Precal unit 4 sample work-
I need help converting the polar to rectangular. I already solved just needing to convert it.
Thank you!

The values of the solution for the triangle is A = 55°, a = 10. 1, b = 12. 3, B = 86.01°, c = 7.68 and C = 39°

Sine rule is used to show the relationship between the sides and angles of a triangle. It is given as:

a/sinA = b/sinB = c/sinC

Where A,B,C are the angles and a,b and c are the opposite sides to the angles.

1)

A = 55°, a = 10. 1, b = 12. 3

10 / sin(55) = 12.3 / sinB

B = 86.01°

A + B + C = 180° (angle in triangle)

55 + C + 86 = 180

C = 39

10 / sin(55) = c / sin(39)

c = 7.68

The values of the solution for the triangle is A = 55°, a = 10. 1, b = 12. 3, B = 86.01°, c = 7.68 and C = 39°

Find out more on sine rule at: https://brainly.com/question/4372174

Answer:

B and B

Step-by-step explanation:

For the first problem, the range is simply the data set rearranged from smallest to largest.

For the second problem, you just have to cross multiply each variable in order to expand the equation and get an answer.

The answer for that one is [tex]12x^{3} -42x^{2} +8x+55[/tex]

Answer:

2, 0.2, 0.02

The first number is 2000.  The term to term rule is 'divide by 10'.

Step-by-step explanation:

To calculate the next term, divide the previous term by 10:

2000 ÷ 10 = 200

200 ÷ 10 = 20

Therefore, the next three terms will be:

20 ÷ 10 = 2

2 ÷ 10 = 0.2

2 ÷ 10 = 0.02

Term to term rule

To work out the term to term rule, give the initial number of the sequence and then describe the pattern:

The first number is 2000.  The term to term rule is 'divide by 10'.

Answer:

B

Step-by-step explanation:

The amount of change Zelma should receive is 20-0.40p, or 20 dollars minus the total amount of the bananas (each pound multiplied by 40 cents).

Answer: Simple the answer is c.

Step-by-step explanation:

First start out with 20 witch is a full number and subtract .40 p from 20

.40 is the cost of each banana and p is the amount of bananas that will be purchased.

Answer:

19

Step-by-step explanation:

(5x+37)+(3x-9)=180

8x= 152

x=19

Answer:

55.75

Step by step explain:

33.00 divided by 4 equals 8.25

then multiply 8.25 by 7 which equals 55.75

Answer:

See below ↓

Step-by-step explanation:

Measures of the angles are equal 360° (total degree measure) - [∠G + ∠E]

Using the t-distribution, as we have the standard deviation for the sample, it is found that it can be concluded that the holes are being punched an average of 1. 84 cm.

At the null hypotheses, it is tested if the mean is of 1.84 cm, that is:

[tex]H_0: \mu = 1.84[/tex]

At the alternative hypothesis, it is tested if the mean is different of 1.84 cm, that is:

[tex]H_1: \mu \neq 1.84[/tex]

The test statistic is given by:

[tex]t = \frac{\overline{x} - \mu}{\frac{s}{\sqrt{n}}}[/tex]

The parameters are:

Considering the hypothesis and the given sample, it is found that the parameters are as follows:

[tex]\overline{x} = 1.85, \mu = 1.84, s = 0.0235, n = 12[/tex].

Hence, the test statistic is given by:

[tex]t = \frac{\overline{x} - \mu}{\frac{s}{\sqrt{n}}}[/tex]

[tex]t = \frac{1.85 - 1.84}{\frac{0.0235}{\sqrt{12}}}[/tex]

[tex]t = 1.47[/tex]

Considering a two-tailed test, as we are testing if the mean is different of a value, with a significance level of 0.1 and 12 - 1 = 11 df, the critical value is of [tex]|t^{\ast}| = 1.7959[/tex]

Since the absolute value of the test statistic is less than the critical value, we do not reject the null hypothesis and it can be concluded that the holes are being punched an average of 1. 84 cm.

More can be learned about the t-distribution at https://brainly.com/question/16313918

Answer: 26

Step-by-step explanation: Add all the booths together and you will get 300. You will get 300 because the t-shirts booth is $26. Now divide 300 by how many booths there are, which is six. And your mean will be 50.

The length of the arc which subtends a [tex]\pi/3[/tex] radians angle on a circle with 6 ft radius is given by: Option C: 6.3 feet approximately.

[tex]2\pi^c = 360^\circ = \text{Full circumference}[/tex]

The superscript 'c' shows angle measured is in radians.

If radius of the circle is of r units, then:

[tex]1^c \: \rm covers \: \dfrac{circumference}{2\pi} = \dfrac{2\pi r}{2\pi} = r\\\\or\\\\\theta^c \: covers \:\:\: r \times \theta \: \rm \text{units of arc}[/tex]

For this case, we have:

Thus, if we take:

Length of the arc = L feet, then:

[tex]L =r \times \theta = 6 \times \dfrac{\pi}{3} = 2\pi \: \rm ft \approx 6.28 \approx 6.3 \: ft[/tex]

Thus, the length of the arc which subtends a [tex]\pi/3[/tex] radians angle on a circle with 6 ft radius is given by: Option C: 6.3 feet approximately.

Learn more about arc length here:

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Answer:

c

Step-by-step explanation:

i did it and got it right

Answer:

[tex]y=14x^2+x-3[/tex]

Step-by-step explanation:

If the zeros of the polynomial are -1/2 and 3/7 then:

[tex]\implies x=-\dfrac12[/tex]

Add 1/2 to both sides:

[tex]\implies x+\dfrac12=0[/tex]

Multiply both sides by 2:

[tex]\implies 2x+1=0[/tex]

[tex]\implies x=\dfrac37[/tex]

Subtract 3/7 from both sides:

[tex]\implies x-\dfrac37=0[/tex]

Multiply both sides by 7:

[tex]\implies 7x-3=0[/tex]

Therefore, the factored form of the polynomial is [tex]y=(2x+1)(7x-3)[/tex]

Expanding the brackets so that the polynomial is in standard form:

[tex]\implies y=14x^2-6x+7x-3[/tex]

[tex]\implies y=14x^2+x-3[/tex]

Their sum of ages is 45

So

Therefore

Step-by-step explanation:

let the tala's age be x and nabil's be y

x+y=45(equation 1)

x=y+27

x-y=27(equation 2)

solving 1 and 2 equation

x+y=45

x-y=27

______

2x=18

x=9

therefore the talas age is 9

putting the value of x in equarion 1

9+y=45

y=45-9

y=36

Step-by-step explanation:

Area =5m×11m=55m²

perimeter =(11m+5m)×2=52m

hope it helps!

Answer:

craig had played approx 5 games..

Step-by-step explanation:

25 is the amount which craig have. 25-5.2=19.9 and when we divide 19.9 with 4 ie. 19.9÷4 = 4.9

Answer:

L: (15+6x) W: 2

L: (10+4x) W: 3

L: (5+2x) W: 6

Step-by-step explanation:

We don't have any numbers here to do calculations, so probably this is just an exercise in FACTORING. Also to practice that area is length times width.

The area given,

30 + 12x

can be factored several ways to be able to fill in the table.

This kind of factoring is like "un-distributive property" where a common factor can be factored out of the expression. Usually its helpful to factor out the greatest common factor (GCF) but in this case any common factor will do.

Also, unless there are more directions, either factor may be the length or the width.

2(15+6x)

3(10+4x)

6(5+2x)

Answer:

A. is the answer because 1/2 x 20 will equal 40 gallons

Answer:

21.75

Step-by-step explanation:

Because 6.00+6.25=12.25+7.00=19.75+8.00=27.75

Answer:

$4

Step-by-step explanation:

12÷4=3

20÷4=5

56÷4=14

Answer:

the answer is 56

Step-by-step explanation:

first off you need to add every number up which adds to be 336,

then you divide by the number of pieces in the data which in this case is 6,

366 divided by 6 is 56

I HOPE THIS HELPED!

Answer:

y=1/3x+2

Step-by-step explanation:

y=mx+b form is where m = the slop and b = the y interecept.

Y - Intercept

we can tell the y-intercept is 2 just by looking at the graph

Slope

For the slope, we can pick two points on the line, in this case, I will pick the points (0,2) and (3,3). Then, we can use the slope formula (y2-y1)/(x2-x1) to find the points, and after plugging the points in, we get 1/3, which is the slope

Plugging the numbers into slop intercept form

So we now know the slope is 1/3 and y-intercept is 2, so after plugging it into slope-intercept form (y=mx+b), we get y=1/3x+2

Answer:

( - y - 3 , - x - 1 )

Step-by-step explanation:

( x , y ) ----> ( - y , x ) ----> ( - y - 3 , x + 1 ) ----> ( - y - 3 , - x - 1 )

Considering the total of peas is 72, Sally's initial number of peas was 56.

Assuming the two brothers did not eat any peas, the total of peas both at the beginning and end is 72 peas.

By the end, Sally has 25 peas and Will has 72 peas.

Before the mother declared none of them would have dessert Sally had given Will half of her peas. This means 25 peas represent half of the peas:

25 x 2 = 50 peas        22 peas in Will's plate

Before this, Will had given Sally half of his peas

22 peas x 2 = 44 peas              28 peas on Sally's plate

Right before this, Sally gave Will half of her peas:

28 x2 = 56 peas                      16 peas on Will's plate

Let's check this answer:

S= 56            W= 16         -Beginning

S= 28            W=44         - Sally gives Will half of her peas

S= 50            W=22          - Will gives sally half of his peas

S=25             W= 47         -Sally gives will half of her peas

Learn more about peas in: https://brainly.com/question/26169406

[tex]\frac{1}{2a}[/tex]

Simplify or expand

[tex](2a)^{-1}[/tex]

Simplify using negative exponent rule [tex]a^{-n}=\frac{1}{a^n}[/tex]

[tex]\frac{1}{2a}[/tex]

I hope this helps you

:)

Answer:

The key to this question is converting all the mass units to the same unit and adding them all up.

The only value that isn't consistent with the other units is 450 gm or grams.

Recall that 1 gram is equal to 0.001 kilo grams. So if you want to convert grams to kilograms you would multiply that amount by 0.001 or 1/1000

[tex]450gm * \frac{1}{1000} = 0.45kg[/tex]

Now let's add up all the masses.

[tex]53.6kg + 0.45kg + 4.5kg = 58.55 kg\\[/tex]

(Now a few footnotes here, that I considered but wasn't sure about. The answer asks for weight, but you're only given mass to work with. That would be fine, if the question asked you to convert it to SI weight units like Newtons, but there's no mention of that. And also I'm not sure if the question requires significant digits. But I'll continue the answer if you think so)

To convert this into weight in Newtons, multiply by 9.81 m/s^2

[tex]58.55kg*9.81m/s^2 = 574.3755 N\\\\= 5.7 * 10^2 N[/tex]

Answer:

8p+5p

=13p

=6a-5b procesa

Answer:

Hope the pictures will help. I have done what I knew

Answer:

Step-by-step explanation:

the area of this rectangle is

(10 + 2x)(8 + 2x) = 168

80 + 20x + 16x + 4x² = 168

4x² + 36x = 88

Step-by-step explanation:

A quadratic equation is an equation whose leading coefficient is of the second degree. The correct option is A.

A quadratic equation is an equation whose leading coefficient is of second degree also the equation has only one unknown while it has 3 unknown numbers. It is written in the form of ax²+bx+c.

Let the width of the frame be represented by x. Therefore, the length and the breadth of the photographer be represented by (10+2x) inches and (8+2x) inches. Therefore, the total area of the photograph can be written as,

Area = Length × Breadth

168 inches² = (10+2x) inches × (8+2x)inches

168 = (10+2x)(8+2x)

168 = 80 + 20x + 16x + 4x²

0 = 80 + 20x + 16x + 4x² - 168

0 = 4x² + 36x - 88

4x² + 36x - 88 = 0

4x² + 36x = 88

Hence, the following quadratic equations that would be used when solving the width of the frame is 4x² + 36x = 88.

Learn more about Quadratic Equations:

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Answer:

x = 5

Step-by-step explanation:

5x+17=42

5x + 17 - 17 = 42 - 17

Answer:

B

Step-by-step explanation: