Directions: Determine whether each relation is a function. Explain your answer.
X
12)
10)
#IN
13)
x
14)
15)
10
1

The solutions for the given equations are x = 9i , -9i , x = 2i,-2i ,

x = [tex]\sqrt{13}[/tex] , -  [tex]\sqrt{13}[/tex] , x = [tex]\sqrt{14}[/tex]i , - [tex]\sqrt{14}[/tex]i .

Given equations ,

[tex]x^{2}[/tex] + 81 = 0  ,[tex]x^{2}[/tex]-22 = -26 , 3[tex]x^{2}[/tex]-18=21 ,2[tex]x^{2}[/tex] +15 = -13

What is Quadratic equation ?

quadratic equation can be defined as the equation which is in the form of a[tex]x^{2}[/tex]+bx + c = 0 .

where a,b,c are constants .

By solving we get ,

[tex]x^{2}[/tex] +81 = 0

[tex]x^{2}[/tex] = -81

x = 9i , -9i

[tex]x^{2}[/tex] - 22 = -26

[tex]x^{2}[/tex] = -26 + 22

[tex]x^{2}[/tex] = -4

x = 2i,-2i

3[tex]x^{2}[/tex] - 18 = 21

3[tex]x^{2}[/tex] = 18+21

3[tex]x^{2}[/tex] = 39

[tex]x^{2}[/tex] = 13

x = [tex]\sqrt{13}[/tex] , -  [tex]\sqrt{13}[/tex]

2[tex]x^{2}[/tex] +15 = -13

2[tex]x^{2}[/tex]  = -13-15

2[tex]x^{2}[/tex]  = -28

[tex]x^{2}[/tex]  = -14

x = [tex]\sqrt{14}[/tex]i , - [tex]\sqrt{14}[/tex]i

Hence the solutions for the given equations are x = 9i , -9i , x = 2i,-2i ,

x = [tex]\sqrt{13}[/tex] , -  [tex]\sqrt{13}[/tex] , x = [tex]\sqrt{14}[/tex]i , - [tex]\sqrt{14}[/tex]i .

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Hello there!

Answer:

Circumference: [tex]l = 2\pi r = 2*3.14*0.9 = 5.652 (m)[/tex]

Area: [tex]S = \pi r^2 = 3.14 * 0.9^2 = 2.5434(m^2)[/tex]

Step-by-step explanation:

We should know 2 important formulas:

Circumference: [tex]l = 2\pi r[/tex]

Area: [tex]S = \pi r^{2}[/tex]

So we need to find the value of r (radius) which equal to a half of diameter:

[tex]r = d/2[/tex]

[tex]r = 1.8/2 = 0.9(m)[/tex]

Circumference: [tex]l = 2\pi r = 2*3.14*0.9 = 5.652 (m)[/tex]

Area: [tex]S = \pi r^2 = 3.14 * 0.9^2 = 2.5434(m^2)[/tex]

The answer of given parabola question is 6.125ft.

a curve produced by the intersection of a cone's surface with a plane perpendicular to a straight line; a curve produced by a moving point whose distance from a fixed point is equal to its distance from a fixed line.

x² = 4py

x=radius which can be found by dividing d=14ft by half

x = d/2 = 11/2 = 7ft

y=2ft is the depth

p is the vertex of the parabola

p = x²/4y

p = 7²/4×2

p=6.125ft

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By solving the interval  : [0,2pi] 4 csc x +6=-2 is  7pi/6 , 11pi/6

[tex]& 4 \csc x+6=-2 \\[/tex]

[tex]& 4 \csc x=-8 \\[/tex]

Simplifying,

[tex]& \csc x=-2 \\[/tex]

[tex]& \frac{1}{\sin x}=-2 \\[/tex]

[tex]& \sin x=-\frac{1}{2} \\[/tex]

We get,

[tex]& x=\frac{7 \pi}{6}, \frac{11 \pi}{6}[/tex]

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a) The after-tax cost of the vehicle Rachel is buying is $29,368.70.

b) The part of the after-tax cost that Rachel will finance after making the down payment is $25,118.70.

c) The total payments after 5 years are $30,659.60.

d) The total interest Rachel paid is $1,290.90.

The interest payment represents the difference between the total monthly payments and the financing part of the after-tax cost of the vehicle.

The total monthly payments ($26,409.60) are obtained by multiplying the monthly payments ($440.16) by the number of payment periods (60).

Value of vehicle = $25,990

Harmonized sales tax (HST) = 13%

After-tax cost of the vehicle = $29,368.70 ($25,990 x 1.13)

Down payment = $4,250

Financing part = $25,118.70 ($29,368.70 - $4,250)

Monthly payments = $440.16

Financing period = 60 months (5 years x 12)

Total monthly payments = $26,409.60 ($440.16 x 60)

The total amount paid for the car = $30,659.60 ($26,409.60 + $4,250)

Total interest = $1,290.90 ($26,409.60 - $25,118.70)

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The Kilograms of type B that are in one bag of the Latoya's Coffee shop blend would be = 3kg

A mixture is defined as the combination of two or more components which can or cannot be separated by ordinary methods.

The coffee blend of LaToya shop = Type A and B

A bag of the coffee blend = 6kg of Type A.

4 bags of coffee blend = 36kg

Therefore 4 bags of coffee blend contains = 6 see×4 = 24 kg of Type A

Type B in each bag = 36 - 24 = 12/4 = 3kg.

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By working a full year, you may expect to earn a total of $19,646.25 in earrings.

This mathematical operation enables the multiplication, division, addition, or subtraction of numbers. The following is the structure of an expression: Expression: (Number/Variable, Math Operator, Math Operator)

An expression, also known as an algebraic expression, is any mathematical statement that consists of numbers, variables, and an arithmetic operation between them. For example, the mathematical sign + separates the phrases 4m and 5 from the variable m in the phrase 4m + 5.

Combining numbers, variables, and operators to represent something's value is known as a mathematical expression. Setting two expressions equal to one another creates an equation, a mathematical statement.

= Total overtime pay of $2,193.75 (first 6 months)

Add the regular and overtime pay after that:

= $7,312.50 + $2,193.75

= $9,506,25 in total income (first 6 months)

$7,800.00totalregularpay(last6months)

Overtime pay:(26weeks in a half year) \=$8\times

7.57.5\times1.51.5\times

$ 26

= Total overtime pay of $2,340.00 (last 6 months)

Add the regular and overtime pay after that:

= $7,800.00 + $2,340.00

= $10,140.00 in total income (last 6 months)

In the end, add the combined earnings from the two half years:

= $9,506.25 + $10,140.00

= Total annual profits of $19,646.25 (expected)

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In this question, we're looking for the number Malcom used to scale the two numbers. We can see there's a pattern, 9 is 1/6 of 54 and 40 is 1/6 of 240!

(54 divided by 9 is 6 and 240 divided by 40 is 6!)

therefore, the scale factor must be 6

An Example of a caravan is eight covered wagons traveling together on the trail. Meaning, option A is correct.

A caravan, travel trailer, camper, tourer, or camper trailer is a trailer towed behind a road vehicle to provide a more comfortable and secure sleeping space than a tent.

It allows people to have their own home on a trip or vacation without relying on a motel or hotel, and it allows them to stay in places where none are available. However, in some countries, campers are restricted to designated sites where fees must be paid.

Caravans range from basic models that are little more than a tent on wheels to those that have several rooms with all of the furniture, furnishings, and equipment of a home. The solid-wall trailers can be made of metal or fibreglass.

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Answer:

15

Step-by-step explanation:

Opposite angles in a parallelogram are equal. (this is a parallelogram because it has 2 pairs of parallel sides.)

So

3x+2=47

3x=45

x=45/3

x= 15

The amount of money that can be saved per ounce by guiding the larger box is $0.009.

Equation modelling is the process of writing a mathematical verbal expression in the form of a mathematical expression for correct analysis of the given problem.

Given is that a 38 ounce box of cat food costs $1.69 and a 24 ounce box costs $1.29.

For the larger box -

38 ounce box of cat food costs $1.69

1 ounce of this box will cost $(1.69/38) = $0.045

For the smaller box -

24 ounce box of cat food costs $1.29

1 ounce of this box will cost $(1.29/24) = $0.054

Money that can be saved per ounce by guiding the larger box -

0.054 - 0.045

0.009

Therefore, the amount of money that can be saved per ounce by guiding the larger box is $0.009.

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The graph of the equation x + 2 would be a straight line that starts at the point (-2, 0) and goes up 2 units on the y-axis. So, the line would pass through the point (0,2) and would be parallel to the x-axis.

The graph of the equation 3x when x is 2 would be a straight line that starts at the point (0,0) and goes up 6 units on the y-axis for each 1 unit on the x-axis. So, the line would pass through the point (2,6) and would have a slope of 3.

In mathematics, a diagram is a visual representation of mathematical concepts or ideas. Diagrams can take many forms, such as graphs, charts, illustrations, and figures, and can be used to help explain or understand mathematical concepts.

For example, a graph is a type of diagram that is used to represent the relationship between two variables. It is commonly used in algebra and calculus to show the relationship between an independent variable (x-axis) and a dependent variable (y-axis).

A chart is a type of diagram that is used to organize and present data. It is commonly used in statistics to show the distribution of data or to compare different sets of data.

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The area of the parallelogram is 72 square units. Option B

The formula for calculating the area of a parallelogram is expressed as;

A = bh

Given that;

From the information given, we have that;

Now, substitute the values

x + y = 8 + 4

add the values

x + y = base = 12 units

h = 6 units

Now, substitute the values into the formula, we get;

Area, A = 12(6)

multiply the values

Area, A = 72 square units

Hence, the value is 72 square units

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Answer:

47 and 53

Step-by-step explanation:

list of prime numbers to 100:

2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97

50 is between 47 and 53

Answer:

-2

Step-by-step explanation:

To find the slope, subtract y1 - y2, then divide by x1-x2

The y numbers in this set is -10 & 8

The x numbers in this set is 9 & 0

-10-8= -18

9-0 = 9

-18/9 = -2

The slope would be -2

The given quadratic equation has two possible roots as -

{x} = -1/2 and {x} = 1.667.

A quadratic equation is a equation that is of the form -

y = f{x} = ax² + bx + c

Given is the statement as -

"12 x squared minus 14 x equals 10"

The given function can be written as -

f(x) = 12x² - 14x - 10

Refer to the graph attached. The x - intercepts show the solution of the given quadratic equation. So, we can write -

(x + 1/2)(x - 1.667) = 0

(x + 1/2) = 0     and     (x - 1.667) = 0

x = -1/2     and      x = 1.667

Therefore, the given quadratic equation has two possible roots as -

{x} = -1/2 and {x} = 1.667.

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Answer:

Step-by-step explanation:

The number of hours does each group member work on the project is 4 hours. Therefore, the correct answer is option B.

In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.

The given equation is x+45/4=4x.

The solution of an equation is the set of all values that, when substituted for unknowns, make an equation true.

4x-x=45/4

3x=45/4

x=15/4

x=3.75

x≈4 hours

Therefore, option B is the correct answer.

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The elements in matrix X is attached below

Matrix is a mathematical construct consisting of an array of numbers, symbols, or expressions, arranged in rows and columns. It is most often used to represent linear relationships between two or more variables. Matrices are commonly used in science and engineering to represent systems of equations and in computer programming for representing data and performing operations on it.

In this problem, we can easily find x by reversing the variables and solve.

A - X = B

X = A - B

The elements in the matrix can be solved easily using an online calculator.

The value of x is attached below

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Answer:

Below

Step-by-step explanation:

Each PERIOD is 3 months     there is   4 periods per year

  periodic interest =  .055/4

   effective interest per year would then be

       (1 + .055/4)^4  - 1  = .056144  = ~ 5.61%

Answer: B strange and harrowing story.

Step-by-step explanation: Based on the description of the stranger's face in the novel, it is likely that the captain would expect the stranger to tell a strange and harrowing story. The stranger's face is described as "wild" and "ghastly," which suggests that the story he is about to tell may be disturbing or unsettling in some way. The captain may also expect the story to be emotionally intense, given the stranger's appearance and demeanor.

So basically what I do is find the formula for slope.

M= y2-y1/x2-x1

So I got

-5-(-6)/-9-(-6) = 1/3

answer = 1/3

:)

The table with correct values of A, B and C is,

⇒ Donuts   2        4        5        8

    Cost     13.80 27.60 34.50 55.20

A ratio indicates how many times one number contain in another number. The ratio of two number is written as x : y, which is equivalent to x/y. Where, x and y are individual amount of two quantities. And, Total quantity gives after combine as x + y.

We have to given that;

The table below shows the ratios of boxed donuts to the cost.

Donuts    A       4        5     C

Cost    13.80  27.60   B   55.20

Now, By definition of ratio, we get;

⇒ A / 13.80 = 4 / 27.60

⇒ A = 13.80 × 4 / 27.60

⇒ A = 2.00

And,

⇒ 4 / 27.60 = 5 / B

⇒ B = 5 × 27.60 / 4

⇒ B = 34.5

⇒ 4 / 27.60 = C / 55.20

⇒ C = 55.20 × 4 / 27.60

⇒ C = 8

Thus, The table with correct values of A, B and C is,

⇒ Donuts   2        4        5        8

    Cost     13.80 27.60 34.50 55.20

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Answer:

a

Step-by-step explanation:

i took the test :)

23.9 dollars I believe (I needa waste characters thi)

ax + by = 6000 and a + 5 = b are two equations that might be used to calculate how many soup cans and frozen dinners were purchased.

There are several methods to define a formula. A mathematical statement that establishes the equivalence of two mathematical expressions is the definition of an equation in algebra. This is best shown by the formula 3x + 5 = 14. In this instance, the word equal comes between the phrases 3x + 5 and 14. Even the most basic algebraic equations include the usage of mathematical variables.

X now has 300 mg of sodium in it.

[tex]x = 300[/tex]

Y also has 450 mg of sodium in it.

[tex]y = 450[/tex]

Samuel reportedly buys five more frozen dinners than soup cans, and they all have a combined salt content of 6000 mg.

Let the number of frozen dinners be "b," and the number of soup cans be "a."

ax + by = 6000

a(300) + b(450) = 6000 .

Samuel bought 5 more frozen dinners than soup cans, according to the inquiry, which results in equation

[tex]a + 5 = b \\a(300) + (a + 5)(450) = 6000\\300a + 450a = 6000 - 2250\\ 750a = 3750\\ a = 3750/750\\ a = 5\\5 + 5 = b\\ b = 10[/tex]

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Answer: 13/15

Step-by-step explanation: Hope this helps, please mark brainliest and give thanks!

2/3+1/5

15÷3*2+15÷5*1

10+3/15

13/15

Answer:

  Coupon A is better by $2.80.

Step-by-step explanation:

You want to know how much better the best price is between coupon A's $55 rebate on $87 worth of pants, or coupon B's 60% off.

The price reduction offered by coupon B is ...

  0.60 × $87 = $52.20

Clearly, the $55 reduction offered by coupon A is a greater reduction than the $52.20 reduction offered by coupon B. The difference in value is ...

  $55.00 -52.20 = $2.80

Coupon A gives the lower price by $2.80.

Answer:

  28 toys

Step-by-step explanation:

Ben has 50 toys, of which 15 are new, 9 are favorites, and 2 are new and favorites. You want to know the number that are neither new nor favorite.

The number of new toys includes (new and favorite) and (new and not favorite). That is ...

  15 = 2 + new and not favorite

So ...

  new and not favorite = 15 -2 = 13

Likewise, the number of favorite toys includes (new and favorite) and (not new and favorite). That is ...

  9 = 2 + not new and favorite

  not new and favorite = 9 -2 = 7

The total of 50 toys includes ...

  total = (new and favorite) + (new and not favorite) + (not new and favorite) + (not new and not favorite)

  50 = 2 + 13 + 7 + (not new and not favorite)

Then the number of (not new and not favorite) is ...

  not new and not favorite = 50 -2 -13 -7 = 28

These are the toys that Ben gives away.

Ben gives away 28 toys.

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Answer:

Below

Step-by-step explanation:

f(t) = 4.1 (sin pi/6 t  - pi/3) + 19.7    <===will be a maximum when the sin portion is equal to 1

   so    sin ( pi/6 t - pi/3) = 1     given that sin is equal to one   at 0 and pi and 2 pi  and 3 pi    and 4 pi   etc

              pi/6 t - pi/3 =  0  or pi , 2 pi, 3 pi  , 4 pi

                  then t = 2 and 8 and 14   and 20 hrs  ( every 6 hrs starting with t = 2)

Answer:

-5/4

Step-by-step explanation:

slope(m)= y2-y1/x2-x1

from the graph 5-0/-2-2

=5/-4

answer = -5/4