E Homework: 3.1 Homework
Evaluate the function f(z) = 3z-8 at the indicated values.
a) Find f(-4).
1
b) Find f
2
c) Find f(z-7).
a) f(-4)=
(Simplify your answer. Type an integer or a simplified fraction.)
THINGS

Problem 13

x = central angle = 360-105 = 255 degrees

r = 8 = radius

A = sector area

A = (x/360)*pi*r^2

A = (255/360)*pi*8^2

A = 142.41887

I used the calculator's stored value of pi to get the most accuracy possible.

Round that decimal value however you need to. The same applies to the other questions as well.

========================================================

Problem 14

x = central angle = 114 degrees

r = radius = unknown

A = sector area = 36 square cm

A = (x/360)*pi*r^2

36 = (114/360)*pi*r^2

36*(360/114) = pi*r^2

113.68421 = pi*r^2

r^2 = 113.68421/pi

r^2 = 36.18681

r = sqrt(36.18681)

r = 6.015547

========================================================

Problem 15

x = area of the full circle

The pizza slice shown has an area of 49 square meters.

This is 68/360 of a full circle, which means,

sector area = (68/360)*(full circle area)

49 = (68/360)*x

x = 49*(360/68)

x = 259.41176

Answer:

13)  142.4 in²

14)  6.0 cm

15)  259.4 m²

Step-by-step explanation:

Formula

[tex]\textsf{Area of a sector of a circle}=\left(\dfrac{\theta}{360^{\circ}}\right) \pi r^2[/tex]

(where r is the radius and [tex]\theta[/tex] is in degrees)

Given:

Substitute the given values into the formula and solve for A:

[tex]\implies \textsf{Area}=\left(\dfrac{255^{\circ}}{360^{\circ}}\right) \pi 8^2[/tex]

[tex]\implies \textsf{Area}=\dfrac{136}{3} \pi[/tex]

[tex]\implies \boxed{\textsf{Area}=142.4\: \sf in^2 \:(nearest\:tenth)}[/tex]

Given:

Substitute the given values into the formula and solve for r:

[tex]\implies 36=\left(\dfrac{114^{\circ}}{360^{\circ}}\right) \pi r^2[/tex]

[tex]\implies \dfrac{36 \cdot 360}{114 \pi}=r^2[/tex]

[tex]\implies r^2=\dfrac{2160}{19 \pi}[/tex]

[tex]\implies r=\sqrt{\dfrac{2160}{19 \pi}}[/tex]

[tex]\implies \boxed{r=6.0\: \sf cm\:(nearest\:tenth)}[/tex]

Given:

Substitute the given values into the formula and solve for r²:

[tex]\implies 49=\left(\dfrac{68^{\circ}}{360^{\circ}}\right) \pi r^2[/tex]

[tex]\implies \dfrac{49 \cdot 360}{68 \pi}= r^2[/tex]

[tex]\implies r^2=\dfrac{4410}{17 \pi}[/tex]

[tex]\textsf{Area of a circle} = \pi r^2[/tex]

[tex]\implies \textsf{Area of a circle N} =\dfrac{4410}{17 \pi} \cdot \pi[/tex]

[tex]\implies \textsf{Area of a circle N} =\dfrac{4410}{17}[/tex]

[tex]\implies \boxed{\textsf{Area of a circle N} =259.4\: \sf m^2\:(nearest\:tenth)}[/tex]

Answer:

see the attachment photo!

Answer:

b

Step-by-step explanation:

Step-by-step explanation:

so, "- 1" is also part of the square root ?

sqrt(x - 1) = x - 3

it is clear that for any value x < 1 we have no solution in R (as this makes the argument of the square root negative, and there is so real number solution for the square root of negative numbers).

now square the whole equation.

x - 1 = (x - 3)² = x² - 6x + 9

x² - 7x + 10 = 0

the general solution for quadratic equations is

x = (-b ± sqrt(b² - 4ac))/(2a)

in our case

a = 1

b = -7

c = 10

x = (7 ± sqrt(49 - 4×1×10))/(2×1) =

= (7 ± sqrt(49 - 40))/2 = (7 ± sqrt(9))/2

x1 = (7 + 3)/2 = 10/2 = 5

x2 = (7 - 3)/2 = 4/2 = 2

x2 is probably (given the answer options) not a valid solution for the original problem, as it represents the negative solution of sqrt(x - 1).

sqrt(2 - 1) = 2 - 3

± 1 = -1

remember, every square root has always 2 solutions : a positive and a negative one.

your teacher clearly only wanted the positive solution, which is x1 = 5.

so, yes,

C. x = 5

is the correct answer.

but please send your teacher my regards and comments. he/she has to state that only the positive solution to the square root is required/allowed.

because, formally, also x = 2 is a valid solution.

and therefore, C. AND D. are correct answers !!!!

The representation of the vector in trigonometry form is t = 13 ❬cos 112.62°, sin 112.62°❭

The representation of complex number in polar form is expressed as;

y = r(cosФ + isinФ)

where;

r is the modulus

Ф is the argument

Given the vector t = –5i + 12j, the modulus of the vector is given as;

r = √(-5)²+(12)²

r = √25 + 144

r = √169

r = 13

Determine the angle between the vectors

Ф = arctan(-12/5)

Ф = -67.38

Since tan is negative in the second quadrant, hence;

Ф = 180 - 67.38

Ф = 112.62°

The representation of the vector in trigonometry form is t = 13 ❬cos 112.62°, sin 112.62°❭

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The simple interest rate​ is 8% if the Jackie decided to open a restaurant. She borrowed 25000 for 5 years. After 5 years, she had paid back 35000.

It is defined as the interest on the based on the principal amount, it does not include the compounded amount. The interest calculate on the initial amount or borrowed amount.

We have:

Jackie decided to open a restaurant. She borrowed 25000 for 5 years. After 5 years, she had paid back 35000.

We know the formula for simple interest is:

A = p(1 + rt)

We have A(final amount) = 35000

P(initial amount0 = 25000

t(time)  = 5 years

35000 = 25000(1 + 5r)

1.4 = 1 + 5r

0.4 = 5r

r = 0.08 or

r = 8%

Thus, the simple interest rate​ is 8% if the Jackie decided to open a restaurant. She borrowed 25000 for 5 years. After 5 years, she had paid back 35000.

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Answer: 64

Step-by-step explanation:

[tex]10x+8+5x-4=12x+16\\15x+4=12x+16\\3x+4=16\\3x=12\\x=4\\\\LN=12(4)+16=\boxed{64}[/tex]

Answer:

The National Housing Act of 1937 established guidelines for maximum rents for low-income families.  Originally the maximum rent threshold was set at 20%, however this increased to 30% in 1981 (and has remained at this level ever since).  This figure is used to determine how much of your gross monthly income you should spend on rent.

The 28% Rule is used for determining how much of your gross monthly income should be used for a mortgage, however the FHA's threshold is a little higher at 31% of your gross monthly income on a mortgage.

Renting:

30% of $1,250 = 0.3 × 1250 = $375

Mortgage 28% Rule:

28% of $1,250 = 0.28 × 1250 = $350

Mortgage 31% FHA:

31% of $1,250 = 0.31 × 1250 = $387.50

Therefore, discounting the higher FHA's threshold, the maximum amount to budget for housing is:

Answer: Heyaa!  :))

60/50 as a percentage is.. 120%

Step-by-step explanation:

Hopefully this helps you! ~

The probability of selecting a jack and a queen is 1/169.

Probability calculates the odds that an event would happen. The odds that the event would happen lies between 0 and 1.

The probability of selecting a jack and a queen = (number of jacks / number of cards in a deck) x (number of queens / number of cards in a deck)

4/52 x 4/52 = 1/169

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Callie will have $104.12 less than what she earned each month.

A number which can be represented in the form p/q where q ≠ 0 are called Rational Numbers.

The complete question is

Callie was billed $416.48 for car repairs. She will pay the service center in 4 equal monthly installments from her bank account.

What is the net change in her bank account balance after each monthly payment? The net change to Callie’s bank account is -$416.48.

The negative sign indicates money leaving Callie’s account. Which rational number represents the number of months that Callie has to pay off the bill? What does the sign on the number mean?

Write an expression to represent the net change to Callie’s account balance each month.

The number of months Callie has to pay the bill is for 4 months, as there are 4 equal installments

The net change in account in Callie's Account balance each month is

-$416.48  / 4 = -$104.12.

The (-) sign indicate the reduction of the net balance from her account.

Callie will have $104.12 less than what she earned each month.

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Answer:

[tex]\bf \sf \dfrac{1}{3}[/tex]

Take points: (6, 2), (3, 1)

[tex]To \ find \ proportionality = \sf \dfrac{y_2-y_1}{x_2-x_1}[/tex]

Insert values

[tex]\rightarrow \sf \dfrac{1-2}{3-6}[/tex]

Simplify

[tex]\rightarrow \sf \dfrac{-1}{-3}[/tex]

Cancel out the negatives

[tex]\rightarrow \sf \dfrac{1}{3}[/tex]

Answer:

B) [tex]\frac{1}{3}[/tex]

Step-by-step explanation:

When y varies directly with x, the relationship is [tex]y=kx[/tex] where [tex]k[/tex] is the constant of proportionality. Hence, [tex]k=\frac{y}{x}[/tex].

So, your answer would not be correct because you did [tex]\frac{x}{y}[/tex] instead of [tex]\frac{y}{x}[/tex], so the correct option would be the reciprocal, or [tex]\frac{1}{3}[/tex].

Answer:

Mean = 3.125 ≈ 3.13

Step-by-step explanation:

Mean = Sum of numbers =  1 + 2 + 3 + 4 + 2 + 6 + 3 + 4 = 25 = 3.125≈3.13

           Amount of number                     8                             8

Add -5 to each side of the inequality:

-3 ≤ x + 5 ≤ 8

-3 - 5 ≤ x + 5 - 5 ≤ 8 - 5

-8 ≤ x ≤ 3

Since x is an integer, there are 12 possible solutions belonging to {-8, -7, ..., 1, 2, 3}. In the sum of these solutions, the integers -3 to 3 cancel out, and the rest give

-8 - 7 - 6 - 5 - 4 = -30

The volume of the rectangular prism is exactly (3/8) of a cubic inch.

Remember that for a rectangular prism of height H, length L, and width W, the volume is:

V = H*L*W

In this case, we have:

Then the volume of the rectangular prism is given by:

[tex]V = (1 in)*(\frac{3}{4} in)*(\frac{1}{2} in)= \frac{3}{4*2} in^3 = \frac{3}{8} in^3[/tex]

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Answer:

2

Step-by-step explanation:

g/5 - h is equal to 20/5 - 2

equal to 20 divided by 5 is equal to 4(20÷5=4)

then 4minus h which is 4- 2 =2

therefore the answer is 2

I hope this helps you

Answer:

[tex]y = mx + b[/tex]

≡ For instance, I have the equation, y = 9x + 5, and I must find the slope. The slope is 9, because 9 is in the m area of the equation, making these equations easier to determine and have less steps than before.

Answer:

45q^10

Step-by-step explanation:

First, we can separate the equation to make it simpler to understand.

5*q^4*9*q^6

Then we group terms that we can multiply:

(5*9)*(q^4*q^6)

Then we simplify

45*q^10

45q^10

Answer:

1) Area of frame: [tex]140cm^2[/tex] ; Area of picture: [tex]40cm^2[/tex] ; Total Area: [tex]180cm^2[/tex].      

2) Area 1 =  [tex]48cm^2[/tex] ; Area 2 = [tex]12cm^2[/tex] ; total area = [tex]60cm^2[/tex] [first answer line : [tex]60cm^2[/tex]]

Step-by-step explanation:

1. So to answer this question, you have to find the inner photo area first (which you will then subtract from the overall rectangle area to get the photo frame area).

To find area, you multiply length x width. For this question, there are not enough measurements given to initially multiply length and width. So, assuming that the photo is centered on the frame and the frame width is consistent along all sides, you find the difference between the overall length (12) and the picture length (5).

12 - 5 = 7

The leftover area (outside of the picture) is 7 cm (half of seven on both sides), so one side can be assumed to be : 3.5 cm

this means that 15 cm - 3.5 cm of both sides lengths (difference between the two lengths given) is the height of the photo, 15 - 3.5(2) = 8

So, the dimensions/measurements of the photo are 5 cm by 8 cm.

This means that the inner photo area is 40 (5 x 8) cm

The area of the frame will be the area of the total rectangle [12 x 15] - the inner photo area [40].  [ (12)(15) - 40 ]

[180 - 40] = 140 cm

(area is measured in squared units, so the area of the frame should be written as [tex]140cm^{2}[/tex] ; and the area of the photo should be written as [tex]40cm^{2}[/tex])

The total area is the entire area of the rectangle: (12)(15) = 180. (This should be written as [tex]180cm^2[/tex])

--------------------------------------

2) Finding the area of a shape that isn't a simple rectangle is easier if you separate the shape into smaller rectangles. I will separate the two rectangles into 4 x 12 and 2 x 6 [6 cm would be the remaining side length if you remove the length of 4].

{you can separate the shape in multiple ways, so my answer is only one answer to this problem out of other splits.}

as mentioned, the area is length x width.

4 x 12 = 48.

2 x 6 = 12. Once again, you should write area in squared units.

(the area 1 should be written as [tex]48cm^{2}[/tex] ; the area 2 should be written as [tex]12cm^2[/tex])

you can combine the separated areas (add them) to find the total area. 48 + 12 = 60.

(the total area should be written in squared units also, so the total area should be written as: [tex]60cm^2[/tex])

The area of the figure is [tex]60cm^2[/tex]

Let May's age be represented with m

Lilian's age 2/3m

Ratio of May's age to Lilian's age = m : 2/3m

Multiply both sides by 3 : 3  : 2

Ratio of Lilian's age their total age: 2 : 5

Lilian's age = 2/5 x 25 = 10 years

May's age = 3/5 x 25 = 15 years

Let the mass of carrots be represented with c

The mass potatoes would be represented with 5/2c

Ratio of carrots to potatoes : 2 : 5

Ratio of the mass of potatoes to the total mass : 5 : 7 = 5/7

Mass of carrots = 5/2c - c = 9

3/2c = 9

3c = 18

c = 6

Mass of potatoes = 5/2 x 6 = 15

Total mass = 15 + 6 = 21 kilograms

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It is true that the line segment AB equals 26

The given parameters are:

AB = x +16

BC = 4x + 11

AC = 77

The two-column proof is as follows:

AC = AB + BC                     Line segment formula

77 = x + 16 + 4x + 11            Substitution property of equation

77 = 5x + 27                        Addition property of equation

5x = 50                               Subtraction property of equation  

x = 10                                    Division property of equation

AB = 10 +16                          Substitution property of equation

AB = 26

Hence, the line segment AB has been proved to equal 26

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For the given relation, the coefficient is (1/5) and the exponent is 1.

For a relation of the form:

[tex]y = a*x^n[/tex]

a is the coefficient and n is the exponent.

In this case, we have:

[tex]y = \frac{x}{5}[/tex]

This can be rewritten to:

[tex]y = \frac{1}{5}*x^1[/tex]

So we can see that the coefficient is (1/5), and the exponent is 1.

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Answer:

Yes

Step-by-step explanation:

The sum must be greater than 8 it can't be 7 anyway. Sums can be 9, 10 or 12. P = (4+3+1)/36 = 3/36

Answer:

A

Step-by-step explanation:

hope this help

The line that contains an example of assonance is C. He fell asleep under the oak tree, feeling fine.

This refers to the similarity of sounds that can be found in nearby words in a sentence, between their vowels and/or consonants.

Furthermore, alliteration means the occurrence of similar words or sounds in a sentence at the beginning of closely connected words.

With this in mind:

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[tex]3^2+y^2=8^2\\9+y^2=64\\y^2=55\\\\x^2+3^2=y^2\\x^2+9=55\\x^2=46\\x=\sqrt{46}=2\sqrt5\approx6,8[/tex]

The statement that matches the vector operation shown on the coordinate grid is v + w = u.

In order to add two vectors a and b graphically by using the tail and tip method, we must draw the tail of b at the tip of vector a.

Then we must draw a line that goes from the tail of vector a to the tip of vector b.

This line represents the sum of a + b.

In the given problem, we notice that the tail of the vector w is on the tip of the vector v.

The line that joins the tail of vector v with the tip of vector w is vector u.

Therefore we can say that v + w = u

The statement that matches the vector operation shown on the coordinate grid is v + w = u.

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The length has [tex]\frac{3.5}{0.5}=\boxed{7}[/tex]

The width has [tex]\frac{2.5}{0.5}=\boxed{5}[/tex]

The height has [tex]\frac{1.5}{0.5}=\boxed{3}[/tex]

The probability that it rains at most 2 days is 0.00005995233 and the variance is 0.516

The given parameters are:

The probability that it rains at most 2 days is represented as:

P(x ≤ 2) = P(0) + P(1) + P(2)

Each probability is calculated as:

[tex]P(x) = ^nC_x * p^x * (1 - p)^{n - x}[/tex]

So, we have:

[tex]P(0) = ^7C_0 * (92\%)^0 * (1 - 92\%)^{7 - 0} = 0.00000002097[/tex]

[tex]P(1) = ^7C_1 * (92\%)^1 * (1 - 92\%)^{7 - 1} = 0.00000168821[/tex]

[tex]P(2) = ^7C_2 * (92\%)^2 * (1 - 92\%)^{7 - 2} = 0.00005824315[/tex]

So, we have:

P(x ≤ 2) =0.00000002097 + 0.00000168821 + 0.00005824315

P(x ≤ 2) = 0.00005995233

Hence, the probability that it rains at most 2 days is 0.00005995233

This is calculated as:

Mean = np

So, we have:

Mean = 7 * 92%

Evaluate

Mean = 6.44

Hence, the mean is 6.44

This is calculated as:

σ = √np(1 - p)

So, we have:

σ = √7 * 92%(1 - 92%)

Evaluate

σ = 0.718

Hence, the standard deviation is 0.718

We have:

σ = 0.718

Square both sides

σ² = 0.718²

Evaluate

σ² = 0.516

This represents the variance

Hence, the variance is 0.516

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