Help on number 1 please!! Thanks.

The graph of the polar curve r = 3 – 2cos(θ) is in the attachment

A graph is a diagram representation on a coordinate system.

A polar curve is a curve represented by the equation r = a + bcosθ where

To find the graph of the polar curve r = 3 – 2cos(θ), we need to determine its maximum and minimum values and also the value as it crosses the axis.

Since r = 3 – 2cos(θ), the maximum value of r is obtained at the minimum value of cos(θ) = -1 at θ = π

So, substituting this into the equation, we have

r = 3 – 2cos(θ)

r = 3 – 2(-1)

r = 3 + 2

r = 5

Since r = 3 – 2cos(θ), the minimum value of r is obtained at the maximum value of cos(θ) = 1 at θ = 0

So, substituting this into the equation, we have

r = 3 – 2cos(θ)

r = 3 – 2(1)

r = 3 - 2

r = 1

Since r = 3 – 2cos(θ), the value of r at the origin is when θ = π/2 and θ = 3π/2

So, substituting this into the equation, we have

r = 3 – 2cos(θ)

r = 3 – 2cos(π/2)

r = 3 – 2(0)

r = 3 - 0

r = 3

So, in polar form, the points we require for the polar curve graph are

Find the graph of the polar curve in the attachment

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Answer:

C: The third graph.

Step-by-step explanation:

Took the quiz

Answer:

the answer is 4

Step-by-step explanation:

the answer is 4

$225 was earned from the craft sales

and $40 was earned from the play.

Given, During a school carnival, students from the middle school raised money by selling crafts, food, game tickets, and school play admissions.

Of each dollar earned, $0.15 came from games. Craft sales earned 3 times as much as games. Food sales were 4 times the amount earned from the play.

Let the amount earned by play be x,

Now, Games earned = 0.15×500 = $75

Also, crafts earned 3×75 = $225

Now, as play earned x, then food earned 4x.

According to question,

x + 75 + 225 + 4x = 500

5x + 300 = 500

5x = 200

x = 40

So, the amount earned by Play be, $40

and the amount earned by Food be $160.

Hence, $225 was earned from the craft sales

and $40 was earned from the play.

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The conclusions for the given points  (1.-2) and (4.-2) are

(A) The slope is 0.

(B) The y-intercept is -2.

(D) The line is horizontal.

(E) The equation of the line is y = -2

The formula used to calculate the equation of the line passing through the points (x₁, y₁) with slope m is given by

Where the formula for Slope is given by

Here we have

Given points  (1, -2) and (4, -2)  

Let us check each point one by one

(A) The slope is 0.

To find the slope of the line with given points using the formula

=> m = (y₂ - y₁) /(x₂ - x₁)

=> m = (-2 - (2)) /(4 - (-2)) = 0/6 = 0

∴ The slope of the line = 0

(B) The y-intercept is -2

To find the y-intercept calculate the equation line using the formula

=> (y -y₁) = m(x - x₁)  

=> [y - (-2) ] = 0 (x - 1)

=> y + 2 = 0

=> y = -2

On comparing with the slope-intercept form y = mx+c, we get

y-intercept = -2

∴ The y-intercept is -2.

(D) Here the line is in the form of y = a then the given line will be a Horizontal line.

(E) The equation of the line is y = -2

Therefore,

The conclusions for the given points  (1.-2) and (4.-2) is

(A) The slope is 0.

(B) The y-intercept is -2.

(D) The line is horizontal.

(E) The equation of the line is y = -2

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The complete question:

What can be concluded about a line that passes through the points (1, -2) and (4, -2) Check all that apply.

The slope is 0.

The y-intercept is -2.

The line is vertical.

The line is horizontal.

The line has no y-intercept.

The equation of the line is y = -2

Answer:

17.8

Step-by-step explanation:

You have to add 9.2 and 63 and the subtract from 90. Hope this helped! <3

Answer: 247.97

Step-by-step explanation:

The nearest cent is two decimal places.

Answer: 25.12 in

Step-by-step explanation:

The circumference of a circle with a diameter of [tex]d[/tex] is [tex]\pi d[/tex].

So, the circumference is [tex]8\pi \approx 25.12[/tex] in.

Answer:

volume is approximately 73.6 to the nearest tenth

Step-by-step explanation:

The volume of a pipe is volume = π * radius² * length

diameter = 2.5

radius = 2.5/2 = 1.25 inches

volume = π * 1.25² * 15

volume = π * 1.5625 * 15

volume =  π * 23.4

which is approximately 73.6 to the nearest tenth

Answer:

160.1 divided by 22.3 = 7.179 miles per litre.

This is 7.179 x 4.544 = 32.62 miles per gallon.

hope that will help

keeping in mind that there are about 1.609 Km in 1 mile and that there are about 3.78L in 1 gallon(US)

[tex]\cfrac{24~~\begin{matrix} Km \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~ }{1~~\begin{matrix} L \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~ }\cdot \cfrac{mile}{1.609~~\begin{matrix} Km \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~ }\cdot \cfrac{3.78~~\begin{matrix} L \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~ }{gallon(US)} \\\\\\ \cfrac{24(3.78)}{1.609}\cfrac{mile}{gallon(US)} ~~ \approx ~~ 56.38\frac{mile}{gallon}[/tex]

The probability of the person favoring rock music is 0.257, favoring country music is 0.285, and favoring something other than rock, country, or classical music is 0.342.

Given that:

Total people = 70

Chose rock = 18

Chose country = 20

Chose classical = 8

Chose something other than rock, country, or classical = 24

a) The empirical probability that the next person entering the store favors rock music is = Total people choosing rock music/ Total people

                                = 18/70 = 9/35 = 0.257

b) The empirical probability that the next person entering the store favors country music is = Total people choosing country music/ Total people = 20/70 = 2/7 = 0.285

c) The empirical probability that the next person entering the store favors something other than rock, country, or classical music is = Total people choosing something other than rock, country, or classical music/ Total people = 24/70 = 12/35 = 0.342.

Hence, the empirical probability that the next person favors rock music is 0.257, favors country music is 0.285, and favors something other than rock, country, or classical music is 0.342.

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A system of linear equations to describe this situation is given by:

A + O = 11.

0.80A + 0.95O = 9.95.

Harry bought six (6) apples and five (5) oranges from this store.

In order to write a system of linear equations to describe this situation, we would assign variables to the amount of apples and oranges respectively, and then translate the word problem into algebraic equation as follows:

Since Harry bought a total of 11 pieces of fruit, we have:

A + O = 11              .....equation 1.

Since the cost of apples is $0.80 each and oranges cost $0.95 each, we have:

0.80A + 0.95O = 9.95      .....equation 2.

From equation 1, we have:

O = 11 - A                   .....equation 3.

Substituting equation 3 into equation 2, we have:

0.80A + 0.95O = 9.95

0.80A + 0.95(11 - O) = 9.95

Apples, A = 0.90/0.15

Apples, A = 6.

For the number of oranges, we have:

Oranges, O = 11 - A

Oranges, O = 11 - 6

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Complete Question:

At a store, apples cost $0.80 each and oranges cost $0.95 each. Harry buys some apples and oranges and spends $9.55 . He buys a total of 11 pieces of fruit.

Part a. Write a system of linear equations to describe this situation.

Part b. How many of each fruit did Harry buy?

According to the concept of translation, the function of g(x) = x² + 2.

Translation:

The concept of translation is defined by using the function f(x) then f(x + a) is a horizontal translation of f(x)

If the value of a > 0 then a shift to the left of a units

If the value of  a < 0 then a shift to the right of a units

Given,

Here we have the function f(x) = x².

Now, we have to find  the equation of the graph of g(x) and how it change in corresponds to f(x).

While we looking the graph, the function f(x) has curved on the origin (0, 0).

Where the function g(x)  has curved the point (2,0).

Which tells the the graph is move left side by 2 units.

So, according to the rule of translation, the value of a is 2.

Then the function g(x) is written as,

=> g(x) = x² + 2.

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Answer:

Y= -1.67x + 0.67

Step-by-step explanation:

Hope this was ok

Answer:-8

Step-by-step explanation:

You are basically adding -4+(-4)

Answer:

Step-by-step explanation:

2(-4)

2 x -4

answer: -8

Round 8.879 to the nearest tenth is 8.9.

Rounding to the nearest tenth:

The combination of a whole number and a fraction, separated by a decimal point, is known as a decimal number in mathematics. The place value of the digits is divided by 10 starting from left to right. Determining the place values of tenths, hundredths, and thousands will therefore be aided by the decimal place value. For instance, the definition of the place value tenth is 1/10.

Think about the decimal 12.345.

Tenth place value in this case is 3.

By substituting the actual number with an approximation, the decimal value can be rounded. To the nearest integer, the decimal number 5.8 is rounded to 6, for instance. The decimal number can also be rounded to the nearest tenths place value. The first integer that appears after the decimal point is the tenth place value. Look at the hundredth number to round the decimal number to the nearest tenth. If it's more than 5, add one to the tenth value. Remove all the numbers that are present after the tenth place and leave the tenth place value alone if it is less than 5.

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Answer:

[tex]m=38[/tex]

Step-by-step explanation:

An interior angle and its corresponding exterior angle are supplementary, so:

[tex]3m-12+2m+2=180 \\ \\ 5m-10=180 \\ \\ 5m=190 \\ \\ m=38[/tex]

to get the equation of any straight line, we simply need two points off of it, let's use those two in red in the picture below

[tex](\stackrel{x_1}{1}~,~\stackrel{y_1}{6})\qquad (\stackrel{x_2}{3}~,~\stackrel{y_2}{12}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{12}-\stackrel{y1}{6}}}{\underset{run} {\underset{x_2}{3}-\underset{x_1}{1}}} \implies \cfrac{ 6 }{ 2 } \implies 3[/tex]

[tex]\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{6}=\stackrel{m}{ 3}(x-\stackrel{x_1}{1}) \\\\\\ y-6=3x-3\implies {\Large \begin{array}{llll} y=3x+3 \end{array}}[/tex]

The function is y = 3(x+3)^2-9

The equation of a parabola is

y=a(x-h)^2+k

where (h,k) are the coordinates of the vertex and a, is a constant.

From the question, we have

(h,k)=(-3,-9)

⇒y=a(x+3)^2-9

To find a, substitute x=-2,y=-6

-6=a(-2+3)^2-9

⇒a=3

The equation, y=3(x+3)^2-9

Multiplication:

Mathematicians use multiplication to calculate the product of two or more numbers. It is a fundamental operation in mathematics that is frequently utilized in everyday life. When we need to combine groups of similar sizes, we utilize multiplication. The fundamental concept of repeatedly adding the same number is represented by the process of multiplication. The results of multiplying two or more numbers are known as the product of those numbers, and the factors that are multiplied are referred to as the factors. Repeated addition of the same number is made easier by multiplying the numbers.

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Answer:

There are two pairs of numbers:

-8      -18

and

18        8

Step-by-step explanation:

a * b = 144      EQ. 1

a - b = 10         EQ. 2

From EQ. 2:

a = 10 + b          EQ. 3

Replacing EQ. 3 in EQ. 1:

(10+b)b = 144

10*b + b*b = 144

b² + 10b - 144 = 0

b = {-10±√((10²)-(4*1*-144))} / (2*1)

b = {-10±√(100+576)} / 2

b = {-10±√676} / 2

b = {-10±26} / 2

b₁ = {-10-26} / 2 = -36/2 = -18

b₂ = {-10+26} / 2 = 16/2 = 8

a₁ - b₁ = 10

a₁ - (-18) = 10

a₁ + 18 = 10

a₁ = 10 - 18

a₁ = -8

a₂ - b₂ = 10

a₂ - 8 = 10

a₂ = 10 + 8

a₂ = 18

Check:

a₁ * b₁ = -8 * -18 = 144

a₂ * b₂ = 8 * 18 = 144

Considering the quadratic equation, it is found that:

a) The initial height of the object is of 58.8 meters.

b) The object first hits the ground after 39.2 seconds.

c) The maximum height reached by the object is of: 1912 meters.

The quadratic equation that models the projectile's height is defined as follows:

s(t) = -4.9t² + 190.6t + 58.8.

Which has the coefficients given as follows:

a = 4.9, b = 190.6, c = 58.8.

The initial height is obtained as follows:

s(0) = -4.9(0)² + 190.6(0) + 58.8 = 58.8 meters.

It hits the ground at the positive root for which s(t) = 0, hence, using a quadratic equation calculator, this root is of:

t = 39.2 seconds.

The maximum height obtained by the object is the y-coordinate of the vertex, hence:

hMAX = -(b² - 4ac)/4a = -(190.6² - 4(-4.9)(58.8))/(4(-4.9)) = 1912 meters.

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Answer:

below

Step-by-step explanation:

(7p^9)^-4     a negative exponent means move the number up or down in the fraction

=   1 / [ (7 p^9) ^4  ]

           = 1 / ( 7^4 p^36) =   1/(2401 p^36)   <===don't omit the parentheses!

The minimum and maximum of the function f(x)=2x³+15x²-36x+1 are 38 and 39 respectively

The maximum value of a function f(x) is also called the absolute maximum value, or the  greatest value of the function f on the closed interval [0, 1]. on the other hand, the minimum value of f(x) at x = 0 is called the absolute minimum value,  or least value of the function f on the closed interval [0, 1)

How to find the minimum and maximum functions?

From the function f(x) = 2x3 − 15x2 + 36x + 1.

Using differential calculus , dy/dx = 6x2 - 30x + 36

= 6(x2 - 5x + 6)

f(x) is a maximum when x = 2 and the maximum value of f(x) = f(2).

This implies that f(2) = 2(23) − 15(22) + 36(2) + 11 = 39

d2y/dx2|x=3 = 12 x 3 - 30 = 6 > 0

This also implies that  f(x) is a minimum when x = 3 and the minimum value of f(x) = f(3) = 2(3)3 − 15(3)2 + 36(3) + 11 = 38

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Answer:

Step-by-step explanation:

Let the required amount of 5% milk is x quartz, then the amount of 2% milk is 90 - x quartz.

Set equation for the fat content:

Answer:

375=5^3 * 3

Step-by-step explanation:

375/5 = 75

75/5 = 15

15/5 = 3

3/3 = 1

Answer:

Step-by-step explanation:

7 1/4 is what i think

Answer:

C) The y-intercept of Function A is 1 unit greater than the y-intercept of Function B

Step-by-step explanation:

The y-int of Function A is (0,1), while the y-int of Function B is (0,0).

Answer:

C

Step-by-step explanation:

For Function A, the y-intercept occurs at 1. For B, it occurs at 0. Therefore, the y-intercept of Function A is 1 unit greater than the y-intercept of Function B.

Answer:

28

Step-by-step explanation:

[tex] {2}^{3} = 8[/tex]

The units digit (8) is the tens digit (2) raised to the third power.

Answer:

Roman numeral representing thousand (1000)

Answer:8 experiments

Step-by-step explanation:

she has 8 feet of copper and she needs one foot for each experiment she can do 8 experiments.