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The vertex form of the equation of a parabola with a vertex at (0,0) and passing through the point (1,2) is [tex]y=2x^2.[/tex]

The vertex form of a parabola is given by: [tex]y = a(x - h)^2 + k[/tex] where (h, k) is the vertex of the parabola.

In this case, the vertex is (0, 0), so h = 0 and k = 0.

Therefore, the equation becomes: [tex]y = a(x - 0)^2 + 0.[/tex] Simplifying further, the equation becomes: [tex]y = ax^2[/tex].

Now, we need to find the value of 'a.' To do this, we can use the given point (1, 2). Substitute these values into the equation:

[tex]2 = a(1)^2[/tex].

Therefore, 'a' is 2. So, the final equation in vertex form is: [tex]y = 2x^2.[/tex]

So, the correct answer is A. [tex]Y = 2x^2.[/tex]

Rounding to the nearest tenth, the circumference of a penny is approximately 6.0 cm.

To find the circumference of a penny, we use the formula for the circumference of a circle:

Circumference = π * diameter

Since the penny's width is given (which is the same as the diameter), we can plug in the values:

Circumference = 3.14 * 1.9 cm

Now, calculate the circumference:

Circumference ≈ 5.966 cm

Rounding to the nearest tenth, the circumference of a penny is approximately 6.0 cm.

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The solution is 17 chairs

The number of chairs placed is 17 and the inequality equation is 2x < 35 , where x is the number of chairs

What is an Inequality Equation?

Inequalities are the mathematical expressions in which both sides are not equal. In inequality, unlike in equations, we compare two values. The equal sign in between is replaced by less than (or less than or equal to), greater than (or greater than or equal to), or not equal to sign.

In an inequality, the two expressions are not necessarily equal which is indicated by the symbols: >, <, ≤ or ≥.

Given data ,

Let the number of chairs be represented as x

Now , the inequality equation will be

Each chair installed in the new chapel requires 24 inches of clearance

So , 24 inches = 2 feet

And , each row cannot be greater than 35 feet

So , the number of 2 feet chairs = 2x

And , 2x cannot be greater than 35 feet

Substituting the values in the equation , we get

2x < 35   be equation (1)

Divide both sides of the equation by 2 , we get

x < 17.5

x < 17 chairs

Therefore , the value of x is 17 chairs

Hence , the number of chairs is 17 chairs

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we know that

[tex] 1L=1000mL [/tex]

we are given 2.5L

so, to find 2.5L into mL, we will have to multiply both sides by 2.5

[tex] 2.5*1L=2.5*1000mL [/tex]

now, we can simplify it

[tex] 2.5L=2500mL [/tex]

so, option-C.............Answer

Final answer:

Mitch has a 1/16 probability of guessing both multiple-choice answers correctly when randomly guessing among four options.

Explanation:

If Mitch guesses on two multiple-choice questions with choices A, B, C, and D, the probability of guessing both correctly is calculated as follows: The probability of correctly guessing one question is 1/4 (since there are 4 possible choices, and only one is correct). To find the probability of guessing both correctly, we multiply the probabilities of each independent event. Thus, the probability of guessing the first question correctly AND the second question correctly is 1/4 × 1/4 = 1/16.

The solution is, There are 198 calories in a 22-oz iced tea.

In mathematics, multiplication is a method of finding the product of two or more numbers. It is one of the basic arithmetic operations, that we use in everyday life.

here, we have,

given that,

a 15-oz iced tea at a certain restaurant had 135 calories.

now we have to find that, How many calories are there in a 22-oz iced tea.

i.e. we have

15/135 = 22/?

let, x calories are there in a 22-oz iced tea.

now, 15/135 = 22/x

or, x = 22 x 135 / 15

we have,

22 x 135 = 2970

2970/15 = 198

so, x = 198

There are 198 calories in a 22-oz iced tea.

Hence, The solution is, There are 198 calories in a 22-oz iced tea.

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Final answer:

The triangle with angles of 120 degrees, 35 degrees, and 25 degrees is classified as an obtuse scalene triangle because it has one angle greater than 90 degrees and all angles of different measures.

Explanation:

To classify the triangle with angles of 120 degrees, 35 degrees, and 25 degrees, we first confirm that the sum of its angles is 180 degrees, which is true for any plane triangle. Given this sum, we can classify the triangle based on its angles and sides.

A triangle with one angle greater than 90 degrees is called an obtuse triangle, as it has an obtuse angle (greater than 90 degrees). Since this triangle has a 120-degree angle, it fits that definition. Furthermore, because all the angles are different, we can classify it as a scalene triangle, meaning all sides have different lengths. Therefore, the correct classification for this triangle is an obtuse scalene triangle.

The calculated quotient of the expression (14x³ - 21x² + 28x) ÷ 7x is 2x² - 3x + 4

How to evaluate the quotient expression

From the question, we have the following parameters that can be used in our computation:

(14x³ - 21x² + 28x) ÷ 7x

Factor out x in the numerator

So, we have

(14x³ - 21x² + 28x) ÷ 7x = x(14x² - 21x + 28) ÷ 7x

Evaluate the quotient

(14x³ - 21x² + 28x) ÷ 7x = (14x² - 21x + 28) ÷ 7

Divide through by 7

(14x³ - 21x² + 28x) ÷ 7x = 2x² - 3x + 4

Hence, the quotient of the expression is 2x² - 3x + 4

After calculating the discount and subtracting it from the original price, Eric's bike cost $135.60, which is $14.35 less than Kurt's bike that cost $149.95.

To determine how much less Eric paid for his bike compared to Kurt's bike, we need to calculate the discount Eric received and subtract it from the original price of his bike. Then, we'll compare it to the price Kurt paid for his bike.

First, we calculate Eric's discount by multiplying the original price of the bike, $169.50, by 1/5 (which represents the 20% discount):

$169.50 times  15= $33.90.

Now, subtract this discount from the original price to find out how much Eric paid for the bike:

$169.50 - $33.90 = $135.60.

Finally, to find out how much less Eric's bike cost than Kurt's, we subtract the price Eric paid from the price Kurt paid:

$149.95 - $135.60 = $14.35.

Eric's bike cost $14.35 less than Kurt's.

A clockmaker is the answer

There are 54 people at the party.

18 people are wearing red which means that 36 people are not wearing red

54 - 18 = 36

The fraction [tex]\frac{36}{54}[/tex] represents the 36 people at the party that are wearing no red. We can find what percent of the people at the party are not wearing red by turning [tex]\frac{36}{54}[/tex] into a percent.

[tex]\frac{36}{54}[/tex] can be reduced to [tex]\frac{2}{3}[/tex]  by dividing both the numerator and denominator by the greatest common factor of 36 and 54.

2 ÷ 3 = 0.667

0.667 × 100 = 66.67%

Therefore, 66.67% of the people at the party are not wearing red