how to write standard form for: (please answer this question soon )
[tex]2x - x ^{2} = 1[/tex]
[tex] - x {}^{2} = 15[/tex]
[tex]4x { }^{2} = 12[/tex]
[tex]5 + x = 3x { }^{2} [/tex]

A sandwich shop offers the following toppings. How many two topping sandwiches can you make?

-lettuce

-tomato

-bacon

-cheese

-mustard

Solution:

There are five toppings available and the five toppings are lettuce, tomato, bacon, cheese, mustard.

We need to make 2 topping sandwiches.

So, we can select any 2 toppings from the available 5 toppings

So, we must use combination here

So, the number of two topping sandwiches is 5 combination 2

Or, Number of 2 topping sandwiches= 5 C 2

The formula is, n C r =[tex]\frac{n!}{(n-r)!r!}[/tex]

So, The number of 2 topping sandwiches= 5 C 2 =[tex]\frac{5!}{(5-2)!2!}[/tex]

The number of 2 topping sandwiches=[tex]\frac{5!}{(3)!2!}[/tex]

The number of 2 topping sandwiches=[tex]\frac{(5*4*3*2*1)}{(3*2*1)(2*1)}[/tex]

The number of 2 topping sandwiches=[tex]\frac{120}{12}[/tex]

The number of 2 topping sandwiches=10

that is,

lettuce, tomato(1)

lettuce, bacon(2)

lettuce, cheese(3)

lettuce, mustard(4)

tomato,bacon(5)

tomato,cheese(6)

tomato,mustard(7)

bacon,cheese(8)

bacon, mustard(9)

cheese,mustard(10)

Answer: So, there are 10 possible two topping sandwiches

The mean scores for all 9 games played is 68

Given Data

Hence the mean is computed is the summation of scores over the number of games played

= 612/9

= 68

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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 inverse of the relation y=6x-3 is y = (x + 3) / 6.

To find an equation for the inverse of the relation y=6x-3, we need to follow a series of steps which involves swapping the variables, and then solving for the new y.

Start with the initial equation: y = 6x - 3.

Swap the variables x and y: x = 6y - 3.

Solve for y to find the inverse relation: Add 3 to both sides to get x + 3 = 6y, then divide both sides by 6 to isolate y, resulting in y = (x + 3) / 6.

There were total 2000 people in the survey.

We can multiply relative frequency of any particular category with the total number of people to find the answer for each part.

Part A: How many males surveyed preferred playing sports?

Total Relative frequencies of Males who preferred playing sports = 0.30  

Number of Males preferred playing sports = 0.30 x 2000 = 600.

Part B: How many people surveyed preferred to read a book?

Total Relative frequencies of people who preferred reading book = 0.10 + 0.15 = 0.25

Number of people preferred reading book = 0.25 x 2000 = 500.

Part C: How many females were surveyed?

Total Relative frequencies of Females = 0.15 + 0.05 + 0.15 = 0.35

Number of Females surveyed = 0.35 x 2000 = 700.

Answer:

80.94 is the answer

Step-by-step explanation:

The coordinates of the vertices of the new figure A'B'C'D' are A'(-8, 5), B' (-8, 8), C' (-5, 7), and D' (5, -4.5).

The coordinates of the vertices of quadrilateral ABCD are A(-6, 2), B(-6, 5), C(-3, 4), and D(-2.5, 2).

To translate the quadrilateral 2 units left and 3 units up, we subtract 2 from the x-coordinates

and add 3 to the y-coordinates of each vertex.

Therefore, the coordinates of the vertices of quadrilateral A'B'C'D' are A'(-8, 5), B' (-8, 8), C' (-5, 7), and D' (5, -4.5).

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To find the area of the plate, we first calculate the radius using the given circumference and then plug this into our formula to find the area. The calculated area of the plate is approximately 94.52 square inches.

The student is asking for the area of a circular plate with a given circumference, using 3.14 for pi. The formula to calculate the area of a circle is A = πr². However, we only have the circumference, which allows us to find the radius using the formula C = 2πr, or rearranged to solve for r, r = C / (2π). Plugging in the given circumference of 34.5 inches, we find the radius to be 34.5 / (2 * 3.14) = 5.49 inches. Now, we can find the area by substitifying this value back into our area formula, A = πr², yielding A = (3.14) * (5.49²) ≈ 94.52 square inches.

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To find the area of the circular plate having its circumference as 34.5 inches, we firstly calculate its radius using the formula r = Circumference/(2π) which gives approximately 5.49 inches. We then substitute the radius value in the formula for area of a circle (Area = πr²), yielding an area of approximately 94.52 square inches.

In mathematics, the circumference of a circle is related to its radius through the formula: Circumference = 2πr.

Given that the circumference of the plate is 34.5 inches, and we use 3.14 for π, we first work out the radius by rearranging the formula like so: r = Circumference / (2π).

Substitute the given values: r = 34.5 inches / (2*3.14)

Do the calculation: r approximately equals 5.49 inches.

Next, use the formula for the area of the circle which is: Area = πr².

Substitute r: Area = 3.14 * (5.49 inches)²

Calculate: Area is approximately 94.52 square inches.

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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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The first line is the line of best fit for this given disperse plot.

"A disperse plot is a kind of plot or numerical graph involving Cartesian directions to show values for regularly two factors for a bunch of information.

On the off chance that the focuses are coded, one extra factor can be shown."

For a particular scatter plot, four different lines are drawn here.

We know, a line drawn on a disperse plot fits it the best is the line that is nearer to a large portion of the places.

Using the proportion of students who enjoy watching Dancing with the Stars from Grace's survey, we can estimate that approximately 133 students at her school are expected to enjoy the show.

Grace surveyed 60 random students at her school and found that 14 enjoy watching Dancing with the Stars. With a total of 570 students in the school, we can establish a proportion to estimate how many students school-wide might enjoy the show. We do this by setting up a ratio of students who enjoy the show to the total number of students surveyed and then use that ratio to estimate the number for the entire school population.

To calculate, we take the ratio from the survey (14/60) and apply it to the total student body (570) like so:

Therefore, approximately 133 students in Grace's school are expected to enjoy watching Dancing with the Stars.

The base number in the given situation is 1.74. This number is commonly referred to as the growth rate.

The equation is defined as mathematical statements that have a minimum of two terms containing variables or numbers that are equal.

The given equation y = 18.36(1.74)ˣ represents the situation.

The base number in this equation is 1.74. In an exponential function, the base is a constant multiplied by itself a certain number of times.

In this case, the base is multiplied by itself x number of times.

For example, on day 1 (x=1), the number of hits is 18.36(1.74)¹ = 32.5 hits.

On day 2 (x=2), the number of hits is 18.36(1.74)² = 56.6 hits. The base number represents the rate at which the number of hits is increasing. If the base is greater than 1, the number of hits is increasing at an exponential rate.

If the base is less than 1, the number of hits is decreasing at an exponential rate. If the base is equal to 1, the number of hits is increasing at a constant rate.

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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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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.

Answer:

1) -12  

2) 32

Step-by-step explanation: