

30x = 27600

x = 920

and y = 1420 - 920

y = 500

Therefore , the number of adult tickets sold is 920, and the number of child tickets sold is 500 .

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[tex] = \sqrt{( {x2 - x1})^{2} + ( {y2 - y1})^{2} } \\ = \sqrt{ (- 1 - 6 )^{2} + ( {14 - 16)}^{2} } \\ = \sqrt{( { - 7)}^{2} + ( { - 2)}^{2} } \\ = \sqrt{49 + 4} \\ = \sqrt{53} [/tex]

ATTACHED IS THE SOLUTION

The percentage profit on the cost of the skirt is 11.1%

Here, the cost of gloves is £4

And the profit on gloves is 100% which will be equal to 4

The selling price of gloves will be = 8

As given in the question,

The total selling price of both items is £48

So, the selling price of a skirt will be = 48-8

= 40

Now, let the Total Cost of both items be x

Then, x*120÷5= 48

On solving the equation we get the x= 40

So, the cost price of the skirt will be = 40 - 4 = 36

Profit percentage of the skirt =( Selling price - cost price÷ cost price)*100

= (40-36÷ 36)*100

=(4÷ 36)*100

= 11.1℅

Hence, the profit percentage on the skirt will be 11.1℅

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Answer:

Hii! This is already written in slope intercept form.

For a refresher, slope intercept form is [tex]y=mx+b[/tex]

[tex]y[/tex] = y-coordinate

[tex]m[/tex] = slope

[tex]x[/tex] = x-coordinate

[tex]b[/tex] = y-intercept

In this equation,

[tex]m[/tex] is [tex]-1/2[/tex]

[tex]b[/tex] is [tex]-5[/tex]

Hope this answers your questions.

a) A circle graph inaccurately displays the data because the data is not about parts of a whole.

b) Line graph would best display the data.

A circle is divided into sectors that each represent a component of a whole to create a circle graph, which is a visual representation of data.

An individual data point is connected by a line in a line graph, sometimes referred to as a line plot or a line chart. A line graph shows numerical values over a predetermined period of time.

a) Since circle graphs are designed to depict data consisting of parts of a whole, a data set consisting of temperature variations over the course of a week would be wrongly displayed by one.

b) Since line graphs are the most appropriate for a data set that is tied to time, a line graph would be the most effective way to display the given data.

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According to the associative property of multiplication, the expression to find the cost will be (1.2 × 25) × 4 based on the property and the value is $120.

It should be noted that the associative property of multiplication simply means that when multiplying three numbers, the answer will be the same regardless of how the numbers are grouped.

In this case, Sanjay bought 4 packages of bottled water and a package contains 25 bottles of water that cost $1.20 each.

From the information, the expression is illustrated as 4 x (25 x 1.2). It should be noted that this can also be written as (1.2 × 25) × 4 based on the property and the answer will be $120.

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Answer:

k = - 5

Step-by-step explanation:

calculate the slope between the 2 points using the slope formula and equate to 9

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = (0, k ) and (x₂, y₂ ) = (1, 4 )

m = [tex]\frac{4-k}{1-0}[/tex] = [tex]\frac{4-k}{1}[/tex] = 4 - k

then equating to 9

4 - k = 9 ( subtract 4 from both sides )

- k = 5 ( multiply both sides by - 1 )

k = - 5

Answer:

86457

Step-by-step explanation:

Answer:

-8

Step-by-step explanation:

[tex]\frac{-6-0}{-9-h} = 6\\6(-9-h)=-6\\-9-h=-1\\-h=8\\h=-8[/tex]

Answer: 5/3

Step-by-step explanation:

[tex]\displaystyle\\1\frac{2}{3}=\\\\\frac{1*3+2}{3}=\\\\\frac{3+2}{3} =\\\\\frac{5}{3}[/tex]