Consider the equation:
24 = x2 - 4x + 3
1) Rewrite the equation by completing the square.
Your equation should look like (x + c)2 = d or (2 — c)2 = d.
2) What are the solutions to the equation?
Choose 1 answer:
X = 2 5
x = -2 +5
x = 2 + 5
x = -2 + 5

The system of equations is,

y = 2/3(x) and y = (-3/4)x -5.

The correct option is A.

One or many equations having the same number of unknowns that can be solved simultaneously called as simultaneous equation. And simultaneous equation is the system of equation.

Given:

Two lines are intersecting each other.

Line 1 passes through two points (0, 0) and (3, 2).

The equation of the line is,

y = 2/3(x)

And line 2 passes through (0, -5) and (4, -2).

The equation of the line is,

y = (-3/4)x -5.

Therefore, the equations are y = 2/3(x) and y = (-3/4)x -5.

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The missing numbers to complete the linear equation that gives the rule for this table are y = 11x-10

A linear equation is an equation that describes a line in a two-dimensional coordinate system. It can be written in the form:

y = mx + b

where y and x are variables representing coordinates on the vertical and horizontal axes, respectively, m is the slope of the line, and b is the y-intercept (the point where the line crosses the y-axis).

The slope of the line represents the rate of change between y and x, or the steepness of the line. A positive slope indicates that the line is increasing from left to right, while a negative slope indicates that the line is decreasing from left to right. A slope of zero indicates a horizontal line, while a slope that is undefined (such as when x is constant) indicates a vertical line.

To find the equation that gives the rule for this table, we need to determine the slope and y-intercept of the line that passes through these points.

We can start by using the two given points (4, 34) and (5, 45) to find the slope:

slope = (change in y) / (change in x)

slope = (45 - 34) / (5 - 4)

slope = 11

Now we can use the point-slope form of a linear equation to write the equation for this line, using the point (4, 34):

y - 34 = 11(x - 4)

Simplifying this equation gives:

y = 11x - 10

So the missing numbers to complete the linear equation that gives the rule for this table are:

y = 11x-10

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Answer:

The possible number of students in Mrs. Hayko's class is limited to 15 or 30, as higher multiples of 15 would exceed the desired class size.

Step-by-step explanation:

a)

Let 'x' be the total number of students in Mrs. Hayko's class.

One-third of the students walk to school: (1/3)x.

The remaining students who do not walk to school: (2/3)x.

Four-fifths of the non-walking students take the bus: (4/5) * (2/3)x.

Simplify to find the fraction of students taking the bus: (8/15)x.

b)

Consider different values for 'x' to find a whole number of students taking the bus.

Start with a small number, such as x = 15.

Calculate the number of students taking the bus using (8/15)x.

If the result is a whole number, it's a possible class size.

Repeat with different values of 'x' until a whole number is obtained.

The possible number of students in Mrs. Hayko's class could be 15, 30, or any other multiple of 15.

By performing the simulation, you can estimate the probability of y being greater than 5, given that x is greater than 3, using physical objects like dice. To simulate the quantity \(p(y > 5|x > 3)\), where x and y are random variables, you can use physical objects like dice.

Here's a step-by-step explanation of how to perform the simulation by hand:

1. Set up: Take two dice and label one as "x" and the other as "y". Each die should have six sides labeled from 1 to 6.

2. Perform one repetition: Roll the "x" die and record the outcome. If the outcome is greater than 3, roll the "y" die and record the outcome. Otherwise, skip the "y" roll.

3. Repeat the above step multiple times: Repeat the previous step a large number of times to generate multiple repetitions of the simulation. For example, you could repeat it 100 times.

4. Use the simulation results: Count the number of times y is greater than 5, given that x is greater than 3, from the generated outcomes. Divide this count by the total number of repetitions (e.g., 100) to estimate the quantity\(p(y > 5|x > 3)\).

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The estimated quantity p(y > 5 | x > 3) would be 5/20, which is equal to 0.25. By performing a simulation involving physical objects like dice and cards, we can estimate the quantity in question, p(y > 5 | x > 3).

To perform a simulation involving physical objects to estimate the quantity in question, we can follow the steps below:

1. Set up: Gather the required physical objects, such as dice and cards, for the simulation. For this specific question, we need a dice and a card deck.

2. Perform the simulation:

  a) Roll the dice: Roll the dice multiple times to obtain the value of x. Each roll will represent one repetition of the simulation. Record the value of each roll.
 
  b) Draw a card: Shuffle the deck of cards and draw a card multiple times to obtain the value of y. Each card drawn will represent one repetition of the simulation. Record the value of each card drawn.

3. Estimation: After performing the simulation and recording the values of x and y, we can estimate the quantity p(y > 5 | x > 3). To do this, we count the number of repetitions where x is greater than 3 and y is greater than 5, and divide it by the total number of repetitions where x is greater than 3.

4. Example: Let's consider that we rolled the dice 50 times and obtained values for x. We also drew a card 50 times and obtained values for y. Out of these 50 repetitions, let's say that x was greater than 3 in 20 repetitions. Now, out of these 20 repetitions, let's say that y was greater than 5 in 5 repetitions.

This approach allows us to understand the concept and estimate probabilities without relying on complex calculations or programming.

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Complete Question : Describe in detail how you could, in principle, perform by hand a simulation involving physical objects (coins, dice, spinners, cards, boxes, etc.) to estimate P(X = 5 | X > 2), where X has a Binomial distribution with parameters n=5 and p=2/7. Be sure to describe (1) what one repetition of the simulation entails, and (2) how you would use the results of many repetitions. Note: You do NOT need to compute any numerical values.

To find the indefinite integral of ∫(5/x - 5/(5√x)) dx, we will integrate each term separately. The indefinite integral of (5/x - 5/(5√x)) with respect to x, on the domain of positive real numbers, is given by 5 ln |x| - 2√x + C.

The integral of 5/x with respect to x is given by:

∫(5/x) dx = 5 ln |x| + C1,

where ln represents the natural logarithm and C1 is the constant of integration.

The integral of -5/(5√x) can be simplified as follows:

∫(-5/(5√x)) dx = -∫(1/√x) dx = -2√x + C2,

where C2 is the constant of integration.

Putting the results together, we have:

∫(5/x - 5/(5√x)) dx = 5 ln |x| - 2√x + C,

where C = C1 + C2 is the combined constant of integration.

Therefore, the indefinite integral of (5/x - 5/(5√x)) with respect to x, on the domain of positive real numbers, is given by 5 ln |x| - 2√x + C.

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Answer:

volume of the hemisphere

\( \frac{2}{3} \times \pi \times {r}^{3} \\ \frac{2}{3} \times \pi \times 1331 \\ = 887.3333333333\pi\)

Answer:

c

Step-by-step explanation:

the answer to the question is 480

103 +98+69+93+117 i think is how it goes easly

The concept of consecutive integers is explained as follows:

Consecutive numbers, or consecutive integers, are integers that follow each other in order. The difference between any two consecutive numbers is always 1. For example, the consecutive numbers starting from 1 would be 1, 2, 3, 4, 5, and so on. Similarly, the consecutive numbers starting from -3 would be -3, -2, -1, 0, 1, 2, and so on.

It is important to note that if we have a consecutive sequence of integers, one number will be even, and the next number will be odd. This is because the parity (evenness or oddness) alternates as we move through consecutive integers.

Furthermore, the sum of two consecutive numbers (and, in fact, the sum of any number of consecutive numbers) is always an odd number. This is because when we add an even number to an odd number, the result is always an odd number.

To generate a sequence of consecutive integers, we can start with any integer n and then use n, n+1, n+2, and so on to obtain consecutive integers. For example, if n is an integer, then n, n+1, and n+2 will be consecutive integers.

Here are some examples of consecutive integers:

- Starting from 1: 1, 2, 3, 4, 5, ...

- Starting from -3: -3, -2, -1, 0, 1, 2, ...

- Starting from 1004: 1004, 1005, 1006, 1007, ...

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Answer:  \(Student 2\)

Step-by-step explanation:

Hi there!

1.Subtract 7 from both sides of the equation

2.Simplify and substract the numbers and you get the answer

Answer:

71 oranges & 213 cookies

Step-by-step explanation:

If there was 3 times cookies than oranges so its can be divided into 4 so 284 divide by four is 71

71x3 is 213 and 213 divided by 3 is 71 and 71 plus 213 is 284

hope this helped!

To design a concrete mix for reinforced concrete foundations and tie beams resting on a soil with a high concentration of sulfates, we need to consider the required slump, mean compressive strength, aggregate properties, and water content.

a) Based on the given information, here's how we can design the concrete mix:

1. Slump: The concrete mix should have a slump of 50 mm, which indicates the workability of the concrete.

2. Compressive Strength: A mean compressive strength of 20 MPa is required at the age of 28 days. This indicates the strength of the concrete after it has cured for 28 days.

3. Coarse Aggregate: The coarse aggregate should meet the ASTM grading requirements and have a maximum aggregate size of 20 mm. It has an absorption of 2%, water content (WC) of 3%, a bulk specific gravity (BSG) of 2.7, and a unit weight of 1480 kg/m³.

4. Fine Aggregates: The fine aggregates have an absorption of 3%, water content (WC) of 1%, a bulk specific gravity (BSG) of 2.5, and a fineness modulus of 2.7.

To design the concrete mix, we need to calculate the proportions of cement, coarse aggregates, fine aggregates, and water.

b) If the coarse aggregate has an absorption of 4% instead of 2%, while maintaining the same water content (WC) of 3%, the concrete mix would need adjustments to account for the increased absorption.

To design the revised concrete mix, we would need to recalculate the proportions of cement, coarse aggregates, fine aggregates, and water, considering the updated absorption value for the coarse aggregate.

Remember, it's essential to accurately measure and control the proportions of the mix components to achieve the desired strength and workability of the concrete. Additionally, it's crucial to follow any local codes, standards, or guidelines for sulfate-resistant concrete in your region to ensure the durability of the foundations and tie beams.

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Answer: v= root[3]  {12}=2.2894

Step-by-step explanation:

Answer:Your answer is V=4

Step-by-step explanation:Need brainliest award

The volume of the solid S, where the base is a triangular region and cross-sections perpendicular to the y-axis are semicircles, can be found using calculus. The volume of S is (3π/8) cubic units.

In the first part, the volume of the solid S is (3π/8) cubic units.

In the second part, we can find the volume of S by integrating the areas of the cross-sections along the y-axis. Since the cross-sections are semicircles, we need to find the radius of each semicircle at a given y-value.

Let's consider a vertical strip at a distance y from the x-axis. The width of the strip is dy, and the height of the semicircle is the x-coordinate of the triangle at that y-value. From the equation of the line, we have x = (3/2)y.

The radius of the semicircle is half the width of the strip, so it is (1/2)dy. The area of the semicircle is then\((1/2)\pi ((1/2)dy)^2 = (\pi /8)dy^2.\)

To find the limits of integration, we note that the base of the triangle extends from y = 0 to y = 2. Therefore, the limits of integration are 0 to 2.

Now, we integrate the area of the semicircles over the interval [0, 2]:

V = ∫\((0 to 2) (\pi /8)dy^2 = (\pi /8) [y^3/3]\) (evaluated from 0 to 2) = (3π/8).

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Answer:

x=8,-2

Step-by-step explanation:

Add 10 to both sides.

{(x-3)}^{2}=15+10

2 Simplify 15+10+25

(x−3) ^2=25

3 Take the square root of both sides.

x-3=+or-√25

The least common multiple refers to the common multiple for the give numbers.

Among the answer choice, number 3 makes more sense. All the product of the common factors is the LCM.

Answer: Top left i'm pretty sure

Step-by-step explanation: Because there isn't a blue line and you need a blue line for it to be an equation

Answer:

Parallel line

Step-by-step explanation:

The parallel line doesn't connect so it a infinite therefore it means its a no solution line

Answer:

Step-by-step explanation:

= (3 + √3) (2 - √3)

= 6 - 3√3 + 2√3 - 3

= 3 - 3√3 + 2√3

= 3 - √3 (3 - 2)

= 3 - √3

= 3 - 1.732 ...... (√3 = 1.732)

= 1.268

To solve this problem, we'll use the concept of permutations.

First, we need to choose a woman for the position of president, then another woman for the position of vice president, and finally, a man for the treasurer position.

1. President: Since there are 20 women, we have 20 options for the president position.
2. Vice President: We're left with 19 women (since we already chose one for the president), so we have 19 options for the vice president position.
3. Treasurer: Since there are 17 men, we have 17 options for the treasurer position.

Now, multiply the number of options for each position together to find the total number of ways to form the committee:

20 (president) × 19 (vice president) × 17 (treasurer) = 6,460 ways.

So, there are 6,460 possible ways to choose three different members with women as president and vice president and a man as treasurer.

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Answer:

Step-by-step explanation:

4 4 4

4 4 6

4 6 6

4 6 4

6 6 6

6 6 4

6 4 4

6 4 6

slope-intercept form of a line (L1): y = mx + b; where m is the slope and b the y - intercept.

If two lines are parallel, that means the slope of both equations are equal.

L2: y = 3x - 7, m = 3

So, m for L1 is m = 3.

Now we just need to find y - intercept, as follows:

L1 passes through (0,4), then:

4 = 3(0) + b

4 = 0 + b

b = 4

The equation for the line is y = 3x + 4

The dataset for the problem is provided by the United States Social Security Administration which lists the frequency of each name given to girls and boys in the 2010s.

The provided version of the dataset only contains names used at least 25 times for at least one gender so far this decade. Following is a sample CSV file that shows some data:

Isabella,42567,Girl
Sophia,42261,Girl
Jacob,42164,Boy
Emma,35951,Girl
Ethan,34523,Boy
Mason,34195,Boy
William,34130,Boy
Olivia,34128,Girl
Jayden,33962,Boy
Ava,30765,Girl
The dataset will be used to answer some questions.

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Answer:

0

Step-by-step explanation:

This is a horizontal line so thhe slope is zero

Answer:

Your answer is 5/8

Step-by-step explanation:

I used Microsoft Math

Answer:

b = (2A)/h

Step-by-step explanation:

\(A = \frac{1}{2} bh \\ = > 2A = bh \\ = > \frac{2A}{h} = b\)

Answer:

Step-by-step explanation:

If you translate the triangle BCD in such a way that vertex B maps onto vertex W, you'll realize that with rotation, you'll map the whole BCD triangle onto triangle WXY.

On the other hand, reflections can't be used here, because the sides of both triangles are not in opposite positions.

Therefore, the right answer is the third choice.

By quadratic formula, the roots of the quadratic function 2 · x² - 2 · x + 5 = 0 are two conjugated complex numbers: x₁ = 0.5 + i 1.5 and x₂ = 0.5 - i 1.5, respectively.

Let be a quadratic function of the form a · x² + b · x + c = 0, whose roots can be found by means of the following formula:

\(x = \frac{-b \pm \sqrt{b^{2}-4\cdot a\cdot c}}{2\cdot a}\)     (1)

Where a, b, c are the coefficients of the quadratic function.

In we know that 2 · x² - 2 · x + 5 = 0, then the roots of the polynomial are, respectively:

\(x_{1} = \frac{2 + \sqrt{(-2)^{2}-4\cdot (2)\cdot (5)}}{2\cdot (2)}\)

\(x_{1} = \frac{2 + \sqrt{4-40}}{4}\)

x₁ = 0.5 + i 1.5

\(x_{2} = \frac{2 - \sqrt{(-2)^{2}-4\cdot (2)\cdot (5)}}{2\cdot (2)}\)

\(x_{2} = \frac{2 - \sqrt{4-40}}{4}\)

x₂ = 0.5 - i 1.5

By quadratic formula, the roots of the quadratic function 2 · x² - 2 · x + 5 = 0 are two conjugated complex numbers: x₁ = 0.5 + i 1.5 and x₂ = 0.5 - i 1.5, respectively.

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Answer:

Did we mention that he's 13 years old?

Step-by-step explanation:

because he inspire alot of people by driving a racecar 80 mph that is fast for a kid at his age.

Answer:

Did we mention that he's 13 years old?

Step-by-step explanation:

Did this in middle school 1 year ago it right

Isolate y by dividing by e^x: y(x) = (1/7)e^(6x) + C*e^(-x). This is the general solution of the given differential equation.

The given differential equation is of the form dy/dx + y = e^(6x). To find the general solution, we can first solve the homogeneous equation dy/dx + y = 0, which has a solution y = Ce^(-x), where C is a constant. To find the particular solution, we can use the method of variation of parameters, which gives us y = (1/7)e^(6x) - (1/7)Ce^(-x), where C is again a constant. Therefore, the general solution of the given differential equation is y = Ce^(-x) + (1/7)e^(6x), where C is any constant. This solution satisfies the differential equation for any value of C. This explanation is 99 words. The given differential equation is dy/dx + y = e^(6x). This is a first-order linear differential equation. To find the general solution, we first determine the integrating factor (IF) by calculating e^(∫1 dx) = e^x. Now, multiply both sides of the equation by the IF: e^x(dy/dx) + e^x*y = e^(7x). The left side is now the derivative of a product, i.e., d/dx(y*e^x).
Next, integrate both sides with respect to x: ∫[d/dx(y*e^x) dx] = ∫[e^(7x) dx]. This results in y*e^x = (1/7)e^(7x) + C, where C is the constant of integration. Finally, isolate y by dividing by e^x: y(x) = (1/7)e^(6x) + C*e^(-x). This is the general solution of the given differential equation.

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Answer:

The origin is included in the shaded region and the shaded region is below the line.

Explanation:

First, let's graph the line that separates the region: y = 1/3 x + 4

So, to graph the line, we need to find two points in the line as follows:

If x = 0, then y is equal to:

y = 1/3 (0) + 4

y = 4

If x = 3, then y is equal to:

y = 1/3 (3) + 4

y = 1 + 4

y = 5

So, using the points (0, 4) and (3, 5), we get:

Now, we can determine whether the origin is included or not replacing x and y by the coordinates of the origin (0, 0) and determine if this point satisfies the inequality. So:

y < 1/3x + 4​

0 < 1/3(0) + 4

0 < 0 + 4

0 < 4

Since 0 is less than 4, the origin is included in the shaded region, so the shaded region is below the line.

Answer: 3x+12

Step-by-step explanation:

Using the distributive property we can distribute the 3 to each of the terms in the parenthesis.

Therefore, 3(x+4) -= 3x+ 3*4 = 3x +12

Answer:

Step-by-step explanation

3x + 12=0

3x= -12

x = -12/3

x= -4: