what is the domain and range of this table?

The equivalent ratio of Pearls to Pizzas would be 13:2 and 13:4.

What is the ratio?

A ratio is an ordered pair of numbers a and b, denoted by the symbol a / b, where b does not equal zero. A proportion is an equation that sets two ratios equal to each other. For example, if there is one boy and three girls, the ratio could be written as 1: 3. (for every one boy there are 3 girls)

Luigi uses 39 mozzarella pearls for every 6 pizzas they make.

So the equivalent ratio would be 39/6

                                                     = 13:2

And similarly, Luigi uses 13 mozzarella pearls for every 4 pizzas they make.

So the equivalent ratio would be 13/4

                                                     = 13:4

Hence, the equivalent ratio of Pearls to Pizzas would be 13:2 and 13:4.

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The scores of geography, economics and science are 38, 76, 80 respectively.

Let Yakubu scored x marks in geography.

Given that the score of him in economics is twice of the score of him in geography.

So, his score in economics = 2x

Again it is given that, the score in science is 4 more than the score in economics.

So the score in science = 2x+4

According to question the combined total score is 194. So the suitable equation is,

x+2x+2x+4 = 194

Solving the equation we get,

5x+4 = 194

5x = 194-4

5x = 190

x = 190/5

x = 38

So the score in geography = 38

the score in economics = 2x = 2*38 = 76

the score in science = 2x+4 = 2*38+4 = 76+4 = 80

Hence the scores of geography, economics and science are 38, 76, 80 respectively.

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The value of x is 7 and the value of y is 37. These values of x and y results in congruence.

For the two triangles, Δ LMN and Δ PQR,

Side LM = Side PQ,

Side LN = Side PR

Side MN = Side QR

⇒ Δ LMN and Δ PQR are congruent by (S.S.S : side side side) property

Since both the triangles are congruent to each other. There corresponding angles will be equal.

i.e. ∠ L = ∠ P, ∠ N = ∠ R and ∠ Q = ∠ M.

⇒ ∠ L = ∠ P

⇒ 3x + 24 = 8x - 11

⇒ 24 + 11 = 8x - 3x

⇒ 5x = 35

⇒ x = 7

In Δ PQR, sum of all angles is 180°

⇒ ∠P + ∠Q + ∠R = 180°

⇒ (8x - 11)° + 84° + ∠R = 180°

⇒ (8×7 - 11)° + 84° + ∠R = 180°

⇒ 45° + 84° + ∠R = 180°

⇒ 129° + ∠R = 180°

⇒ ∠R = 180° - 129° = 51°

We know that ∠N = ∠R

⇒ (2x + y) = 51

⇒ (2×7) + y = 51

⇒ y = 51 - 14 = 37

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The final polynomial equation after synthetic division is [tex]x^5-3x^4-81x+243[/tex]

We need to solve;

Put the solution in the appropriate spot on the grid after using synthetic division to divide the following polynomial. Respond with descending powers of x.

The polynomial equation given is;

[tex]\left(x^4-81\right)\left(x-3\right)[/tex]

By using synthetic division;

⇒ [tex]x^4x+x^4\left(-3\right)-81x-81\left(-3\right)[/tex]

    [tex]x^5-3x^4-81x+243[/tex]

→ The required final equation in descending powers of x is [tex]x^5-3x^4-81x+243[/tex] .

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The line parallel to line AB will have the same slope with different

y-intercepts.

We know lines have various types of equations, the general type is

Ax + By + c = 0, and the equation of a line in slope-intercept form is

y = mx + b.

Where slope = m and b = y-intercept.

the slope is the rate of change of the y-axis with respect to the x-axis and the y-intercept is the (0,b) where the line intersects the y-axis at x = 0.

We know lines parallel to each other have the same slope with a different y-intercept.

Suppose the line AB has an equation y = mx + b.

∴ The line parallel to line AB will have an equation y = mx + c.

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Answer:

y=1/2x-3

Step-by-step explanation: if you are using edmentum this is correct.

Atleast 212 meal tickets need to sold to raise atleast $2,000 as fund.

Given:

Meal tickets for 8.50 per dinner

Donation = $200 donation

To raise at least = $2000

To find the number of meal tickets to be sold for raise at least $2000

Now, According to the question:

Based on the given condition:

$(8.50 x n + 200) = $2,000

=> 8.5n + 200 = 2,000

=> 8.5n = 2,000 - 200

=> 8.5n = 1,800

n = 1800/8.5

n = 211.76

n ≅ 212 {as tickets sold in integers }

Hence, Atleast 212 meal tickets need to sold to raise atleast $2,000 as fund.

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Answer:

Step-by-step explanation:

According to triangle proportionality theorem we have equal ratios:

The value of x will be 6 units.

What is mean by Triangle?

A triangle is a three sided polygon, which has three vertices and three angles which has the sum 180 degrees.

Given that;

The triangle is shown is figure.

Now,

By the definition of triangle proportionality theorem, we get;

⇒(6x - 1 - 14)/14 = (15 - 6)/6

Solve for x as;

⇒ (6x - 15)/14 = 9/6

⇒ 6x - 15 = 9×14/6

⇒6x - 15 = 21

⇒ 6x = 21 + 15

⇒ 6x = 36

⇒ x = 6 units

Thus, The value of x will be 6 units.

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An exponential function that best represents the value of the computer in months is V(t) = 1500(0.9763)^m.

In Mathematics, an exponential function simply refers to a mathematical function whose values are generated by a constant that is raised to the power of the argument. Mathematically, an exponential function can be modeled by using this equation:

f(x) = ab^t

Where:

From the information provided, the value, V, of a computer is modeled by this function:

V(t) = 1500(0.75)^t

Where:

t represents the number of years since the computer was purchased.

Note: one (1) year is equal to 12 months (m).

Now, we can remodel the value of this computer in months:

V(t) = 1500(0.75)^m/t

V(t) = 1500(0.75)^m/12

V(t) = 1500(0.75^{1/12})^m

V(t) = 1500(0.9763)^m

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The  slope of the line passes through the point (40,89) and (28,7) is   [tex]\frac{41}{6}[/tex].

What is slope?

It is possible to determine a line's direction and steepness by looking at its slope. Without using a compass, determining the slope of lines in a coordinate plane can assist forecast whether the lines are parallel, perpendicular, or none at all. The slope of any line can be computed using any two distinct locations on the line. Calculated using the slope of a line formula, the ratio of "vertical change" to "horizontal change" between two different locations on a line is determined.

Here the given points are

[tex](x_1,y_1)=(40,89)\\(x_2,y_2)=(28,7)[/tex]

Now using slope formula ,

=> Slope m = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]

=> slope m = [tex]\frac{7-89}{28-40}[/tex]

=> slope m=[tex]\frac{82}{12}[/tex]

=> slope m = [tex]\frac{41}{6}[/tex]

Hence slope of the line passes through the point (40,89) and (28,7) is   [tex]\frac{41}{6}[/tex].

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Answer:

0.375

Step-by-step explanation:

The maximum value is; +√21 and the minimum value is; -√21

Function is a type of relation, or rule, that maps one input to specific single output.

We are given that

f(x,y,z) = x² + y² + z²

g(x,y,z) = x⁴ + y⁴ + z⁴ - 7 = 0

Using Lagrange multipliers as follows;

df/dx = λg/dx,

df/dy = λg/dy.

df/dz = λg/dz

Thus, df/dx = 2x, df/dy = 2y, df/dz = 2z

dg/dx = 4x³,  dg/dy = 4y³, dg/dz = 4z³

So, df/dx = λg/dx

2x = 4λx³     (1)

df/dy = λg/dy

2y = 4λy³           (2)

df/dz = λg/dz

2z = 4λz³           (3)

From (1) 4λx³ - 2x = 0

2λx³ - x = 0

x(2λx² - 1) = 0

Now solving; x = 0 or (2λx² - 1) = 0

2λx² = 1

x = ±1/√(2λ)

since x ≠ 0

From (2) 4λy³ - 2y = 0

2λy³ - y = 0

y(2λy² - 1) = 0

Now solving, y = 0 or (2λy² - 1) = 0

2λy² = 1

y = ±1/√(2λ) since y ≠ 0

From (3) 4λz³ - 2z = 0

2λz³ - z = 0

z(2λz² - 1) = 0

now solving, z = 0 or (2λz² - 1) = 0

2λz² = 1

z = ±1/√(2λ) since z ≠ 0

Then we have g(x,y,z) = x⁴ + y⁴ + z⁴ - 7 = 0

(1/√(2λ))⁴ + (1/√(2λ))⁴ + (1/√(2λ))⁴ - 7 = 0

3 (1/√(2λ))⁴ = 7

(1/√(2λ))⁴ = 7/3

1/√(2λ) = ⁴√7/3

√(2λ) = ⁴√3/7

2λ = √3/7

λ = 1/2(√3/7)

Since we know that x = 1/√(2λ) = 1/√(2 [1/2(√3/7)]) = 1/⁴√3/7 = ±⁴√7/3

Also, y = 1/√(2λ) = 1/√(2 [1/2(√3/7)]) = 1/⁴√3/7 = ±⁴√7/3

and, z = 1/√(2λ) = 1/√(2 [1/2(√3/7)]) = 1/⁴√3/7 = ±⁴√7/3

Now Substituting x,y and z into f(x,y,z) we have;

f(x,y,z) = (⁴√7/3)² + (⁴√7/3)² + (⁴√7/3)² = 3(⁴√7/3)² = 3(√7/3) = √(7 × 3) = ±√21

Hence, the maximum value is +√21 and the minimum value is -√21

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The inverse of the given function is, h^(-1)(x) = (x - 8)/6.

What is inverse of function?

What a function's inverse function is F is a function that reverses what F did. The inverse of f is represented by f-1 if it exists and only if f is a bijective function.

Consider, the given function

h(x) = 6x + 8

Let,

y = 6x + 8

Replace x with y,

x = 6y + 8

Solving the equation for y,

x - 8 = 6y

y = (x - 8)/6

Replace y with h^(-1)(x),

So,

h^(-1)(x) = (x - 8)/6.

Hence the inverse of the given function is, h^(-1)(x) = (x - 8)/6.

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Trigonometric value equal to 0 is tan 900 degrees.

What are trigonometric ratios ?

As specified by the definition of a right-angled triangle's side ratio, trigonometric ratios are the values of all trigonometric functions. The trigonometric ratios of any acute angle in a right-angled triangle are the ratios of its sides to that angle.

Main Body:

The value of trigonometric ratios in the question are

assuming the function as-

Sin (30°) = 1/2

cos(360°) =1

tan (900°) = 0

cot (0°) =∞

Hence the trigonometric ratio that has value = 0 is tan(900°).

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Answer:

A, C, D

Step-by-step explanation:

edge 2023

AC is not perpendicular to XZ, because the slope of AC is -1 and the slope of XZ is 2/3. Therefore, the correct answer options are:

B. Is not

A. -1

Mathematically, the slope of any straight line can be calculated by using this formula;

Slope, m = (Change in y-axis, Δy)/(Change in x-axis, Δx)

Slope, m = (y₂ - y₁)/(x₂ - x₁)

For the slope of AC, we have the following:

Point at A = (-1, 3)

Point at C = (4, -2)

Slope, m of AC = (-2 - 3)/(4 - (-1))

Slope, m of AC = (-2 - 3)/(4 + 1)

Slope, m of AC = -5/5.

Slope, m of AC = -1.

For the slope of XZ, we have the following:

Point at X = (12, 2)

Point at Z = (6, -2)

Slope, m of XZ = (-2 - 2)/(6 - 12)

Slope, m of XZ = -4/-6.

Slope, m of XZ = 2/3.

In Mathematics, a condition that must be met for two lines to be perpendicular is given by:

m₁ × m₂ = -1

-1 × 2/3 = -1

-2/3 = -1 (False).

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The annual interest rate of Niyati's invested to accumulate the accrued amount is 10%.

The formula for calculating compound interest is expressed as;

A = P( 1 + r )^t

Where A is accrued amount, P is principal , r is interest rate and t is time.

Given the data in the question;

To determine the annual interest rate, plug the given values into the equation and solve for r.

A = P( 1 + r )^t

r = (A/P)^1/t - 1

r = (( $1,210 / $1,000 )^1/2 ) - 1

r = (( 1.21 )^1/2 ) - 1

r  = 1.1 - 1

r = 0.1

Now, convert rate as percentage.

r = 0.1 × 100%

r = 10%

Therefore, the annual interest rate is 10%.

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The complete table of values is:

x  -2  -1  0  1  2

y 1/9  1/3 1  3  9

From the question, we have the following equation:

f(x) = 3ˣ

From the table of values, we have the following x values

x = -2, -1, 0, 1 and 2

Substitute x = -2, -1, 0, 1 and 2 in the equation f(x) = 3ˣ

When x = -2

f(-2) = 3⁻² = 1/9

When x = -1

f(-1) = 3⁻¹ = 1/3

When x = 0

f(-1) = 3⁰ = 1

When x = 1

f(1) = 3¹ = 3

When x = 2

f(2) = 3² = 9

Hence, the complete table of values is:

x  -2  -1  0  1  2

y 1/9  1/3 1  3  9

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Answer:

1 < x ≤ 6 is the solution

Step-by-step explanation:

Given

6 < x + 5 ≤ 11

Solution

Subtract 5 from the 3 terms. You do this so you can isolate x

6 - 5 < x + 5 - 5 ≤ 11 - 5

1 < x≤ 6

x lies between 1 and 6.

The minimum unit cost is 8099.

Given:

A supply company manufactures copy machines. the unit cost C (the cost in dollars to make each copy machine) depends on the number of machines made. If x machines are made, then the unit cost is given by the function.

C(x)=0.8x^2-208x+21,619

derivative of C(x):

C'(x) = 0.8*2 x - 208+0

0 = 1.6 x - 208

1.6x = 208

divide by 1.6 on both sides

x = 208/1.6

= 208/16/10

= 208*10/16

= 2080/16

= 1040/8

= 520/4

= 260/2

x = 130

C(130) = 0.8*130^2-208*130+21619

= 16900*0.8 - 27040 + 21619

= 13520 - 5421

= 8099

Therefore the minimum unit cost is 8099.

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a. The number of students that this school is going to have to enroll abroad in the year 2001 is 150

b. In the 2018 academic year, it can be said that the school would also have to enroll 468 students in the school

a. The equation is as follows:

y = 123.1 * (1.069)^x

The value of x would be years that have changed.

To get the value of x we would have to find the differences that lies in the two years.

Hence

2001 - 1998 = 3

We would place the value of x in the equation

y = 123.1(1.069)³

Then

y = 150.4

This is approximately 150.

In conclusion, There would be 150 students enrolled in the school, according to estimates, in 2001.

b. For the year 2018

We would have to carry out similar calculation

x = 2018 - 1998

This would give us  20 years difference

Place x = 20 in the equation

y = 123.1(1.069)²⁰

y = 467.5

This is approximately

y ~ 468

468 would be enrolled in the school in 2018.

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The largest Volume of the box possible is 4000 cm³ .

In the question ,

it is given that

the box has a square base ,

let the length and width of the box = "x" , because it is a square

let the height of the box [tex]=[/tex] h

the total surface area of the box = 1200

also the total  surface area with open top is = x² + 4xh

So , x² + 4xh = 1200

h = (1200 - x²)/4x

According to the question ,

the volume of the box = x²h

Substituting the value of h = (1200 - x²)/4x ,

we get ,

Volume = x² × (1200 - x²)/4x

V = (1/4)(1200x - x³)

to Maximize the volume dV/dx = 0

(1/4)(1200 - 3x²) = 0

1200 - 3x² = 0

3x² = 1200

x² = 400

x = -20 , +20

length cannot be in negative , hence x = 20 ,

So , Volume = (1/4)[1200(20) - 20³]

= 4000 cm³

Therefore , The largest Volume of the box possible  is 4000 cm³ .

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A sequence of transformations that maps △DEF to △D′E′F′ is a  rotation of  180° about the origin followed by a translation by 1 unit to the left

We have given the graph of  triangle DEF with coordinates as;

D( -2 ,-1 )

E(-2 ,-4)

F( -1 , -1 )

Now, the coordinates of the transformed triangle D'E'F' are;

D' (1  ,1)

E' ( 1 ,4)

F' (0 ,1)

Now, the transformation rule for a rotation by 180° about the origin is (x, y) → (−x, −y) .

This means that the first transformation is a rotation of  180° about the origin to get;

D"( 2 ,1 )

E"(2 ,4)

F"( 1 , 1 )

Transformation rule ( x ,y) → (x- 1 , y) will now translate by 1 unit to the left.

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The value of 2x - yz with x = 34, y = 0.2, and z = 6 we get 69.2.

Here it is given that

x = 34

y = -0.2

z = 6

We need to calculate 2x - yz

If we first calculate 2x then we get

2x = 2 X 34

= 68

Now, if we calculate -yz next then we see

yz = -0.2 X 6

= -1.2

Hence

- yz = -(-1.2)

= 1.2

Therefore, adding up these two we get

2x - yz

= 68 + 1.2

= 69.2

Hence the value of 2x - yz is 69.2

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Correct Question

Evaluate the expression 2x - yz , where x = 34 , y = -0.2, and z = 6

Answer:

45c−20c2

Step-by-step explanation:

have great day

Answer:

0.00896057348

Step-by-step explanation:

maybe I think I read it right but don't count on me

Answer: 1/4

Step-by-step explanation:  If you divide them both you get 0.25 and that's just 1/4.  Hope it helps.

a) The perimeter of Martin's cat enclosure is 220 inch.

b) Martin need to buy 22 bundles each 10 ft long.

The whole distance that a rectangle's boundaries, or its sides, cover is known as its perimeter. Given that a rectangle has four sides, the perimeter of the rectangle will be equal to the sum of its four sides.

Given,

Wide = 48 inches

Length = 62 inches

a) Perimeter of enclosure:

2 × (length + width)

2× (48 + 62)

2 × 110

220

The perimeter of Martin's cat enclosure is 220 inch.

b)  Wire mesh is sold in rolls that are each 10 ft long.

Dividing it by perimeter:

220 ÷ 10

22

Martin need to buy 22 bundles each 10 ft long.

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150cm² is the area of the given parallelogram.

So we understand that Rectangles are parallelograms.

They have the same formula for finding the perimeter and area.

Therefore, 150cm² is the area of the given parallelogram.

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The value of n is 1, compound interest of the end of year.

What is compound interest?

The interest on savings that is computed on both the initial principal and the interest accrued over time is known as compound interest. Compound interest is calculated by multiplying the starting principal amount by one and the annual interest rate raised to the number of compound periods minus one. The final step is to deduct the initial loan principal from the calculated value.

When the amount compounds quarterly, it means that the amount compounds 4 times in a year. i.e., n = 4. We use this fact to derive the quarterly compound interest formula. Thus, the quarterly compound interest formula is:

A = P (1 + r/4)4t

where S= Amount at the end of n years = 3445.51

P = Principal = 2400

r = Rate of interest = 0.075

n = 1 as interest is compounded annually

Try to find it's value by solving. The number of years will be provided.

Hence the value of n is 1.

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For a lower tail test, the p-value is the probability of obtaining a value for the test statistic as small as or smaller than that provided by the sample. For an upper tail test, the p-value is the probability of obtaining a value for the test statistic as large as or larger than that provided by the test statistic.

In statistics, the p-value is the probability of obtaining results at least as extreme as the observed results of a statistical hypothesis test, assuming that the null hypothesis is correct. The p-value serves as an alternative to rejection points to provide the smallest level of significance at which the null hypothesis would be rejected. A smaller p-value means that there is stronger evidence in favor of the alternative hypothesis.

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