What are the four ways to solve a system of equations?

The hypotenuse is 17 units.

Pythagoras theorem states that “In a right-angled triangle,  the square of the hypotenuse side is equal to the sum of squares of the other two sides“.

The hypotenuse of a right triangle can be found using the Pythagorean theorem which states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides (legs).

So the hypotenuse of a right triangle with legs 8 units and 15 units can be found by:

c = √(a² + b²)

Where c is the hypotenuse and a and b are the legs of the triangle.

c = √(8² + 15²) = √(64 + 225) = √289 = 17

So the hypotenuse of a right triangle with legs 8 units and 15 units is 17 units.

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Answer: 6

Step-by-step explanation:

    GCF is the greatest common factor of both values. First, we will list all factors of both numbers. Then, we will find the largest number that overlaps between both.

30 ➜ 1, 2, 3, 5, 6, 10, 15 and 30

54 ➜ 1, 2, 3, 6, 9, 18, 27 and 54

    The greatest common factor (GCF) is 6.

Answer:

the GCF of 30 and 54 is 6

Step-by-step explanation:

The greatest common factor (GCF) of two numbers can be found using the following steps:

For 30 and 54:

Prime factorization:

[tex]\sf:\implies{30 = 2 \times 3 \times 5}[/tex]

[tex]\sf:\implies{54 = 2 \times 3 \times 3 \times 3}[/tex]

Common factors:

[tex]\sf:\implies{2 \: and \: 3 }[/tex]

Multiply the common factors:

[tex]\sf:\implies{GCF = 2 \times 3 = 6}[/tex]

Therefore, the GCF of 30 and 54 is 6.

The value of k is 6.

The condition of the unique solution is

a1/a2[tex]\neq[/tex]b1/b2

Here a1=4,b1=k,a2=2,b2=3

4/2=k/3

k=6

The value of k is 6.

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The correct  question is below:

Find the value of k such that the following pair of linear equations has a unique solution.

4x+ky+8=0;          2x+3y+7=0

It will travel a distance of 15 km in 20 minutes and it will cover a distance of 250 km in 3 hours and 20 minutes.

The given problem is a straightforward one involving time, speed, and distance. The given body travels at a constant 75 km/hr. According to the law of universal motion, the distance traveled by any body in any interval of time equals its speed times the elapsed time. Finding the distance the body must go in 20 minutes is the first step of the presented problem. This period of time is equal to one-third of an hour. Distance is now equal to speed multiplied by time. Using this relationship, we may calculate that the body travels 15 km in 20 minutes. Using the aforementioned relation once more, we can determine that it will take 3 hours and 20 minutes to travel 250 kilometers.

                                   [tex]Distance=speed*time[/tex]

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To find the roots of a quadratic equation by factoring, you can use the following steps: Write the quadratic equation in standard form, Set the equation equal to zero and factor out a common factor if possible, Factor the remaining trinomial and set each factor equal to zero and solve for x. These solutions are the roots of the equation.

Write the quadratic equation in standard form, ax² + bx + c = 0, where a, b, and c are constants.

Set the equation equal to zero and factor out a common factor if possible.

Factor the remaining trinomial using a method such as the difference of squares or the sum/difference of cubes.

Once you have factored the trinomial, set each factor equal to zero and solve for x. These solutions are the roots of the equation.

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The value of the car in 8 years after it has depreciated is $8,348.

To find the value of the car in 8 years, we can use the formula for the future value of a depreciating asset:

future value = original value * (1 - rate of depreciation)^number of years

In this case, the original value is $18,000, the rate of depreciation is 12% per year (or 0.12), and the number of years is 8. Plugging these values into the formula, we get:

future value = 18,000 * (1 - 0.12)^8

future value = 18,000 * 0.4630

future value = $8,348

So the value of the car in 8 years is $8,348.

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Answer:

To predict when the brothers will have the same amount in their college accounts, we can set up an equation using the information given. Let x be the number of months from April.

We know that:

Nico's account balance = $2,000 + $50x

Noah's account balance = $1,600 + $100x

We want to find when the two balances are equal, so we can set the two equations equal to each other:

$2,000 + $50x = $1,600 + $100x

Now we can solve for x. Subtracting $1,600 from both sides gives:

$400 = $50x + $100x

Now we can combine like terms:

$400 = $150x

Finally, we can solve for x by dividing both sides by 150:

x = 2.67

This means that the brothers will have the same amount in their college accounts after 2.67 months or 2 months and 2 weeks.

Our amount of daylight hours depends on our latitude and how Earth orbits the sun.

Our location and the Earth's orbit around the sun both affect how many hours of daylight we receive. The axis of rotation of the Earth is inclined with respect to its orbital plane and always faces the North Star.

Every day of the year, there are precisely twelve hours of daylight and twelve hours of darkness where the equator is. Although not by much, atmospheric refraction causes sunrise to occur a bit earlier and dusk to occur a little later.

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The relationship between consecutive angles a and b is a° + b° = 180°

A quadrilateral is a polygon that has four sides and four angles. Types of quadrilaterals are square, rectangle, parallelogram, kite etc.

A parallelogram is a quadrilateral in which opposite sites are equal and parallel to each other. All the angles sum up to 360 degrees and the diagonals bisect each other.

The opposite angles of a parallelogram are equal to each other while the consecutive angles are supplementary. Also, the perimeter is gotten by adding all the individual sides

a° + b° = 180° (consecutive angles)

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The logarithm of 7 with base 7 is equal to 1, since any number to the power of 1 is equal to itself.

The logarithm of a number is the exponent to which a base number must be raised to produce that number. For example, the logarithm of 10 with base 2 is 3, since 2 to the power of 3 is equal to 10. In this case, the logarithm of 7 with base 7 is equal to 1, since any number to the power of 1 is equal to itself.

This is because logarithms have the property that logb b = 1. This means that the logarithm of a number with the same base as the number itself is always equal to 1. This is why, in the case of log7 7, the answer is 1.

Logarithms can be used to simplify mathematical equations, as logarithms of multiplication and division are equal to the sums and differences of the logarithms of the individual numbers. They are also used in many scientific and engineering applications, such as calculating the pH of a solution.

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The type of graph of x = -2 is a vertical line.

Equations of the form x = a, where a is a constant, are represented by vertical lines, and the x-coordinate of that line is the value of a. Similarly, the equations of the form y = b, where b is a constant, are represented by horizontal lines and the y-coordinate of that line is the value of b.

x = -2 is a vertical line, the graph of this equation is a line that goes vertically through the point (-2,0) and extends infinitely in the upward and downward direction.

It is worth to note that if you want to graph an equation like x = -2 or y = -2, you only need to plot the point that satisfies the equation, and then extend that point infinitely in the direction of the other variable.

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The number of tigers that Joe need to have in January is 57 tigers.

It should be noted that this question has to do with an arithmetic sequence. This is a sequence where there's a common difference

In this case, Joe Exoctic needs 200 tigers by December and the tiger population grows by 13 every month

The 12 the term is 200

Common difference = 13

First term = a = Unknown

a + 11d = 200.

a + 11(13) = 200

a + 143 = 200

Collect the like terms

a = 200 - 143

a = 57

Therefore, there'll be 57 tigers in the first month.

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When the line is perpendicular to either the y-axis or the x-axis, the absolute value will be preferred above the distance coordinate formula.

How can I calculate the separation between two coordinates?

The formula used to calculate the separation between two coordinates is commonly represented as;

D = √[(x₂ - x₁)² + (y₂ - y₁)²]

Now, this formula is particularly helpful when the line is parallel to either the y axis or the x axis and the two coordinates do not have identical x or y coordinates.

It is important to remember that opposites have the same distance from zero whether the line is parallel to either the y or the x axis when one coordinate is negative and the other is positive.

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y - y1 = m(x - x1) Is the answer

[tex]{ \qquad\qquad\huge\underline{{\sf Answer}}} [/tex]

Here we go ~

First, calculate the slope of line joining points (-7 , 1) and (-3 , 9) :

[tex]\qquad \sf  \dashrightarrow \: m = \dfrac{y2 -y1 }{x2 - x1} [/tex]

[tex]\qquad \sf  \dashrightarrow \: m = \dfrac{9 - 1}{ - 3 - ( - 7)} [/tex]

[tex]\qquad \sf  \dashrightarrow \: m = \dfrac{8}{ - 3 + 7} [/tex]

[tex]\qquad \sf  \dashrightarrow \: m = \dfrac{8}{ 4} [/tex]

[tex]\qquad \sf  \dashrightarrow \: m = 2[/tex]

Slope of the line (m) = 2

Equation of line in point slope form :

[tex]\qquad \sf  \dashrightarrow \: y - y1 = m(x - x1)[/tex]

[ Put in the values ~ ]

[tex]\qquad \sf  \dashrightarrow \: y - 9 = 2(x - ( - 3))[/tex]

[tex]\qquad \sf  \dashrightarrow \: y - 9 = 2(x + 3)[/tex]

[ That's our required equation in point slope form ]

But it can be simplified further, it depends on it, if that's asked or not.

[tex]\qquad \sf  \dashrightarrow \: y - 9 = 2x + 6[/tex]

[tex]\qquad \sf  \dashrightarrow \: y = 2x + 6 + 9[/tex]

[tex]\qquad \sf  \dashrightarrow \: y = 2x + 15[/tex]

The band has $300 + $60 = $360 to spend on recording the album.

what is equation?

An equation is a statement of equality between two expressions, usually involving one or more variables. It is written in the form of "expression1 = expression2" or sometimes "expression1 + expression2 = expression3" and so on. The goal is to find the value of the variable(s) that makes the equation true. Equations can be used to model real-world situations and can be used to make predictions and solve problems. There are different types of equations like linear equations, quadratic equations, polynomial equations, differential equations, etc. Each type has its own method of solving them and they can be solved using algebraic and/or numerical methods.

Let H be the number of hours recorded in the studio.

The total cost of recording in the studio for H hours is

$180 + $20H = $180 + $20H = $180 + $20H

The band can record for H hours if the cost is less than or equal to their budget, so we have:

$180 + $20H <= $360

Solving for H, we get:

$20H <= $360 - $180 = $180

$H <= 9

So, the range of hours the band can record at the studio within their budget is [0,9] in interval notation.

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5 more than D is represented as D + 5.

You can also represent it as D + 5 = (D+5) or D+5 = (5+D)

The answer of 5 more than D is 5+D.

For Example, The answer of 5 more than 5 is 10 which can be derived using simple mathematical calculations.

To find 5 more than 5, you can add 5 to the original number 5.

5 + 5 = 10

It's a simple arithmetic operation where you add a specific number, in this case 5, to the original number.

An arithmetic operation is a mathematical process that combines two or more numbers to produce a new number. The most basic arithmetic operations are addition, subtraction, multiplication, and division.

Addition: It is the process of combining two or more numbers to find their sum. For example, 2 + 3 = 5 is an addition operation.

Subtraction: It is the process of finding the difference between two numbers. For example, 5 - 3 = 2 is a subtraction operation.

Multiplication: It is the process of finding the product of two or more numbers. For example, 3 x 4 = 12 is a multiplication operation.

Division: It is the process of finding the quotient of two numbers. For example, 12 ÷ 3 = 4 is a division operation.

Therefore, The answer of 5 more than 5 is 10.

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The degree of the polynomial is 4. The degree of a polynomial is the highest exponent of the polynomial. In this polynomial, the highest exponent is 4 (4x^4), so the degree of the polynomial is 4.

The polynomial is 4x^4 + 0x^3 + 0x^2 + 5x + 7. The degree of the polynomial is 4, as the highest exponent is 4 (4x^4).

The polynomial 4x^4 + 0x^3 + 0x^2 + 5x + 7 has a degree of 4, as this is the highest exponent in the polynomial. This means that the polynomial is a fourth degree polynomial, as the highest exponent is 4, and all other exponents are lower. This means that the highest power of x in the polynomial is 4, and all other powers of x are lower. As such, the degree of the polynomial is 4.

The degree of the polynomial is 4.

The degree of a polynomial is the highest exponent of the polynomial. In this polynomial, the highest exponent is 4 (4x^4), so the degree of the polynomial is 4.

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When we write a number in fraction with denominator 1, then we evaluate an expression with fractions like evaluating an expression with whole numbers.

But when we write a fraction with denominator other that 0 and 1, then we evaluate an expression with fractions is different from evaluating an expression with whole numbers.

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Here, We know that;

To evaluating an expression with fractions like evaluating an expression with whole numbers is possible only when we write a number in fraction with denominator 1.

And, To evaluating an expression with fractions is different from evaluating an expression with whole numbers is possible only when we write a number in fraction with denominator other that 0 and 1.

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So, the area of the placemat is 155 square inches.

To find the area of the circular placemat, we can use the formula for the area of a circle, which is πr^2, where r is the radius of the circle.

We know that the placemat has 44 inches of braid around the edge, which represents the circumference of the circle. We can use the formula for circumference of a circle which is C = 2πr.

By substituting the value of C = 44 inches

C = 2πr

44 = 2πr

r = 44/(2π)

Now we have the value of the radius, we can substitute it into the formula of the area of a circle

A = πr^2

A = π(44/(2π))^2

A = (44^2)/(4π)

A = (1936)/(12.56) = 154.8 square inches

To the nearest square inch, the area of the placemat is 155 square inches.

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Acute angles can be measured with the help of a protractor.

Find the measure of x, y, and z?

The angles 2x x+2 =180°

2x+x+2=180°

3x+2=180°

3x=180-2

3x=178

x=178/2

X=88

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Answer:78400

Step-by-step explanation:

The P-value for this hypothesis test is 0.00215

The p-value hypothesis test gives a measure of how much evidence is present to reject the null hypothesis. The smaller the p-value, the higher the evidence against the null hypothesis.

Given that:

Null Hypothesis: mu1 = mu2

Alternative Hypothesis: mu1<mu2

Notice that the alternative hypothesis is a one-tailed test

Now, when a one-tailed alternative hypothesis is used, To obtain a one-tailed alternative probability value i.e p-value, we divide the result by two (2).

so, given output ( z=3.25, p=0.0043)

since its one-tailed test:

P-value for this hypothesis test = 0.0043/2 = 0.00215

Therefore, the P-value for this hypothesis test is 0.00215

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Answer:

Step-by-step explanation:

What you can do in this case is the following rule of three to find the result:

1 light year ---> 5.88 * 10 ^ 12 miles

3.2 * 10 ^ 2 light year ---> x

Clearing x we have:

x = ((3.2 * 10 ^ 2) / (1)) * (5.88 * 10 ^ 12)

x = 1.88 * 10 ^ 15 miles

answer:

In scientific notation, approximately it is 1.88 * 10 ^ 15 miles

The annual percentage yield is 3.40%.

To find the annual percentage yield (APY) given an interest rate and the compounding frequency, we can use the following formula:

APY = (1 + (interest rate / compounding frequency))^compounding frequency - 1

In this case, the interest rate is 3% and the compounding frequency is monthly, so we can plug these values into the formula:

APY = (1 + (0.03 / 12))^12 - 1

APY = (1 + 0.0025)^12 - 1

APY = (1.0025)^12 - 1

APY = 1.0340406779661017 - 1

APY = 0.0340406779661017 or 3.40406779661017%

Thus, the annual percentage yield is 3.40% (rounded to the nearest hundredth of a per cent).

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Answer: A quartile is a type of quantile that splits a data set into four equal parts. The first quartile (Q1) is also known as the lower quartile and is the value that separates the lowest 25% of the data from the rest. The second quartile (Q2) is also known as the median and is the value that separates the lowest 50% of the data from the highest 50%. The third quartile (Q3) is also known as the upper quartile and is the value that separates the lowest 75% of the data from the highest 25%.

In this case, the lower quartile (Q1) is 65, the median is 78, and the upper quartile (Q3) is 92.

Step-by-step explanation:

Answer:

[tex]y=-\frac{4}{3} + 2[/tex]

Step-by-step explanation:

[tex]y=mx+b\\(-8)=-(\frac{4}{3} )(3)+b\\-8=-4 +b\\2=b\\y=-\frac{4}{3} + 2[/tex]

Therefore , the solution of the given problem of unitary method  comes out to be  $312  he will make.

To perform a task using the unitary approach, one must first determine the quantity of a narrow subset that exists, and then multiply it by two. Simply put, the unit approach is used to isolate a programming value from either a given set. For instance, 40 pens cost 400 rupees ($1.01), which is equal to Rs. It's possible that only one country will have control over the method utilized to accomplish this. Almost all creatures have a distinctive trait. It is equally capable of integration and reciprocity (mathematics, algebra).

Here,

Given :

We get $6 an hour and 6% commission on sales,

So,

In a week he work 40 hours and did $1200 worth of sales

Thus,

He will make:

=> 40*6 + 6/100*1200

=> 240 + 72

=> $312

Therefore , the solution of the given problem of unitary method  comes out to be  $312  he will make.

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-6p³ + 14p² -6 is the final polynomial after all operations

In order to get final polynomial we nedd to complete all operations on different polynomials provided velow.

A polynomial is a mathematical expression involving a sum of powers in one or more variables with real or complex coefficients. It is a type of algebraic expression which can be of degree 0,1,2,3,..n. It is represented by a letter such as "P" or "f", with one or more variables such as x, y, z, etc. and coefficients, which are numbers or constants. The degree of a polynomial is the highest power of the variable in it.

-3p³ - 3p³ + 5p² + 2p² + 7p² - 3 - 3

=> -6p³ + 14p² -6

so the required polynomial is -6p³ + 14p² -6 which is obtained after all the operation on the numbers.

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The program has to be made keeping the conversion of the required units in mind.

Here we need to keep in mind that

1 gallon is equal to 0.5 ounce

1 quart is equal to 2 ounces

1 pint is equal to 4 ounces

int main(int argc, char** argv) {

float ounce, gallons, quarts, pints;

std:: cout << "Please input the value in ounce to be converted";

std:: cin >> ounces;

gallons = ounce * .5;

quarts = ounce * 2;

pints = ounce * 4;

std:: cout << "That many ounce is equal to ";

cout<<"\n";

std:: cout << "Gallons ";

std:: cout<<gallons;

cout<<"\n";

std:: cout << "Quarts ";

std:: cout<<quarts;

cout<<"\n";

std:: cout << "Pints ";

std:: cout<<pints;

return 0;

}

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