You are selling pizzas to raise money for a school field trip. Cheese pizza cost $8 and pepperoni pizza cost $9. You need to sell at least two of each kind of pizza, and you want to sell at least $180 worth of pizza. Write an inequality.

The given sequence appears to be an arithmetic sequence, as the difference between consecutive terms is 9. To find the 43rd term, we can use the formula for the nth term of an arithmetic sequence:

a_n = a_1 + (n - 1)d

where a_n is the nth term, a_1 is the first term (11 in this case), n is the term number (43 in this case), and d is the common difference (9 in this case).

Plugging in the values, we get:

a_43 = 11 + (43 - 1) * 9

a_43 = 11 + 42 * 9

a_43 = 11 + 378

a_43 = 389

So the 43rd term of the sequence is 389.

Answer:

Answers are in the boxes

Step-by-step explanation:

Remember that i² = -1

Proof of the similarity of triangle AMN and Triangle ABC is shown below.

We have to given that;

In a figure,

⇒ MN is parallel to BC.

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

And, Two rays (half-lines) combined into an angle have a single terminal. The latter is known as the vertex of the angle, while the rays are known as its sides, occasionally as its legs, and occasionally as its arms.

Now, By definition of alternate angle of parallel lines, we get;

⇒ ∠ AMN and ∠ ABC are equal.

⇒ ∠ ANM and ∠ ACB are equal.

And, In triangles AMN and ABC;

⇒ ∠ A is common angle.

Hence, By AAA postulates we can say that;

⇒ Δ AMN ≈ Δ ABC

Thus, triangle AMN and Triangle ABC are similar by AAA postulates.

Learn more about the triangle visit;

brainly.com/question/1058720

#SPJ1

The integral ∫ (sin x + 3sin³ x - sin x)cos x dx upon evaluation is

(3/4)(sin x)⁴ + C

Let's assign u = sin x. This implies du = cos x dx.

By substituting u and du into the integral, we have:

∫ (u + 3u³ - u) du

Simplifying the expression inside the integral, we obtain:

∫ (3u³) du

Now we can integrate the simplified expression. Using the power rule for integration, which states that the integral of x^n dx is (1/(n+1))x^(n+1) + C, we find:

∫ (3u³) du = (3/4)u⁴ + C

Finally, substituting back u = sin x, we get:

∫ (sin x + 3sin³ x - sin x)cos x dx = (3/4)(sin x)⁴ + C

In conclusion, the integral of (sin x + 3sin³ x - sin x)cos x dx, using u-substitution, simplifies to (3/4)(sin x)⁴ + C, where C is the constant of integration.

Learn more about integral here:

https://brainly.com/question/31433890

#SPJ11

Solution: the lateral faces are always triangles with a common vertex. The vertex of a pyramid (the point, the apex) is not in the same plane as the base

Answer:

9-16y

Step-by-step explanation:

9-x^2y when x=4

plus in 4: 9- (4)^2y

=9-16y

Answer:

t ≈ 16.0 units

Step-by-step explanation:

Using the Sine rule in Δ TUV , that is

\(\frac{t}{sinT}\) = \(\frac{v}{sinV}\) , substitute values

\(\frac{t}{sin135}\) = \(\frac{11}{sin29}\) ( cross- multiply )

t sin29° = 11 sin135° ( divide both sides by sin29° )

t = \(\frac{11sin135}{sin29}\) ≈ 16.0 ( to the nearest tenth )

The x-intercept of the line calculator is (-1,0) while the y-intercept is (0,-3).

To determine the x-intercept, let y = 0 and solve for x in the equation y = 3x - 1.

Substitute 0 for y in the equation.0 = 3x - 1

Add 1 to both sides1 = 3x

Divide both sides by 3x = 1/3

The x-intercept of the line is (1/3, 0).

To find the y-intercept, let x = 0 and solve for y in the equation y = 3x - 1.

Substitute 0 for x in the equation.y = 3(0) - 1y = -1

The y-intercept of the line is (0, -1).

Therefore, the x-intercept is (1/3, 0), and the y-intercept is (0, -1).

Therefore, The x-intercept of the line calculator is (-1,0) while the y-intercept is (0,-3). The calculation above supports the conclusion.

To know more about, line calculator, visit

https://brainly.com/question/30763905

#SPJ11

Answer:

16,384

Step-by-step explanation:

Answer:

It is 1/36

Step-by-step explanation:

Brainliest plzzz

The value of the variable x is 53

A minor arc is defined as an arc whose measure is less than 180

Also, a major  arc is defined as an arc whose measure is greater than 180 degrees.

An arc whose measure equals 180 degrees is a semicircle

Then, we have from the the information given;

Equate the angles to 180 degrees, we get;

80 + 2x - 6 = 180

collect the like terms, we get;

2x = 180 - 80 + 6

Add the values first

2x = 180 - 74

Subtract the values

2x = 106

Divide both sides by the coefficient of  x, we get;

x = 106/2

x = 53

Learn more about arcs at: https://brainly.com/question/28108430

#SPJ1

Answer:

yes because its closer to 1

Step-by-step explanation:

Answer:

yes, -4 is greater than -5

Step-by-step explanation:

0 > -1 > -2 > -3 > -4 > -5 > -6

The statement "When eliminating a loop-carried dependency that adds a constant, the closed-form direct solution will likely contain a multiplication" is true because eliminating a loop-carried dependency that adds a constant simplifies the equation, but to obtain a closed-form direct solution, we need to express the result as a function of the current iteration's variables only

When eliminating a loop-carried dependency that adds a constant, the closed-form direct solution will likely contain a multiplication. This is because the loop-carried dependency adds a constant to the result of the previous iteration, which means that the current iteration's result is a function of both the current iteration's variables and the previous iteration's result.

By eliminating this dependency, we remove the need to use the previous iteration's result, which simplifies the equation. However, to obtain a closed-form direct solution, we need to express the result as a function of the current iteration's variables only, which often involves a multiplication. This is because multiplication is a fundamental mathematical operation that allows us to combine variables in a way that preserves their individual values.

Learn more about multiplication here

brainly.com/question/23269091

#SPJ4

True. When eliminating a loop-carried dependency that adds a constant, the closed-form direct solution will likely contain a multiplication. This is because the loop-carried dependency is typically expressed as an addition, and removing it would result in a product of the loop index and the constant.

when eliminating a loop-carried dependency that adds a constant, the closed-form direct solution will likely contain a multiplication. This is because the process often involves applying mathematical transformations that result in multiplications to simplify the loop and eliminate dependencies.

learn more about loop-carried dependency

https://brainly.com/question/31563150

#SPJ11

The Laplace transform of the motion equation is mx(t) + dx(t) + kx(t) = f(t).

Given: Motion equation is mx(t) + dx(t) + kx(t) = f(t); X(s) and

F(s) be the Laplace transforms of the position x(t) and external force f(t) respectively.

Transfer function is G(s)= X(s)/F(s) = 1/ms² + ds + k

To derive a transfer function of a mass-spring-damper system from its equation of motion, we have to follow these steps:

Step 1: Take the Laplace transform of the motion equation.

Laplace Transform of the given equation is,  mX(s)s² + dX(s)s + kX(s) = F(s)

Step 2: Write X(s) in terms of F(s)X(s) = F(s) / m s² + d s + k

Step 3: Now the transfer function can be derived using the ratio of X(s) to F(s).

Transfer Function = G(s) = X(s) / F(s)G(s) = 1 / ms² + ds + k

Hence, the transfer function of a mass-spring-damper system from its equation of motion is G(s) = 1 / ms² + ds + k. 

In order to derive a transfer function of a mass-spring-damper system from its equation of motion, the following steps are necessary:

  Take the Laplace transform of the motion equation.

The Laplace transform of the motion equation is mx(t) + dx(t) + kx(t) = f(t).

X(s) and F(s) are the Laplace transforms of the position x(t) and external force f(t), respectively.

Learn more about motion equation

brainly.com/question/31314651

#SPJ11

An algebraic expression which models the given context would be written as s + 0.02s = 1.05s.

Price can be define as an amount of money which is primarily set by the seller of a good (product), and it must be paid by a buyer to the seller, so as to enable the acquisition of this good (product).

An algebraic expression can be defined as a mathematical equation which is used to show the relationship existing between two or more variables and numerical quantities.

Let s represent the price of a pair of shoes.

Therefore, an algebraic expression which models the given context would be written as follows:

s + 0.02s = 1.05s.

Read more on algebraic expression here: https://brainly.com/question/17615109

#SPJ4

Answer:

There isn't a plot.

Step-by-step explanation:

Answer:

No real solution implies that there could possibly be imaginary solutions.

Step-by-step explanation:  Extraneous solutions are created be using certain methods to solve the problem. They are not, never were, or never will be solutions. They are created by the process that is used to solve. hope this helps you :)

The area of the customer's yard is 580π.

The distance formula is given as -

d = √(x₂ - x₁)² + (y₂ - y₁)²

Given is that this grid represents the customer’s yard. The bottom left corner is the origin point  O(0, 0), and the x- and y- axes represent the two fences. The rose bush is at point P(16, 18).

We can write the area of the customer's yard -

A = πr²

Here -

r = d

r² = d²

We can write -

A = πd²

A = π {(x₂ - x₁)² + (y₂ - y₁)²}

A = π{16 x 16 + 18 x 18}

A = 580π

Therefore, the area of the customer's yard is 580π.

To solve more questions on scale factor , visit the link below -

brainly.com/question/30215119

#SPJ1

Answer:

a and c statements are true

Step-by-step explanation:

closure property of multiplication states that the product of two rational expressions as a rational expression

C. the associative property holds true for both multiplication and addition of rational expressions

Answer:

The answer is a, b, and e

Step-by-step explanation:

Answer:

D

Step-by-step explanation:

The graph show that the corn stalk grown to 21 inches at week 5.

Step-by-step explanation:

\( - 3(2x + 4) + 4x = 3x + 10\)

or,

\( - 6x - 12 + 4x = 3x + 10\)

or,

\( - 12 - 10 = 3x + 6x - 4x\)

or,

\( - 22 = 5x\)

or

\( - 22 \div 5 = x\)

or

\(x = - 22 \div 5 \: \: ans\)

The roots of 2x^2+4x+7 are -1 + i√5 and -1 - i√5.

A quadratic function has the generic form f(x)=ax²+bx+c. A parabola, a kind of two-dimensional curve, is the graph of a quadratic function. A polynomial function of degree two in one or more variables is known in algebra as a quadratic function, quadratic polynomial, polynomial of degree 2, or simply a quadratic. The phrase "quadratic" in mathematics refers to something that has to do with squares, the squaring operation, terms of the second degree, or equations or formulas that contain such terms. Latin's word for square is quadratus.

Function:

2x² + 4x + 7 = 0

ax² + bx + c = 0

x = \(\frac{-b +-\sqrt{}b^{2}- 4ac }{2a}\)

a = 2

b = 4

c = 7

Using quadratic function,

x = \(\frac{-4\sqrt{} 4^{2} -4(2)(7)}{2(2)}\)

x = \(\frac{-4+-\sqrt{-40} }{4}\)

So,

i = √-1

x = \(\frac{-4+-2i\sqrt{10} }{4}\)

Simplifying,

x = -1 +-√10/2

Roots are:

x = -1 + i√10/2

x = -1 - i√10/2

The roots of 2x^2+4x+7 are -1 + i√5 and -1 - i√5.

To learn more about quadratic function, visit:

https://brainly.com/question/14737980

#SPJ1

Answer:

The answer is 80

Step-by-step explanation:

56 / 7= 8

8x10 =80

the inequality to determine if a child's height satisfies the regulation is:

30in < h < 50 in.

Here we know that the allowed height of the child can be any value between 30 inches and 50 inches (not included, so we need to use the symbols > and <)

So, if we define h as the height, then h must be larger than 30 inches, so we can wrte:

h > 30 in

And h must be smaller than 50 inches, then:

h < 50 in.

If we write these two inequalities as one, we get:

30in < h < 50 in.

That is the inequality to determine if a child's height satisfies the regulation.

If you want to learn more about inequalities:

https://brainly.com/question/24372553

#SPJ1

Answer:

A. y = 5/4x - 3

B. slope is 5/4

C. y intercept is -3

D. Increasing

Step-by-step explanation:

5x - 4y = 12

Slope intercept form: y = mx + b

4y = 5x - 12

y = 5/4x - 3

Slope is 5/4

Y intercept is when x = 0 so it is -3

the slope is positive, therefore the line is increasing

Answer:

top left

Step-by-step explanation:

\(▪▪▪▪▪▪▪▪▪▪▪▪▪  {\huge\mathfrak{Answer}}▪▪▪▪▪▪▪▪▪▪▪▪▪▪\)

Thickness of the book is ~

Refer to the attachment for solution ~

Answer:

1.5 pound ever dollar

Step-by-step explanation:

just calculate

Answer:

2.25 answer

Step-by-step explanation:

9÷4=2.25answer thanks