Write a quadratic function for the following characteristics

Riley bought  2 boxes of  thank you cards and 3 boxes of get well cards.

What is linear equation?
A linear equation is a first-order (linear) term plus a constant in the algebraic form y=mx+b, where m is the slope and b is the y-intercept. Sometimes, the aforementioned is referred to as a "linear equation of two variables," where x and y are the variables.

Let Riley have bought x boxes of  thank you cards and y boxes of get well cards.

Therefore according to the question,
x + y = 5.......(1)
9x + 4y = 30........(2)

Multiplying equation 1  with 4 we get.
4x + 4y = 20.......(a)
Subtracting (a) form (2) we get:
5x = 10
=> x = 2
Putting the value of in (1) we get y= 3

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Answer:

B: 2.3 x 10^18

expination:

Substitute values into the formula.

F x L = 3.0 x 10*10

F x 1.3 x 10^−8 = 3.0 x 10^10

F = 3.0 x 10^10 1.3 x 10^−8 F = 2.3 x 10^18

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Answer:

.457

Step-by-step explanation:

The WHOLE area is = 1

so   1 - .543 = .457

To determine the z-value so that the area to the right of z is 0.9429

The equations which show the total volume of the boxes Marcus shipped are as follows:

A. (20 × 10 × 7) + [2× (20 × 4 × 4)]

C. (20 × 10 × 7) + (20 × 4 × 4) + (20 × 4 × 4)

F. (200 × 7) + [2 × (80 × 4)]

Mathematically, the volume of a rectangular prism can be calculated by using this equation:

Volume = L × W × H

Where:

For rectangular prism 1, the volume is given by:

Volume 1 = L × W × H

Volume 1 = 20 × 7 × 10

Volume 1 = 200 × 7

Volume 1 = 1,400 cubic inches.

For rectangular prism 2, the volume is given by:

Volume 2 = L × W × H

Volume 2 = 20 × 4 × 4

Volume 2 = 80 × 4

Volume 2 = 320 cubic inches.

Since Marcus shipped 1 of the larger boxes and 2 of the smaller boxes, the total volume of the boxes Marcus shipped is given by these three (3) equations:

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The function f is positive on the domain (-∞, 3)

The f(x) values corresponding to x-values are given. Also f(x) is a continuous linear function.

If we analyze the function values, the first 3 entries are positive, then from there the function values becomes negative.

Also it is clear from the function values that the function is decreasing from positive values to negative values.

The corresponding x-values for the positive values of the function are x = -3, x = 0 and x = 3.

Since f(x) is continuous linear function, the given x-values and f(x) values are not the only ones there. The domain and images are actually in the form of intervals, but here only certain values are given in the table.

Therefore, the function must be positive for x < -3 too.

Hence the domain where the function is positive becomes (-∞, 3).

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we know that

the coordinates of point A are (0,1) and point C(3,3)

Applying the formula to calculate the distance between two points

therefore

The correct answer is [B]

Binary and unary operations are the two most popular forms of operations. Trigonometric functions and negation are examples of unary operations that use only one value. Contrarily, binary operations, which include addition, subtraction, multiplication, division, and exponentiation, only accept two values. Here the same expression will be 5 ∑([tex]([/tex][tex]\frac{1}{3}[/tex][tex])^{i}[/tex]

Mathematical objects other than numbers can be used in operations. Logic operations like and, or, and not can be used to combine the logical values true and false. It is possible to add and subtract vectors. Utilizing the function composition operation, it is possible to combine rotations by first performing the first rotation and then the second. The binary operations union and intersection as well as the unary operation of complementation are operations on sets. Composition and convolution are two operations on functions.

Not all possible values of the domain may be covered by an operation's definition. For instance, it is impossible to square the roots of negative integers or divide by zero in real numbers. An operation's domain of definition, also known as the active domain, is the set of values for which the operation is specified. However, the set of real values obtained by the operation is its codomain of definition, active codomain, image, or range. The set that contains the values created is referred to as the codomain. [failed to verify] For instance, only non-negative numbers are produced by the squaring operation when applied to the real numbers; the set of real numbers is the codomain, but the non-negative numbers are the range.

4

∑(5[tex]([/tex][tex]\frac{1}{3}[/tex][tex])^{i}[/tex])

i=0

4

∑(5[tex]([/tex][tex]\frac{1}{3}[/tex][tex])^{i}[/tex])= (5[tex]([/tex][tex]\frac{1}{3}[/tex][tex])^{0}[/tex])+(5[tex]([/tex][tex]\frac{1}{3}[/tex][tex])^{1}[/tex])+(5[tex]([/tex][tex]\frac{1}{3}[/tex][tex])^{2}[/tex])+(5[tex]([/tex][tex]\frac{1}{3}[/tex][tex])^{3}[/tex])+(5[tex]([/tex][tex]\frac{1}{3}[/tex][tex])^{4}[/tex])

0          

              = 5([tex]([/tex][tex]\frac{1}{3}[/tex][tex])^{0}[/tex])+([tex]([/tex][tex]\frac{1}{3}[/tex][tex])^{1}[/tex])+([tex]([/tex][tex]\frac{1}{3}[/tex][tex])^{2}[/tex])+([tex]([/tex][tex]\frac{1}{3}[/tex][tex])^{3}[/tex])+([tex]([/tex][tex]\frac{1}{3}[/tex][tex])^{4}[/tex])

                    4

             = 5 ∑([tex]([/tex][tex]\frac{1}{3}[/tex][tex])^{i}[/tex])

                   i=0

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If the tangent of θ equals one (1), the true statement about the right-angled triangle side lengths is that: C. The sides opposite and adjacent to theta are the same length.

In geometry, a tangent is also referred to as a tangent line and it can be defined as a straight line that touches a plane curve at a specific point.

Mathematically, the tangent of an angle is given by this expression:

Tanθ = Opp/Adj

Where:

For this right-angled triangle, the tangent of the angle (θ) is given by:

Tanθ = Opp/Adj = 1

Opposite/Adjacent = 1

Cross-multiplying, we have:

Opposite = Adjacent

In conclusion, the opposite side length of this right-angled triangle is equal to its adjacent side length.

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The required expression equivalent to the given expression is 3²² .

An expression in mathematics is said to be algebraic if it was constructed using integer variables, constants, and algebraic operations (addition, subtraction, multiplication, division and exponentiation by an exponent that is a rational number)

Given : the expression of the form ( 3 ⁴ ) ⁶ ÷ 3²

Simplifying we get:

= ( 3 ⁴ ) ⁶ ÷ 3²

= 3⁽²⁴⁻²⁾

=  3²²

Therefore the required expression equivalent to the given expression is

3²² .

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Answer:

slope = [tex]\frac{1}{2}[/tex]

Step-by-step explanation:

calculate the slope m using the slope formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = (0, - 2) and (x₂, y₂ ) = (2, - 1) ← 2 points on the line

m = [tex]\frac{-1-(-2)}{2-0}[/tex] = [tex]\frac{-1+2}{2}[/tex] = [tex]\frac{1}{2}[/tex]

You have to determine which of the given square roots can be expressed as a fraction:

1) The square root of one is 1

One can be expressed as a fracion:

So it is a rational number.

2) The square root of 2 is an irrational number and cannot be expressed as a fraction.

Its decimal expantion has no end, i.e. it has infinite decimal values.

3) Square root of three is an irrational number and cannot be expressed as a fraction.

4) The square root of 5 is an irrational number and cannot be expressed as a fraction.

In conclusion the only rational number in the given set is the square root of 1.

The constant of variation is 0.4.

What is constant of variation?

A direct variation's product of two variables or the product of two variables in an inverse variation The constant of variation is used in the direct variation equations = k and y = kx as well as the inverse variation equations xy = k and y = k.

We know that  y is directly proportional to the square of x.

Therefore we can use the formula,

y = kx^2

Putting the values of x and y,

10 = k (5)^2

=> 10 = k .25

=> 10/25 = k

=> k = 0.4

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Given that

The figure is of a cone and we have to find the volume of the cone.

Explanation -

The diameter of the cone is 22km and the height is also 22 km.

So the radius will be

radius = r = d/2 = 22/2 km = 11 km

Hence, r = 11 km and h = 22 km

The formula for the volume of the cone will be

On substituting the values we have

So B is the correct option.

Final answer -

Answer:

I can see that (0, 2) is the solution to this equation because that is the point where the lines intersect.

Step-by-step explanation:

[tex] - 3x + 2 = \frac{1}{2} x + 2[/tex]

[tex] - 3x = \frac{1}{2} x[/tex]

[tex]x = 0[/tex]

[tex]y = 2[/tex]

Looking at the series, we have a geometric sequence, where the first term is a1 = 5 and the common ratio is q = -3/5.

(This ratio can be calculated by dividing one term by the term before)

To find the sum of an infinite geometric sequence, we can use the formula below:

Since a1 = 5 and q = -3/5, we have:

Therefore the correct option is C.

Answer:

second and fourth are correct

Step-by-step explanation:

remembering the rule of exponents

• [tex]a^{m}[/tex] × [tex]a^{n}[/tex] = [tex]a^{(m +n)}[/tex]

then

- 7x²(4x³ + 2) = - 28[tex]x^{5}[/tex] - 14x² ≠ - 28[tex]x^{6}[/tex] - 14x²

- 2b³(6b² + 5) = - 12[tex]b^{5}[/tex] - 10b³ ← correct

- 3[tex]y^{4}[/tex] (5y² + 2) = - 15[tex]y^{6}[/tex] - 3[tex]y^{4}[/tex] ≠ - 15[tex]y^{8}[/tex] - 6[tex]y^{4}[/tex]

- 5d³ (3d² + 4) = - 15[tex]d^{5}[/tex] - 20d³ ← correct

7 * the smaller of two consecutive even integers is the same as -248 minus 6 * the larger integer. find the integers​

let

x ----> the smaller of two consecutive even integers

x+2 -----> the second integer

so

7x=-248-6(x+2)

solve for x

7x=-248-6x-12

7x+6x=-248-12

13x=-260

x=-20

the second number is

-20+2=-18

Using equation, the number of children and adult tickets sold are 33 and 78 respectively

111 people attend the concert and tickets for adults cost $3.5 while tickets for children cost $2.25 and total receipts for the concert was $347.25.

Therefore, the number of ticket sold for adult and children can be calculated as follows :

let

x = number of children ticket sold

y = number of adult tickets sold.

Therefore, the equation that represent the situation is as follows:

2.25x + 3.5y = 347.25

x  + y = 111

multiply equation(ii) by 3.5

2.25x + 3.5y = 347.25

3.5x + 3.5y = 388.5

subtract equation(i) from equation(ii)

1.25x = 41.25

divide both sides by 1.25

x = 41.25 / 1.25

x = 33

Hence,

y = 111 - 33

y = 78

Therefore,

number of children ticket = 33

number of adult ticket = 78

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Answer:

12

Step-by-step explanation:

4xA+7=55

using PEMDAS multiplication comes first

A4+7=55

A4=55-7

A4=48

A=48/4

A=12

check:

4x12+7=12

Answer: it should be 5

we can multiply 3x4 to get twelve so it must be the same for the other one

So 5x4=20

Step-by-step explanation:

have a great day!

Answer:

5

Step-by-step explanation:

12/4 = 3. 20/4 = 5

Side 12 divided by side 3 is four. You know four is now your key. Side 12 divided by 4 is Side 3. Side 20 divided by 4 is 5. So 5 is your answer.

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The probability that in a given year it will not snow on January 1st in that town is 0.572.

It should be noted that from the information, the meteorological records illustrates that the probability that it will snow in a certain town on January 1st is 0.428.

Therefore, the probability that in a given year it will not snow on January 1st in that town will be:

= 1 - 0.428

= 0.572

The probability is 0.572.

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The graph of the linear function y = 2/3x + 1 is given at the end of the answer.

A linear function, in slope-intercept format, is modeled according to the following rule:

y = mx + b

In which:

For this problem, the function is given as follows:

y = 2/3x + 1.

From this, we have that:

From the slope, when x changes by 3, y changes by 2, hence:

Thus the linear function also passes through point (3,3), and it's graph is sketched at the end of the answer.

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1. The statements that are true about the variables involved in this situation and the values for each variable are:

2. The number of rides Dina can go on using all of her tickets are

3. Yes, The number of rides equals the total number of tickets while maintaining going for a ride most once

The answer makes sense in the context of the situation because the numbers of rides are A. 7 and the number of tickets totals B. 24

given data

Dina has 24 tickets for carnival rides

She plans to go on a ride most once

Rides with no height requirement cost 3 tickets

Rides with a height requirement cost 4 tickets

1. The given statement includes: She plans to go on a ride most once. This means that Dina will not have a zero ride.

zero is a real number and a non negative integer hence option A is correct

2. Option C maintains she plans to go on a ride most once and the number of tickets used totals 24

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Answer:

{x ∈ R: x ≠ -5 and x ≠ 1}.

Step-by-step explanation:

x^2+8/x^2+4x-5

= x^2+8 / (x - 1)(x + 5)

The denominator is zero when x = 1 or x = -5

So:

Domain is:

{x ∈ R : x ≠ -5 and x ≠ 1}.

From the scrabble information given above, the odds in favor of selecting E is given as 0.073 while the odds against selecting an E is 13.667.

The odds are defined as the chance of the event occurring divided by the probability of the event not occurring. If the chance of an event happening is Y, the probability of it not happening is 1-Y.

Given:

Total number of tiles = 100

Number of E tiles = 12 [See attached image]

The odds in favor of selecting E =

= no of cases in favor of E / no of cases against E

= 12 / ( 100 - 12)

= 6 / 82

= 0.0731707317

[tex]\approx[/tex] 0.073

Given the above,

The odds against selecting E = 82/6

= 13.6666666667

[tex]\approx[/tex] 13.667

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As x approach to +∞ function y approaches -∞

And as x approach to -∞ function y approaches -∞

A coordinate plane is a two-dimensional surface created when two number lines are combined. When a horizontal line crosses the origin, which is the location where the X and Y axes meet, it is generated. A coordinate grid's integers are used to locate points. A coordinate plane can be used to graph points, lines, and a variety of other objects. It functions as a map and offers straightforward directions between two sites.

F(x)=[tex]x^{2} +2x^{2} -4x^{2}[/tex]

F(x)=-[tex]x^{2}[/tex]

if x =0 then y = 0

if x = 1 then y = -1

End behavior

As x approach to +∞ function y approaches -∞

And as x approach to -∞ function y approaches -∞

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Answer:

4.5

Step-by-step explanation:

2/1 x 9/4 = 18/4 = 4.5

Answer:

4.5 is your answer

Step-by-step explanation:

hope it helps