13. Solve the simultaneous equations using an elimination method.
a) 2x + 5y = 27
2x - 3y = 3
You must show how you worked out your answers​

Answer:

D. g(-13) = 20

Step-by-step explanation:

Given information:

Option A, g(-4) = -11 cannot be true for g since the y-value of -11 is not in the given range.

Option B, g(7) = -1 cannot be true for g since the x-value of 7 is not in the given domain.

Option C, g(0) = 2 cannot be true for g since we have been given g(0) = -2.

Option D, g(-13) = 20 is true for g since the x-value of -13 is in the given domain, and the y-value of 20 is in the given range.

The sequence is going to be {2,−5,2,−5,…}. Since we can see that options A and B are one and the same, the correct answer is options A and B.

A sequence is a successive arrangement of two or more things that are constructed on the basis of a given formula.

Here, the first term is = 2

Each previous term has been multiplied by = -1

And then, it has been subtracted by = 3

So, following the formula given, we conclude that the second value will be = 2×(-1)-3 = -5

Similarly, the formula is going to be applied to the second term now which is -5, and then the third term is going to be = -5×(-1)-3 = 2

In this fashion, we can make the sequence. Options A and B is the correct answer.

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Answer:

80

Step-by-step explanation:

Answer:

9.

Step-by-step explanation:

The square root of 10 is approximately 3.16 so it would be closer to 9.

The volume of the given solid is equal to the triple integral of 1 over the region bounded by the coordinate planes and the plane 6x + 7y + z = 42. This can be written as:

[tex]$\iiint 1\, dV = \iiint 1\, dx\, dy\, dz$[/tex]

The region of integration is bounded by the coordinate planes x = 0, y = 0, and z = 0, and the plane 6x + 7y + z = 42. This is a right triangular prism with vertices (0,0,0), (6,0,0), and (0,6,42). To calculate the volume, we will use the triple integral in cylindrical coordinates, which can be written as:

[tex]$\iiint 1\, dV = \int0^{2\pi}\int0^6\int_0^{42/7} r\, dz\, dr\, d\theta$[/tex]

The volume of the given solid is given by:

[tex]$\frac{504\pi}{7}$[/tex]

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X is 55 after rearranging the equation given

Answer:

The answer to this question is x= 51/4

Answer:

b is 256 c is 48

Step-by-step explanation:

On solving the provided question, we can say that vertices of pentagon are (-1, -1), (-3, 4), (1, 7), (6, 5) and (3, -1); Area = 30 sq unit

A pentagon is a polygon with five sides that is used in geometry. The inner angles of a straightforward pentagon add up to 540°. Simple or self-intersecting pentagons are both possible. A pentagram is a self-intersecting regular pentagon. Five angles and all sides of a regular pentagon are equal. It is referred to as an irregular pentagon if the side lengths and angle measurements do not match. All outside angles, as far as we are aware, balance out inside angles. The polygon's exterior angle total is therefore equal to n(360°/n). There are five sides to a pentagon, therefore n must equal five. Consequently, 5(360°/5) = 360° is the sum of the pentagon's outer angles.

vertices of a convex pentagon are (-1, -1), (-3, 4), (1, 7), (6, 5) and (3, -1).

Area = 1/2 [ 24+3+15+0-3] - [3-30-3+9-0]

Area = 1/2| 60 |

Area of pentagon  = 30 sq unit

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Answer:

h = 8

Step-by-step explanation:

5.50h=44

Divided both sides by 5.50

h = 8

Let's check

5.50(8) = 44

44 = 44

So, h = 8 is the correct answer!

Answer:

201.00

Step-by-step explanation:

Answer:

1) Small-Cherry-Green, 2) Small-Cherry-Purple, 3) Small-Cherry-Red, 4) Small-Vanilla-Green, 5) Small-Vanilla-Purple, 6) Small-Vanilla-Red, 7) Small-Strawberry-Green, 8) Small-Strawberry-Purple, 9) Small-Strawberry-Red, 10) Small-bubble gum-Green, 11) Small-Bubble gum-Purple, 12) Small-Bubble gum-Red , 13) Huge-Cherry-Green, 14) Huge-Cherry-Purple, 15) Huge-Cherry-Red, 16) Huge-Vanilla-Green, 17) Huge-Vanilla-Purple, 18) Huge-Vanilla-Red, 19) Huge-Strawberry-Green, 20) Huge-Strawberry-Purple, 21) Huge-Strawberry-Red, 22) Huge-Bubble gum-Green, 23) Huge-Bubble gum-Purple, 24) Huge-Bubble gum-Red

b) 24

2) Tree diagram method

b) Each unique snow cone has an element of each category

3) 2

i) By counting

ii) By finding out the possible combinations

Step-by-step explanation:

The details of the options at Tia's Snow Xpress includes;

2 (different) sizes; Small or huge size

4 (different) flavors; Cherry, vanilla, strawberry, bubble gum

3 glow-in-the-dark spoon choices; Green, purple, red

1) Let the 'a' represent the small size let 'b' represent the huge size, let 'c' represent cherry, let 'v' represent vanilla, let 's' represent strawberry, let 'b' represent bubble gum, let '1' represent green, let '2' represent purple and let '3' represent red, we have;

The possible outcomes are;

ac1, ac2, ac3, av1, av2, av3, as1, as2, as3, ab1, ab2, ab3

bc1, bc2, bc3, bv1, bv2, bv3, bs1, bs2, bs3, bb1, bb2, bb3

With the use of MS Word, we have;

1) Small-Cherry-Green, 2) Small-Cherry-Purple, 3) Small-Cherry-Red, 4) Small-Vanilla-Green, 5) Small-Vanilla-Purple, 6) Small-Vanilla-Red, 7) Small-Strawberry-Green, 8) Small-Strawberry-Purple, 9) Small-Strawberry-Red, 10) Small-bubble gum-Green, 11) Small-Bubble gum-Purple, 12) Small-Bubble gum-Red

13) Huge-Cherry-Green, 14) Huge-Cherry-Purple, 15) Huge-Cherry-Red, 16) Huge-Vanilla-Green, 17) Huge-Vanilla-Purple, 18) Huge-Vanilla-Red, 19) Huge-Strawberry-Green, 20) Huge-Strawberry-Purple, 21) Huge-Strawberry-Red, 22) Huge-Bubble gum-Green, 23) Huge-Bubble gum-Purple, 24) Huge-Bubble gum-Red

Therefore;

b) There are 24 different combinations in total

2) The method used to find the combinations is a tree diagram with branches extending from, the size of the Snow Cone Xpress to the choices for the glow-in-the-dark spoons

b) The method was used because of there are more than two categories each with different number of items and each unique Snow Cone Xpress option comprises of an element of each category

3) The number of Snow Cones that includes the cherry flavor and a green spoon = 2 different Snow cones

b) The answer can be arrived at by either;

i) Counting from the listed snow cone options

ii) Noting that a setting the only options for flavor as cherry and the only option for the glow-in-the-dark spoon as green and then combining both categories into one category option with the connection 'and' we have the possible combination as 3 items taking 2 at a time less the combination of the small and huge snow cones as follows;

Combinations = ₃C₂ - 1 = 2

Answer:

sin

Step-by-step explanation:

its opposite over hypotenuse

Answer:

it should be sin

hope this work

Answer: To write an equation

y= 7x+38

Answer:

A group of tourists orders a special meal at a restaurant. The cost of each person's meal is $38. Each person will pay a $7 tip. What is the total restaurant bill for the group?

Answer:

52m

Step-by-step explanation:

Seperate each place into its own section

Multiply each section

Add the product you get from each section

Answer:

x- coordinate of P is - 6

Step-by-step explanation:

The coordinates of any point in the form of an ordered pair (x, y )

Point P has coordinates P (- 6, 2 )

Answer:

Step-by-step explanation:

Every point has two coordinates

the first is x-coordinate (we read it from X-axis)

the second is y-coordinate (we read it from Y-axis)

coordinates of poin P: (-6, 2)

so, the x-coordunate of point P is -6

Answer:

Step-by-step explanation:

We know the perimeter of a triangle is the sum of all the sides( two legs and one hypotenuse).

By pythagoras we know that

[tex]h^2= a^2+b^2.[/tex]

and the perimeter is [tex]P=h+a+b[/tex].

Since P=24 and a=6  we have these equations:

[tex]h^2=36+b^2\\24=h+6+b[/tex]

From the last equation we have [tex]h=18-b[/tex]. Replace h in the first equation we get that

[tex](18-b)^2=36+b^2[/tex]

[tex]18^2-36b+b^2=36+b^2\\288=36b\\b=\frac{288}{36}=8[/tex]

and h=18-8=10

Answer:

13/24x - 3

Step-by-step explanation:

Hope this helps!

The simplified form of expression 1/6x+3/4(1/2x−4) is 7/24x-3.

An expression is combination of variables, numbers and operators.

The given expression is  1/6x+3/4(1/2x−4)

One by six times of x plus three by four times of one by to of x minus four.

Apply distributive property to remove the parenthesis

1/6x+3/4(1/2)x-3/4(4)

1/6x+3/8x-3

The LCM of 6 and 8 is 24.

4x+3x-72/24

Add the like terms in the above expression.

7x/24-72/24

7x/24-3

Hence, the simplified form of 1/6x+3/4(1/2x−4) is 7/24x-3.

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Answer:

10.5 inches, 14 inches, 7 inches

Step-by-step explanation:

Let's say x is the multiplier of the ratio value and the actual length of the sides:

1/4 * x = side 1

1/3 * x = side 2

1/6 * x = side 3

Since the perimeter is the sum of all sides, the perimeter is equal to:

31.5 = 1/4 * x + 1/3 * x + 1/6 * x  ==> 31.5 inches is the perimeter

(31.5 = x/4 + x/3 + x/6)*12  ==> multiply the equation by 12 since 12 is the

                                           LCM (Least Common Multiple) of 4, 3, and 6

12 * 31.5 = 12 * x/4 + 12 * x/3 + 12 * x/6  ==> multiply each term by 12

378 = 12x/4 + 12x/3 + 12x/6 ==> simplify

378 = 3x + 4x + 2x

378 = 9x

x = 378/9 ==> divide both sides by 9

x = 42

Now find each side length [Refer to the first three equations] :

Side length 1: 1/4 * 42 = 42/4 = 10.5 inches

Side length 2: 1/3 * 42 = 42/3 = 14 inches

Side length 3: 1/6 * 42 = 42/6 = 7 inches

Answer: 10.5 inches, 14 inches, 7 inches

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Answer:

14 students

Step-by-step explanation:

15 do not play any.

50-15=35

21 students play basketball.

35-21=14

14 students play only soccer

Answer is 3h after simplification.

Function is a mathematical expression that represent the relationship between an independent variable and dependent variable. The set of values of independent variable is termed as input of function and the set of value of dependent variable is called output.

given, a function. f(x) = 3x -8

if we want to write x + h instead of x

then the function will be f(x + h) = 3(x + h) - 8

f (x + h) - f(x) = 3(x+ h) - 8- (3x -8)

f( x + h) - f(x) = 3(x +h) - 8 - 3x+ 8

f(x + h) - f(x) = 3(x + h) - 3x

f(x + h) - f(x) = 3x + 3h - 3x

f(x +h) - f(x) = 3h

hence, the above is the result.

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On solving the provided question, we can say that An arithmetic sequence is a sequence of numbers such that the difference of any two successive members of the sequence is a constant.

Arithmetic sequences are groups of integers that are arranged in a certain order and share a common difference between each term. The tolerance, for instance, is six in the mathematical progression 3, 9, 15, 21, and 27. Arithmetic progression can also be referred to as such. a series that is produced by adding the same value repeatedly. for instance, 1, 4, 7, 10, 13, 16, 19, 22, and 25. Sequences that have an arithmetic difference between two successive phrases are known as arithmetic sequences. A progression in math with a tolerance of 2 is 2,4,6,8,10.

An arithmetic sequence is a sequence of numbers such that the difference of any two successive members of the sequence is a constant. 2,4,6,8,10….is an arithmetic sequence with the common difference 2.

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So Gale made a profit of 55.6% by selling the purse to Brenda. Therefore the correct answer would be B. 55.6%

Profit and Loss is a financial statement that shows a company's revenue, costs, and expenses over a certain period of time, such as a month or a year. The purpose of a P&L statement is to show the company's financial performance and to determine whether the company is making a profit or incurring a loss.

The proportion that the retailer makes after selling a good at a price greater than its cost is the product's profit margin. P% indicates it.

Profit Percentage P% = {(selling price – cost price) / cost price} x 100.

The selling price of the purse is $35 and the original cost of the purse is $22.50. So the profit is $35 - $22.50 = $12.50

Profit as a percent = (Profit / Original cost) * 100

Profit as a percent = ($12.50 / $22.50) * 100 = 55.6%

So Gale made a profit of 55.6% by selling the purse to Brenda. Therefore the correct answer would be B. 55.6%

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Answer:

Step-by-step explanation:

The difference quotient in general looks like

[tex]\frac{f(x+h)-f(x)}{h}[/tex]   Sometimes the symbol "delta x"  [tex]\Delta x[/tex]   is used instead of h.

For the exponential function, the difference quotient is

[tex]\frac{e^{x+h}-e^x}{h}[/tex]

Answer:

For those who dont want to read, its A.

Step-by-step explanation:

Edge 2021

Step-by-step explanation:

Area = 2LH + 2LW + 2WH

= 2(LH + LW + WH)

=2(30*90+30*60+60*90)

=2(2700+1800+5400)

=2(9900)

=19800cmsquare

Therefore to paint the solid box it will cost

0.03 * 19800

= £594

Answer:

a = 45

b = 105

c = 30