f(x)-x^2+10x-22
What is the y-intercept of this quadratic function

Answer:

(-2,-8)

Step-by-step explanation:

6x + 7y = -68

-2x + 7y = -52

Time the first equation by -1

-6x - 7y = 68

-2x + 7y = -52

-8x = 16

x = -2

Now put -2 in for x and solve for y

6(-2) + 7y = -68

-12 + 7y = -68

7y = -56

y = -8

Let's Check

6(-2) + 7(-8) = -68

-12 - 56 = -68

-68 = -68

So, (-2, -8) is the correct answer.

the correct answer is option b) 0.11. To find the experimental probability of drawing a K or 6, we need to first determine how many K's and 6's are in a standard deck of cards.

A standard deck of cards contains 52 cards, divided into four suits: hearts, diamonds, clubs, and spades. Each suit contains 13 cards, including an ace, numbered cards 2-10, and face cards (jack, queen, king).

Out of the 52 cards in the deck, there are four K's and four 6's, for a total of eight cards that satisfy the condition of being a K or 6.

To calculate the experimental probability of drawing a K or 6 from the table, we need to add up the frequency of drawing a K and the frequency of drawing a 6, and then divide by the total number of draws (100).

From the table, we see that the frequency of drawing a K is 4, and the frequency of drawing a 6 is 7. Therefore, the total frequency of drawing a K or 6 is:

4 (K's) + 7 (6's) = 11

So the experimental probability of drawing a K or 6 is:

11/100 = 0.11

Therefore, the correct answer is option b) 0.11.

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Answer:

An event that is less likely to occur would have a lower probability than 0.45. Therefore, the options that show a probability less than 0.45 are:

A) 0.42

C) 0.29

D) 0.37

So options A, C, and D are the correct answers.

Step-by-step explanation:

a quadratic function means it has an "x²" based term as highest x exponent.

and as such it has 2 zeroes.

the request here simply means that both zeros must be equal and 5.

remember, factoring the function expression tells us the zeroes right away.

now we reverse the process.

we know the zeroes (5 - two times).

so we define the factors to have the desired zeroes :

y = (x - 5)(x - 5)

you see what i did there ? we need to have a quadratic equation, and therefore 2 zeroes. both with the value of 5.

y = (x - 5)(x - 5) = x² - 5x - 5x + 25 = x² - 10x + 25

A quadratic function with only one zero can be derived using the vertex form of a quadratic function, where h equals the zero. Hence, a possible quadratic function with five as the only zero is f(x) = (x - 5)^2.

In mathematics, a quadratic function is written in the form f(x) = ax2 + bx + c.

So, a potential function could be f(x) = (x - 5)2.

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the true statements about the circle equation are:

Remember that the equation of a circle whose center is at(a, b) and has a radius of R units is:

(x -a )²+ (y - b)² = R²

Here the equation is:

x² + y² - 2x - 8 = 0

Completing squares in x we will get:

(x² - 2x) + y² - 8 = 0

(x² - 2x + 1) -1 + y² - 8 =

(x - 1)² + (y - 0)² = 9 = 3²

So the center is (1, 0) and the radius is 3, so the true statements are:

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By answering the presented question, we may conclude that To prepare ratio 5 litres of cold drink, we'll need 625 millilitres of pure fruit concentrate.

In mathematics, ratios demonstrate how frequently one number is contained in another. For example, if there are 8 oranges and 6 lemons in a fruit plate, the ratio of oranges to lemons is 8 to 6. In a similar vein, the orange-to-whole-fruit ratio is 8, whereas the lemon-to-orange ratio is 6:8. A ratio is an ordered pair of integers a and b represented as a / b, where b is not zero. A ratio is an equation that equates two ratios. For example, if there is one male and three girls (for every boy she has three daughters), 3/4 are girls and 1/4 are boys.

If the concentrate-to-water ratio is 1:7, it signifies that the final product requires 7 parts water for every 1 part concentrate. As a result, the total number of components in the combination is 1+7=8.

To produce 5 litres of the cold drink, we must first establish the quantity of concentrate necessary to make 8 parts, and then multiply this figure by 5 litres.

As a result, we need 1 part concentrate and 7 parts water to create 8 parts.

As a result, we require 1/8th of 5,000 millilitres of concentrate, or 625 millilitres.

To prepare 5 litres of cold drink, we'll need 625 millilitres of pure fruit concentrate.

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Answer: 7.5

Step-by-step explanation: Because Noah has five dollars, 100% of 5 is 5, and 50% of 5 is 2.5 so Diego has 7.5 dollars.

Answer:

$7.5

Step-by-step explanation:

There are two ways to solve this:

1) First, write the equation:

150% of 5

Then calculate:

[tex]\frac{150}{100} *5[/tex]

Finally, simplify 1 zero with the 0 in 15:

1.5 * 5

= $7.5

2) For the second way, because 150 is more than over 100 (percent), you deduct 150 and 100:

150 - 100 = 50

Then find 50% of 50:

[tex]\frac{50}{100} *5[/tex]

Then cancel 1 zero in 100 with the zero in 50:

0.5 * 5

= 2.5

Finally, add the product with the original amount of Noah:

5 + 2.5

= $7.5

Step-by-step explanation:

You need to find 85% of 125 points :

85% * 125 =  .85  * 125 = ~ 106 points

Answer: A = 3

Step-by-step explanation:

4x-2=10

4x=12

x =12/4

x=3

The solution to the inequality is y < 9

Inequalities are simply described as a relation with the reflection of a non-equal comparison between two numbers, mathematical expressions or even elements.

The comparison of these expressions or numbers is mostly based on their sizes on the number line.

It is used to compare two values such that one is less than, greater than, or simply not equal to another value.

From the information given, we have the inequality;

-3 + y< 6

To solve for y, collect like terms

y < 6 + 3

add the values

y< 9

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the solution to the system of equations is x = 7.14 and y = 13.57.

In mathematics, an equation is a statement that asserts the equality of two mathematical expressions, usually containing one or more variables.

Given equations are:

5 - 0.7x = 0.2y ...........(1)

-y + 0.4x = 4.3 ...........(2)

To solve for x and y, we can use the elimination method, which involves multiplying one or both equations by a constant to eliminate one of the variables. Here's how we can do it:

First, let's multiply equation (1) by 5 and equation (2) by 2 to eliminate the y variable:

25 - 3.5x = y (multiplying equation (1) by 5)

-2y + 0.8x = 8.6 (multiplying equation (2) by 2)

Now we can substitute the expression for y from equation (1) into equation (2) and solve for x:

25 - 3.5x = 0.2(25 - 3.5x) (substituting y from equation (1))

25 - 3.5x = 5 - 0.7x

-2.8x = -20

x = 7.14

Substituting this value of x back into equation (1), we can solve for y:

5 - 0.7(7.14) = 0.2y

y = 13.57

Therefore, the solution to the system of equations is x = 7.14 and y = 13.57.

By using ALEKS graphing calculator, we get the same values of x and y.

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As a result, x = 2 and x = -5 are the roots of the quadratic function y = (x - 2)(x + 5). They also serve as the function's x-intercepts on the graph.

Typically, it includes one or more variables that stand in for unknowable values and may include exponents, roots, multiplication, division, and other mathematical operations. Finding the value(s) of the variable(s) necessary to make an equation true is the aim of equation solving. In algebra, calculus, and other areas of mathematics, equations are frequently employed to model and resolve issues.

given

This is because the values of x are provided by a quadratic function's factored form.

Let's use Corey's equation, y = (x - 2)(x + 5), as an illustration. We solve for x and put y equal to zero to obtain the roots of this function:

0 = (x - 2)(x + 5)

Only when one of the factors on the left side equals zero is this equation true. As a result, we may set each factor to 0 and find x:

In each equation, the result of solving for x is:

x = 2 or x = -5

This is because the values of x are provided by a quadratic function's factored form.

Let's use Corey's equation, y = (x - 2)(x + 5), as an illustration. We solve for x and put y equal to zero to obtain the roots of this function:

0 = (x - 2)(x + 5)

Only when one of the factors on the left side equals zero is this equation true. As a result, we may set each factor to 0 and find x:

x - 2 = 0 or x + 5 = 0

In each equation, the result of solving for x is:

x = 2 or x = -5

As a result, x = 2 and x = -5 are the roots of the quadratic function y = (x - 2)(x + 5). They also serve as the function's x-intercepts on the graph.

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The measure of the angle POB is equal to 46°. Thus, option C is correct.

The cοllectiοn οf all pοints in the plane that make up a circle are all equally spaced frοm a certain pοint knοwn as the "centre," making the fοrm a clοsed twο-dimensiοnal shape. The symmetry line οf reflectiοn is fοrmed by each line that traverses the circle.

Mοreοver, it pοssesses rοtatiοnal symmetry arοund the centre fοr each angle. A circle is a circular shape that can be created by tracing a mοving pοint in a plane sο that its distance frοm a specified pοint remains cοnstant.

Given

Angle AOC = 46°  

Now, ΔAOP ≅ ΔBOP

As SSS criteria is possible

Then

By CPCT

∠AOC = ∠BOC = ∠POB

∠POB = 46°  

Thus, the measure of the angle POB is equal to 46°. Thus, option C is correct.

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The cube's surface area would be 96m².

The surface area of the right rectangular prism is 37.5 ft².

The height of the prism is 4/3 in.

The approximate lengths of the sides of the base is height of 9 cm and a base of 8.2 cm.

To find the surface area, first find the side length of the cube. The volume of a cube is V = s³, where s is the side length. So:

64m³ = s³ => s = (64)^(1/3) = 4m

Now, the surface area (SA) of a cube is given by the formula SA = 6s². Plugging in the side length:

SA = 6(4m)² = 6(16m²) = 96m²

To find the surface area of the right rectangular prism:

First, find the Lateral Area (LA): LA = Perimeter × height

Perimeter = (2 ft + 1 1/2 ft) × 2 = 7 ft

Height = 4 1/2 ft

LA = 7 ft × 4 1/2 ft = 31.5 ft²

Now, find the Surface Area (SA): SA = LA + 2B

SA = 31.5 ft² + 2(3 ft²) = 31.5 ft² + 6 ft² = 37.5 ft²

To find the height h of the prism:

First, find the Base Area (B): B = Length × Width

B = 3 in × 7 in = 21 in²

Now, use the Surface Area (SA) formula to find the Lateral Area (LA):

SA = LA + 2B => LA = SA - 2B

LA = 68 2/3 in² - 2(21 in²) = 68 2/3 in² - 42 in² = 26 2/3 in²

Now, use the Lateral Area (LA) formula to find the height (h):

LA = Ph => h = LA / P

Perimeter (P) = 2(Length + Width) = 2(3 in + 7 in) = 20 in

h = (26 2/3 in²) / 20 in = 4/3 in

The right triangular prism has two equilateral triangular bases and three rectangular sides. Since the distance between the bases is 9 cm, we can use the surface area of the prism to find the total area of the three rectangular sides:

Surface area = 2 * A (triangle bases) + Lateral area (rectangular sides)

319.5 cm² = 2 * 29.1 cm² + Lateral area

Lateral area ≈ 261.3 cm²

Each of the three rectangular sides has a height of 9 cm and a base of 8.2 cm.

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The team can be expected to score about 15 goals in 10 games based on their relative frequency of scoring 24 goals in 16 games.

The proportion or percentage of times that even an event or category occurs in a dataset is measured by relative frequency. It is derived by dividing the total number of observations in the dataset by the frequency with which the event or category occurs. In statistics, relative frequency is frequently used to compare the occurrence of various events or categories and to characterise the distribution of a dataset. Also, depending on a sample, it is used to calculate the likelihood that an event will occur in a population.

The goals scored in 10 games can be calculated using proportions:

Given that,

24 goals / 16 games = 1.5 goals per game

For 10 games we have:

1.5 goals per game × 10 games = 15 goals

Hence, the team can be expected to score about 15 goals in 10 games based on their relative frequency of scoring 24 goals in 16 games.

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The distance traveled after t seconds is given by:

[tex]d = |-\frac{(2t^2 + 2t + 1)e^{-2t}}{4}|[/tex]

Here we know that the particle moves along a straight line with the velocity:

[tex]v(t) = t^2*e^{-2t}[/tex]

Remember that the velocity is the rate of change of the position, so if we want to find the distance traveled after t seconds, we need to integrate this between 0 and t, we will get:

[tex]\int\limits^t_0 {t'^2*e^{-2t'}} \, dt' = -\frac{(2t^2 + 2t + 1)e^{-2t}}{4}[/tex]

That is the expression that gives the distance traveled after t seconds, if we want to get it more exactly, we should take the absolute value, then we get:

[tex]d = |-\frac{(2t^2 + 2t + 1)e^{-2t}}{4}|[/tex]

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Answer: 20.99

Step-by-step explanation: you multiply by 0.428571 which is 3/7

The function family name of the parent function shown in the graph above is radical.

In Mathematics, a cube root function is sometimes referred to as a cubic root polynomial or radical function and it can be defined as a type of polynomial that is an inverse of a cubic function.

Generally mathematics, a radical function or a cube root function can be represented or modeled by using the following mathematical equation:

f(x) = a∛(x - h) + k

where:

In this context, we can reasonably infer and logically deduce that the function family name of the parent function shown in the graph above is a radical function or a cube root function.

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Using fractions, we can find that   [tex]1\frac{1}{16}[/tex] length of material remains.

In mathematics, a fraction is represented by a number that identifies a portion of a whole. A fraction is a component or section taken from a whole, which can be any number, a certain amount, or an object.

A fraction is a non-integer that consists of a numerator and a denominator. A mixed fraction is made up of a whole number and a proper fraction. A proper fraction is a fraction where the numerator is less than the denominator.

Material left = initial length - length of the first plate - length of the second plate - (2 x 1/16)

= 123/8 - 33/4 - 95/16 - 2/16

= 17/16

=  [tex]1\frac{1}{16}[/tex].

Therefore,  [tex]1\frac{1}{16}[/tex] length of material remains.

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Answer:

The graph shows a proportional relationship because it is a line, and the difference between each point is the same.

explanation: The difference between all points are approximately 2.236.

The calculated probability of a friend being born on a Friday is 1/7

Assuming that people are equally likely to have been born on any of the 7 days of the week, the probability of the first friend being born on a Friday is 1/7 or approximately 0.143.

This is because there is only one day out of the seven days of the week  that is Friday, and each day has an equal chance of being chosen.

Therefore, the probability of the first friend being born on a Friday is 1/7.

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Complete question

Suppose that people are equally likely to have been born on any of the 7 days of the week. You meet two new friends independently, and ask each of them on what day of the week they were born. (Enter your answers as fractions.) What is the probability that the first friend was born on a Friday

Answer:

To find the average rate of change of a function over an interval, you can use the formula:

average rate of change = [f(b) - f(a)] / (b - a)

where a and b are the endpoints of the interval.

In this case, you have the function g(x) = log2(x + 3) - 4 and the interval [-2, 5]. So, plugging in the values, you get:

average rate of change = [g(5) - g(-2)] / (5 - (-2))

First, let's evaluate g(5) and g(-2).

g(5) = log2(5 + 3) - 4 = log2(8) - 4 = 3 - 4 = -1

g(-2) = log2((-2) + 3) - 4 = log2(1) - 4 = 0 - 4 = -4

Now you can substitute these values into the formula:

average rate of change = (-1 - (-4)) / (5 - (-2))

= 3 / 7

And the average rate of change of g(x) over the interval [-2, 5] is 3/7.

Answer:the scale factor of dilation from circle P to Q is 2.5

for among us

Step-by-step explanation:

The similar circles P and Q can be made equal by dilation and translation

The horizontal distance between the center of circles P and Q is 11.70 units

The scale factor of dilation from circle P to Q is 2.5

The horizontal distance between their centers?

From the figure, we have the centers to be:

P = (-5,4)

Q = (6,8)

The distance is then calculated using:

d = √(x2 - x1)^2 + (y2 - y1)^2

So, we have:

d = √(6 + 5)^2 + (8 - 4)^2

Evaluate the sum

d = √137

Evaluate the root

d = 11.70

Hence, the horizontal distance between the center of circles P and Q is 11.70 units

The scale factor of dilation from circle P to Q

We have their radius to be:

P = 2

Q = 5

Divide the radius of Q by P to determine the scale factor (k)

k = Q/P

k = 5/2

k = 2.5

Hence, the scale factor of dilation from circle P to Q is 2.5

Probability in sandwich choices analysis refers to the likelihood of a particular sandwich being chosen, based on factors such as taste, price, and availability.

1. To calculate the total number of possible sandwiches, we need to consider the number of options for each category: bread, protein, cheese, and vegetables.

Bread: There are 3 options - Italian, white, and wheat.

Protein: There are 4 options - tuna, ham, turkey, and beans.

Cheese: There are 4 options - provolone, Swiss, American, and none.

Vegetables: There are 5 options, and since we need to choose two, we use combinations. Therefore, there are (5 choose 2) = 10 possible combinations of vegetables: lettuce and tomatoes, lettuce and peppers, lettuce and onions, lettuce and pickles, tomatoes and peppers, tomatoes and onions, tomatoes and pickles, peppers and onions, peppers and pickles, and onions and pickles.

To calculate the total number of possible sandwiches, we multiply the number of options for each category:

3 x 4 x 4 x 10 = 480

Therefore, there are 480 different possible sandwiches.

2. Since Andre only cares about the ham, lettuce, and tomatoes, we only need to consider the number of options for vegetables. He needs to choose two vegetables, so we need to count the number of possible combinations of lettuce, tomatoes, and the remaining vegetables. Since we don't care about the bread or cheese, we can ignore those options.

There are (3 choose 2) = 3 possible combinations of vegetables that would make Andre happy: lettuce and tomatoes, lettuce and peppers, or tomatoes and peppers. Since we don't care about the bread or cheese, there are no restrictions on those categories, so there are 4 options for cheese and 3 options for bread, for a total of 12 possible sandwiches that would make Andre happy.

3. To calculate the probability of randomly choosing a sandwich that would make Andre happy, we divide the number of sandwiches that would make him happy by the total number of possible sandwiches:

3/480 = 1/160

Therefore, the probability is 1/160, or approximately 0.00625. This means that if we were to randomly choose a sandwich, there is a 0.625% chance that it would be a sandwich that would make Andre happy.

The complete question is:

1. A submarine sandwich shop makes sandwiches with one kind of bread, one protein, one choice of cheese, and two vegetables. How many different sandwiches are possible? Explain your reasoning. You do not need to write out the sample space.

Breads: Italian, white, wheat

Proteins: Tuna, ham, turkey, beans

Cheese: Provolone, Swiss, American, none

Vegetables: Lettuce, tomatoes, peppers, onions, pickles.

2. Andre knows he wants a sandwich that has ham, lettuce, and tomatoes on it. He doesn’t care about the type of bread or cheese. How many of the different sandwiches would make Andre happy?

3. If a sandwich is made by randomly choosing each of the options, what is the probability it will be a sandwich that Andre would be happy with?

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answer :

630

explanation

it's a graph question in the form of a word problem

question says if

(10, 390) & (15, 440) then (34, y)?

if x = 34 then what is y

get slope

m = (440 - 390) / (15 - 10) = 10

get graph

y - y1 = m(x - x1)

y - 440 = 10(34 - 15)

y - 440 = 190

y = 630

chatgpt

Water output rate for Mitchell family's sprinkler was 20 L per hour and for Garcia family's sprinkler was 15 L per hour. Their sum is 35 L per hour and total water output was 1075L of water.

Let's denote the water output rate of the Mitchell family's sprinkler by x and the water output rate of the Garcia family's sprinkler by y. We know that the sum of the two rates is 35 L per hour, so equation:

x + y = 35

We also know that the Mitchell family's sprinkler was used for 35 hours, so it produced a total of 35x liters of water. Similarly, the Garcia family's sprinkler was used for 25 hours, so it produced a total of 25y liters of water. The combined total output of 1075L of water will be written as:

35x + 25y = 1075

We use first equation to solve for one of variables in terms of the other. For example, we solve for y:

y = 35 - x

Now substitute this expression for y into second equation:

35x + 25(35 - x) = 1075

Simplifying the equation:

10x + 875 = 1075

Solve for x:

x = 20

Substitute x value into expression for y:

y = 35 - 20 = 15

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Step-by-step explanation:

your answers for a. are correct.

b.

(f○g)(x) = f(g(x))

that means we are using the expression of g(x) as input to f(x). so, for f(x), x turns into g(x) = 0.9x

(f○g)(x) = f(g(x)) = 0.9x - 220

what it does is it reduces the price by 10% and then gives on to of that an additional absolute value discount if $220.

Therefore, the length of z is approximately 2330.0 cm.

Length is a physical quantity that describes the distance between two points. It is typically measured in units such as meters, feet, inches, centimeters, or kilometers. Length can refer to the size of an object or the distance traveled by an object over a period of time. In geometry, length refers to the size of a line segment, which is the distance between two points in a plane. In physics, length is a fundamental concept that is used to describe the size of objects and the distances between them, and is an important factor in many calculations involving motion, energy, and other physical phenomena.

To find the length of side z, we can use the Law of Sines, which states that the ratio of the length of a side of a triangle to the sine of the angle opposite that side is the same for all three sides of the triangle.

Using this law, we have:

[tex]z/sin(141°) = x/sin(25°)[/tex]

Solving for z, we get:

[tex]z = x*sin(141°)/sin(25°)[/tex]

[tex]z = 830*sin(141°)/sin(25°)[/tex]

z ≈ 2329.9 cm

Rounding to the nearest tenth of a centimeter, we get:

z ≈ 2330.0 cm

Therefore, the length of z is approximately 2330.0 cm.

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