y=3x+2

-4x+2y=8

elimination method

a. The two firing angles of the projectile are 5.65° and 174.35°

b. The time it takes the projectile to hit the ground is 4.02 s

A projectile is an object that follows a parabolic path when thrown into the air.

Given that a projectile travels a distance of 800 meters with an initial velocity of 200 m/s, to find the firing angles, we use the formula for the range of a projectile.

The range of a projectile is its horizontal distance. It is given by R = u²sin2Ф/g where

Given that we require Ф, the angle of projection. Making it subject of the formula, we have that

Ф = [sin⁻¹(gR/u²)]/2

Given that

Substituting the values of the variables into the equation, we have

Ф = [sin⁻¹(gR/u²)]/2

Ф = [sin⁻¹(9.8 m/s² × 800 m/(200 m/s)²)]/2

Ф = [sin⁻¹(9.8 m/s² × 800 m/(40000 m²/s²)]/2

Ф = [sin⁻¹(9.8 m²/s² × 1/50 m²/s²)]/2

Ф = [sin⁻¹(0.196)]/2

Ф = 11.30°/2

Ф = 5.65°

Since sin is positive in the second qudrant also, the second angle is

Ф = 180° - 5.65°

= 174.35°

So, the angle are 5.65° and 174.35°

To find how long it takes the projectile to hit the ground, we use the formula for time of flight of a projectile.

T = 2usinФ/g where

Since

Substituting the values of the variables into the equation, we have

T = 2usinФ/g

T = 2(200 m/s)sin5.65° ÷ 9.8 m/s²

T = 400 m/s × 0.09845 ÷ 9.8 m/s²

T = 39.381 m/s ÷ 9.8 m/s²

T = 4.02 s

So, the time it takes the projectile to hit the ground is 4.02 s

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Answer:

Step-by-step explanation:

First, we need to evaluate the expression inside the parenthesis: 4(12) = 4 * 12 = 48.

Next, we can simplify the expression: 42 - 6 * 48 = 42 - 288 = -246.

Finally, we raise the result to the third power: (-246)^3 = (-246) * (-246) * (-246) = -158,048.

So, the result is -158,048.

Answer: First, we'll round the values of A and b:

A = 340 rounded to the nearest 10 = 340

b = 49.8 rounded to 1 decimal place = 49.8

Next, we'll find the product of A and b:

A × b = 340 × 49.8 = 16872

Finally, we'll find the minimum of A × b:

Minimum of A × b = 16872

So, the minimum value of A × b is 16872.

Step-by-step explanation:

Answer: Decagon

Step-by-step explanation:

That would be a decagon because it has 10 sides. It does not matter if the shape looks wonky.

Hope this helps :)

Answer:

x = 8 - 3y - 2z

Step-by-step explanation:

Step-by-step explanation:

x + 3y + 2z = 8

3x + y + 3z = -10

-2x - 2y - z = 10

we solve this by eliminating variables or expressing sine variables by others, and then solve for the remaining one. with that value we then cancer back to solve for the other variables.

in our case the easiest way is the elimination via combinations of equations.

let's first multiply equating 1 by -3 and then add that to equation 2 :

-3x - 9y - 6z = -24

3x + y + 3z = -10

----------------------------

0 - 8y - 3z = -34

8y + 3z = 34

then multiply equation 1 by 2 and add it to equation 3 :

2x + 6y + 4z = 16

-2x - 2y - z = 10

--------------------------

0 4y + 3z = 26

now we subtract this result from the previous result :

8y + 3z = 34

- 4y + 3z = 26

----------------------------

4y 0 = 8

y = 8/4 = 2

4×2 + 3z = 26

3z = 18

z = 18/3 = 6

x + 3×2 + 2×6 = 8

x = -10

so,

x = -10

y = 2

z = 6

Answer: 1024

Step-by-step explanation:

2 x 2 is 4

4 x 2 is 8

8 x 2 is 16

16 x 2 is 32

32 x 2 is 64

64 x 2 is 128

128 x 2 is 256

256 x 2 is 512

512 x 2 is 1024

Answer:

32x95%?

Step-by-step explanation:

Im so confused with this question statement.

The equation 2(x - 4) = 2x - 8 has infinitely many solutions.

An equation is the statement of two expressions located on two sides connected with an equal to sign. The two sides of an equation is usually called as left hand side and right hand side.

Given equation is 2(x - 4) = 2x - 8.

Solving this,

Using the distributive property, a (b + c) = ab + ac, 2(x - 4) = (2 × x) - (2 × 4).

Substituting in the original equation,

(2 × x) - (2 × 4) = 2x - 8

2x - 8 = 2x - 8

2x - 2x = -8 + 8

0 = 0

Right hand side and left hand side are equal if we put any value for x.

So it has infinitely many solutions for x.

Hence the given equation has infinitely many solutions.

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Answer:

Step-by-step explanation:

because if you multipled 7 times 8 you will get 56 and if you add it with 45 you will get 101

i hope this help

After 8 weeks of saving, Alexa will have a total of $101. The expression to show the money Alexa saves in 'w' weeks is 45 + 7w.

The subject of this question is

Mathematics

and it is geared towards

Middle School

grades. To solve this problem, we need to use

algebraic expressions

. Based on the problem given, Alexa has $45 initially and saves $7 per week additionally from her after school job. So if she saves for 8 weeks, Alexa would have accumulated an additional $7 times 8 = $56. Therefore, the total amount of money Alexa would have after 8 weeks is her initial amount of $45 plus the additional $56, which equals $101. To represent this in terms of an expression, where 'w' stands for weeks, you can write 45 + 7w. This expression lets us calculate the total savings for any number of weeks 'w'.

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Answer: $35.

Step-by-step explanation: Let A = 2 movers and one truck for hour = $65

B = 3 movers and one truck for hour = $80

So, 1 mover = B - A

                  = $80 - $65

                  = $15

Hence, 2 movers cost = 2 × $15

                                  = $30

SO, rent of the truck hourly = A - cost of 2 movers

                                          = $65 - $30

                                          = $35

Therefore cost of renting the truck for an hour = $35

The value of the equation 8x² - 8x + 2 -( 6x² - 10x + 4) is 2x² + 2x - 2.

It should be noted that an equation simply has to do with the statement that illustrates the variables given. In this case, it is vital to note that

two or more components are considered in order to be able to describe the scenario.

It is important to note that an equation is the mathematical statement which can be made up of two expressions which are connected by an equal sign.

The equation can be illustrated thus:

8x² - 8x + 2 -( 6x² - 10x + 4)

8x² - 8x + 2 - 6x² + 10x - 4

= 2x² + 2x - 2

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Answer:

3√10

Step-by-step explanation:

[tex]GM=\sqrt{(3\sqrt{5})(6\sqrt{5})}=\sqrt{18*5}=\sqrt{90}=3\sqrt{10}[/tex]

Answer:   [tex]3\sqrt{10}[/tex]

Work Shown:

Part 1

[tex]g = \text{geometric mean of x and y}\\\\g = \sqrt{\text{x}\text{y}}\\\\g = \sqrt{3\sqrt{5}*6\sqrt{5}}\\\\g = \sqrt{(3*6)*(\sqrt{5}*\sqrt{5})}\\\\g = \sqrt{18\sqrt{5*5}}\\\\g = \sqrt{18\sqrt{5^2}}\\\\g = \sqrt{18*5}\\\\g = \sqrt{90}\\\\[/tex]

Part 2

[tex]g = \sqrt{90}\\\\g = \sqrt{9*10}\\\\g = \sqrt{9}*\sqrt{10}\\\\g = 3\sqrt{10}\\\\[/tex]

Answer: Change x to a number, and that number + 1 will be y

Step-by-step explanation: the reason for this is simple, change the independent variable, which is always in the problem, and you can figure out the dependent variable.

Answer:

X +1

Step-by-step explanation:

the graph is x +1.....

Answer: To solve this problem, we can use the formula for calculating the future value of an investment:

FV = PV * (1 + r/n)^(nt)

where:

FV is the future value of the investment

PV is the present value of the investment (the initial amount Louise has to invest)

r is the annual interest rate (4.28%)

n is the number of times the interest is compounded in a year

t is the number of years the investment is made

Since the interest is compounded monthly, we need to convert the annual interest rate to a monthly rate:

r/12 = 4.28% / 12 = 0.3566666666666667%

Now, we can use the formula to calculate the future value of Louise's investment:

FV = $20,000 * (1 + 0.3566666666666667%)^(12t)

We can use trial and error or iterative methods to find the value of t that satisfies the condition: FV = $30,000.

A quick approximation is to use the formula for simple interest:

FV = PV * (1 + r * t) = $20,000 * (1 + 0.0428 * t)

t = ($30,000 - $20,000) / ($20,000 * 0.0428) = 2.857142857142857 years, or approximately 2.9 years.

This is an approximation, but it should be close to the actual answer. To get a more accurate answer, we can use an iterative method, such as Newton-Raphson or bisection, to solve for t in the formula above.

Step-by-step explanation:

If number of pencils are triple the number of pens, then the number of pens is 30

Total number of pens and pencils = 120

Number of pencil is triple the number of pens

Consider the number of pens as x

Number of pencils = 3x

Sum of the pens and pencils = 120

Then the equation will be

Number of pens +  Number of pencils = Sum of number of pens and pencils

Substitute the values in the equation

x + 3x = 120

Add the like terms

(1 + 3)x = 120

4x = 120

Move 4 to the right hand side of the equation

x = 120 / 4

x = 30

Therefore, the number of pens is 30

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The slope-intercept equation of this linear function is y = -3x + 5.

Mathematically, the point-slope form of a straight line can be calculated by using this mathematical expression:

y - y₁ = m(x - x₁) or y - y₁ = (y₂ - y₁)/(x₂ - x₁)(x - x₁)

Where:

Based on the information provided, we can logically deduce the following data points on the line:

At point (0, 5), a linear equation of this line can be calculated in slope-intercept form as follows:

y - 5 = (2 - 5)/(1 - 0)(x - 0)

y - 5 = -3(x - 0)

y = -3x + 5

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The baseball field takes up 3/8 or 37.5% of Hannah’s school playground. This means that the remaining 62.5% of the playground is taken up by other materials and the grassy area not occupied by the baseball field.

Hannah’s school playground is divided into two parts, with the majority of it being covered in grass. Specifically, 3/5 of the playground is grassy and the remaining 2/5 is taken up by other materials such as pavement or gravel. Of the grassy area, 5/8 is taken up by the baseball field. This means that the baseball field occupies a total of 15/40 or 3/8 of the entire playground.

In terms of proportions, if we consider the entire playground to be 100%, then the amount of the playground taken up by the baseball field is 3/8, or 37.5%. This means that 62.5% of the playground is taken up by the other materials and the remaining grassy area not occupied by the baseball field.In terms of area, the total size of the playground can be determined by multiplying the length of the playground by its width. If we assume that the length and width are equal, then the area of the playground can be calculated as the length squared. The area of the baseball field can then be calculated by multiplying 3/8 by the total area of the playground. This will give us the total area of the baseball field.

Overall, the baseball field takes up 3/8 or 37.5% of Hannah’s school playground. This means that the remaining 62.5% of the playground is taken up by other materials and the grassy area not occupied by the baseball field.

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Answer:

58585

Step-by-step explanation:

i know

We can write the equivalent expression as -

{5.95 × 10⁸ + 8.87 × 10⁸} = {10⁸ x 14.82}.

In mathematics, an expression or mathematical expression is combination of terms both constants and variables. For example -

23 + 54

2x + 5

3x + 5y + z

Given is that after gathering information, Kara decided to add up some distances. She decided to add the distance from Earth to Saturn with the distance from Earth to Jupiter. He wrote -

5.95 × 10⁸ + 8.87 × 10⁸

The given expression is -

5.95 × 10⁸ + 8.87 × 10⁸

10⁸ x (5.95 + 8.87)

10⁸ x 14.82

Therefore, we can write the equivalent expression as -

5.95 × 10⁸ + 8.87 × 10⁸ = 10⁸ x 14.82.

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{Question in english -

1) Operations with numbers written in scientific notation

a) After gathering information, Kara decided to add up some distances. decided to add the distance from Earth to Saturn with the distance from Earth to Jupiter. Here is what he wrote.

5.95×108 + 8.87×108

Do you know what the result is?}

An irrational number is created by adding two rational numbers, according to the answer to the given question. If the oppositely irrational numbers a and b.

Rational numbers are those that may be written as a ratio (or fraction) of two integers. A fraction with a non-zero denominator is said to be rational.

A few instances of rational numbers are 1/2, 1/5, and 3/4. A rational number, “0,” can also be stated in a number of different ways, such as 0/1, 0/2, and 0/3. But 1/0, 2/0, 3/0, and so forth.

The number seven makes sense. A rational number is produced when two integers are split. To get the rational number 7, divide the whole number 7 by the whole number 1. Since 7 can be obtained by dividing two integers, it is referred to as a rational number.

Two rational integers added together yield an irrational number. Ab is irrational if and only if a and b are mutually exclusive irrational numbers.

Therefore, a = 2 and b = ab = 2 is an irrational number.

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The product of 2√3 and 3√12 in simplified form is 6√36. To simplify this expression, we can first multiply 2 and 3 to get 6. Then, we can simplify the square root of 3 and the square root of 12 by finding their prime factorizations:

√3 = √(3 * 1) = √3

√12 = √(12 * 1) = √(2^2 * 3) = 2√3

So, 2√3 = 2 * √3 = 2 * √3

And, 3√12 = 3 * 2√3 = 6√3

Finally, the product of 2√3 and 3√12 is 6 * 6√3 = 6√36.

Answer:

Step-by-step explanation:

o find the solution of a system of linear equations, we can find the point where the two lines intersect. The point of intersection represents the solution to the system of equations.

The first linear equation can be determined by finding its slope and y-intercept using the given points:

m = (7 - 6) / (3 - 1) = 1

b = 6 - m * 1 = 6 - 1 * 1 = 5

y = mx + b

y = x + 5

The second linear equation can be found similarly:

m = (8 - 6) / (5 - 3) = 1

b = 6 - m * 3 = 6 - 1 * 3 = 3

y = mx + b

y = x + 3

Since the two lines have the same slope, they are coincident and represent the same line. The solution to the system of equations is therefore any point on this line, but since we were asked for a specific point, we can choose (3,6) as the solution.

The sampling distribution of p hat follows a normal distribution thus, the value of Mu Subscript p hat = p = 0.12. Option 1 is the correct answer.

A probability distribution that is symmetric about the mean is the normal distribution, sometimes referred to as the Gaussian distribution. It demonstrates that data that are close to the mean occur more frequently than data that are far from the mean.

The most typical form of distribution assumed in technical stock market analysis and other statistical investigations is the normal distribution. The mean and the standard deviation are the two variables that make up the standard normal distribution.

The sampling distribution of p hat follows a normal distribution thus,

Mu Subscript p hat = p

Here, the value of p = 0.12

Hence, the value of Mu Subscript p hat = p = 0.12. Option 1 is the correct answer.

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Answer:

A. Mu Subscript p hat = p = 0.12

Step-by-step explanation:

If after the second hour, the increase in ticket sales every hour was 20 more than the increase of the previous hour, it will take 12 hours to sell 10,000 tickets for the Boulders concert.

To solve this problem, we need to find the number of hours it will take to sell 10,000 tickets for the concert. We are given the number of tickets sold in the first three hours and the rate at which ticket sales increase each hour after the second hour.

Let's denote the number of tickets sold in the fourth hour by "x". Then, the number of tickets sold in the fifth hour will be "x + 20", and the number of tickets sold in the sixth hour will be "x + 40", and so on.

Using this information, we can set up an equation to find "x":

500 + 560 + x + (x + 20) + (x + 40) + ... = 10,000

Simplifying the equation, we get:

3x + 1020 + 20n = 9500

where "n" is the number of hours after the third hour.

Solving for "n", we get:

n = (10,000 - 1020 - 3x) / 20

Now, we need to find the value of "x" that satisfies this equation. We can do this by testing different values of "x" until we find the one that gives an integer value for "n".

Let's start by trying "x = 640 + 20 = 660". Plugging this value into the equation, we get:

n = (10,000 - 1020 - 3(660)) / 20 = 9

We arrived at this solution by using the given information about the rate of increase in ticket sales and setting up an equation to solve for the number of hours it will take to sell 10,000 tickets. We then tested different values of "x" until we found the one that satisfied the equation and gave an integer value for "n".

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The correct option is SE is 0.04. In statistics, a sample proportion is a statistic that represents the proportion of individuals in a sample who have a particular characteristic or belong to a certain category.

The standard error of the sample proportion can be calculated as follows:

SE = sqrt(p * (1 - p) / n)

Where p is the sample proportion and n is the sample size. In this case, the sample proportion is 0.2, and the sample size is 200. So, plugging these values into the formula, we get:

SE = sqrt(0.2 * (1 - 0.2) / 200)

SE = sqrt(0.16 / 200)

SE = 0.04

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Answer: The tip is $14.00

Step-by-step explanation: 20% of 70 is 14.

Answer:aaaa

Step-by-step explanation:because

Answer: A geometric sequence is a sequence of numbers such that the ratio of any two consecutive terms is constant. Let's call the common ratio "r". We can use this property to find "r" and then calculate other terms in the sequence.

Given that t3 = 24 and t9 = 1536, we can use the formula for the nth term in a geometric sequence: tn = t1 * r^(n-1), where t1 is the first term in the sequence.

Since we know t3 and t9, we can find r by dividing t9 by t3:

r = t9/t3 = 1536/24 = 64

Now that we have found "r", we can use it to find t1 by dividing t3 by r^(3-1):

t1 = t3 / r^(3-1) = 24 / 64^(3-1) = 24 / 64 = 3/2

Now that we know t1 and r, we can find any term in the sequence by using the formula: tn = t1 * r^(n-1).

Therefore, there are two possible sequences with two different first terms:

Sequence 1: t1 = 3/2, r = 64

Sequence 2: t1 = -3/2, r = -64

These are the two possible geometric sequences that satisfy the conditions t3 = 24 and t9 = 1536.

Step-by-step explanation: