Match the parametric equations with the correct graph.
x=t cos (t), y=t, z=t sin(t), t ≥ 0

a) Let x be the number of games played and let y be the total price.

What in mathematics is a linear equation?

A linear equation is an algebraic equation of the form y=mx+b, where m is the slope and b is the y-intercept, and only a constant and a first-order (linear) term are included. The variables in the preceding equation are y and x, and it is occasionally referred to as a "linear equation of two variables."

(b)

Pin Lanes: y = 10 + 3x

Strike Lanes: y = 4 + 6x

(c) To find the number of games at which the total price is the same at both places, we can set the two equations equal to each other and solve for x:

10 + 3x = 4 + 6x

6x = 6

x = 1

So the total price would be the same if you played 1 game at both Pin Lanes and Strike Lanes.

(d) Since you want to play 4 games, you can substitute x = 4 into the equation for each place:

Pin Lanes: y = 10 + 3(4) = 22

Strike Lanes: y = 4 + 6(4) = 28

Since 4 games at Pin Lanes costs $22 and 4 games at Strike Lanes costs $28, it would be cheaper to play at Pin Lanes.

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To write the equation of a line that goes through the point (3,2) and has a y-intercept of 1, we can use the point-slope form of a line. The point-slope form is:

y - y1 = m(x - x1)

Where (x1, y1) is a point on the line, and m is the slope of the line. The slope is a measure of the steepness of the line, and it is calculated as the rise (the change in y) over the run (the change in x).

To find the slope of the line, we can use the two points (3,2) and (3,1). The rise is 1 - 2 = -1 and the run is 3 - 3 = 0, so the slope is -1/0, which is undefined. This means that the line is a vertical line and does not have a slope.

Since the line is a vertical line, we cannot use the point-slope form to write its equation. Instead, we can use the slope-intercept form, which is:

y = mx + b

Where m is the slope of the line and b is the y-intercept. In this case, the slope is 0 (since the line is vertical), and the y-intercept is 1, so the equation of the line is:

y = 0x + 1

To write the equation of a line that is perpendicular to line a and goes through the point (-4,2), we need to find the slope of line a. Since line a is a vertical line, its slope is undefined. However, we know that the slope of a line perpendicular to it must be 0.

Using the point-slope form, the equation of line b is:

y - 2 = 0(x - (-4))

Simplifying, we get:

y = 0x + 2

So, the equation of line b is:

y = 0x + 2

Yes, the expressions S+S+S+S AND 4S as required in the task content are equivalent expressions.

It follows from the task content that the expressions given S+S+S+S AND 4S are to be compared and determine if they are equivalent or not.

Since the given expressions are; S + S + S + S and 4S.

S + S + S + S can be written by factorisation as;

S ( 1 + 1 + 1 + 1 ) = S (4)

= 4S.

On this note, it can be inferred that the two expressions given are equivalent expressions.

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Yes. Coupon B gives the lower price.

The price of coupon B is less than the price with Coupon A

Discount is defined as a deduction from the usual cost of something

Since there is a $16 rebate on a $55 jacket using Coupon A. The price when Coupon A is used will be:

price using Coupon A = $55 - $16 = $39

Since Coupon B gives a 35% discount on the price of the jacket. The price when Coupon B is used will be:

price using Coupon B = $55 - (0.35×55) = $35.75

Thus, the price of coupon B is less than the price with Coupon A

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Julian uses ordered pairs to record the temperature variations over time during a chemistry experiment (time in minutes, temperature in °C). (0, 15), (5, 20), (10, 50), (15, 80), (20, 100), (25, 100) (25, 100).

It is the cause that is the independent variable. Its worth is unrelated to other study variables. The effect serves as the dependent variable. The independent variable's modifications determine its value. It is a thing that is dependent on other things. The amount of study you did, how much sleep you had the night before the test, or even how hungry you were when you took it.

Could all affect your test result, which makes it a dependent variable. The dependent variable is impacted by the independent variable. For instance, your exam results are influenced by how much sleep you get (an independent variable) (dependent variable). This is understandable, but Ex. How much sleep you get depends on your test results.

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Answer:

12(7-3) and 2-0.5

Step-by-step explanation:

All the rest are either terms or equations. The top left one is a term, and all the rest have equal signs, so they're equations. Only the bottom left and bottom right ones are expressions.

Answer:

4

Step-by-step explanation:

m = Δy/Δx = (6-(-2))/(5-3) =8/2 = 4

Answer:

b = -8

Step-by-step explanation:

To determine the value of b, we can use the factoring method. We can factor the expression

(5b + 16)(b + 32) as (b + 8)(5b + 16).

Setting each factor to 0, we get b + 8 = 0 and 5b + 16 = 0.

Solving for b in the first equation, we get b = -8.

Substituting this value into the second equation, we get 5(-8) + 16 = 0, which simplifies to -40 + 16 = 0.

This equation is true only when the value of b is -8. Therefore, the value of b is -8.

Answer: 4t

Step-by-step explanation:

You just do t times the amount of boxes you have, which is 4. So you have 4 times t, but in algebra, we don't write the multiplication sign. So the expression would be written as 4t. Yw!

Also please tell me if I was unhelpful/incorrect, thanks!

Answer: B

Step-by-step explanation:

The amount of white paint used by Tamara to paint the bedroom walls is 2.125.

Fractions are numbers which are of the form a/b where a and b are real numbers. This implies that a parts of a number b.

Total amount of paint = 8.5

Three fourths of this amount is blue paint.

Amount of blue paint = (3/4) × 8.5 = 6.375

Rest is white paint.

Amount of white paint = Total paint - Amount of blue paint

                                     = 8.5 - 6.375

                                     = 2.125

Hence the amount of white paint used to paint bedroom walls is 2.125.

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Answer: C. 20

Step-by-step explanation:

1 inch is equal to 2.54 cm.

So we have to divide the amount of centimeters given by how many centimeters are in an inch to find how many inches.

50.8 ÷ 2.54 = 20

Hope this helps!!! :)

The value of the principal investment would be = $12,500.75

A principal investment is defined as the capital amount of money that is being deposited into an account with the purpose of receiving interest for a particular period of time.

The years of investment (t) = 9 years

The annual interest rate (r) = 3.9% = 3.9/100= 0.039

The total worth of the investment (A) = $17,757.16

Then, solve the equation for P

P = A / ert

P = 17,757.16 / e(0.039*9)

P = $12,500.75

Therefore, the principal amount that is needed which can be compounded continuously to get the total amount given = $12,500.75

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Therefore, the solution of given problem of percentage  indicates that from the beginning of 2000 and the end of 2001, there was no net change in the workforce.

A% is a number that expresses a quantity as a percentage of 100; it can also be expressed as a decimal or a fraction. Placing 100 in the denominator and the percentage value in the numerator will allow you to convert a percentage to a fraction.

Here,

Before any changes,

let w represent the size of the workforce. There are:

50 percent growth is equivalent to increasing by 1.5, therefore w(2000) = w(1999) * 1.5

A 50% drop is equal to dividing by 1.5, therefore w(2001) = w(2000)/1.5

Reverse the first equation to create the second equation.

w(2001) = w(1999) * 1.5/1.5

Remove the 1.5 from the top and bottom so that w(2001) = w (1999)

Therefore, this indicates that from the beginning of 2000 and the end of 2001, there was no net change in the workforce.

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Answer:

Step-by-step explanation:

axf

The error in the work lies in line 3 where the square root is calculated inaccurately.

The opposite of squaring an integer is finding its square root. The square root of a number can be found by looking for a number that, when squared, yields the original value.

The error is in line 3, line 4 and line 5.

The error in line 3 is inaccurate calculation of the value of square root of 4.

The error in line 4 is a mathematical calculation error.

The error in line 5 is a mathematical calculation error.

The correct answer in Line 3 is:

[tex]6 * 2 *\sqrt{5} -3\sqrt{5}[/tex]

The correct answer in Line 4 is:

[tex]12\sqrt{5} - 3\sqrt{5}[/tex]

The correct answer in Line 5 is:

[tex]9\sqrt{5}[/tex]

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On solving the provided question, we can say that - by doing the fraction we have 3/12 = 1/4

Any number of equal portions, or fractions, can be used to represent a whole. Fractions in standard English indicate how many units of a certain size there are. 8, 3/4. A whole includes fractions. The ratio of the numerator to the denominator is how numbers are expressed in mathematics. Each of these is an integer in simple fractions. In the numerator or denominator of a complex fraction is a fraction. True fractions have numerators that are less than their denominators. A fraction is a sum that constitutes a portion of a total. By breaking the entire up into smaller bits, you can evaluate it. Half of a full number or item, for instance, is represented as 12.

balloons is 12

blew up is  1/3

friend blew up is  5

1/3*12 = 4

4+5 = 9

3/12 = 1/4

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The domain of the function f(x, y, z) = ln(144 − 9x² − 16y² − z²) is x ∈ (-4, 4), y ∈ (-3, 3) and z ∈ (-12, 12) which forms an ellipsoid.

Domain of a function is the set of all values possible for the input parameters for real output parameter or output parameter in given range.

Given the function as f(x, y, z) = ln(144 − 9x² − 16y² − z²)

For f(x, y, z) to be real, the function 144 − 9x² − 16y² − z² should be greater than 0. So,

144 − 9x² − 16y² − z² > 0

9x² + 16y² + z² < 144

x²/ 4² + y²/ 3² + z²/ 12² < 1

Therefore, the domain is an ellipsoid.

Therefore x ∈ (-4, 4)

y ∈ (-3, 3)

z ∈ (-12, 12)

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The total length needed in inches will be 490.5 inches.

A fraction simply means a piece of a whole. In this situation, the number is represented as a quotient such that the numerator and denominator are split. In this situation, in a simple fraction, the numerator as well as the denominator are both integers.

Since the machinist must cut 12 strips of metal that are each 3 ft 4 7/8 in. long The total length needed in inches will be:

= (3 ft 4 7/8 inch × 12)

Note that 1 feet = 12 inches

= (12 × 3) + (4 7/8) × 12

= (36 + 4.875) × 12

= 490.5 inches

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Answer:

RM832.29

Step-by-step explanation:

Calculate PV Savings

To calculate the present value of the savings, we can use the formula:

PV = cash savings / (1 + r)^t

Where PV is the present value, r is the discount rate, and t is the number of years.

Plugging in the values given in the problem, we get:

PV = RM2,000 / (1 + 0.15)^20

= RM2,000 / 1.15^20

= RM832.29

So the present value of the savings is RM832.29.

Answer: RM25,919.89.

Step-by-step explanation:

The present value of the cash savings is the sum of the present value of each year's cash savings.

To calculate this, the formula for the present value of a single cash flow is used:

Present Value = Future Value / (1 + r)^n

Where r is the discount rate, and n is the number of years.

So, for the first year's cash savings, the present value would be:

PV = 2000 / (1 + 0.15)^1 = 1739.13

For the second year's cash savings, the present value would be:

PV = 2000 / (1 + 0.15)^2 = 1510.71

This can be repeated for the remaining 18 years, and the sum of all the present values is the total present value of the cash savings over 20 years:

Total PV = 1739.13 + 1510.71 + .... + 437.66 = RM25,919.89

Therefore, the present value of the cash savings over 20 years with a 15% discount rate is RM25,919.89.

Answer:

Step-by-step explanation:

Let's assume that,

→ Length = 2x

→ Width = x

→ Perimeter = 30

Perimeter of rectangle formula,

→ P = 2(L + W)

Now the value of x will be,

→ P = 2(L + W)

→ 2(2x + x) = 30

→ 2 × 3x = 30

→ 6x = 30

→ x = 30/6

→ [ x = 5 ]

Then required dimensions are,

→ Length = 2x = 2 × 5 = 10

→ Width = x = 5

Hence, these are the dimensions.

Length = 10

width = 5

Given-

Perimeter =30

l=2b........................................................ i

so

P =2(l+b)

here

30 = 2(2b +b)... ... ..............         as l=2b from i

30 = 2*3b

30 = 6b

b= 5

which implies l= 2*5 --->10............................................ from i

so

Length = 10

width = 5

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Answer:3.8

Step-by-step explanation:

On solving the provided question, we can say that - by doing the equation, we have -12 +18 = p + 7 => 6 = p + 7 => p = -1

An equation is a formula in mathematics that joins two statements with the equal symbol = to represent equality. The definition of an equation in algebra is a mathematical statement proving the equality of two mathematical expressions. In the equation 3x + 5 = 14, for instance, the terms 3x + 5 and 14 are separated by an equal sign. The link between two phrases on either side of a letter is expressed mathematically. There is often only one variable, which is also the symbol. instance: 2x - 4 Equals 2.

here,

-12 +18 = p + 7

6 = p + 7

p = -1

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Answer:

70

Step-by-step explanation:

Well -37 plus 70 would give you 33, so therefore 70 is the answer. You can also check your answer by subtracting -37 from 33 which would give you 70.

Answer:

y > X/2 - 3

I think that's the answer.

Answer:

2(x-3)

Step-by-step explanation: 2 is being multiplied by the difference (subtraction) of x-3.

Answer:

no

Step-by-step explanation:

y > 2x - 5

9 > 2(7) - 5

9 > 14 - 5

9 > 9. not a solution

9=9

Answer:

g(f(x)) = 4x² - 12x + 10

Step-by-step explanation:

to find g(f(x)) substitute x = f(x) ino g(x)

g(f(x))

= g(2x - 3)

= (2x - 3)² + 1 ← expand parenthesis using FOIL

= 4x² - 6x - 6x + 9 + 1

= 4x² - 12x + 10

The cost of one adult ticket is 3.6 and cost of one student ticket is 4.3

Either 4 or is the appropriate response.

Chris spends a total of 2 x + 3 dollars on x student tickets and a total of x adult tickets because each student ticket costs $ 2 and each adult ticket costs $ 3.

Because Chris spends at least $ 11 but no more than $ 14 on the tickets, the entire inequality 2 x + 3 1 can be written.

x = 4 and x = 5.5 are obtained by subtracting 3 from each side of both inequalities and then dividing each side of both inequalities by 2.

A number higher than or equal to 4 and less than or equal to 5.5 must both be integers in order for x to have a value.

Therefore, either x = 4 or x = 5.

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Answer:

both are right

Step-by-step explanation:

2/5x = 14

multiply both sides by 5/2:

(5/2)(2/5)x = 14(5/2)

x = 70/2 = 35

However, dividing by 2/5 is the same as multiplying by 5/2, so you are BOTH right.  Dividing by a fraction is the same as multiplying by the reciprocal of the fraction.